Related papers: Mathematical Modeling of Heat Conduction
The paper considers heat conduction in a model chain of composite particles with hard core and elastic external shell. Such model mimics three main features of realistic interatomic potentials - hard repulsive core, quasilinear behavior in…
This paper proposes a new methodological framework within which the heat conductance in 1D lattices can be studied. The total process of heat conductance is separated into two parts where the first one is the equilibrium process at equal…
This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems. We consider a simple model of two-dimensional steady-state heat conduction described by elliptic partial differential equations…
This paper is devoted to the study of the flatness property of linear time-invariant fractional systems. In the framework of polynomial matrices of the fractional derivative operator, we give a characterization of fractionally flat outputs…
We study the non equilibrium statistical properties of a one dimensional hard-rod fluid undergoing collisions and subject to a spatially non uniform Gaussian heat-bath and periodic potential. The system is able to sustain finite currents…
Understanding heat transfers in fibrous materials, particularly conduction, is a major challenge due to their heterogeneous and multiscale nature, and the unknown contribution of fiber-to-fiber contacts. In most previous modeling studies,…
The one-dimensional hard rod model describes impenetrable bosons with finite diameter, extending the Lieb-Liniger model to systems with excluded volume interactions. Here, we investigate the thermodynamics of quantum HRs using Yang-Yang…
Heating and heat conduction in molecular junctions are considered within a general NEGF formalism. We obtain a unified description of heating in current carrying molecular junctions as well as the electron and phonon contributions to the…
The specific heat of the Coulomb glass is studied by numerical simulations. Both the lattice model with various strengths of disorder, and the random-position model are considered for the one- to three-dimensional cases. In order to extend…
This study compares different methods to predict the simultaneous effects of conductive and radiative heat transfer in a Polymethylmethacrylate (PMMA) sample. PMMA is a kind of polymer utilized in various sensors and actuator devices.…
We estimate a statistical model to predict the superconducting critical temperature based on the features extracted from the superconductor's chemical formula. The statistical model gives reasonable out-of-sample predictions: $\pm 9.5$ K…
We study heat transport in quantum spin systems analytically and numerically. First, we demonstrate that heat current through a two-level quantum spin system can be modulated from zero to a finite value by tuning a magnetic field. Second,…
Finite-temperature calculations are relevant for rationalizing material properties yet they are computationally expensive because large system sizes or long simulation times are typically required. Circumventing the need for performing many…
The modeling and simulation of heat source trajectories through phase-change materials is a relevant problem both for space exploration and for terrestrial climate research, among other fields. In space, the DLR and NASA are both interested…
Among the three heat conduction modes, the ballistic propagation is the most difficult to model. In the present paper, we discuss its physical interpretations and showing different alternatives to its modeling. We highlight two of them: a…
Size-dependence of energy transport and the effects of reduced dimensionality on transport coefficients are of key importance for understanding nonequilibrium properties of matter on the nanoscale. Here, we perform nonequilibrium and…
We propose a thermodynamically consistent general-purpose model describing diffusion of a solute or a fluid in a solid undergoing possible phase transformations and damage, beside possible visco-inelastic processes. Also heat…
A thermal simulation methodology is developed for interconnects enabled by a data-driven learning algorithm accounting for variations of material properties, heat sources and boundary conditions (BCs). The methodology is based on the…
In this paper mathematical models are formulated in order to simulate heat production and corresponding temperature changes which accompany the propagation of an axon potential. Based on earlier experimental results, several models are…
We consider the problem of heat diffusion in branched systems and networks on the basis of a model described in terms of heat equation on metric graphs. Using the explicit analytical solutions of the latter, evolution of the temperature…