Edited by - City University of New Yorkwebsupport1.citytech.cuny.edu/faculty/hyuce/wetland_model.pdf · Microstructure design by twinning in high-temperature superconductor ... superconductors

Review CopyEdited

byLaina Karthikeyan

Ariyeh Maller

Costas Panayotakis

Alexander Rozenblyum

Hans Schoutens

Publications, Inc.Linus

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Copyright © 2007 Laina Karthikeyan, Ariyeh Maller, Costas Panayotakis,Alexander Rozenblyum and Hans Schoutens

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Table of Contents

1. Microstructure design by twinning in high-temperature superconductorY Ba2Cu3O7-8 for enhanced Jc at high magnetic fields ..................................... 1

1. Introduction ........................................................................................... 1

2. Theoretical Consideration ..................................................................... 2

3. Discussion ............................................................................................... 7

References ................................................................................................... 9

2. A Hydrological Event Model of the Tollgate Wetland ...................................... 11

1. Introduction ......................................................................................... 11

2. Runoff Modeling .................................................................................. 13

3. Recirculation Pump.............................................................................. 17

4. Actual Figures ....................................................................................... 19

5. Simulation ............................................................................................ 20

6. Discussion ............................................................................................. 24

7. Conclusion ............................................................................................ 26

References ................................................................................................. 27

Appendix .................................................................................................. 28

3. Chemotherapy by Drug Polymer Delivery in Brain Tumor Slices .................. 31

1. Camptothecin ...................................................................................... 31

2. Camptothecin Conjugates ................................................................... 32

3. Camptothecin Measurements .............................................................. 33

4. Spheroids .............................................................................................. 34

5. Camptothecin Conjugates in Spheroids on Brain Slices .................... 35

6. Limitations of Drug Delivery ............................................................... 36

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5. Camptothecin Conjugates in Spheroids on Brain Slices .................... 35

6. Limitations of Drug Delivery ............................................................... 36

7. Preclinical Safety of PCPP: SA............................................................ 37

8. Kinetics of PCPP: SA........................................................................... 37

9. Glioma Migration ................................................................................ 38

10. Recommendations .............................................................................. 39

11. Conclusions ........................................................................................ 40

References ................................................................................................. 42

4. In-band OSNR Monitoring for Synchronous Traffic Using Beating-noiseMeasurement of Header Signals ....................................................................... 45

1. Introduction ......................................................................................... 45

2. Experiment for SONET Traffic ........................................................... 48

3. Osnr monitoring for Synchronous Packet-Switched Traffic ............... 50

4. Summary .............................................................................................. 51

References ................................................................................................. 52

5. The Solar Collector: A Method of Protecting Earth from ThreateningAsteroids and Comets ....................................................................................... 53

1. Introduction ......................................................................................... 53

2. Conclusions .......................................................................................... 55

References ................................................................................................. 56

6. Capitalism’s Dialectic of Scarcity: A Project Report ....................................... 57

References ................................................................................................. 61

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Microstructure design by twinning in high-temperature superconductor Y Ba2Cu3O7-8 forenhanced Jc at high magnetic fieldsV. S. Boyko*, Siu-Wai Chan**

ABSTRACT

The principles of microstructure design by twinning in Y Ba 2 Cu 3 O 7 (YBCO) crystals for enhanced J c athigh magnetic fields are developed. The resources of twin microstructure design in YBCO by twining areanalyzed by comparing pinning capability of different microstructures: system of plane-parallel twin lamellas;system of wedge-shaped twins; microstructure composed of twin intersections. Rough estimations of relativepinning strength of the basic crystal defect for each specific type of twin microstructure were done.

1. INTRODUCTION

Mechanical twinning is one of the main forms of plastic deformation of crystals.Mechanical properties related to twinning have been important materials issues[1–3]. The dislocation description of twining turned out to be productive. Itcould be attributed, in particular, to dislocation thin twins theory developedstarting from [4] by A.M. Kosevich and his disciples (for details see [5, 6]) Wededicate this article in memory of A.M. Kosevich. Generalization of the approach[5,6] to the case of pile-ups of transformation dislocations in the external elastic,

* Physics Department, New York City College of Technology of the City University of New York, 300Jay Street, Brooklyn, NY, 11201, United States

** Department of Applied Physics and Applied Mathematics Columbia University, New York, NY10027, United States

This work is supported by a grant from the City University of New York PSC CUNY Research AwardProgram (Project # 671500-00-36).

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V. S. Boyko, Siu-Wai Chan

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thermal, electrical, and magnetic fields allowed to develop a new unifiedapproach to describe all basic manifestations of reversible plasticity of crystals:elastic twinning, thermoelastic martensitic transformation, superelasticity,shape memory effect, reversible behavior of ferroelastic domains [6 – 9]. Thenew materials satisfying the requirements of new technology very often havemechanical properties different from those of traditional materials. As a rule,they have low-symmetry crystal lattices. These materials frequently do notexhibit slip, in contrast to the traditional materials, but do exhibit twinning[10]. Good examples are high-T c superconductors in which twins wereobserved from the first structural investigations of these materials [11, 12].The twinning and influence of twin structures of traditional and high-Tcsuperconductors on their superconductive parameters were intensivelydiscussed (see, for example, [6, 13]). Time showed that the major problem forindustrial applications of high temperature superconductors is their low criticalcurrent density J c caused by the poor current transmission across high anglegrain boundaries (see for details [14]). Contrary to these boundaries, twinboundaries (TBs) in YBCO improve superconductive properties [15]. It isknown that twin boundary pinning becomes more effective than bulk pinningat temperatures closed to the T c . Therefore the design of twin microstructurein YBCO has risen as an important problem.

In [16], the applicability of dislocation thin twins theory [5, 6] to twinning ofYBCO was demonstrated and numerical values of phenomenologicalparameters of the theory were determined. In [16], we suggested a new method(twin tip shape method) of determination of TB energy tw using electronmicroscopy measurements of twin tip shape and relating them to the predictionfrom the dislocation theory of thin twins [5, 6]. This method can be applied tothe general case of twin structure when twin tips are observable in addition tothe traditional twin spacing method (see, for example, [17]). We proposedalso a method of determination of frictional force frS acting on a singletwinning dislocation in YBCO. This force determines the stability of twinmicrostructure and allows for an estimation of the natural limit of its reduction.The theoretical considerations and experimental investigations demonstratethe validity of proposed methods [16, 18 – 20]. In this article, we try to estimatethe resources of twin microstructure design in YBCO by twinning for enhancedJ c at high magnetic fields. We will compare pinning capabilities of differentmicrostructures: system of plane-parallel twin lamellas; system of wedge-shapedtwins; microstructure composed of twin intersections.

2. THEORETICAL CONSIDERATIONMost of twins in YBCO stem from phase transformation from non-superconducting tetragonal phase to the superconducting orthorhombic phase.This structural change results in the strain penetrating the whole lattice. Strainusually can be released by twinning. Twins in this case usually form a

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microstructure named polysynthetic twin [2]: a crystal is penetrated by paralleltwin lamellas. The situation was considered using energy approach [17, 21 –24]. The intertwin distance wT between lamellas can be estimated from thisapproach from the relationship (see, for example, [17]).

wT = 2t

coltw RN(1)

Where wT is the distance between centers of lamellas, colR is the size of thetwin colony, t is the twin strain, is the elastic modulus, N is a numericalfactor.

Estimating a density of vortexes typical for this type of twin microstructure,we assume by analogy to [20] that 2 flux quanta are pinned per square withsides bounded by adjacent TBs. In this case, the internal (trapped) magneticfield trH can be estimated as following: trH 12 )(~ wT 0 ( 0 is elementarymagnetic flux, 0 07.2 )10 15Wb . The internal field created by a colony ofplane-parallel lamellas now can be written as following

20 /~ wtr TH

coltw

t

RN

2

0~ (2)

Generally speaking, twin microstructure can be designed by variation of anyquantity in (2) — tw or colR . In a single crystal, colR could be substituted bya size of the sample, in polycrystals — by the average grain size. Actually twinmicrostructure usually has been manipulated only by changing the size ofgrains in YBCO,. but this strategy becomes counterproductive. Hoping toimprove superconductive properties of polycrystal YBCO we can make twinmicrostructure finer by decreasing grain size, but this increases total area ofGBs and drops J c . A method was found to control twin microstructure largegrain YBCO without changing the grain size by incorporating in the YBCOmatrix large well-dispersed volume fractions of dispersed addition of

2Y 5BaCuO (211) in the form of small particles [15], dopants [16], and additivessuch as yttrium nanoparticles [18]. In those cases, the samples were heavilytwinned and demonstrate better superconductive properties. The presence ofembedded particles gives highly nonuniform stress distribution creatingwedge-shaped twins (in uniform elastic field, as a rule, only plane-paralleltwins will appear [6]). In the common case, we have to deal with twins that donot cross samples as plane-parallel lamellas. Sharp tips are substantial part oftheir lengths. Applicability of (2) becomes questionable here.

We will use the dislocation theory of thin twins [5, 6] for consideration ofwedged shaped twins formed in the matrix with embedded particles. Thistheory has two phenomenological parameters that are related to the lattice

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forces acting on a twinning dislocation in YBCO: lattice frictional force frS (oneof the phenomenological parameters) and surface tension force thatincorporated in the second phenomenological parameter M. It is related tothe twin boundary energy tw as following

tw =2)1( M

(3)

where is the shear modulus, is the Poisson ratio. After determination ofnumerical values of phenomenological parameters in YBCO [16] we can usethe relationships of the thin twins theory to calculate the length L and shape ofthe twins in elastic field e . The length of a twin is determined according to[5, 6] by equation

LMLF )(

frS (4)

where

)(LF2

L

022

)(

xL

dxxe(5)

e is now the stress in the matrix near the vicinity of the embedded particle;L is the length of the twin. Integration is performed along the twin. The twinoriginates at the origin of coordinates and is situated along X - axis. The situationcan be simplified by considering the 2D-problem of the stress distributionaround stiff inclusion [25]. It is supposed that there is the stress 0 at theboundary between the matrix and inclusion. When the materials of inclusionand matrix have essentially different elastic constants (it is actually so in ourcase), we can treat the inclusion to be absolutely rigid. Then, the spatialdistribution of the shear stress causing twin appearance can be estimated as

2

2

0 ra

e (6)

where a is the radius of the inclusion, r is the distance from the center of theinclusion.

In the condition of twin microstructure formation (comparatively hightemperatures and short twins) we can neglect frS in (4) that yields

LMLF /)( . Using (4), (5) and (6), one can get an expression for length ofthe twin appearing in the vicinity of inclusion

22

MbaL tw (7)

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If we take M » 5´10 4 N/m 2/3 , g tw ~ 10 2 J/m², b ~ 10 11 m, then for a particlewith radius ma 610~ we will get mL 410~ , that correlates by order ofmagnitude with experimental data [26]. The colony of parallel wedged-tiptwins is often observed in YBCO (see, for example, [20]). If we assume byanalogy with [27] that each twinning dislocation can pin a vortex, then we candeduce that each wedged-tip twin will be able to pin additional number ofvortices N vor = h tw /a latt where h tw is the thickness of the twin, a latt is thelattice constant.

The twin intersections are very strong pinning centers [28, 29]. They tend topin a fluxoid simultaneously in both directions with the twin boundariesbehaving as high energy barriers, which prevent vortex motion. Such defectspossess a very intense elastic field and would tend to suppress the orderparameter locally, hence improving flux pinning. At the place of twinintersection, the very serious material distortion can occur: Rose canals, forexample (for details see [2]). The scenario of formation of this type ofmicrostructure could be as follows. The stress 0 corresponding to theappearance of a wedged twin can be estimated as 0 btw / , where b is theBurgers vector of the twinning dislocation. The wedged twin appears in thepoint of a crystal where this condition is fulfilled. The appearance of twinsinitiates the appearance of twin colonies around it. The lengths of twins ineach colony will increase until they come into a collision with twins of theneighbor colony. Inside each colony the intertwin distance wT can be estimatedfrom relationship (1). If each twin intersection can be considered as pinningone vortex, we can estimate the trapped magnetic field trH using relationship(2) but now the colR is not so high as the size of a single crystal or a grain in apolycrystal but can be made much smaller. One can expect that there are twodifferent regimes of formation of intersected areas. In the first regime,concentration of embedded particles is high, and the distance between particlesdetermines the size of a colony. In the second regime, the concentration ofparticles is small and the size of a colony is smaller than the distance betweenparticles. Assuming that colR ~ L and substituting {7} in {2}, we will get

trH = 0 ( t ² M² b²) / ( tw ³ a ²) (8)

To get rid of M, we take into account (3) that yields

22

222

0 abH

tw

ttr (9)

If we take 32 10~t , 22 /10~ mJtw , mb 1110~ , Pa1110~ then for theparticle with radius ma 610~ we will get GsmTH tr 100~10~ ,whichcorrelates by the order of magnitude with experimental data obtained in [28]for the samples with a small concentration of particles.

