scholarly journals Constructive Study of Modulational Instability in Higher Order Korteweg-de Vries Equations

Fluids ◽  
2019 ◽  
Vol 4 (1) ◽  
pp. 54 ◽  
Author(s):  
Elena Tobisch ◽  
Efim Pelinovsky
Keyword(s):  
Modulational Instability ◽  
Stokes Wave ◽  
Arbitrary Integer ◽  
Research Directions ◽  
Open Questions ◽  
De Vries ◽  
Rate Maximum ◽  
Instability Growth ◽  
Instability Interval ◽  
Growth Rate Maximum

Our present study is devoted to the constructive study of the modulational instability for the Korteweg-de Vries (KdV)-family of equations u t + s u p u x + u x x x (here s = ± 1 and p > 0 is an arbitrary integer). For deducing the conditions of the instability, we first computed the nonlinear corrections to the frequency of the Stokes wave and then explored the coefficients of the corresponding modified nonlinear Schrödinger equations, thus deducing explicit expressions for the instability growth rate, maximum of the increment and the boundaries of the instability interval. A brief discussion of the results, open questions and further research directions completes the paper.

scholarly journals Plasmonic Cu2−xS nanoparticles: a brief introduction of optical properties and applications

2021 ◽  
Vol 2 (3) ◽  
pp. 907-926
Author(s):  
Lihui Chen ◽  
Haifeng Hu ◽  
Yuzhou Chen ◽  
Jing Gao ◽  
Guohua Li
Keyword(s):  
Optical Properties ◽  
Research Directions ◽  
Open Questions

LSPR of Cu2−xS and the resulting plasmonic applications are summarized. Remaining open questions and further research directions are proposed.

scholarly journals Reducibility and Solvability of Some Classes of Kryuchkov Binary Tree Pairs

10.37236/2028 ◽  
2012 ◽  
Vol 18 (2) ◽  
Author(s):  
Maria Madonia ◽  
Giuseppe Scollo
Keyword(s):  
Induction Hypothesis ◽  
Binary Tree ◽  
Binary Trees ◽  
Equal Size ◽  
Future Research ◽  
Theoretic Approach ◽  
Research Directions ◽  
Open Questions ◽  
Future Research Directions

This paper addresses the problem of characterizing classes of pairs of binary trees of equal size for which a signed reassociation sequence, in the Eliahou-Kryuchkov sense, can be shown to exist, either with a size induction hypothesis (reducible pairs), or without it (solvable pairs). A few concepts proposed by Cooper, Rowland and Zeilberger, in the context of a language-theoretic approach to the problem, are here reformulated in terms of signed reassociation sequences, and some of their results are recasted and proven in this framework. A few strategies, tactics and combinations thereof for signed reassociation are introduced, which prove useful to extend the results obtained by the aforementioned authors to new classes of binary tree pairs. In particular, with reference to path trees, i.e. binary trees that have a leaf at every level, we show the reducibility of pairs where (at least) one of the two path trees has a triplication at the first turn below the top level, and we characterize a class of weakly mutually crooked path tree pairs that are neither reducible nor solvable by any previously known result, but prove solvable by appropriate reassociation strategies. This class also includes a subclass of mutually crooked path tree pairs. A summary evaluation of the achieved results, followed by an outline of open questions and future research directions conclude the paper.

scholarly journals 3D quantum Hall effects and nonlinear Hall effect

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Shuai Li ◽  
C. M. Wang ◽  
Z. Z. Du ◽  
Fang Qin ◽  
Hai-Zhou Lu ◽  
...  
Keyword(s):  
Hall Effect ◽  
Condensed Matter ◽  
Quantum Hall ◽  
Future Research ◽  
Research Directions ◽  
New Members ◽  
Quantum Hall Effects ◽  
Open Questions ◽  
Hall Effects ◽  
Future Research Directions

AbstractThe classical and quantum Hall effects are important subjects in condensed matter physics. The emergent 3D quantum Hall effects and nonlinear Hall effect have attracted considerable interest recently, with the former elevating the quantum Hall effect to a higher dimension and the latter extending the Hall effect to higher-order responses. In this perspective, we briefly introduce these two new members of the Hall family and discuss the open questions and future research directions.

scholarly journals Kinetic modulational instability of broadband dispersive Alfvén waves in plasmas

2007 ◽  
Vol 73 (2) ◽  
pp. 153-157 ◽  
Author(s):  
P.K. SHUKLA ◽  
NITIN SHUKLA ◽  
L. STENFLO
Keyword(s):  
Modulational Instability ◽  
Random Phase ◽  
Alfven Waves ◽  
Nonlinear Propagation ◽  
Alfvén Waves ◽  
Nonlinear Dispersion Relation ◽  
Laboratory Plasmas ◽  
Interstellar Media ◽  
Bow Shocks ◽  
Instability Growth

Abstract.We consider a kinetic modulational instability of broadband (random phase) magnetic-field-aligned circularly polarized dispersive Alfvén waves in plasmas. By treating random phase Alfvén waves as quasi-particles, we consider their nonlinear interactions with ion quasi-modes within the framework of the wave-kinetic and Vlasov descriptions. A nonlinear dispersion relation governing such interactions is derived and analyzed. An explicit expression for the kinetic modulational instability growth rate is presented. Our results can be of relevance to the nonlinear propagation of incoherent Alfvén waves, which have been frequently observed in interstellar media, in the solar corona and in the solar wind, as well as in the foreshock regions of planetary bow-shocks and laboratory plasmas.

