A new regime of anomalous penetration of relativistically strong laser radiation into an overdense plasma

It is shown that penetration of relativistically intense laser light into an overdense plasma, accessible by self-induced transparency, occurs over a finite length only. The penetration length depends crucially on the overdense plasma parameter and increases with increasing incident intensity after exceeding the threshold for self-induced transparency. Exact analytical solutions describing the plasma-field distributions are presented.Comment: 6 pages, 2 figures in 2 separate eps files; submitted to JETP Letter

Bilateral symmetry breaking in a nonlinear Fabry-Perot cavity exhibiting optical tristability

We show the existence of a region in the parameter space that defines the field dynamics in a Fabry-Perot cylindrical cavity, where three output stable stationary states of the light are possible for a given localized incident field. Two of these states do not preserve the bilateral (i.e. left-right) symmetry of the entire system. These broken-symmetry states are the high-transmission nonlinear modes of the system. We also discuss how to excite these states.Comment: 5 pages, 5 figure

Electromagnetic energy penetration in the self-induced transparency regime of relativistic laser-plasma interactions

Two scenarios for the penetration of relativistically intense laser radiation into an overdense plasma, accessible by self-induced transparency, are presented. For supercritical densities less than 1.5 times the critical one, penetration of laser energy occurs by soliton-like structures moving into the plasma. At higher background densities laser light penetrates over a finite length only, that increases with the incident intensity. In this regime plasma-field structures represent alternating electron layers separated by about half a wavelength by depleted regions.Comment: 9 pages, 4 figures, submitted for publication to PR

Stability of narrow beams in bulk Kerr-type nonlinear media

We consider (2+1)-dimensional beams, whose transverse size may be comparable to or smaller than the carrier wavelength, on the basis of an extended version of the nonlinear Schr\"{o}dinger equation derived from the Maxwell`s equations. As this equation is very cumbersome, we also study, in parallel to it, its simplified version which keeps the most essential term: the term which accounts for the {\it nonlinear diffraction}. The full equation additionally includes terms generated by a deviation from the paraxial approximation and by a longitudinal electric-field component in the beam. Solitary-wave stationary solutions to both the full and simplified equations are found, treating the terms which modify the nonlinear Schr\"{o}dinger equation as perturbations. Within the framework of the perturbative approach, a conserved power of the beam is obtained in an explicit form. It is found that the nonlinear diffraction affects stationary beams much stronger than nonparaxiality and longitudinal field. Stability of the beams is directly tested by simulating the simplified equation, with initial configurations taken as predicted by the perturbation theory. The numerically generated solitary beams are always stable and never start to collapse, although they display periodic internal vibrations, whose amplitude decreases with the increase of the beam power.Comment: 7 pages, 6 figures Accepted for publication in PR

Multi-filament structures in relativistic self-focusing

A simple model is derived to prove the multi-filament structure of relativistic self-focusing with ultra-intense lasers. Exact analytical solutions describing the transverse structure of waveguide channels with electron cavitation, for which both the relativistic and ponderomotive nonlinearities are taken into account, are presented.Comment: 21 pages, 12 figures, submitted to Physical Review

Light self-focusing in the atmosphere:thin window model

Ultra-high power (exceeding the self-focusing threshold by more than three orders of magnitude) light beams from ground-based laser systems may find applications in space-debris cleaning. The propagation of such powerful laser beams through the atmosphere reveals many novel interesting features compared to traditional light self-focusing. It is demonstrated here that for the relevant laser parameters, when the thickness of the atmosphere is much shorter than the focusing length (that is, of the orbit scale), the beam transit through the atmosphere in lowest order produces phase distortion only. This means that by using adaptive optics it may be possible to eliminate the impact of self-focusing in the atmosphere on the laser beam. The area of applicability of the proposed "thin window" model is broader than the specific physical problem considered here. For instance, it might find applications in femtosecond laser material processing

A comparison of arbitration procedures for risk averse disputants

We propose an arbitration model framework that generalizes many previous quantitative models of final offer arbitration, conventional arbitration, and some proposed alternatives to them. Our model allows the two disputants to be risk averse and assumes that the issue(s) in dispute can be summarized by a single quantifiable value. We compare the performance of the different arbitration procedures by analyzing the gap between the disputants' equilibrium offers and the width of the contract zone that these offers imply. Our results suggest that final offer arbitration should give results superior to those of conventional arbitration.Natural Sciences & Engineering Research Council (NSERC) Discovery Gran

Academic Performance and Behavioral Patterns

Identifying the factors that influence academic performance is an essential part of educational research. Previous studies have documented the importance of personality traits, class attendance, and social network structure. Because most of these analyses were based on a single behavioral aspect and/or small sample sizes, there is currently no quantification of the interplay of these factors. Here, we study the academic performance among a cohort of 538 undergraduate students forming a single, densely connected social network. Our work is based on data collected using smartphones, which the students used as their primary phones for two years. The availability of multi-channel data from a single population allows us to directly compare the explanatory power of individual and social characteristics. We find that the most informative indicators of performance are based on social ties and that network indicators result in better model performance than individual characteristics (including both personality and class attendance). We confirm earlier findings that class attendance is the most important predictor among individual characteristics. Finally, our results suggest the presence of strong homophily and/or peer effects among university students