1,941 research outputs found
Critical Collapse of an Ultrarelativistic Fluid in the Limit
In this paper we investigate the critical collapse of an ultrarelativistic
perfect fluid with the equation of state in the limit of
. We calculate the limiting continuously self similar (CSS)
solution and the limiting scaling exponent by exploiting self-similarity of the
solution. We also solve the complete set of equations governing the
gravitational collapse numerically for and
compare them with the CSS solutions. We also investigate the supercritical
regime and discuss the hypothesis of naked singularity formation in a generic
gravitational collapse. The numerical calculations make use of advanced methods
such as high resolution shock capturing evolution scheme for the matter
evolution, adaptive mesh refinement, and quadruple precision arithmetic. The
treatment of vacuum is also non standard. We were able to tune the critical
parameter up to 30 significant digits and to calculate the scaling exponents
accurately. The numerical results agree very well with those calculated using
the CSS ansatz. The analysis of the collapse in the supercritical regime
supports the hypothesis of the existence of naked singularities formed during a
generic gravitational collapse.Comment: 23 pages, 16 figures, revised version, added new results of
investigation of a supercritical collapse and the existence of naked
singularities in generic gravitational collaps
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.
Accurate discretization of advection-diffusion equations
We present an exact mathematical transformation which converts a wide class
of advection-diffusion equations into a form allowing simple and direct spatial
discretization in all dimensions, and thus the construction of accurate and
more efficient numerical algorithms. These discretized forms can also be viewed
as master equations which provides an alternative mesoscopic interpretation of
advection-diffusion processes in terms of diffusion with spatially varying
hopping rates
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
On the scaling of entropy viscosity in high order methods
In this work, we outline the entropy viscosity method and discuss how the
choice of scaling influences the size of viscosity for a simple shock problem.
We present examples to illustrate the performance of the entropy viscosity
method under two distinct scalings
Finite difference lattice Boltzmann model with flux limiters for liquid-vapor systems
In this paper we apply a finite difference lattice Boltzmann model to study
the phase separation in a two-dimensional liquid-vapor system. Spurious
numerical effects in macroscopic equations are discussed and an appropriate
numerical scheme involving flux limiter techniques is proposed to minimize them
and guarantee a better numerical stability at very low viscosity. The phase
separation kinetics is investigated and we find evidence of two different
growth regimes depending on the value of the fluid viscosity as well as on the
liquid-vapor ratio.Comment: 10 pages, 10 figures, to be published in Phys. Rev.
Head-on collisions of binary white dwarf--neutron stars: Simulations in full general relativity
We simulate head-on collisions from rest at large separation of binary white
dwarf -- neutron stars (WDNSs) in full general relativity. Our study serves as
a prelude to our analysis of the circular binary WDNS problem. We focus on
compact binaries whose total mass exceeds the maximum mass that a cold
degenerate star can support, and our goal is to determine the fate of such
systems. A fully general relativistic hydrodynamic computation of a realistic
WDNS head-on collision is prohibitive due to the large range of dynamical time
scales and length scales involved. For this reason, we construct an equation of
state (EOS) which captures the main physical features of NSs while, at the same
time, scales down the size of WDs. We call these scaled-down WD models
"pseudo-WDs (pWDs)". Using pWDs, we can study these systems via a sequence of
simulations where the size of the pWD gradually increases toward the realistic
case. We perform two sets of simulations; One set studies the effects of the NS
mass on the final outcome, when the pWD is kept fixed. The other set studies
the effect of the pWD compaction on the final outcome, when the pWD mass and
the NS are kept fixed. All simulations show that 14%-18% of the initial total
rest mass escapes to infinity. All remnant masses still exceed the maximum rest
mass that our cold EOS can support (1.92 solar masses), but no case leads to
prompt collapse to a black hole. This outcome arises because the final
configurations are hot. All cases settle into spherical, quasiequilibrium
configurations consisting of a cold NS core surrounded by a hot mantle,
resembling Thorne-Zytkow objects. Extrapolating our results to realistic WD
compactions, we predict that the likely outcome of a head-on collision of a
realistic, massive WDNS system will be the formation of a quasiequilibrium
Thorne-Zytkow-like object.Comment: 24 pages, 14 figures, matches PRD published version, tests of HRSC
schemes with piecewise polytropes adde
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
- …