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Now we will consider regime number one for which the concentration ofembedded particles is high, and the size of colony colR is determined by thedistance between particles 211R : colR ~ 211R . In this case

211

2

0 RH

tw

ttr (10)

If we take Pa1110~ , 32 10~t , 22 /10~ mJtw , 211R m510~ ,0 07.2 Wb1510 , we will get TH tr 1~ . This agrees with the estimate of the

maximum trapped magnetic field (4.8 T) in [28].

Comparing the pinning ability of different twin microstructures, we, strictlyspeaking, should compare not only the corresponding densities of pinningcenters that we actually did above. We also should compare pinning strengthof basic crystal defects characteristic of each type of twin microstructure.Capability of a crystal defect to pin a vortex evidently depends on the size ofthe nonsuperconducting region enveloping a defect. Below we will compareby rough estimation pinning ability of a plane-parallel TB, of a TB with twinningdislocations, and a twin intersection. We will do this using thephenomenological strain criterion of superconductivity [30]. Chisholm andPennycook [30] suggested that dislocation cores are nontransparent for thesupercurrent because superconductivity is suppressed in the region of thecrystal lattice where strains achieve some critical value ecrit. It seems logical toexpand this approach to any crystal defect if its elastic field is known. In [31],this approach was applied for the determination of the thickness of anonsuperconducting layer enveloping a TB in YBCO. The distribution of strainnear TB was found by computer simulation methods. According to [31], wecan estimate a thickness of the nonsuperconducting layer h n enveloping a TBas h n » 5 ú. We can expect that wedged-tip twins are stronger pinning centersthan plane parallel twins. We estimate the strain field around dislocation (see,for example, [32, 33]} as e ~ b/r. Then the radius of a nonsuperconductiveregion around a dislocation r n will be r n ~ b/e crit . If we take e crit ~ 0.01, wewill get for twinning dislocation in YBCO r n ~10 ú (that is a little greater thanh n for TB). A large density of twinning dislocations at the tip of the twin (seeexperimental observation in [16]} creates an intensive elastic field that can pinadditional number of vortices. Moreover, in the case of plane-parallel TB, avortex can readily change its position or orientation in the plane of TB. In thecase of wedged-tip twin a vortex is pinned along a twinning dislocation andcan change its position only together with it. It is not easy because of theexistence of lattice friction force frS . However, we can expect that twinintersections are still the strongest pinning centers. Actually the elastic field ofthe twin intersection can be treated like that of a very short wedged twin.These secondary twins very often really appear at twin intersections. Usingthe expression of the stress concentration near the pile-up of dislocations (see,for example, [33]), one can make rough estimate of the radius of the

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nonsuperconducting region around the tip of the secondary twin as r n ~(N d ²´b²)/(e crit ²´ L d ) where N d is the number of dislocations in the domainand L d is the length of the domain. If we take N d = 10², L d = 10 6 m, and e crit~ 0.01 (actually, as it was shown in [34], e crit at lattice level in YBCO could besomewhat greater) then we will get r n ~ 100 ú. Thus, the r n for twinintersection is pretty large and approximates the radius of damage around theion track when columnar pinning centers are created by the heavy-ionirradiation [35].

3. DISCUSSION

Twin boundary energy and twin colony size are important factors forengineering twin morphology for the strong flux pinning and high criticalcurrent density. To improve magnetic properties of YBCO we should investigatepossibilities to decrease tw , frS colR , and take into account a pinning capabilityof corresponding basic unit of the twin microstructure.

Flux pinning by plane-parallel twin boundaries in YBCO was studied startingfrom [12] in the series of investigations (see for details [36 –38]). The essentialfeature of this pinning is high anisotropy. The anisotropic nature and moderatepinning strength make the application of plane-parallel twin boundary pinningcomplicated for practical purposes. Our consideration in the theory sectionalso attributes a modest pinning capability to the system of plane-parallel twinsthough there is some possibility to increase pinning capability of thismicrostructure by decreasing tw .

From (9) one can deduce that trH µ 1/ tw ². Thus we can substantially increaseinternal magnetic field trH by decreasing twin boundary energy tw . It isshown in [16] that addition of PtO2 to YBCO decreases tw by two times.Therefore we should expect that samples with PtO2 addition should increasetrapped magnetic field by four times in comparison with samples with CeO2,because the addition of CeO2 does not affect the tw as compared to PtO2.Exactly this enhancement of trH was experimentally observed by [39] thougha special experimental investigation is needed to relate directly thisenhancement with changing of tw . From this point of view, it is interesting toanalyze results of articles [19, 20]. In [20], tw has been measured as a functionof oxygenation temperature using both the twin tip method developed in [16]and traditional twin spacing method (for details see [17]). Twin boundaryentropy was found positive and its numerical value for YBCO was estimated[19]. In [20], the positive entropy of TB was exploited to decrease tw . It wasshown that the increase of the annealing temperature decreases tw and colR .As a result the critical current density and the magnetic field at the maximumpinning force substantially increases. For example, from experimental data ofthese two articles [19, 20] we can deduce following: when annealingtemperature is 873 K, tw = 29.5 mJ/m², colR = 2.8´10 5 m, trH = 0.3 T; when

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annealing temperature is 953 K tw = 17.5mJ/m², colR = 1.8´10 5 m, trH =1.43 T. As a result of increasing the annealing temperature and correspondinglydecreasing the tw , internal field trH becomes substantially greater. We canexpect that the twin intersections are very perspective pinning centers. In[40], authors identified pinning centers in YBCO and others high-T csuperconductors using high-resolution AC susceptibility measurements. It wasshown that pinning by twin intersections usually dominates. The maximumtrapped magnetic field in YBCO containing a completely intersectedmicrostructure at 77 K can be estimated based on preliminary data to be equal4.8 T [28].

Thus, the key points of microstructure design for enhanced J c at high magneticfields can be formulated as follows: decreasing twin boundary energy;decreasing twin colony size; increasing the area of twin intersections.

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References

[1] R.W. Cahn, Adv. Phys. 3 (1954). 363.

[2] M.V. Klassen-Neklyudova, Mechanical Twinning of Crystals, Consultants Bureau,New York (1964).

[3] W. Christian and S. Mahajan, Progr. Mater. Sci. 39 (1995) 1.

[4] A.M. Kosevich and L.A. Pastur, Sov. Phys. -Solid State 3 (1961) 935.

[5] A.M. Kosevich and V.S. Boiko, Sov. Phys. – Uspekhi 14 (1971) 286.

[6] V.S. Boyko, R.I. Garber, A.M. Kossevich, Reversible Crystal Plasticity, AmericanInstitute of Physics, New York. (1994).

[7] V.S. Boiko, A.M. Kosevich, and E.P. Fel’dman, Sov. Phys. – Solid State 29(1987) 94.

[8] V.S. Boyko, A.M. Kosevich, and V.A. Lobodjuk, Russ. Metall. 1 (1992) 83.

[9] A.M. Kosevich and V.S. Boiko, Mater. Sci. Eng. A, 164 (1993) 111.

[10] M.H. Yoo and M.Wuttig, Twinning in Advanced Materials, TMS, Warrendale,PA, 1994, p. V.

[11] M. Hervieu, B. Domenges, C. Michel, G. Heger, J. Provost, and B. Raveau, Phys.Rev. B 36 (1987) 3920.

[12] L.Ya. Vinnikov, L.A. Gurevich, G.A. Emel’chenko, and Yu.A. Ossipyan, SolidState Commun. 67 (1988) 421.

[13] V.S. Boiko, A.M. Kosevich, and Yu.A. Kosevich, Sov. J. Low Temp. Phys. 17(1991) 1.

[14] S.-W. Chan, J. Phys. Chem. Sol. 55 (1994) 1415.

[15] M. Chopra, S.-W. Chan, R.L. Meng, and C. Chu, J. Mater. Res. 11 (1996) 1616.

[16] V.S. Boyko, S.-W. Chan, and M. Chopra, Phys. Rev. B 63 (2001) 224521.

[17] T. Roy and T.E. Mitchell, Phil. Mag. A 63 (1991) 225.

[18] O. Jonprateep and S.-W. Chan, IEEE Trans. Appl. Supercond. 13 (2003) 3502.

[19] L. Mei and S.-W. Chan, J. Appl. Phys. 98 (2005) 033908.

[20] L. Mei, V.S. Boyko, and S.-W. Chan, Physica C 439 (2006) 78.

[21] D.S. Lieberman, M.S. Wechsler, and T.A. Read, J. Appl. Phys. 26 (1955) 473.

[22] A.L. Roytburd, in Solid State Physics, edited by H. Ehrenreich, F. Seitz, and D.Turnbull, vol.~33 of Advances in research and applications of solid statephysics, Academic Press, New York (1978) p. 317.

[23] A.G. Khachaturyan, Theory of Structural Transformations in Solids, Wiley,New York (1983).

[24] T.E. Mitchell and J.P. Hirth, Acta Metall. Mater. 39 (1991) 1711.

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[25] N.I. Muskhelishvili, Some Basic Problems of the Mathematical Theory ofElasticity, P. Noordhoff Ltd., Groningen (1963).

[26] M. Chopra, S.-W. Chan, V.S. Boyko, R.L. Meng, and C.W. Chu, in Abstracts, 10thAnniversary HTS Workshop on Physics, Materials and Applications, edited byC.W. Chu and K.A. Muller, Houston, Texas (1996) p.49.

[27] M.E. McHenry and R.A. Sutton, in Progress in Materials Science, edited by J.W.Christian and T.B. Massalski, 38,Pergamon, Oxford – New York (1994) p. 159.

[28] M. Chopra, Doctoral Thesis, Columbia University, New York (1997).

[29] S.W. Chan, M. Chopra, L. Mei, and V.S. Boyko, in Program of MRS 2006 SpringMeeting, MRS, San Franciso (2006), p. 230.

[30] M.F. Chisholm and S.J. Pennycook, Nature 351 (1991) 47.

[31] V.S. Boyko, J. Malinsky, N. Abdellatif, and V.V. Boyko, Phys. Lett. A 244 (1998)561.

[32] A.M. Kosevich, in Dislocations in Solids, edited by F.R.N. Nabarro, NorthHolland Publishing Company, Amsterdam - New York - Oxford (1979) v. 1,p. 34.

[33] L.D. Landau, E.M. Lifshitz, A.M. Kosevich, and L.P. Pitaevskii, Theory ofElasticity, Pergamon Press, Oxford, New York (1986), p. 131.

[34] V.S. Boyko and A.M. Levine, Phys. Rev. B 64 (2001) 224525.

[35] R. Weinstein, R. Sawh, A. Gandini, and D. Parks, Supercond. Sci. Technol 18(2005) S188.

[36] L.J. Swartzendruber, A. Roitburd, D.L. Kaiser, F.W. Gayle, and L.H. Bennet,Phys. Rev. Lett. 64 (1990) 483.

[37] W.K. Kwok, U. Welp, G.W. Crabtree, K.V.R. Hulscher, and J.Z. Liu, Phys. Rev.Lett. 64 (1990) 966.

[38] U. Welp, T. Gardiner, D. Gunter, J. Fendrich, G.W. Crabtree, V.K. Vlasko-Vlasov,and V.I. Nikitenko, Physica C 235-240 (1994) 241.

[39] M.P. Delamare, M. Hervieu, J. Wang, J. Provost, I. Monot, K. Verbist, and G.V.Tendeloo, Physica C 262 (1996) 220.

[40] D. Crete, R. Bernard, J. Pommereau, G. Gadois, S. Berger, J. Bratico, J. Contour,O. Durand, J. Maurice, J. Groller, and K. Bouzehouane, Phys. Stat. Solidi (c)(2004) 1935

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2A Hydrological Event Model of the TollgateWetlandBen Pfaff *, Hüseyin Yüce **

1. INTRODUCTION

Federal legislation (The Clean Water Act of 1972 as amended in 1987) mandatescontrol of the flow of pollution from storm water into rivers. In most cases, thisrequirement is carried out through installation of an expensive system of pipesand pumps. For small communities, the cost of traditional implementation ofthis requirement through installation of pipes and pumps can be prohibitive. Analternate approach is to drain storm water into a constructed wetland designed tonaturally clean the district’s storm water. This approach is used in the TollgateDrainage District of Ingham County, Michigan, depicted below in Figure 1.

The primary design goal for the system was as a storage reservoir: it is designedto be large enough, in conjunction with overflow to the neighboring golf course,to hold the runoff from a 100-year storm , a storm of magnitude such that onaverage it will occur only once in 100 years [1].

However, storage is not the only point of interest in the Tollgate wetland.Questions of interest not addressed in the original Tollgate engineering workinclude the following:

* Stanford University, Department of Computer Science** New York City College of Technology, Department of Mathematics

The authors wish to express their thanks to Charles MacCluer of the Michigan State University (MSU)Department of Mathematics, Randy Abbott, Don Cuthbert, Pat Lindemann, Katie Palmer, Dave Solberg, andKaren Wayland of the Ingham County Drain Commissioner’s office, Roger Wallace of the MSU Departmentof Civil Engineering, Tom Volkening of the MSU Engineering Library, John LeFevre of Fishbeck, Thompson,Carr, and Huber, Philip FitzSimons of FitzSimons Automation, fellow students Md. Nazrul Islam and AsadQazi. Without the valuable contributions of all of these people, this work would not have been possible.

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• How does water move through the system as the total volume handledincreases?

