The Fermi-Pasta-Ulam recurrence and related phenomena for 1D shallow-water waves in a finite basin

In this work, different regimes of the Fermi-Pasta-Ulam (FPU) recurrence are simulated numerically for fully nonlinear "one-dimensional" potential water waves in a finite-depth flume between two vertical walls. In such systems, the FPU recurrence is closely related to the dynamics of coherent structures approximately corresponding to solitons of the integrable Boussinesq system. A simplest periodic solution of the Boussinesq model, describing a single soliton between the walls, is presented in an analytical form in terms of the elliptic Jacobi functions. In the numerical experiments, it is observed that depending on a number of solitons in the flume and their parameters, the FPU recurrence can occur in a simple or complicated manner, or be practically absent. For comparison, the nonlinear dynamics of potential water waves over nonuniform beds is simulated, with initial states taken in the form of several pairs of colliding solitons. With a mild-slope bed profile, a typical phenomenon in the course of evolution is appearance of relatively high (rogue) waves, while for random, relatively short-correlated bed profiles it is either appearance of tall waves, or formation of sharp crests at moderate-height waves.Comment: revtex4, 10 pages, 33 figure

Corruption dynamics in the post-crisis world

Corruption is typical for all states of the world, but its level differs significantly. In the present work, an attempt is made at spatio-temporal analysis of its changes through the period of 2012-2015 for the entire world and some particular large regions (Europe, Africa, Latin America, South-East Asia). Mean and median values of the corruption index are calculated, and specific indices reflecting the degree of differences in the distribution of corruption by countries between pairs of years are established. These specific indices are based on the correlation coefficient, the Quantified Czekanowski’s Coefficient and the Gower Index. The results of the analysis imply that the level of corruption in the world has hardly changed and remained generally high during the past four years. Some positive trends are observed only in Europe. The spatial dynamics was weak. This means that the level of corruption in the states almost did not change relatively to that in the other states. Essentially, this indicates the absence of competition between the countries for a better situation in terms of corruption. Clear tendencies are almost non-existent. Further discussion of the results suggests that the by-country distribution of corruption changed stronger in the cases of its very high and very low levels. The global financial (economic) crisis would facilitate multi-directional tendencies in the change of the corruption level and, consequently, the relatively intense dynamics. However, conclusions made in the present work point to the opposite. This may be explained by an insufficiently deep understanding of the factor of corruption and the fact that some countries with a relatively high level of corruption resisted the crisis successfully because of certain economic or geopolitical causes. Moreover, the administrative discretion that increased in the crisis times might have had its impact, too. Generally, the almost unchanged situation as regards corruption in the world does not allow for making optimistic prognoses about future economic development (also based on innovations), as well as it does not exclude the recurrence of crisis phenomena in the economy.Коррупция характерна для всех государств мира, однако ее уровень существенно различается. В настоящей работе предпринят пространственно-временной анализ его изменений за период 2012-2015 гг. для мира в целом и отдельных крупных регионов (Европа, Африка, Латинская Америка, Юго-Восточная Азия). Определялись средние и медианные значения показателя коррупции, а также рассчитывались специфические показатели, отражающие меру отличий в распределении коррупции по странам мира между двумя годами. Эти специфические показатели имеют в своей основе коэффициент корреляции, числовой коэффициент Чекановского и индекс Гоуэра. По результатам анализа установлено, что за последние четыре года уровень коррупции в мире практически не изменился и при этом остался сравнительно высоким. Некоторая позитивная тенденция отмечена лишь в Европе. Пространственная динамика была предельно слабой. Это означает, что уровень коррупции в одних государствах практически не менялся в сравнении с таковым в других. По сути это указывает на отсутствие конкуренции между странами за лучшую в отношении коррупции обстановку. Четко выраженных тенденций практически не прослеживается. Последующее обсуждение полученных результатов свидетельствует о том, что распределение коррупции по странам менялось гораздо сильнее при очень высоком и очень низком ее уровнях. Мировой финансовый (экономический) кризис должен был способствовать возникновению разнонаправленных тенденций изменения уровня коррупции в странах мира и, следовательно, достаточно интенсивной динамике. Однако сделанные в настоящей работе выводы свидетельствуют об обратном. Это может быть связано с недостаточно глубоким осознанием фактора коррупции и с тем, что целый ряд стран со сравнительно высоким уровнем коррупции в силу тех или иных экономических или геополитических причин достаточно успешно справился с кризисными явлениями. Кроме того, влияние могла оказать увеличившаяся во время кризиса управленческая дискреция. В целом практически неизменная ситуация с коррупцией в мире не позволяет делать оптимистических прогнозов в отношении будущего экономического развития (в т. ч. основанного на инновациях), равно как и не исключает повтора кризисных явлений в экономике

