Almost periodic evolution systems with impulse action at state-dependent moments

We study the existence of almost periodic solutions for semi-linear abstract parabolic evolution equations with impulse action at state-dependent moments. In particular, we present conditions excluding the beating phenomenon in these systems. The main result is illustrated with an example of impulsive diffusive logistic equation.Comment: 16 pages, minor changes from the previous versio

Study of the effectiveness of various cannabinoid receptor 1 (CB1) agonists using molecular docking and molecular dynamics modeling

The binding of a series of small organic molecules, acting as agonists of the cannabinoid receptor CB1, was investigated by means of three methods of computational chemistry. Binding modes were predicted by means of molecular docking, and binding free energy was estimated via docking, molecular-mechanics Poisson-Boltzmann surface area method, and multistate Bennett acceptance ratio. No evident correlation was observed for the molecules between the experimental characteristics of affinity and three computed binding free energy estimates. The reasons for the discrepancy were discussed

Bounded and Almost Periodic Solvability of Nonautonomous Quasilinear Hyperbolic Systems

The paper concerns boundary value problems for general nonautonomous first order quasilinear hyperbolic systems in a strip. We construct small global classical solutions, assuming that the right hand side is small. For the nonhomogeneous version of a linearized problem, we provide stable dissipativity conditions ensuring a unique bounded continuous solution for any smooth right-hand side. In the autonomous case, this solution is two times continuously differentiable. In the nonautonomous case, the continuous solution is differentiable under additional dissipativity conditions, which are essential. A crucial ingredient of our approach is a perturbation theorem for general linear hyperbolic systems. In the case that all data of the quasilinear problem are almost periodic, we prove that the bounded solution is also almost periodic.Comment: 42 pages. The main result is generalized to cover more general first order quasilinear hyperbolic systems; improved presentation, a correction in Example in Subsection 3.

Frequency locking by external forcing in systems with rotational symmetry

We study locking of the modulation frequency of a relative periodic orbit in a general $S^1$-equivariant system of ordinary differential equations under an external forcing of modulated wave type. Our main result describes the shape of the locking region in the three-dimensional space of the forcing parameters: intensity, wave frequency, and modulation frequency. The difference of the wave frequencies of the relative periodic orbit and the forcing is assumed to be large and differences of modulation frequencies to be small. The intensity of the forcing is small in the generic case and can be large in the degenerate case, when the first order averaging vanishes. Applications are external electrical and/or optical forcing of selfpulsating states of lasers.Comment: 5 figure

Various damage mechanisms in carbon and silicon materials under femtosecond x-ray irradiation

We review the results of our research on damage mechanisms in materials irradiated with femtosecond free-electron-laser (FEL) pulses. They were obtained using our hybrid approach, XTANT (X-ray-induced Thermal And Nonthermal Transitions). Various damage mechanisms are discussed with respect to the pulse fluence and material properties on examples of diamond, amorphous carbon, C60 crystal, and silicon. We indicate conditions: producing thermal melting of targets as a result of electron-ion energy exchange; nonthermal phase transitions due to modification of the interatomic potential; Coulomb explosion due to accumulated net charge in finite-size systems; spallation or ablation at higher fluences due to detachment of sample fragments; and warm dense matter formation. Transient optical coefficients are compared with experimental data whenever available, proving the validity of our modeling approach. Predicted diffraction patterns can be compared with the results of ongoing or future FEL experiments. Limitations of our model and possible future directions of development are outlined.Comment: This brief review is submitted for publicatio

