The (radiation) field of an electric dipole p
Thomson and Compton Scattering processes
and Klein-Nishina formula
Electromagnetic wave incident on a charged particle set up oscillatory motion via
Lorentz force, the charged particle, in turn, radiates elect

NE-255 Numerical Methods in Reactor Analysis
Lecture 21: Neutron Diffusion Equation- Two-Dimensional Problems
Jasmina Vujic
Professor
Department of Nuclear Engineering
University of California, Berkeley
November 13, 2014
Department of Nuclear Engi

Legendre Polynomials
Introduced in 1784 by the French mathematician A. M. Legendre(1752-1833).
We only study Legendre polynomials which are special cases of Legendre functions. See sections 4.3,
4.7, 4.8, and 4.9 of Kreyszig.
Legendre functions are imp

NE-255 Numerical Methods in Reactor Analysis
Lecture 22: Neutron Diffusion Equation Multigroup Equations
Jasmina Vujic
Professor
Department of Nuclear Engineering
University of California, Berkeley
November 18, 2014
Department of Nuclear Enginee

Department of Nuclear Engineering
University of California
Berkeley, California
NE 255/J.Vujic
November 29, 2012
MIDTERM II (Closed books)
1. Describe the overall simulation algorithm in the Monte Carlo method. Include the
flow chart.
SOLUTION:
2. Derive

NE-255 Nuclear Reactor Theory
Lecture 23: Numerical Solution for Integral Transport Equation
Jasmina Vujic
Professor
Department of Nuclear Engineering
University of California, Berkeley
November 20, 2014
Department of Nuclear Engineering, Univ

CHAPTER
TWELVE
XII. NEUTRON TRANSPORT THEORY
Our goal is to determine the distribution of neutrons as a function of time, their position in space,
and their velocities, i.e., we want to know n ( r, v, t ) . If we know the distribution of neutrons in a
nuc

V.
NUMERICAL SOLUTION OF THE TRANSPORT
EQUATION
The neutron transport equation can be solved analytically only for highly idealized congurations. For most transport problems of practical interest we resort to approximations.
These can be physical (for exa

Massively Parallel Deterministic
Transport
Rachel Slaybaugh
NE 255
October 7, 2014
Outline
Introduction
Solvers and Denovo
Space-Angle Parallelism
Upscattering and Energy
Decomposition
Choose your own adventure
2
Transport Problems are Large
Six dim

Now the iteration errors are negligable, and the only errors one has to be concerned about
are those arising from the discretization of the angular and spatial variables. The relative
pointwise convergence criterion is, however, not without its difﬁcultie

NE-255 Numerical Methods in Reactor Analysis
Lecture 1: INTRODUCTION
Jasmina Vujic
Professor
Department of Nuclear Engineering
University of California, Berkeley
August 28, 2014
Department of Nuclear Engineering, University of California, Berkeley

The arguments for this "local" convergence criterion are: (i) in the early stages of the
calculation, when f is not very accurate, it does not make sense to fully converge the inner
iterations, and (ii) the inner iterations should always be converged to a

NE-255 Nuclear Reactor Theory
Lecture 19: Numerical Solution of Neutron Diffusion Equation -1
Jasmina Vujic
Professor
Department of Nuclear Engineering
University of California, Berkeley
November 4, 2014
Department of Nuclear Engineering, Univ

NE-255 Nuclear Reactor Theory
Lecture 20: Numerical Solution of Neutron Diffusion Equation
Jasmina Vujic
Professor
Department of Nuclear Engineering
University of California, Berkeley
November 6, 2014
Department of Nuclear Engineering, Univers

NE-255 Numerical Methods in Reactor Analysis
Lecture 18: Monte Carlo Method Eigenvalue Calculations, Statistical Error
Analysis, Parallel Monte Carlo
Jasmina Vujic
Professor
Department of Nuclear Engineering
University of California, Berkeley
Octo

NE-255 Numerical Methods in Reactor Analysis
Lecture 2: Neutron Transport Equation - I
Jasmina Vujic
Professor
Department of Nuclear Engineering
University of California, Berkeley
September 2, 2014
Department of Nuclear Engineering, University of

NE-255 Numerical Methods in Reactor Analysis
Lecture 3: Neutron Transport Equation - II
Jasmina Vujic
Professor
Department of Nuclear Engineering
University of California, Berkeley
September 4, 2014
Department of Nuclear Engineering, University of

NE-255 Numerical Methods in Reactor Analysis
Lecture 8: Discretization of the Neutron Transport Equation
September 22, 2014
Jasmina Vujic
Professor
Department of Nuclear Engineering
University of California, Berkeley
Department of Nuclear Enginee

NE-255 Numerical Methods in Reactor Analysis
Lecture 9: Finite Volume (in space) Discrete Ordinates SN (in angle) Method
Jasmina Vujic
Professor
Department of Nuclear Engineering
University of California, Berkeley
September 25, 2014
Department of N

NE-255 Numerical Methods in Reactor Analysis
Lecture 10: Discrete Ordinates Sn Method - continued
Jasmina Vujic
Professor
Department of Nuclear Engineering
University of California, Berkeley
September 30, 2014
Department of Nuclear Engineering, Un

NE-255 Numerical Methods in Reactor Analysis
Lecture 11: Discrete Ordinates Sn Method - continued
Jasmina Vujic
Professor
Department of Nuclear Engineering
University of California, Berkeley
October 2, 2014
Department of Nuclear Engineering, Unive

NE-255 Numerical Methods in Reactor Analysis
Lecture 6: Numerical Solutions of the Neutron Transport Equation
September 16, 2014
Jasmina Vujic
Professor
Department of Nuclear Engineering
University of California, Berkeley
Department of Nuclear En

NE-255 Numerical Methods in Reactor Analysis
Lecture 15: Monte Carlo Method - continued
Jasmina Vujic
Professor
Department of Nuclear Engineering
University of California, Berkeley
October 21, 2014
Department of Nuclear Engineering, University of

NE 255 - Numerical Simulation in Radiation Transport
Massimiliano Fratoni
fratoni1@llnl.gov
August, 31st 2010
One-line Problem Title Card
Cell Cards
Blank Line Delimiter
Surface Cards
Blank Line Delimiter
Data Cards
Blank Line Terminator
2
! Geometry
Sur

NE-255 Numerical Methods in Reactor Analysis
Lecture 13: Introduction to Monte Carlo Method
Jasmina Vujic
Professor
Department of Nuclear Engineering
University of California, Berkeley
October 9, 2014
Department of Nuclear Engineering, University

NE-255 Numerical Methods in Reactor Analysis
Lecture 16: Monte Carlo Method - continued
Jasmina Vujic
Professor
Department of Nuclear Engineering
University of California, Berkeley
October 23, 2014
Department of Nuclear Engineering, University o

NE-255 Numerical Methods in Reactor Analysis
Lecture 17: Monte Carlo Method Statistical Error Analysis
Jasmina Vujic
Professor
Department of Nuclear Engineering
University of California, Berkeley
October 28, 2014
Department of Nuclear Engineering,

then, treating (x2 1)n = (x 1)n (x + 1)n as a product and using Leibnitz rule to dierentiate n
times, we have
1
v (x) = n (n!(x + 1)n + terms with (x 1) as a factor) ,
2 n!
so that
Chapter C
v (1) =
C2.3
Properties of Legendre Polynomials
n!2n
= 1.
2n n!