1,528 research outputs found
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
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\'
A non-variational approach to nonlinear stability in stellar dynamics applied to the King model
In previous work by Y. Guo and G. Rein, nonlinear stability of equilibria in
stellar dynamics, i.e., of steady states of the Vlasov-Poisson system, was
accessed by variational techniques. Here we propose a different,
non-variational technique and use it to prove nonlinear stability of the King
model against a class of spherically symmetric, dynamically accessible
perturbations. This model is very important in astrophysics and was out of
reach of the previous techniques
The Einstein-Vlasov sytem/Kinetic theory
The main purpose of this article is to guide the reader 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 where the main focus has
been on nonrelativistic- and special relativistic physics, e.g. 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. The Vlasov equation describes matter
phenomenologically and it should be stressed that most of the theorems
presented in this article are not presently known for other such matter models
(e.g. fluid models). The first part of this paper gives an introduction to
kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is
introduced. We believe that a good understanding of kinetic theory in
non-curved spacetimes is fundamental in order to get a good comprehension of
kinetic theory in general relativity.Comment: 31 pages. This article has been submitted to Living Rev. Relativity
(http://www.livingreviews.org
Circular Dichroism of Partially Purified Cytochrome P450 from Rabbit Liver Microsomes
The heme-related circular dichroic bands of solubilized cytochrome
P450 from rabbit liver microsomes and some of its liganded
derivatives were measured in the Soret region. All P450 derivatives
exhibit negative circular dichroic bands in the region of the Soret
absorption. The wavelengths of the dichroic bands and their ellipticities
vary with ligand substitution and the oxidation state of the
iron. The results are compared with CD-data from other hemoproteins
and discussed with respect to stereochemical conclusions
concerning the geometry and the physicochemical character of the
vicinity of the heme group with regard to results obtained from
other studies
Evidence of the Existence of a High Spin Low Spin Equilibrium in Liver Microsomal Cytochrome P450, and its Role in the Enzymatic Mechanism
In rabbit liver microsomal cytochrome P450 a high spin (S =
= 5/2) low spin (S = 1/2) equilibrium has been proved to exist by
recording temperature difference spectra in the Soret and in the
visible region of the absorption spectrum of solubilized cytochrome
P450. In the presence of type II substrates the predominantly low
spin state of cytochrome P450 is maintained, only a very small shift
to lower spin is observed. Ligands of the heme iron, such as cyanide
and imidazole, pr9duce a pure low spin state and therefore in the
presence of these ligands no temperature difference spectra can be
obtained. In the presence of type I substrate, however, the spin
equilibrium is shifted to the high spin state. The extent of this
shift (1) depends on specific properties of the substrate and (2) it is
generally relatively small, up to about 80/o in the case of substrates
investigated so far
The Vlasov limit and its fluctuations for a system of particles which interact by means of a wave field
In two recent publications [Commun. PDE, vol.22, p.307--335 (1997), Commun.
Math. Phys., vol.203, p.1--19 (1999)], A. Komech, M. Kunze and H. Spohn studied
the joint dynamics of a classical point particle and a wave type generalization
of the Newtonian gravity potential, coupled in a regularized way. In the
present paper the many-body dynamics of this model is studied. The Vlasov
continuum limit is obtained in form equivalent to a weak law of large numbers.
We also establish a central limit theorem for the fluctuations around this
limit.Comment: 68 pages. Smaller corrections: two inequalities in sections 3 and two
inequalities in section 4, and definition of a Banach space in appendix A1.
Presentation of LLN and CLT in section 4.3 improved. Notation improve
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