Universality in the profile of the semiclassical limit solutions to the focusing Nonlinear Schroedinger equation at the first breaking curve

We consider the semiclassical (zero-dispersion) limit of the one-dimensional focusing Nonlinear Schroedinger equation (NLS) with decaying potentials. If a potential is a simple rapidly oscillating wave (the period has the order of the semiclassical parameter epsilon) with modulated amplitude and phase, the space-time plane subdivides into regions of qualitatively different behavior, with the boundary between them consisting typically of collection of piecewise smooth arcs (breaking curve(s)). In the first region the evolution of the potential is ruled by modulation equations (Whitham equations), but for every value of the space variable x there is a moment of transition (breaking), where the solution develops fast, quasi-periodic behavior, i.e., the amplitude becomes also fastly oscillating at scales of order epsilon. The very first point of such transition is called the point of gradient catastrophe. We study the detailed asymptotic behavior of the left and right edges of the interface between these two regions at any time after the gradient catastrophe. The main finding is that the first oscillations in the amplitude are of nonzero asymptotic size even as epsilon tends to zero, and they display two separate natural scales; of order epsilon in the parallel direction to the breaking curve in the (x,t)-plane, and of order epsilon ln(epsilon) in a transversal direction. The study is based upon the inverse-scattering method and the nonlinear steepest descent method.Comment: 40 pages, 10 figure

Orthonormal Polynomials on the Unit Circle and Spatially Discrete Painlev\'e II Equation

We consider the polynomials $\phi_n(z)= \kappa_n (z^n+ b_{n-1} z^{n-1}+ >...)$ orthonormal with respect to the weight $\exp(\sqrt{\lambda} (z+ 1/z)) dz/2 \pi i z$ on the unit circle in the complex plane. The leading coefficient $\kappa_n$ is found to satisfy a difference-differential (spatially discrete) equation which is further proved to approach a third order differential equation by double scaling. The third order differential equation is equivalent to the Painlev\'e II equation. The leading coefficient and second leading coefficient of $\phi_n(z)$ can be expressed asymptotically in terms of the Painlev\'e II function.Comment: 16 page

Networked Families

Presents survey results on the use of the Internet and ownership of cell phones and computers, by household type. Examines how technology ownership affects the frequency, form, purpose, and quality of communications among family members and friends

Sanctioning resistance to sexual objectification: An integrative system justification perspective

In this article, we describe an integrated theoretical approach for promoting resistance to the system of sexual objectification. Drawing from system justification and objectification theories, we propose a two-arm approach that would harness the system justification motive and adjust the lens of self-objectification in order to facilitate social change. We suggest that it is necessary to frame a rejection of the system of sexual objectification as a way to preserve (rather than threaten) the societal status quo. Further, we argue that it is critical to alter and expand the self-objectified lens through which many women come to view themselves in order to reduce their dependence on the system that constructs and sustains that lens. Although we recognize that multiple approaches and perspectives are needed, we argue that a disruption of the system at its ideological roots is essential to ultimately transcend sexual objectification as a cultural practice

Current moments of 1D ASEP by duality

We consider the exponential moments of integrated currents of 1D asymmetric simple exclusion process using the duality found by Sch\"utz. For the ASEP on the infinite lattice we show that the $n$th moment is reduced to the problem of the ASEP with less than or equal to $n$ particles.Comment: 13 pages, no figur

Characterization of cavity flow fields using pressure data obtained in the Langley 0.3-Meter Transonic Cryogenic Tunnel

Static and fluctuating pressure distributions were obtained along the floor of a rectangular-box cavity in an experiment performed in the LaRC 0.3-Meter Transonic Cryogenic Tunnel. The cavity studied was 11.25 in. long and 2.50 in. wide with a variable height to obtain length-to-height ratios of 4.4, 6.7, 12.67, and 20.0. The data presented herein were obtained for yaw angles of 0 deg and 15 deg over a Mach number range from 0.2 to 0.9 at a Reynolds number of 30 x 10(exp 6) per ft with a boundary-layer thickness of approximately 0.5 in. The results indicated that open and transitional-open cavity flow supports tone generation at subsonic and transonic speeds at Mach numbers of 0.6 and above. Further, pressure fluctuations associated with acoustic tone generation can be sustained when static pressure distributions indicate that transitional-closed and closed flow fields exist in the cavity. Cavities that support tone generation at 0 deg yaw also supported tone generation at 15 deg yaw when the flow became transitional-closed. For the latter cases, a reduction in tone amplitude was observed. Both static and fluctuating pressure data must be considered when defining cavity flow fields, and the flow models need to be refined to accommodate steady and unsteady flows

Market Structure, Strike Activity, and Union Wage Settlements

We attempt a synthesis of the industrial relations market structure hypothesis with the modern asymmetric information theory of wage and strike outcomes The industrial relations literature contains a variety of arguments indicating that wage settlements should be positively related to the degree of product market sales concentration and the degree of product market coverage by the union. An asymmetric information bargaining model is specified that relates these same variables to strike probabilities as well as wage settlements. Our empirical analysis is conducted for :he periods from 1970-1380 (strikes) and 1976-1980 (wages). We find that the relation between trade-adjusted sales concentration and wage settlements is positive at low levels of concentration but negative at high levels of concentration. The relation is always negative for strike probabilities. We also find that the relation between the trade-adjusted percent of the product market covered by the same union and the percentage covered by other union are positively related to both wage settlements and strike probabilities. Our empirical analysis includes a rich set of controls including unrestricted time and industry effects, which do not affect the major conclusions.

On ASEP with Step Bernoulli Initial Condition

This paper extends results of earlier work on ASEP to the case of step Bernoulli initial condition. The main results are a representation in terms of a Fredholm determinant for the probability distribution of a fixed particle, and asymptotic results which in particular establish KPZ universality for this probability in one regime. (And, as a corollary, for the current fluctuations.)Comment: 16 pages. Revised version adds references and expands the introductio

Riemann-Hilbert approach to multi-time processes; the Airy and the Pearcey case

We prove that matrix Fredholm determinants related to multi-time processes can be expressed in terms of determinants of integrable kernels \`a la Its-Izergin-Korepin-Slavnov (IIKS) and hence related to suitable Riemann-Hilbert problems, thus extending the known results for the single-time case. We focus on the Airy and Pearcey processes. As an example of applications we re-deduce a third order PDE, found by Adler and van Moerbeke, for the two-time Airy process.Comment: 18 pages, 1 figur