# A generalized Boltzmann equation for "non-classical" particle transport

@inproceedings{Larsen2007AGB, title={A generalized Boltzmann equation for "non-classical" particle transport}, author={Edward W. Larsen}, year={2007} }

We are interested in non-standard transport equations where the description of the scattering events involves an additional “memory variable”. We establish the well posedness and investigate the diffusion asymptotics of such models. While the questions we address are quite classical the analysis is original since the usual dissipative properties of collisional transport equations is broken by the introduction of the memory terms.

#### 33 Citations

On a generalized Boltzmann equation for non-classical particle transport

- Physics
- 2010

We are interested in non-standard transport equations where the description of the scattering events involves an additional "memory variable''.
We establish the well posedness and investigate the… Expand

A generalized linear Boltzmann equation for non-classical particle transport

- Physics
- 2011

This paper presents a derivation and initial study of a new generalized linear Boltzmann equation (GLBE), which describes particle transport for random statistically homogeneous systems in which the… Expand

The nonclassical diffusion approximation to the nonclassical linear Boltzmann equation

- Computer Science, Mathematics
- Appl. Math. Lett.
- 2016

Abstract We show that, by correctly selecting the probability distribution function p ( s ) for a particle’s distance-to-collision, the nonclassical diffusion equation can be represented exactly by… Expand

Exact Transport Representations of the Classical and Nonclassical Simplified PN Equations

- Physics
- Journal of Computational and Theoretical Transport
- 2018

Abstract We show that the recently introduced nonclassical simplified PN equations can be represented exactly by a nonclassical transport equation. Moreover, we validate the theory by showing that a… Expand

The Equivalence of “ Forward ” and “ Backward ” Nonclassical Particle Transport Theories

- 2017

In this paper, two distinct “nonclassical" particle transport theories – in which the distribution function P(s) for the distance s between collisions is not exponential – are discussed. The two… Expand

Non-classical particle transport with angular-dependent path-length distributions. I: Theory

- Mathematics, Physics
- 2014

Abstract This paper extends a recently introduced theory describing particle transport for random statistically homogeneous systems in which the distribution function p ( s ) for chord lengths… Expand

The Nonclassical Boltzmann Equation and DIffusion-Based Approximations to the Boltzmann Equation

- Mathematics, Physics
- SIAM J. Appl. Math.
- 2015

It is shown that several diffusion-based approximations to the linear Boltzmann equation can (for an infinite, homogeneous medium) be represented exactly by a non-classical transport equation, and indicated a method to solve diffusion- based approximation to the Boltzman equation via Monte Carlo, with only statistical errors - no truncation errors. Expand

A spectral approach for solving the nonclassical transport equation

- Computer Science, Physics
- J. Comput. Phys.
- 2020

A spectral method is used to represent the non classical flux as a series of Laguerre polynomials in the free-path variable $s, resulting in a nonclassical equation that has the form of a classical transport equation. Expand

Mathematical modeling and numerical methods for non-classical transport in correlated media

- Physics
- 2015

In this work, we investigate a new and non-classical linear transport equation for the transport of particles in correlated background media. We derive a time-dependent non-classical transport… Expand

An improved spectral approach for solving the nonclassical neutron particle transport equation

- Physics
- 2021

An improvement modification of the Spectral Approach (SA) used for approximating the nonclassical neutral particle transport equation is described in this work. The main focus of the modified SA lies… Expand

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