Evolution of Massive Black Hole Binaries

We present the result of large-scale N-body simulations of the stellar-dynamical evolution of a massive black-hole binary at the center of a spherical galaxy. We focus on the dependence of the hardening rate on the relaxation timescale of the parent galaxy. A simple theoretical argument predicts that a binary black hole creates the ``loss cone'' around it. Once the loss cone is formed, the hardening rate is determined by the rate at which field stars diffuse into the loss cone. Therefore the hardening timescale becomes proportional to the relaxation timescale. Recent N-body simulations, however, have failed to confirm this theory and various explanations have been proposed. By performing simulations with sufficiently large N (up to $10^6$) for sufficiently long time, we found that the hardening rate does depend on N. Our result is consistent with the simple theoretical prediction that the hardening timescale is proportional to the relaxation timescale. This dependence implies that most massive black hole binaries are unlikely to merge within the Hubble time through interaction with field stars and gravitational wave radiation alone.Comment: Reviced version accepted for publication in ApJ. Scheduled to appear in the February 10, 2004 issu

Monte-Carlo simulation of localization dynamics of excitons in ZnO and CdZnO quantum well structures

Localization dynamics of excitons was studied for ZnO/MgZnO and CdZnO/MgZnO quantum wells (QW). The experimental photoluminescence (PL) and absorption data were compared with the results of Monte Carlo simulation in which the excitonic hopping was modeled. The temperature-dependent PL linewidth and Stokes shift were found to be in a qualitatively reasonable agreement with the hopping model, with accounting for an additional inhomogeneous broadening for the case of linewidth. The density of localized states used in the simulation for the CdZnO QW was consistent with the absorption spectrum taken at 5 K.Comment: 4 figures, to appear in J. Appl. Phy

Biosynthesis, structure, and biological activities of envelope protein gp65 of murine coronavirus.

We have previously shown that gp65 (E3) is a virion structural protein which varies widely in quantity among different strains of mouse hepatitis virus (MHV). In this study, the biosynthetic pathway and possible biological activities of this protein were examined. The glycosylation of gp65 in virus-infected cells was inhibited by tunicamycin but not by monensin, suggesting that it contains an N-glycosidic linkage. Glycosylation is cotranslational and appears to be complete before the glycoprotein reaches the Golgi complex. Pulse-chase experiments showed that this protein decreased in size after 30 min of chase, suggesting that the carbohydrate chains of gp65 undergo trimming during its transport across the Golgi. This interpretation is supported by the endoglycosidase treatment of gp65, which showed that the peptide backbone of gp65 did not decrease in size after pulse-chase periods. This maturation pathway is distinct from that of the E1 or E2 glycoproteins. Partial endoglycosidase treatment indicated that gp65 contains 9 to 10 carbohydrate side chains; thus, almost all of the potential glycosylation sites of gp65 were glycosylated. In vitro translation studies coupled with protease digestion suggest that gp65 is an integral membrane protein. The presence of gp65 in the virion is correlated with the presence of an acetylesterase activity. No hemagglutinin activity was detected

All Maximal Independent Sets and Dynamic Dominance for Sparse Graphs

We describe algorithms, based on Avis and Fukuda's reverse search paradigm, for listing all maximal independent sets in a sparse graph in polynomial time and delay per output. For bounded degree graphs, our algorithms take constant time per set generated; for minor-closed graph families, the time is O(n) per set, and for more general sparse graph families we achieve subquadratic time per set. We also describe new data structures for maintaining a dynamic vertex set S in a sparse or minor-closed graph family, and querying the number of vertices not dominated by S; for minor-closed graph families the time per update is constant, while it is sublinear for any sparse graph family. We can also maintain a dynamic vertex set in an arbitrary m-edge graph and test the independence of the maintained set in time O(sqrt m) per update. We use the domination data structures as part of our enumeration algorithms.Comment: 10 page

Post-Oligarchic Evolution of Protoplanetary Embryos and the Stability of Planetary Systems

We investigate the orbit-crossing time (T_c) of protoplanet systems both with and without a gas-disk background. The protoplanets are initially with equal masses and separation (EMS systems) scaled by their mutual Hill's radii. In a gas-free environment, we find log (T_c/yr) = A+B \log (k_0/2.3). Through a simple analytical approach, we demonstrate that the evolution of the velocity dispersion in an EMS system follows a random walk. The stochastic nature of random-walk diffusion leads to (i) an increasing average eccentricity ~ t^1/2, where t is the time; (ii) Rayleigh-distributed eccentricities (P(e,t)=e/\sigma^2 \exp(-e^2/(2\sigma^2)) of the protoplanets; (iii) a power-law dependence of T_c on planetary separation. As evidence for the chaotic diffusion, the observed eccentricities of known extra solar planets can be approximated by a Rayleigh distribution. We evaluate the isolation masses of the embryos, which determine the probability of gas giant formation, as a function of the dust and gas surface densities.Comment: 15 pages, 13 figures (2 color ones), accepted for publication in Ap

