Discrete Self-Similarity in Type-II Strong Explosions

We present new solutions to the strong explosion problem in a non-power law density profile. The unperturbed self-similar solutions discovered by Waxman & Shvarts describe strong Newtonian shocks propagating into a cold gas with a density profile falling off as $r^{-\omega}$, where $\omega>3$ (Type-II solutions). The perturbations we consider are spherically symmetric and log-periodic with respect to the radius. While the unperturbed solutions are continuously self-similar, the log-periodicity of the density perturbations leads to a discrete self-similarity of the perturbations, i.e. the solution repeats itself up to a scaling at discrete time intervals. We discuss these solutions and verify them against numerical integrations of the time dependent hydrodynamic equations. Finally we show that this method can be generalized to treat any small, spherically symmetric density perturbation by employing Fourier decomposition

Superlinear Increase of Photocurrent due to Stimulated Scattering into a Polariton Condensate

We show that when a monopolar current is passed through an n-i-n structure, superlinear photocurrent response occurs when there is a polariton condensate. This is in sharp contrast to the previously observed behavior for a standard semiconductor laser. Theoretical modeling shows that this is due to a stimulated exciton-exciton scattering process in which one exciton relaxes into the condensate, while another one dissociates into an electron-hole pair.Comment: 17 pages with 10 figure

The Non-Relativistic Evolution of GRBs 980703 and 970508: Beaming-Independent Calorimetry

We use the Sedov-Taylor self-similar solution to model the radio emission from the gamma-ray bursts (GRBs) 980703 and 970508, when the blastwave has decelerated to non-relativistic velocities. This approach allows us to infer the energy independent of jet collimation. We find that for GRB 980703 the kinetic energy at the time of the transition to non-relativistic evolution, t_NR ~ 40 d, is E_ST ~ (1-6)e51 erg. For GRB 970508 we find E_ST ~ 3e51 erg at t_NR ~ 100 d, nearly an order of magnitude higher than the energy derived in Frail, Waxman and Kulkarni (2000). This is due primarily to revised cosmological parameters and partly to the maximum likelihood fit we use here. Taking into account radiative losses prior to t_NR, the inferred energies agree well with those derived from the early, relativistic evolution of the afterglow. Thus, the analysis presented here provides a robust, geometry-independent confirmation that the energy scale of cosmological GRBs is about 5e51 erg, and additionally shows that the central engine in these two bursts did not produce a significant amount of energy in mildly relativistic ejecta at late time. Furthermore, a comparison to the prompt energy release reveals a wide dispersion in the gamma-ray efficiency, strengthening our growing understanding that E_gamma is a not a reliable proxy for the total energy.Comment: Submitted to ApJ; 13 pages, 6 figures, 1 table; high-resolution figures can be found at: http://www.astro.caltech.edu/~ejb/NR

Low-Mass Star Formation, Triggered by Supernova in Primordial Clouds

The evolution of a gas shell, swept by the supernova remnant of a massive first generation star, is studied with H_2 and HD chemistry taken into account. When a first-generation star explodes as a supernova, H_2 and HD molecules are formed in the swept gas shell and effectively cool the gas shell to temperatures of 32 K - 154 K. If the supernova remnant can sweep to gather the ambient gas, the gas shell comes to be dominated by its self-gravity, and hence, is expected to fragment. Our result shows that for a reasonable range of temperatures (200 K - 1000 K) of interstellar gas, the formation of second-generation stars can be triggered by a single supernova or hypernova.Comment: 38pages, 10 figures, The Astrophysical Journal, accepted 8 Dec. 200

Universal scaling dynamics in a perturbed granular gas

We study the response of a granular system at rest to an instantaneous input of energy in a localised region. We present scaling arguments that show that, in $d$ dimensions, the radius of the resulting disturbance increases with time $t$ as $t^{\alpha}$, and the energy decreases as $t^{-\alpha d}$, where the exponent $\alpha=1/(d+1)$ is independent of the coefficient of restitution. We support our arguments with an exact calculation in one dimension and event driven molecular dynamic simulations of hard sphere particles in two and three dimensions.Comment: 5 pages, 5 figure

An all-optical event horizon in an optical analogue of a Laval nozzle

Exploiting the fact that light propagation in defocusing nonlinear media can mimic the transonic flow of an equivalent fluid, we demonstrate experimentally the formation of an all-optical event horizon in a waveguide structure akin to a hydrodynamic Laval nozzle. The analogue event horizon, which forms at the nozzle throat is suggested as a novel platform for analogous gravity experiments

The initial development of a jet caused by fluid, body and free surface interaction with a uniformly accelerated advancing or retreating plate. Part 1. The principal flow

The free surface and flow field structure generated by the uniform acceleration (with dimensionless acceleration σ) of a rigid plate, inclined at an angle α ∈ (0, π/2) to the exterior horizontal, as it advances (σ > 0) or retreats (σ < 0) from an initially stationary and horizontal strip of inviscid, incompressible fluid under gravity, are studied in the small-time limit via the method of matched asymptotic expansions. This work generalises the case of a uniformly accelerating plate advancing into a fluid as studied in Needham et al. (2008). Particular attention is paid to the innermost asymptotic regions encompassing the initial interaction between the plate and the free surface. We find that the structure of the solution to the governing initial boundary value problem is characterised in terms of the parameters α and μ (where μ = 1+σ tan α), with a bifurcation in structure as μ changes sign. This bifurcation in structure leads us to question the well-posedness and stability of the governing initial boundary value problem with respect to small perturbations in initial data in the innermost asymptotic regions, the discussion of which will be presented in the companion paper Gallagher et al. (2016) . In particular, when (α, μ) ∈ (0, π/2) × R+, the free surface close to the initial contact point remains monotone, and encompasses a swelling jet when (α, μ) ∈ (0, π/2)×[1,∞), or a collapsing jet when (α, μ) ∈ (0, π/2) × (0, 1). However, when (α, μ) ∈ (0, π/2) × R−, the collapsing jet develops a more complex structure, with the free surface close to the initial contact point now developing a finite number of local oscillations, with near resonance type behaviour occurring close to a countable set of critical plate angles α = α∗n ∈ (0, π/2) (n = 1, 2, . . .)

Floquet engineering of the Lifshitz phase transition in the Hubbard model

Within the Floquet theory of periodically driven quantum systems, we demonstrate that an off-resonant high-frequency electromagnetic field can induce the Lifshitz phase transition in periodical structures described by the one-dimensional repulsive Hubbard model with the nearest and next-nearest neighbor hopping. The transition changes the topology of electron energy spectrum at the Fermi level, transforming it from the two Fermi-points to the four Fermi-points, what facilitates the emergence of the superconducting fluctuations in the structure. Possible manifestations of the effect and conditions of its experimental observability are discussed

Magnetic relaxation in the Bianchi-I universe

Extended Einstein-Maxwell model and its application to the problem of evolution of magnetized Bianchi-I Universe are considered. The evolution of medium magnetization is governed by a relaxation type extended constitutive equation. The series of exact solutions to the extended master equations is obtained and discussed. The anisotropic expansion of the Bianchi-I Universe is shown to become non-monotonic (accelerated/decelerated) in both principal directions (along the magnetic field and orthogonal to it). A specific type of expansion, the so-called evolution with hidden magnetic field, is shown to appear when the magnetization effectively screens the magnetic field and the latter disappears from the equations for gravitational field.Comment: 32 page