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

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.

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

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

Construction and Test of a Flux Modulation Superconducting Machine for Aircraft

International audienceThe increasing of drives towards More Electric Aircraft (MEA) or the development of electric propulsion aircraft calls for MW-class electrical machines with more compact and power dense designs. One way is to explore the use of superconducting materials to create a high magnetic field in order to reduce the mass of ferromagnetic components. This paper presents the construction and the test of a brushless axial flux superconducting machine. The brushless topology satisfies the aeronautics industry requirements in terms of maintenance, while the axial configuration ensures an optimal use of the anisotropic HTS tapes. The machine is classed as partially superconducting, only the inductor is made with superconducting materials. A special design concerning the use of a stationary cryostat is presented. This improvement reduces significantly the electromagnetic air-gap length. A 50kW prototype is manufactured with a minimal mass objective. The prototype constitutes a first step to a scale-up MW-class machine design

A model for shock wave chaos

We propose the following model equation: $$u_{t}+1/2(u^{2}-uu_{s})_{x}=f(x,u_{s}),$$ that predicts chaotic shock waves. It is given on the half-line $x<0$ and the shock is located at $x=0$ for any $t\ge0$. Here $u_{s}(t)$ is the shock state and the source term $f$ 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 characteristic initial data for a star orbiting a black hole

We take further steps in the development of the characteristic approach to enable handling the physical problem of a compact self-gravitating object, such as a neutron star, in close orbit around a black hole. We examine different options for setting the initial data for this problem and, in order to shed light on their physical relevance, we carry out short time evolution of this data. To this end we express the matter part of the characteristic gravity code so that the hydrodynamics are in conservation form. The resulting gravity plus matter relativity code provides a starting point for more refined future efforts at longer term evolution. In the present work we find that, independently of the details of the initial gravitational data, the system quickly flushes out spurious gravitational radiation and relaxes to a quasi-equilibrium state with an approximate helical symmetry corresponding to the circular orbit of the star.Comment: 20 pages, 10 figure

A conservative coupling algorithm between a compressible flow and a rigid body using an Embedded Boundary method

This paper deals with a new solid-fluid coupling algorithm between a rigid body and an unsteady compressible fluid flow, using an Embedded Boundary method. The coupling with a rigid body is a first step towards the coupling with a Discrete Element method. The flow is computed using a Finite Volume approach on a Cartesian grid. The expression of numerical fluxes does not affect the general coupling algorithm and we use a one-step high-order scheme proposed by Daru and Tenaud [Daru V,Tenaud C., J. Comput. Phys. 2004]. The Embedded Boundary method is used to integrate the presence of a solid boundary in the fluid. The coupling algorithm is totally explicit and ensures exact mass conservation and a balance of momentum and energy between the fluid and the solid. It is shown that the scheme preserves uniform movement of both fluid and solid and introduces no numerical boundary roughness. The effciency of the method is demonstrated on challenging one- and two-dimensional benchmarks