A model for the heat of transport in ionic conductors

The ion flow caused by a temperature gradient originates the ionic thermopower which is quantified by the heat of transport. Experimentally, it is known that in superionic conductors, the heat of transport Q is nearly equal to the activation energy for ion transport E_a. In the present paper, a model for the heat of transport in ionic conductors has been proposed based on a lattice dynamical theory of diffusion. We have shown that the relationship between Q and E_a is determined by the participation degree of different phonon modes, in particular the short wavelength phonons to the atomic jump processes. The implication of this finding to the transport properties of superionic conductors has been discussed, and it is suggested that the degree of the collective motion in ionic conductors increases with the increase in Q/E_a. The model predicts that good ionic conductors will show large value of Q/E_a. The importance of the acoustic phonons in the ion transport processes has been also pointed out.     

Effect of boundary treatments on quantum transport current in the Green’s function and Wigner distribution methods for a nano-scale DG-MOSFET

In this paper, we conduct a study of quantum transport models for a two-dimensional nano-size double gate (DG) MOSFET using two approaches: non-equilibrium Green’s function (NEGF) and Wigner distribution. Both methods are implemented in the framework of the mode space methodology where the electron confinements below the gates are pre-calculated to produce subbands along the vertical direction of the device while the transport along the horizontal channel direction is described by either approach. Each approach handles the open quantum system along the transport direction in a different manner. The NEGF treats the open boundaries with boundary self-energy defined by a Dirichlet to Neumann mapping, which ensures non-reflection at the device boundaries for electron waves leaving the quantum device active region. On the other hand, the Wigner equation method imposes an inflow boundary treatment for the Wigner distribution, which in contrast ensures non-reflection at the boundaries for free electron waves entering the device active region. In both cases the space-charge effect is accounted for by a self-consistent coupling with a Poisson equation. Our goals are to study how the device boundaries are treated in both transport models affects the current calculations, and to investigate the performance of both approaches in modeling the DG-MOSFET. Numerical results show mostly consistent quantum transport characteristics of the DG-MOSFET using both methods, though with higher transport current for the Wigner equation method, and also provide the current–voltage (I–V) curve dependence on various physical parameters such as the gate voltage and the oxide thickness.     

Quantum Transport of Particles and Entropy

A unified view on macroscopic thermodynamics and quantum transport is presented. Thermodynamic processes with an exchange of energy between two systems necessarily involve the flow of other balancable quantities. These flows are first analyzed using a simple drift-diffusion model, which includes the thermoelectric effects, and connects the various transport coefficients to certain thermodynamic susceptibilities and a diffusion coefficient. In the second part of the paper, the connection between macroscopic thermodynamics and quantum statistics is discussed. It is proposed to employ not particles, but elementary Fermi- or Bose-systems as the elementary building blocks of ideal quantum gases. In this way, the transport not only of particles but also of entropy can be derived in a concise way, and is illustrated both for ballistic quantum wires, and for diffusive conductors. In particular, the quantum interference of entropy flow is in close correspondence to that of electric current.     

Carrier transport mechanisms in the ZnO based heterojunctions grown by MBE

This paper presents a review of models of the current transport in different kind of heterojunctions (HJs) and their characteristics. In order to effectively deduce the dominant electron transport for the HJs based on ZnO or Zn_1?xMg_xO layers grown on Si substrate by MBE a comparison is performed – which type of the HJ exhibits better electrical properties. The current–voltage characteristics for the studied HJs were measured within 280–300 K. The transport properties of the HJs are explained in terms of Anderson model with reference to aforementioned current transport models. It is found, that the mechanisms of current transport for all of the studied HJs are similar. At a low forward voltage bias the tunneling current dominates while at medium voltage bias (0.5–1 V) multitunneling capture-emission prevails with the electron trap located at 0.1–0.25 eV below the bottom of a ZnO (Zn_1?xMg_xO) conduction band. Beyond this voltage bias space charge limited current governs the current transport.     

