Spectroscopic peculiarities in a 2D Coulomb potential under Aharonov-Bohm effect

In this paper we demonstrate some spectroscopic peculiarities which occur in the presence of the Aharonov-Bohm effect. As an object of investigation the system of a two-dimensional (2D) Coulomb potential in the presence of the Aharonov-Bohm flux is considered. It is shown, that the bound states in such a system “feel” the presence of the magnetic flux. In particular, the numerical analysis shows that the oscillator strengths of optical transitions turn into zero at some “special” values of the Aharonov-Bohm flux. As a result, some spectral lines (namely, the intensities of spectral lines) will disappear and this fact may be considered as an observable optical manifestation of the Aharonov-Bohm effect in the considered system. The dynamic polarisability of the bound states of an electron in such a system is also analyzed. It is shown numerically that the dynamic polarisability “strongly” depends on the values of the Aharonov-Bohm flux

On the state feedback control of inverted pendulum with hysteretic nonlinearity

In this paper we consider the mathematical model of the inverted pendulum with the hysteretic nonlinearity (in the form of backlash) under state feedback control. The analytic results for the stability criteria as well as for the solution of the linearized equation are observed and analyzed. The theorems that determine the stabilization of the considered system are also formulated and discussed

Efficiency of hysteretic damper in oscillating systems

This paper is dedicated to comparative analysis of nonlinear damping in the oscillating systems. More specifically, we present the particular results for linear and nonlinear viscous dampers, fractional damper, as well as for the hysteretic damper in linear and nonlinear (Duffing-like) oscillating systems. We consider a constructive mathematical model of the damper with hysteretic properties on the basis of the Ishlinskii-Prandtl model. Numerical results for the observable characteristics, such as the force transmission function and the “force-displacement” transmission function are obtained and analyzed for both cases of the periodic affection, as well as for the impulse affection (in the form of δ-function). A comparison of an efficiency (in terms of the corresponding transmission functions) of the nonlinear viscous damper and the hysteretic damper is also presented and discussed

A Model of Optimal Production Planning Based on the Hysteretic Demand Curve

The article considers a hysteretic model of consumer behaviour in mono-product markets. Demand generation with regard to an individual consumer is modeled using a non-ideal relay with inverted thresholds. Therefore, the sales rate is defined as an analogue of the Preisach converter. The article considers the problem of the optimal production, storage, and distribution of goods, taking into account the hysteretic nature of the demand curve. The problem is reduced to a non-classical optimal control problem with hysteretic non-linearities. The latter is solved using Pontryagin’s maximum principle. The adopted economic model is based on the binary relationship of consumers to the product: the product is bought or the product is not bought. Transitions between these states are determined within the framework of our model only by the price of the goods; therefore, only the operator of a non-ideal relay can accurately describe such a dependence. The article presents the results of computational experiments illustrating the theoretical assumptions

Self-oscillations in a system with hysteresis: the small parameter approach

The paper investigates a modified van der Pol equation with hysteresis nonlinearity which is formalized within the Preisach approach. The system considered in the work is a mathematical model of an electrical system similar to the classical van der Pol system where characteristics of the nonlinear part are of hysteresis nature. The main method for studying this system is the classical small parameter approach. Within this method, an analytical solution to the equation describing the system under consideration was obtained. Numerical results are presented and a comparative analysis of the dynamics of the system under consideration with the dynamics of the classical van der Pol oscillator is carried out. Dynamic modes of the modified oscillator are investigated depending on the parameters of the system. Spectral characteristics are also compared to the corresponding characteristics of the classical van der Pol oscillator

Heat removing under hypersonic conditions

In this paper we consider the heat transfer properties of the axially symmetric body with parabolic shape at hypersonic speeds (with a Mach number M > 5). We use the numerical methods based on the implicit difference scheme (Fedorenko method) with direct method based on LU-decomposition and iterative method based on the Gauss-Seigel method. Our numerical results show that the heat removing process should be performed in accordance with the nonlinear law of heat distribution over the surface taking into account the hypersonic conditions of motion

Hysteretic damper based on the Ishlinsky-Prandtl model

In this paper we consider the mathematical model of hysteretic damper based on the Ishlinsky-Prandtl model. The numerical results for the observable characteristics such as force transmission function and “force-displacement” transmission function are obtained and analyzed. The comparison of the efficiency of non-linear viscous damper and hysteretic damper is also presented and discussed

Hysteretic damper based on the Ishlinsky-Prandtl model

In this paper we consider the mathematical model of hysteretic damper based on the Ishlinsky-Prandtl model. The numerical results for the observable characteristics such as force transmission function and “force-displacement” transmission function are obtained and analyzed. The comparison of the efficiency of non-linear viscous damper and hysteretic damper is also presented and discussed

Heat removing under hypersonic conditions

In this paper we consider the heat transfer properties of the axially symmetric body with parabolic shape at hypersonic speeds (with a Mach number M > 5). We use the numerical methods based on the implicit difference scheme (Fedorenko method) with direct method based on LU-decomposition and iterative method based on the Gauss-Seigel method. Our numerical results show that the heat removing process should be performed in accordance with the nonlinear law of heat distribution over the surface taking into account the hypersonic conditions of motion