GRB afterglows: deep Newtonian phase and its application

Gamma-ray burst afterglows have been observed for months or even years in a few cases. It deserves noting that at such late stages, the remnants should have entered the deep Newtonian phase, during which the majority of shock-accelerated electrons will no longer be highly relativistic. To calculate the afterglows, we must assume that the electrons obey a power-law distribution according to their kinetic energy, not simply the Lorentz factor.Comment: Poster at the 4th workshop "Gamma-Ray Bursts in the Afterglow Era" (Rome, 2004), accepted for publication in the proceedings. 4 pages, with 3 figures inserte

Beaming effects in GRBs and orphan afterglows

The overall dynamical evolution and radiation mechanism of $\gamma$-ray burst jets are briefly introduced. Various interesting topics concerning beaming in $\gamma$-ray bursts are discussed, including jet structures, orphan afterglows and cylindrical jets. The possible connection between $\gamma$-ray bursts and neutron star kicks is also addressed.Comment: 10 Pages, 4 figures, to appear in a special issue of ApSS. Oral report presented at "The Multiwavelength Approach to Unidentified Gamma-Ray Sources" (Hong Kong, June 1 - 4, 2004; Conference organizers: K.S. Cheng and G.E. Romero

A Generic Dynamical Model of Gamma-ray Burst Remnants

The conventional generic model is deemed to explain the dynamics of $\gamma$-ray burst remnants very well, no matter whether they are adiabatic or highly radiative. However, we find that for adiabatic expansion, the model could not reproduce the Sedov solution in the non-relativistic phase, thus the model needs to be revised. In the present paper, a new differential equation is derived. The generic model based on this equation has been shown to be correct for both radiative and adiabatic fireballs, and in both ultra-relativistic and non-relativistic phase.Comment: 10 pages, LaTeX, 4 postscript figures, accepted for publication in MNRA

Optical Flashes and Very Early Afterglows in Wind Environments

The interaction of a relativistic fireball with its ambient medium is described through two shocks: a reverse shock that propagates into the fireball, and a forward shock that propagates into the medium. The observed optical flash of GRB 990123 has been considered to be the emission from such a reverse shock. The observational properties of afterglows suggest that the progenitors of some GRBs may be massive stars and their surrounding media may be stellar winds. We here study very early afterglows from the reverse and forward shocks in winds. An optical flash mainly arises from the relativistic reverse shock while a radio flare is produced by the forward shock. The peak flux densities of optical flashes are larger than 1 Jy for typical parameters, if we do not take into account some appropriate dust obscuration along the line of sight. The radio flare always has a long lasting constant flux, which will not be covered up by interstellar scintillation. The non-detections of optical flashes brighter than about 9th magnitude may constrain the GRBs isotropic energies to be no more than a few $10^{52}$ ergs and wind intensities to be relatively weak.Comment: 21 pages, 6 figures, accepted by MNRAS on March 7, 200

Transverse momentum dependence in the perturbative calculation of pion form factor

By reanalysing transverse momentum dependence in the perturbative calculation of pion form factor an improved expression of pion form factor which takes into account the transverse momentum dependenc in hard scattering amplitude and intrinsic transverse momentum dependence associated with pion wave functions is given to leading order, which is available for momentum transfers of the order of a few GeV as well as for $Q \to \infty$. Our scheme can be extended to evaluate the contributions to the pion form factor beyond leading order.Comment: 13 pages in LaTeX, plus 3 Postscript figure

Solvent coarse-graining and the string method applied to the hydrophobic collapse of a hydrated chain

Using computer simulations of over 100,000 atoms, the mechanism for the hydrophobic collapse of an idealized hydrated chain is obtained. This is done by coarse-graining the atomistic water molecule positions over 129,000 collective variables that represent the water density field and then using the string method in these variables to compute the minimum free energy pathway (MFEP) for the collapsing chain. The dynamical relevance of the MFEP (i.e. its coincidence with the mechanism of collapse) is validated a posteriori using conventional molecular dynamics trajectories. Analysis of the MFEP provides atomistic confirmation for the mechanism of hydrophobic collapse proposed by ten Wolde and Chandler. In particular, it is shown that lengthscale-dependent hydrophobic dewetting is the rate-limiting step in the hydrophobic collapse of the considered chain.Comment: 11 pages, 7 figures, including supporting informatio