Related papers: Shape optimization of a thermal insulation problem
We consider Cheeger-like shape optimization problems of the form $$\min\big\{|\Omega|^\alpha J(\Omega) : \Omega\subset D\big\}$$ where $D$ is a given bounded domain and $\alpha$ is above the natural scaling. We show the existence of a…
We discuss the initial boundary value problem for a heat equation in a domain surrounded by a layer. The main features of this problem are twofold: on one hand, the layer is thin compared to the scale of the domain, and on the other hand,…
We prove that among all doubly connected domains of $\R^n$ bounded by two spheres of given radii, $Z(t)$, the trace of the heat kernel with Dirichlet boundary conditions, achieves its minimum when the spheres are concentric (i.e., for the…
The heat transfer model for a one-dimensional supercooled melt during the final stage of solidification is considered. The Stefan problem for the determination of the temperature distribution is solved under the condition that (i) the…
We formalize and prove the extension to finite temperature of a class of quantum phase transitions, acting as condensations in the space of states, recently introduced and discussed at zero temperature~(Ostilli and Presilla 2021 \textit{J.…
We establish existence of global-in-time weak solutions to the one dimensional, compressible Navier-Stokes system for a viscous and heat conducting ideal polytropic gas (pressure $p=K\theta/\tau$, internal energy $e=c_v \theta$), when the…
We consider three-dimensional models for rate-independent processes describing materials undergoing phase transformations with heat transfer. The problem is formulated within the framework of generalized standard solids by the coupling 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…
Internally heated convection involves the transfer of heat by fluid motion between a distribution of sources and sinks. Focusing on the balanced case where the total heat added by the sources matches the heat taken away by the sinks, we…
This paper extends the nonsmooth Relaxed Variational Approach (RVA) to topology optimization, proposed by the authors in a preceding work, to the solution of thermal optimization problems. First, the RVA topology optimization method is…
In this paper, a one-phase Stefan-type problem for a semi-infinite material which has as its main feature a variable latent heat that depends on the power of the position and the velocity of the moving boundary is studied. Exact solutions…
This paper investigates the numerical modeling of a time-dependent heat transmission problem by the convolution quadrature boundary element method. It introduces the latest theoretical development into the error analysis of the numerical…
We compute steady planar incompressible flows and wall shapes that maximize the rate of heat transfer (Nu) between and hot and cold walls, for a given rate of viscous dissipation by the flow (Pe$^2$). In the case of no flow, we show…
In this paper, we investigate an optimal design problem motivated by some issues arising in population dynamics. In a nutshell, we aim at determining the optimal shape of a region occupied by resources for maximizing the survival ability of…
Experimental results for condensation in compact heat exchangers show that the heat transfer due to condensation is significantly better compared to classical heat exchangers, especially when using R134a instead of water as the refrigerant.…
In this paper we consider a one-dimensional one-phase Stefan problem corresponding to the solidification process of a semi-infinite material with a convective boundary condition at the fixed face. The exact solution of this problem,…
A central problem in discrete geometry, known as Hadwiger's covering problem, asks what the smallest natural number $N\left(n\right)$ is such that every convex body in ${\mathbb R}^{n}$ can be covered by a union of the interiors of at most…
In this paper, we generalize the notion of relative $p$-capacity of $K$ with respect to $\Omega$, by replacing the Dirichlet boundary condition with a Robin one. We show that, under volume constraints, our notion of $p$-capacity is minimal…
This article revolves around shape and topology optimization, in the applicative context where the objective and constraint functionals depend on the solution to a physical boundary value problem posed on the optimized domain. We introduce…
Heating induced by the noise postulated in wave function collapse models leads to a lower bound to the temperature of solid objects. For the noise parameter values $\lambda ={\rm coupling~strength}\sim 10^{-8} {\rm s}^{-1}$ and $r_C ={\rm…