When a fluid with a bulk liquid-vapor critical point is placed inside a static external field with spatial periodic oscillations in one direction, a new phase arises. This new phase-the so-called "zebra" phase-is characterized by an average density roughly between that of the liquid and vapor phases. The presence of the zebra phase gives rise to two new phase transitions: one from the vapor to ...

An increased clinical interest in shame has been reflected in the growing number of research studies in this area. However, clinically orientated empirical investigation has mostly been restricted to the investigation of individual differences in dispositional shame. This study reviews recent work on dispositional shame but then argues that the primacy of this construct has been problematic in ...

We study positive supersolutions to an elliptic equation (∗) −∆u = c|x|u, p, s ∈ R, in cone–like domains in R (N ≥ 2). We prove that in the sublinear case p < 1 there exists a critical exponent p∗ < 1 such that equation (∗) has a positive supersolution if and only if −∞ < p < p∗. The value of p∗ is determined explicitly by s and the geometry of the cone.

The Cover shows the human cortex overlayed with ocean waves and sand, to illustrate two forms of neuronal dynamics investigated in this thesis. Designed with help from Matthew Jarvis.

Abstract: In this paper we focus on the problem of the degree sequence for the following random graph process. At any time-step t, one of the following three substeps is executed: with probability α1, a new vertex xt and m edges incident with xt are added; or, with probability α− α1, m edges are added; or finally, with probability 1 − α, m random edges are deleted. Note that in any case edges a...

with u0 ∈ H1 = {u,∇u ∈ L2(RN )} in dimension N ≥ 1. This equation for N = 2 appears in physics as a universal model to describe self trapping of waves propagating in nonlinear media. The physical expectation for large smooth data is the concentration of part of the L2 mass in finite time corresponding to the focusing of the laser beam. If some explicit examples of this phenomenon are known, and...

Radiation emitted by an electric dipole consists of traveling and evanescent plane waves. Usually, only the traveling waves are observable by a measurement in the far field, since the evanescent waves die out over a length of approximately a wavelength from the source. We show that when the radiation is passed through an interface with a medium with an index of refraction larger than the index ...

Spatial disorder in the large box, one-dimensional, complex Ginzburg-Landau problem is investigated quantitatively. The transition from phase to amplitude turbulence is studied in detail. This transition is described by the dimension of the space series, as, that estimates the number of normal (independent) medium perturbations forming the chaotic space series. It is found that at a critical po...

The Nlonw Carlo Renormalization Group (A4CRG) methods and the theory behind thcm arc reviewed, The Cllpta-Cordcry improved A4CRG method is described and cumparcd with the standard one. The emphasis is on the progress made in understanding the truncation errols in the Linearized Transformation Ma+,rix and on open problems. Lastly, some of t!lc existing methods for calculating the renormalized Ha...