420 Nonlinear science abstracts

104 (B9,T9) STATISTICAL MECHANICS OF RED BLOOD CELL AGGREGATION: THE DISTRIBUTION OF ROULEAUX IN THERMAL EQUILIBRIUM. Frederik W. Wiegel, Department of Applied Physics, Twente University of Technology, P. O. Box 217, Enschede, The Netherlands, and Alan S. Perelson, Theoretical Division, University of California, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.

When placed in suspension red blood cells adhere face to face and form long, cylindrical, and sometimes branched structures called rouleaux. We use methods developed in statistical mechanics to compute various statistical properties describing the sze and shape of rouleaux in thermodynamic equilibrium. This leads to analytical expressions for (I) the average number of rouleaux consisting of n cells and having m branchpoints; (2) the average number of cells per rouleau; (3) the average number of branch points per rouleau; and (4) the number of rouleaux with n cells in a system containing a total of N cells. We also derive asymptotic formulae that simplify these analytic expressions, and present numerical comparisons of the exact and asymptotic results.

JOURNAL: Submitted to J. Stat. Phys.

105 (M2,E3) EXISTENCE AND BIFURCATION THEOREMS FOR NONLINEAR ELLIPTIC EIGENVALUE PROBLEMS ON UNBOUNDED DOMAINS. Achim Bongers, Adam Opel AG, D-609 Russelsheim; Hans-Peter Heinz, Fachbereich Mathematik der Universit~t Mainz, Saarstr. 21, D-6500 Mainz, West Germany; Tassilo K~pper, Mathematisches Institut der Universitat KSln, Weyertal 88, D-5000 Cologne 41, West Germany.

We consider nonlinear elliptic eigenvalue problems on unbounded domains G C R n. Using an extended Ljusternik-Schnirelman theory we prove the existence of infinitely many eigenfunctions on every sphere in L2(G). Moreover, we establish that the infimum %* of the spectrum of the linearized problem L is always a bifurcation point. In addition, there is an infinity of branches emanating at %* from the trivial line of solutions if %* belongs to the essential spectrum of L.

JOURNAL: Journal of Differential Equations

106 (M1,R2) THE EXISTENCE OF PERIODIC TRAVELLING WAVES FOR SINGULARLY PERTURBED PREDATOR PREY EQUATIONS VIA THE CONLEY INDEX. R. Gardner and

J. Smoller. We prove the existence of a periodic travelling wave for predator-

prey equations via a topological method which uses the Conley Index. The equations take the form of an ode system in F 4, and we use a device introduced by Conley; namely, we build a solution around a "singular" solution, which is a discontinuous solution of a mixed algebraic-differential system. The desired solution is "close" to this one.

JOURNAL: Journal of Differential Equations

107 (P4,T6) DYNAMIC PHASE TRANSITIONS IN A VAN DER WAALS FLUID. M. Slemrod, Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12181, USA.

This paper proves the existence of traveling wave solutions connecting liquid and vapor phases in a van der Waals fluid. The main constitutive assumptions are that the fluid be an elastic fluid (with pressure