4,557 research outputs found
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
Pseudo-epsilon expansion and the two-dimensional Ising model
Starting from the five-loop renormalization-group expansions for the
two-dimensional Euclidean scalar \phi^4 field theory (field-theoretical version
of two-dimensional Ising model), pseudo-\epsilon expansions for the Wilson
fixed point coordinate g*, critical exponents, and the sextic effective
coupling constant g_6 are obtained. Pseudo-\epsilon expansions for g*, inverse
susceptibility exponent \gamma, and g_6 are found to possess a remarkable
property - higher-order terms in these expansions turn out to be so small that
accurate enough numerical estimates can be obtained using simple Pade
approximants, i. e. without addressing resummation procedures based upon the
Borel transformation.Comment: 4 pages, 4 tables, few misprints avoide
Quantum Resonances of Kicked Rotor and SU(q) group
The quantum kicked rotor (QKR) map is embedded into a continuous unitary
transformation generated by a time-independent quasi-Hamiltonian. In some
vicinity of a quantum resonance of order , we relate the problem to the {\it
regular} motion along a circle in a -component inhomogeneous
"magnetic" field of a quantum particle with intrinsic degrees of freedom
described by the group. This motion is in parallel with the classical
phase oscillations near a non-linear resonance.Comment: RevTeX, 4 pages, 3 figure
Relative dispersion in fully developed turbulence: The Richardson's Law and Intermittency Corrections
Relative dispersion in fully developed turbulence is investigated by means of
direct numerical simulations. Lagrangian statistics is found to be compatible
with Richardson description although small systematic deviations are found. The
value of the Richardson constant is estimated as , in a close
agreement with recent experimental findings [S. Ott and J. Mann J. Fluid Mech.
{\bf 422}, 207 (2000)]. By means of exit-time statistics it is shown that the
deviations from Richardson's law are a consequence of Eulerian intermittency.
The measured Lagrangian scaling exponents require a set of Eulerian structure
function exponents which are remarkably close to standard ones
known for fully developed turbulence
Magnetic Effects Change Our View of the Heliosheath
There is currently a controversy as to whether Voyager 1 has already crossed
the Termination Shock, the first boundary of the Heliosphere. The region
between the Termination Shock and the Heliopause, the Helisheath, is one of the
most unknown regions theoretically. In the Heliosheath magnetic effects are
crucial, as the solar magnetic field is compressed at the Termination Shock by
the slowing flow. Recently, our simulations showed that the Heliosheath
presents remarkable dynamics, with turbulent flows and the presence of a jet
flow at the current sheet that is unstable due to magnetohydrodynamic
instabilities \cite{opher,opher1}. In this paper we review these recent
results, and present an additional simulation with constant neutral atom
background. In this case the jet is still present but with reduced intensity.
Further study, e.g., including neutrals and the tilt of the solar rotation from
the magnetic axis, is required before we can definitively address how the
Heliosheath behaves. Already we can say that this region presents remarkable
dynamics, with turbulent flows, indicating that the Heliosheath might be very
different from what we previously thought.Comment: 6 pages, 5 figures, to appear in IGPP 3rd Annual International
Astrophysics Conference, "PHYSICS OF THE OUTER HELIOSPHERE
Anharmonicity of BaTiO_3 single crystals
By analyzing the dielectric non-linearity with the Landau thermodynamic
expansion, we find a simple and direct way to assess the importance of the
eighth order term. Following this approach, it is demonstrated that the eighth
order term is essential for the adequate description of the para/ferroelectric
phase transition of BaTiO_3. The temperature dependence of the quartic
coefficient \beta is accordingly reconsidered and is strongly evidenced by the
change of its sign above 165 C. All these findings attest to the strong
polarization anharmonicity of this material, which is unexpected for classical
displacive ferroelectrics.Comment: 4 figures, to be published in Phys. Rev.
Thermal deformation of concentrators in an axisymmetric temperature field
Axisymmetric thermal deformations of paraboloid mirrors, due to heating, are examined for a mirror with a optical axis oriented toward the Sun. A governing differential equation is derived using Mushtari-Donnel-Vlasov simplifications, and a solution is presented which makes it possible to determine the principal deformation characteristics
Interface states in junctions of two semiconductors with intersecting dispersion curves
A novel type of shallow interface state in junctions of two semiconductors
without band inversion is identified within the envelope function
approximation, using the two-band model. It occurs in abrupt junctions when the
interband velocity matrix elements of the two semiconductors differ and the
bulk dispersion curves intersect. The in-plane dispersion of the interface
state is found to be confined to a finite range of momenta centered around the
point of intersection. These states turn out to exist also in graded junctions,
with essentially the same properties as in the abrupt case.Comment: 1 figur
- …