Solid weak BCC-algebras

We characterize weak BCC-algebras in which the identity $(xy)z=(xz)y$ is satisfied only in the case when elements $x,y$ belong to the same branch

Off-Axis Afterglow Light Curves from High-Resolution Hydrodynamical Jet Simulations

Numerical jet simulations serve a valuable role in calculating gamma-ray burst afterglow emission beyond analytical approximations. Here we present the results of high resolution 2D simulations of decelerating relativistic jets performed using the RAM adaptive mesh refinement relativistic hydrodynamics code. We have applied a separate synchrotron radiation code to the simulation results in order to calculate light curves at frequencies varying from radio to X-ray for observers at various angles from the jet axis. We provide a confirmation from radio light curves from simulations rather than from a simplified jet model for earlier results in the literature finding that only a very small number of local Ibc supernovae can possibly harbor an orphan afterglow. Also, recent studies have noted an unexpected lack of observed jet breaks in the Swift sample. Using a jet simulation with physical parameters representative for an average Swift sample burst, such as a jet half opening angle of 0.1 rad and a source redshift of z = 2.23, we have created synthetic light curves at 1.5 keV with artificial errors while accounting for Swift instrument biases as well. A large set of these light curves have been generated and analyzed using a Monte Carlo approach. Single and broken power law fits are compared. We find that for increasing observer angle, the jet break quickly becomes hard to detect. This holds true even when the observer remains well within the jet opening angle. We find that the odds that a Swift light curve from a randomly oriented 0.1 radians jet at z = 2.23 will exhibit a jet break at the 3 sigma level are only 12 percent. The observer angle therefore provides a natural explanation for the lack of perceived jet breaks in the Swift sample.Comment: 4 pages, 3 figures. First of two contributions to proceedings GRB2010 Maryland conference. Editors: McEnery, Racusin and Gehrels. The data from this paper is publicly available from http://cosmo.nyu.edu/afterglowlibrary

An on-line library of afterglow light curves

Numerical studies of gamma-ray burst afterglow jets reveal significant qualitative differences with simplified analytical models. We present an on-line library of synthetic afterglow light curves and broadband spectra for use in interpreting observational data. Light curves have been calculated for various physics settings such as explosion energy and circumburst structure, as well as differing jet parameters and observer angle and redshift. Calculations gave been done for observer frequencies ranging from low radio to X-ray and for observer times from hours to decades after the burst. The light curves have been calculated from high-resolution 2D hydrodynamical simulations performed with the RAM adaptive-mesh refinement code and a detailed synchrotron radiation code. The library will contain both generic afterglow simulations as well as specific case studies and will be freely accessible at http://cosmo.nyu.edu/afterglowlibrary . The synthetic light curves can be used as a check on the accuracy of physical parameters derived from analytical model fits to afterglow data, to quantitatively explore the consequences of varying parameters such as observer angle and for accurate predictions of future telescope data.Comment: 4 pages, 2 figures. Second of two contributions to proceedings GRB2010 Maryland conference. Editors: McEnery, Racusin and Gehrels. The data from this paper is publicly available from http://cosmo.nyu.edu/afterglowlibrary

Domain Walls in Superfluid 3He-B

We consider domain walls between regions of superfluid 3He-B in which one component of the order parameter has the opposite sign in the two regions far from one another. We report calculations of the order parameter profile and the free energy for two types of domain wall, and discuss how these structures are relevant to superfluid 3He confined between two surfaces.Comment: 6 pages with 3 figures. Conference proceedings of QSF 2004, Trento, Ital

Universal Properties of the Ultra-Cold Fermi Gas

We present some general considerations on the properties of a two-component ultra-cold Fermi gas along the BEC-BCS crossover. It is shown that the interaction energy and the ground state energy can be written in terms of a single dimensionless function $h({\xi,\tau})$, where $\xi=-(k_Fa_s)^{-1}$ and $\tau=T/T_F$. The function $h(\xi,\tau)$ incorporates all the many-body physics and naturally occurs in other physical quantities as well. In particular, we show that the RF-spectroscopy shift \bar{\d\o}(\xi,\tau) and the molecular fraction $f_c(\xi,\tau)$ in the closed channel can be expressed in terms of $h(\xi,\tau)$ and thus have identical temperature dependence. The conclusions should have testable consequences in future experiments

Effective nucleon-nucleon interactions and nuclear matter equation of state

Nuclear matter equations of state based on Skyrme, Myers-Swiatecki and Tondeur interactions are written as polynomials of the cubic root of density, with coefficients that are functions of the relative neutron excess $\delta$. In the extrapolation toward states far away from the standard one, it is shown that the asymmetry dependence of the critical point ($\rho_c, \delta_c$) depends on the model used. However, when the equations of state are fitted to the same standard state, the value of $\delta_c$ is almost the same in Skyrme and in Myers-Swiatecki interactions, while is much lower in Tondeur interaction. Furthermore, $\delta_c$ does not depend sensitively on the choice of the parameter $\gamma$ in Skyrme interaction.Comment: 15 pages, 9 figure

Nuclear matter properties and relativistic mean-field theory

Nuclear matter properties are calculated in the relativistic mean field theory by using a number of different parameter sets. The result shows that the volume energy $a_1$ and the symmetry energy $J$ are around the acceptable values 16MeV and 30MeV respectively; the incompressibility $K_0$ is unacceptably high in the linear model, but assumes reasonable value if nonlinear terms are included; the density symmetry $L$ is around $100MeV$ for most parameter sets, and the symmetry incompressibility $K_s$ has positive sign which is opposite to expectations based on the nonrelativistic model. In almost all parameter sets there exists a critical point $(\rho_c, \delta_c)$, where the minimum and the maximum of the equation of state are coincident and the incompressibility equals zero, falling into ranges 0.014fm$^{-3}<\rho_c<0.039$fm$^{-3}$ and $0.74<\delta_c\le0.95$; for a few parameter sets there is no critical point and the pure neutron matter is predicted to be bound. The maximum mass $M_{NS}$ of neutron stars is predicted in the range 2.45M$_\odot\leq M_{NS}\leq 3.26$M$_\odot$, the corresponding neutron star radius $R_{NS}$ is in the range 12.2km$\leq R_{NS}\leq 15.1$km.Comment: 10 pages, 5 figure

Quantum quench dynamics of the Bose-Hubbard model at finite temperatures

We study quench dynamics of the Bose-Hubbard model by exact diagonalization. Initially the system is at thermal equilibrium and of a finite temperature. The system is then quenched by changing the on-site interaction strength $U$ suddenly. Both the single-quench and double-quench scenarios are considered. In the former case, the time-averaged density matrix and the real-time evolution are investigated. It is found that though the system thermalizes only in a very narrow range of the quenched value of $U$, it does equilibrate or relax well in a much larger range. Most importantly, it is proven that this is guaranteed for some typical observables in the thermodynamic limit. In order to test whether it is possible to distinguish the unitarily evolving density matrix from the time-averaged (thus time-independent), fully decoherenced density matrix, a second quench is considered. It turns out that the answer is affirmative or negative according to the intermediate value of $U$ is zero or not.Comment: preprint, 20 pages, 7 figure