Richard Vasques

The Ohio State University | OSU · Department of Mechanical and Aerospace Engineering

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 distribution function for chord lengths between scattering centers is non-exponential. Such problems have recently been proposed for the description of...

In nonclassical transport, the free-path length variable s is modeled as an independent variable, and a nonclassical linear Boltzmann transport equation incorporating s has been derived. To model transport in diffusive regimes, the simplified spherical harmonic equations (SPN) have been successfully employed. To model nonclassical transport in diff...

This paper introduces a mathematical approach that allows one to numerically solve the nonclassical transport equation in a deterministic fashion using classical numerical procedures. The nonclassical transport equation describes particle transport for random statistically homogeneous systems in which the distribution function for free-paths betwee...

We present in this work an extension of the Response Matrix (RM) method for the numerical solution of slab-geometry neutral particle transport equation in the discrete ordinates (SN) and energy multigroup formulations considering non-uniform sources. By using the term non-uniform we mean that the particle source is not spatially uniform inside the...

An improved modification of the Spectral Approach (SA) used for approximating the nonclassical neutral particle transport equation is described in this work. The term “Spectral” is used to indicate that the nonclassical angular flux is approximated as an expansion in terms of spectral basis functions. In the SA the basis functions are the Laguerre...

Described here is the occurrence of linearly dependent eigenvectors in the analytical solution of the spectral approximation of the nonclassical transport equation in the discrete ordinates (SN) formulation. To our knowledge, this characteristic does not arise in the analytical solution of the classical SN transport equations. Therefore, classical...

In this work we investigate the use of the Analytical Discrete Ordinates (ADO) method when solving the spectral approximation of the nonclassical transport equation. The spectral approximation is a recently developed method based on the representation of the nonclassical angular flux as a series of Laguerre polynomials. This representation generate...

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 on a slight modification of the nonclassical angular flux representation as a function of truncated Laguerre series. This leads, in some cases, to a c...

The nonclassical transport equation models particle transport processes in which the particle flux does not decrease as an exponential function of the particle’s free-path. Recently, a spectral approach was developed to generate nonclassical spectral SN equations, which can be numerically solved in a deterministic fashion using classical numerical...

In this work we investigate the use of the Analytical Discrete Ordinates (ADO) method when solving the spectral approximation of the nonclassical transport equation. The spectral approximation is a recently developed method based on the representation of the nonclassical angular flux as a series of Laguerre polynomials. This representation generate...

This paper introduces a new acceleration technique for the convergence of the solution of transport problems with highly forward-peaked scattering. The technique is similar to a conventional high-order/low-order (HOLO) acceleration scheme. The Fokker-Planck equation, which is an asymptotic limit of the transport equation in highly forward-peaked se...

Nonlinear fokker-planck acceleration for forward-peaked transport problems

We introduce and present a preliminary investigation of P1 and S2 synthetic acceleration for spectral SN equations.

We develop a multiphysics-based model to predict the response of localized tumors to combined-hyperthermia-radiotherapy (CHR) treatment. This procedure combines hyperthermia (tumor heating) with standard radiotherapy to improve efficacy of the overall treatment. In addition to directly killing tumor cells, tumor heating amends several parameters wi...

The use of machine learning algorithms to address classification problems is on the rise in many research areas. The current study is aimed at testing the potential of using such algorithms to auto-select the best solvers for transport problems in uniform slabs. Three solvers are used in this work: Richardson, diffusion synthetic acceleration, and...

Therapies such as combined-hyperthermia-radiotherapy (CHR) take advantage of excellent radiosensitization properties of hyperthermia and treat of tumors with both radiation and heat. To appropriately model a CHR treatment, features like tumor heating (heat transfer), dosimetry (radiation transport), and tumor dynamics (cell population dynamics) mus...

The use of machine learning algorithms to address classification problems is on the rise in many research areas. The current study is aimed at testing the potential of using such algorithms to auto-select the best solvers for transport problems in uniform slabs. Three solvers are used in this work: Richardson, diffusion synthetic acceleration, and...

We develop a multiphysics-based model to predict the response of localized tumors to combined-hyperthermia-radiotherapy (CHR) treatment. This procedure combines hyperthermia (tumor heating) with standard radiotherapy to improve efficacy of the overall treatment. In addition to directly killing tumor cells, tumor heating amends several parameters wi...

This paper introduces a mathematical approach that allows one to numerically solve the nonclassical transport equation in a deterministic fashion using classical numerical procedures. The nonclassical transport equation describes particle transport for random statistically homogeneous systems in which the distribution function for free-paths betwee...

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 Monte Carlo transport code sampling from the appropriate nonexponential free-path distribution function reproduces the solutions of the classical and nonclassic...

An asymptotic analysis is used to derive a set of diffusion approximations to the nonclassical transport equation with isotropic scattering. These approximations are shown to reduce to the simplified P N equations under the assumption of classical transport, and therefore are labeled nonclassical SP N equations. In addition, the nonclassical SP N e...

We investigate the accuracy of the recently proposed nonclassical transport equation. This equation contains an extra independent variable compared to the classical transport equation (the path-length $s$), and models particle transport taking place in homogenized random media in which a particle's distance-to-collision is not exponentially distrib...

