On a non-isothermal model for nematic liquid crystals

A model describing the evolution of a liquid crystal substance in the nematic phase is investigated in terms of three basic state variables: the {\it absolute temperature} \teta, the {\it velocity field} \ub, and the {\it director field} \bd, representing preferred orientation of molecules in a neighborhood of any point of a reference domain. The time evolution of the velocity field is governed by the incompressible Navier-Stokes system, with a non-isotropic stress tensor depending on the gradients of the velocity and of the director field \bd, where the transport (viscosity) coefficients vary with temperature. The dynamics of \bd is described by means of a parabolic equation of Ginzburg-Landau type, with a suitable penalization term to relax the constraint |\bd | = 1. The system is supplemented by a heat equation, where the heat flux is given by a variant of Fourier's law, depending also on the director field \bd. The proposed model is shown compatible with \emph{First and Second laws} of thermodynamics, and the existence of global-in-time weak solutions for the resulting PDE system is established, without any essential restriction on the size of the data

Institutional relocation : examination of effects and efficacy of two preparatory training programs

Individuals previously exposed to a high frequency of stressful life events have been reported to have a high incidence of physiological and psychological problems, and a higher incidence of problems as compared to individuals exposed to few stressful life events. However, research examining these issues has methodological problems. In an attempt to examine the effects of a life event change in an experimentally controlled manner, the present investigation focused on one specific life event change, interinstitutional relocation of elderly. A review of the literature examining the effects of relocation on the elderly revealed frequent inconsistencies among the studies, which were further confounded by methodological difficulties. The first aim of the present study was to collect a data base (verbal, behavioral, and physiological indices) prior to and after relocation, in an effort to determine exactly what changes occur as a result of relocation. Secondly, the influence of two preparatory training programs on the effects of relocation was examined

Instigative aggression: traditional versus liberal sex roles

A review of the literature on sex differences in aggression reveals that in the majority of studies males are physically more aggressive than females (Buss, 1963; 1966; Taylor and Epstein, 1967). However, most experimenters have grouped male and female data with respect to sex differences rather than on specific characteristics of the individual. The present study addresses itself to the question whether there are some males who are equally or less aggressive than females and whether there are males who do not differentiate between the sex of the target of aggression, when sex role attitudes are taken into account. Most of the studies on sex differences in aggression also have examined the overt expression of aggression in a simple shock exchange paradigm which involves just the subject and victim. It seems apparent that in society all aggressiveness is not that simple, but in fact involves the presence of others. Gaebelein (1973a) modified Taylor's (1967) paradigm such that third party instigation of aggression was investigated. This paradigm was used in the present study. Briefly, 40 male subjects were preselected according to their score on the Attitude Toward Women Scale (Spence & Helmreich, 1972). The subject (advisor) and a confederate (responder) were told that they were to work together in a competitive task against two other people. On each trial the confederate (responder) was to attempt to attain a faster reaction time than his competitor, since the one with the slower reaction time would receive a shock

Constructing solutions to the Bj\"orling problem for isothermic surfaces by structure preserving discretization

In this article, we study an analog of the Bj\"orling problem for isothermic surfaces (that are more general than minimal surfaces): given a real analytic curve $\gamma$ in ${\mathbb R}^3$, and two analytic non-vanishing orthogonal vector fields $v$ and $w$ along $\gamma$, find an isothermic surface that is tangent to $\gamma$ and that has $v$ and $w$ as principal directions of curvature. We prove that solutions to that problem can be obtained by constructing a family of discrete isothermic surfaces (in the sense of Bobenko and Pinkall) from data that is sampled along $\gamma$, and passing to the limit of vanishing mesh size. The proof relies on a rephrasing of the Gauss-Codazzi-system as analytic Cauchy problem and an in-depth-analysis of its discretization which is induced from the geometry of discrete isothermic surfaces. The discrete-to-continuous limit is carried out for the Christoffel and the Darboux transformations as well.Comment: 29 pages, some figure

A Novel Mechanism for Switching a Neural System from One State to Another

An animal's ability to rapidly adjust to new conditions is essential to its survival. The nervous system, then, must be built with the flexibility to adjust, or shift, its processing capabilities on the fly. To understand how this flexibility comes about, we tracked a well-known behavioral shift, a visual integration shift, down to its underlying circuitry, and found that it is produced by a novel mechanism – a change in gap junction coupling that can turn a cell class on and off. The results showed that the turning on and off of a cell class shifted the circuit's behavior from one state to another, and, likewise, the animal's behavior. The widespread presence of similar gap junction-coupled networks in the brain suggests that this mechanism may underlie other behavioral shifts as well

Breakdown of smoothness for the Muskat problem

In this paper we show that there exist analytic initial data in the stable regime for the Muskat problem such that the solution turns to the unstable regime and later breaks down i.e. no longer belongs to $C^4$.Comment: 93 pages, 10 figures (6 added

Local and Global Analytic Solutions for a Class of Characteristic Problems of the Einstein Vacuum Equations in the "Double Null Foliation Gauge"

The main goal of this work consists in showing that the analytic solutions for a class of characteristic problems for the Einstein vacuum equations have an existence region larger than the one provided by the Cauchy-Kowalevski theorem due to the intrinsic hyperbolicity of the Einstein equations. To prove this result we first describe a geometric way of writing the vacuum Einstein equations for the characteristic problems we are considering, in a gauge characterized by the introduction of a double null cone foliation of the spacetime. Then we prove that the existence region for the analytic solutions can be extended to a larger region which depends only on the validity of the apriori estimates for the Weyl equations, associated to the "Bel-Robinson norms". In particular if the initial data are sufficiently small we show that the analytic solution is global. Before showing how to extend the existence region we describe the same result in the case of the Burger equation, which, even if much simpler, nevertheless requires analogous logical steps required for the general proof. Due to length of this work, in this paper we mainly concentrate on the definition of the gauge we use and on writing in a "geometric" way the Einstein equations, then we show how the Cauchy-Kowalevski theorem is adapted to the characteristic problem for the Einstein equations and we describe how the existence region can be extended in the case of the Burger equation. Finally we describe the structure of the extension proof in the case of the Einstein equations. The technical parts of this last result is the content of a second paper.Comment: 68 page

Critical points of Wang-Yau quasi-local energy

In this paper, we prove the following theorem regarding the Wang-Yau quasi-local energy of a spacelike two-surface in a spacetime: Let $\Sigma$ be a boundary component of some compact, time-symmetric, spacelike hypersurface $\Omega$ in a time-oriented spacetime $N$ satisfying the dominant energy condition. Suppose the induced metric on $\Sigma$ has positive Gaussian curvature and all boundary components of $\Omega$ have positive mean curvature. Suppose $H \le H_0$ where $H$ is the mean curvature of $\Sigma$ in $\Omega$ and $H_0$ is the mean curvature of $\Sigma$ when isometrically embedded in $R^3$. If $\Omega$ is not isometric to a domain in $R^3$, then 1. the Brown-York mass of $\Sigma$ in $\Omega$ is a strict local minimum of the Wang-Yau quasi-local energy of $\Sigma$, 2. on a small perturbation $\tilde{\Sigma}$ of $\Sigma$ in $N$, there exists a critical point of the Wang-Yau quasi-local energy of $\tilde{\Sigma}$.Comment: substantially revised, main theorem replaced, Section 3 adde