Analysis of anomalous transport with temporal fractional transport equations in a bounded domain

Anomalous transport in magnetically confined plasmas is investigated using temporal fractional transport equations.The use of temporal fractional transport equations means that the order of the partial derivative with respect to time is a fraction. In this case, the Caputo fractional derivative relative to time is utilized, because it preserves the form of the initial conditions. A numerical calculation reveals that the fractional order of the temporal derivative α(α ∈(0, 1), sub-diffusive regime) controls the diffusion rate. The temporal fractional derivative is related to the fact that the evolution of a physical quantity is affected by its past history, depending on what are termed memory effects. The magnitude of α is a measure of such memory effects. When α decreases, so does the rate of particle diffusion due to memory effects. As a result,if a system initially has a density profile without a source, then the smaller the α is, the more slowly the density profile approaches zero. When a source is added, due to the balance of the diffusion and fueling processes, the system reaches a steady state and the density profile does not evolve. As α decreases, the time required for the system to reach a steady state increases. In magnetically confined plasmas, the temporal fractional transport model can be applied to off-axis heating processes. Moreover, it is found that the memory effects reduce the rate of energy conduction and hollow temperature profiles can be sustained for a longer time in sub-diffusion processes than in ordinary diffusion processes.

SPIRAL SOLUTION TO THE TWO-DIMENSIONAL TRANSPORT EQUATIONS

The existence of spiral solution for the two-dimensional transport equations is considered in the present paper. Based on the notion of generalized solutions in the sense of Lebesgue-stieltjes integral, the global weak solution of transport equations which includes δ-shocks and vacuum is constructed for some special initial data.

NONLINEAR SEMIGROUP APPROACH TOTRANSPORT EQUATIONS WITH DELAYED NEUTRONS

This paper deal with a nonlinear transport equation with delayed neutron andgeneral boundary conditions. We establish, via the nonlinear semigroups approach, the exis-tence and uniqueness of the mild solution, weak solution, strong solution and local solutionon LP-spaces （1 ≤ p 〈 ＋∞）. Local and non local evolution problems are discussed.

High Order IMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings

In this paper,we consider the high order method for solving the linear transport equations under diffusive scaling and with random inputs.To tackle the randomness in the problem,the stochastic Galerkin method of the generalized polynomial chaos approach has been employed.Besides,the high order implicit-explicit scheme under the micro-macro decomposition framework and the discontinuous Galerkin method have been employed.We provide several numerical experiments to validate the accuracy and the stochastic asymptotic-preserving property.

Investigation of Acoustomagnetoelectric Effect in Bandgap Graphene by the Boltzmann Transport Equation

We study the acoustomagnetoelectric (AME) effect in two-dimensional graphene with an energy bandgap using the semiclassical Boltzmann transport equation within the hypersound regime, (where represents the acoustic wavenumber and is the mean free path of the electron). The Boltzmann transport equation and other relevant equations were solved analytically to obtain an expression for the AME current density, consisting of longitudinal and Hall components. Our numerical results indicate that both components of the AME current densities display oscillatory behaviour. Furthermore, geometric resonances and Weiss oscillations were each defined using the relationship between the current density and Surface Acoustic Wave (SAW) frequency and the inverse of the applied magnetic field, respectively. Our results show that the AME current density of bandgap graphene, which can be controlled to suit a particular electronic device application, is smaller than that of (gapless) graphene and is therefore, more suited for nanophotonic device applications.

WEAK SOLUTIONS OF MONGE-AMPRE TYPE EQUATIONS IN OPTIMAL TRANSPORTATION

This paper concerns the weak solutions of some Monge-Amp^re type equa- tions in the optimal transportation theory. The relationship between the Aleksandrov solutions and the viscosity solutions of the Monge-Ampere type equations is discussed. A uniform estimate for solution of the Dirichlet problem with homogeneous boundary value is obtained.

Two Uniform Tailored Finite Point Schemes for the Two Dimensional Discrete Ordinates Transport Equations with Boundary and Interface Layers

This paper presents two uniformly convergent numerical schemes for the two dimensional steady state discrete ordinates transport equation in the diffusive regime,which is valid up to the boundary and interface layers.A five-point nodecentered and a four-point cell-centered tailored finite point schemes(TFPS)are introduced.The schemes first approximate the scattering coefficients and sources by piecewise constant functions and then use special solutions to the constant coefficient equation as local basis functions to formulate a discrete linear system.Numerically,both methods can not only capture the diffusion limit,but also exhibit uniform convergence in the diffusive regime,even with boundary layers.Numerical results show that the five-point scheme has first-order accuracy and the four-point scheme has second-order accuracy,uniformly with respect to the mean free path.Therefore a relatively coarse grid can be used to capture the two dimensional boundary and interface layers.