• How do conservative and nonconservative pollutants move throughthe system?

• What special maintenance needs might the system be expected tohave, and given these, what is the system’s expected lifespan asdesigned?

This work provides answer to the first question, by constructing an event modelof the Tollgate wetland detention system. This model predicts an answer tothe following question: Given a set of initial conditions in the system and apattern of precipitation, what response, in terms of a short-term water flowpattern, can be expected within the system?

Most of the literature in the subject turned out to lack the desired depth andprecision necessary for mathematical modeling. The given case studies in [2,3, 4, 5] were described qualitatively, not quantitatively. Indeed, some of theliterature does provide [6, 7] do provide some qualitative insight and presentssome data in graphical form, but it is primarily oriented toward those havinglarge amounts of sample data.

Figure 1. Sketch of Tollgate wetland [1].

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A Hydrological Event Model of the Tollgate Wetland

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This work examines the mechanisms at work in the Tollgate wetland, proposesa unit hydrograph and model for water flow, describes and discusses asimulation of the system designed by the authors based on these proposals,and gives conclusions and recommendations for further study. The workcommences with a decomposition of the problem and follows with anexamination of precipitation and resulting runoff, then with a study of howwater enters the system. These principles are then applied directly to theTollgate system via an event model simulation, and results and conclusionsare given, along with recommendations for further study. The appendix actsas a user’s guide to the event model.

2. RUNOFF MODELING

When precipitation occurs over a watershed, some of the precipitated water isretained within the watershed, above or below the soil. The rest, called runoff,flows (directly or indirectly) into storm sewers [10, p. 204-206]. In the Tollgatewatershed, runoff travels to the Tollgate wetland.

The amount of runoff from a given storm depends on the area of the watershed,the amount of precipitation, and the imperviousness of the watershed area.The total amount of runoff can thus be represented as

= ,R CpA (1)

where C is a coefficient representing soil permittivity taken as an averageover the area of the watershed, p is the precipitation depth, and A is thewatershed’s area [8].

A hydrograph is “a graph of stage or discharge versus time” [10, p. 117]. In theTollgate watershed, the hydrograph of interest is runoff from the watershedinto the grit chamber and the detention pond. In Figure 1, this hydrograph ismeasured at the bottom of the diagram where the inflow divides between thegrit chamber and the detention pond.

A unit hydrograph is a defining hydrograph for a system given a unit amountof precipitation over the basin, such as 1 inch. As the duration of rainfallapproaches zero, keeping the amount of precipitation constant, the unithydrograph becomes an instantaneous unit hydrograph (IUH). Given a rainfallpattern ( )f t and an IUH ei , runoff q at time t can be calculated via theconvolution

0( ) = ( ) ( )

t

eq t f i t d (2)

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Hydrographs and unit hydrographs can be constructed from actual datameasured during particular events, or they can be devised synthetically usingheuristic methods. The former is preferable: “[U]nit hydrographs derived bysynthetic and transposition methods seem to be of limited value” [10, p.225].However, the latter methods have the advantage of not requiring as muchdata as the former methods. Since measured event data is not available for theTollgate wetland, heuristics will be used here.

Several methods have evolved for synthetically constructing a unit hydrographbased on minimal actual data from a watershed. Many of these methods havethe following two-part structure:

• Heuristically determine values for pt , pQ , and bt (defined later).

• Fit a curve to the points determined by pt , pQ , and bt .

These two parts are discussed separately below.

2.1 Parameter Estimation

The shape of a theoretical unit hydrograph can be determined by threeparameters: pt , the time of maximum runoff or peak time , pQ , themaximum runoff flow rate , and bt , the time base or time for runoff flow torecede to zero. The time origin = 0t is taken to be the start time of precipitation[11, p. 175-179].

The literature gives numerous ways to estimate values for these parameters.One common method, due to Snyder [11, p. 206-208], makes use of simplemeasurements of the watershed’s sewer system. Snyder’s equations give peaktime, in hours, as

0.3= ( )p t ct C LL (3)

where L is the length of the main stream from outlet to divide, in miles, cL isthe distance from the outlet to a point on the stream nearest to the centroid ofthe basin, also in miles, and tC is the lag factor, coefficient varying between1.8 and 2.2 depending on the slope of the basin.

Snyder calculates peak flow as

640= p

pp

C AQ

t (4)

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where A is drainage area in square miles, pC is the peak flow factor, coefficientranging from 0.56 to 0.69, and 640 is a conversion factor to cause pQ to be inft3/s. Lastly, Snyder’s time base is

3 324

pb

tt (5)

where pt is peak time as calculated above [10, p. 223].

2.2 Curve Fitting

The parameters determined using the techniques of the previous section specifythree points: (0,0) , ( , )p pt Q , and ( ,0)bt . Any number of techniques can beused to fit a curve to these three points. Two such techniques are examinedbelow.

The simplest approach draws straight lines among the points:

, 0 ,

( ) = , ,

0,

pp

p

pp p p b

b p

b

Qt t t

tQ

f t Q t t t t tt t

t t(6)

A problem with this approach is that it does not necessarily produce a functionhaving unit area under its curve. The more refined approach below avoidsthis difficulty. Use of a two-parameter gamma distribution function, suggestedin [11], is given by

/

1( ) =( 1)

tt ef t (7)

Where 0 t , 1 is dimensionless, and 0 has the same units as t .Figure 2 shows the gamma distribution function’s shape for selected parametervalues.

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Note that the area under the gamma distribution is always 1, regardless ofparameters. For our purposes, the gamma distribution function has two helpfulproperties: first, its shape is the same as observed hydrographs, and second,there is unit area under its curve for all values of and .

Since we want the maximum value of ( )f t to occur at = pt t , we can find oneconstraint on and by finding ( )f t ‘s maximum:

1 / / = 0t ttt e e ,

Simplifying above, 1 = 0.t t Then we obtain,

= = pt t (8)

A second constraint on and can be found by setting = ( )pQ f :

1

1

( )( ) = =( 1) ( 1)p

eft e .

Figure 2. Shape of the gamma distribution (7) for peak time 1pt and peak values pQ .

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Let A be the area of the basin and vC A be a unit volume. Then

1

= = ( )( 1)

v vp

p p

C A C AQt e t (9)

According to [11, p. 205], ( ) can be estimated as the cubic

2 3= 0.045 0.5 5.6 0.3 . (10)

Combining Equations (9) and (10), we arrive at

2 3

= 0.045 0.5 5.6 0.3p p p p p p

v v v

Q t Q t Q tC A C A C A . (11)

Using Equations (8) and (11), we can calculate and given pt and pQ .

The gamma distribution function has an infinite tail, so it cannot be made topass through ( ,0)bt . However, it approaches the x -axis arbitrarily closely asx approaches infinity, so in practice the unit hydrograph function ( )g t canbe written in a piecewise fashion:

( ), 0( ) =

0,b

b

f t t tg t

t t . (12)

3. RECIRCULATION PUMP

In the Tollgate wetland, water in the grit chamber is pumped to the waterfall,flowing into the deadwood swamp, as shown in Figure 1. Therefore, theoperation of the pump directly affects the circulation of water in the system.In this section, we examine the pump’s operating characteristics.

There are actually two pumps in the Tollgate wetland. These pumps are identicalin specifications. Their operation is guided by a set of water level sensors,which are positioned such that the following relationships are satisfied:

1 2off on onl l l (13)

When the level l in the grit chamber is minimal, such that 1onl l , neitherpump runs. When the level rises, such that 1 2on onl l l , one pump operates.If the level then falls such that offl l , the pump stops. Contrariwise, if thelevel continues rising such that 2onl l , both pumps run until the level againfalls such that offl l , at which point both pumps stop.

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The flow rate of a pump depends primarily on the presented head, or thevertical distance between the water level on the inlet and outlet sides of thepump. For the particular pump used in the Tollgate wetland, regression onsampled points from supplied pump curves yielded the following theoreticalflow rate approximation

3 4 2 6 3( ) = 21.45 (7.821 10 ) (7.129 10 ) (1.388 10 )pQ h h h h , (14)

Where h is head in feet, giving a result in hundreds of gallons per minute[12]. Figure 3 shows this theoretical pump rate as a solid line. Note that thetheoretical output of two identical pumps is twice that of a single pump of thesame type.

Because of flow resistance, the actual pump rate is lower than the theoreticalpump rate. The actual pump rate at a given head h can be found via aniterative process, described below:

1. Figure an initial guess for ( )L fH , the head loss due to friction in thepump output pipe. Zero is acceptable as an initial guess if no bettervalue is known.

2. Calculate pQ for ( )L fh H , using (14).

3. Calculate water velocity v from pQ :

2= pQv

r(15)

where r is the radius of the pipe (5 in).

Figure 3. Theoretical and actual pump rates for pump in Tollgate system.

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4. Calculate Re , the Reynolds number for the flow, given v :

2= v rRe (16)

where is the density of water (62.32 lb/ft3) and is the viscosityof water (2.39 lb/h ft) [13, p. 2-3].

5. Calculate f , the Fanning friction factor for the flow, given Re [13,p.2, 9]:

50.25

0.3164= for 10f ReRe (17)

5 60.237

0.221= 0.0032 for 10 3 10f ReRe . (18)

6. Calculate1

( )L fH , the head loss due to friction [13, p. 2, 9]:

1

2

( ) =2 2L fL vH fr g (19)

where L is the length of the pipe and g is the force of gravity(32.17 ft/s2).

7. If1

( ) ( ) <L f L fH H , where is the maximum acceptable error,,then accept the pQ calculated most recently in step 2 as a goodapproximated real value. Otherwise, set

1( ) ( )L f L fH H and repeat

from step 2.

When the above process is applied to a range of heads, a function givingreal pump rate in terms of theoretical pump rate is obtained. This functionis shown as a solid line in Figure 3 for the cases of one and two pumps inoperation.

4. ACTUAL FIGURES

Many of the preceding sections dealt with wetlands in general, with little regardfor the specific case of the Tollgate wetland. However, actual figures for theTollgate wetland must be used to obtain much insight. This section enumeratesTollgate parameters and their sources.

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The Tollgate watershed is 210 acres in size [1]. Snyder’s L , the main streamchannel from outlet to divide, is 0.9219 miles. Snyder’s CL , the main streamchannel from outlet to the point nearest the watershed centroid, is 0.9583miles [14]. Synder’s tC and pC are both estimated as 0.3 [11, p. 208]. Runoffpermittivity C is estimated at 43% [15].

The grit chamber is box-shaped, 10 ft by 7.5 ft by 7 ft, with a 10 in by 7.5 ft by2 ft unusable filled volume. Its floor has an elevation of 838 ft. It is connectedto the pump chamber by a 24 in pipe of unknown length. The pump chamberis cylindrical with 6 ft diameter and 11 ft height with a minimum elevation of834 ft. The pump’s outlet in the waterfall is at an elevation of 859.5 ft [16].Therefore, the usable volume of the grit chamber and pump chamber togetheris approximately 824 ft3, ignoring the connecting pipe.

The deadwood swamp has a surface area of 12,668 ft2 [14]. The shallow pondhas a surface area of 12,128 ft2. Both exhibit 0.5 ft difference in depth betweenlow-water and high-water conditions [16].

The shortest distance through the sand-peat filter, from inlet to outlet, is 305ft. Following an orthogonal path, the distance is 350 ft [14].

The ditch has area 5,528 ft2 at elevation 845 ft and area 15,810 ft2 at its highelevation, 847 ft [14]. Using a trapezoidal approximation to its cross-sectionalarea, its maximum capacity is 21,338 ft3.

The detention pond has surface area 273,450 ft2 with a 3.5 ft maximum normalchange in depth [16]. The product, 957,075 ft3, is a lower bound on itsmaximum expected capacity.

5. SIMULATION

Figure 4 is a block diagram of the flow of water in the Tollgate wetland. Eachblock represents one stage that water passes through. Our knowledge of theindividual elements in the system, as discussed in earlier sections, along withthis illustration of how the elements work together, allows a simulation of thesystem to be constructed.

In Figure 4, solid lines mark direction of gravity flow; dashed lines denotepumps; dotted lines indicate raised pipes. The simulation based on this levelof knowledge makes a number of simplifying assumptions. Only the rainfallpattern, hydrograph, grit chamber, pump, and detention pond are explicitlymodeled. The system of ponds is arbitrarily reduced to a one-hour delaybetween the grit chamber and the detention pond. Water is assumed not toflow from the detention pond into the grit chamber (See the Discussion forjustification of the two final assumptions). This model is suitable only as an

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event model, because it does not account for water leaving the wetland viaevaporation, transpiration, or infiltration. Modifying the model to deal withthese phenomena would be a logical extension. The model does not accountfor the ponds in the system. Obviously, learning more about the ponds andthe streams connecting them is important for future work.

The model is implemented with a software package called Simulink for Matlab5.3 by Mathworks, Inc. This program allows control systems to be builtschematically, in a hierarchical manner, and their behavior to be simulated.Matlab and Simulink files for the Tollgate model are included with this report,and their usage is documented in the appendix. Two types of measurementsappear in the system: water flow rates, in ft3/min, and water volumes, in ft3.The underlying theme of the model is that integrating a water flow rate over aperiod of time gives a water volume. The input to the system is provided by auser-specified hyetograph or rainfall pattern; e.g., 1 inch of water over a 1-hour period. This flow passes into the grit chamber, or if the grit chamber isfull, into the detention pond. Thus, when it is not bypassed by high-flowconditions, the grit chamber acts as a buffer between the watershed and thewetland.

