Microscopic origin of self-similarity in granular blast waves

The self-similar expansion of a blast wave, well-studied in air, has peculiar counterparts in dense and dissipative media such as granular gases. Recent results have shown that, while the traditional Taylor-von Neumann-Sedov (TvNS) derivation is not applicable to such granular blasts, they can nevertheless be well understood via a combination of microscopic and hydrodynamic insights. In this article, we provide a detailed analysis of these methods associating Molecular Dynamics simulations and continuum equations, which successfully predict hydrodynamic profiles, scaling properties and the instability of the self-similar solution. We also present new results for the energy conserving case, including the particle-level analysis of the classic TvNS solution and its breakdown at higher densities.Comment: 47 pages, 9 figures Supplementary Materials: 2 appendices, 3 figure

Particle Acceleration at Relativistic Shocks

I review the current status of Fermi acceleration theory at relativistic shocks. I first discuss the relativistic shock jump conditions, then describe the non-relativistic Fermi mechanism and the differences introduced by relativistic flows. I present numerical calculations of the accelerated particle spectrum, and examine the maximum energy attainable by this process. I briefly consider the minimum energy for Fermi acceleration, and a possible electron pre-acceleration mechanism.Comment: 17 pages, 4 figures. To appear in "Relativistic Flows in Astrophysics", A.W. Guthmann, M. Georganopoulos, A. Marcowith and K. Manolokou, eds., Lecture Notes in Pysics, Springer Verla

The role of unsteadiness in direct initiation of gaseous detonations

An analytical model is presented for the direct initiation of gaseous detonations by a blast wave. For stable or weakly unstable mixtures, numerical simulations of the spherical direct initiation event and local analysis of the one-dimensional unsteady reaction zone structure identify a competition between heat release, wave front curvature and unsteadiness. The primary failure mechanism is found to be unsteadiness in the induction zone arising from the deceleration of the wave front. The quasi-steady assumption is thus shown to be incorrect for direct initiation. The numerical simulations also suggest a non-uniqueness of critical energy in some cases, and the model developed here is an attempt to explain the lower critical energy only. A critical shock decay rate is determined in terms of the other fundamental dynamic parameters of the detonation wave, and hence this model is referred to as the critical decay rate (CDR) model. The local analysis is validated by integration of reaction-zone structure equations with real gas kinetics and prescribed unsteadiness. The CDR model is then applied to the global initiation problem to produce an analytical equation for the critical energy. Unlike previous phenomenological models of the critical energy, this equation is not dependent on other experimentally determined parameters and for evaluation requires only an appropriate reaction mechanism for the given gas mixture. For different fuel–oxidizer mixtures, it is found to give agreement with experimental data to within an order of magnitude

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

Baryon Loaded Relativistic Blastwaves in Supernovae

We provide a new analytic blastwave solution which generalizes the Blandford-McKee solution to arbitrary ejecta masses and Lorentz factors. Until recently relativistic supernovae have been discovered only through their association with long duration Gamma Ray Bursts (GRB). The blastwaves of such explosions are well described by the Blandford-McKee (in the ultra relativistic regime) and Sedov-Taylor (in the non-relativistic regime) solutions during their afterglows, as the ejecta mass is negligible in comparison to the swept up mass. The recent discovery of the relativistic supernova SN 2009bb, without a detected GRB, opens up the possibility of highly baryon loaded mildly relativistic outflows which remains in nearly free expansion phase during the radio afterglow. In this work, we consider a massive, relativistic shell, launched by a Central Engine Driven EXplosion (CEDEX), decelerating adiabatically due to its collision with the pre-explosion circumstellar wind profile of the progenitor. We compute the synchrotron emission from relativistic electrons in the shock amplified magnetic field. This models the radio emission from the circumstellar interaction of a CEDEX. We show that this model explains the observed radio evolution of the prototypical SN 2009bb and demonstrate that SN 2009bb had a highly baryon loaded, mildly relativistic outflow. We discuss the effect of baryon loading on the dynamics and observational manifestations of a CEDEX. In particular, our predicted angular size of SN 2009bb is consistent with VLBI upper limits on day 85, but is presently resolvable on VLBI angular scales, since the relativistic ejecta is still in the nearly free expansion phase.Comment: 13 pages, 6 figures, Accepted for publication in Ap

On the formation of Hubble flow in Little Bangs

A dynamical appearance of scaling solutions in the relativistic hydrodynamics applied to describe ultra-relativistic heavy-ion collisions is studied. We consider the boost-invariant cylindrically symmetric systems and the effects of the phase transition are taken into account by using a temperature dependent sound velocity inferred from the lattice simulations of QCD. We find that the transverse flow acquires the scaling form r/t within the short evolution times, 10 - 15 fm, only if the initial transverse flow originating from the pre-equilibrium collective behavior is present at the initial stage of the hydrodynamic evolution. The amount of such pre-equilibrium flow is correlated with the initial pressure gradient; larger gradients require smaller initial flow. The results of the numerical calculations support the phenomenological parameterizations used in the Blast-Wave, Buda-Lund, and Cracow models of the freeze-out process.Comment: 11 page

Analyzing Correlation Functions with Tesseral and Cartesian Spherical Harmonics

The dependence of inter-particle correlations on the orientation of particle relative-momentum can yield unique information on the space-time features of emission in reactions with multiparticle final states. In the present paper, the benefits of a representation and analysis of the three-dimensional correlation information in terms of surface spherical harmonics is presented. The harmonics include the standard complex tesseral harmonics and the real cartesian harmonics. Mathematical properties of the lesser-known cartesian harmonics are illuminated. The physical content of different angular harmonic components in a correlation is described. The resolving power of different final-state effects with regarding to determining angular features of emission regions is investigated. The considered final-state effects include identity interference and strong and Coulomb interactions. The correlation analysis in terms of spherical harmonics is illustrated with the cases of gaussian and blast-wave sources for proton-charged meson and baryon-baryon pairs.Comment: 32 pages 10 figure

Modeling and control of complex dynamic systems: Applied mathematical aspects

The concept of complex dynamic systems arises in many varieties, including the areas of energy generation, storage and distribution, ecosystems, gene regulation and health delivery, safety and security systems, telecommunications, transportation networks, and the rapidly emerging research topics seeking to understand and analyse. Such systems are often concurrent and distributed, because they have to react to various kinds of events, signals, and conditions. They may be characterized by a system with uncertainties, time delays, stochastic perturbations, hybrid dynamics, distributed dynamics, chaotic dynamics, and a large number of algebraic loops. This special issue provides a platform for researchers to report their recent results on various mathematical methods and techniques for modelling and control of complex dynamic systems and identifying critical issues and challenges for future investigation in this field. This special issue amazingly attracted one-hundred-and eighteen submissions, and twenty-eight of them are selected through a rigorous review procedure