Kinetics of electron-positron pair plasmas using an adaptive Monte Carlo method

A new algorithm for implementing the adaptive Monte Carlo method is given. It is used to solve the relativistic Boltzmann equations that describe the time evolution of a nonequilibrium electron-positron pair plasma containing high-energy photons and pairs. The collision kernels for the photons as well as pairs are constructed for Compton scattering, pair annihilation and creation, bremsstrahlung, and Bhabha & Moller scattering. For a homogeneous and isotropic plasma, analytical equilibrium solutions are obtained in terms of the initial conditions. For two non-equilibrium models, the time evolution of the photon and pair spectra is determined using the new method. The asymptotic numerical solutions are found to be in a good agreement with the analytical equilibrium states. Astrophysical applications of this scheme are discussed.Comment: 43 pages, 7 postscript figures, to appear in the Astrophysical Journa

Description of superdeformed bands in light N=Z nuclei using the cranked HFB method

Superdeformed states in light $N=Z$ nuclei are studied by means of the self-consistent cranking calculation (i.e., the P + QQ model based on the cranked Hartree-Fock-Bogoliubov method). Analyses are given for two typical cases of superdeformed bands in the $A \simeq 40$ mass region, that is, bands where backbending is absent ($^{40}$Ca) and present ($^{36}$Ar). Investigations are carried out, particularly for the following points: cross-shell excitations in the sd and pf shells; the role of the g$_{9/2}$ and d$_{5/2}$ orbitals; the effect of the nuclear pairing; and the interplay between triaxiality and band termination.Comment: 17 pages, 18 figures, accepted in Phys. Rev.

Hardness of Graph Pricing through Generalized Max-Dicut

The Graph Pricing problem is among the fundamental problems whose approximability is not well-understood. While there is a simple combinatorial 1/4-approximation algorithm, the best hardness result remains at 1/2 assuming the Unique Games Conjecture (UGC). We show that it is NP-hard to approximate within a factor better than 1/4 under the UGC, so that the simple combinatorial algorithm might be the best possible. We also prove that for any $\epsilon > 0$, there exists $\delta > 0$ such that the integrality gap of $n^{\delta}$-rounds of the Sherali-Adams hierarchy of linear programming for Graph Pricing is at most 1/2 + $\epsilon$. This work is based on the effort to view the Graph Pricing problem as a Constraint Satisfaction Problem (CSP) simpler than the standard and complicated formulation. We propose the problem called Generalized Max-Dicut($T$), which has a domain size $T + 1$ for every $T \geq 1$. Generalized Max-Dicut(1) is well-known Max-Dicut. There is an approximation-preserving reduction from Generalized Max-Dicut on directed acyclic graphs (DAGs) to Graph Pricing, and both our results are achieved through this reduction. Besides its connection to Graph Pricing, the hardness of Generalized Max-Dicut is interesting in its own right since in most arity two CSPs studied in the literature, SDP-based algorithms perform better than LP-based or combinatorial algorithms --- for this arity two CSP, a simple combinatorial algorithm does the best.Comment: 28 page

Time dependent numerical model for the emission of radiation from relativistic plasma

We describe a numerical model constructed for the study of the emission of radiation from relativistic plasma under conditions characteristic, e.g., to gamma-ray bursts (GRB's) and active galactic nuclei (AGN's). The model solves self consistently the kinetic equations for e^\pm and photons, describing cyclo-synchrotron emission, direct Compton and inverse Compton scattering, pair production and annihilation, including the evolution of high energy electromagnetic cascades. The code allows calculations over a wide range of particle energies, spanning more than 15 orders of magnitude in energy and time scales. Our unique algorithm, which enables to follow the particle distributions over a wide energy range, allows to accurately derive spectra at high energies, >100 \TeV. We present the kinetic equations that are being solved, detailed description of the equations describing the various physical processes, the solution method, and several examples of numerical results. Excellent agreement with analytical results of the synchrotron-SSC model is found for parameter space regions in which this approximation is valid, and several examples are presented of calculations for parameter space regions where analytic results are not available.Comment: Minor changes; References added, discussion on observational status added. Accepted for publication in Ap.

X-ray Variability Characteristics of the Seyfert 1 Galaxy NGC 3783

We have characterized the energy-dependent X-ray variability properties of the Seyfert~1 galaxy NGC 3783 using archival XMM-Newton and Rossi X-ray Timing Explorer data. The high-frequency fluctuation power spectral density function (PSD) slope is consistent with flattening towards higher energies. Light curve cross correlation functions yield no significant lags, but peak coefficients generally decrease as energy separation of the bands increases on both short and long timescales. We have measured the coherence between various X-ray bands over the temporal frequency range of 6e-8 to 1e-4 Hz; this range includes the temporal frequency of the low-frequency power spectral density function (PSD) break tentatively detected by Markowitz et al. and includes the lowest temporal frequency over which coherence has been measured in any AGN to date. Coherence is generally near unity at these temporal frequencies, though it decreases slightly as energy separation of the bands increases. Temporal frequency-dependent phase lags are detected on short time scales; phase lags are consistent with increasing as energy separation increases or as temporal frequency decreases. All of these results are similar to those obtained previously for several Seyfert galaxies and stellar-mass black hole systems. Qualitatively, these results are consistent with the variability models of Kotov et al. and Lyubarskii, wherein the X-ray variability is due to inwardly propagating variations in the local mass accretion rate.Comment: Accepted for publication in The Astrophysical Journal, 2005, vol. 635, p. 180; version 2 has minor grammatical changes; 23 pages; uses emulateapj

