Багдоев А.Г., Нуриджанян А.В. «Волновые рассмотрения нестационарных процессов в биофизике, астрофизике, сейсмологии, экономике, волновой механике методами нелинейной волновой динамики» Нелинейный мир, 7, № 7, с. 518-525 (2009)

Рассмотрены линейные и нелинейные волны, возникающие при описании стохастических марковских диффузионных процессов в биофизике, астрофизике, сейсмологии, экономике, волновой механике. This paper presents investigations of stochastic processes in astrophysics, biology, economics, physics of sparse plasma with generalization of diffusive equations by adding nonlinearity and determining probabilities of the processes with an existence of shock waves. Nonlinear equations are proposed for the probabilistic processes, initial and boundary conditions for them are formulated and solution and shock wave of probability is obtained. It is shown, that equation will be the same for the probability-averaged random variable or it's mean value. The obtained solutions are applied to the problems of astrophysics about processes, which describe the number of flared stars in a time unit and phage genetics. In all these problems curves of the mentioned mean value of a random function, which for nonlinear equations is close to the shock wave front, are being used, and probability and the process function is determined. It's shown that the same considerations are true for the problems of economics. In addition we present a comparison of distant Newtonian interactions in astrophysics and distant Coulomb interactions in physics of plasma and it is shown that obtained values for relaxation times for these processes agree. In astrophysics this is the value that provides an approximate time for evolution of stellar systems, when it's distribution function reaches equilibrium.

Герасимов С.И. «Диагностика при исследовании эффектов, сопровождающих выход ударной волны на свободную поверхность при ударно-волновом нагружении» Нелинейный мир, 7, № 7, с. 526-527 (2009)

Продемонстрированы возможности теневой фототехники для экспериментов по изучению неустойчивости Тейлора в материалах. The processes associated with the emergence of a shock from the free surface of a solid were studied in terms of shadow diagnostics. The handled data can be used for testing the corresponding numerical models. Ejecta driven ahead of the free surface of a metal during its run is an example of action of hydrodynamic instability. The used experimental study for this effect included optical and X-ray diagnostics. The first method has recorded the ejecta on obtaining a weak intermittent luminescence produced from the sample free surface-sensor collision. The second has measured the mass distribution of the ejecta on obtaining the darkness density of the X-ray film with a known characteristic curve. The tests reported herein dealt with direct shadow technique to record optically the effects followed the emergence of a shock from the free surface of a metal. The shock was generated on initiating a detonator mounted on the opposite side of the sample.

Диденкулов И.Н. «Нелинейная акустическая модовая томография в дефектоскопии» Нелинейный мир, 7, № 7, с. 528-532 (2009)

Рассмотрен метод нелинейной акустической модовой томографии для определения местоположения трещин в образцах; на экспериментальных примерах продемонстрированы его возможности. Acoustic methods of nondestructive testing are widely used in various industrial fields. Methods of nonlinear diagnostics, based on the property of strong acoustic nonlinearity of cracks are intensively investigated during the last decade. For development and implementation of nonlinear methods of nondestructive testing it is important to develop techniques of crack location. In this a method of the nonlinear acoustic modal tomography for crack location in sample is considered. Feasibility tests were conducted.

Морозов А.Н., Назолин А.Л. «Имитационное моделирование виброакустических колебаний корпуса статора турбогенератора с дефектом ослабления крепления упругой подвески» Нелинейный мир, 7, № 7, с. 556-562 (2009)

Проведена идентификация механической конструкции статора турбогенератора и определены волновые частотные характеристики статора; построена упрощенная математическая модель сильно-нелинейной виброударной системы "стяжное ребро–сердечник"; на ее основе проведен расчет сил и выполнено имитационное моделирование виброакустических колебаний статора. The article describes the relation between the vibroimpact processes in the node of easing of stator suspension and the sound vibration of the body stator of a turbogenerator. On working generator the defect in node of fastening a "prism–stator core" represents non-linear vibroimpact system influencing the sound vibration of the body stator. The method of shock testing is used to study the frequency response function of the body stator. The estimation of linearity of system is given. The simplified of non-linear vibroimpact system a "prism–stator core" is considered. Results of the mathematical modeling for the estimation of intensity of elastic forces and the shock forces in vibroimpact system and the analysis of results of imitating modeling of the compelled reactions of the body stator are given. It is shown that the vibroimpact processes is possible if exists clearance in the system a 'prism – stator core'. In the established mode of vibroimpact process a spectrum of periodic sequence of shock impulses of force and spectrum of acceleration of the body stator is discrete. Frequencies of discrete harmonics are multiple to frequency of magnetic vibrations of core stator (nominally 100 Hz). Bending around a discrete spectrum it is defined by the frequency response function of stator and the shape of a shock impulse. It is established that defect of easing of a suspension stator has no general image of a spectrum and powerful vibroimpact process takes place in resonant and not resonant vibroimpact a mode of movement. The analysis of results of modeling shows, that the sound vibration of the body stator with defect of easing of elastic suspension are defined mainly by the shocks in system a "prism–stator core".

Сапожников О.А., Крейдер В., Бэйли М.Р. «Влияние упругих волн в металлическом рефлекторе на динамику кавитационных пузырьков в фокальной области электрогидравлического литотриптера» Нелинейный мир, 7, № 7, с. 575-580 (2009)

Исследовано влияние на кавитацию дополнительных акустических возмущений, обусловленных упругими волнами, возникающими в металлическом рефлекторе. In extracorporeal electrohydraulic lithotripters, a hemi-ellipsoidal metal reflector is used to focus a spherical wave generated by an electrical discharge. The spark source is positioned at one of the ellipsoid foci; this makes the reflected wave focused at the other focus. Despite the common assumption that the reflector behaves as a rigid mirror, the true reflection phenomenon includes the generation and reverberation of elastic waves in the reflector, which reradiate to the medium. Although these waves are much lower in amplitude than the specularly reflected wave, they may influence cavitation. To explore such effects, waves in water and a brass reflector were modeled in finite differences based on the linearized equations of elasticity. The bubble response was simulated based on a Rayleigh-type equation for the bubble radius. It is shown that the elastic waves in the reflector give rise to a long ringing tail, which results in nonmonotonic behavior of the bubble radius during its inertial growth after shock wave passage. This numerical result is qualitatively confirmed by experimental observations of bubble behavior using high-speed photography.