1,662 research outputs found
Type II critical phenomena of neutron star collapse
We investigate spherically-symmetric, general relativistic systems of
collapsing perfect fluid distributions. We consider neutron star models that
are driven to collapse by the addition of an initially "in-going" velocity
profile to the nominally static star solution. The neutron star models we use
are Tolman-Oppenheimer-Volkoff solutions with an initially isentropic,
gamma-law equation of state. The initial values of 1) the amplitude of the
velocity profile, and 2) the central density of the star, span a parameter
space, and we focus only on that region that gives rise to Type II critical
behavior, wherein black holes of arbitrarily small mass can be formed. In
contrast to previously published work, we find that--for a specific value of
the adiabatic index (Gamma = 2)--the observed Type II critical solution has
approximately the same scaling exponent as that calculated for an
ultrarelativistic fluid of the same index. Further, we find that the critical
solution computed using the ideal-gas equations of state asymptotes to the
ultrarelativistic critical solution.Comment: 24 pages, 22 figures, RevTeX 4, submitted to Phys. Rev.
A model for shock wave chaos
We propose the following model equation:
that predicts chaotic shock waves.
It is given on the half-line and the shock is located at for any
. Here is the shock state and the source term is assumed
to satisfy certain integrability constraints as explained in the main text. We
demonstrate that this simple equation reproduces many of the properties of
detonations in gaseous mixtures, which one finds by solving the reactive Euler
equations: existence of steady traveling-wave solutions and their instability,
a cascade of period-doubling bifurcations, onset of chaos, and shock formation
in the reaction zone.Comment: 4 pages, 4 figure
Dynamics of Three Agent Games
We study the dynamics and resulting score distribution of three-agent games
where after each competition a single agent wins and scores a point. A single
competition is described by a triplet of numbers , and denoting the
probabilities that the team with the highest, middle or lowest accumulated
score wins. We study the full family of solutions in the regime, where the
number of agents and competitions is large, which can be regarded as a
hydrodynamic limit. Depending on the parameter values , we find six
qualitatively different asymptotic score distributions and we also provide a
qualitative understanding of these results. We checked our analytical results
against numerical simulations of the microscopic model and find these to be in
excellent agreement. The three agent game can be regarded as a social model
where a player can be favored or disfavored for advancement, based on his/her
accumulated score. It is also possible to decide the outcome of a three agent
game through a mini tournament of two-a gent competitions among the
participating players and it turns out that the resulting possible score
distributions are a subset of those obtained for the general three agent-games.
We discuss how one can add a steady and democratic decline rate to the model
and present a simple geometric construction that allows one to write down the
corresponding score evolution equations for -agent games
Numerical evolution of multiple black holes with accurate initial data
We present numerical evolutions of three equal-mass black holes using the
moving puncture approach. We calculate puncture initial data for three black
holes solving the constraint equations by means of a high-order multigrid
elliptic solver. Using these initial data, we show the results for three black
hole evolutions with sixth-order waveform convergence. We compare results
obtained with the BAM and AMSS-NCKU codes with previous results. The
approximate analytic solution to the Hamiltonian constraint used in previous
simulations of three black holes leads to different dynamics and waveforms. We
present some numerical experiments showing the evolution of four black holes
and the resulting gravitational waveform.Comment: Published in PR
On Dispersive and Classical Shock Waves in Bose-Einstein Condensates and Gas Dynamics
A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to
interesting shock wave nonlinear dynamics. Experiments depict a BEC that
exhibits behavior similar to that of a shock wave in a compressible gas, eg.
traveling fronts with steep gradients. However, the governing Gross-Pitaevskii
(GP) equation that describes the mean field of a BEC admits no dissipation
hence classical dissipative shock solutions do not explain the phenomena.
Instead, wave dynamics with small dispersion is considered and it is shown that
this provides a mechanism for the generation of a dispersive shock wave (DSW).
Computations with the GP equation are compared to experiment with excellent
agreement. A comparison between a canonical 1D dissipative and dispersive shock
problem shows significant differences in shock structure and shock front speed.
Numerical results associated with the three dimensional experiment show that
three and two dimensional approximations are in excellent agreement and one
dimensional approximations are in good qualitative agreement. Using one
dimensional DSW theory it is argued that the experimentally observed blast
waves may be viewed as dispersive shock waves.Comment: 24 pages, 28 figures, submitted to Phys Rev
Projected SO(5) Hamiltonian for Cuprates and Its Applications
The projected SO(5) (pSO(5)) Hamiltonian incorporates the quantum spin and
superconducting fluctuations of underdoped cuprates in terms of four bosons
moving on a coarse grained lattice. A simple mean field approximation can
explain some key feautures of the experimental phase diagram: (i) The Mott
transition between antiferromagnet and superconductor, (ii) The increase of T_c
and superfluid stiffness with hole concentration x and (iii) The increase of
antiferromagnetic resonance energy as sqrt{x-x_c} in the superconducting phase.
We apply this theory to explain the ``two gaps'' problem found in underdoped
cuprate Superconductor-Normal- Superconductor junctions. In particular we
explain the sharp subgap Andreev peaks of the differential resistance, as
signatures of the antiferromagnetic resonance (the magnon mass gap). A critical
test of this theory is proposed. The tunneling charge, as measured by shot
noise, should change by increments of Delta Q= 2e at the Andreev peaks, rather
than by Delta Q=e as in conventional superconductors.Comment: 3 EPS figure
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