Figure 4. Block diagram of water flow in Tollgate wetland.

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Figure 5 shows the top-level Simulink model for the wetland system. Theinput hydrograph is connected to the input divider, which routes water to thegrit chamber, unless it is full, in which case it goes to the detention ponddirectly. The grit chamber is connected to the wetland system, arbitrarilyrepresented as a one-hour delay, whose output connects to the detention pond.A virtual oscilloscope records the hyetograph and characteristics of the system’sresponse.

The model for the grit chamber and pump is illustrated by Figure 6. In thismodel, the integral of the flow rate into the chamber produces the volume ofwater in the chamber. This volume is used to calculate the water level and thepump head, i.e., the vertical distance that the pump or pumps must lift water.The water level in turn determines the number of pumps operating; the headdetermines the rate at which the pumps operate. An amplifier converts the

Figure 5. Control system model for the Tollgate system.

Figure 6. Control system model for grit chamber and pump.

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pump rate from gal/min to ft3/min for conformability of units with theremainder of the system. Finally, the outflow is fed back into the input inorder to ensure consistency of the grit chamber volume.

The grit chamber model uses a submodel, shown in Figure 7, to convert gritchamber volume to water level and pump head. The piecewise linear formulasused in this submodel are easily derived from the grit chamber dimensionsspecified in Section 2.

The input divider model compares the grit chamber volume to its capacity.Water is routed into the grit chamber unless it is full, in which case the wateris passed into the detention pond directly. For hysteresis’ sake a relay is usedinstead of an exact comparator; if this is not done, Simulink iteratesindefinitely.

Figure 7. Control system model for conversion between grit chamber volume and pump head.

Figure 8. Control system model for input divider.

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6. DISCUSSION

Figure 9 shows the simulated response of the Tollgate system to three sampleevents. Each response is shown as five graphs against time (in minutes). Thegraphs, from top to bottom, represent:

• Hyetograph or rainfall pattern, in in/h.

• Hydrograph or wetland inflow, in ft3/min.

• Amount of water passed through grit chamber during event, in ft3.

• Amount of water passed into detention pond, bypassing grit chamber,during event, in ft3.

• Total amount of runoff, in ft3.

Figure 9.

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The three sample events are (1) one inch ofrain over a one-hour period, (2) 0.5 inch,then 1.5 inch, then 0.5 inch of rain insuccessive half-hour periods, and (3) 0.2inch of rain over one hour. Examination ofsimulation results (1) or (2) reveals asurprising result: the water passing into thedetention pond is about the same as thetotal runoff volume. This means that in arainstorm, the grit chamber fills quickly,causing much of the storm runoff to flowdirectly into the detention pond. One of thestated purposes of the grit chamber is toremove large pieces of debris fromincoming water, so water bypassing the gritchamber would seem to be undesirable andrun counter to the system’s design goals.Conservative calculations can verify that thesimulation matches the Tollgate model inthis case. Suppose that 1 inch of rain fallson the watershed over a 1-hour period. Therunoff amount R is approximately 43% ofthe total precipitation volume, as (1):

R = CpA = 0.43 x1in x 210 acre = 3.3 x 105 ft3.

Suppose further that the runoff is dischargeduniformly across a 3-hour period, noting thatthe unit hydrograph for the system predictsa shorter discharge time with a high peak.Then, if the pump rate from the gritchamber is considered to be the maximum,4300 gal/min (see Figure 3), then for the grit chamber the ratio k of water inflowversus outflow is

5 33.3 10 ft / 3h 3.174300gal/min

k

Since the volume of the grit chamber is just 824 ft3 (2.6 fewer orders ofmagnitude) it quickly fills under these conditions. Simulation result (3)shows a result closer to that originally expected, for which most of therunoff passes through the grit chamber on its way into the system. Therainfall pattern of 0.2 inch over an hour to produce this result wasempirically determined.

Figure 9. Results of simulation of three sample events. Fromtop to bottom and left to right, the events are (1) one inch ofrain over a one-hour period, (2) 0.5 inch, then 1.5 inch, then 0.5inch of rain in successive half-hour periods, and (3) 0.2 inchof rain over one hour.

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7. CONCLUSION

This work has examined the properties of the Tollgate constructed wetland inIngham County, Michigan, beginning with a review of the literature onconstructed wetlands. We have constructed a synthetic hydrograph for theTollgate watershed, figured the behavior of the grit chamber and pump, andconstructed an event simulation.

The results of the simulation showed that, in a storm of magnitude larger than0.2 in/h, most of the storm runoff is not filtered through the grit chamber, butrather bypasses it, directly flowing into the detention pond. This is undesirabledue to the useful filtering of large particles that the grit chamber provides.The main idea of having a constructed wetland is that to move the waterthrough the system to clean.

The simulated model, suggested here, can be used to model or simulate othersimilar systems up to model specific measurements. In principal, constructedwetlands have the same base idea: collect the runoff from watershed andcirculate it through the system (wetland). Thus the model constructed herewill help design and simulate other constructed wetlands by changingparameters and specifications of the system in consideration.

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References

[1] K. Wayland. Private communication, 2000.

[2] J. Persson, N. L. G. Somes, and T. H. F. Wong, Hydraulics efficiency of constructedwetlands and ponds, Water Science and Technology, V. 40, no. 3, P. 291-300, 1999.

[3] N. L. G. Somes and T. H. F. Wong, Designing outlet characteristics for optimal wetlandperformance, Water Science and Technology, V. 36, no. 8-9, P. 235-240, 1997.

[4] R. B. E. Shutes, D. M. Revitt, A. S. Mungur, and L. N. L. Scholes, The design ofwetland systems for the treatment of urban runoff, Water Science and Technology, V.35, no. 5, P. 19-25, 1997.

[5] T. H. F. Wong and N. L. G. Somes, A stochastic approach to designing wetlands forstormwater pollution-control, Water Science and Technology, V. 32, no. 1, P. 145-151,1995.

[6] S. Tatalovich and J. Harbor, Trap efficiency of a small constructed wetland, Publishedon CD-ROM in ASCE [7].

[7] American Society of Mechanical Engineers, Proceedings of the ASCE WetlandsEngineering River Restoration Conference, Published on CD-ROM, 1998.

[8] T. Koob, M. E. Barber, and W. E. Hathhorn, Hydrologic design considerations ofconstructed wetlands for urban stormwater runoff, Journal of the American WaterResources Association, V. 35, no. 2, P. 323-331, 1999.

[9] G. L. Oberts and R. A. Osgood, Water-quality effectiveness of a detention wetlandtreatment system and its effect on an urban lake, Environmental Management, V. 15,no. 1, P. 131-138, 1991.

[10] R. K. Linsley, Jr., M. A. Kohler, and J. L. H. Paulhus, Hydrology for Engineers.McGraw-Hill, third ed., 1975.

[11] W. Viessman, Jr., G. L. Lewis, and J. W. Knapp, Introduction to Hydrology. Harper& Row, third ed., 1989.

[12] Gorman-Rupp Company, P.O. Box 1217, Mansfield, Ohio 44901-1217,Engineering Order for Gorman-Rupp Water/Wastewater Pumping Equipment,November 1996.

[13] American Society of Heating, Refrigeration, and Air-Conditioning Engineers,ASHRAE Hand-book: Fundamentals, 1997.

[14] J. R. LeFevre, Tollgate contract 2, tech. rep., Fishbeck, Thompson, Carr & Huber,1996. Derived from measurement in contract blueprints.

[15] A. Qazi. Private communication, 2000.

[16] J. R. LeFevre, Tollgate contract 2,” tech. rep., Fishbeck, Thompson, Carr & Huber,1996. As labeled in contract blueprints.

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APPENDIX

Simulation Model User’s Guide

The simulation model for the Tollgate wetland is provided as a set of files forThe Mathworks’ Matlab 5.3 with Simulink option. The model was developedusing, and the instructions below reflect the use of, the Unix version of Matlab,but versions for other operating systems should be similar. The model issegmented into two parts: a Matlab code module for converting a hyetographinto a hydrograph, and a Simulink model to simulate the system response toa hydrograph. The former module is invoked from the Matlab commandline. To use it, first be sure that the current directory contains the Tollgate .mfiles: hydro.m, iuh.m, make_rain.m, s_hydrograph.m, andunit_hydrograph.m. The hydrograph synthesis function, hydro, takes a singleargument, rainpat, that specifies the pattern of rainfall. rainpat takes the formof an n-row by 2-column matrix. The first column in each row specifies a lengthof time, in hours, and the second column specifies the amount of rainfall, ininches, during the corresponding time period. The hydro function returns apair of structures specifying the hydrograph and the hyetograph, respectively.The primary use of these return values is as input to the Tollgate Simulinkmodel. For this purpose, the returned structured must be assigned to Matlabworkspace variables h and r.

The following examples show how the hydrographs for the three sample eventsillustrated in Figure 9 can be reconstructed.

• [h, r] = hydro ([1 1]);

• [h, r] = hydro ([.5 .5; .5 1.5; .5 .5]);

• [h, r] = hydro ([1 .2]);

The Simulink model is invoked from Simulink. To launch Simulink, typesimulink at the Matlab command prompt. Shortly an additional windowshould pop up. In that window, select “Open...” from the “File” menu, andselect the provided file finalmodel.mdl from the list of files. The modelshown in Figure 5 should appear. An oscilloscope readout resembling Figure9 should also be displayed. If not, double-click on the oscilloscope icon in themodel window.

Once a hydrograph has been created using syntax similar to that given above,the model can be run. To do this, choose “Start” on the “Simulation” menu.

The oscilloscope window can be used to examine the system response. Thegraphs in the window are in the order shown in Figure 9. If some of the graphsgo off the charts, click on the “Autoscale” button on the oscilloscope’s toolbar

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to rescale them. Other buttons on the toolbar can be used to zoom in onparticular parts of the graphs, to print the graphs, or to change properties ofthe oscilloscope window.

If the chosen rainfall pattern is much longer than 1.5 h, it may be desirable tosimulate the system for longer than 3 h. If so, two settings must be adjusted:the simulation runtime and the oscilloscope display time. Use the “Parameters”item on the “Simulation” menu of the model system to change the former,and the “Properties” button on the oscilloscope’s toolbar to change the latter.Normally, both should be set to the same values. Also, note that both settingsare specified in minutes.

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Appendix

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3Chemotherapy by Drug Polymer Delivery inBrain Tumor Slices

Victoria Ying*

1. CAMPTOTHECIN

Camptothecin (CPT) is a naturally occurring cancer drug found in the bark andwood of the Chinese tree, Camptotheca acuminata. CPT binds to topoisomeraseI and stabilizes the enzyme-DNA complex, causing cytotoxic damage to cancercells. Camptothecin has a five ring structure with a chiral center located at C-20in the last lactone ring (Figure 1). The topoisomerase I inhibitory activity isstereospecific, with the naturally occurring (S)-isomer of CPT being a muchmore potent inhibitor than the (R)-isomer. Substitutions at C-9 or C-10 canenhance water solubility without interfering with drug activity (Figure 5). TheCPT carboxylate is more water soluble than the lactone, but is 1000 times lessactive in inhibiting topoisomerase I [Takimoto C.H., Arbuck S.G.].

In phosphate buffered saline (PBS) at pH 7.4, human serum albumin (HSA)bound preferentially to CPT carboxylate with 150 times greater affinity thanthe lactone form. These interactions result in greater conversion to CPTcarboxylate in the presence of HSA than in the absence of protein. In humanplasma at pH 7.4 and 37oC, the CPT lactone opens rapidly to the carboxylateform in 11 minutes, resulting in 0.2% lactone and 99.8% carboxylate atequilibrium [Mi Z., Burke T.G., Differential Interactions].

The poor solubility of CPT in water makes direct addition of this powdery drugto culture medium nearly impossible. An organic solvent such as dimethyl

*Assistant Professor, Biological Sciences Department

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Victoria Ying, Ph.D.

32

sulfoxide (DMSO) can be used to prepare intermediate stock solutions of CPT.DMSO is an excellent solvent for most drugs and the stock solutions obtainedare sterile. The only drawback is that DMSO has been reported to be adifferentiating agent and its possible effects on invasion should be testedseparately whenever it is used as a drug solvent in confronting cultures.However, no effect on invasion is detected for DMSO concentrations up to1% in culture medium (v/v) [Lund-Johansen M. et al].

2. CAMPTOTHECIN CONJUGATES

Conjugation of CPT to polyethylene glycol (PEG) by an ester bond stabilizesthe lactone. Conjugation of CPT also increases the water solubility from 0.025mg/ml to 2 mg/ml [Conover C.D. et al, 1998]. Also, biodistribution studiesshow that PEG-GLY-CPT in saline provides more available labeled CPT incirculation than unconjugated CPT dissolved in intralipid. In addition, morelabeled CPT accumulates in solid tumors when delivered in the PEG-GLY-CPT form, with greater preference for tumor tissue than normal tissue [ConoverC.D. et al, 1999].

