2,409 research outputs found
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.
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
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
Bosonic String in Affine-Metric Curved Space
The sigma model approach to the closed bosonic string on the affine-metric
manifold is considered. The two-loop metric counterterms for the nonlinear
two-dimensional sigma model with affine-metric target manifold are calculated.
The correlation of the metric and affine connection is considered as the result
of the ultraviolet finiteness (or beta-function vanishing) condition for the
nonlinear sigma model. The examples of the nonflat nonRiemannian manifolds
resulting in the trivial metric beta-function are suggested.Comment: 15 pages, LaTe
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
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
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