218 research outputs found
Null Cones in Schwarzschild Geometry
Light cones of Schwarzschild geometry are studied in connection to the Null
Surface Formulation and gravitational lensing. The paper studies the light cone
cut function's singularity structure, gives exact gravitational lensing
equations, and shows that the "pseudo-Minkowski" coordinates are well defined
within the model considered.Comment: 31 pages, 5 figure
Mathematics of Gravitational Lensing: Multiple Imaging and Magnification
The mathematical theory of gravitational lensing has revealed many generic
and global properties. Beginning with multiple imaging, we review
Morse-theoretic image counting formulas and lower bound results, and
complex-algebraic upper bounds in the case of single and multiple lens planes.
We discuss recent advances in the mathematics of stochastic lensing, discussing
a general formula for the global expected number of minimum lensed images as
well as asymptotic formulas for the probability densities of the microlensing
random time delay functions, random lensing maps, and random shear, and an
asymptotic expression for the global expected number of micro-minima. Multiple
imaging in optical geometry and a spacetime setting are treated. We review
global magnification relation results for model-dependent scenarios and cover
recent developments on universal local magnification relations for higher order
caustics.Comment: 25 pages, 4 figures. Invited review submitted for special issue of
General Relativity and Gravitatio
Large time wellposdness to the 3-D Capillary-Gravity Waves in the long wave regime
In the regime of weakly transverse long waves, given long-wave initial data,
we prove that the nondimensionalized water wave system in an infinite strip
under influence of gravity and surface tension on the upper free interface has
a unique solution on [0,{T}/\eps] for some \eps independent of constant
We shall prove in the subsequent paper \cite{MZZ2} that on the same time
interval, these solutions can be accurately approximated by sums of solutions
of two decoupled Kadomtsev-Petviashvili (KP) equations.Comment: Split the original paper(The long wave approximation to the 3-D
capillary-gravity waves) into two parts, this is the first on
Photoemission studies of GaMnAs: Mn-concentration dependent properties
Using angle-resolved photoemission, we have investigated the development of
the electronic structure and the Fermi level pinnning in GaMnAs
with Mn concentrations in the range 1--6%. We find that the Mn-induced changes
in the valence-band spectra depend strongly on the Mn concentration, suggesting
that the interaction between the Mn ions is more complex than assumed in
earlier studies. The relative position of the Fermi level is also found to be
concentration-dependent. In particular we find that for concentrations around
3.5--5% it is located very close to the valence-band maximum, which is in the
range where metallic conductivity has been reported in earlier studies. For
concentration outside this range, larger as well as smaller, the Fermi level is
found to be pinned at about 0.15 eV higher energy.Comment: REVTeX style; 7 pages, 3 figure
Fuchsian convex bodies: basics of Brunn--Minkowski theory
The hyperbolic space \H^d can be defined as a pseudo-sphere in the
Minkowski space-time. In this paper, a Fuchsian group is a group of
linear isometries of the Minkowski space such that \H^d/\Gamma is a compact
manifold. We introduce Fuchsian convex bodies, which are closed convex sets in
Minkowski space, globally invariant for the action of a Fuchsian group. A
volume can be associated to each Fuchsian convex body, and, if the group is
fixed, Minkowski addition behaves well. Then Fuchsian convex bodies can be
studied in the same manner as convex bodies of Euclidean space in the classical
Brunn--Minkowski theory. For example, support functions can be defined, as
functions on a compact hyperbolic manifold instead of the sphere.
The main result is the convexity of the associated volume (it is log concave
in the classical setting). This implies analogs of Alexandrov--Fenchel and
Brunn--Minkowski inequalities. Here the inequalities are reversed
Diversity of metaxylem vessel elements in three Syagrus palms (Arecaceae) of different habits
Global well-posedness of the 3-D full water wave problem
We consider the problem of global in time existence and uniqueness of
solutions of the 3-D infinite depth full water wave problem. We show that the
nature of the nonlinearity of the water wave equation is essentially of cubic
and higher orders. For any initial interface that is sufficiently small in its
steepness and velocity, we show that there exists a unique smooth solution of
the full water wave problem for all time, and the solution decays at the rate
.Comment: 60 page
Dark soliton states of Bose-Einstein condensates in anisotropic traps
Dark soliton states of Bose-Einstein condensates in harmonic traps are
studied both analytically and computationally by the direct solution of the
Gross-Pitaevskii equation in three dimensions. The ground and self-consistent
excited states are found numerically by relaxation in imaginary time. The
energy of a stationary soliton in a harmonic trap is shown to be independent of
density and geometry for large numbers of atoms. Large amplitude field
modulation at a frequency resonant with the energy of a dark soliton is found
to give rise to a state with multiple vortices. The Bogoliubov excitation
spectrum of the soliton state contains complex frequencies, which disappear for
sufficiently small numbers of atoms or large transverse confinement. The
relationship between these complex modes and the snake instability is
investigated numerically by propagation in real time.Comment: 11 pages, 8 embedded figures (two in color
Large time existence for 3D water-waves and asymptotics
We rigorously justify in 3D the main asymptotic models used in coastal
oceanography, including: shallow-water equations, Boussinesq systems,
Kadomtsev-Petviashvili (KP) approximation, Green-Naghdi equations, Serre
approximation and full-dispersion model. We first introduce a ``variable''
nondimensionalized version of the water-waves equations which vary from shallow
to deep water, and which involves four dimensionless parameters. Using a
nonlocal energy adapted to the equations, we can prove a well-posedness
theorem, uniformly with respect to all the parameters. Its validity ranges
therefore from shallow to deep-water, from small to large surface and bottom
variations, and from fully to weakly transverse waves. The physical regimes
corresponding to the aforementioned models can therefore be studied as
particular cases; it turns out that the existence time and the energy bounds
given by the theorem are always those needed to justify the asymptotic models.
We can therefore derive and justify them in a systematic way.Comment: Revised version of arXiv:math.AP/0702015 (notations simplified and
remarks added) To appear in Inventione
Brain iron accumulation in Wilson disease: a post-mortem 7 Tesla MRI - histopathological study
Aims: In Wilson disease (WD), T2/T2*-weighted (T2*w) MRI frequently shows hypointensity in the basal ganglia that is suggestive of paramagnetic deposits. It is currently unknown whether this hypointensity is related to copper or iron deposition. We examined the neuropathological correlate of this MRI pattern, particularly in relation to iron and copper concentrations. Methods: Brain slices from nine WD and six control cases were investigated using a 7T-MRI system. High resolution T2*w images were acquired and R2* parametric maps were reconstructed using a multi-gradient recalled echo sequence. R2* was measured in the globus pallidus (GP) and the putamen. Corresponding histopathological sections containing the lentiform nucleus were examined using Turnbull iron staining, and double staining combining Turnbull with immunohistochemistry for macrophages or astrocytes. Quantitative densitometry of the iron staining as well as copper and iron concentrations were measured in the GP and putamen and correlated to R2* values. Results: T2*w hypointensity in the GP and/or putamen was apparent in WD cases and R2* values correlated with quantitative densitometry of iron staining. In WD, iron and copper concentrations were increased in the putamen compared to controls. R2* was correlated with the iron concentration in the GP and putamen whereas no correlation was observed for the copper concentration. Patients with more pronounced pathological severity in the putamen displayed increased iron concentration, which correlated with an elevated number of iron-containing macrophages. Conclusions: T2/T2*w hypointensity observed in vivo in the basal ganglia of WD patients is related to iron rather than copper deposits
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