Related papers: Multilayer heat equations and their solutions via …
The heat capacity of solids at intermediate-to-high temperatures is of fundamental importance to several fields ranging from geology to material science. It depends on a variety of factors, with anharmonicity and, ultimately, melting…
We provide a simple method for obtaining new Liouville theorems for scaling invariant superlinear parabolic problems with gradient structure. To illustrate the method we prove Liouville theorems (guaranteeing nonexistence of positive…
The dynamic heat transfer between two half-spaces separated by a vacuum gap due to coupling of their surface modes is modelled using the theory that describes the dynamic energy transfer between two coupled harmonic oscillators each…
We introduce a numerical method for reconstructing a multidimensional surface using the gradient of the surface measured at some values of the coordinates. The method consists of defining a multidimensional spline function and minimizing…
Sturm-Liouville problems are abundant in the numerical treatment of scientific and engineering problems. In the present contribution, we present an efficient and highly accurate method for computing eigenvalues of singular Sturm-Liouville…
A surface integral equation solver is proposed for fast and accurate simulation of interconnects embedded in stratified media. A novel technique for efficient computation of the multilayer Green's function is proposed. Using the Taylor…
We obtain classes of two dimensional static Lorentzian manifolds, which through the supersymmetric formalism of quantum mechanics admit the exact solvability of Dirac equation on these curved backgrounds. Specially in the case of a modified…
Since the thermal conduction equation has form invariance under coordinate transformation, one can design thermal metamaterials with novel functions by tailoring materials' thermal conductivities. In this work, we establish a different…
We use a powerful extension of the classical method of heat potentials, recently developed by the present author and his collaborators, to solve several significant problems of financial mathematics. We consider the following problems in…
We derive new all-purpose methods that involve the Dirac Delta distribution. Some of the new methods use derivatives in the argument of the Dirac Delta. We highlight potential avenues for applications to quantum field theory and we also…
The author extends the idea of Jodeit and Levitan for constructing isospectral problems of the classical scalar Sturm-Liouville differential equations to the vectorial Sturm-Liouville differential equations. Some interesting relations are…
The 'vertical modes and horizontal rays' method, commonly applied for simulating acoustic wave propagation in shallow water is advanced in this research. Our approach to this method involves the use of the so-called space-time rays, which…
We study the rotational and vibrational heating of diatomic molecules placed near a surface at finite temperature on the basis of macroscopic quantum electrodynamics. The internal molecular evolution is governed by transition rates that…
We study the diffusion (or heat) equation on a finite 1-dimensional spatial domain, but we replace one of the boundary conditions with a "nonlocal condition", through which we specify a weighted average of the solution over the spatial…
We study the triviality of the solutions of weighted superlinear heat equations on Riemannian manifolds with nonnegative Ricci tensor. We prove a Liouville--type theorem for solutions bounded from below with nonnegative initial data, under…
In this article, we construct the multivariate fractal interpolation functions for a given data points and explore the existence of $\alpha$-fractal function corresponding to the multivariate continuous function defined on $[0,1]\times…
We study integrable deformations of sine-Liouville conformal field theory. Every integrable perturbation of this model is related to the series of quantum integrals of motion (hierarchy). We construct the factorized scattering matrices for…
The inverse spectral problem is studied for the Sturm-Liouville operator with a complex-valued potential and arbitrary entire functions in one of the boundary conditions. We obtain necessary and sufficient conditions for uniqueness, and…
The thermal properties of the three-dimensional Dirac oscillator are considered. The canonical partition function is determined, and the high-temperature limit is assessed. The degeneracy of energy levels and their physical implications on…
We construct a class of exponential type solutions for the linear, delayed heat equation. These representations may be used to provide a priori ansatzes for certain boundary and/or initial-value problems arising in heat transfer. Several of…