2,567 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 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 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
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