相关论文: On the Formalization of the Heat Conduction Proble…
In this paper, we study the heat equation with an irregular spatially dependent thermal conductivity coefficient. We prove that it has a solution in an appropriate very weak sense. Moreover, the uniqueness result and consistency with the…
We present a theoretical framework to investigate quantum thermodynamic processes under non-Markovian system-bath interactions on the basis of the hierarchical equations of motion (HEOM) approach, which is convenient to carry out…
In the present paper a detailed mathematical model is derived for district heating networks. After semidiscretization of the convective heat equation and introducing coupling conditions at the nodes of the network one gets a…
Current-carrying conductors inevitably experience resistive heating due to the material's finite electrical conductivity. The resulting temperature distribution within the wire has essential implications for structural integrity,…
Technological progress in electronics usually requires their use in increasingly aggressive environments, such as rapid thermal cycling and high power density. Thermal diodes appear as excellent candidates to thermally protect critical…
Thermal issue is a major concern in 3D integrated circuit (IC) design. Thermal optimization of 3D IC often requires massive expensive PDE simulations. Neural network-based thermal prediction models can perform real-time prediction for many…
The layout optimization of the heat conduction is essential during design in engineering, especially for thermal sensible products. When the optimization algorithm iteratively evaluates different loading cases, the traditional numerical…
We propose a novel finite element-based physics-informed operator learning framework that allows for predicting spatiotemporal dynamics governed by partial differential equations (PDEs). The proposed framework employs a loss function…
The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but…
The discrete element method (DEM) coupled with computational fluid dynamics (CFD), has been developed to simulate complex solid-fluid flow systems. Today, DEM is regarded as an established approach, with extensive applications in industrial…
When the variations of surface temperature are measured both spatially and temporally, analytical expressions that correctly account for multi-dimensional transient conduction can be applied. To enhance the accessibility of these accurate…
In this review, we present the key aspects of modern thermal perturbation theory based on the hard thermal loop (HTL) approximation, including its theoretical foundations and applications within quantum electrodynamics (QED) and quantum…
We study numerical algorithms to solve a specific Partial Differential Equation (PDE), namely the Stefan problem, using Physics Informed Neural Networks (PINNs). This problem describes the heat propagation in a liquid-solid phase change…
The understanding of the underlying dynamical mechanisms which determine the macroscopic laws of heat conduction is a long standing task of non-equilibrium statistical mechanics. A better understanding of the mechanism of heat conduction…
We consider the heat equation with spatially variable thermal conductivity and homogeneous Dirichlet boundary conditions. Using the Method of Fokas or Unified Transform Method, we derive solution representations as the limit of solutions of…
A heat conduction equation on a lattice composed of nodes and bonds is formulated assuming the Fourier law and the energy conservation law. Based on this equation, we propose a higher-order topological heat conduction model on the breathing…
An inverse problem for a stationary heat transfer process is studied for a totally isolated bar on its lateral surface, made up of two consecutive sections of different, isotropic and homogeneous materials, perfectly assembly, where one of…
We present a method that employs physics-informed deep learning techniques for parametrically solving partial differential equations. The focus is on the steady-state heat equations within heterogeneous solids exhibiting significant phase…
In this paper, we consider the exponential stabilization and observation of an unstable heat equation in a general multi-dimensional domain by combining the finite-dimensional spectral truncation technique and the recently developed…
We study anomalous transport in a one-dimensional system with two conserved quantities in presence of thermal baths. In this system we derive exact expressions of the temperature profile and the two point correlations in steady state as…