Related papers: An optimization problem in heat conduction with mi…
Inverse Stefan problem arising in modeling of laser ablation of biomedical tissues is analyzed, where information on the coefficients, heat flux on the fixed boundary, and density of heat sources are missing and must be found along with the…
We consider shape optimization problems for elasticity systems in architecture. A typical question in this context is to identify a structure of maximal stability close to an initially proposed one. We show the existence of such an…
In traditional thermodynamics the Carnot cycle yields the ideal performance bound of heat engines and refrigerators. We propose and analyze a minimal model of a heat machine that can play a similar role in quantum regimes. The minimal model…
We study anomalous transport in a one-dimensional system with two conserved quantities in presence of thermal baths. In this system we derive exact expressions of the temperature profile and the two point correlations in steady state as…
In this paper, we obtain some regularities of the free boundary in optimal transportation with the quadratic cost. Our first result is about the $C^{1,\alpha}$ regularity of the free boundary for optimal partial transport between convex…
It is well known that thermal insulation is a leading strategy for reducing energy consumption associated to heating or cooling processes in buildings. Nevertheless, building insulation can generate high expenditures so that the selection…
In a series of papers, we will develop systematically the basic spectral theory of (self-adjoint) boundary value problems for operators of Dirac type. We begin in this paper with the characterization of (self-adjoint) boundary conditions…
In this paper, we summarize the historical development of finite-time thermodynamics and review the current state of research over the past two decades in this field, focusing on fundamental constraints of finite-time thermodynamic cycles,…
This article is concerned with the solution of a time-dependent shape identification problem. Specifically we consider the heat equation in a domain, which contains a time-dependent inclusion of zero temperature. The objective is to detect…
We study dynamic cooling, where an externally driven two-level system is cooled via reservoir, a quantum system with initial canonical equilibrium state. We obtain explicitly the minimal possible temperature $T_{\rm min}>0$ reachable for…
This paper is devoted to the homogenization of the heat conduction equation, with a homogeneous Dirichlet boundary condition, having a periodically oscillating thermal conductivity and a vanishing volumetric heat capacity. A homogenization…
We present a first-principles study of heat conduction in a class of models which exhibit a new multi-step local thermalization mechanism which gives rise to Fourier's law. Local thermalization in our models occurs as the result of binary…
This paper deals with an optimal control problem related to a phase field system of Caginalp type with a dynamic boundary condition for the temperature. The control placed in the dynamic boundary condition acts on a part of the boundary.…
We study the parabolic free boundary problem of obstacle type $$ \lap u-\frac{\partial u}{\partial t}= f\chi_{{u\ne 0}}. $$ Under the condition that $f=Hv$ for some function $v$ with bounded second order spatial derivatives and bounded…
A finite element code for heat conduction, together with an adjoint solver and a suite of optimization tools was applied for the solution of Calderon's problem. One of the questions whose answer was sought was whether the solution to these…
This paper revisits the problem of heat conduction in relativistic fluids, associated with issues concerning both stability and causality. It has long been known that the problem requires information involving second order deviations from…
The stable and efficient operation of the transmission network is fundamental to the power system's ability to deliver electricity reliably and cheaply. As average temperatures continue to rise, the ability of the transmission network to…
By tailoring the geometry of the upper boundary in turbulent Rayleigh-B\'enard convection we manipulate the boundary layer -- interior flow interaction, and examine the heat transport using the Lattice Boltzmann method. For fixed amplitude…
We optimize the operation of a fuel cell hybrid train using convex optimization. The main objective is to minimize hydrogen fuel consumption for a target journey time while considering battery thermal constraints. The state trajectories:…
We study the problem of optimizing released heat or dissipated work in stochastic thermodynamics. In the overdamped limit these functionals have singular solutions, previously interpreted as protocol jumps. We show that a regularization,…