2,648 research outputs found
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 , where (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
On the theory of unsteady planing and the motion of a wing with vortex separation
The disturbance imparted to water by a planing body give rise to a wave form of motion on the free surface, the length of the waves increasing indefinitely with increase in the Froude number and being directly proportional to the latter in the case of the plane or two-dimensional problem. At large Froude numbers the effect of the weight shows up to any appreciable extent only at some distance from the body, so that the flow near the body can be considered as part of a flow of an infinitely extending weightless fluid. This paper is a consideration of these characteristics as well as a formulation of the planing problem and its relation to the problem of a thin wing
Mathematical methods of constructing new models of continua
Mathematical methods of constructing new models of continu
Stability of an Ultra-Relativistic Blast Wave in an External Medium with a Steep Power-Law Density Profile
We examine the stability of self-similar solutions for an accelerating
relativistic blast wave which is generated by a point explosion in an external
medium with a steep radial density profile of a power-law index > 4.134. These
accelerating solutions apply, for example, to the breakout of a gamma-ray burst
outflow from the boundary of a massive star, as assumed in the popular
collapsar model. We show that short wavelength perturbations may grow but only
by a modest factor <~ 10.Comment: 12 pages, 3 figures, submitted to Physical Review
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
Uniform materials and the multiplicative decomposition of the deformation gradient in finite elasto-plasticity
In this work we analyze the relation between the multiplicative decomposition
of the deformation gradient as a product
of the elastic and plastic factors and the theory of uniform materials. We
prove that postulating such a decomposition is equivalent to having a uniform
material model with two configurations - total and the inelastic
. We introduce strain tensors characterizing different types of
evolutions of the material and discuss the form of the internal energy and that
of the dissipative potential. The evolution equations are obtained for the
configurations and the material metric .
Finally the dissipative inequality for the materials of this type is
presented.It is shown that the conditions of positivity of the internal
dissipation terms related to the processes of plastic and metric evolution
provide the anisotropic yield criteria
An exact self-similar solution for an expanding ball of radiation
We give an exact solution of the Einstein equations which in 4D can be
interpreted as a spherically symmetric dissipative distribution of matter, with
heat flux, whose effective density and pressure are nonstatic, nonuniform, and
satisfy the equation of state of radiation. The matter satisfies the usual
energy and thermodynamic conditions. The energy density and temperature are
related by the Stefan-Boltzmann law. The solution admits a homothetic Killing
vector in , which induces the existence of self-similar symmetry in 4D,
where the line element as well as the dimensionless matter quantities are
invariant under a simple "scaling" group.Comment: New version expanded and improved. To appear in Int. J. Mod. Phys.
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
Self-similar imploding relativistic shock waves
Self-similar solutions to the problem of a strong imploding relativistic
shock wave are calculated. These solutions represent the relativistic
generalisation of the Newtonian Gouderley-Landau-Stanyukovich problem of a
strong imploding spherical shock wave converging to a centre. The solutions are
found assuming that the pre-shocked flow has a uniform density, and are
accurate for sufficiently large times after the formation of the shock wave.Comment: 22 pages, 4 figures. Minor corrections and a discussion of the
singular C_ characteristic added. Accepted for publication in Physics of
Fluid
Confinement of supernova explosions in a collapsing cloud
We analyze the confining effect of cloud collapse on an expanding supernova
shockfront. We solve the differential equation for the forces on the shockfront
due to ram pressure, supernova energy, and gravity. We find that the expansion
of the shockfront is slowed and in fact reversed by the collapsing cloud.
Including radiative losses and a potential time lag between supernova explosion
and cloud collapse shows that the expansion is reversed at smaller distances as
compared to the non-radiative case. We also consider the case of multiple
supernova explosions at the center of a collapsing cloud. For instance, if we
scale our self-similar solution to a single supernova of energy 10^51 ergs
occurring when a cloud of initial density 10^2 H/cm^3 has collapsed by 50%, we
find that the shockfront is confined to ~15 pc in ~1 Myrs. Our calculations are
pertinent to the observed unusually compact non-thermal radio emission in blue
compact dwarf galaxies (BCDs). More generally, we demonstrate the potential of
a collapsing cloud to confine supernovae, thereby explaining how dwarf galaxies
would exist beyond their first generation of star formation.Comment: 3 pages, 4 figure
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