4,206 research outputs found
On the steady states of the spherically symmetric Einstein-Vlasov system
Using both numerical and analytical tools we study various features of
static, spherically symmetric solutions of the Einstein-Vlasov system. In
particular, we investigate the possible shapes of their mass-energy density and
find that they can be multi-peaked, we give numerical evidence and a partial
proof for the conjecture that the Buchdahl inequality , the quasi-local mass, holds for all such steady states--both
isotropic {\em and} anisotropic--, and we give numerical evidence and a partial
proof for the conjecture that for any given microscopic equation of state--both
isotropic {\em and} anisotropic--the resulting one-parameter family of static
solutions generates a spiral in the radius-mass diagram.Comment: 34 pages, 18 figures, LaTe
The Validity of the Super-Particle Approximation during Planetesimal Formation
The formation mechanism of planetesimals in protoplanetary discs is hotly
debated. Currently, the favoured model involves the accumulation of meter-sized
objects within a turbulent disc, followed by a phase of gravitational
instability. At best one can simulate a few million particles numerically as
opposed to the several trillion meter-sized particles expected in a real
protoplanetary disc. Therefore, single particles are often used as
super-particles to represent a distribution of many smaller particles. It is
assumed that small scale phenomena do not play a role and particle collisions
are not modeled. The super-particle approximation can only be valid in a
collisionless or strongly collisional system, however, in many recent numerical
simulations this is not the case.
In this work we present new results from numerical simulations of
planetesimal formation via gravitational instability. A scaled system is
studied that does not require the use of super-particles. We find that the
scaled particles can be used to model the initial phases of clumping if the
properties of the scaled particles are chosen such that all important
timescales in the system are equivalent to what is expected in a real
protoplanetary disc. Constraints are given for the number of particles needed
in order to achieve numerical convergence.
We compare this new method to the standard super-particle approach. We find
that the super-particle approach produces unreliable results that depend on
artifacts such as the gravitational softening in both the requirement for
gravitational collapse and the resulting clump statistics. Our results show
that short range interactions (collisions) have to be modelled properly.Comment: 10 pages, 7 figures, accepted for publication in Astronomy and
Astrophysic
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
Experimental study of the formation and collapse of an overhang in the lateral spread of smouldering peat fires
Smouldering combustion is the driving phenomenon of wildfires in peatlands, and is responsible for large amounts of carbon emissions and haze episodes world wide. Compared to flaming fires, smouldering is slow, low-temperature, flameless, and most persistent, yet it is poorly understood. Peat, as a typical organic soil, is a porous and charring natural fuel, thus prone to smouldering. The spread of smouldering peat fire is a multidimensional phenomenon, including two main components: in-depth vertical and surface lateral spread. In this study, we investigate the lateral spread of peat fire under various moisture and wind conditions. Visual and infrared cameras as well as a thermocouple array are used to measure the temperature profile and the spread rate. For the first time the overhang, where smouldering spreads fastest beneath the free surface, is observed in the laboratory, which helps understand the interaction between oxygen supply and heat losses. The periodic formation and collapse of overhangs is observed. The overhang thickness is found to increase with moisture and wind speed, while the spread rate decreases with moisture and increases with wind speed. A simple theoretical analysis is proposed and shows that the formation of overhang is caused by the spread rate difference between the top and lower peat layers as well as the competition between oxygen supply and heat losses
Global existence and asymptotic behaviour in the future for the Einstein-Vlasov system with positive cosmological constant
The behaviour of expanding cosmological models with collisionless matter and
a positive cosmological constant is analysed. It is shown that under the
assumption of plane or hyperbolic symmetry the area radius goes to infinity,
the spacetimes are future geodesically complete, and the expansion becomes
isotropic and exponential at late times. This proves a form of the cosmic no
hair theorem in this class of spacetimes
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\'
The formation of black holes in spherically symmetric gravitational collapse
We consider the spherically symmetric, asymptotically flat Einstein-Vlasov
system. We find explicit conditions on the initial data, with ADM mass M, such
that the resulting spacetime has the following properties: there is a family of
radially outgoing null geodesics where the area radius r along each geodesic is
bounded by 2M, the timelike lines are incomplete, and for r>2M
the metric converges asymptotically to the Schwarzschild metric with mass M.
The initial data that we construct guarantee the formation of a black hole in
the evolution. We also give examples of such initial data with the additional
property that the solutions exist for all and all Schwarzschild time,
i.e., we obtain global existence in Schwarzschild coordinates in situations
where the initial data are not small. Some of our results are also established
for the Einstein equations coupled to a general matter model characterized by
conditions on the matter quantities.Comment: 36 pages. A corollary on global existence in Schwarzschild
coordinates for data which are not small is added together with minor
modification
Leadership Lessons: The Campaigns for Vicksburg, 1862-1863
Taking Civil War Leaders to Task
Kevin Doughertyâs Leadership Lessons: The Campaigns for Vicksburg, 1862-1863 offers a concise summary of the events that led to the cityâs capture in July, 1863, but focuses on the campaignâs utility as a primer for modern leaders in âwar, busines...
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