相关论文: Identification of nonlinear heat conduction laws
Understanding heat transport in one-dimensional systems remains a major challenge in theoretical physics, both from the quantum as well as from the classical point of view. In fact, steady states of one-dimensional systems are commonly…
By means of a recent Birkhoff-Kellogg type theorem set in affine cones, we discuss the solvability of a parameter-dependent thermostat problem subject to deviated arguments. We illustrate in a specific example the constants that occur in…
A class of inverse problems for a heat equation with involution perturbation is considered using four different boundary conditions, namely, Dirichlet, Neumann, periodic and anti-periodic boundary conditions. Proved theorems on existence…
We study thermal fluctuation corrections to charge and heat conductivity in systems with locally conserved energy and charge, but without locally conserved momentum. Thermal fluctuations may naturally lead to a lower bound on diffusion…
We analyze some exact and approximate solutions to nonlinear equations for heat transfer models. We prove that recent results derived from a method based on Lie algebras are either trivial or wrong. We test a simple analytical expression…
We consider a boundary value problem (BVP) modelling one-dimensional heat-conduction with radiation, which is derived from the Stefan-Boltzmann law. The problem strongly depends on the parameters, making difficult to estimate the solution.…
Recently a novel concise representation of the probability distribution of heat conducting nonequilibrium steady states was derived. The representation is valid to the second order in the ``degree of nonequilibrium'', and has a very…
We show how the local temperature of out-of-equilibrium, quantum electron systems can be consistently defined with the help of an external voltage and temperature probe. We determine sufficient conditions under which the temperature…
We consider unsteady ballistic heat transport in a semi-infinite Hooke chain with a free end and an arbitrary heat source. An analytical description of the evolution of the kinetic temperature is proposed in both discrete (exact) and…
An asymptotic limit of a class of Cahn-Hilliard systems is investigated to obtain a general nonlinear diffusion equation. The target diffusion equation may reproduce a number of well-known model equations: Stefan problem, porous media…
We present a new method for learning control law that stabilizes an unknown nonlinear dynamical system at an equilibrium point. We formulate a system identification task in a self-supervised learning setting that jointly learns a controller…
In the present Letter we present an analytical and numerical solution of the self-consistent mode-coupling equations for the problem of heat conductivity in one-dimensional systems. Such a solution leads us to propose a different scenario…
Numerical methods are developed to solve the problem of abnormal changes of current (conductivity) in polymer composite films which may be used as current, pressure or temperature sensors. General nonlinear model includes the heat equation,…
In the paper, we investigate the nonlinear thermoelasticity model in two- and three-dimensional convex and bounded domains. We propose new boundary conditions for the displacement. These conditions are not usual in thermoelasticity.…
The existence of global weak solutions to a parabolic energy-transport system in a bounded domain with no-flux boundary conditions is proved. The model can be derived in the diffusion limit from a kinetic equation with a linear collision…
The paper investigates nonlinear control laws obtained from linear one by two types of substitutions using odd functions. The first substitution consists in passing each component of the state vector through a nonlinear function, the second…
We study in momentum-conserving systems, how nonintegrable dynamics may affect thermal transport properties. As illustrating examples, two one-dimensional (1D) diatomic chains, representing 1D fluids and lattices, respectively, are…
We derive a Thermodynamic Uncertainty Relation bounding the mean squared displacement of a Gaussian process with memory, driven out of equilibrium by unbalanced thermal baths and/or by external forces. Our bound is tighter with respect to…
In the real world, one almost never knows the parameters of a thermodynamic process to infinite precision. Reflecting this, here we investigate how to extend stochastic thermodynamics to systems with uncertain parameters, including…
We report a model-based method for quantifying heat flow and storage in thermal systems using data from multiple thermal sensors. This approach avoids stringent requirements on the system geometry and sensor positions and enables…