BITS: an efficient transport solver based on a collocation method with B-spline basis

A B-spline Interpolation Transport Solver(BITS) based on a collocation method is developed. It solves transport equations as a generalized interpolation problem, taking the first-order accuracy in time and the second-order accuracy in space along with a predictor–corrector or under-relaxation iteration method. Numerical tests show that BITS can solve one-dimensional transport equations for tokamak plasma more accurately without additional computation cost, compared to the finite difference method transport solver which is widely used in existing tokamak transport codes.

NUMERICAL SIMULATION OF SINGLE-GROUP, STEADY STATE AND ISOTROPIC NEUTRON TRANSPORT EQUATION IN DIFFUSIVE REGIMES

We present an algorithm for numerical solution of transport equation in diffusive regimes, in which the transport equation is nearly singular and its solution becomes a solution of a diffusion equation. This algorithm, which is based on the Least-squares FEM in combination with a scaling transformation, presents a good approximation of a diffusion operator in diffusive regimes and guarantees an accurate discrete solution. The numerical experiments in 2D and 3D case are given, and the numerical results show that this algorithm is correct and efficient.

A SPECTRAL STREAMLINE DIFFUSION FINITE ELEMENT COUPLING METHOD OF UNSTEADY TRANSPORT EQUATION IN THE FIELD OF NEUTRON LOGGING

In this paper, a new numerical method, the coupling method of spherical harmonic function spectral and streamline diffusion finite element for unsteady Boltzmann equation in the neutron logging field, is discussed. The convergence and error estimations of this scheme are proved. Its applications in the field of neutron logging show its effectiveness.

Asymptotic Behavior of Solutions for a Periodic Transport Equation with Delay

This paper analyzes a class of first order partial differential equations with delay (a model for the blood production system). The asymptotic behavior of solutions are studied.

First-principles analysis of phonon thermal transport properties of two-dimensional WS2/WSe2 heterostructures

The van der Waals(vdW)heterostructures of bilayer transition metal dichalcogenide obtained by vertically stacking have drawn increasing attention for their enormous potential applications in semiconductors and insulators.Here,by using the first-principles calculations and the phonon Boltzmann transport equation(BTE),we studied the phonon transport properties of WS2/WSe2 bilayer heterostructures(WS2/WSe2-BHs).The lattice thermal conductivity of the ideal WS2/WSe2-BHs crystals at room temperature(RT)was 62.98 W/mK,which was clearly lower than the average lattice thermal conductivity of WS2 and WSe2 single layers.Another interesting finding is that the optical branches below 4.73 THz and acoustic branches have powerful coupling,mainly dominating the lattice thermal conductivity.Further,we also noticed that the phonon mean free path(MFP)of the WS2/WSe2-BHs(233 nm)was remarkably attenuated by the free-standing monolayer WS2(526 nm)and WSe2(1720 nm),leading to a small significant size effect of the WS2/WSe2-BHs.Our results systematically demonstrate the low optical and acoustic phonon modes-dominated phonon thermal transport in heterostructures and give a few important guidelines for the synthesis of van der Waals heterostructures with excellent phonon transport properties.

ON THE TRANSPORT EQUATION WITH INTEGRAL BOUNDARY CONDITIONS AND ITS CONSERVAIVE LAW

The well-posedness for the time-dependent neutron transport equationwith integral boundary conditions is established in L^1 space. Some spectral propertiesof the transport operator are discussed, the dominant eigenvalue is proved existing,and furthermore, the conservative law of migrating particle numbers is established.

A Domain-Boundary Integral Treatment of Transient Scalar Transport with Memory

It is well known that the boundary element method (BEM) is capable of converting a boundary- value equation into its discrete analog by a judicious application of the Green’s identity and complementary equation. However, for many challenging problems, the fundamental solution is either not available in a cheaply computable form or does not exist at all. Even when the fundamental solution does exist, it appears in a form that is highly non-local which inadvertently leads to a sys-tem of equations with a fully populated matrix. In this paper, fundamental solution of an auxiliary form of a governing partial differential equation coupled with the Green identity is used to discretize and localize an integro-partial differential transport equation by conversion into a boundary-domain form amenable to a hybrid boundary integral numerical formulation. It is observed that the numerical technique applied herein is able to accurately represent numerical and closed form solutions available in literature.

Unified semiclassical approach to electronic transport from diffusive to ballistic regimes

We show that by integrating out the electric field and incorporating proper boundary conditions,a Boltzmann equation can describe electron transport properties,continuously from the diffusive to ballistic regimes.General analytical formulas of the conductance in D = 1,2,3 dimensions are obtained,which recover the Boltzmann–Drude formula and Landauer–B ¨uttiker formula in the diffusive and ballistic limits,respectively.This intuitive and efficient approach can be applied to investigate the interplay of system size and impurity scattering in various charge and spin transport phenomena,when the quantum interference effect is not important.