Simple esters are rapidly cleaved from drugs, but the carboxylesteraseactivity is much slower in humans than in rodents. However, the hydrolysisrate is significant to allow for controlled localized drug release in tumortissues. Esterase hydrolysis declines with increasing complexity of the esteror with steric hindrance. Long chain alkyl esters are often highly lipophilicand tend to bind heavily to plasma proteins, which are difficult to administerbecause they end up being distributed to the liver and bile instead[Grieg N.H.].

Camptothecin lactone Camptothecin carboxylate

CH9

CH

CH10

CH

CH

N

CH2N

CH

O

CH2

COHCH2

O

O

CH320

CH9

CH

CH10

CH

CH

N

CH2N

CH

O

CH2

COHCH2O

OH

CH320

OHOH-

H+

Figure 1. CPT Isomerization Between Carboxylate and Lactone. CPT converts to the carboxylate when pH ³ 7.4. Thecarboxylate is 1000 times less active than the lactone and generates significant side effects.

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Chemotherapy by Drug Polymer Delivery in Brain Tumor Slices

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3. CAMPTOTHECIN MEASUREMENTS

The fluorescence of CPT is measured at 434 nm after excitation at 370 nm.The lower limit of detection for CPT in plasma or urine is 5 ng/ml. At highconcentrations, the drug can be assayed by ultraviolet absorption. When CPTis acidified, it converts to the lactone form which shows greater fluorescenceintensity [Hart L.G. et al]. We used this method to determine [CPT] releasedfrom PCPP:SA loaded drug polymers in PBS and [CPT] in three sections ofeach given brain slice group.

+ CH2

O

O

OHCH2

CH2 O

CH2

OH

O

3400

Carboxyl-methyl-polyethylene glycol

+

Carboxyl-methyl-polyethylene glycol-camptothecin

Carboxyl-methyl-polyethylene glycol-di-camptothecin

3400

CH

CHCH

CH

CH

N

CH2N

CH

OCH2

COCH2

O

O

CH3

CH2 O

O

CH2CH2 O

CH2OH

O

3400

CH

CHCH

CH

CH

N

CH2 N

CH

OCH2

COCH2

O

O

CH3

CH2 O

O

CH2CH2 O

CH2

O

CH

CHCH

CH

CH

N

CH2N

CH

OCH2

CO CH2

O

O

CH3

Camptothecin lactone

CH

CH

CH

CH

CH

N

CH2N

CH

O

CH2

C

OHCH2

O

O

CH3

Figure 2. CPT Lactone Stabilized by Conjugation to PEG. In the presence of aqueous solutions, the fifth lactone ringopens and converts to the carboxylate isomer, which generates significant side effects. By conjugating CPT to PEG, anester bond forms that stabilizes the lactone and reduces toxicity. In addition, PEG which is a hydrophilic polymerincreases the solubility and bioavailability of CPT in plasma.

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4. SPHEROIDS

Studies on spheroids or clumps of tumor cells demonstrate that the distributionof proliferating cells, quiescent cells, antigen expression, pH and pO2 gradients,and penetration of growth factors within the spheroid closely parallel those oftumors in vivo. Spheroids offer other advantages with respect to monolayercultures such as the possibility of investigating therapeutically effectivecompounds under strictly controlled conditions in vitro where many of thevariables affecting in vivo studies (clearance, unequal blood supply, host defensemechanisms, etc.) can be minimized [Fracasso G., Colombatti M.].

There are three different ways to grow spheroids: 1. liquid overlay, 2. gyratoryflask, and 3. spinner flask. The liquid overlay technique involves the placementof trypsinized monolayer cells onto agarose coated dishes. Spheroids form in

Figure 3. Tumor Spheroid on Brain Slices Setup. Brain slices were sectioned at 350 mðm and placed onto a moist cultureplate membrane. Spheroids were added to the slices at one end of the brain slice. The polymer was placed in the center (nearimplant) or at the opposite end of the spheroid (far implant) on the brain slice. The half-life of each drug was determined inPBS at pH of 7.4, 37oC, and 75 rpm. One half-life is when 50% CPT is hydrolyzed and released from PEG into solution.

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1-3 days because the tumor cells do not like the agarose and aggregate toreduce contact with such surface [Santini M.T., Rainaldi G.]. This methodwas used to grow spheroids for the rat brain slice experiment.

Spheroids show greater chemotherapeutic resistance than monolayer cells dueto the contact effect. The contact effect consists of: 1. gap junctional ‘reciprocity’or the ability of healthy cells to nourish neighboring sick or deprived cells, 2.presence of cell-shape mediated changes in repair related gene expression,and 3. alterations in chromatin packaging that influence DNA repair. Withthe contact effect, the spheroids show greater intercellular communicationwith enhanced recovery from chemotherapy or damage. This is caused by achange in nuclear shape, change in DNA packaging, more efficient DNA repair,change in cell shape, and change in gene expression of enzymes and cofactorsinvolved in cell repair of spheroids [Olive P.L., Durand R.E.].

The outer spheroid layer consists of well nourished and rapidly dividingcells. In contrast, the inner spheroid layer near the center is made up ofnutrient deprived cells due to limited diffusion. As a result, the inner layerof cells usually exit the cell cycle to G0 or to a non-proliferating state.Chemotherapeutic agents that target DNA synthesis or cell proliferation affectthe outer layer more than the inner layer of non-proliferating cells [OliveP.L., Durand R.E.].

5. CAMPTOTHECIN CONJUGATES IN SPHEROIDS ONBRAIN SLICES

The first hypothesis tested is CPT conjugated to CM-PEG increases the efficacyof CPT because such modification will stabilize the active CPT lactone andincrease the solubility and bioavailability of CPT. The second hypothesis isaltering the linker between CPT and CM-PEG or changing the CM-PEG toDI-NH-PEG or SUCC-PEG will improve the treatment of cancer. There mightbe an ideal half-life or hydrolysis rate of CPT from PEG for maximal treatmentof tumors and/or if specific tumor targeting with specific linker moleculesthat can enhance the treatment of cancer. These two hypotheses are tested on9L and CNS-1 spheroids in rat brain slices (Figure 3). Such measurementswere made by changes in spheroid area and changes in cell migration distancesfrom spheroid mass. We compared 9L and CNS-1 spheroids in the brainslices. The CNS-1 glioma cell line displayed diffuse and infiltrative growthpatterns similar to human gliomas [Kruse C.A. et al]. The CNS-1 cells didindeed migrate more than 9L and were more diffuse appearance, as stated inliterature.

In addition, time delayed drug treatments to mimic controlled drug releasefrom PCPP:SA were studied. The distance of treatment of near or far drug

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implants with respect to spheroid is also considered. The second hypothesisthat states there are differences in the performance of different PEGs or linkersin spheroids was observed. We did see greater reduction in tumor cellmigration distances among DI-NH-PEG-CPT, CM-PEG-GLY-CPT, CM-PEG-GLY-BIO-CPT, and SUCC-PEG-CPT than compared to CM-PEG-CPT. Thebrain slice model enabled rapid screening of many drugs and helped determinethe CPT conjugate with the greatest potential to treat brain cancer.

Although the 3-day delay drug treatment was used to mimic delayed drugrelease from polymer pellets where the polymer had to degrade before releasingdrug, drug release from polymer was not as well defined with no drug releasefor 3 days that was suddenly exposed to drug following those 3 days. However,the 3-day delay experiment did emphasize that prevention and early detectionof tumor growth was crucial in preventing the growth of significant cellmigrations before the drugs could no longer be as useful in reducing migration.Such migrating cells are the seeds for tumor re-growth in the brain. Controlledrelease of CM-PEG-GLY-BIO-CPT near implants were able to overcome themigrating cells with respect to PCPP:SA, demonstrating that continual drugrelease was more effective than bolus dosing with one time exposure to drugdissolved in medium.

6. LIMITATIONS OF DRUG DELIVERY

Drug delivery is most effective when the drug targets the appropriate site atthe correct concentration. Otherwise, there is no guarantee that drug moleculeswill permeate through capillary walls, diffuse through the extracellular space(ECS), traverse the tumor cell membrane, and reach the proper intracellulartarget. Also, the drug might become unstable and may be subject tospontaneous or metabolic elimination during this process. This could happenif the drug enters the vascular system, gets transported to the rest of the body,and is eliminated systemically. As a result, drug concentrations at the targetsite may be low [Fung L.K., Saltzman W.M.].

However, only controlled release systems and infusion provide sustained drugdelivery. The advantage of polymer implants is that they protect unreleaseddrug from degradation and allow extremely high doses of drug to be localizedto a specific site in the brain. Otherwise, drug molecules released into theinterstitial fluid must penetrate some distance into the brain tissue to reachand treat tumor cells. Before these drug molecules reach the target site, theymight be eliminated from the brain interstitium by partitioning into braincapillaries or cells. They could also enter the cerebrospinal fluid or be inactivatedby extracellular enzymes [Mak M. et al]. These reasons justify the need forinterstitial chemotherapy so that there is sustained local drug release at thetumor site.

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7. PRECLINICAL SAFETY OF PCPP: SA

Following clinical trials for glioma patients, regulatory agencies in 22 countriesand the Food and Drug Administration (FDA) approved Gliadel PCPP:SA.PCPP:SA polymer protects the drug from degradation, allows for controlledrelease of drug, achieves log orders higher of drug concentration, and hasminimal systemic toxicity [Brem H., Gabikian P.].

Laurencin et al. administered polyanhydrides subcutaneously in rats for eightweeks. Histological evaluations of 33 organ sites including heart, lung, liver,kidney, and brain were performed. Results from evaluations of bloodchemistry, hematology data, and organ and local implant site analyses,demonstrate that these polyanhydrides possessed excellent in vivobiocompatibility [Laurencin C. et al]. The biocompatibility of a biodegradablepolyanhydride, the copolymer of poly[bis(p-carboxyphenoxy)propane]anhydride and sebacic acid (PCPP:SA) in a 50:50 formulation, was studied inthe rat brain. None of the animals showed behavioral changes or neurologicaldeficits that would suggest toxicity and all of them survived. The polymerswere also tested in the rabbit cornea bioassay and did not induce aninflammatory response [Brem H. et al].

8. KINETICS OF PCPP: SA

Drug release from PCPP:SA is independent of initial PCPP:SA molecularweight. Instead, drug release is affected by a combination of drug diffusionand PCPP:SA erosion [Dang W. et al]. Wu et al. found that degradation ofPCPP:SA is slower in vivo than in vitro. During the initial two days of in vivoerosion, PCPP:SA with drug displayed more erosion than PCPP:SA with nodrug, but the overall long term degradation was similar to PCPP:SA with nodrug. The degradation time in vivo for 1 mm thick PCPP:SA (20:80) pelletswas 6-8 weeks [Wu M.P. et al].

Water availability and pH, but not rotational speed, affect PCPP:SA degradationrates. Lower water availability (more saturated PCPP:SA monomer buffer solutionfrom 1 mg/ml to 20 mg/ml) lowers the driving force for dissolution, which mightbe occurring in the brain. Lower pH from 7.4, 6.4, 4.0, to 2.0 significantly reducesthe amount of erosion for both CPP and SA. Rotational speeds of 60 rpm and120 rpm result in about the same degradation rate [Wu M.P. et al].

Increasing the ratio of carboxyphenoxypropane (CPP) to sebacic acid (SA) inthe polymer increases its hydrolytic stability, thus prolonging its half-life invivo, and extending the period of drug release. A second approach is to increasethe dose of drug loaded into the polymer. At the highest dose tested, Sipos etal. found that the 50:50 polymer released drug 2.5 times as long in vitro as the

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20:80 polymer. The 20:80 and 50:50 polymers were equally effective in therat intracranial 9L glioma model. The 20% drug loaded 20:80 polymer achievedthe best balance of toxicity and antitumor efficacy, yielding a 75% long termsurvival rate. A dose escalation strategy for improving drug controlled releasepolymers is more effective than adjusting the ratio of CPP to SA to prolongdrug release [Sipos E.P. et al].

9. GLIOMA MIGRATION

Matrix metalloproteinases (MMPs) play important roles in glioblastoma cellinvasion by degrading almost all known extracellular matrix components[Chintala S.K. et al]. Gliomas infiltrate so diffusely that they cannot be curedby resection alone. The more extensive the resection, the greater the lifeexpectancy. The measurements of growth and diffusion predict survival ratesbetter than the current histological estimates of the type and grade of gliomas[Woodward D.E. et al]. Besides measuring changes in spheroid areas in brainslices, the measurement of cell migration distances was an important factor ingauging the efficacy of CPT and various CPT conjugates.

CH CH

CC

CH CH

CO

O

C

CH2

O

CH2CH2 CH2

CH

C

CH

CH

C

CHO

CH2CH2

CH2O

CO

O CH2 CH2

CH2CH2

C

O

HH

+OH2

CH CH

CC

CH CH

C

OCH

C

CH

CH

C

CHO

CH2CH2

CH2O

CO

OH OH

OH C

CH2

O

CH2

CH2 CH2

CH2 CH2

CH2 CH2

C

O

H

+

Bis(p-carboxyphenoxy)propane Sebacic acid20 80

Bis(p-carboxyphenoxy)propane

Sebacic acid

Figure 4. Chemistry of PCPP:SA Hydrolysis. PCPP:SA is a compatible biodegradable polymer that may be used to loaddrug for controlled drug release. When the polymer erodes and degrades, the drug is released locally to the surroundingarea for treatment.