Current-sheet formation in incompressible electron magnetohydrodynamics

The nonlinear dynamics of axisymmetric, as well as helical, frozen-in vortex structures is investigated by the Hamiltonian method in the framework of ideal incompressible electron magnetohydrodynamics. For description of current-sheet formation from a smooth initial magnetic field, local and nonlocal nonlinear approximations are introduced and partially analyzed that are generalizations of the previously known exactly solvable local model neglecting electron inertia. Finally, estimations are made that predict finite-time singularity formation for a class of hydrodynamic models intermediate between that local model and the Eulerian hydrodynamics.Comment: REVTEX4, 5 pages, no figures. Introduction rewritten, new material and references adde

Nonlinear interfacial waves in a constant-vorticity planar flow over variable depth

Exact Lagrangian in compact form is derived for planar internal waves in a two-fluid system with a relatively small density jump (the Boussinesq limit taking place in real oceanic conditions), in the presence of a background shear current of constant vorticity, and over arbitrary bottom profile. Long-wave asymptotic approximations of higher orders are derived from the exact Hamiltonian functional in a remarkably simple way, for two different parametrizations of the interface shape.Comment: revtex, 4.5 pages, minor corrections, summary added, accepted to JETP Letter

"Breathing" rogue wave observed in numerical experiment

Numerical simulations of the recently derived fully nonlinear equations of motion for weakly three-dimensional water waves [V.P. Ruban, Phys. Rev. E {\bf 71}, 055303(R) (2005)] with quasi-random initial conditions are reported, which show the spontaneous formation of a single extreme wave on the deep water. This rogue wave behaves in an oscillating manner and exists for a relatively long time (many wave periods) without significant change of its maximal amplitude.Comment: 6 pages, 12 figure

Detection and Classification of Three Phase Power Quality Events Using Wavelets Transforms and Soft Computing Techniques

Analysis of power quality and its related problems is of very much important for both the utilities and end users. There are a large number of concerned authorities to monitor and mitigate the power quality problems. It requires a larger amount to deliver a poor power. So by considering the global economical losses, it is very much urgent to mitigate the various problems affecting the true power. Classification of problems is equally important to mitigation. The common power quality problems occurring are voltage sag, swell, harmonics, flickers etc. Good power determines the fitness of electric power to consumer devices and appliances. It is very important to maintain the detection accuracy of power quality events throughout the operation span. This paper deals with a study based on signal processing algorithms and soft computing techniques for the detection, classification and estimation of power quality events. The literature review points toward the application of wavelet transforms with different filters for achieving feature extraction. The power quality disturbance model is simulated using Simulink toolbox. It is observed that every power quality wavelet disturbance will show unique characteristics and it is generally used to provide an adoptable classification of power quality events. Because of the non-stationary and transitory behavior of the power quality events, the classification goes on challenging and demanding. Thus the feature extraction along with artificial neural network and fuzzy logic incorporated as a powerful too

Magnetic Brane-worlds

We investigate brane-worlds with a pure magnetic field and a perfect fluid. We extend earlier work to brane-worlds, and find new properties of the Bianchi type I brane-world. We find new asymptotic behaviours on approach to the singularity and classify the critical points of the dynamical phase space. It is known that the Einstein equations for the magnetic Bianchi type I models are in general oscillatory and are believed to be chaotic, but in the brane-world model this chaotic behaviour does not seem to be possible.Comment: 21 pages, 3 ps figures; To appear in CQ

Nonlinear stage of the Benjamin-Feir instability: Three-dimensional coherent structures and rogue waves

A specific, genuinely three-dimensional mechanism of rogue wave formation, in a late stage of the modulational instability of a perturbed Stokes deep-water wave, is recognized through numerical experiments. The simulations are based on fully nonlinear equations describing weakly three-dimensional potential flows of an ideal fluid with a free surface in terms of conformal variables. Spontaneous formation of zigzag patterns for wave amplitude is observed in a nonlinear stage of the instability. If initial wave steepness is sufficiently high ($ka>0.06$), these coherent structures produce rogue waves. The most tall waves appear in ``turns'' of the zigzags. For $ka<0.06$, the structures decay typically without formation of steep waves.Comment: 11 pages, 7 figures, submitted to PR

Gravitational Collapse of Dust with a Cosmological Constant

The recent analysis of Markovic and Shapiro on the effect of a cosmological constant on the evolution of a spherically symmetric homogeneous dust ball is extended to include the inhomogeneous and degenerate cases. The histories are shown by way of effective potential and Penrose-Carter diagrams.Comment: 2 pages, 2 figures (png), revtex. To appear in Phys. Rev.