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The electron and phonon temperature distribution function are calculated in semiconductors. We solved the coupled one-dimensional heat-diffussion equations in the linear approximation in which the physical parameters on the sample are…
We develop a small distance expansion for the radiative heat transfer between gently curved objects, in terms of the ratio of distance to radius of curvature. A gradient expansion allows us to go beyond the lowest order proximity transfer…
Stefan problems relevant to burning oil-water systems are formulated. Two moving boundary sub-problems are defined: burning liquid surface and formation of a distillation ("hot zone") layer beneath it. The basic model considers a heat…
Here, we develop a theory of radiative heat transfer based on an equivalent electrical network representation for the hot material slabs in an arbitrary multilayered environment with arbitrary distribution of temperatures and…
Path integral quantization of dilaton gravity in two dimensions is applied to the CGHS model to the first nontrivial order in matter loops. Our approach is background independent as geometry is integrated out exactly. The result is an…
In this paper we explore the weak solutions of the Cauchy problem and an inverse source problem for the heat equation in the quantum calculus, formulated in abstract Hilbert spaces. For this we use the Fourier series expansions. Moreover,…
Warming in complex physical systems, in particular global warming, attracts significant contemporary interest. It is essential, therefore, to understand basic physical mechanisms leading to overheating. It is well known that application of…
We obtained a new representation of a solution of the heat conduction equation with boundary condition of the third kind for a layer. The result is presented as a superposition of fundamental solutions for an unbounded system with variable…
We study Hawking radiation and wave scattering of charged scalar fields in a charged $C$-metric black hole background. The conformally invariant wave equation for charged scalar fields can be separated into radial and angular parts, each…
Pennes' differential equation for bioheat transfer and the heat transfer equation are solved for the temperature distribution in a living tissue with spherical inclusions, irradiated by microwave power. It is shown that relative temperature…
We consider an ideal Fermi gas of tachyons and derive a low temperature expansion of its thermodynamical functions. The tachyonic specific heat is linear dependent on temperature $C_V=\epsilon_Fk_FT$ and formally coincides with the specific…
Optical data is encoded with information on the microscopic interaction between charge carriers. For an electron-phonon system, the Eliashberg equations apply and a Kubo formula can be used to get the infrared conductivity. The task of…
The physical interpretation of black hole's quasinormal modes is fundamental for realizing unitary quantum gravity theory as black holes are considered theoretical laboratories for testing models of such an ultimate theory and their…
Power Series Solution method has been used traditionally for to solve Linear Differential Equations, in Ordinary and Partial form. But this method has been limited to this kind of problems. We present the solution of problems of Non Linear…
We extend Kubo's Linear Response Theory (LRT) to periodic input signals with arbitrary shapes and obtain exact analytical formulas for the energy dissipated by the system for a variety of signals. These include the square and sawtooth…
A short informal overview about recent progress in the calculation of the effective action in quantum gravity is given. I describe briefly the standard heat kernel approach to the calculation of the effective action and discuss the…
For a system of bosons that interact through a class of general memory kernels, a recurrence relation for the partition function is derived within the path-integral formalism. This approach provides a generalization to previously known…
The paper surveys recent progress in establishing uniqueness and developing inversion formulas and algorithms for the thermoacoustic tomography. In mathematical terms, one deals with a rather special inverse problem for the wave equation.…
A novel numerical method for solving inverse scattering problem with fixed-energy data is proposed. The method contains a new important concept: the stability index of the inversion problem. This is a number, computed from the data, which…
In the context of brane-world theories, the production cross-section for black holes may be greatly enhanced. Such black holes can in principle lead to detectable signals via their Hawking evaporation to brane-localized modes. We calculate,…