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When the variations of surface temperature are measured both spatially and temporally, analytical expressions that correctly account for multi-dimensional transient conduction can be applied. To enhance the accessibility of these accurate…
The heat kernel transform H_t for the Heisenberg group is studied in detail. The main result shows that the image of H_t is a direct sum of two weighted Bergman spaces whose associated weighted functions are of oscillatory nature, i.e.…
Finite temperature boson and fermion field theories on ultrastatic space-times with a d-sphere spatial section are discussed with one eye on the questions of temperature inversion symmetry and modular invariance. For conformally invariant…
This is a direct computation of the spectral representation of homogeneous spin-weighted spherical random fields with arbitrary integer spin. It generalises known results from Cosmology for the spin-2 Cosmic Microwave Background…
In this paper, we consider the heat equation with strongly singular potentials and prove that it has a "very weak solution". Moreover, we show the uniqueness and consistency results in some appropriate sense. The cases of positive and…
We compute the black hole radiation spectrum in the presence of high-frequency dispersion in a large set of situations. In all cases, the spectrum diverges like the inverse of the Killing frequency. When studying the low-frequency spectrum,…
The Boltzmann transport equation for phonons is recast directly in terms of the heat-flux by means of iteration followed by truncation at the second order in the spherical harmonic expansion of the distribution function. This procedure…
Measuring the spectral phase of a pulse is key for performing wavelength resolved ultrafast measurements in the few femtosecond regime. However, accurate measurements in real experimental conditions can be challenging. We show that the…
When focusing an image, depth of field, aperture and distance from the camera to the object, must be taking into account, both, in visible and in infrared spectrum. Our experiments reveal that in addition, the focusing problem in thermal…
We report first-principles calculations of the phonon dispersion spectrum, thermal expansion, and heat capacity of uranium dioxide. The so-called direct method, based on the quasiharmonic approximation, is used to calculate the phonon…
In this paper, we establish existence and uniqueness of weak solutions to general time fractional equations and give their probabilistic representations. We then derive sharp two-sided estimates for fundamental solutions of a family of time…
The separated radial part of a sourceless massive complex scalar field equation on the Kerr-Newman black hole background is shown to be a generalized spin-weighted spheroidal wave equation of imaginary number order. While the separated…
We present a rigorous and efficient approach to the calculation of classical lattice-dynamical quantities from simulations that do not require an explicit solution of the time evolution. We focus on the temperature-dependent vibrational…
We propose a general inverse formula for extracting inflationary parameters from the observed power spectrum of cosmological perturbations. Under the general slow-roll scheme, which helps to probe the properties of inflation in a model…
This paper deals with the investigation of a closed form solution of a generalized fractional reaction-diffusion equation. The solution of the proposed problem is developed in a compact form in terms of the H-function by the application of…
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…
A solution is presented for the spectrum of high-energy gamma-ray burst photons confined to a quasi-thermal baryonic photosphere. The solution is valid in the steady-state limit assuming the region under consideration is optically thick to…
This is a series of studies devoted to modeling and solving heat and mass transfer problems occurring in electric contacts where we employ and develop mathematical apparatus along with quantum algorithms for solving moving boundary value…
The Milne-Eddington approximation provides an analytic and simple solution to the radiative transfer equation. It can be easily implemented in inversion codes that are used to fit spectro-polarimetric observations to infer average values of…
Ballistic heat transport and second sound propagation in solids is of direct relevance in electronic and energy applications at short length scales and low temperatures. Measurement or calculation of thermal conductivity, which is typically…