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With a study of bulk GaAs and GaP, we report detailed infrared spectra and their temperature dependence from first principles. Fine features and low-temperature trends in the predicted response are confirmed by experiment. The spectra are…

We derive a nice representation for point symmetry transformations of the (1+1)-dimensional linear heat equation and properly interpret them. This allows us to prove that the pseudogroup of these transformations has exactly two connected…

Nuclear response theory beyond the one-loop approximation is formulated for the case of finite temperature. For this purpose, the time blocking approximation to the time-dependent part of the in-medium nucleon-nucleon interaction amplitude…

We propose a prescription based on the Fokker-Planck equation in the Stratonovich approach, with the diffusion coefficient dependent on temporal and spatial coordinates, for describing heat conduction by phonons in small structures. This…

Short distance structure of spacetime may show up in the form of high freqency dispersion. Although such dispersion is not locally Lorentz invariant, we show in a scalar field model how it can nevertheless be incorporated into a generally…

The inverse spectral transform for the Zakharov-Shabat equation on the semi-line is reconsidered as a Hilbert problem. The boundary data induce an essential singularity at large k to one of the basic solutions. Then solving the inverse…

The Thomas - Fermi equation describing the screening of the Coulomb potential inside heavy neutral atoms is reconsidered. An accurate representation for its numerical solution was obtained by means of the variational principle. The proposed…

Some exact high temperature expansions are derived using a temperature inversion symmetry of the internal energy for conformal scalars and spinors on the Einstein Universe.

In this paper, we study a class of explicit positive solutions to $G$-heat equations by solving second order nonlinear ordinary differential equations. Based on the positive solutions, we give the sharp order of $G$-capacity…

We consider a free particle coupled with finite strength to a bath and investigate the evaluation of its specific heat. A harmonic oscillator bath of Drude type with cutoff frequency omega_D is employed to model an ohmic friction force with…

A class of inverse problems for a heat equation with involution perturbation is considered using four different boundary conditions, namely, Dirichlet, Neumann, periodic and anti-periodic boundary conditions. Proved theorems on existence…

The specific heat of ultra-thin free-standing membranes is calculated using the elastic continuum model. We first obtain the dispersion relations of the discrete set of acoustic modes in the system. The specific heat is then calculated by…

In this article we study a mathematical model of the heat transfer in semi infinite material with a variable cross section, when the radial component of the temperature gradient can be neglected in comparison with the axial component is…

Vibrations in materials and nanostructures at sufficiently high temperatures result in anharmonic atomic displacements, which leads to new phenomena such as thermal expansion and multiphonon scattering processes, with a profound impact on…

We consider weak solutions of the fractional heat equation posed in the whole $n$-dimensional space, and establish their asymptotic convergence to the fundamental solution as $t\to\infty$ under the assumption that the initial datum is an…

In this paper we consider the problem of radiation from a vertical short dipole above flat ground with losses, which represents the well known in the literature Sommerfeld radiation problem. We end up with a closed form analytical solution…

We consider the heat equation with spatially variable thermal conductivity and homogeneous Dirichlet boundary conditions. Using the Method of Fokas or Unified Transform Method, we derive solution representations as the limit of solutions of…

The paper considers the heat transfer characteristics of a thin film flow over a hot horizontal flat plate resulting from a cold vertical liquid jet falling onto a surface. A numerical solution of high accuracy is obtained for large…

We study the spectral theory and inverse problem on asymptotically hyperbolic manifolds. The main subjects are as follows: (1)Location of the essential spectrum. (2)Absence of eigenvalues embedded in the continuous spectrum. (3)Limiting…

In this paper we consider two different Stefan problems for a semi-infinite material for the non classical heat equation with a source which depends on the heat flux at the fixed face x = 0. One of them (with constant temperature on x = 0)…