The Thermonuclear Explosion Of Chandrasekhar Mass White Dwarfs

The flame born in the deep interior of a white dwarf that becomes a Type Ia supernova is subject to several instabilities. We briefly review these instabilities and the corresponding flame acceleration. We discuss the conditions necessary for each of the currently proposed explosion mechanisms and the attendant uncertainties. A grid of critical masses for detonation in the range $10^7$ - $2 \times 10^9$ g cm$^{-3}$ is calculated and its sensitivity to composition explored. Prompt detonations are physically improbable and appear unlikely on observational grounds. Simple deflagrations require some means of boosting the flame speed beyond what currently exists in the literature. ``Active turbulent combustion'' and multi-point ignition are presented as two plausible ways of doing this. A deflagration that moves at the ``Sharp-Wheeler'' speed, $0.1 g_{\rm eff} t$, is calculated in one dimension and shows that a healthy explosion is possible in a simple deflagration if the front moves with the speed of the fastest floating bubbles. The relevance of the transition to the ``distributed burning regime'' is discussed for delayed detonations. No model emerges without difficulties, but detonation in the distributed regime is plausible, will produce intermediate mass elements, and warrants further study.Comment: 28 pages, 4 figures included, uses aaspp4.sty. Submitted to Ap

Transport efficiency and dynamics of hydraulic fracture networks

Acknowledgments This study is carried out within the framework of DGMK (German Society for Petroleum and Coal Science and Technology) research project 718 “Mineral Vein Dynamics Modeling,” which is funded by the companies ExxonMobil Production Deutschland GmbH, GDF SUEZ E&P Deutschland GmbH, RWE Dea AG and Wintershall Holding GmbH, within the basic research programme of the WEG Wirtschaftsverband Erdöl- und Erdgasgewinnung e.V. We thank the companies for their financial support and their permission to publish our results. We further acknowledge support by Deutsche Forschungsgemeinschaft and Open Access Publishing Fund of University of Tübingen.Peer reviewedPublisher PD

Theory of the Spatio-Temporal Dynamics of Transport Bifurcations

The development and time evolution of a transport barrier in a magnetically confined plasma with non-monotonic, nonlinear dependence of the anomalous flux on mean gradients is analyzed. Upon consideration of both the spatial inhomogeneity and the gradient nonlinearity of the transport coefficient, we find that the transition develops as a bifurcation front with radially propagating discontinuity in local gradient. The spatial location of the transport barrier as a function of input flux is calculated. The analysis indicates that for powers slightly above threshold, the barrier location $x_b(t) \sim ( D_n t (P-P_c)/P_c)^{1/2},$ where $P_c$ is the local transition power threshold and $D_n$ is the neoclassical diffusivity . This result suggests a simple explanation of the high disruptivity observed in reversed shear plasmas. The basic conclusions of this theory are insensitive to the details of the local transport model.Comment: 21 page Tex file, 10 postscript file

Structure and properties of transition fronts in accretion discs

We use high-resolution time-dependent numerical simulations of accretion discs around white dwarfs to study the structure and properties of transition fronts in the context of the thermal-viscous disc instability model. The thermal structure of cooling and heating fronts is dominated by radiative cooling and viscous heating, respectively, except in a very narrow precursor region in heating fronts where advection and radial transport of energy dominate. Cooling fronts are much broader than heating fronts, but the widths of both types of fronts scale with the local vertical scale height of the disc. We confirm that during a fair fraction of the propagation time of a cooling front, the structure of the inner disc is close to self-similar. The speed of heating fronts is ~ a few km/s, while the speed of cooling fronts is ~ a fraction of a km/s. We show that direct measurements of the speed of transition fronts probably cannot discriminate between various prescriptions proposed for the viscosity parameter alpha. A natural prediction of the disc instability model is that fronts decelerate as they propagate in the disc, independent of the prescription for alpha. Observation of this effect would confirm that dwarf nova outbursts are driven by the thermal-viscous instability. Most of our results also apply to low mass X-ray binaries in which the accreting object is a neutron star or a black hole.Comment: LateX, 12 pages, 10 figures, uses mn.sty; Submitted to MNRA

