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[en] Chorus in the inner magnetosphere has been observed frequently at geomagnetically active times, typically exhibiting a two-band structure with a quasi-parallel lower band and an upper band with a broad range of wave normal angles. But recent observations by Van Allen Probes confirm another type of lower band chorus, which has a large wave normal angle close to the resonance cone angle. It has been proposed that these waves could be generated by a low-energy beam-like electron component or by temperature anisotropy of keV electrons in the presence of a low-energy plateau-like electron component. This paper, however, presents an alternative mechanism for generation of this highly oblique lower band chorus. Through a nonlinear three-wave resonance, a quasi-parallel lower band chorus wave can interact with a mildly oblique upper band chorus wave, producing a highly oblique quasi-electrostatic lower band chorus wave. This theoretical analysis is confirmed by 2-D electromagnetic particle-in-cell simulations. Furthermore, as the newly generated waves propagate away from the equator, their wave normal angle can further increase and they are able to scatter low-energy electrons to form a plateau-like structure in the parallel velocity distribution. As a result, the three-wave resonance mechanism may also explain the generation of quasi-parallel upper band chorus which has also been observed in the magnetosphere.
[en] This manuscript attempts an informal, relatively concept-heavy/mathematics-lean presentation to all experts on group processes about how many group processes might unfold upon a generic sort of scaffolding called “multifractal structure.” Explaining group processes poses complementary challenges of explaining similarity among agents belonging to a group and, also, explaining frustrating dissimilarities when agents pull apart and begin to wander from the fold, showing deep multi-scaled texture (e.g., groups containing subgroups, agents containing subagents). Whereas time-varying, multi-scaled texture hampers many linear models, multifractality does what so few other formalisms can: it allows predicting similarities and dissimilarities from nonlinear interactions across scale. Empirical estimates of the multifractal spectrum offer continuously-varying but compact logical support for portraying both the qualitative similarities and the more frustrating qualitative dissimilarities. This story begins at one level to meet the organism at an intuitively behavioral scale, zooms in to a within-organism view, and zooms out to an across-organism view. At each view, resonance of multifractal modeling with the multi-scale structure of group processes reveals new insights into how group behaviors support perception, action, and cognition. This tale of social coordination told in three separate acts has a moral: Multifractality may be a ready tool for wider social-psychological application.
[en] A simple experiment for determining the nonlinear stress–strain relation of duct tape is described. After weights are added and subsequently removed, the tape does not return to its original state and is no longer taut. The tape exhibits hysteresis, which implies the loss of work during the cyclical process. The exponent describing the nonlinearity is related to the fractional work loss. (paper)
[en] This paper investigates the stability and stabilization problem of fractional-order linear systems with nonlinear uncertain parameters, which allow second-order uncertain parameters. The uncertainty in the fractional-order model appears in the form of a combination of additive uncertainty and multiplicative uncertainty. It is shown that the fractional-order model has a strong practical background. Sufficient conditions for the stability and stabilization of such fractional-order model are presented in terms of linear matrix inequalities. Two examples are given to show the effectiveness of the proposed results.
[en] An existence, uniqueness and regularity result for a nonlinear Schroedinger equation is given
[fr]On donne un resultat d'existence, unicite et regularite pour une equation de Sroedinger non lineaire
[en] We describe the results of an accurate and comprehensive numerical study of instability saturation by mode coupling in a three wave system. Particular emphasis is placed upon distinguishing bifurcations leading to motions characteristic of a strange attractor. The tools used in this investigation include power spectral analysis, surface of section plots, and reduction of the latter to one dimensional mapping
[en] In this work, we investigate the amplitude death in coupled system with small number of nonlinear oscillators. We show how the transitions to the partial and the complete amplitude deathes happen. We also show that the partial amplitude death can be found in globally coupled oscillators either. (general)
[en] A hidden nonlinear bosonized supersymmetry was revealed recently in the Poeschl-Teller and finite-gap Lame systems. In spite of the intimate relationship between the two quantum models, the hidden supersymmetry in them displays essential differences. In particular, the kernel of the supercharges of the Poeschl-Teller system, unlike the case of the Lame equation, includes nonphysical states. By means of the Lame equation, we clarify the nature of these peculiar states, and show that they encode essential information not only on the original hyperbolic Poeschl-Teller system, but also on its singular hyperbolic and trigonometric modifications, and reflect the intimate relation of the model to a free-particle system
[en] A smooth non-linear map is studied in a neighbourhood of an abnormal (degenerate) point. Inverse function and implicit function theorems are proved. The proof is based on the examination of a family of constrained extremal problems; second-order necessary conditions, which make sense also in the abnormal case, are used in the process. If the point under consideration is normal, then these conditions turn into the classical ones
[en] The book consists of the Proceedings of the School on Qualitative Aspects and Applications of Nonlinear Evolution equations held at the ICTP Trieste between 10 September-5 October 1990. It includes Main Courses (5 lectures), Special Lectures (7 lectures) and Talks Given at the Seminars (13 lectures). A separate abstract was prepared for each lecture. Refs, figs and tabs