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V. B. Tlyachev

Publications and source records attributed to V. B. Tlyachev.

6 recordsLinked to original sources
arXiv2021

Stochastic stability criteria for two-dimensional linear autonomous systems perturbed by white noise

We give necessary and/or sufficient conditions for stochastic stability of second-order linear autonomous systems with parameters, which are perturbed by a random process of the "white noise" type. The Ito's and Stratonovich's forms of stochastic differential equations representing the system with white noise are considered. The investigation of stochastic stability of the systems considered is based on the construction of special Lyapunov functions in the quadratic forms. The bifurcation value of the white noise intensity at which a system first becomes unstable is presented in the analytical expression. As an example a damped harmonic oscillator with randomly perturbed parameters is considered.

math.DS↗
arXiv2020

On Cross Hyperoperatorial Migration of Properties, Related to Natural Number Division Operator

In the article integer divisibility properties and related prime factors natural number representation concepts have been defined over the whole infinite hyperoperation hierarchy. The definitions have been made across and above of unique arithmetic operations, composing this hierarchy (addition, multiplication, exponentiation, tetration and so on). It allows the habitual concepts of "prime factor", "multiplier", "divider", "natural number factors representation" etc., to be associated mainly with the same sense, with the each of those operations. As analogy of multiplication-based Fundamental Theorem of Arithmetic (FTA), an exponentiation-based theorem is formulated. The theorem states that any natural number $M$ can be uniquely represented as a tower-like exponentiation: $M=a_n\uparrow(a_{n-1}\uparrow (\ldots (a_2\uparrow a_1)\ldots )),$ where $a_i\neq 1 (i=1,\ldots,n)$ are primitive in some sense (related to the exponentiation operation), exponentiation components, following one by one in some unique order and named in the article as biprimes.

math.NT↗
arXiv2002

Angular dependence of synchrotron radiation intensity

The detailed analysis of angular dependence of the synchrotron radiation (SR) is presented. In particular, we analyze the angular dependence of the integral SR-intensity and peculiarities of the angular dependence of the first harmonics SR. Studying spectral SR-intensities, we have discovered their unexpected angular behavior, completely different from that of the integral SR-intensity. Namely, for any given synchrotron frequency, maxima of the spectral SR-intensities recede from the orbit plane with increasing particle energy. Thus, in contrast with the integral SR-intensity, the spectral ones have the tendency to deconcentrate themselves on the orbit plane.

physics.acc-ph↗
arXiv2002

Solutions of relativistic wave equations in superpositions of Aharonov-Bohm, magnetic, and electric fields

We present new exact solutions (in 3+1 and 2+1 dimensions) of relativistic wave equations (Klein-Gordon and Dirac) in external electromagnetic fields of special form. These fields are combinations of Aharonov-Bohm solenoid field and some additional electric and magnetic fields. In particular, as such additional fields, we consider longitudinal electric and magnetic fields, some crossed fields, and some special non-uniform fields. The solutions obtained can be useful to study Aharonov-Bohm effect in the corresponding electromagnetic fields.

hep-th↗
arXiv2000

Aharonov-Bohm Effect in Cyclotron and Synchrotron Radiations

We study the impact of Aharonov-Bohm solenoid on the radiation of a charged particle moving in a constant uniform magnetic field. With this aim in view, exact solutions of Klein-Gordon and Dirac equations are found in the magnetic-solenoid field. Using such solutions, we calculate exactly all the characteristics of one-photon spontaneous radiation both for spinless and spinning particle. Considering non-relativistic and relativistic approximations, we analyze cyclotron and synchrotron radiations in detail. Radiation peculiarities caused by the presence of the solenoid may be considered as a manifestation of Aharonov-Bohm effect in the radiation. In particular, it is shown that new spectral lines appear in the radiation spectrum. Due to angular distribution peculiarities of the radiation intensity, these lines can in principle be isolated from basic cyclotron and synchrotron radiation spectra

hep-th↗