Modulational Instability in Equations of KdV Type

It is a matter of experience that nonlinear waves in dispersive media, propagating primarily in one direction, may appear periodic in small space and time scales, but their characteristics --- amplitude, phase, wave number, etc. --- slowly vary in large space and time scales. In the 1970's, Whitham developed an asymptotic (WKB) method to study the effects of small "modulations" on nonlinear periodic wave trains. Since then, there has been a great deal of work aiming at rigorously justifying the predictions from Whitham's formal theory. We discuss recent advances in the mathematical understanding of the dynamics, in particular, the instability of slowly modulated wave trains for nonlinear dispersive equations of KdV type.Comment: 40 pages. To appear in upcoming title in Lecture Notes in Physic

Steady water waves with multiple critical layers: interior dynamics

We study small-amplitude steady water waves with multiple critical layers. Those are rotational two-dimensional gravity-waves propagating over a perfect fluid of finite depth. It is found that arbitrarily many critical layers with cat's-eye vortices are possible, with different structure at different levels within the fluid. The corresponding vorticity depends linearly on the stream function.Comment: 14 pages, 3 figures. As accepted for publication in J. Math. Fluid Mec

Parametrization of nonlinear and chaotic oscillations in driven beam-plasma diodes

Nonlinear phenomena in a driven plasma diode are studied using a fluid code and the particle-in-cell simulation code XPDPI. When a uniform electron beam is injected to a bounded diode filled with uniform ion background, the beam is destabilized by the Pierce instability and a perturbation grows to exhibit nonlinear oscillations including chaos. Two standard routes to chaos, period doubling and quasiperiodicity, are observed. Mode lockings of various winding numbers are observed in an ac driven system. A new diagnostic quantity is used to parametrize various nonlinear oscillations.open10

Star clusters near and far; tracing star formation across cosmic time

© 2020 Springer-Verlag. The final publication is available at Springer via https://doi.org/10.1007/s11214-020-00690-x.Star clusters are fundamental units of stellar feedback and unique tracers of their host galactic properties. In this review, we will first focus on their constituents, i.e.\ detailed insight into their stellar populations and their surrounding ionised, warm, neutral, and molecular gas. We, then, move beyond the Local Group to review star cluster populations at various evolutionary stages, and in diverse galactic environmental conditions accessible in the local Universe. At high redshift, where conditions for cluster formation and evolution are more extreme, we are only able to observe the integrated light of a handful of objects that we believe will become globular clusters. We therefore discuss how numerical and analytical methods, informed by the observed properties of cluster populations in the local Universe, are used to develop sophisticated simulations potentially capable of disentangling the genetic map of galaxy formation and assembly that is carried by globular cluster populations.Peer reviewedFinal Accepted Versio

Catching up with wonderful women: The women-are-wonderful effect is smaller in more gender egalitarian societies

Inequalities between men and women are common and well-documented. Objective indexes show that men are better positioned than women in societal hierarchies—there is no single country in the world without a gender gap. In contrast, researchers have found that the women-are-wonderful effect—that women are evaluated more positively than men overall—is also common. Cross-cultural studies on gender equality reveal that the more gender egalitarian the society is, the less prevalent explicit gender stereotypes are. Yet, because self-reported gender stereotypes may differ from implicit attitudes towards each gender, we reanalysed data collected across 44 cultures, and (a) confirmed that societal gender egalitarianism reduces the women-are-wonderful effect when it is measured more implicitly (i.e. rating the personality of men and women presented in images) and (b) documented that the social perception of men benefits more from gender egalitarianism than that of women. © 2017 International Union of Psychological Scienc