2,469 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
Are gauge shocks really shocks?
The existence of gauge pathologies associated with the Bona-Masso family of
generalized harmonic slicing conditions is proven for the case of simple 1+1
relativity. It is shown that these gauge pathologies are true shocks in the
sense that the characteristic lines associated with the propagation of the
gauge cross, which implies that the name ``gauge shock'' usually given to such
pathologies is indeed correct. These gauge shocks are associated with places
where the spatial hypersurfaces that determine the foliation of spacetime
become non-smooth.Comment: 7 pages, 5 figures, REVTEX 4. Revised version, including corrections
suggested by referee
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.
Analysis of Diffusion of Ras2 in Saccharomyces cerevisiae Using Fluorescence Recovery after Photobleaching
Binding, lateral diffusion and exchange are fundamental dynamic processes
involved in protein association with cellular membranes. In this study, we
developed numerical simulations of lateral diffusion and exchange of
fluorophores in membranes with arbitrary bleach geometry and exchange of the
membrane localized fluorophore with the cytosol during Fluorescence Recovery
after Photobleaching (FRAP) experiments. The model simulations were used to
design FRAP experiments with varying bleach region sizes on plasma-membrane
localized wild type GFP-Ras2 with a dual lipid anchor and mutant GFP-Ras2C318S
with a single lipid anchor in live yeast cells to investigate diffusional
mobility and the presence of any exchange processes operating in the time scale
of our experiments. Model parameters estimated using data from FRAP experiments
with a 1 micron x 1 micron bleach region-of-interest (ROI) and a 0.5 micron x
0.5 micron bleach ROI showed that GFP-Ras2, single or dual lipid modified,
diffuses as single species with no evidence of exchange with a cytoplasmic
pool. This is the first report of Ras2 mobility in yeast plasma membrane. The
methods developed in this study are generally applicable for studying diffusion
and exchange of membrane associated fluorophores using FRAP on commercial
confocal laser scanning microscopes.Comment: Accepted for publication in Physical Biology (2010). 28 pages, 7
figures, 3 table
Raman signatures of classical and quantum phases in coupled dots: A theoretical prediction
We study electron molecules in realistic vertically coupled quantum dots in a
strong magnetic field. Computing the energy spectrum, pair correlation
functions, and dynamical form factor as a function of inter-dot coupling via
diagonalization of the many-body Hamiltonian, we identify structural
transitions between different phases, some of which do not have a classical
counterpart. The calculated Raman cross section shows how such phases can be
experimentally singled out.Comment: 9 pages, 2 postscript figures, 1 colour postscript figure, Latex 2e,
Europhysics Letters style and epsfig macros. Submitted to Europhysics Letter
Lattice Boltzmann - Langevin simulations of binary mixtures
We report a hybrid numerical method for the solution of the model H
fluctuating hydrodynamic equations for binary mixtures. The momentum
conservation equations with Landau-Lifshitz stresses are solved using the
fluctuating lattice Boltzmann equation while the order parameter conservation
equation with Langevin fluxes are solved using the stochastic method of lines.
Two methods, based on finite difference and finite volume, are proposed for
spatial discretisation of the order parameter equation. Special care is taken
to ensure that the fluctuation-dissipation theorem is maintained at the lattice
level in both cases. The methods are benchmarked by comparing static and
dynamic correlations and excellent agreement is found between analytical and
numerical results. The Galilean invariance of the model is tested and found to
be satisfactory. Thermally induced capillary fluctuations of the interface are
captured accurately, indicating that the model can be used to study nonlinear
fluctuations
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
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