343 research outputs found
Regularity results for the spherically symmetric Einstein-Vlasov system
The spherically symmetric Einstein-Vlasov system is considered in
Schwarzschild coordinates and in maximal-isotropic coordinates. An open problem
is the issue of global existence for initial data without size restrictions.
The main purpose of the present work is to propose a method of approach for
general initial data, which improves the regularity of the terms that need to
be estimated compared to previous methods. We prove that global existence holds
outside the centre in both these coordinate systems. In the Schwarzschild case
we improve the bound on the momentum support obtained in \cite{RRS} for compact
initial data. The improvement implies that we can admit non-compact data with
both ingoing and outgoing matter. This extends one of the results in
\cite{AR1}. In particular our method avoids the difficult task of treating the
pointwise matter terms. Furthermore, we show that singularities never form in
Schwarzschild time for ingoing matter as long as This removes an
additional assumption made in \cite{A1}. Our result in maximal-isotropic
coordinates is analogous to the result in \cite{R1}, but our method is
different and it improves the regularity of the terms that need to be estimated
for proving global existence in general.Comment: 25 pages. To appear in Ann. Henri Poincar\'
Global existence for the spherically symmetric Einstein-Vlasov system with outgoing matter
We prove a new global existence result for the asymptotically flat,
spherically symmetric Einstein-Vlasov system which describes in the framework
of general relativity an ensemble of particles which interact by gravity. The
data are such that initially all the particles are moving radially outward and
that this property can be bootstrapped. The resulting non-vacuum spacetime is
future geodesically complete.Comment: 16 page
A numerical investigation of the stability of steady states and critical phenomena for the spherically symmetric Einstein-Vlasov system
The stability features of steady states of the spherically symmetric
Einstein-Vlasov system are investigated numerically. We find support for the
conjecture by Zeldovich and Novikov that the binding energy maximum along a
steady state sequence signals the onset of instability, a conjecture which we
extend to and confirm for non-isotropic states. The sign of the binding energy
of a solution turns out to be relevant for its time evolution in general. We
relate the stability properties to the question of universality in critical
collapse and find that for Vlasov matter universality does not seem to hold.Comment: 29 pages, 10 figure
On the area of the symmetry orbits in symmetric spacetimes
We obtain a global existence result for the Einstein equations. We show that
in the maximal Cauchy development of vacuum symmetric initial data with
nonvanishing twist constant, except for the special case of flat Kasner initial
data, the area of the group orbits takes on all positive values. This
result shows that the areal time coordinate which covers these spacetimes
runs from zero to infinity, with the singularity occurring at R=0.Comment: The appendix which appears in version 1 has a technical problem (the
inequality appearing as the first stage of (52) is not necessarily true), and
since the appendix is unnecessary for the proof of our results, we leave it
out. version 2 -- clarifications added, version 3 -- reference correcte
Bounds on the mass-to-radius ratio for non-compact field configurations
It is well known that a spherically symmetric compact star whose energy
density decreases monotonically possesses an upper bound on its mass-to-radius
ratio, . However, field configurations typically will not be
compact. Here we investigate non-compact static configurations whose matter
fields have a slow global spatial decay, bounded by a power law behavior. These
matter distributions have no sharp boundaries. We derive an upper bound on the
fundamental ratio max_r{2m(r)/r} which is valid throughout the bulk. In its
simplest form, the bound implies that in any region of spacetime in which the
radial pressure increases, or alternatively decreases not faster than some
power law , one has . [For
the bound degenerates to .] In its general version, the bound
is expressed in terms of two physical parameters: the spatial decaying rate of
the matter fields, and the highest occurring ratio of the trace of the pressure
tensor to the local energy density.Comment: 4 page
An All-Photonic Molecule-Based D Flip-Flop
The photochromic fluorescence switching of a fulgimide derivative was used to implement the first molecule-based D (delay) flip-flop device, which works based on the principles of sequential logic. The device operates exclusively with photonic signals and can be conveniently switched in repeated cycles. \ua9 2011 American Chemical Society
The Einstein-Vlasov System/Kinetic Theory
The main purpose of this article is to provide a guide to theorems on global
properties of solutions to the Einstein--Vlasov system. This system couples
Einstein's equations to a kinetic matter model. Kinetic theory has been an
important field of research during several decades in which the main focus has
been on non-relativistic and special relativistic physics, i.e., to model the
dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In
1990, Rendall and Rein initiated a mathematical study of the Einstein--Vlasov
system. Since then many theorems on global properties of solutions to this
system have been established.Comment: Published version http://www.livingreviews.org/lrr-2011-
Existence of axially symmetric static solutions of the Einstein-Vlasov system
We prove the existence of static, asymptotically flat non-vacuum spacetimes
with axial symmetry where the matter is modeled as a collisionless gas. The
axially symmetric solutions of the resulting Einstein-Vlasov system are
obtained via the implicit function theorem by perturbing off a suitable
spherically symmetric steady state of the Vlasov-Poisson system.Comment: 32 page
8-Triazolylpurines: Towards Fluorescent Inhibitors of the MDM2/p53 Interaction
Small molecule nonpeptidic mimics of alpha-helices are widely recognised as protein-protein interaction (PPIs) inhibitors. Protein-protein interactions mediate virtually all important regulatory pathways in a cell, and the ability to control and modulate PPIs is therefore of great significance to basic biology, where controlled disruption of protein networks is key to understanding network connectivity and function. We have designed and synthesised two series of 2,6,9-substituted 8-triazolylpurines as alpha-helix mimetics. The first series was designed based on low energy conformations but did not display any biological activity in a biochemical fluorescence polarisation assay targeting MDM2/p53. Although solution NMR conformation studies demonstrated that such molecules could mimic the topography of an alpha-helix, docking studies indicated that the same compounds were not optimal as inhibitors for the MDM2/p53 interaction. A new series of 8-triazolylpurines was designed based on a combination of docking studies and analysis of recently published inhibitors. The best compound displayed low micromolar inhibitory activity towards MDM2/p53 in a biochemical fluorescence polarisation assay. In order to evaluate the applicability of these compounds as biologically active and intrinsically fluorescent probes, their absorption/emission properties were measured. The compounds display fluorescent properties with quantum yields up to 50%
Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials
In this paper it is shown that unique solutions to the relativistic Boltzmann
equation exist for all time and decay with any polynomial rate towards their
steady state relativistic Maxwellian provided that the initial data starts out
sufficiently close in . If the initial data are continuous then
so is the corresponding solution. We work in the case of a spatially periodic
box. Conditions on the collision kernel are generic in the sense of
(Dudy{\'n}ski and Ekiel-Je{\.z}ewska, Comm. Math. Phys., 1988); this resolves
the open question of global existence for the soft potentials.Comment: 64 page
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