Related papers: An optimization problem in heat conduction with mi…
The heat capacity $\mathcal{C}$ of a given probe is a fundamental quantity that determines, among other properties, the maximum precision in temperature estimation. In turn, $\mathcal{C}$ is limited by a quadratic scaling with the number of…
The energetic optimization problem, e.g., searching for the optimal switch- ing protocol of certain system parameters to minimize the input work, has been extensively studied by stochastic thermodynamics. In current work, we study this…
We study the optimal control of district heating networks using a reduced order model based on a system theoretic description close to the underlying Euler equations. In the presented scenarios, the central task is to limit the maximal…
This paper deals with optimal control problems of integral equations, with initial-final and running state constraints. The order of a running state constraint is defined in the setting of integral dynamics, and we work here with…
This paper develops a mathematical framework that aims to control the temperature and rotational speed in the activation process of a gas turbine in an optimal way. These controls influence the deformation and the stress in the component…
In this paper, we study an insulation problem that seeks the optimal distribution of a fixed amount $m>0$ of insulating material coating an insulated boundary $\Gamma_I\subseteq \partial\Omega$ of a thermally conducting body…
Motivated by the search for sharp bounds on turbulent heat transfer as well as the design of optimal heat exchangers, we consider incompressible flows that most efficiently cool an internally heated disc. Heat enters via a distributed…
A methodology is presented for bounding all higher moments of the local hydrostatic stress field inside random two phase linear thermoelastic media undergoing macroscopic thermomechanical loading. The method also provides a lower bound on…
In this paper, we study optimal actuator location of the minimum norm controls for a multi-dimensional heat equation with control defined in the space $L^p(0,T;L^2(\Omega))$. The actuator domain $\omega$ is quite general in the sense that…
Linear programming is used as a standard tool for optimising unit commitment or power flows in energy supply systems. For heat supply systems, however, it faces a relevant limitation: For them, energy yield depends on the output…
This paper considers the initial-boundary value problem for the heat equation with a dynamic type boundary condition. Under some regularity, consistency and orthogonality conditions, the existence, uniqueness and continuous dependence upon…
In this paper, we consider a class of optimal control problems governed by state-equations of Kobayashi--Warren--Carter type. The control is given by physical temperature. The focus is on problems in dimensions less than equal to 4. The…
Optimization plays a significant role in many areas of science and technology. Most of the industrial optimization problems have inordinately complex structures that render finding their global minima a daunting task. Therefore, designing…
The context of the present paper is stochastic thermodynamics - an approach to nonequilibrium thermodynamics rooted within the broader framework of stochastic control. In contrast to the classical paradigm of Carnot engines, we herein…
This thesis is devoted to studying two tasks: refrigeration and the creation of correlations. In the refrigeration part, two different paradigms of cooling, namely coherent and incoherent, are defined. The connection that these paradigms…
We consider the optimal control of singular nonlinear partial differential equation which is the distributional formulation of the multiphase Stefan type free boundary problem for the general second order parabolic equation. Boundary heat…
Thermodynamic transport phenomena in the system consisting of many hard-disks confined in a circular tube with a temperature difference are discussed. Here, temperatures on parts of the walls of the tube are imposed by stochastic boundary…
We generalize a recent method for computing optimal 2D convection cooling flows in a horizontal layer to a wide range of geometries, including those relevant for technological applications. We write the problem in a conformal pair of…
We study the boundary regularity for the normalised $\infty$-heat equation $u_t = \Delta_{\infty}^Nu$ in arbitrary domains. Perron's Method is used for constructing solutions. We characterize regular boundary points with barrier functions,…
Inverse problems associated with designing cylindrical thermal cloaking shells are studied. Using the optimization method these inverse problems are reduced to corresponding control problems in which the diagonal components of diagonal in…