MYRIAD: A new N-body code for simulations of Star Clusters

We present a new C++ code for collisional N-body simulations of star clusters. The code uses the Hermite fourth-order scheme with block time steps, for advancing the particles in time, while the forces and neighboring particles are computed using the GRAPE-6 board. Special treatment is used for close encounters, binary and multiple sub-systems that either form dynamically or exist in the initial configuration. The structure of the code is modular and allows the appropriate treatment of more physical phenomena, such as stellar and binary evolution, stellar collisions and evolution of close black-hole binaries. Moreover, it can be easily modified so that the part of the code that uses GRAPE-6, could be replaced by another module that uses other accelerating-hardware like the Graphics Processing Units (GPUs). Appropriate choice of the free parameters give a good accuracy and speed for simulations of star clusters up to and beyond core collapse. Simulations of Plummer models consisting of equal-mass stars reached core collapse at t~17 half-mass relaxation times, which compares very well with existing results, while the cumulative relative error in the energy remained below 0.001. Also, comparisons with published results of other codes for the time of core collapse for different initial conditions, show excellent agreement. Simulations of King models with an initial mass-function, similar to those found in the literature, reached core collapse at t~0.17, which is slightly smaller than the expected result from previous works. Finally, the code accuracy becomes comparable and even better than the accuracy of existing codes, when a number of close binary systems is dynamically created in a simulation. This is due to the high accuracy of the method that is used for close binary and multiple sub-systems.Comment: 24 pages, 29 figures, accepted for publication to Astronomy & Astrophysic

CW high intensity non-scaling FFAG proton drivers

Accelerators are playing increasingly important roles in basic science, technology, and medicine including nuclear power, industrial irradiation, material science, and neutrino production. Proton and light-ion accelerators in particular have many research, energy and medical applications, providing one of the most effective treatments for many types of cancer. Ultra high-intensity and high-energy (GeV) proton drivers are a critical technology for accelerator-driven sub-critical reactors (ADS) and many HEP programs (Muon Collider). These high-intensity GeV-range proton drivers are particularly challenging, encountering duty cycle and space-charge limits in the synchrotron and machine size concerns in the weaker-focusing cyclotrons; a 10-20 MW proton driver is not presently considered technically achievable with conventional re-circulating accelerators. One, as-yet, unexplored re-circulating accelerator, the Fixed-field Alternating Gradient, or FFAG, is an attractive alternative to the cyclotron. Its strong focusing optics are expected to mitigate space charge effects, and a recent innovation in design has coupled stable tunes with isochronous orbits, making the FFAG capable of fixed-frequency, CW acceleration, as in the classical cyclotron. This paper reports on these new advances in FFAG accelerator technology and references advanced modeling tools for fixed-field accelerators developed for and unique to the code COSY INFINITY.Comment: 3 pp. Particle Accelerator, 24th Conference (PAC'11) 2011. 28 Mar - 1 Apr 2011. New York, US

On Randomized Fictitious Play for Approximating Saddle Points Over Convex Sets

Given two bounded convex sets X\subseteq\RR^m and Y\subseteq\RR^n, specified by membership oracles, and a continuous convex-concave function F:X\times Y\to\RR, we consider the problem of computing an \eps-approximate saddle point, that is, a pair $(x^*,y^*)\in X\times Y$ such that \sup_{y\in Y} F(x^*,y)\le \inf_{x\in X}F(x,y^*)+\eps. Grigoriadis and Khachiyan (1995) gave a simple randomized variant of fictitious play for computing an \eps-approximate saddle point for matrix games, that is, when $F$ is bilinear and the sets $X$ and $Y$ are simplices. In this paper, we extend their method to the general case. In particular, we show that, for functions of constant "width", an \eps-approximate saddle point can be computed using O^*(\frac{(n+m)}{\eps^2}\ln R) random samples from log-concave distributions over the convex sets $X$ and $Y$. It is assumed that $X$ and $Y$ have inscribed balls of radius $1/R$ and circumscribing balls of radius $R$. As a consequence, we obtain a simple randomized polynomial-time algorithm that computes such an approximation faster than known methods for problems with bounded width and when \eps \in (0,1) is a fixed, but arbitrarily small constant. Our main tool for achieving this result is the combination of the randomized fictitious play with the recently developed results on sampling from convex sets