Method of spectral analysis of traction current of AC electric locomotives

An improved method for spectral analysis of traction current of an Alternating Current (AC) electric locomotive is considered in the article. A new method of spectral analysis considers the change in voltage in the catenary system as a non-deterministic, non-ergodic and non-Gaussian process. It has been established that higher voltage harmonics in the catenary system have a significant negative effect on the operation of non-traction railway consumers of electricity. In addition, electric locomotives operating in the same feeder zone have a mutual influence on each other. Electric railway transport is a source of higher voltage harmonics and strongly distorts the shape of the sinusoidal voltage of the catenary system, which are caused by the higher spectral components of the current in the electric locomotive traction drive circuit. These spectral components of the traction current arise in the traction drive circuit due to the nonlinearity of the current-voltage characteristics of the electronic devices of an electric locomotive, for example, a contact rectifier, a capacitor circuit of traction motors. Reactive power compensators are used in electric locomotives to eliminate components of higher harmonic traction current in the catenary system. Traditionally, spectral analysis in such systems is performed using Fourier methods. However, the determination of the spectral components of the traction current by the Fourier method for constructing a control system for a reactive power compensator is possible only if the process of voltage variation is a deterministic or ergodic Gaussian process. Otherwise, the application of Fourier transform methods will be incorrect. An analysis of the factors that affect voltage changes in the catenary system showed that this process is significantly different from the ergodic Gaussian process. Such factors include the following: the operating mode of the electric locomotives; number and total capacity of electric locomotives in one feeder zone; electric locomotives passing through feeder zones; instability of collection current. Thus, in the case under consideration, the application of the Fourier methods is incorrect for the analysis of the spectral components of the traction current. This affects the quality of compensation of the higher harmonic components of the traction current, and in some cases, the unstable operation of the control system of the active part of the reactive power compensator. Proposed scientific approach is based on the Levinson–Durbin linear prediction algorithm. On the one hand, this allows adapting the control system of the compensator to the voltage parameters of the catenary system. On the other hand, this allows taking into account the operating modes of electric rail vehicle with reactive power compensation. The construction of a compensator control system using the Levinson–Durbin algorithm significantly simplifies thensynchronization scheme of the compensator and power circuits of the traction electric drive of AC electric locomotive. A comparison of the traditional method of spectral analysis, based on the Fast Fourier Transform (FFT), and the method, based on the Levinson–Durbin algorithm, proposed by the authors, showed the high efficiency of the latter. First published online 21 January 202

Температурная зависимость диффузии в периодических наклонных потенциалах: от недодемпфированых систем к передемпфированым

В последнее время появились как экспериментальные данные, так и теоретические исследования, в которых коэффициент диффузии ведет себя немонотонно с температурой. Одним из примеров систем с аномальной температурной зависимостью диффузии является движение броуновских частиц в пространственно-периодических структурах. Целью работы было исследование изменения температурной зависимости коэффициента диффузии с изменением трения, как в недодемпфированых, так и передемпфированых системах. В работе изучена диффузия частиц в наклонных пространственно-периодических потенциалах в широком диапазоне температур. Показано, что как в недодемпфированых, так и в передемпфированых системах, коэффициент диффузии достигает максимального значения при определенном значении внешней силы, величина которой зависит от величины коэффициента трения. Однако в системах с малым и большим трением температурная зависимость коэффициента диффузии  различается. Показано, что в системах с малым уровнем трения γ’ наблюдается температурно-аномальная диффузия (ТАД) при которой коэффициент диффузии D возрастает с понижением температуры. В то же время при больших значениях γ’ диффузия усиливается с ростом температуры. В работе исследовано, каким образом с ростом γ’ осуществляется переход от экспоненциальной зависимости ТАД к обычной степенной температурной зависимости. Показано, что с увеличением коэффициента трения энергетический барьер ε, разделяющий “бегущие” и “локализованные” решения, уменьшается, исчезая при γ -> 0 . Одновременно с уменьшением ε также происходит сужение температурного интервала температурно-аномальной диффузии. Установлено, что при промежуточных значениях коэффициента трения возникает область температурно-ограниченной ТАД. В некотором интервале сил коэффициент диффузии сначала возрастает с уменьшением температуры, а затем снова начинает падать. Построены диаграммы существования таких областей. Полученные результаты открывает перспективы создания новых технологий управления процессами диффузии. Это имеет большое значение для получения наноматериалов с заданной структурой, создания поверхностных наноструктур и пр

Starting currents of modes in cylindrical cavities with mode-converting corrugations for second-harmonic gyrotrons

A self-consistent system of equations (known as single-mode gyrotron equations) is extended to describe the beam-wave interaction in a cylindrical gyrotron cavity with mode-converting longitudinal corrugations, which produce coupling of azimuthal basis modes. The system of equations is applied to investigate the effect of corrugations on starting currents of the cavity modes. For these modes, eigenvalues, ohmic losses, field structure, and beam-wave coupling coefficients are investigated with respect to the corrugation parameters. It is shown that properly sized mode-converting corrugations are capable of improving the selectivity properties of cylindrical cavities for second-harmonic gyrotrons