Related papers: Heat content determines planar triangles
We consider a nonlinear heat equation with a gradient term. We construct a blow-up solution for this equation with a prescribed blow-up profile. For that, we translate the question in selfsimilar variables and reduce the problem to a finite…
We study the interplay of conductive and radiative heat transfer (RHT) in planar geometries and predict that temperature gradients induced by radiation can play a significant role on the behavior of RHT with respect to gap sizes, depending…
We use a variational principle to prove an existence and uniqueness theorem for planar weighted Delaunay triangulations (with non-intersecting site-circles) with prescribed combinatorial type and circle intersection angles. Such weighted…
Thermal convection in fluid layers heated from below are usually realized experimentally as well as treated theoretically with fixed boundaries on which conditions for the temperature and the velocity field are prescribed. The thermal and…
In this paper we investigate the diffusion of the thermal pulse in Planck Gas. We show that the Fourier diffusion equation gives the speed of diffusion, v > c and breaks the causality of the thermal processes in Planck gas .For hyperbolic…
According to conventional wisdom, a system placed in an environment with a different temperature tends to relax to the temperature of the latter, mediated by the flows of heat and/or matter that are set solely by the temperature difference.…
Multidimensional integral transformations with non-separated variables for problems with discontinuous coefficients are constructed in this work. The coefficient discontinuities focused on the of parallel hyperplanes. In this work explicit…
We show in detail how the presence of a heat bath of photons effectively gives charged particles in the final state of a decay process a temperature-dependent mass, and changes the effective strength of the force responsible for the decay.…
In this paper we consider $\beta[0; s]$, Brownian motion of time length $s > 0$, in $m$-dimensional Euclidean space $\mathbb R^m$ and on the $m$-dimensional torus $\mathbb T^m$. We compute the expectation of (i) the heat content at time $t$…
We give a unified and optimized proof of the sharp bounds for the Jacobi heat kernel, which were obtained gradually in several papers in recent years. We lay particular emphasis on tracing and estimating all constants appearing throughout…
In this paper we consider the homogenization of a time-dependent heat conduction problem on a planar one-dimensional periodic structure. On the edges of a graph the one-dimensional heat equation is posed, while the Kirchhoff junction…
Motivated by recent experimental observations, we consider a steady-state Prandtl-Blasius boundary layer flow with polymers above a slightly heated horizontal plate and study how the heat transport might be affected by the polymers. We…
A quantitative description of the properties of hot nuclear matter will be needed for the interpretation of the available and forthcoming astrophysical data, providing information on the post merger phase of a neutron star coalescence. We…
In this write-up, I list the key ingredients for formulating the vector manifestation in hot matter together with several predictions made so far.
We study numerically the thermal conductivity in several different one dimensional chains. We show that the phonon-lattice interaction is the main ingredient of the Fourier heat law. Our argument provides a rather satisfactory explanation…
We show that, in general, any complex weakly nonlinear highly multimode system can reach thermodynamic equilibrium that is characterized by a unique temperature and chemical potential. The conditions leading to either positive or negative…
Let $(M, g)$ be a smooth n-dimensional Riemannian manifold for $n\ge 2$. Consider the conformal perturbation $\tilde{g}=h g$ where $h$ is a smooth bounded positive function on $M$. Denote by $\tilde{p}_t(x,y)$ the heat kernel of manifolds…
Plasmonic structures are renowned for their capability to efficiently convert light into heat at the nanoscale. However, despite the possibility to generate deep sub-wavelength electromagnetic hot spots, the formation of extremely localized…
A self-consistent approach to nonequilibrium radiation temperature is introduced using the distribution of the energy over states. We begin rigorously with ensembles of Hilbert spaces and end with practical examples based mainly on the far…
This paper explores the concept of near-cloaking in the context of time-dependent heat propagation. We show that after the lapse of a certain threshold time instance, the boundary measurements for the homogeneous heat equation are close to…