Abstract The paper considers a class of linear Boltzmann transport equations which models charged particle transport, for example in dose calculation of radiation therapy. The equation is an approximation of the exact transport equation containing hyper-singular integrals in its collision terms. The paper confines to the global case where the spatial domain G is the whole space R 3 . Existence results

Abstract The study of the eigenvalues of the neutron transport operator yields an important insight into the physical features of the neutronic phenomena taking place in a nuclear reactor. Although the multiplication eigenvalue is the most popular because of its implication in the engineering design of multiplying structures, alternative interesting formulations are possible. In this paper the interest

Abstract Knowledge of an energy functioning of nanoscale system is essential both in the theoretical description and the experimental research. One of the energy behavior aspects which is critical for nanoscale system is dependence between energy and temperature that related to so called thermodynamic uncertainty relation (TUR). Existence of thermodynamic uncertainty relation (TUR) with the meaning

Abstract In this work, we apply the Ronen method to obtain highly-accurate approximations to the solution of the neutron transport equation in simple homogeneous problems. Slab, cylindrical, and spherical geometries are studied. This method demands successive resolutions of the diffusion equation, where the local diffusion constants are modified in order to reproduce new estimates of the currents by

Abstract Traffic modeling often keeps the mesoscopic scale in the theoretical sphere because of the integro-differential nature of its equations. In the present work, it is suggested to use the lattice Boltzmann method to overcome these difficulties while benefiting the strong theoretical foundation of the method. An alternative version of the lattice Boltzmann method for multi-class and heterogeneity

Abstract We study the validity of the time-dependent asymptotic PN approximation in radiative transfer of photons. The time-dependent asymptotic PN is an approximation which uses the standard PN equations with a closure that is based on the asymptotic solution of the exact Boltzmann equation for a homogeneous problem, in space and time. The asymptotic PN approximation for radiative transfer requires

Abstract The main goal of this work is to propose a non-Markovian model for a subdiffusive transport of particles with nonlinear interaction that involves adhesion affects on escape rates from position x, in inhomogeneous media. In this case, the escape rates to be dependent on the particle density and also effected by the density at the neighbors as well as the chemotactic gradient. We systematically

Abstract The scattering term within the Boltzmann equation was for decades approximated either through the Legendre polynomial for deterministic solvers or by S ( α , β ) /free gas model approach for Monte Carlo solvers. This, to some extent, inaccurate approach led to the assumption in several cases that the scattering term can be further “tuned” to simplify complex mathematical solver of the transport

Abstract In recent years, the first author has developed three successful numerical methods to solve the 1D radiative transport equation yielding highly precise benchmarks. The second author has shown a keen interest in novel solution methodologies and an ability for their implementation. Here, we combine talents to generate yet another high precision solution, the Matrix Riccati Equation Method (MREM)

Abstract The linear transport theory is developed to describe the time dependence of the number density of tracer particles in porous media. The advection is taken into account. The transport equation is numerically solved by the analytical discrete ordinates method. For the inverse Laplace transform, the double-exponential formula is employed. In this paper, we consider the travel distance of tracer

Abstract 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 diffusive regimes, nonclassical versions of the

Abstract We study numerical solution of Singular Integral Equations (SIE) of particle transport theory. We convert them into matrix equations by standard discretization process. It is found that the matrices are highly ill-conditioned and can be solved by Singular Value Decomposition (SVD) method. One expects that matrices resulting from expansions over Partial Range will not be ill-conditioned. We

Abstract Graphene has attracted the attention of several researchers because of its peculiar features. In particular, the study of charge transport in graphene is challenging for future electron devices. Usually, the physical description of electron flow in graphene given by the semiclassical Boltzmann equation is considered to be a good one. However, due to the computational complexity, its use in

Abstract In preparation for determining material properties such as Sieverts’ constant (solubility) and diffusivity (transport rate) we give a detailed discussion on a model describing some gas release experiment. Aiming to simulate the time-dependent hydrogen fluxes and concentration profiles efficiently, we provide an analytical solution for the diffusion equations on a cylindrical specimen and a

Abstract In this article, different angular flux discretization options, namely discrete ordinates representation and spherical harmonics expansion are compared from the viewpoint of the accuracy of perturbation calculations. The PARTISN discrete ordinates neutron transport solver was coupled with the SEnTRi code, developed at BME, in order to perform perturbation theory calculations in different types

Abstract We mathematically describe the apparently paradoxical phenomenon that the electric current in a semiconductor can flow because of collisions, and not despite them. A model of charge transport in a one-dimensional semiconductor crystal is considered, where each electron follows the periodic Hamiltonian trajectories, determined by the semiconductor band structure, and undergoes non-elastic collisions

