Related papers: An optimization problem in heat conduction with mi…
Situations where a spontaneous process of energy or matter transfer is enhanced by an external device are widespread in nature (human sweating system, enzyme catalysis, facilitated diffusion across bio-membranes, industrial heat…
In this paper, optimal time control problems and optimal target control problems are studied for the approximately null-controllable heat equations. Compared with the existed results on these problems, the boundary of control variables are…
In this paper we show how to efficiently achieve thermal cloaking from a computational standpoint in several virtual scenarios by controlling a distribution of active heat sources. We frame this problem in the setting of PDE-constrained…
Optimization analyses of thermoelectric generators operation is of importance both for practical applications and theoretical considerations. Depending on the desired goal, two different strategies are possible to achieve high performance:…
In this paper, we present first-order accurate numerical methods for solution of the heat equation with uncertain temperature-dependent thermal conductivity. Each algorithm yields a shared coefficient matrix for the ensemble set improving…
We study the space of optimal schedules for a heat pump with thermal energy storage used in heating a residential building. We model the heating system as a Mixed Integer Linear Program with the objective to minimise the cost of heating. We…
We prove optimal regularity and derive several geometric properties for solutions of a free boundary problem with fractional diffusion. Additionally, we deduce local $C^{1,\alpha}$ regularity results for the corresponding interior and…
From the final and interior temperature measurements identifying the source term with initial temperature simultaneously is an inverse heat conduction problem which is a kind of ill-posed. The optimal control framework has been found to be…
In this paper, we study the approximate controllability for the stochastic heat equation over measurable sets, and the optimal actuator location of the minimum norm controls. We formulate a relaxed optimization problem for both actuator…
In high-contrast composites, the electric (or stress) field may exhibit significant amplification in the narrow region between inclusions. The behavior of the solution depends on the distance $\epsilon$ between the inclusions, which tends…
The problem of heat conduction on networks of multiply connected rods is solved by providing an explicit solution of the one-dimensional heat equation in each domain. The size and connectivity of the rods is known, but neither temperature…
We study bounds on ratios of fluctuations in steady-state time-reversal heat engines controlled by multi affinities. In the linear response regime, we prove that the relative fluctuations (precision) of the output current (power) is always…
A holonomic constraint is used to enforce a constant instantaneous configurational temperature on an equilibrium system. Three sets of equations of motion are obtained, differing according to the way in which the holonomic constraint is…
Method-of-lines discretizations are demanding test problems for stiff integration methods. However, for PDE problems with known analytic solution the presence of space discretization errors or the need to use codes to compute reference…
Metastability is a formidable challenge to Markov chain Monte Carlo methods. In this paper we present methods for algorithm design to meet this challenge. The design problem we consider is temperature selection for the infinite swapping…
We study solutions to a variational equation that models heat control on the boundary. This problem can be thought of as the two phase parabolic Signorini problem. We show that when the solution has a sign on the boundary, the study of the…
In this paper we consider the minimization of a continuous function that is potentially not differentiable or not twice differentiable on the boundary of the feasible region. By exploiting an interior point technique, we present first- and…
In this note, we extend the regularity theory for monotone measure-preserving maps, also known as optimal transports for the quadratic cost optimal transport problem, to the case when the support of the target measure is an arbitrary convex…
In this article we study optimization problems ruled by $\alpha$-fractional diffusion operators with volume constraints. By means of penalization techniques we prove existence of solutions. We also show that every solution is locally of…
In this article a topology optimization method is developed, which is aware of material uncertainties. The uncertainties are handled in a worst-case sense, i.e. the worst possible material distribution over a given uncertainty set is taken…