Related papers: Microscopic limits of PDEs modeling macroscopic he…
We present and analyze a new derivation of the meso-level behavior of a discrete microscopic model of heat transfer. This construction is based on the principle of dynamic consistency. Our work reproduces and corrects, when needed, all the…
The energetics of the stochastic process has shown the balance of energy on the mesoscopic level. The heat and the energy defined there are, however, generally different from their macroscopic counterpart. We show that this discrepancy can…
The Fourier law of heat conduction describes heat diffusion in macroscopic systems. This physical law has been experimentally tested for a large class of physical systems. A natural question is to know whether it can be derived from the…
Starting from microscopic mechanics, we derive thermodynamic relations for heat conducting nonequilibrium steady states. The extended Clausius relation enables one to experimentally determine nonequilibrium entropy to the second order in…
Heat conduction in one-dimensional (1D) systems is studied based on an analytical S-matrix method, which is developed in the mesoscopic electronic transport theory and molecular dynamic (MD) simulations. It is found that heat conduction in…
Common techniques for the spatial discretisation of PDEs on a macroscale grid include finite difference, finite elements and finite volume methods. Such methods typically impose assumed microscale structures on the subgrid fields, so…
Microcanonical Thermodynamics allows the application of Statistical Mechanics on one hand to closed finite and even small systems and on the other to the largest,self-gravitating ones. However, one has to reconsider the fundamental…
Partial Differential Equations (PDEs) are widely used for modeling the physical phenomena and analyzing the dynamical behavior of many engineering and physical systems. The heat equation is one of the most well-known PDEs that captures the…
We develop a geometric framework to describe the thermodynamics of microscopic heat engines driven by slow periodic temperature variations and modulations of a mechanical control parameter. Covering both the classical and the quantum…
Heat and energy are conceptually different, but often are assumed to be the same without justification. An effective method for investigating diffusion properties in equilibrium systems is discussed. With this method, we demonstrate that…
We discuss the problem of partitioning a macroscopic system into a collection of independent subsystems. The partitioning of a system into replica-like subsystems is nowadays a subject of major interest in several field of theoretical and…
The modeling of multi-phase flow is very challenging, given the range of scales as well as the diversity of flow regimes that one encounters in this context. We revisit the discrete equation method (DEM) for two-phase flow in the absence of…
The macroscopic control of ubiquitous heat flow remains poorly explored due to the lack of a fundamental theoretical method. Here, by establishing temperature-dependent transformation thermotics for treating materials whose conductivity…
This report describes a mathematical model of heat conduction. The differential equation for heat conduction in one dimensional rod has been derived. The explicit finite difference numerical method is used to solve this differential…
Thermodynamics allows the application of Statistical Mechanics to finite and even small systems. As surface effects cannot be scaled away, one has to be careful with the standard arguments of splitting a system into two or bringing two…
We obtain macroscopic isothermal thermodynamic transformations by space-time scalings of a microscopic Hamiltonian dynamics in contact with a heat bath. The microscopic dynamics is given by a chain of anharmonic oscillators subject to a…
We introduce a new class of mesoscopic heat engines consisting of a tunnel junction coupled to a linear thermal bath. Work is produced by transporting electrons up against a voltage bias like in ordinary thermoelectrics but heat is…
We introduce the heat method for computing the shortest geodesic distance to a specified subset (e.g., point or curve) of a given domain. The heat method is robust, efficient, and simple to implement since it is based on solving a pair of…
Direct numerical simulations of mechanical metamaterials are prohibitively expensive due to the separation of scales between the lattice and the macrostructural size. Hence, multiscale continuum analysis plays a pivotal role in the…
Microwave electromagnetic heating are widely used in many industrial processes. The mathematics involved is based on the Maxwell's equations coupled with the heat equation. The thermal conductivity is strongly dependent on the temperature,…