On generalized fractional Cattaneo’s equations

This paper studies a family of generalized fractional Cattaneo’s equations for which passive (i.e., spontaneous) transport is possible. This is done by using fractional substitutions in integer-order rational transfer functions and showing conditions for positive realness.     

Entropy-Regularized Optimal Transport on Multivariate Normal and q-normal Distributions

The distance and divergence of the probability measures play a central role in statistics, machine learning, and many other related fields. The Wasserstein distance has received much attention in recent years because of its distinctions from other distances or divergences. Although computing the Wasserstein distance is costly, entropy-regularized optimal transport was proposed to computationally efficiently approximate the Wasserstein distance. The purpose of this study is to understand the theoretical aspect of entropy-regularized optimal transport. In this paper, we focus on entropy-regularized optimal transport on multivariate normal distributions and q-normal distributions. We obtain the explicit form of the entropy-regularized optimal transport cost on multivariate normal and q-normal distributions; this provides a perspective to understand the effect of entropy regularization, which was previously known only experimentally. Furthermore, we obtain the entropy-regularized Kantorovich estimator for the probability measure that satisfies certain conditions. We also demonstrate how the Wasserstein distance, optimal coupling, geometric structure, and statistical efficiency are affected by entropy regularization in some experiments. In particular, our results about the explicit form of the optimal coupling of the Tsallis entropy-regularized optimal transport on multivariate q-normal distributions and the entropy-regularized Kantorovich estimator are novel and will become the first step towards the understanding of a more general setting.     

The Monge Problem for Distance Cost in Geodesic Spaces

We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish space and d _L is a geodesic Borel distance which makes (X, d _L ) a non branching geodesic space. We show that under the assumption that geodesics are d-continuous and locally compact, we can reduce the transport problem to 1-dimensional transport problems along geodesics. We introduce two assumptions on the transport problem π which imply that the conditional probabilities of the first marginal on each geodesic are continuous or absolutely continuous w.r.t. the 1-dimensional Hausdorff distance induced by d _L . It is known that this regularity is sufficient for the construction of a transport map. We study also the dynamics of transport along the geodesic, the stability of our conditions and show that in this setting d _L -cyclical monotonicity is not sufficient for optimality.     

Direct numerical simulation of scalar transport using unstructured finite-volume schemes

An unstructured finite-volume method for direct and large-eddy simulations of scalar transport in complex geometries is presented and investigated. The numerical technique is based on a three-level fully implicit time advancement scheme and central spatial interpolation operators. The scalar variable at cell faces is obtained by a symmetric central interpolation scheme, which is formally first-order accurate, or by further employing a high-order correction term which leads to formal second-order accuracy irrespective of the underlying grid. In this framework, deferred-correction and slope-limiter techniques are introduced in order to avoid numerical instabilities in the resulting algebraic transport equation. The accuracy and robustness of the code are initially evaluated by means of basic numerical experiments where the flow field is assigned a priori. A direct numerical simulation of turbulent scalar transport in a channel flow is finally performed to validate the numerical technique against a numerical dataset established by a spectral method. In spite of the linear character of the scalar transport equation, the computed statistics and spectra of the scalar field are found to be significantly affected by the spectral-properties of interpolation schemes. Although the results show an improved spectral-resolution and greater spatial-accuracy for the high-order operator in the analysis of basic scalar transport problems, the low-order central scheme is found superior for high-fidelity simulations of turbulent scalar transport.     

Sparse Regularized Optimal Transport with Deformed q-Entropy

Optimal transport is a mathematical tool that has been a widely used to measure the distance between two probability distributions. To mitigate the cubic computational complexity of the vanilla formulation of the optimal transport problem, regularized optimal transport has received attention in recent years, which is a convex program to minimize the linear transport cost with an added convex regularizer. Sinkhorn optimal transport is the most prominent one regularized with negative Shannon entropy, leading to densely supported solutions, which are often undesirable in light of the interpretability of transport plans. In this paper, we report that a deformed entropy designed by q-algebra, a popular generalization of the standard algebra studied in Tsallis statistical mechanics, makes optimal transport solutions supported sparsely. This entropy with a deformation parameter q interpolates the negative Shannon entropy (q=1) and the squared 2-norm (q=0), and the solution becomes more sparse as q tends to zero. Our theoretical analysis reveals that a larger q leads to a faster convergence when optimized with the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm. In summary, the deformation induces a trade-off between the sparsity and convergence speed.     

