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Using simple holographic models in $D=4$ spacetime dimensions we construct black hole solutions dual to $d=3$ CFTs at finite charge density with a Q-lattice deformation. At zero temperature we find new ground state solutions with broken…
We consider a space-time finite element method for the numerical solution of a distributed tracking-type optimal control problem subject to the heat equation with state constraints. The cost or regularization term is formulated in an…
We investigate heat transport in a spin-1/2 Heisenberg chain, coupled locally to independent thermal baths of different temperature. The analysis is carried out within the framework of the theory of open systems by means of appropriate…
The thermo-electrical properties of a complex silicon cantilever structure used in thermal scanning probe lithography are modeled based on well established empirical laws for the thermal conductivity in silicon, the electrical conductivity…
By parameterizing the t-j model we present a new electron correlation model with one free parameter for high-temperature superconductivity. This model is of $SU_{q}(1,2)$ symmetry. The energy spectrums are shown to be modulated by the free…
We apply the Green-Kubo (G-K) approach to obtain the thermal conductivity tensor of $\beta$-1,3,5,7-tetranitro-1,3,5,7-tetrazocane ($\beta$-HMX) as a function of pressure and temperature from equilibrium molecular dynamics (MD) simulations.…
We study a free boundary problem arising from the theory of thermal insulation. The outstanding feature of this set optimization problem is that the boundary of the set being optimized is not a level surface of a harmonic function, but…
We consider an elliptic boundary value problem with unilateral constraints and subdifferential boundary conditions. The problem describes the heat transfer in a domain $D\subset\R^d$ and its weak formulation is in the form of a…
A finite element code for heat conduction, together with an adjoint solver and a suite of optimization tools was applied for the solution of Calderon's problem. One of the questions whose answer was sought was whether the solution to these…
Analytical solutions to heat or diffusion type equations are numerous, but there are rather few explicit solutions for conditions where the thermal conductivity or diffusion tensors are anisotropic. Such solutions have some use in making…
We develop a space-time spectral element method for topology optimization of transient heat conduction. The forward problem is discretized with summation-by-parts (SBP) operators, and interface/boundary and initial/terminal conditions are…
This paper demonstrates the application of the density-based topology optimisation approach for the design of heat sinks and micropumps based on natural convection effects. The problems are modelled under the assumptions of steady-state…
This paper is divided into three parts. The first part focuses on periodic layer heat potentials, demonstrating their smooth dependence on regular perturbations of the support of integration. In the second part, we present an application of…
An accurate and comprehensive numerical solution to the parabolic free boundary problem arising from thin film flow with both velocity and temperature distribution at large Reynolds numbers is obtained using a modified Keller box method. A…
The design of heat exchanger fields is a key phase to ensure the long-term sustainability of such renewable energy systems. This task has to be accomplished by modelling the relevant processes in the complex system made up of different…
We study the electric and heat current response resulting from an electric field quench in a holographic model of momentum relaxation at nonzero charge density. After turning the electric field off, currents return to equilibrium as…
Different variants of the method of weighted residual finite element method are used to get a solution for the parabolic heat equation, which is considered to be the model equation for the steady state Navier-Stokes equations. Results show…
The electronic transport experiments on topological insulators exhibit a dilemma. A negative cusp in magnetoconductivity is widely believed as a quantum transport signature of the topological surface states, which are immune from…
A theoretical study is presented in this paper to investigate the conjugate heat transfer across a vertical finite wall separating two forced and free convection flows at different temperatures. The heat conduction in the wall is in the…
We study the problem of electronic conduction in mesoscopic systems when the electrons are allowed to interact not only with static impurities, but also with a scatterer (a phase breaker(PB)) that possesses internal degrees of freedom. We…