Abstract In this study, a nonlocal approach to neutron diffusion equation with a memory is constructed in terms of moments of the displacement kernel with a modified geometric buckling. This approach leads to a family of partial differential equations which belong to the class of Fisher-Kolmogorov and Swift-Hohenberg equations. The stability of the problem depends on the signs of the second and fourth

Abstract Symbolic Implicit Monte Carlo (SIMC) is fully implicit in the value of matter temperature used to calculate the thermal emission. However, it means that the temporal precision of this method is limited, despite this method being more robust than Fleck and Cummings’ IMC method. In this article, we develop a new Monte Carlo method which is accurate for the thermal emission in one time step.

Abstract Two-dimensional/one-dimensional (2D/1D) methods have become popular for solving the 3D Boltzmann neutron transport equation on medium-to-large computing platforms. These methods can have a wide range of accuracy that depends largely on the fidelity of the coupling between the 2D and 1D solutions in the spatial and angular variables. In general, methods with higher-order coupling are both more

The implicit Monte Carlo (IMC) method can exhibit teleportation error in problems with strong coupling between radiation and material. Source tilting method is a technique to reduce the teleportation error by representing the emission source as a linear or higher order function in each zone. In this paper, we propose a new spatial reconstruction scheme for the emission source term in the implicit Monte

The present work deals with the performance assessment of the finite volume method (FVM) and discrete transfer method (DTM) in term of their abilities to accurately satisfy conservation of both scattered energy and asymmetry factor of the scattering phase function, after angular discretization and their computational time to calculate the scattering phase function, in radiative transfer problems. Studies

One of the common methods for solving the radiation transport equation is to use a polynomial expansion for the angle variable(s). Recent research that reduces the oscillations and improves the positivity of the gray transport equation solutions is here applied to the multigroup transport equations. Constant scale factors that stretch the time axis and constant scattering opacities that filter the

In this work, an explicit formulation to solve two-dimensional radiative transfer problems in anisotropic scattering media is developed. A nodal technique along with the Analytical Discrete Ordinates (ADO) method are used to solve the discrete ordinates approximation of the radiative transfer equation, in Cartesian geometry. To make it possible, the discrete ordinates equations are transversally integrated

This paper presents an expansion of the Probability Density Function (PDF) at any time t for the distribution of the microorganism cells movement on the planar surface. A 2-dimensional random walk process accurately models this movement. These cells move linearly on the surface with constant speed and change their direction after exponentially distributed time intervals. In addition, the path length

Monte Carlo (MC) schemes for photonics have been intensively studied throughout the past decades. The recent ISMC scheme presents many advantages (no teleportation error, converging behavior with respect to the spatial and time discretisations). But it is rather different from the IMC one (it is based on a different linearization and needs a slightly different code architecture). On another hand, legacy

This article reports a comparative study of the convergence rate of an axially symmetric binary gas flow inside a rotating cylinder using an improved direct simulation Monte Carlo algorithm for rarefied gases (v-DSMC) and the conventional DSMC. Subsequently, a comparison between the convergence behavior of the v-DSMC and analytical data is carried out to scrutinize the validity of the v-DSMC algorithm

In recent years the computer processors underpinning the large, distributed, workhorse computers used to solve the Boltzmann transport equation have become ever more parallel and diverse. Traditional CPU architectures have increased in core count, reduced in clock speed and gained a deep memory hierarchy. Multiple processor vendors offer a collectively diverse range of both CPUs and GPUs, with the

Goal-based error estimation due to spatial discretization and adaptive mesh refinement (AMR) has previously been investigated for the one dimensional, diamond difference, discrete ordinate (1-D DD-SN) method for discretizing the Neutron Transport Equation (NTE). This paper investigates the challenges of extending goal-based error estimation to multi-dimensions with supporting evidence provided on 2-D

We study the dynamics of charge carriers jumping from one trap to the other of potential trap depth Φ in a one-dimensional semiconductor layer with the help of thermal noise. Applying a nonuniform temperature, colder around the center and hotter on moving away from it, favors the charge carriers to migrate toward the center and populate around the center. However, exposing the system to another additional

We solve the classic albedo and Milne problems of plane-parallel illumination of an isotropically-scattering half-space when generalized to a Euclidean domain Rd for arbitrary d≥1. A continuous family of pseudo-problems and related H functions arises and includes the classical 3D solutions, as well as 2D “Flatland” and rod-model solutions, as special cases. The Case-style eigenmode method is applied

