Energy exchange and transition to localization in the asymmetric Fermi-Pasta-Ulam oscilliatory chain

A finite (periodic) FPU chain is chosen as a convenient point for investigating the energy exchange phenomenon in nonlinear oscillatory systems. As we have recently shown, this phenomenon may occur as a consequence of the resonant interaction between high-frequency nonlinear normal modes. This interaction determines both the complete energy exchange between different parts of the chain and the transition to energy localization in an excited group of particles. In the paper, we demonstrate that this mechanism can exist in realistic (asymmetric) models of atomic or molecular oscillatory chains. Also, we study the resonant interaction of conjugated nonlinear normal modes and prove a possibility of linearization of the equations of motion. The theoretical constructions developed in this paper are based on the concepts of "effective particles" and Limiting Phase Trajectories. In particular, an analytical description of energy exchange between the "effective particles" in the terms of non-smooth functions is presented. The analytical results are confirmed with numerical simulations.Comment: 15 pages, 8 figure

О преимуществах бассейнового подхода при изучении закономерностей распространения наледей

Formation of aufeises (naleds) is rather widely distributed cryogenic process in the permafrost zone, therefore naleds are reasonably called the seasonal glaciation of the planet. The ever-increasing interest in aufeises significantly extends the thematic focus of studying them. Various methodological approaches (basin, geological-structural, lithologic-facies, statistical, etc.) are used to reveal regularities of the aufeis occurrence. Using several river basins in Yakutia and its territory as the examples, the perspectivity of the basin approach for investigation of the aufeis distribution is substantiated in this study. The results demonstrated the clear relationship between the quantitative indicators of areal distribution of naleds and altitudes of places of their formation for individual river basins. This relationship suggests that aufeises in river basins of the permafrost zones are important elements in the water-balance and water exchange, which is closely interrelated with not only climatic and morphometric characteristics of a basin, but it does also correlate with its hydrological, hydrogeological, geological, geocryological, landscape and other conditions.Для конкретных речных бассейнов Якутии и территории республики в целом автором рассчитаны количественные показатели площадного распространения наледей и высотного распределения мест их формирования. Выявленные закономерности подчёркивают, что наледи представляют собой важный водно-балансовый и водообменный элемент речных бассейнов криолитозоны

Transformación del sistema legal en la era digital: planteamiento del problema

This paper discusses the prospects for the development of the legal system, the system of legislation and the judicial system of the Russian Federation in the context of the fourth industrial revolution associated primarily with the digitalization of all spheres of social life, all social institutions, including the law, of course. There is a range of problematic issues that will require their resolution in the near future. It is suggested that the process which can be described as "technologization of law" is inevitable. The possibility of revising the key institutions of law and actually forming new terminology is not ruled out.Este documento analiza las perspectivas para el desarrollo del sistema legal, el sistema legislativo y el sistema judicial de la Federación de Rusia en el contexto de la cuarta revolución industrial asociada principalmente con la digitalización de todas las esferas de la vida social, todas las instituciones sociales, incluidas la ley, por supuesto. Hay una variedad de problemas problemáticos que requerirán su resolución en un futuro cercano. Se sugiere que el proceso que puede describirse como "tecnologización de la ley" es inevitable. No se descarta la posibilidad de revisar las instituciones jurídicas clave y, de hecho, formar una nueva terminología

Low-frequency linear vibrations of single-walled carbon nanotubes: Analytical and numerical models

Low-frequency vibrations of single-walled carbon nanotubes with various boundary conditions are considered in the framework of the Sanders–Koiter thin shell theory. Two methods of analysis are proposed. The first approach is based on the Rayleigh–Ritz method, a double series expansion in terms of Chebyshev polynomials and harmonic functions is considered for the displacement fields; free and clamped edges are analysed. This approach is partially numerical. The second approach is based on the same thin shell theory, but the goal is to obtain an analytical solution useful for future developments in nonlinear fields; the Sanders–Koiter equations are strongly simplified neglecting in-plane circumferential normal strains and tangential shear strains. The model is fully validated by means of comparisons with experiments, molecular dynamics data and finite element analyses obtained from the literature. Several types of nanotubes are considered in detail by varying aspect ratio, chirality and boundary conditions. The analyses are carried out for a wide range of frequency spectrum. The strength and weakness of the proposed approaches are shown; in particular, the model shows great accuracy even though it requires minimal computational effort

Original Russian Text ©

. The development of the diagnostic methods for the subpicosecond timescale was of exceptional importance. With these methods, not only the generation, but also the measurement of fast pro cesses initiated by a femtosecond laser became possi ble. The initiation and measurements are performed with a pair of ultrashort pulses using the stroboscope principle Femtosecond lasers are very efficient generators of shock waves in a condensed phase. They are used together with the pump-probe measurement method Interesting results on the superelastic behavior of a crystal under ultrashort shock compression were obtained in The results on superelasticit