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Effects of collective modes on thermoelectric properties of a charge density system is studied. We derive the temperature dependence of thermoelectric power and thermal conductivity by applying the linear response theory to Fr\"ohlich…
We present a theoretical study of radiative heat transport in nonlinear solid-state quantum circuits. We give a detailed account of heat rectification effects, i.e. the asymmetry of heat current with respect to a reversal of the thermal…
We analyze the asymptotic behavior corresponding to the arbitrary high conductivity of the heat in the thermoelectric devices. This work deals with a steady-state multidimensional thermistor problem, considering the Joule effect and both…
One of the key objectives in investigating small stochastic systems is the development of micrometer-sized engines and the understanding of their thermodynamics. However, the primary mathematical tool used for this purpose, the overdamped…
A framework for studying the effect of the coupling to the heat bath in models exhibiting anomalous heat conduction is described. The framework is applied to the harmonic chain with momentum exchange model where the non-trivial temperature…
We propose an approach to the problem of low but finite temperature dynamical correlation functions in integrable one-dimensional models with a spectral gap. The approach is based on the analysis of the leading singularities of the operator…
Thermodynamic parameters such as temperature and pressure can be defined from the statistical behavior of a system. Therefore, thermal fluctuation is an inseparable characteristic of these parameters which eventually finds its way into…
Solid-state cooling based on i-caloric effects may be an alternative to conventional vapor-compression refrigeration systems. The adiabatic temperature change ($\Delta T_{S}$) is one of the parameters that characterize the i-caloric…
A non-isothermal phase field model that captures both displacive and diffusive phase transformations in a unified framework is presented. The model is developed in a formal thermodynamic setting, which provides guidance on admissible…
We consider the problem of recovering the initial condition in the one-dimensional one-phase Stefan problem for the heat equation from the knowledge of the position of the melting point. We first recall some properties of the free boundary…
Many seemingly different macroscopic systems (magnets, ferroelectrics, CDW, vortices,..) can be described as generic disordered elastic systems. Understanding their static and dynamics thus poses challenging problems both from the point of…
Predicting solid-solid phase transitions remains a long-standing challenge in materials science. Solid-solid transformations underpin a wide range of functional properties critical to energy conversion, information storage, and thermal…
Many metal manufacturing processes involve phase change phenomena, which include melting, boiling, and vaporization. These phenomena often occur concurrently. A prototypical 1D model for understanding the phase change phenomena is the…
The behavior of thermal fluctuations of a superconducting order parameter with extended $ s $ and chiral $ d + id $ symmetry is investigated. The study is carried out on a triangular lattice within the framework of the quasi-two-dimensional…
Recent experimental results: (i) the measurement of the $T \ln T$ specific heat in cuprates and the earlier such results in some heavy fermion compounds, (ii) the measurement of the single-particle scattering rates, (iii) the density…
This work deals with the problem of determining a non-homogeneous heat conductivity profile in a steady-state heat conduction boundary-value problem with mixed Dirichlet-Neumann boundary conditions over a bounded domain in $\mathbb{R}^n$,…
We consider a class of singular perturbations to the stochastic heat equation or semilinear variations thereof. The interesting feature of these perturbations is that, as the small parameter epsilon tends to zero, their solutions converge…
We consider the identification of nonlinear heat conduction laws in stationary and instationary heat transfer problems. Only a single additional measurement of the temperature on a curve on the boundary is required to determine the unknown…
Thermal conduction force plays a crucial role in manipulating the local thermal conductivity of crystals. However, due to the diffusive nature of thermal conduction, investigating the force effect is challenging. Recently, researchers have…
Nonlinear thermoelastic systems play a crucial role in understanding thermal conductivity, stresses, elasticity, and temperature interactions. This research focuses on finding solutions to these systems in their fractional forms, which is a…