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We study a three-dimensional holographic CFT under the influence of a background electric field on a spacetime containing two black hole horizons. The electric background is fixed such that there is potential difference between the two…
In this work we derive and study the analytical solution of the voltage and current diffusion equation for the case of a finite-length resistor-constant phase element (CPE) transmission line (TL) network that can represent a model for…
This paper deals with thermoelectric problems including the Peltier and Seebeck effects. The coupled elliptic and doubly quasilinear parabolic equations for the electric and heat currents are stated, respectively, accomplished with…
This paper is concerned with the optimal control problem governed by a linear parabolic equation and subjected to box constraints on control variables. This type of problem has important applications in heating and cooling systems. By…
The heat equation is considered in the complex medium consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies an impedance boundary condition is imposed. An equation for the limiting…
The emergence of data-driven science has opened up new avenues for understanding the thermophysical properties of materials. For decades, alloys are known to possess very low thermal conductivity, but the extreme thermal conductivity can be…
Separating heat from charge in a material is an extremely challenging task since they are transported by the very same carriers, i.e. electrons or holes. In this Letter we show that such separation can reach 100% efficiency in a hybrid…
This paper studies a two-material optimal design problem for the time-averaged duality pairing between a (possibly time-dependent) heat source and the weak solution of an initial-boundary value problem for the heat equation with a…
Tuning thermal transport in nanostructured materials is a powerful approach to develop high-efficiency thermoelectric materials. Using a recently developed approach based on the phonon mean free path dependent Boltzmann transport equation,…
The present work investigates the causal parameter space of the Mueller-Israel-Stewart second-order theory for heat-conducting fluids in the Eckart frame for one-dimensional fluid flow in systems with finite baryon density. It is shown that…
We consider the optimal control of singular nonlinear partial differential equation which is the distributional formulation of the multiphase Stefan type free boundary problem for the general second order parabolic equation. Boundary heat…
Toward measuring the thermal properties of exfoliated atomically thin materials, we demonstrate simultaneous measurements of the thermal conductivity and specific heat in suspended membranes. We use the 3{\omega} technique applied to…
In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with…
For a thermal conductivity that is spatially uniform and independent of temperature, Fourier's law of heat transfer predicts a curl-free heat-flux. In the quasi-ballistic phonon transport regime, where the Fourier law breaks down, it has…
Self-heating in surrounding gate transistors can degrade its on-current performance and reduce lifetime. If a transistor heats/cools with time-constants less than the inverse of the operating frequency, a predictable, frequency-independent…
An efficient semi-implicit second-order-accurate finite-difference method is described for studying incompressible Rayleigh-Benard convection in a box, with sidewalls that are periodic, thermally insulated, or thermally conducting.…
Aim of this short note is to show that a dimension-free Harnack inequality on an infinitesimally Hilbertian metric measure space where the heat semigroup admits an integral representation in terms of a kernel is suffcient to deduce a sharp…
We consider two steady-state heat conduction systems called, $S$ and $S_\alpha$, in a multidimensional bounded domain $D$ for the Poisson equation with source energy $g$. In one system, we impose mixed boundary conditions (temperature $b$…
This paper aims to provide directly the observability inequality of backward stochastic heat equations for measurable sets. As an immediate application, the null controllability of the forward heat equations is obtained. Moreover, an…
We introduce a new method of solution for the convective heat transfer under forced laminar flow that is confined by two parallel plates with a distance of 2a or by a circular tube with a radius of a. The advection-conduction equation is…