On the linearization of the generalized Ermakov systems

A linearization procedure is proposed for Ermakov systems with frequency depending on dynamic variables. The procedure applies to a wide class of generalized Ermakov systems which are linearizable in a manner similar to that applicable to usual Ermakov systems. The Kepler--Ermakov systems belong into this category but others, more generic, systems are also included

New FEM - Programs for modeling coupled processes of selective vapor condensation during laser processing of materials

This research presents a computer model for conjugate heat and mass transfer during laser processing of materials. The computer programs based on FEM, which allow to predict the processes of formation of evaporation and condensation zones on the surface areas surrounding the crater are implemented. There is the presence of three modes of operation, differing in the configuration of evaporation zones - condensation. The identified control parameters change modes. A phase diagram for the implementation of process modes is proposed. Finally, the research discusses the possibility of managing the process. © 2020 American Institute of Physics Inc.. All rights reserved

Resonant enhancement of the jump rate in a double-well potential

We study the overdamped dynamics of a Brownian particle in the double-well potential under the influence of an external periodic (AC) force with zero mean. We obtain a dependence of the jump rate on the frequency of the external force. The dependence shows a maximum at a certain driving frequency. We explain the phenomenon as a switching between different time scales of the system: interwell relaxation time (the mean residence time) and the intrawell relaxation time. Dependence of the resonant peak on the system parameters, namely the amplitude of the driving force A and the noise strength (temperature) D has been explored. We observe that the effect is well pronounced when A/D > 1 and if A/D 1 the enhancement of the jump rate can be of the order of magnitude with respect to the Kramers rate.Comment: Published in J. Phys. A: Math. Gen. 37 (2004) 6043-6051; 6 figure

Lie symmetries for two-dimensional charged particle motion

We find the Lie point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries comprise a quasi-invariance transformation, a time-dependent rotation, a time-dependent spatial translation and a dilation. The associated electromagnetic fields satisfy a system of first-order linear partial differential equations. This system is solved exactly, yielding four classes of electromagnetic fields compatible with Lie point symmetries

Phase formation and structural characteristics of Cd-Pb-S nanopowder compositions produced by modification of CdS powder in a citrate-ammonia solution of a lead salt

Nanopowders obtained by modification of a cadmium sulfide powder in a citrate-ammonia solution of lead acetate have been studied by X-ray diffraction, electron microscopy, and thermal analysis. The type of crystal structure and composition of Cd-Pb-S nanopowders depend on the conditions of their synthesis. The thermoanalytical curves show a well-defined endotherm in the temperature range 284-321 C. The position of this endotherm depends on the duration of contact of a CdS powder with an aqueous solution of a lead salt. Heating nanopowders to 600 C in an argon flow leads to formation of oxygen-containing phases: lead sulfate and cadmium oxide. © 2013 Pleiades Publishing, Ltd

Generalized Hamiltonian structures for Ermakov systems

We construct Poisson structures for Ermakov systems, using the Ermakov invariant as the Hamiltonian. Two classes of Poisson structures are obtained, one of them degenerate, in which case we derive the Casimir functions. In some situations, the existence of Casimir functions can give rise to superintegrable Ermakov systems. Finally, we characterize the cases where linearization of the equations of motion is possible

New Data on the Anomalies of Tailless Amphibians of the Volga Basin

This paper presents new findings on abnormal specimens of amphibians in the Volga basin. Some anomalies have been noted for the first time: macrophthalmia, eardrum anomalies in marsh frogs (P. ridibundus), the absence of a tympanic membrane in green toads and ectromelia in spadefoot Pallas samples (P. vespertinus)

Applications of Lie systems in dissipative Milne--Pinney equations

We use the geometric approach to the theory of Lie systems of differential equations in order to study dissipative Ermakov systems. We prove that there is a superposition rule for solutions of such equations. This fact enables us to express the general solution of a dissipative Milne--Pinney equation in terms of particular solutions of a system of second-order linear differential equations and a set of constants.Comment: To be published in the Int. J. Geom. Methods Mod. Phy

Symmetry, singularities and integrability in complex dynamics III: approximate symmetries and invariants

The different natures of approximate symmetries and their corresponding first integrals/invariants are delineated in the contexts of both Lie symmetries of ordinary differential equations and Noether symmetries of the Action Integral. Particular note is taken of the effect of taking higher orders of the perturbation parameter. Approximate symmetries of approximate first integrals/invariants and the problems of calculating them using the Lie method are considered