1,224 research outputs found
Effect of Catecholamines on the Adenosine 3':5'-Cyclic Monophosphate Concentrations of Clonal Satellite Cells of Neurons
Non-Existence of Positive Stationary Solutions for a Class of Semi-Linear PDEs with Random Coefficients
We consider a so-called random obstacle model for the motion of a
hypersurface through a field of random obstacles, driven by a constant driving
field. The resulting semi-linear parabolic PDE with random coefficients does
not admit a global nonnegative stationary solution, which implies that an
interface that was flat originally cannot get stationary. The absence of global
stationary solutions is shown by proving lower bounds on the growth of
stationary solutions on large domains with Dirichlet boundary conditions.
Difficulties arise because the random lower order part of the equation cannot
be bounded uniformly
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
Global embedding of the Kerr black hole event horizon into hyperbolic 3-space
An explicit global and unique isometric embedding into hyperbolic 3-space,
H^3, of an axi-symmetric 2-surface with Gaussian curvature bounded below is
given. In particular, this allows the embedding into H^3 of surfaces of
revolution having negative, but finite, Gaussian curvature at smooth fixed
points of the U(1) isometry. As an example, we exhibit the global embedding of
the Kerr-Newman event horizon into H^3, for arbitrary values of the angular
momentum. For this example, considering a quotient of H^3 by the Picard group,
we show that the hyperbolic embedding fits in a fundamental domain of the group
up to a slightly larger value of the angular momentum than the limit for which
a global embedding into Euclidean 3-space is possible. An embedding of the
double-Kerr event horizon is also presented, as an example of an embedding
which cannot be made global.Comment: 16 pages, 13 figure
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
Differential Geometry of Quantum States, Observables and Evolution
The geometrical description of Quantum Mechanics is reviewed and proposed as
an alternative picture to the standard ones. The basic notions of observables,
states, evolution and composition of systems are analised from this
perspective, the relevant geometrical structures and their associated algebraic
properties are highlighted, and the Qubit example is thoroughly discussed.Comment: 20 pages, comments are welcome
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
Impulse control disorders in Parkinson's disease: decreased striatal dopamine transporter levels
Objective Impulse control disorders are commonly associated with dopaminergic therapy in Parkinson's disease (PD). PD patients with impulse control disorders demonstrate enhanced dopamine release to conditioned cues and a gambling task on [11C]raclopride positron emission tomography (PET) imaging and enhanced ventral striatal activity to reward on functional MRI. We compared PD patients with impulse control disorders and age-matched and gender-matched controls without impulse control disorders using [123I]FP-CIT (2β-carbomethoxy-3β-(4-iodophenyl)tropane) single photon emission computed tomography (SPECT), to assess striatal dopamine transporter (DAT) density.
Methods The [123I]FP-CIT binding data in the striatum were compared between 15 PD patients with and 15 without impulse control disorders using independent t tests.
Results Those with impulse control disorders showed significantly lower DAT binding in the right striatum with a trend in the left (right: F(1,24)=5.93, p=0.02; left: F(1,24)=3.75, p=0.07) compared to controls.
Conclusions Our findings suggest that greater dopaminergic striatal activity in PD patients with impulse control disorders may be partly related to decreased uptake and clearance of dopamine from the synaptic cleft. Whether these findings are related to state or trait effects is not known. These findings dovetail with reports of lower DAT levels secondary to the effects of methamphetamine and alcohol. Although any regulation of DAT by antiparkinsonian medication appears to be modest, PD patients with impulse control disorders may be differentially sensitive to regulatory mechanisms of DAT expression by dopaminergic medications
Desingularization of vortices for the Euler equation
We study the existence of stationary classical solutions of the
incompressible Euler equation in the plane that approximate singular
stationnary solutions of this equation. The construction is performed by
studying the asymptotics of equation -\eps^2 \Delta
u^\eps=(u^\eps-q-\frac{\kappa}{2\pi} \log \frac{1}{\eps})_+^p with Dirichlet
boundary conditions and a given function. We also study the
desingularization of pairs of vortices by minimal energy nodal solutions and
the desingularization of rotating vortices.Comment: 40 page
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