Critical Collapse of an Ultrarelativistic Fluid in the Γ→1\Gamma\to 1 Limit

In this paper we investigate the critical collapse of an ultrarelativistic perfect fluid with the equation of state $P=(\Gamma-1)\rho$ in the limit of $\Gamma\to 1$. 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 $(\Gamma-1) = 10^{-2},...,10^{-6}$ 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

Numerical Simulation of the Hydrodynamical Combustion to Strange Quark Matter

We present results from a numerical solution to the burning of neutron matter inside a cold neutron star into stable (u,d,s) quark matter. Our method solves hydrodynamical flow equations in 1D with neutrino emission from weak equilibrating reactions, and strange quark diffusion across the burning front. We also include entropy change due to heat released in forming the stable quark phase. Our numerical results suggest burning front laminar speeds of 0.002-0.04 times the speed of light, much faster than previous estimates derived using only a reactive-diffusive description. Analytic solutions to hydrodynamical jump conditions with a temperature dependent equation of state agree very well with our numerical findings for fluid velocities. The most important effect of neutrino cooling is that the conversion front stalls at lower density (below approximately 2 times saturation density). In a 2-dimensional setting, such rapid speeds and neutrino cooling may allow for a flame wrinkle instability to develop, possibly leading to detonation.Comment: 5 pages, 3 figures (animations online at http://www.capca.ucalgary.ca/~bniebergal/webPHP/research.php

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

Consistent thermodynamic derivative estimates for tabular equations of state

Numerical simulations of compressible fluid flows require an equation of state (EOS) to relate the thermodynamic variables of density, internal energy, temperature, and pressure. A valid EOS must satisfy the thermodynamic conditions of consistency (derivation from a free energy) and stability (positive sound speed squared). When phase transitions are significant, the EOS is complicated and can only be specified in a table. For tabular EOS's such as SESAME from Los Alamos National Laboratory, the consistency and stability conditions take the form of a differential equation relating the derivatives of pressure and energy as functions of temperature and density, along with positivity constraints. Typical software interfaces to such tables based on polynomial or rational interpolants compute derivatives of pressure and energy and may enforce the stability conditions, but do not enforce the consistency condition and its derivatives. We describe a new type of table interface based on a constrained local least squares regression technique. It is applied to several SESAME EOS's showing how the consistency condition can be satisfied to round-off while computing first and second derivatives with demonstrated second-order convergence. An improvement of 14 orders of magnitude over conventional derivatives is demonstrated, although the new method is apparently two orders of magnitude slower, due to the fact that every evaluation requires solving an 11-dimensional nonlinear system.Comment: 29 pages, 9 figures, 16 references, submitted to Phys Rev

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.

Hyperbolic slicings of spacetime: singularity avoidance and gauge shocks

I study the Bona-Masso family of hyperbolic slicing conditions, considering in particular its properties when approaching two different types of singularities: focusing singularities and gauge shocks. For focusing singularities, I extend the original analysis of Bona et. al and show that both marginal and strong singularity avoidance can be obtained for certain types of behavior of the slicing condition as the lapse approaches zero. For the case of gauge shocks, I re-derive a condition found previously that eliminates them. Unfortunately, such a condition limits considerably the type of slicings allowed. However, useful slicing conditions can still be found if one asks for this condition to be satisfied only approximately. Such less restrictive conditions include a particular member of the 1+log family, which in the past has been found empirically to be extremely robust for both Brill wave and black hole simulations.Comment: 11 pages, revtex4. Change in acknowledgment

High-Order Discontinuous Galerkin Method for Boltzmann Model Equations

High-order Runge-Kutta discontinuous Galerkin (DG) method is applied to the kinetic model equations describing rarefied gas flows. A conservative DG discretization of nonlinear collision relaxation term is formulated for Bhatnagar-Gross-Krook and ellipsoidal statistical models. The numerical solutions using RKDG method of order up to four are obtained for two flow problems: the heat transfer between parallel plates and the normal shock wave. The convergence of RKDG method is compared with the conventional secondorder finite volume method for the heat transfer problem. The normal shock wave solutions obtained using RKDG are compared with the experimental measurements of density and velocity distribution function inside the shock