Related papers: Two optimization problems in thermal insulation
An optimal control problem for the continuity equation is considered. The aim of a "controller" is to maximize the total mass within a target set at a given time moment. The existence of optimal controls is established. For a particular…
Inverse problems of electric conductivity are studied that arise in the design of spherical shielding or cloaking shells and other functional devices used to control DC electric fields. The shells are considered consisting of a finite…
We calculate the thermal noise in half-infinite mirrors containing a layer of arbitrary thickness and depth made of excessively lossy material but with the same elastic material properties as the substrate. For the special case of a thin…
Under study is the new class of geometrical extremal problems in which it is required to achieve the best result in the presence of conflicting goals; e.g., given the surface area of a convex body $\mathfrak x$, we try to maximize the…
The authors use two insulator layers in thermotunnel refrigerator to modify the shape of the tunneling barrier so that electrons with high kinetic energy pass it with increased probability. Theoretical analysis show that the overall…
In this paper, we design real-time decentralized and distributed control schemes for Heating Ventilation and Air Conditioning (HVAC) systems in energy efficient buildings. The control schemes balance user comfort and energy saving, and are…
In this paper, we address energy management for heating, ventilation, and air-conditioning (HVAC) systems in buildings, and present a novel combined optimization and control approach. We first formulate a thermal dynamics and an associated…
A support structure is required to successfully create structural parts in the powder bed fusion process for additive manufacturing. In this study, we present the topology optimization of a support structure that improves the heat…
This paper addresses optimal design problems governed by multi-state stationary diffusion equations, aiming at the simultaneous optimization of the domain shape and the distribution of two isotropic materials in prescribed proportions.…
The isoperimetric problem asks for the maximum area of a region of given perimeter. It is natural to consider other measurements of a region, such as the diameter and width, and ask for the extreme value of one when another is fixed. The…
In recent years, due to the unnecessary wastage of electrical energy in residential buildings, the requirement of energy optimization and user comfort has gained vital importance. In the literature, various techniques have been proposed…
Given a system with a finite heat capacity and a heat reservoir, and two values of initial temperatures, $T_+$ and $T_- (< T_+)$, we enquire, in which case the optimal work extraction is larger: when the reservoir is an infinite source at…
Optimal percolation is the problem of finding the minimal set of nodes such that if the members of this set are removed from a network, the network is fragmented into non-extensive disconnected clusters. The solution of the optimal…
The typical goal of surface remeshing consists in finding a mesh that is (1) geometrically faithful to the original geometry, (2) as coarse as possible to obtain a low-complexity representation and (3) free of bad elements that would hamper…
One of the ways natural and synthetic systems regulate temperature is via circulating fluids through vasculatures embedded within their bodies. Because of the flexibility and availability of proven fabrication techniques, vascular-based…
This article is devoted to the study of spectral optimisation for inhomogeneous plates. In particular, we optimise the first eigenvalue of a vibrating plate with respect to its thickness and/or density. Our result is threefold. First, we…
The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but…
Radiative coolers that can passively cool objects by radiating heat into the outer space have recently received much attention. However, the ultimate limits of their performance as well as their ideal spectral design are still unknown. We…
We study the Newton-like problem of minimal resistance for a two-dimensional body moving with constant velocity in a homogeneous rarefied medium of moving particles. The distribution of the particles over velocities is centrally symmetric.…
We study the double bubble problem where the perimeter is taken with respect to the hexagonal norm, i.e. the norm whose unit circle in $\mathbb{R}^2$ is the regular hexagon. We provide an elementary proof for the existence of minimizing…