SOLUTION TO A PARAMETRIC EQUATION WITH GENERALIZED BOUNDARY CONDITION IN TRANSPORT THEORY

This paper deals with the solution of a parametric equation with generalized boundary condiiton in transport theory. It gives the distribution of parameter (so called delta-eigenvalue [1]) with which the equation has non-zero solution. A necessary and sufficient condition for the existence of; he control critical eigenvalue delta0 is established.

Analysis of High Concentration Spikes Appearing in Mass Plume in Nearly Homogeneous Turbulent Flow Based on the PDF Transport Equation

To evaluate the pollutant dispersion in background turbulent flows, most researches focus on statistical variation of concentrations or its fluctuations. However, those time-averaged quantities may be insufficient for risk assessment, because there emerge many high-intensity pollutant areas in the instantaneous concentration field. In this study, we tried to estimate the frequency of appearance of the high concentration areas in a turbulent flow based on the Probability Density Function (PDF) of concentration. The high concentration area was recognized by two conditions based on the concentration and the concentration gradient values. We considered that the estimation equation for the frequency of appearance of the recognized areas consisted of two terms based on each condition. In order to represent the two terms with physical quantities of velocity and concentration fields, simultaneous PIV (Particle Image Velocimetry) and PLIF (Planar Laser-Induced Fluorescence) measurement and PLIF time-serial measurement were performed in a quasi-homogeneous turbulent flow. According to the experimental results, one of the terms, related to the condition of the concentration, was found to be represented by the concentration PDF, while the other term, by the streamwise mean velocity and the integral length scale of the turbulent flow. Based on the results, we developed an estimation equation including the concentration PDF and the flow features of mean velocity and integral scale of turbulence. In the area where the concentration PDF was a Gaussian one, the difference between the frequencies of appearance estimated by the equation and calculated from the experimental data was within 25%, which showed good accuracy of our proposed estimation equation. Therefore, our proposed equation is feasible for estimating the frequency of appearance of high concentration areas in a limited area in turbulent mass diffusion.

An optimized smearing scheming for first Brillouin zone sampling and its application on thermal conductivity prediction of graphite

We propose an optimized scheme to determine the smearing parameter in the Gaussian function that is used to replace the Dirac δ function in the first Brillouin zone sampling. The broadening width is derived by analyzing the difference of the results from the phase-space method and Gaussian broadening method. As a demonstration, using the present approach,we investigate the phonon transport in a typical layered material, graphite. Our scheme is benchmarked by comparing with other zone sampling methods. Both the three-phonon phonon scattering rates and thermal conductivity are consistent with the prediction from the widely used tetrahedron method and adaptive broadening method. The computational efficiency of our scheme is more than one order of magnitude higher than the two other methods. Furthermore, the effect of fourphonon scattering in phonon transport in graphite is also investigated. It is found that four-phonon scattering reduces the through-plane thermal conductivity by 10%. Our methods could be a reference for the prediction of thermal conductivity of anisotropic material in the future.

Numerical Modelling of Nitrogen Thermal Effects Produced by the Negative DC Corona Discharge

In this work, we simulate numerically the thermal effects in nitrogen at atmospheric pressure caused by a negative corona DC discharge of low current. A mathematical function that simulates the injection of the thermal transfer in gas is proposed. The simulated discharge is of a negative point to plane mass type, with an interelectrode distance of 12 mm and a symmetry about the axis of discharge. The spatial and temporal evolution of neutrals is analyzed based upon the equations of continuity, momentum and energy in a cylindrical geometry. For the geometry of the system, the FCT （flux corrected transport） procedure was adopted.

Implementation of a Conservative Two-step Shape-Preserving Advection Scheme on a Spherical Icosahedral Hexagonal Geodesic Grid

An Eulerian flux-form advection scheme, called the Two-step Shape-Preserving Advection Scheme （TSPAS）, was generalized and implemented on a spherical icosahedral hexagonal grid （also referred to as a geodesic grid） to solve the transport equation. The C grid discretization was used for the spatial discretization. To implement TSPAS on an unstructured grid, the original finite-difference scheme was further generalized. The two-step integration utilizes a combination of two separate schemes （a low-order monotone scheme and a high-order scheme that typically cannot ensure monotonicity） to calculate the fluxes at the cell walls （one scheme corresponds to one cell wall）. The choice between these two schemes for each edge depends on a pre-updated scalar value using slightly increased fluxes. After the determination of an appropriate scheme, the final integration at a target cell is achieved by summing the fluxes that are computed by the different schemes. The conservative and shape-preserving properties of the generalized scheme are demonstrated. Numerical experiments are conducted at several horizontal resolutions. TSPAS is compared with the Flux Corrected Transport （FCT） approach to demonstrate the differences between the two methods, and several transport tests are performed to examine the accuracy, efficiency and robustness of the two schemes.