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10. RECOMMENDATIONS

Here we suggest two possible ways to improve the treatment of cancer. Thefirst method is to chemically modify CPT to create better analogs. In thebrain slice experiment, CM-PEG-GLY-BIO-CPT was able to control CNS-1spheroid areas but not migrations in 3-day delay. Despite the fact that CM-PEG-GLY-BIO-CPT implanted near the CNS-1 spheroid was able to controlmigrations, other methods such as immunotherapy could help enhance thetargeting of these outlying invasive tumor cells.

10.1 Chemical Modification of Camptothecin Structure

The topoisomerase I inhibitory activity of CPT is stereospecific with thenaturally occurring (S)-isomer being many times more potent than the (R)-isomer. In general, substitutions at C7, C9, and C10 tend to increasetopoisomerase I inhibition and sometimes increase water solubility. In contrast,substitutions at C12 decrease antitumor activity. The addition of certain ringstructures between C7 and C11 also increase CPT activity.

8

13

C9

CH12

C10

C11

C7

6

N14

CH25

N

15

43

CH16 17

O

CH22

C18

OHCH219 1 O

O

CH320

R3

R4

R2 R1

Hydroxy/methoxyincreases activity;bulky substituentsdecrease activity

(M)ethylenedioxymoiety increases

activity

Aza substitutionsincrease activity Substitutions

decrease activity

R-isomer is inactive;intact lactone required

Substitutionsincrease activity

Alkylationimproves activity

7-membered ringstabilizes lactone

Oxygenrequired

Pyridone ring isessential for activity

Certain groupsimprove activity

A B C

D

E

Figure 5. Modulation of Camptothecin in the Treatment of Cancer. There are many ways to increase the efficacy of CPT bychemically altering the structure of CPT to create analogs with better potential in treating cancer. The original author ofthis figure comes Diederik F.S. Keherer.

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The equilibrium between the lactone and carboxylate form is dependent onboth pH and the presence of serum binding proteins such as human serumalbumin (HSA). The lactone form can be favored by introducing bulky groupsto R1 and R2. The resulting steric hindrance will make it more difficult forHSA to bind to the carboxylate forms, which will drive the equilibrium to thelactone form [Keher D.F.S.]. Such chemical modifications to create betterCPT analogs can then be conjugated to CM-PEG with a targeting molecule forfuture drug testing in animal tumors.

As new therapies significantly improve the treatment of brain tumor mass,the outlying or infiltrating tumor cells become more of an issue because theyare the sources of tumor recurrence. These disseminated tumor cells can betargeted by leukocytes through cell mediated immunotherapy [Lampson L.A.et al]. Immunotargeting of biotin or biotinylated compounds to tumors canbe achieved by pre-targeting the tumor with specific biotinylated monoclonalantibodies (MoAbs). Avidin is added to remove excess circulating MoAbswhile streptavidin is added to target tumor tissue. Finally, the biotinylateddrug can be added for specific tumor targeting [Caliceti P. et al].

10.2 Immunotherapy for Targeting Outlying and Infiltrating Tumor Cells

Potent immune responses against malignant brain tumors can be elicited byparacrine intracranial immunotherapy with interleukin-2 (IL-2). Thecombination of paracrine immunotherapy with non-replicating geneticallyengineered tumor cells produced IL-2 and local chemotherapy bybiodegradable polymers, which prolonged survival in a synergistic manner.Rodents receiving IL-2 transduced cells and polymers containing 10% 1,3-bis(2-chloroethyl)-1-nitrosourea (BCNU) had significantly improved survivalcompared to rodents receiving IL-2 transduced cells or 10% BCNU alone[Sampath P. et al].

It will be interesting to test the effects of CM-PEG-GLY-BIO-CPT on CNS-1spheroids in brain slices in combination with IL-2 therapy to target outlyinginvasive and migrating cells. While CM-PEG-GLY-BIO-CPT successfully treatsthe tumor mass, IL-2 will help destroy migrating cells with 3-day delay orcontrolled drug release from PCPP:SA treatment. If such treatment issuccessful, this may be significant towards the cure for cancer.

11. CONCLUSIONS

The main objective of this review paper is to demonstrate greater efficacy ofCPT by conjugation to CM-PEG, which would stabilize the lactone form.Greater efficacy of CPT conjugate was seen where CM-PEG-CPT, CM-PEG-GLY-CPT, and CM-PEG-SAR-CPT were significantly better than CPT inreducing 9L glioma cell migration of spheroids and spheroid areas.

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The CPT conjugates were chemically modified with significantly shorter andlonger half-lives to test if the rate of release of CPT was the factor affecting thechemotherapy of tumor spheroids on brain slices. In order to accomplish thistask, different PEGs were used such as DI-NH-PEG and SUCC-PEG to alterthe hydrolysis rate of CPT release. Another idea was to include a targetingmolecule such as biotin since biotin targeted the SMVT receptors of tumorcells. The biotin incorporated in CM-PEG-GLY-BIO-CPT could be comparedto CM-PEG-GLY-CPT with no targeting molecule.

Many drugs were efficiently and quickly screened in spheroids grown inneonatal rat brain slices. CM-PEG-GLY-BIO-CPT worked better than CM-PEG-GLY-CPT and CM-PEG-CPT, demonstrating that it was not the half-lifeaffecting the efficacy of the CPT conjugate. The key idea was specific drugtargeting for improved treatment of cancer. In the 3-day delay, only CNS-1spheroid area growth could be controlled well, but the cells continued to migratefrom the tumor mass. The problem was remedied by using PCPP:SA forcontrolled release of CM-PEG-GLY-BIO-CPT to reduce migration whenimplanted near the spheroid.

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References

[1] Brem H., Gabikian P. Biodegradable polymer implants to treat brain tumors.Journal of Controlled Release, 74: 63-67, 2001.

[2] Brem H., Kader A., Epstein J.I., Tamargo R.J., Domb A., Langer R., Leong K.W.Biocompatibility of a Biodegradable Controlled-Release Polymer in the RabbitBrain. Selective Cancer Therapeutics, 5(2): 55-65, 1989.

[3] Caliceti P., Chinol M., Roldo M., Veronese F.M., Semenzato A., Salmaso S.,Paganelli G. Poly(ethylene glycol)-avidin bioconjugates: suitable candidatesfor tumor pretargeting. Journal of Controlled Release, 83: 97-108, 2002.

[4] Chintala S.K., Tonn J.C., Rao J.S. Matrix Metalloproteinases And TheirBiological Function In Human Gliomas. International Journal ofDevelopmental Science, 17(5-6): 495-502, 1999.

[5] Conover C.D., Greenwald R.B., Pendri A., Gilbert C.W., Shum K.L.Camptothecin delivery systems: enhanced efficacy and tumor accumulation ofcamptothecin following its conjugation to polyethylene glycol via a glycinelinker. Cancer Chemotherapy and Pharmacology, 42: 407-414, 1998.

[6] Conover C.D., Greenwald R.B., Pendri A., Shum K.L. Camptothecin deliverysystems: the utility of amino acid spacers for the conjugation of camptothecinwith polyethylene glycol to create prodrugs. Anti-Cancer Drug Design, 14:499-506, 1999.

[7] Dang W., Daviau T., Ying P., Zhao Y., Nowotnik D., Clow C.S., Tyler B., Brem H.Effects of GLIADEL wafer initial molecular weight on the erosion of wafer andrelease of BCNU. Journal of Controlled Release, 42: 83-92, 1996.

[8] Fracasso G., Colombatti M. Effect of therapeutic macromolecules in spheroids.Critical Reviews in Oncology/Hematology, 36: 159-178, 2000.

[9] Fung L.K., Saltzman W.M. Polymeric implants for cancer chemotherapy.Advanced Drug Delivery Reviews, 26: 209-230, 1997.

[10] Grieg N.H. Optimizing drug delivery to brain tumors. Cancer TreatmentReviews, 14: 1-28, 1987.

[11] Hart L.G., Call J.B., Oliverio V.T. A Fluorimetric Method for Determination ofCamptothecin in Plasma and Urine. Cancer Chemotherapy Reports Part I, 53:211-214, 1969.

[12] Keher D.F.S, Soepenberg O., Loos W.J., Verweij J., Sparreboom A. Modulation ofcamptothecin analogs in the treatment of cancer: a review. Anti-CancerDrugs, 12: 89-105, 2001.

[13] Kruse C.A., Molleston M.C., Parks E.P., Schiltz P.M., Kleinschmidt-DeMastersB.K., Hickey W.F. A rat glioma model, CNS-1, with invasive characteristicssimilar to those of human gliomas: A comparison to 9L gliosarcoma. Journal ofNeuro-Oncology, 22: 191-200, 1994.

[14] Lampson L.A., Wen P., Roman V.A., Morris J.H. Sarid J.A. Disseminating TumorCells and Their Interactions with Leukocytes Visualized in the Brain. CancerResearch, 52: 1018-1025, 1992.

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[15] Laurencin C., Domb A., Morris C., Brown V., Chasin M., McConnell R., LangeN., Langer R. Poly(anhydride) administration in high doses in vivo: Studies ofbiocompatibility and toxicology. Journal of Biomedical Materials Research, 24:1463-1481, 1990.

[16] Lund-Johansen M., Bjerkvig R., Rucklidge G.J. Tumor Spheroids FromMonolayer Cultures. In: Bjerkvig R, ed. Spheroid Culture in Cancer Research.Boca Raton, CRC Press. 80, 1992.

[17] Mak M., Fung L., Strasser J.F., Saltzman W.M. Distribution of drugs followingcontrolled delivery to the brain interstitium. Journal of Neuro-Oncology, 26:91-102, 1995.

[18] Mi Z., Burke T.G. Differential Interactions of Camptothecin Lactone andCarboxylate Forms with Human Blood Components. Biochemistry, 33: 10325-10336, 1994.

[19] Mi Z., Burke T.G. Marked Interspecies Variations Concerning the Interactionsof Camptothecin with Serum Albumins: A Frequency-Domain FluorescenceSpectroscopic Study. Biochemistry, 33: 12540-12545, 1994.

[20] Olive P.L., Durand R.E. Drug and radiation resistance in spheroids: cell contactand kinetics. Cancer and Metastasis Reviews, 13: 121-138, 1994.

[21] Sampath P., Hanes J., DiMeco F., Tyler B.M., Brat D., Pardoll D.M., Brem H.Paracrine Immunotherapy with Interleukin-2 and Local Chemotherapy IsSynergistic in the Treatment of Experimental Brain Tumors. Cancer Research,59: 2107-2114, 1999.

[22] Santini M.T., Rainaldi G. Three-Dimensional Spheroid Model in TumorBiology. Pathobiology. 67:148-157, 1999.

[23] Sipos E.P., Tyler B., Piantadosi S., Burger P.C., Brem H. Optimizing interstitialdelivery of BCNU from controlled release polymers for the treatment of braintumors. Cancer Chemotherapy and Pharmacology, 39: 383-389, 1997.

[24] Takimoto C.H., Arbuck S.G. The Camptothecins; in Chabner B.A., Longo D.L.(eds): Cancer Chemotherapy and Biotherapy. Philadelphia, PA, Lippincott-Raven Publishers, 463-484, 1996.

[25] Woodward D.E., Cook J., Tracqui P., Cruywagen G.C., Murray J.D., Alvord E.C.A mathematical model of glioma growth: the effect of extent of surgicalresection. Cell Proliferation, 29: 269-288, 1996.

[26] Wu M.P., Tamada J.A., Brem H., Langer R. In vivo versus in vitro degradation ofcontrolled release polymers for intracranial surgical therapy. Journal ofBiomedical Materials Research, 28: 387-395, 1994.

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4In-band OSNR Monitoring for SynchronousTraffic Using Beating-noise Measurement ofHeader Signals

X. Tian, Y. Su, L. Yi, L. Leng, W. Hu, and P. Hu*

ABSTRACT

We demonstrate a new in-band optical signal-to-noise ratio (OSNR) monitoring scheme suitable for synchronoustraffic such as SONET traffic and scheduled optical packets. By using beating-noise measurement of gatedheaders with fixed format, the noise spectrum can be resolved by a RF spectrum analyzer. The scheme is inprinciple robust to any polarization effects. We experimentally verify the effectiveness of the scheme in a 4x10GWDM SONET link, and a two-packet interleaved system.

Index Terms—Optical performance monitoring, optical signal-to-noise-ratio (OSNR), spectral analysis, polarizationscattering

1. INTRODUCTION

IN-band optical signal-to-noise ratio (OSNR) monitoring is an important issue indynamic wavelength-routed networks. Previously a number of polarization-assisted OSNR monitoring schemes have been proposed, such as polarization-nulling method [1-3] and degree of polarization (DOP) correlation approach [4].These schemes are based on the assumptions that the optical signal has well-defined polarization and that the amplified spontaneous emission (ASE) noisesare fully randomly polarized. However, these assumptions are not always valid in

* X. Tian, Y. Su, and W. Hu are with State Key Laboratory of Advanced Optical CommunicationSystems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China.L. Leng is with New York City College of Technology, Brooklyn, NY 11201, USA.

