Related papers: Simple series solutions to specific heat-phonon sp…
In this paper we explore the weak solution of a time-dependent inverse source problem and inverse initial problem for $q$-analogue of the heat equation. As an over-determination condition we have used integral type condition on…
We invert the second order, single field, general slow-roll formula for the power spectrum, to obtain a second order formula for inflationary parameters in terms of the primordial power spectrum.
The world communicates to our senses of vision, hearing and touch in the language of waves, as the light, sound, and even heat essentially consist of microscopic vibrations of different media. The wave nature of light and sound has been…
For a singularly perturbed system of reaction--diffusion equations, assuming that the 0th order solutions in regular and singular regions are all stable, we construct matched asymptotic expansions for formal solutions to any desired order…
We provide a theoretical framework for the development of a solid-state thermal rectifier through a confinement in the available population of phonons on one side of an asymmetrically graded film stack. Using a modification of the phonon…
In this work, the power series solutions are given around a regular-singular point, in the case of variable coefficients for homogeneous sequential linear conformable fractional differential equations of order 2{\alpha}.
We consider a one-dimensional one-phase inverse Stefan problem for the heat equation. It consists in recovering a boundary influx condition from the knowledge of the position of the moving front, and the initial state. We derived a…
We address a keystone problem for the progress of phononics: the proposal of efficient thermal diodes. Aiming the disclosure of an easy itinerary for the building of a heat rectifier, we investigate unsophisticated systems linked to simple…
Calculations of electronic and optical properties of solids at finite temperature including electron-phonon interactions and quantum zero-point renormalization have enjoyed considerable progress during the past few years. Among the emerging…
We show the existence of Fano resonances in the context of near-field radiative heat transfer, which enable the strong suppression and enhancement of the spectral heat flux at specific wavelengths. This is demonstrated by making use of the…
In this chapter we consider different approximations for the one-dimensional one-phase Stefan problem corresponding to the fusion process of a semi-infinite material with a temperature boundary condition at the fixed face and non-linear…
We present the hyperasymptotic expansions for a certain group of solutions of the heat equation. We extend this result to a more general case of linear PDEs with constant coefficients. The generalisation is based on the method of Borel…
This is a short note on the black hole remote-sensing problem, i.e., finding out `surface' temperature distributions of various types of small (micron-sized) black holes from the spectral measurements of their Hawking grey pulses. Chen's…
We present a family of closed form inversion formulas in thermoacoustic tomography in the case of a constant sound speed. The formulas are presented in both time-domain and frequency-domain versions. As special cases, they imply most of the…
We study the recently proposed effective field theory for the phonon of an arbitrary non-relativistic superfluid. After computing the one-loop phonon self-energy, we obtain the low temperature T contributions to the phonon dispersion law at…
In this paper, we study the heat equation with an irregular spatially dependent thermal conductivity coefficient. We prove that it has a solution in an appropriate very weak sense. Moreover, the uniqueness result and consistency with the…
The asymptotic expansion of the heat-kernel for small values of its argument has been studied in many different cases and has been applied to 1-loop calculations in Quantum Field Theory. In this thesis we consider this asymptotic behavior…
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…
This paper is divided into three parts. The first part focuses on periodic layer heat potentials, demonstrating their smooth dependence on regular perturbations of the support of integration. In the second part, we present an application of…
Let $L = -1/4 (\sum_{j=1}^n(X_j^2+Y_j^2)+i\gamma T)$ where $\gamma$ is a complex number, $X_j$, $Y_j$, and $T$ are the left invariant vector fields of the Heisenberg group structure for $R^n \times R^n \times R$. We explicitly compute the…