Related papers: Nonlinear heat conduction equations with memory: p…
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,…
We formulate a geometric framework that allows to study momentum and energy transport in non-relativistic systems. It amounts to coupling of the non-relativistic system to the Newton-Cartan geometry with torsion. The approach generalizes…
We unify two paradigmatic mesoscopic mechanisms for the emergence of nonextensive statistics, namely the multiplicative noise mechanism leading to a {\it linear} Fokker-Planck (FP) equation with {\it inhomogenous} diffusion coefficient, and…
We consider the Allen-Cahn equations with memory (a partial integro-differential convolution equation). The prototype kernels are exponentially decreasing functions of time and they reduce the integrodifferential equation to a hyperbolic…
Thermal transport at short length and time scales inherently constitutes a nonlocal relation between heat flux and temperature gradient, but this is rarely addressed explicitly. Here, we present a formalism that enables detailed…
We propose the concept of global temperature for spatially non-uniform heat conduction systems. With this novel quantity, we present an extended framework of thermodynamics for the whole system such that the fundamental relation of…
We use a relationship between response and correlation function in nonequilibrium systems to establish a connection between the heat production and the deviations from the equilibrium fluctuation-dissipation theorem. This scheme extends the…
We present a generalization of AEMD approach, routinely applied to estimate thermal conductivity, to the more general case in which Soret and Dufour effects determine a coupled heat-mass transfer. We show that, by starting from…
Planck's law of thermal radiation depends on the temperature, $T$, and the emissivity, $\epsilon$, of a body, where emissivity is the coupling of heat to radiation that depends on both phonon-electron nonradiative interactions and…
We study the large-time behavior in all $L^p$ norms of solutions to an inhomogeneous nonlocal heat equation in $\mathbb{R}^N$ involving a Caputo $\alpha$-time derivative and a power $\beta$ of the Laplacian when the dimension is large, $N>…
An exact description of the statistical motion of active particles in three dimension is presented in the framework of a generalized diffusion equation. Such a generalization contemplates a non-local, in time and space, connecting (memory)…
We present a general nonequilibrium Green's function formalism for modeling heat transfer in systems characterized by linear response that establishes the formal algebraic relationships between phonon and radiative conduction, and reveals…
Combining analytical and numerical methods, we study within the framework of the homogeneous non-linear Boltzmann equation, a broad class of models relevant for the dynamics of dissipative fluids, including granular gases. We use the new…
As we typically teach in an introductory mechanics course, choosing a "good" reference frame with convenient axes may present a major simplification to a problem. Additionally, knowing some conserved quantities provides an extremely…
Understanding ballistic phonon transport effects in transient thermoreflectance experiments and explaining the observed deviations from classical theory remains a challenge. Diffusion equations are simple and computationally efficient but…
In this note we analyse the propagation of a small density perturbation in a one-dimensional compressible fluid by means of fractional calculus modelling, replacing thus the ordinary time derivative with the Caputo fractional derivative in…
We derive an analytical expression for the intermediate scattering function of a particle on a flat surface obeying the Generalised Langevin Equation, with exponential memory friction. Numerical simulations based on an extended phase space…
Standard Navier--Stokes--Fourier theory and Maxwellian-based Grad 13-moment closures yield no independent pressure-gradient driving of the conductive heat flux in an isothermal, single-component gas in the hydrodynamic (small-Knudsen)…
Standard diffusion equation is based on Brownian motion of the dispersing species without considering persistence in the movement of the individuals. This description allows for the instantaneous spreading of the transported species over an…
We establish a unified fluctuation-response relation for Langevin dynamics. By exploiting the common mathematical structures underlying fluctuations and responses of empirical density and current, we derive a unified identity that…