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practice, especially in the presence of inter-channel cross-phase modulation(XPM) induced polarization scattering effect [1, 5]. Polarization scattering refersto the bit-level randomization of the signal polarization originating from thenonlinear polarization rotation induced by adjacent channels. In [5], large OSNRmonitoring errors were observed when the signals experienced polarizationscattering in a wavelength-division-multiplexed (WDM) system.

Beating-noise measurement method [6-8] is an alternative approach to in-band OSNR monitoring through the measurement of the signal-ASE beatingnoise power density after the photo-detection to reconstruct the OSNR. Afeature of this scheme is that the O/E conversion process is insensitive topolarization effects such as polarization scattering and polarization modedispersion (PMD). However, the main issue of this method is how todifferentiate the signal-ASE beating noise from the signal in the RF spectrumdomain. The previously proposed schemes either are not applicable for on-offkeying (OOK) signals with pseudo random bit sequence (PRBS) lengths longerthan 215-1 or truly random data [6], whose spectral tones are too close to resolve,

Figure.1 (a) Frame structure of a synchronous traffic (b) spectrum of the synchronous traffic (c) gated synchronoustraffic with only fixed headers left (d) spectrum of the fixed headers

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or are limited to certain modulation formats such as differential phase shiftkeying (DPSK) [7], or signals with symmetric spectra [8] but would fail forvestigial side band (VSB) or single-side band (SSB) signals.

Figure.2. Experimental setup for the SONET system. PPG: Pulse Pattern Generator, MZM: Mach-Zehnder Modulator, SMF:Single Mode Fiber, OSA: Optical Spectrum Analyzer, VOA: Variable Optical attenuator.

Fig.3. RF spectrum of the gated signal (a) RES=3 MHz (b) Central frequency=300 MHz, RES=1 kHz. Inset is thegated optical pulses

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In this paper, we propose and demonstrate a novel OSNR monitoring techniqueusing gated-signal beating-noise measurement for synchronous traffic such asSONET traffic or scheduled optical packets. This was motivated by the fact thatrepetitive fixed patterns exist in the headers of synchronous traffic, as illustratedin Fig.1 (a). Due to the periodic nature of the headers, discrete spectral tones canbe seen in the spectrum. For the payload with a PRBS pattern length of 223-1,the spacing between adjacent spectral tones is 1.2 kHz for a 10-Gb/s non return-to-zero (NRZ) signal (Dðf=1/ (2n-1) Tb), which cannot be resolved by the spectrumanalyzer. Therefore the beating noise is ‘buried’ by the RF spectrum of the payload(Fig. 1 (b)). For truly random data, there are even no discrete spectral tones. Inorder to reveal the noise spectrum, the payload must be suppressed in the spectraldomain. This can be achieved by gating the synchronous data stream so thatonly the repetitive short patterns in the headers are detected and their discretetones in the spectral domain can be distinguished regardless of the payloadpattern length, as shown in Fig. 1 (c) and Fig.1 (d). The beating noise betweenthe spectral tones can be monitored and used for OSNR monitoring.

We experimentally demonstrate the proposed OSNR monitoring technique fortwo possible application scenarios: SONET for point-to-point connections, andoptical packet switching in scheduled networks. We also study its performance incombating polarization effects, in particular, the XPM induced polarizationscattering in a 4x10G WDM system. Compared with polarization-nulling method,the proposed scheme significantly reduces monitoring errors due to the fact thatO/E conversion is independent of the signal polarization; the monitoring setup issimple and does not require high-speed receiver at the line rate; it is independentof the signal format, and is in principle also robust to PMD.

2. EXPERIMENT FOR SONET TRAFFIC

Fig.2 shows the experimental setup for monitoring SONET traffic, which is obtainedfrom an Anritsu MX176401A SONET pattern editor. Four WDM signals from1558.16 nm to 1560.56 nm, spaced by 100 GHz, are combined. The data patternsof the neighboring channels are inversed. The WDM signals are amplified andlaunched into a 50-km single mode fiber (SMF). The channel power is adjustedto 14 dBm so significant XPM induced polarization scattering effect occurs throughtransmission. At the receiving end, an ASE source is added to the signal to changethe OSNR levels. A small portion of the multiplexed signal is tapped off and sentto an optical spectrum analyzer (OSA) to monitor the out-of-band OSNR, whilethe other part is injected into an arrayed waveguide grating (AWG) filter. Thesignal centered at 1559.76 nm is filtered and sent to the in-band OSNR monitoringmodule. The OSNR monitoring setup consists of an intensity modulator to gatethe SONET headers, a power meter to measure the total optical power, and aphoto-detector followed by a RF spectrum analyzer to measure the spectralcomponents. The data generated by the SONET pattern editor has a frame lengthof 13.8 mðs with a 690-ns header in the form of “A1...A1A1A2A2…A2”, where A1

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is 0xF6 or “11110110”, and A2 is 0x28 or “00101000”, as shown in the inset ofFig.2. The minimum frequency spacing between the spectral tones of the gatedsignal is 72.4 kHz, corresponding to the 13.8-mðs frame period. After O/Econversion, the beating-noise power density can be described by [6, 9]:

22 // OSNRBOSNRAPN sigbeat (1)

where A, B are coefficients relating to the characteristics of the photodiodes,the RF amplifier gain, and the filter properties. A and B can be calibrated inadvance. The measured total power is given by:

OSNRPP sigtotal /11 (2)

Figure.4 (a) Measured beating noise power density (b) OSNRs and monitoring errors by RF spectral analysisat different signal powers. (c) OSNRs and monitoring errors with the polarization-nulling method.

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Note that the OSNR in these equations is calculated using the bandwidth ofthe AWG filter, and the OSNR can be obtained from Nbeat and Ptotal.

Fig.3 (a) shows the RF spectrum of the gated signal at a resolution bandwidth(RES) of 3 MHz. The frequency tone centered at 1.25 GHz corresponds to therepetition of A1 or A2 with a period of 800 ps. Fig.3 (b) is the zoom-in spectrumat a center frequency of 300 MHz and a RES of 1 kHz, and the inset is thetime-domain waveform of the gated optical signal. Between the spectral tones,the noise floor is clearly revealed and can be used for OSNR monitoring.

Fig.4 provides the OSNR measurement results. The measured beating-noisepower density (4a), and the resulting OSNR values (4b), are plotted versus theOSNRs measured by the OSA. In the OSNR range of 10 - 27 dB, the maximalmonitoring error of the proposed method is less than 0.8 dB. For higher OSNRvalues, the errors are mainly caused by the limited extinction ratio of themodulator, which leads to the payload power leakage and results inoverestimation of the beating noise. For comparison purpose, we alsoperformed an experiment based on the polarization nulling method using thesetup in Fig. 4c and show the results. When the OSNR changes from 10 to 27dB, the monitoring errors range from 2 to 7.5 dB, which are attributed to theXPM induced polarization scattering effect [5].

3. OSNR MONITORING FOR SYNCHRONOUS PACKET-SWITCHED TRAFFIC

Our proposed OSNR monitoring method based on gated-signal beating-noisemeasurement can also be used for synchronous packet-switched traffic inscheduled optical networks, due to the fact that most packets start with headersemploying fixed pattern for synchronization purpose. Here we perform anexperiment using 10-Gb/s packets to show its effectiveness. Data is obtainedfrom a pulse pattern generator set in ‘zero substitute’ mode with a period of

Fig.5 (a) Combined traffic of packet 1 and packet 2 (b) OSNR monitoring setup using gated signal RF spectral analysis.Inset shows the gated pulses.

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204.8 ns, or 2048 bits. The duration of the non-zero part, is 94.8 ns. The signal isthen split and interleaved in time with different amplitudes using couplers, anattenuator, and a fiber delay line. They are then combined with ASE noise sourceand pass through the AWG. The waveform of the multiplexed packets is shownin Fig. 5 (a). The optical power of packet 1 is set to be 2.5-dB higher than that ofpacket 2, resulting in higher OSNR. In the monitoring module, the gatingfunction is performed for packet 1 and packet 2, respectively, by shifting thegating signal position. The period of the gating pulse is set to 6.4 ns, as shown inFig.5 (b). After the optical gating, only the fixed, repetitive headers are sent intothe OSNR monitoring module for beating-noise measurement.

Fig.6 shows the beating noise and OSNR monitoring results for packet 1 andpacket 2, respectively. It should be noted that the OSNRs measured by theOSA are the average values for packets with different powers, thereforecorrections have been made on the x-axis, respectively, to ensure faircomparisons. It can be seen that the maximal OSNR errors measured by ourmethod are less than 0.6 dB for the two packets.

4. SUMMARY

We have proposed a novel OSNR monitoring method based on gated-signalbeating-noise measurement for synchronous traffic, such as point-to-pointSONET traffic and scheduled optical packets with repetitive headers. Weperformed experiments to show the effectiveness of the method in the twoapplication scenarios. The scheme is simple and effective, independent of themodulation formats, and also insensitive to the polarization effects. We haveexperimentally verified that it is robust to XMP induced polarization scatteringin a 4x10G WDM system.

Fig.6. (a) Measured beating noise power density for packet 1 and packet 2 (b) monitored OSNRs and monitorin errors byRF spectral analysis for different packets

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References

[1] J. H. Lee, D. K. Jung, C. H. Kim, and Y. C. Chung, “OSNR monitoring techniqueusing polarization-nulling method,” IEEE Photon. Technol. Lett., vol. 13, pp.88-90, Jan, 2001.

[2] M. H. Cheung, L. K. Chen, and C. K. Chan, “PMD-insensitive OSNR monitoringbased on polarization-nulling with off-center narrow-band filtering,” IEEEPhoton. Technol. Lett., vol. 16, pp.2562-2564, Nov. 2004.

[3] Xiangqing Tian, Yikai Su, Weisheng Hu, Lufeng Leng, Peigang Hu, Hao He, YiDong and Lilin Yi, “Precise In-Band OSNR and Spectrum Monitoring UsingHigh-Resolution Swept Coherent Detection”, IEEE Photon. Technol. Lett., vol. 18,pp.145-147, Jan, 2006.

[4] M. Sköld, B. E. Olsson, H. Sunnerud, and M. Karlsson, “PMD-insensitive DOP-based OSNR Monitoring by Spectral SOP Measurements”, in Tech. Dig.OFC’2005, OTHh3.

[5] C. Xie and D. C. Kilper, “Influence of polarization scattering on polarization-assisted OSNR monitoring in dense WDM systems with NZ-DSF and Ramanamplification,” in Tech. Dig. OFC’2005, JWA40.

[6] S. K. Shin, K. J. Park, and Y. C. Chung, “A Novel Optical Signal-to-Noise RatioMonitoring Technique for WDIM Networks”, in Tech. Dig. OFC’2000, WK6.

[7] C. Dorrer and X. Liu, “Noise Monitoring of Optical Signals Using RF SpectrumAnalysis and Its Application to Phase-Shift-Keyed Signals”, IEEE Photon.Technol. Lett., vol. 16, pp.1781-1783, July, 2004.

[8] Wei Chen, Rodney S. Tucker, Xingwen Yi, William Shieh, and Jamie S. Evans,“Optical Signal-to-Noise Ratio Monitoring Using Uncorrelated Beat Noise”,IEEE Photon. Technol. Lett., vol. 17, pp.1781-1783, Nov, 2005.

[9] N. A. Olsson, “Lightwave systems with Optical Amplifiers”, IEEE/OSA J.Lightwave Technol., vol. 7, pp.1071-1082, July, 1989

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5The Solar Collector: A Method of ProtectingEarth from Threatening Asteroids andComets

Gregory L. Matloff *

1. INTRODUCTION

The Threat to Earth

In the mid-2020’s, around the time that NASA’s new interplanetary capabilitywill become operational, a Near-Earth asteroid called Apophis will approachthe Earth within about 30,000 kilometers. Although too small to cause a massextinction (with a diameter of about 300 meters), this object, if it ever strikesthe Earth, would impact with an energy equivalent to that of a 10-20 megatonhydrogen bomb. If it struck a major city, tens of millions would die.

Apophis will not strike the Earth on this pass, but if it is suitably disrupted byterrestrial gravitational tides, there could be problems six years after this passwhen this Near Earth Object (NEO) returns to Earth’s vicinity.

Responding to public pressure, the NASA Marshall Space Flight Center (MSFC)conducted a study in early 2007 of how humanity’s new interplanetary capabilitiescould reduce the danger of an impact by a NEO of asteroidal (rocky or stony) orcometary (icy) origin. I was one of about 20 participants in this effort. The initialresults of the study are published as Ref. 1 and are to be incorporated in aNASA report.

* Assistant Professor, Dept. of Physics, NYCCT, CUNY

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Threat Mitigation Strategy

The basic MSFC strategy of NEO-impact mitigation is to first launch a numberof ‘Observer” payloads aboard an Aries 1 rocket. With an Earth-escape massof the order of 10,000 kilograms, these observer probes could orbit, flyby,land upon, or penetrate the surface of an offending NEO. Characteristics ofthe body including composition, density, and structure would then bedetermined.