In this paper we study stability and convergence for hp-streamline diffusion (SD) finite element method for the, relativistic, time-dependent Vlasov–Maxwell (VM) system. We consider spatial domain Ωx⊂R3 and velocities v∈Ωv⊂R3. The objective is to show globally optimal a priori error bound of order O(h/p)s+1/2, for the SD approximation of the VM system; where h (=maxKhK) is the mesh size and p (=maxKpK)

When lifting the assumption of spatially-independent scattering centers in classical linear transport theory, collision rate is no longer proportional to angular flux/radiance because the macroscopic cross-section Σt(s) depends on the distance s to the previous collision or boundary. This creates a nonlocal relationship between collision rate and flux and requires revising a number of familiar deterministic

The implicit Monte Carlo (IMC) method has been widely used for solving the nonlinear thermal radiative transport equations for over 40 years. It is well known that the solutions of IMC method may non-physically violate the maximum principle for large time steps. In this article, we propose a variant of the IMC method called essentially implicit Monte Carlo (EIMC) method, which can eliminate the violations

One of the common methods for solving the radiation transport equation is to use a polynomial expansion for the angle variable(s). While each solution technique has its disadvantages, in some instances this method can result in oscillations large enough to give a negative radiation energy density, which is nonphysical. Some authors have recast the closure of the transport equations to guarantee positivity

Coarse mesh rebalance (CMR) method is formulated for the acceleration of fission source iteration (FSI) in the multigroup transport theory analysis of subcritical source-driven systems. The within-group equations are solved by diamond-differenced SN method and CMR has been employed also for the acceleration of scattering source iterations. By numerical experiments, carried out in spherical geometry

An analytical approach for the solution of the equation for phonon transport is presented for the combination thin films system. The transient phonon radiative transport model is considered and the combination of the silicon–diamond–silicon films is accommodated in the analysis. The multi-film system is thermally disturbed from the edges through introducing temperature difference across the combined

This work focuses on the conceptual problem of the intermixing of two samples of the same ideal gas under identical conditions (p,V,T) giving rise to the riddle known as Gibbs paradox. Starting from the very general entropy definition of the kinetic theory, for clearly focusing the question, we found that a careful analysis both from the points of view of classical kinetic theory and thermodynamics

We spatially discretize the discrete ordinates radiation transport equation using high-order discontinuous Galerkin finite elements in R-Z geometry. Previous research has demonstrated first-order methods have 2nd-order spatial convergence rates in R-Z geometry. Presently, we demonstrate that higher-order (HO) methods preserve the p + 1 convergence rates on smooth solutions, where p is the finite element

Case eigenfunctions are normally defined over the interval [−1,1]. We examine the consequences of defining such eigenfunctions over any segment of real axis. It is shown that there are always one or two discrete eigenvalues, in addition to the continuum of eigenvalues consisting of the segment of real axis.

A comparison between two numerical approximation methods i.e., Euler-Murayama and 1.5 strong Taylor methods have been established in this article. The stochastic point reactor kinetics equations consist of a system of Itô stochastic differential equations (SDEs) and this system is solved over each time-step size using Euler-Murayama and 1.5 strong Taylor methods. The obtained results establish the

The ballistic electron transport characteristics of hyperbolic Pöschl-Teller double-barrier resonant tunneling structures are investigated. The transmission coefficient and the current density-voltage characteristic in electrically biased one dimensional hyperbolic Pöschl-Teller double-barrier structures with different structure parameters have been calculated by using non-equilibrium Green’s function

This paper describes the application of machine learning (ML) tools to the prediction of bias in the criticality safety analysis. In particular, a set of over 1000 experiments included in the Whisper package were utilized in a variety of ML algorithms (notably Random Forest and AdaBoost implemented in SciKit-Learn) using neutron multiplication (keff) sensitivities (with and without energy dependence)

(2018). The 25th International Conference on Transport Theory, Monterey, California, October 16–20, 2017. Journal of Computational and Theoretical Transport: Vol. 47, Proceedings of the 25th International Conference on Transport Theory, Part I: Transport Theory, pp. 1-2.