We propose an approach to solve the stochastic neutron point kinetics equations using an adaptation of the diagonalization-decomposition method (DDM). This new approach (Double-DDM) yields a nonstiff solution for the stochastic formulation, allowing the calculation of the neutron and precursor densities at any time of interest without the need of u...

This paper provides numerical results that demonstrate the validity of the nonclassical diffusion approximation to the nonclassical transport equation in certain 1-D diffusive systems. This result provides a more solid foundation in which to improve this theory for relevant nuclear applications.

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 the nonclassical linear Boltzmann equation for an infinite homogeneous medium. This choice of $p(s)$ preserves the $true$ mean-squared free path of the system, wh...

The neutron point kinetics equation, which models the time-dependent behavior of nuclear reactors, is often used to understand the dynamics of nuclear reactor operations. It consists of a system of coupled differential equations that models the interaction between (i) the neutron population; and (ii) the concentration of the delayed neutron precurs...

We present a first numerical investigation of the accuracy of the recently proposed {\em non-classical transport equation}. This equation contains an extra independent variable (the path-length $s$), and models particle transport taking place in random media in which a particle's distance-to-collision is {\em not} exponentially distributed. To solv...

This paper presents a multiple length-scale asymptotic analysis that shows that, for transport problems in 1-D diffusive random media, the Levermore-Pomraning (LP) equations can be adjusted in order to achieve the correct asymptotic behavior. This analysis does not require the material layers to be optically thin. This adjustment appears in the for...

The neutron point kinetics equations, which model the time-dependent behavior of nuclear reactors (Aboander and Hamada, Ann. Nucl. Eng. 30:1111–1122, 2003; Hayes and Allen, Ann. Nucl. Eng. 32:572–587, 2005; Hetrick, Dynamics of Nuclear Reactors. University of Chicago Press, Chicago, 1971; Sánchez, Nucl. Sci. Eng. 103:94–99, 1989), are often used to...

We show that several diffusion-based approximations (classical diffusion or SP1, SP2, SP3) to the linear Boltzmann equation can (for an infinite, homogeneous medium) be represented exactly by a non-classical transport equation. As a consequence, we indicate a method to solve diffusion-based approximations to the Boltzmann equation via Monte Carlo,...

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 between scattering centers is non-exponential. Here, we relax the previous assumption that p(s) does not depend on the direction of flight \Omega; this leads to an exten...

We describe an analysis of neutron transport in the interior of model pebble bed reactor (PBR) cores, considering both crystal and random pebble arrangements. Monte Carlo codes were developed for (i) generating random realizations of the model PBR core, and (ii) performing neutron transport inside the crystal and random heterogeneous cores; numeric...

Radioactive waste has to undergo a process of quality checking in order to check its conformance with national regulations prior to its transport, intermediate storage and final disposal. Within the quality checking of radioactive waste packages non-destructive assays are required to characterize their radio-toxic and chemo-toxic contents. The Inst...

Due to the arrangement of the pebbles in a Pebble Bed Reactor (PBR) core, if a neutron is located close to a boundary wall, its path length probability distribution function in directions of flight parallel to the wall is significantly different than in other directions. Hence, anisotopic diffusion of neutrons near the boundaries arises. We describ...

We describe an analysis of neutron transport in a modeled 2-D (transport in a plane) pebble-bed reactor (PBR) core consisting of fuel discs stochastically piled up in a square box. Specifically, we consider the question of whether the force of gravity, which plays a role in this piling, affects the neutron transport within the system. Monte Carlo c...

A multiple length-scale asymptotic analysis shows that 1-D diffusive heterogeneous-media transport problems are accurately modeled by the atomic mix approximation when the optical widths of the “chunks” of different materials are O(1). (The atomic mix approximation is commonly known to be valid only when the chunks of different materials are optica...

The aim of this work is to present a review of particle transport theory in randomly mixed binary media. To accomplish this objective we briefly report some basic concepts of transport theory, and then we discuss in detail the derivation of two approaches developed to predict the solutions of such problems: the atomic mix and the Levermore-Pomranin...

In this work we report the state of art of particle transport theory in stochastic media, discussing in detail the derivation of the atomic mix and the Levermore-Pomraning models. We consider time independent stochastic transport in a randomly mixed binary medium. A Monte Carlo procedure is used to generate a physical realization of the statistics,...

Recentemente, foi proposta uma solução da equação de transporte de nêutrons em uma placa através de uma versão do método LTAN baseada na diagonaliza ção de uma matriz (2Nx2N). Neste trabalho, visando melhorar o tempo computacional do método LTAN, apresentamos uma nova versão deste método baseada na diagonalização de uma matriz NxN. Simulações numér...

In this work we report a solution of a neutron transport equation in a slab by a new version of the LTAN approach based upon LTAN matrix diagonalization. We present numerical simulations for transport problems with severe anisotropy.

In this work we report the solution of the neutron transport equation with isotropic scattering in a sphere by the LTSN method. We present numerical simulations as well a new idea to solve the transport anisotropic problem in a sphere.

Neste trabalho é apresentado um método analítico alternativo para obter a distribuição de concentração de poluentes em meio aquático. O método é baseado no uso de transformações conformes e modelos auxiliares em microescala usando conceitos da termodinâmica estatística. Simulações numéricas são apresentadas.