Interpretation of thermoelectric power behaviour of Zinc nanowire composites: Phonon-scattering mechanism

We develop a theoretical model for quantitative analysis of temperature-dependent thermoelectric power (S) of Zn nanowires. In doing so, we first use the Mott expression to compute the electron diffusive thermoelectric power (S_c^diff.) using Fermi energy as electron-free parameter, S_c^diff. shows linear temperature dependence. Further, the S_c^diff. contribution is subtracted from the experimental data and the difference (S_experimental-S_c^dif) is characterized as phonon drag thermoelectric power (S_ph^drag) which is obtained within the relaxation time approximation where the thermoelectric power is limited by the scattering of phonons with impurities, grain boundaries, charge careers and phonons in the nanowires. The S_ph^drag shows anomalous temperature-dependent behaviour, which is an artifact of various operating scattering mechanisms. The observed anomalies are well accounted in terms of interaction among the phonons-impurity, phonon-grain boundaries, phonon-electron and the umklapp scattering. It is also shown that for phonons the scattering and transport cross-sections are proportional to ω⁴ in the Rayleigh regime where ω is the frequency of the phonons. Numerical analysis of thermoelectric power from the present model shows similar results as those revealed from experiments.     

A multistep flux-corrected transport scheme

A multistep flux-corrected transport (MFCT) scheme is developed to achieve conservative and monotonic tracer transports for multistep dynamical cores. MFCT extends Zalesak two-time level scheme to any multistep time-differencing schemes by including multiple high-order fluxes in the antidiffusive flux, while computing the two-time level low-order monotone solution. The multistep time-differencing scheme used in this study is the third-order Adams–Bashforth (AB3) scheme implemented in a finite-volume icosahedral shallow-water model. The accuracy of AB3 MFCT is quantified by the shape-preserving advection experiments in non-divergent flow, as well as a cosine bell whose shape changes during advection in shear flow. AB3 MFCT has been shown to be insensitive to time step size. This make AB3 MFCT an attractive transport scheme for explicit high resolution model applications with small time step. MFCT is tested in shallow-water model simulations to demonstrate that the use of MFCT maintains positive-definite tracer transport, while at the same time conserving both fluid mass and tracer mass within round-off errors in the AB3 dynamic core.     

An Exner-based coupled model for two-dimensional transient flow over erodible bed

Transient flow over erodible bed is solved in this work assuming that the dynamics of the bed load problem is described by two mathematical models: the hydrodynamic model, assumed to be well formulated by means of the depth averaged shallow water equations, and the Exner equation. The Exner equation is written assuming that bed load transport is governed by a power law of the flow velocity and by a flow/sediment interaction parameter variable in time and space. The complete system is formed by four coupled partial differential equations and a genuinely Roe-type first order scheme has been used to solve it on triangular unstructured meshes. Exact solutions have been derived for the particular case of initial value Riemann problems with variable bed level and depending on particular forms of the solid discharge formula. The model, supplied with the corresponding solid transport formulae, is tested by comparing with the exact solutions. The model is validated against laboratory experimental data of different unsteady problems over erodible bed.     

A unified Monte Carlo treatment of the transport of electromagnetic energy, electrons, and phonons in absorbing and scattering media

The scalar Boltzmann transport equation (BTE) is often applicable to radiative energy transfer, electron-beam propagation, as well as thermal conduction by electrons and phonons provided that the characteristic length of the system is much larger than the wavelength of energy carriers and that certain interference phenomena and the polarization nature of carriers are ignored. It is generally difficult to solve the BTE analytically unless a series of assumptions are introduced for the particle distribution function and scattering terms. Yet, the BTE can be solved using statistical approaches such as Monte Carlo (MC) methods without simplifying the underlying physics significantly. Derivations of the MC methods are relatively straightforward and their implementation can be achieved with little effort; they are also quite powerful in accounting for complicated physical situations and geometries. MC simulations in radiative transfer, electron-beam propagation, and thermal conduction by electrons and phonons have similar simulation procedures; however, there are important differences in implementing the algorithms and scattering properties between these simulations. The objective of this review article is to present these simulation procedures in detail and to show that it is possible to adapt an existing MC computer code, for instance, in radiative transfer, to account for physics in electron-beam transport or phonon (or electronic thermal) conduction by sorting out the differences and implementing the correct corresponding steps. Several simulation results are presented and some of the difficulties associated with different applications are explained.     