A new model, based on an asymptotic procedure for solving the spinor kinetic equations of carriers and phonons is proposed, which gives naturally the displaced Fermi-Dirac distribution function at the leading order. The balance equations for the carrier numbers, energy and momentum densities, plus the Poisson's equation, constitute now a system of nine equations. Moreover two equations for the evolution

We explore a different aspect of handling the transport (mobility) of charge carriers (electrons) in a doped semiconductor layer under thermal stress. The traps are nonhomogeneously distributed such that denser around the center. Such type of traps distribution biases the electrons to concentrate around the center. Putting on the system to a nonuniform hot temperature around the center makes the electrons

We derive a priori error estimates for the standard Galerkin and streamline diffusion finite element methods for the Fermi pencil-beam equation obtained from a fully three-dimensional Fokker–Planck equation in space x=(x,y,z) and velocity v˜=(μ,η,ξ) variables. For a constant transport cross-section, there is a closed form analytic solution available for the Fermi equation with a data as product of

Thermal energy transfer across a silicon–aluminum thin films pair is considered. The thin films pair is thermally disturbed from the silicon film edge by a repetitive temperature pulses while phonon transport in the film pairs is examined. The transient frequency dependent Boltzmann transport equation is solved numerically incorporating the appropriate initial and boundary conditions. Thermal boundary

The phenomenological Landau theory of the spin precession has been used to reproduce the out-of-equilibrium properties of many magnetic systems. However, such an approach suffers from some serious limitations. The main reason is that the spin and the angular momentum of the atoms are described by the classical theory of the angular momentum. We derive a discrete model that extends the Landau theory

Presented here is the application of an adjoint technique for solving source-detector discrete ordinates (SN) transport problems by using a spectral nodal method. For slab-geometry adjoint SN model, the adjoint spectral Green’s function method (SGF†) is extended to multigroup problems considering arbitrary L′th order of scattering anisotropy, and the possibility of nonzero prescribed boundary conditions

Several numerical schemes for solving the transport equation in two-dimensional geometries have been proposed in last decades, but it is still a challenge to build a high accurate and efficient method. In this work, the transport equation in X–Y geometry with semi-reflective boundary conditions and isotropic scattering was solved by Nyström method. The approach consists in discretizing the integral

This work is a natural continuation of Boulanouar’s work of 2013, in which a mathematical model has been studied. This model is based on maturation-velocity structured bacterial population. The bacterial mitosis is mathematically described by a non-compact boundary condition. We investigate the asymptotic behavior of the generated semigroup and we prove that the bacterial population possesses Asynchronous

The solution of integro-differential form of the monoenergetic time independent linear transport equation can be obtained as in FN method using Placzek lemma and the infinite medium Green’s function. A new approximation has been used to calculate the half-space albedo, slab albedo and transmission factor in the half-space albedo and slab albedo problems. The numerical results are in good agreement

This is the investigation into the generation of high-fidelity multigroup multiband cross sections from Monte Carlo neutron transport simulations. Previous methods for generating multigroup multiband (MGMB) cross sections, and multigroup cross sections, assume an approximate shape for the scalar flux. This approximate flux shape is the product of an energy-dependent spectrum and a cross-section-dependent

An analytical solution to the discrete ordinates approximation of the adjoint to the multigroup transport equation in one-dimensional slab geometry is developed in this work, in order to be used in source estimation problems. The solution is firstly tested in a source-detector problem, where explicit expressions are derived to approximate the absorption rate of particles of internal detectors. Noisy

Paul Zweifel served as the founding editor of the Transport Theory and Statistical Physics journal from 1971 to 1981. An overview of his professional life gives a detailed list of his publications, broken down by his research interests, and also illustrates his leadership of the International Conference on Transport Theory meetings over the past 50 years. This paper provides supplementary material

The importance of the correct determination of the relaxation times, entering the electron–phonon coupling, is crucial for a proper evaluation of the rise of the crystal lattice temperature induced by a flow of electrons that undergo an external electric field. We describe the crystal heating by simulating the dynamics of all the phonon branches, i.e. acoustic, optical, K and Z phonons in a suspended

We study the problem of radiative heat (Marshak) waves using advanced approximate approaches. Supersonic radiative Marshak waves that are propagating into a material are radiation dominated (i.e., hydrodynamic motion is negligible), and can be described by the Boltzmann equation. However, the exact thermal radiative transfer problem is a non-trivial one, and there still exists a need for approximations

The present work considers an electron gas where ion contributions to the static potential may be neglected. The influence of temperature on the static potential and also on the screening length are derived. In the present contribution the temperature issue for a Fermi gas is treated in its non-relativistic as well as relativistic form. The effect of an extraneous ion in a degenerate Fermi plasma is

A numerically stable version of the PN method for solving the one-speed problem of neutron transport in the exterior of a sphere is developed. A transformation is used to obtain a plane-geometry-like neutron transport equation, where the angular derivative part of the streaming term in spherical geometry is considered as a source. In this way, conventional PN solutions developed for plane geometry

Previous proposals to permit nonexponential free-path statistics in radiative transfer have not included support for volume and boundary sources that are spatially uncorrelated from the scattering events in the medium. Birth-collision free paths are treated identically to collision–collision free paths and application of this to general, bounded scenes with inclusions leads to nonreciprocal transport