956 research outputs found
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 in , and two analytic non-vanishing orthogonal
vector fields and along , find an isothermic surface that is
tangent to and that has and 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 , 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 .Comment: 93 pages, 10 figures (6 added
Time reversal in thermoacoustic tomography - an error estimate
The time reversal method in thermoacoustic tomography is used for
approximating the initial pressure inside a biological object using
measurements of the pressure wave made on a surface surrounding the object.
This article presents error estimates for the time reversal method in the cases
of variable, non-trapping sound speeds.Comment: 16 pages, 6 figures, expanded "Remarks and Conclusions" section,
added one figure, added reference
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
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