Existence and stability of modulated dust-acoustic wave packets in the presence of nonthermal ions

2015 ◽  
Vol 93 (3) ◽  
pp. 271-277
Author(s):  
H. Alinejad ◽  
M. Mahdavi
Keyword(s):  
Modulational Instability ◽  
Wave Packets ◽  
Dusty Plasmas ◽  
Dust Acoustic Wave ◽  
Envelope Solitons ◽  
Fast Ions ◽  
Dust Temperature ◽  
Dust Acoustic ◽  
Existence And Stability ◽  
Instability Growth

The effects of dust temperature and energetic (nonthermal) ions are incorporated in the study of modulated instability of dust-acoustic (DA) waves in a dusty plasma containing warm adiabatic dust grains, isothermal electrons and hot ions obeying a nonthermal distribution. Based on the multiple space and time scales perturbation, a nonlinear Schrödinger equation is derived with a solution showing a new relationship between the modulated DA wave packets and ion nonthermality. It is shown that as the population of fast ions increases, the transition from stable dark envelope solitons to unstable ones shifts to the smaller wavelength regions. The instability growth rate reduces owing to the presence of nonthermal ions. It is also found that the effects of dust temperature and electron concentration modify the criteria for the modulational instability of DA waves. The results could be useful for understanding the properties of modulated wave packets and their evolution in space and laboratory dusty plasmas, such as those in and around the Earth’s foreshock.

The Market, the Firm, and Behavioral Antitrust

2014 ◽  
pp. 538-567
Author(s):  
Avishalom Tor
Keyword(s):  
Empirical Evidence ◽  
Law And Economics ◽  
Individual Behavior ◽  
Future Research ◽  
Antitrust Law ◽  
Research Directions ◽  
Enforcement Policy ◽  
Open Questions ◽  
Future Research Directions ◽  
Behavioral Evidence

This Handbook chapter examines the main distinct concerns facing the application of empirical behavioral evidence to antitrust law and economics—also known as “behavioral antitrust.” More than many (though not all) other legal fields, antitrust law is primarily concerned with the conduct of firms in markets rather than in individual behavior per se. Yet much of the empirical evidence that behavioral antitrust draws on concerns individual behavior outside the firm, often in nonmarket settings. Hence besides adducing additional, direct empirical evidence on behavioral phenomena within firms and markets, there is a need to determine when and how the behavioral evidence on human judgment and decision behavior more generally is informative for antitrust. To this end, the chapter considers the ways in which markets and firms shape behavior. Direct evidence and theoretical analysis both reveal these institutions variously to facilitate rationality and deviations from it. After illustrating the implications of the complex interaction among markets, firms, and the rationality of antitrust actors across different areas of the law and enforcement policy, the chapter concludes by sketching some important open questions and future research directions in behavioral antitrust.

scholarly journals Two-dimensional semi-Lagrangian Vlasov simulations of laser–plasma interaction in the relativistic regime

1999 ◽  
Vol 62 (4) ◽  
pp. 367-388 ◽  
Author(s):  
M. L. BÉGUÉ ◽  
A. GHIZZO ◽  
P. BERTRAND ◽  
E. SONNENDRÜCKER ◽  
O. COULAUD
Keyword(s):  
Phase Space ◽  
Modulational Instability ◽  
Particle Dynamics ◽  
Two Dimensional ◽  
Nonlinear Saturation ◽  
Laser Plasma Interaction ◽  
Relativistic Regime ◽  
Coherent Vortex ◽  
Instability Growth ◽  
Good Agreement

A semi-Lagrangian two-dimensional fully relativistic Vlasov code for multicomputer environments is developed to study trapped-particle dynamics in phase space induced by relativistic modulational and Raman instabilities. Attention is focused on the efficiency properties of the numerical scheme, which allows a very fine description of particle dynamics in phase space. Vlasov simulations show the appearance of coherent vortex structures as a result of the nonlinear saturation mechanism of the relativistic modulational instability. Growth rates are computed and found to be in good agreement with theoretical values obtained from the dispersion relation by Quesnel et al, [Phys. Plasmas4, 3358–3368 (1997)] and Guérin et al. [Phys. Plasmas2, 2807–2814 (1995)]. In the case of coupling between the relativistic modulational instability and two-plasmon decay, stochastic behaviour can be observed due to the competition between different plasmas waves.

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