Cryomagma ascent on Europa

Europa's surface exhibits morphological features which, associated with a low crater density, might be interpreted to have formed as a result of recent cryovolcanic activity. In particular, the morphology of smooth deposits covering parts of the surface, and their relationship to the surrounding terrains, suggest that they result from liquid extrusions. Furthermore, recent literature suggests that the emplacement of liquid-related features, such as double ridges, lenticulae and chaos could result from the presence of liquid reservoirs beneath the surface. We model the ascent of liquid water through a fracture or a pipe-like conduit from a subsurface reservoir to Europa\textquoteright s surface and calculate the eruption time-scale and the total volume extruded during the eruption, as a function of the reservoir volume and depth. We also estimate the freezing time of a subsurface reservoir necessary to trigger an eruption. Our model is derived for pure liquid water and for a briny mixture outlined by Kargel (1991): 81 wt% H$_{2}$O + 16 wt% MgSO$_{4}$ + 3 wt% Na$_{2}$SO$_{4}$. Considering compositional data for salt impurities for Europa, we discuss the effect of MgSO$_{4}$ and Na$_{2}$SO$_{4}$ on the cryomagma freezing time-scale and ascent. For plausible reservoir volumes and depths in the range of $\mathrm{10^{6}\:m^{3}\leq V\leq10^{10}\:m^{3}}$ and $\mathrm{1\:km\leq H\leq10\:km}$ respectively, the total extruded cryolava volume ranges from $10^{3}\,\mathrm{m^{3}}$ to $10^{8}\,\mathrm{m^{3}}$ and the duration of the eruptions varies from few minutes to few tens of hours. The freezing time-scale of the cryomagma reservoirs varies with cryomagma composition and the temperature gradient in the ice shell: from a few days to a thousand years for pure water cryomagma, and from a few months to a 10$^{4}$ years for briny cryomagma.Comment: 31 pages, 11 figure

Role of heat generation and thermal diffusion during frontal photopolymerization

Frontal photopolymerization (FPP) is a rapid and versatile solidification process that can be used to fabricate complex three-dimensional structures by selectively exposing a photosensitive monomer-rich bath to light. A characteristic feature of FPP is the appearance of a sharp polymerization front that propagates into the bath as a planar traveling wave. In this paper, we introduce a theoretical model to determine how heat generation during photopolymerization influences the kinetics of wave propagation as well as the monomer-to-polymer conversion profile, both of which are relevant for FPP applications and experimentally measurable. When thermal diffusion is sufficiently fast relative to the rate of polymerization, the system evolves as if it were isothermal. However, when thermal diffusion is slow, a thermal wavefront develops and propagates at the same rate as the polymerization front. This leads to an accumulation of heat behind the polymerization front which can result in a significant sharpening of the conversion profile and acceleration of the growth of the solid. Our results also suggest that a novel way to tailor the dynamics of FPP is by imposing a temperature gradient along the growth directio

Spatially hybrid computations for streamer discharges with generic features of pulled fronts: I. Planar fronts

Streamers are the first stage of sparks and lightning; they grow due to a strongly enhanced electric field at their tips; this field is created by a thin curved space charge layer. These multiple scales are already challenging when the electrons are approximated by densities. However, electron density fluctuations in the leading edge of the front and non-thermal stretched tails of the electron energy distribution (as a cause of X-ray emissions) require a particle model to follow the electron motion. As super-particle methods create wrong statistics and numerical artifacts, modeling the individual electron dynamics in streamers is limited to early stages where the total electron number still is limited. The method of choice is a hybrid computation in space where individual electrons are followed in the region of high electric field and low density while the bulk of the electrons is approximated by densities (or fluids). We here develop the hybrid coupling for planar fronts. First, to obtain a consistent flux at the interface between particle and fluid model in the hybrid computation, the widely used classical fluid model is replaced by an extended fluid model. Then the coupling algorithm and the numerical implementation of the spatially hybrid model are presented in detail, in particular, the position of the model interface and the construction of the buffer region. The method carries generic features of pulled fronts that can be applied to similar problems like large deviations in the leading edge of population fronts etc.Comment: 33 pages, 15 figures and 2 table

Deblocking of interacting particle assemblies: from pinning to jamming

A wide variety of interacting particle assemblies driven by an external force are characterized by a transition between a blocked and a moving phase. The origin of this deblocking transition can be traced back to the presence of either external quenched disorder, or of internal constraints. The first case belongs to the realm of the depinning transition, which, for example, is relevant for flux-lines in type II superconductors and other elastic systems moving in a random medium. The second case is usually included within the so-called jamming scenario observed, for instance, in many glassy materials as well as in plastically deforming crystals. Here we review some aspects of the rich phenomenology observed in interacting particle models. In particular, we discuss front depinning, observed when particles are injected inside a random medium from the boundary, elastic and plastic depinning in particle assemblies driven by external forces, and the rheology of systems close to the jamming transition. We emphasize similarities and differences in these phenomena.Comment: 20 pages, 8 figures, submitted for a special issue of the Brazilian Journal of Physics entitled: Statistical Mechanics of Irreversible Stochastic Models - I