Broken space-time symmetries and mechanisms of rectification of ac fields by nonlinear (non)adiabatic response

We consider low-dimensional dynamical systems exposed to a heat bath and to additional ac fields. The presence of these ac fields may lead to a breaking of certain spatial or temporal symmetries which in turn cause nonzero averages of relevant observables. Nonlinear (non)adiabatic response is employed to explain the effect. We consider a case of a particle in a periodic potential as an example and discuss the relevant symmetry breakings and the mechanisms of rectification of the current in such a system.Comment: 11 pages, 10 figure

Simulation of a Casimir-like effect in a granular pile with avalanches

Using a modified Bak-Tang-Wiesenfeld model for sand piles, we simulate a Casimir-like effect in a granular pile with avalanches. Results obtained in the simulation are in good agreement with results previously acquired experimentally: two parallel walls are attracted to each other at small separation distances, with a force decreasing with increasing distance. In the simulation only, at medium distances a weak repulsion exists. Additionally, with the aim of avalanche prevention, the possibility of suppressing self-organized criticality with an array of walls placed on the slope of the pile is investigated, but the prevention effect is found to be negligible. © 2011 American Physical Society

The absolutely continuous spectrum of one-dimensional Schr"odinger operators

This paper deals with general structural properties of one-dimensional Schr"odinger operators with some absolutely continuous spectrum. The basic result says that the omega limit points of the potential under the shift map are reflectionless on the support of the absolutely continuous part of the spectral measure. This implies an Oracle Theorem for such potentials and Denisov-Rakhmanov type theorems. In the discrete case, for Jacobi operators, these issues were discussed in my recent paper [19]. The treatment of the continuous case in the present paper depends on the same basic ideas.Comment: references added; a few very minor change

Vortex and translational currents due to broken time-space symmetries

We consider the classical dynamics of a particle in a $d=2,3$-dimensional space-periodic potential under the influence of time-periodic external fields with zero mean. We perform a general time-space symmetry analysis and identify conditions, when the particle will generate a nonzero averaged translational and vortex currents. We perform computational studies of the equations of motion and of corresponding Fokker-Planck equations, which confirm the symmetry predictions. We address the experimentally important issue of current control. Cold atoms in optical potentials and magnetic traps are among possible candidates to observe these findings experimentally.Comment: 4 pages, 2 figure

Oscillons: an encounter with dynamical chaos in 1953?

We present evidences that Ben F. Laposky (1914-2000) might have been the first person who created a family of nonlinear analog circuits that allowed him to observe chaotic attractors and other trademarks of nonlinear science as early as 1953.Comment: accepted to Chao

Direct Measurement of Effective Magnetic Diffusivity in Turbulent Flow of Liquid Sodium

The first direct measurements of effective magnetic diffusivity in turbulent flow of electro-conductive fluids (the so-called beta-effect) under magnetic Reynolds number Rm >> 1 are reported. The measurements are performed in a nonstationary turbulent flow of liquid sodium, generated in a closed toroidal channel. The peak level of the Reynolds number reached Re \approx 3 10^6, which corresponds to the magnetic Reynolds number Rm \approx 30. The magnetic diffusivity of the liquid metal was determined by measuring the phase shift between the induced and the applied magnetic fields. The maximal deviation of magnetic diffusivity from its basic (laminar) value reaches about 50% .Comment: 5 pages, 6 figuser, accepted in PR

The mean electromotive force due to turbulence of a conducting fluid in the presence of mean flow

The mean electromotive force caused by turbulence of an electrically conducting fluid, which plays a central part in mean--field electrodynamics, is calculated for a rotating fluid. Going beyond most of the investigations on this topic, an additional mean motion in the rotating frame is taken into account. One motivation for our investigation originates from a planned laboratory experiment with a Ponomarenko-like dynamo. In view of this application the second--order correlation approximation is used. The investigation is of high interest in astrophysical context, too. Some contributions to the mean electromotive are revealed which have not been considered so far, in particular contributions to the $\alpha$--effect and related effects due to the gradient of the mean velocity. Their relevance for dynamo processes is discussed. In a forthcoming paper the results reported here will be specified to the situation in the laboratory and partially compared with experimental findings.Comment: 16 pages, 2 figures, in PRE pres

Синтез цифрового регулятора головного контуру триконтурної системи лінійного електроприводу робочого органу механізму бортової авіаційної техніки

Goal The purpose of the article is to further develop analytical methods for calculating and synthesizing power electronics systems with deep pulse width modulation (PWM). A three-circuit linear electric drive system for positioning the working body of the mechanism of onboard aircraft equipment, in which the linear electric motor is controlled from a pulse width converter (PWC), is considered. The power converter is included in the current loop. It has a noticeable effect on the level of current ripple, travel speed and positioning accuracy of the operating mechanism of a linear electric drive. Methodology. To analyze the processes in the current loop, a discrete transfer function of a pulse-width converter for PWM in the final zone and «in the large» is obtained on the basis of the statistical linearization of the modulation characteristics of the multi-loop PWM model. The modulation characteristic of each circuit of the model is obtained as a result of the Fourier series expansion in Walsh functions of the output voltage of the PWM during the PWM process. Statistical linearization of modulation characteristics is performed based on Hermite polynomials. Results. During the analysis, discrete transfer functions of closed current loops, velocity and open loop position were obtained, for which a digital controller was synthesized in the form of a recursive filter. Originality. The parameters of the regulator links are found, which make it possible to complete the transient process in four PWC switching periods with an overshoot of no more than 6 %. The analysis of the speed-optimized positioning process of a linear electric drive based on the LED AT 605TU motor is carried out. Practical significance. The purpose of the analysis was to establish the relationship between the switching period of the PWM and the value of the uncompensated constant, at which the pulsations of the positioning process are minimal while ensuring the minimum overshoot and maximum speed. It was found that the specified requirements are satisfied by the ratio between the switching period, PWC and uncompensated constant in the range of one or two.В триконтурній системі лінійного електроприводу, робочий орган якого реалізує поступальне переміщення при виконанні команди бортового комп’ютера літального апарату, врахований вплив пульсацій широтно-імпульсного перетворювача постійної напруги на процес позиціонування. З умови кінцевої тривалості процесу позиціонування синтезовано цифровий регулятор головного контуру системи і запропонована його реалізація у вигляді рекурсивного цифрового фільтру