Studying anomalous scaling and heat transport of turbulent thermal convection using a dynamical model

Turbulent thermal convection is a well-studied problem with various issues of interest. In this paper, we review our work which shows the nature and origin of anomalous scaling and heat transport in the limit of very strong thermal forcing, can be gained by studying a dynamical model, known as shell model, of homogeneous turbulent thermal convection in which buoyancy acts directly at most scales. Specifically, we have obtained two results. The first result is that when buoyancy acts directly at most scales such that the dynamics are governed by a cascade of entropy, the scaling behavior is described by Bolgiano and Obukhov scaling plus corrections that are due to the variations of the local entropy transfer rate. This result indicates the validity of the extension of refined similarity hypothesis to turbulent thermal convection. The second result is that when buoyancy is acting directly at most scales, a damping term acting on the largest scale, which has to be added for the system to achieve stationarity, plays a crucial role in heat transport, and that the heat transport depends on the strength of thermal forcing in the same manner as that predicted for the ultimate state of very strong thermal forcing. With our interpretation of the damping term representing the effect of the boundaries, this result indicates that in the ultimate state of turbulent thermal convection, when buoyancy is acting at most scales, boundaries would play a significant role in heat transport.     

Effects of pulsatile flow and straight length on low-density lipoprotein transport in a curved arterial wall

Abnormal accumulation of macromolecules such as low-density lipoproteins (LDLs) in the arterial wall causes narrowing and blockage of vessels, which leads to atherosclerosis. Effects of pulsatile nature of blood flows as well as the initial length on transport of the LDL species in the arterial boundary layer region are analyzed numerically in the present work. The set of governing equations consisting of continuity, Navier-Stokes, and species transport is solved using a projection method based on the second-order central difference discretization. The obtained results are in excellent agreement with the pertinent data. The computational results imply that the flow field and concentration distribution are time dependent but the variation of the filtration velocity can be ignored. The LDL concentration boundary layer thickness decreases in the outer part and increases in the inner part for both with or without straight length. Presence of initial straight length generates about 26% growth in the boundary layer thickness, although its effect on the LDL surface concentration (LSC) is negligible. The maximum LSC is related to the regions with minimum wall shear stress in the inner part of the curved artery, which have more potential for formation of atherosclerosis. A new numerical correlation between the LSC and boundary layer thickness is proposed and examined.     

Aggregation equations with gradient potential as Radon measure and initial data in Besov-Morrey spaces

In this work, we present conditions to obtain a global-in-time existence of solutions to a class of nonlinear viscous transport equations describing aggregation phenomena in biology with sufficiently small initial data in Besov-Morrey spaces and gradient potential as a Radon measure. We also study the self-similarity and asymptotic stability of solutions at large times.     

Unbalanced optimal transport: Dynamic and Kantorovich formulations

This article presents a new class of distances between arbitrary nonnegative Radon measures inspired by optimal transport. These distances are defined by two equivalent alternative formulations: (i) a dynamic formulation defining the distance as a geodesic distance over the space of measures (ii) a static “Kantorovich” formulation where the distance is the minimum of an optimization problem over pairs of couplings describing the transfer (transport, creation and destruction) of mass between two measures. Both formulations are convex optimization problems, and the ability to switch from one to the other depending on the targeted application is a crucial property of our models. Of particular interest is the Wasserstein–Fisher–Rao metric recently introduced independently by [7], [15]. Defined initially through a dynamic formulation, it belongs to this class of metrics and hence automatically benefits from a static Kantorovich formulation.     

A degenerate elliptic-parabolic system arising in competitive contaminant transport

The objective of this work is to study a coupled system of degenerate and nonlinear partial differential equations governing the transport of reactive solutes in groundwater. We show that this system admits a unique weak solution provided the nonlinear adsorption isotherm associated with the reaction process satisfies certain physically reasonable structural conditions, by addressing a more general problem. In addition, we conclude, that the solute concentrations stay non-negative if the source term is componentwise non-negative and investigate numerically the finite speed of propagation of compactly supported initial concentrations, in a two-component test case.     

Doubly nonlocal Cahn–Hilliard equations

We consider a doubly nonlocal nonlinear parabolic equation which describes phase-segregation of a two-component material in a bounded domain. This model is a more general version than the recent nonlocal Cahn–Hilliard equation proposed by Giacomin and Lebowitz [26], such that it reduces to the latter under certain conditions. We establish well-posedness results along with regularity and long-time results in the case when the interaction between the two levels of nonlocality is strong-to-weak.