On the viscosity and thermal conductivity of dense gases

The modified Enskog theory (MET) of transport in dense gases can be used to predict the density dependence of transport coefficients provided the function y, which is a product of a dimensionless density and a pair correlation function, is known as a function of density. In this communication we consider the inverse problem, extracting information on the y function from measured transport property data, both to resolve some peculiarities found by others, and to provide the basis for improved MET predictions.     

Kinetic theory of reacting systems

In this paper transport processes of reacting systems are investigated, based on the Boltzmann equations. The Boltzmann equations are solved by means of Grad's moment method to thirteen moments and some formal results are obtained for transport properties. It is shown that the rate coefficients are quadratic functions of hydrodynamic fluxes and are in the form

where

are the scalar moments associated with the reaction and q, J, Π are heat flux, material flux and traceless symmetric stress tensor. k⁽⁰⁾_i is the usual local equilibrium formula for reaction rate constant. Iterative solutions for the equations of change for

, q, J and Π are obtained from which transport coefficients are calculated for the reacting system. It is shown that the solutions, when specialized to nonreacting mixtures, lead to results for the transport coefficients which are exactly in agreement with the Chapman-Enskog theory results. The modifications of the transport coefficients due to reactions are obtained from the iterative solutions and the bracket integrals necessary for their calculations are explicitly given in an appendix.     

A dynamical flux expansion for the three-dimensional bond percolation problem

A new expansion for treating diffusive transport on bond disordered lattices is presented and applied to the bond percolation problem in 3 dimensions. Our approach, when combined with standard resummation techniques, leads to a prediction for the 3-dimensional transport threshold p_c = 0.252, which is in excellent agreement with known results. This agreement is obtained without recourse to renormalization group techniques or self-consistent arguments. It originates from a new t-matrix representation for the frequency-dependent diffusion coefficient and is a direct consequence of the equations of motion for the probability currents.     

Hydrodynamic parameters and correlation functions of superfluid 3He

In this paper we present the first of two closely related studies devoted to the connection between the phenomenological hydrodynamics and microscopic theories of superfluid ³He. In this first part, we express in a systematical way all the phenomenological parameters appearing in the hydrodynamic equations in terms of microscopically well defined correlation functions. The method used for this purpose goes back to the work of Kadanoff and Martin on normal fluids and has recently been formulated in the framework of Mori's projector formalism by Forster. Apart from the assumptions about the structure of the superfluid phases of ³He and certain regularity assumptions about the collision-dominated part of the correlation functions, which have to be satisfied if the hydrodynamic limit exists at all, but which remain unproven, this part of our work is nearly exact. The only approximation made is the perturbative treatment of the very small magnetic dipole energy. The k → O limit of various correlation functions is considered. Novel consequences of the directional long range order for the transverse momentum density correlation function of the A phase, which are unique to that phase, are obtained. The instantaneous reactive parameters of the system are expressed as equal time commutators and evaluated rigorously. Some reactive parameters, e.g. the one leading to “orbit waves” are shown to have a collisional part, which has not yet been evaluated in a microscopic theory. NMR is considered as the k → O limit of spin wave resonances with an energy gap due to the magnetic dipole-dipole interaction at k = 0. The NMR linewidth is thereby fixed by the same transport parameter, which determines the spin wave damping in the theory where the gap is neglected. The relevant transport parameter is expressed along with all others by the rigorous Kubo formulae of the theory in which the magnetic dipole energy is neglected. The close analogy of the NMR linewidth parameter to transport parameters like the shear viscosity, which are measured in quite different experiments, is thereby elucidated. Further, approximate evaluations of the Kubo relations of these parameters, within a common microscopic approach will be given in a second related study.     

