3,147 research outputs found
Phase-Transition Theory of Instabilities. II. Fourth-Harmonic Bifurcations and Lambda-Transitions
We use a free-energy minimization approach to describe the secular and
dynamical instabilities as well as the bifurcations along equilibrium sequences
of rotating, self-gravitating fluid systems. Our approach is fully nonlinear
and stems from the Ginzburg-Landau theory of phase transitions. In this paper,
we examine fourth-harmonic axisymmetric disturbances in Maclaurin spheroids and
fourth-harmonic nonaxisymmetric disturbances in Jacobi ellipsoids. These two
cases are very similar in the framework of phase transitions. Irrespective of
whether a nonlinear first-order phase transition occurs between the critical
point and the higher turning point or an apparent second-order phase transition
occurs beyond the higher turning point, the result is fission (i.e.
``spontaneous breaking'' of the topology) of the original object on a secular
time scale: the Maclaurin spheroid becomes a uniformly rotating axisymmetric
torus and the Jacobi ellipsoid becomes a binary. The presence of viscosity is
crucial since angular momentum needs to be redistributed for uniform rotation
to be maintained. The phase transitions of the dynamical systems are briefly
discussed in relation to previous numerical simulations of the formation and
evolution of protostellar systems.Comment: 34 pages, postscript, compressed,uuencoded. 7 figures available in
postscript, compressed form by anonymous ftp from asta.pa.uky.edu (cd
/shlosman/paper2 mget *.ps.Z). To appear in Ap
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
Self-Similar Scalar Field Collapse: Naked Singularities and Critical Behaviour
Homothetic scalar field collapse is considered in this article. By making a
suitable choice of variables the equations are reduced to an autonomous system.
Then using a combination of numerical and analytic techniques it is shown that
there are two classes of solutions. The first consists of solutions with a
non-singular origin in which the scalar field collapses and disperses again.
There is a singularity at one point of these solutions, however it is not
visible to observers at finite radius. The second class of solutions includes
both black holes and naked singularities with a critical evolution (which is
neither) interpolating between these two extremes. The properties of these
solutions are discussed in detail. The paper also contains some speculation
about the significance of self-similarity in recent numerical studies.Comment: 27 pages including 5 encapsulated postcript figures in separate
compressed file, report NCL94-TP1
Improving the Price of Anarchy for Selfish Routing via Coordination Mechanisms
We reconsider the well-studied Selfish Routing game with affine latency
functions. The Price of Anarchy for this class of games takes maximum value
4/3; this maximum is attained already for a simple network of two parallel
links, known as Pigou's network. We improve upon the value 4/3 by means of
Coordination Mechanisms.
We increase the latency functions of the edges in the network, i.e., if
is the latency function of an edge , we replace it by
with for all . Then an
adversary fixes a demand rate as input. The engineered Price of Anarchy of the
mechanism is defined as the worst-case ratio of the Nash social cost in the
modified network over the optimal social cost in the original network.
Formally, if \CM(r) denotes the cost of the worst Nash flow in the modified
network for rate and \Copt(r) denotes the cost of the optimal flow in the
original network for the same rate then [\ePoA = \max_{r \ge 0}
\frac{\CM(r)}{\Copt(r)}.]
We first exhibit a simple coordination mechanism that achieves for any
network of parallel links an engineered Price of Anarchy strictly less than
4/3. For the case of two parallel links our basic mechanism gives 5/4 = 1.25.
Then, for the case of two parallel links, we describe an optimal mechanism; its
engineered Price of Anarchy lies between 1.191 and 1.192.Comment: 17 pages, 2 figures, preliminary version appeared at ESA 201
How to detect an anti-spacetime
Is it possible, in principle, to measure the sign of the Lapse? We show that
fermion dynamics distinguishes spacetimes having the same metric but different
tetrads, for instance a Lapse with opposite sign. This sign might be a physical
quantity not captured by the metric. We discuss its possible role in quantum
gravity.Comment: Article awarded with an "Honorable Mention" from the 2012 Gravity
Foundation Award. 6 pages, 8 (pretty) figure
High-Temperature Activated AB2 Nanopowders for Metal Hydride Hydrogen Compression
A reliable process for compressing hydrogen and for removing all contaminants
is that of the metal hydride thermal compression. The use of metal hydride
technology in hydrogen compression applications though, requires thorough
structural characterization of the alloys and investigation of their sorption
properties. The samples have been synthesized by induction - levitation melting
and characterized by Rietveld analysis of the X-Ray diffraction (XRD) patterns.
Volumetric PCI (Pressure-Composition Isotherm) measurements have been conducted
at 20, 60 and 90 oC, in order to investigate the maximum pressure that can be
reached from the selected alloys using water of 90oC. Experimental evidence
shows that the maximum hydrogen uptake is low since all the alloys are
consisted of Laves phases, but it is of minor importance if they have fast
kinetics, given a constant volumetric hydrogen flow. Hysteresis is almost
absent while all the alloys release nearly all the absorbed hydrogen during
desorption. Due to hardware restrictions, the maximum hydrogen pressure for the
measurements was limited at 100 bars. Practically, the maximum pressure that
can be reached from the last alloy is more than 150 bars.Comment: 9 figures. arXiv admin note: text overlap with arXiv:1207.354
Final fate of spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity
We give a model of the higher-dimensional spherically symmetric gravitational
collapse of a dust cloud in Einstein-Gauss-Bonnet gravity. A simple formulation
of the basic equations is given for the spacetime with a perfect fluid and a cosmological constant. This is a
generalization of the Misner-Sharp formalism of the four-dimensional
spherically symmetric spacetime with a perfect fluid in general relativity. The
whole picture and the final fate of the gravitational collapse of a dust cloud
differ greatly between the cases with and . There are two
families of solutions, which we call plus-branch and the minus-branch
solutions. Bounce inevitably occurs in the plus-branch solution for ,
and consequently singularities cannot be formed. Since there is no trapped
surface in the plus-branch solution, the singularity formed in the case of
must be naked. In the minus-branch solution, naked singularities are
massless for , while massive naked singularities are possible for
. In the homogeneous collapse represented by the flat
Friedmann-Robertson-Walker solution, the singularity formed is spacelike for , while it is ingoing-null for . In the inhomogeneous collapse with
smooth initial data, the strong cosmic censorship hypothesis holds for and for depending on the parameters in the initial data, while a
naked singularity is always formed for . These naked
singularities can be globally naked when the initial surface radius of the dust
cloud is fine-tuned, and then the weak cosmic censorship hypothesis is
violated.Comment: 23 pages, 1 figure, final version to appear in Physical Review
Welfare guarantees for proportional allocations
According to the proportional allocation mechanism from the network
optimization literature, users compete for a divisible resource -- such as
bandwidth -- by submitting bids. The mechanism allocates to each user a
fraction of the resource that is proportional to her bid and collects an amount
equal to her bid as payment. Since users act as utility-maximizers, this
naturally defines a proportional allocation game. Recently, Syrgkanis and
Tardos (STOC 2013) quantified the inefficiency of equilibria in this game with
respect to the social welfare and presented a lower bound of 26.8% on the price
of anarchy over coarse-correlated and Bayes-Nash equilibria in the full and
incomplete information settings, respectively. In this paper, we improve this
bound to 50% over both equilibrium concepts. Our analysis is simpler and,
furthermore, we argue that it cannot be improved by arguments that do not take
the equilibrium structure into account. We also extend it to settings with
budget constraints where we show the first constant bound (between 36% and 50%)
on the price of anarchy of the corresponding game with respect to an effective
welfare benchmark that takes budgets into account.Comment: 15 page
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