Thermonuclear supernova simulations with stochastic ignition

We apply an ad hoc model for dynamical ignition in three-dimensional numerical simulations of thermonuclear supernovae assuming pure deflagrations. The model makes use of the statistical description of temperature fluctuations in the pre-supernova core proposed by Wunsch & Woosley (2004). Randomness in time is implemented by means of a Poisson process. We are able to vary the explosion energy and nucleosynthesis depending on the free parameter of the model which controls the rapidity of the ignition process. However, beyond a certain threshold, the strength of the explosion saturates and the outcome appears to be robust with respect to number of ignitions. In the most energetic explosions, we find about 0.75 solar masses of iron group elements. Other than in simulations with simultaneous multi-spot ignition, the amount of unburned carbon and oxygen at radial velocities of a few 1000 km/s tends to be reduced for an ever increasing number of ignition events and, accordingly, more pronounced layering results.Comment: 7 pages, 6 figures, accepted for publication in Astron. Astrophys.; PDF version with full resolution figures available from http://www.astro.uni-wuerzburg.de/~schmidt/Paper/StochIgnt_AA.pd

Numerical dissipation and the bottleneck effect in simulations of compressible isotropic turbulence

The piece-wise parabolic method (PPM) is applied to simulations of forced isotropic turbulence with Mach numbers $\sim 0.1... 1$. The equation of state is dominated by the Fermi pressure of an electron-degenerate fluid. The dissipation in these simulations is of purely numerical origin. For the dimensionless mean rate of dissipation, we find values in agreement with known results from mostly incompressible turbulence simulations. The calculation of a Smagorinsky length corresponding to the rate of numerical dissipation supports the notion of the PPM supplying an implicit subgrid scale model. In the turbulence energy spectra of various flow realisations, we find the so-called bottleneck phenomenon, i.e., a flattening of the spectrum function near the wavenumber of maximal dissipation. The shape of the bottleneck peak in the compensated spectrum functions is comparable to what is found in turbulence simulations with hyperviscosity. Although the bottleneck effect reduces the range of nearly inertial length scales considerably, we are able to estimate the value of the Kolmogorov constant. For steady turbulence with a balance between energy injection and dissipation, it appears that $C\approx 1.7$. However, a smaller value is found in the case of transonic turbulence with a large fraction of compressive components in the driving force. Moreover, we discuss length scales related to the dissipation, in particular, an effective numerical length scale $\Delta_{\mathrm{eff}}$, which can be regarded as the characteristic smoothing length of the implicit filter associated with the PPM.Comment: 23 pages, 7 figures. Revised version accepted by Comp. Fluids. Not all figures included due to size restriction. Complete PDF available at http://www.astro.uni-wuerzburg.de/%7Eschmidt/Paper/NumDiss_CF.pd

Context unification is in PSPACE

Contexts are terms with one `hole', i.e. a place in which we can substitute an argument. In context unification we are given an equation over terms with variables representing contexts and ask about the satisfiability of this equation. Context unification is a natural subvariant of second-order unification, which is undecidable, and a generalization of word equations, which are decidable, at the same time. It is the unique problem between those two whose decidability is uncertain (for already almost two decades). In this paper we show that the context unification is in PSPACE. The result holds under a (usual) assumption that the first-order signature is finite. This result is obtained by an extension of the recompression technique, recently developed by the author and used in particular to obtain a new PSPACE algorithm for satisfiability of word equations, to context unification. The recompression is based on performing simple compression rules (replacing pairs of neighbouring function symbols), which are (conceptually) applied on the solution of the context equation and modifying the equation in a way so that such compression steps can be in fact performed directly on the equation, without the knowledge of the actual solution.Comment: 27 pages, submitted, small notation changes and small improvements over the previous tex

A near deterministic linear optical CNOT gate

We show how to construct a near deterministic CNOT using several single photons sources, linear optics, photon number resolving quantum non-demolition detectors and feed-forward. This gate does not require the use of massively entangled states common to other implementations and is very efficient on resources with only one ancilla photon required. The key element of this gate are non-demolition detectors that use a weak cross-Kerr nonlinearity effect to conditionally generate a phase shift on a coherent probe, if a photon is present in the signal mode. These potential phase shifts can then be measured using highly efficient homodyne detection.Comment: 4 pages, 3 figure