After this initial probe, a larger Aries 5 rocket (with an Earth-escape mass ofabout 100,000 kilograms would be launched towards the Earth-threateningNEO. One or more Interceptor payloads would be directed towards the NEO.

Several interceptor options are available. Impact warning time and NEOcharacteristics are the main technical factors influencing interceptor design.

If the threatening NEO is found to be rocky or metallic and /or if the impact-warning time is small, a large nuclear explosive might be the most effectiveapproach to convert an Earth-impact into a near miss. But nukes have obvioussocio-political drawbacks.

An alternative to “nuclear devices” is kinetic deflection. The Earth (and anyNEO) orbits the Sun at about 30 kilometers per second. If an advanced spacedrive such as the solar-electric rocket or solar sail were utilized to place themassive interceptor in a retrograde solar orbit, it could impact the NEO at 60kilometers per second. At such a high relative velocity, some models indicatea significant trajectory deflection. But some classes of NEOs might insteadfragment or “calve,” with each portion targeting Earth. Aim is also critical atsuch high relative velocities.

Solar-Collector Application to NEO Deflection

Because of my experience with solar-sail research most of my contribution tothe MSFC NEO-deflection study centered around the Solar Collector (SC).First proposed by Melosh et al in 1996 [2], the SC is a solar-sail derivative inwhich a beam of concentrated sunlight is directed upon the offending NEO.As the NEO rotates beneath the sunbeam, a swath of NEO soil or regolith isenergized by the concentrated solar energy.

For NEO classes with sandy or soil-like surface layers, a jet of heated materialcould be ejected from the NEO at a velocity of about 1 kilometer per second.By Newton’s Third Law (action = reaction), this jet of material could cause aNEO trajectory deflection. If the SC could be maintained on-station a fewhundred meters from the NEO for a year or more, even solar collectors assmall as 100-meters could readily cause an Earth-threatening NEO tocomfortably miss our planet.

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I noticed that the model utilized by Melosh et al {2} assumed a 1-kilometer/second jet velocity. Further research, included in a manuscript I submitted toa peer-reviewed journal after clearing the NASA ITAR review process, revealedthat a significant parameter in determining SC-excited NEO-jet velocity is theelectromagnetic penetration depth of the NEO surface layers [3]. Thepenetration depth is the depth at which a pulse of concentrated sunlight willbe 99% attenuated by the NEO surface material.

For optimum performance, the penetration depth is about 100 microns.Happily, experiments cited in Ref. 3 reveal that many terrestrial soils havepenetration depths approximating 100 microns

2. CONCLUSIONS

Potential and Future Research Possibilities.

For NEOs of cometary origin or for rocky asteroids coated in layers of dust,the SC offers a viable method of Earth-defense if the impact warning-time is 1year or more. But there are a number of developmental issues. Can the SC bemaintained on-station close to a rotating, irregular NEO? Will the thin-filmreflective surface of the SC degrade significantly during its year-long exposureto the space environment? Will certain NEOs possess orbital dust clouds thatcould render an SC useless?

If these issues are solved after further investigation, some small NEOs couldbe maneuvered by the SC from solar orbits to eccentric Earth-centered orbitsand mined for their materials. As we discuss in Ref. 4, such a resource base inEarth-Moon space could speed the eventual development of an off-planethuman civilization.

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References

[1] R. B. Adams, J. W. Campbell, R. Hopkins, S. Smith, W. Arnold, M. Baysinger, T.Crane, P. Capizzo, S. Sutherlin, J. Dankovich, G. Woodcock, G. Edlin, J. Rushing,L. Fabisiniki, D. Jones, S. McKamey, S. Thomas, C. Maccone, G. Matloff, and J.Remo, ‘Continuing efforts at MSFC to Develop Mitigation Technologies forNear Earth Objects,”

Presented at the AIAA/Aerospace Corporation 2007 Planetary DefenseConference, George Washington University, Washington,

D.C., March 5-8, 2007.

[2] H. J. Melosh, I. V. Nemchinov, and Yu. I. Zetzer, ‘Non-nuclear Strategies forDeflecting Comets and Asteroids, in Hazards due to Comets and Asteroids, T.Gehrels ed., University of Arizona Press, Tuscon, AZ (1994), 1111-1132.

[3] G. L. Matloff, “The Solar Collector and Near-Earth Object Deflection,”submitted to Acta Astronautica (2007).

[4] G. L. Matloff, L. Johnson, and C Bangs, Living Off the Land in Space, Springer-Copernicus, NY (2007).

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6Capitalism’s Dialectic of Scarcity: A ProjectReport

Costas Panayotakis (Social Science)

Two attitudes dominate scholars’ reaction to the dramatic, and often tragic,developments of the twentieth century. The first attitude is encapsulated byFrancis Fukuyama’s proclamation of the end of history. Reacting to the rise andfall of Soviet-style communism, Fukuyama (1992) argues that history has cometo an end in the sense that the combination of liberal democracy and free marketcapitalism has finally triumphed as the most effective and desirable vehicle forthe organization of human affairs. This is a view that is in line with the belief inprogress that has characterized Western societies since at least the Enlightenment.

The second attitude is the mirror image of Fukuyama’s view. Rather than viewingthe twentieth century as the culmination of humanity’s centuries-long pursuitof progress, post-modern scholars tend to emphasize all the different ways inwhich the twentieth century turned out to be an unmitigated disaster. Theythen conclude that traditional ideas of human progress are bankrupt anddangerous, since they have often been used to support various forms of socialoppression.1

My own work is motivated by the conviction that a third alternative to thesetwo viewpoints is both possible and necessary. In my view, giving up on theidea of progress is problematic because it amounts to giving up on the potentialfor human liberation that modern technology generates. On the other hand,viewing the world today as the culmination of this centuries-long quest forprogress obscures the great irrationalities, injustices and problems generatedby contemporary capitalist societies. Soviet communism’s failure

1 For an influential example of the post-modern attitude and its rejection of the ‘grand narrative’ ofprogress, see Lyotard (1984).

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notwithstanding, the challenge facing humanity is the one identified by Marxover a hundred fifty years ago, namely, how to rearrange society so as to ensurethat modern technological advances serve human needs and enrich humanlife rather than turning into means of exploitation and social domination.

Technological developments have long been a reference point for interpretationsof modern society in terms of progress. These interpretations, moreover, arenot unique to intellectuals, since they have been operationalized by politiciansas policies aimed at securing economic growth. This is where the question ofscarcity becomes important. The optimism animating Western societies sincethe Industrial Revolution is inseparable from a tacit assumption thattechnological development and economic growth were likely to alleviate thematerial scarcity responsible for war, poverty, crime and the various social illsthat continue to plague our societies to this day.

The fact that these ills persist proves, of course, the naivete of optimistic theoriesof progress from the Enlightenment to Fukuyama. Given the unprecedentedlevels of technological development and economic growth that the world hasexperienced in recent decades and centuries, it is remarkable how full ourworld still is with scarcity-related problems. In fact, the way we have addressedthese problems ends up compounding them, as the connection betweencompulsive economic growth and environmental destruction makes clear.Thus, although addressing material scarcity is indeed as essential as optimistictheories of progress have long assumed, the way to do so clearly has to bereconsidered. This, in short, is the purpose of my research.

I have been rethinking the relationship between capitalism and scarcity througha critical evaluation of existing theoretical approaches to this question. Thedominant approach is that of neoclassical economics, which basically arguesthat free-market, competitive economies represent the most efficient adaptationto and alleviation of material scarcity. The problem with neoclassical economics,however, is that it fails to differentiate between the market mechanism, on theone hand, and capitalist social relations, on the other. Because of this failure itobscures the irrationalities of modern capitalist societies, as well as their inabilityto translate technological advances into genuine human progress.

The most important critique of capitalist society has historically been providedby Marxist theory. One of the problems with traditional Marxist theory,however, is that it did not differentiate itself sufficiently from the imaginary ofgrowth. Instead of locating the irrationality of capitalist society in its pursuitof never-ending but futile growth, traditional Marxism expected that capitalismwould collapse because its ability to increase the productive potential of societywould eventually be exhausted.

There is finally, what I call the constructionist approach to the question ofscarcity. In this view, material scarcity is as much a function of the level ofmaterial needs as it is a function of a society’s productive potential. Thus,

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Marshall Sahlins (1972) argues that hunters and gatherers were the firstaffluent society, because they were able to meet their limited material needsby exerting much less effort than has been common in technologically moreadvanced societies.

The constructionist approach is right to draw our attention to theimportance of consumption. At the same time, Sahlins’ own analysisundercuts both his claim that hunters and gatherers were indeed able tomeet all their material needs and his conclusion that the conquest of scarcitydoes not pressupose the attainment of a minimum level of technologicaldevelopment. Thus, for example, Sahlins points out that infanticide andsenilicide was common in hunting and gathering societies because of thechallenges implicit in these societies’ nomadic way of life. This way of lifemade it hard for those unable to carry themselves to follow their group,thus condemning them to death. What this means, however, is that thehunting and gathering mode of subsistence gave rise to needs fortransportation that it could not satisfy, thus contradicting Sahlins’ claimthat hunting and gathering societies could, even in the absence of advancedtechnology, easily provide for the needs of their members.

In my own work, I have also focused on consumption as a locus of capitalistsociety’s irrationalities and contradictions. I have analyzed, for example, howthe structural characteristics of capitalist society account for the fact that, asmany scholars recognize, affluent capitalist societies are unable to translateeconomic growth into a richer, more satisfying life for their members (seePanayotakis 2006).

This analysis has important implications both for addressing urgentecological problems, such as global warming, and for addressing the greatglobal inequalities responsible for the unnecessary suffering of billions ofhuman beings around the world. If capitalist society turns technologicaladvances into compulsive economic growth that is as likely to compoundscarcity-related problems as to alleviate them, the only rational way to dealwith such problem is to pursue a more democratic non-capitalist societythat would make it possible to revise the consumerist standards of richcountries, while also redistributing wealth globally so as to meet theneeds of the majority of the world’s population that continues to live inextreme poverty.

I have developed this argument by analyzing what I call ‘capitalism’s dialecticof scarcity’. This dialectic accounts for capitalism’s paradoxical tendency toreproduce scarcity-related problems, such as poverty, hunger and war, evenafter it has developed the technological means that could make such problemsa thing of the past. Capitalism creates the possibility of going beyond scarcitynot just because its technology creates the possibility for an alternative socialsystem capable of resolving scarcity-related problems and the unnecessary

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human suffering that these problems continue to produce. Capitalism alsopoints beyond scarcity in the sense that, as a number of studies has shown bynow, the compulsive economic growth that it gives rise to no longer leads toincreased human satisfaction (Easterlin1996).

This last fact forces us to rethink our definition of scarcity. In neoclassicaleconomics scarcity is defined as “[a] situation in which the needs and wants ofan individual or group of individuals exceed the resources available to satisfythem” (Bannock et. al. 2003, 345). The task that neoclassical economics setsfor itself, then, is to analyze the conditions under which as many of theseneeds and wants can be satisfied given the scarcity of resources. Once scarcityis defined in this way, it is tempting to assume that economic growth is boundto increase people’s satisfaction with life. But it is precisely this assumptionthat is wrong, at least for middle- and high-income countries. In these countriesthe point has been reached where economic growth no longer leads to higherreported levels of life satisfaction. In this sense, capitalism has transcendedscarcity, even as its inequalities keep reproducing scarcity-related problemsthat exact a high toll on people around the world.

Marx (1978) thought that the fundamental contradiction of capitalist societyhad to do with the tendency of its relations of production to become an obstacleto the further development of the technological forces of production2. It mayvery well be that capitalism’s contradiction may not so much consist incapitalism’s inability to continue developing the technological forces ofproduction but in its inability to translate this technological development intoa richer and happier life for all human beings.

2 Marx’s analysis of this contradiction was embedded in a broader theory of history, which I haveanalyzed and related to capitalism’s dialectic of scarcity elsewhere (Panayotakis 2004).

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References

[1] G. Bannock, R. E. Baxter, and E. Davis, The Penguin Dictionary of Economics.Penguin Books, seventh ed., 2003.

[2] R. A. Easterlin, Growth Triumphant: The Twenty-First Century in Historical Perspective.University of Michigan Press, 1996.

[3] F. Fukuyama, The End of History and the Last Man. Free Press, 1992.

[4] J. F. Lyotard, The Postmodern Condition: A Report on Knowledge. University ofMinnesota Press, 1984.

[5] K. Marx, A Contribution to the Critique of Political Economy. InternationalPublishers, 1970.

[6] C. Panayotakis, A Marxist Critique of Marx’s Theory of History: Beyond the DichotomyBetween Scientific and Critical Marxism, Sociological Theory, V. 22, No 1, P. 123-139,2004.

[7] —————, Working More, Selling More, Consuming More: Capitalism’s ‘ThirdContradiction’. In L. Panitch and C. Leys, Coming to Terms with Nature:Socialist Register 2007, The Merlin Press, Monthly Review Press andFernwood Publishing, 2006.

[8] M. D. Sahlins, Stone Age Economics. Aldine-Atherton, 1972.

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