Kinetic theory of dense fluids

A kinetic theory of dense fluids is presented in this series of papers. The theory is based on a kinetic equation for subsystems which represents a subset of equations structurally invariant to the sizes of the subsystem that includes the Boltzmann equation as an element at the low density limit. There exists a H-function for the kinetic equation and the equilibrium solution is uniquely given by the canonical distribution functions for the subsystems comprising the entire system. The cluster expansion is discussed for the N-body collision operator appearing in the kinetic equation. The kinetic parts of transport coefficients are obtained by means of a moment method and their density expansions are formally obtained. The Chapman-Enskog method is discussed in the subsequent paper.     

Effect of temperature,electric and magnetic field on spin relaxation in single layer graphene: A Monte Carlo simulation study

In this article, we employ the semiclassical Monte Carlo approach to study the spin polarized electron transport in single layer graphene channel. The Monte Carlo method can treat non-equilibrium carrier transport and effects of external electric and magnetic fields on carrier transport can be incorporated in the formalism. Graphene is the ideal material for spintronics application due to very low Spin Orbit Interaction. Spin relaxation in graphene is caused by D'yakonov-Perel (DP) relaxation and Elliott-Yafet (EY) relaxation. We study effect of electron electron scattering, temperature, magnetic field and driving electric field on spin relaxation length in single layer graphene. We have considered injection polarization along z-direction which is perpendicular to the plane of graphene and the magnitude of ensemble averaged spin variation is studied along the x-direction which is the transport direction. This theoretical investigation is particularly important in order to identify the factors responsible for experimentally observed spin relaxation length in graphene.     

Towards nonlinear stability of sources via a modified Burgers equation

Coherent structures are solutions to reaction-diffusion systems that are time-periodic in an appropriate moving frame and spatially asymptotic at x=±∞ to spatially periodic travelling waves. This paper is concerned with sources which are coherent structures for which the group velocities in the far field point away from the core. Sources actively select wave numbers and therefore often organize the overall dynamics in a spatially extended system. Determining their nonlinear stability properties is challenging as localized perturbations may lead to a non-localized response even on the linear level due to the outward transport. Using a Burgers-type equation as a model problem that captures some of the essential features of sources, we show how this phenomenon can be analysed and asymptotic nonlinear stability be established in this simpler context.     

Helical-edge transport near ν = 0 of monolayer graphene

The complex nature of filling factor ν = 0 of monolayer graphene is studied in magnetotransport experiments. As a function of perpendicular magnetic field a metal-insulator transition is observed, which is attributed to disorder-induced Landau level broadening in the canted antiferromagnetic phase. In the metallic regime a separation of the zeroth Landau level appears and signs of the quantum spin Hall effect are seen near ν = 0. In addition to local transport, nonlocal transport experiments show results being consistent with helical edge transport.     

Experimental confirmation by galvanomagnetic methods of a complex transport model in In0.53Ga0.47As layers deposited by MBE on SI-InP

At low temperatures In_0.53Ga_0.47As samples show an increase of carrier concentration, which can be explained in terms of a two carriers transport model. This type of problem exists since the beginning of the semiconductor era, dating back to monocrystalline germanium.We propose that in all the investigated layers, there are X atoms or charged dislocations in the region of the first monolayers, which are built in during epitaxial growth. The layers were intentionally undoped. They form an impurity band in which low mobility carriers dominate over the localised electron scattering due to the s-d exchange interaction. These carriers do not freeze out at liquid helium temperature and give rise to two transport media for electrons; a conduction band at higher temperatures and an impurity band at lower temperatures. The electron which fall down onto the previously ionised X atoms, then move by thermally activated hopping. We show that the two carriers model for In_0.53Ga_0.47As epitaxial layers are confirmed by the carrier concentration-temperature, carrier concentration-magnetic field, resistivity-magnetic field behaviour, and also by YKA theory also. The differences between the two transport models are so distinctive that observed phenomena may exist. This paper presents experimental results, which constitute comprehensive evidence for the complicated structure of the semiconductor epitaxial layers on the sample of n-type In_0.53Ga_0.47As/InP layer with n=2.2×10¹⁵/cm³.