Ju LiKord Smith Ben Forget Felix Para Sid Yip

22.107 Computational Nuclear Science and Engineering(New) 3-0-9 H-LEVEL Grad Credit (Spring)

Prerequisites: 12.010, 18.085, or permission of instructor

Mathematical insights into how algorithms work

Practical programming /

debugging skills

Model construction & interpretation of numerical results

by Doing Nuclear Science and Engineering Problems!

MIT NSE Undergraduate Curriculum

all MIT NSE undergraduates reach basic level of

Mathematical insights into how algorithms work

Practical programming /

debugging skills

OR

Course 12: Earth, Atmospheric, and Planetary Sciences

Course 6: Electrical Engineering and Computer Science

4

Excerpts from http://math.mit.edu/classes/18.085/

Homework 3 is due FRIDAY Sept 30:MATLAB Question : This uses the codes just added to the website for advection-diffusion -Du_xx + vu_x = 1 in the earlier hwk problem 1.2.19. Those codes use finite differences (u_x is centered or upwind) and compare with the true u(x).

Part 1: Derive the true solution given in the code. A particular solution is u=x/v. Add the general solution to -D u_xx + v u_x = 0 with constants A and B, then find A and B. Part 2: Decide the accuracy (both centered and upwind) using the new code Ch1Q19FiniteDiffsConvergence.m that is also on the website The max error decreases with what power of h as h goes to 0 ? Part 3: Continue the experiment for very small h. We think the error may start to increase and we don't know why. Why ?

Notes on Homework 2 - [L,U] = lu(A) includes any row exchanges in L (so it may not be triangular) [L,U,P] = lu(A) will separate out that permutation matrix - The product of pivots in U is MINUS the determinant of A after an odd number of row exchanges - derivative of delta function : Integrate by parts to see that it picks out -g'(0)- to avoid row exchanges for positive definite matrices K, use chol(K) where chol = Cholesky

Course 18: Mathematics

But nothing systematically computational exist at the Graduate level

3 graduate core subjects: Applied Nuclear Physics (22.101)

Electromagnetic Interactions (22.105) Neutron Interactions and Applications (22.106)

in dissonance with the facts that

- Computation has become the third method of inquiry in nuclear science and engineering, in addition to experiments and analytical

theory

- Knowing how to identify and use computers to solve problems (model construction, programming, compiling, debugging, profiling,

interpreting) is a key survival skill in workplace.

22.212 Nuclear Reactor Analysis II Prereq: 22.106, 22.211, permission of instructor Units: 3-2-7

Addresses advanced topics in nuclear reactor physics with an additional focus towards computational methods and algorithms (towards transport). Covers current computational methods employed in lattice physics calculations such as resonance models, critical spectrum

adjustments, advanced homogenization techniques and fine mesh transport theory models. Deterministic transport approximation techniques such as the method of characteristics, discrete ordinates methods, response matrix methods and finite elements methods presented as well as

adaptivity methods. Acceleration techniques for these various solution schemes and extension to 3-D core calculations discussed. Non-linear algorithms for eigenvalue problems and

multiphysics coupling also covered. Requires a strong computational background and knowledge of C/C++ or Fortran. B. Forget

22.106 Neutron Interactions and Applications Prereq: 22.101 Units: 3-0-9

Comprehensive treatment of neutron interactions in condensed matter at energies from thermal to MeV, focusing on particle distributions most relevant to fission, fusion and radiation research

applications. Neutron distributions in reactor, accelerator and material structures resulting from single and multiple reactions, and in wave phenomena (optics) and inelastic scattering

experiments. Comparison of neutron and fluid transport. Particle simulations (Monte Carlo simulations). Term paper and presentation required. B. Forget

22.617 Plasma Turbulence and Transport Prereq: 22.616 or permission of instructor Units: 3-0-9

Introduces plasma turbulence and turbulent transport, with a focus on fusion plasmas. Covers theory of mechanisms for turbulence in confined plasmas, fluid and kinetic equations, and linear

and nonlinear gyrokinetic equations; transport due to stochastic magnetic fields, magnetohydrodynamic (MHD) turbulence, and drift wave turbulence; and suppression of

turbulence, structure formation, intermittency, and stability thresholds. Emphasis on comparing experiment and theory. Discusses experimental techniques, simulations of plasma turbulence,

and predictive turbulence-transport models. A. White

22.251 Systems Analysis of the Nuclear Fuel Cycle Prereq: 22.05 Units: 3-2-7 Lecture: MW1-2.30 (24-115)

Study of the relationship between the technical and policy elements of the nuclear fuel cycle. Topics include uranium supply, enrichment, fuel fabrication, in-core reactivity and fuel management of uranium and other fuel types, used fuel reprocessing and waste disposal.

Principles of fuel cycle economics and the applied reactor physics of both contemporary and proposed thermal and fast reactors are presented. Nonproliferation aspects, disposal of excess weapons plutonium, and transmutation of long lived radioisotopes in spent fuel are examined.

Several state-of-the-art computer programs relevant to reactor core physics and heat transfer are provided for student use in problem sets and term papers. Kord Smith

22.107 Course Goal

Mathematical insights into how algorithms work

Practical programming /

debugging skills

Model construction & interpretation of numerical results

by Doing Nuclear Science and Engineering Problems!

Intermediate LevelReached

Intermediate LevelReached

Intermediate LevelReached

• incoming MIT NSE graduate students have diverse backgrounds• but, NSE don’t need or have time to reinvent the wheels

22.107 Course Pre-requisite: 12.010, 18.085 -Assumes basic level of numerical linear algebra, finite difference, FFT etc.

(if not confident, take 18.085)- Assumes basic level of programming skills (if not confident, take 12.010)

22.107 Course Approach• Not gonna babysit and spoon feed: lectures provide pointers (references, websites) and inspirational examples

• Self study and self-motivated programming a must

• Problem set centric: develop critical analysis and synthetic problem-solving skills by asking them to solve problems with fewer and fewer constraints, end course with completely open-ended term project

• Arbitrary programming language: ask to show excerpts of source code and intermediate data

• Have fun programming and solving problems.

Develops practical scientific computing skills with applications

in radiation physics, reactor engineering and design, nuclear

materials, fusion, etc. Compiling/profiling/time and memory

complexities/debugging. Solvers of ordinary differential

equations and partial differential equations. Error versus

stability. Pre-and post-processing. Survey of visualization and

parallel computing. Case studies in quantum mechanics,

neutron diffusion and transport, simple CFD, and radiation

cascade simulations. Homework requires programming in one

or several languages of choice: some Matlab-free homeworks

enforced.

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Beyond 22.107…

A separate Monte Carlo course (maybe 22.108) in the works, by

Kord Smith

Ju Li will develop the initial 22.107 offering in an “open-

source” fashion…

22.107: Mainly deterministic,

continuum fieldmethods

22.108: Mainly stochastic,

discrete-agents based methods