A localised subgrid scale model for fluid dynamical simulations in astrophysics II: Application to type Ia supernovae

The dynamics of the explosive burning process is highly sensitive to the flame speed model in numerical simulations of type Ia supernovae. Based upon the hypothesis that the effective flame speed is determined by the unresolved turbulent velocity fluctuations, we employ a new subgrid scale model which includes a localised treatment of the energy transfer through the turbulence cascade in combination with semi-statistical closures for the dissipation and non-local transport of turbulence energy. In addition, subgrid scale buoyancy effects are included. In the limit of negligible energy transfer and transport, the dynamical model reduces to the Sharp-Wheeler relation. According to our findings, the Sharp-Wheeler relation is insuffcient to account for the complicated turbulent dynamics of flames in thermonuclear supernovae. The application of a co-moving grid technique enables us to achieve very high spatial resolution in the burning region. Turbulence is produced mostly at the flame surface and in the interior ash regions. Consequently, there is a pronounced anisotropy in the vicinity of the flame fronts. The localised subgrid scale model predicts significantly enhanced energy generation and less unburnt carbon and oxygen at low velocities compared to earlier simulations.Comment: 13 pages, 10 figures, accepted for publication in Astron. Astrophys.; 3D visualisations not included; complete PDF version can be downloaded from http://www.astro.uni-wuerzburg.de/%7Eschmidt/Paper/SGSModel_II_AA.pd

Thermonuclear explosions of rapidly rotating white dwarfs - II. Detonations

Context: Superluminous type Ia supernovae (SNe Ia) may be explained by super-Chandrasekhar-mass explosions of rapidly rotating white dwarfs (WDs). In a preceding paper, we showed that the deflagration scenario applied to rapidly rotating WDs generates explosions that cannot explain the majority of SNe Ia. Aims: Rotation of the progenitor star allows super-Chandrasekhar-mass WDs to form that have a shallower density stratification. We use simple estimates of the production of intermediate and iron group elements in pure detonations of rapidly rotating WDs to assess their viability in explaining rare SNe Ia. Methods: We numerically construct WDs in hydrostatic equilibrium that rotate according to a variety of rotation laws. The explosion products are estimated by considering the density stratification and by evaluating the result of hydrodynamics simulations. Results: We show that a significant amount of intermediate mass elements is produced for theoretically motivated rotation laws, even for prompt detonations of WDs. Conclusions: Rapidly rotating WDs that detonate may provide an explanation of rare superluminous SNe Ia in terms of both burning species and explosion kinematics.Comment: 7 pages, 5 figures, accepted for publication by A&

Comment on "Bounding and approximating parabolas for the spectrum of Heisenberg spin systems" by Schmidt, Schnack and Luban

Recently, Schmidt et al. proved that the energy spectrum of a Heisenberg spin system (HSS) is bounded by two parabolas, i.e. lines which depend on the total spin quantum number S as S(S+1). The prove holds for homonuclear HSSs which fulfill a weak homogenity condition. Moreover, the extremal values of the exact spectrum of various HSS which were studied numerically were found to lie on approximate parabolas, named rotational bands, which could be obtained by a shift of the boundary parabolas. In view of this, it has been claimed that the rotational band structure (RBS) of the energy spectrum is a general behavior of HSSs. Furthermore, since the approximate parabolas are very close to the true boundaries of the spectrum for the examples discussed, it has been claimed that the methods allow to predict the detailed shape of the spectrum and related properties for a general HSS. In this comment I will show by means of examples that the RBS hypothesis is not valid for general HSSs. In particular, weak homogenity is neither a necessary nor a sufficient condition for a HSS to exhibit a spectrum with RBS.Comment: Comments on the work of Schmidt et al, Europhys. Lett. 55, 105 (2001), cond-mat/0101228 (for the reply see cond-mat/0111581). To be published in Europhys. Let