Related papers: Homotopy perturbation method: when infinity equals…
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…
A new analogy between optical propagation and heat diffusion in heterogeneous anisotropic media has been proposed recently [S. Guenneau, C. Amra, and D. Veynante, Optics Express Vol. 20, 8207-8218 (2012)]. A detailed derivation of this…
We propose a numerical approach for solving conjugate heat transfer problems using the finite volume method. This approach combines a semi-implicit scheme for fluid flow, governed by the incompressible Navier-Stokes equations, with an…
A number of modern learning tasks involve estimation from heterogeneous information sources. This includes classification with labeled and unlabeled data as well as other problems with analogous structure such as competitive (game…
This paper is devoted to deal with some mathematical and numerical aspects of the radiative integral transfer equations. First, the properties of the raidative integral operators are analyzed. Based on these results, the existence and…
In this paper we establish an observability inequality for the heat equation with bounded potentials on the whole space. Roughly speaking, such a kind of inequality says that the total energy of solutions can be controlled by the energy…
In the present Letter we present an analytical and numerical solution of the self-consistent mode-coupling equations for the problem of heat conductivity in one-dimensional systems. Such a solution leads us to propose a different scenario…
We consider the ultrahyperbolic equation in the Euclidean space. The behavior at the infinity of a certain class of solutions is studied. We examine the issue of existence of solutions to the scattering problem: for a given asymptotics at…
Raising the temperature of a material enhances the thermal motion of particles. Such an increase in thermal energy commonly leads to the melting of a solid into a fluid and eventually vaporises the liquid into a gaseous phase of matter.…
A perturbation theory modification of the Flory-Huggins polymer solution theory is presented. The proposed perturbation equation utilizes the results by Tukur et al [J. Chem. Phys. 110 (7), 3463, 1999] for hard-sphere binary mixture at…
Heat rectifiers would facilitate energy management operations such as cooling, or energy harvesting, but devices of practical interest are still missing. Understanding heat rectification at a fundamental level is key to help us find or…
We discuss a homological method for transferring algebra structures on complexes along suitably nice homotopy equivalences, including those obtained after an application of the Perturbation Lemma. We study the implications for the Homotopy…
We summarise three applications of the obstacle problem to membrane contact, elastoplastic torsion and cavitation modelling, and show how the resulting models can be solved using mixed finite elements. It is challenging to construct fixed…
In this note we give a complete obstruction for two homotopic embeddings of a 2-sphere into a 5-manifold to be isotopic. The results are new even though the methods are classical, the main tool being the elimination of double points via a…
We develop a homotopical variant of the classic notion of an algebraic theory as a tool for producing deformations of homotopy theories. From this, we extract a framework for constructing and reasoning with obstruction theories and spectral…
Integral equation based numerical methods are directly applicable to homogeneous elliptic PDEs, and offer the ability to solve these with high accuracy and speed on complex domains. In this paper, extensions to problems with inhomogeneous…
We consider the problem of defining the integers in Homotopy Type Theory (HoTT). We can define the type of integers as signed natural numbers (i.e., using a coproduct), but its induction principle is very inconvenient to work with, since it…
Heat can generally transfer via thermal conduction, thermal radiation, and thermal convection. All the existing theories of transformation thermotics and optics can treat thermal conduction and thermal radiation, respectively.…
Controlled heat transfer and thermal rectification in a system of two coupled cavities connected to thermal reservoirs are discussed. Embedding a dispersively interacting two-level atom in one of the cavities allows switching from a…
Solution of the Dyson equation for the small-gap systems can be plagued by large non-converging iterations. In addition to the convergence issues, due to a high non-linearity, the Dyson equation may have multiple solutions. We apply the…