Money in monetary policy design: monetary cross-checking in the New-Keynesian model

In the New-Keynesian model, optimal interest rate policy under uncertainty is formulated without reference to monetary aggregates as long as certain standard assumptions on the distributions of unobservables are satisfied. The model has been criticized for failing to explain common trends in money growth and inflation, and that therefore money should be used as a cross-check in policy formulation (see Lucas (2007)). We show that the New-Keynesian model can explain such trends if one allows for the possibility of persistent central bank misperceptions. Such misperceptions motivate the search for policies that include additional robustness checks. In earlier work, we proposed an interest rate rule that is near-optimal in normal times but includes a cross-check with monetary information. In case of unusual monetary trends, interest rates are adjusted. In this paper, we show in detail how to derive the appropriate magnitude of the interest rate adjustment following a significant cross-check with monetary information, when the New-Keynesian model is the central bank’s preferred model. The cross-check is shown to be effective in offsetting persistent deviations of inflation due to central bank misperceptions. Keywords: Monetary Policy, New-Keynesian Model, Money, Quantity Theory, European Central Bank, Policy Under Uncertaint

Plasma Ejection from Magnetic Flares and the X-ray Spectrum of Cygnus X-1

The hard X-rays in Cyg X-1 and similar black hole sources are possibly produced in an active corona atop an accretion disk. We suggest that the observed weakness of X-ray reflection from the disk is due to bulk motion of the emitting hot plasma away from the reflector. A mildly relativistic motion causes aberration reducing X-ray emission towards the disk. This in turn reduces the reprocessed radiation from the disk and leads to a hard spectrum of the X-ray source. The resulting spectral index is Gamma=1.9B^{1/2} where B=gamma(1+beta) is the aberration factor for a bulk velocity beta=v/c. The observed Gamma=1.6 and the amount of reflection, R=0.3, in Cyg X-1 in the hard state can both be explained assuming a bulk velocity beta=0.3. We discuss one possible scenario: the compact magnetic flares are dominated by e+- pairs which are ejected away from the reflector by the pressure of the reflected radiation. We also discuss physical constraints on the disk-corona model and argue that the magnetic flares are related to magneto-rotational instabilities in the accretion disk.Comment: The final version, accepted for publication in ApJ Letter

Influence of corruption on economic growth rate and foreign investments

In order to investigate whether government regulations against corruption can affect the economic growth of a country, we analyze the dependence between Gross Domestic Product (GDP) per capita growth rates and changes in the Corruption Perceptions Index (CPI). For the period 1999-2004 on average for all countries in the world, we find that an increase of CPI by one unit leads to an increase of the annual GDP per capita by 1.7 %. By regressing only European transition countries, we find that $\Delta$CPI = 1 generates increase of the annual GDP per capita by 2.4 %. We also analyze the relation between foreign direct investments received by different countries and CPI, and we find a statistically significant power-law functional dependence between foreign direct investment per capita and the country corruption level measured by the CPI. We introduce a new measure to quantify the relative corruption between countries based on their respective wealth as measured by GDP per capita.Comment: 8 pages, 3 figures, elsart styl

Labeling Uncertainty in Multitarget Tracking

In multitarget tracking, the problem of track labeling (assigning labels to tracks) is an ongoing research topic. The existing literature, however, lacks an appropriate measure of uncertainty related to the assigned labels that has a sound mathematical basis as well as clear practical meaning to the user. This is especially important in a situation where well separated targets move in close proximity with each other and thereafter separate again; in such a situation, it is well known that there will be confusion on target identities, also known as "mixed labeling." In this paper, we specify comprehensively the necessary assumptions for a Bayesian formulation of the multitarget tracking and labeling (MTTL) problem to be meaningful. We provide a mathematical characterization of the labeling uncertainties with clear physical interpretation. We also propose a novel labeling procedure that can be used in combination with any existing (unlabeled) MTT algorithm to obtain a Bayesian solution to the MTTL problem. One advantage of the resulting solution is that it readily provides the labeling uncertainty measures. Using the mixed labeling phenomenon in the presence of two targets as our test bed, we show with simulation results that an unlabeled multitarget sequential Monte Carlo (M-SMC) algorithm that employs sequential importance resampling (SIR) augmented with our labeling procedure performs much better than its "naive" extension, the labeled SIR M-SMC filter