Starburst models of merging galaxies

In the past decade, infrared observations have shown that interacting and merging galaxies have higher luminosities than isolated systems, with the luminosities in mergers as high as 10(exp 12) solar luminosity. However, the origin of the luminosity found in mergers is controversial, with two main competing theories. The first is the starburst scenario. As two gas rich galaxies start to merge, cloud-cloud collisions induce fast shocks in the molecular gas. This gas cools, collapses, and fragments, producing a blast of star formation. The main rival to this theory is that the infrared luminosity is produced by a dust embedded active nucleus, the merger of two gas rich galaxies providing the 'fuel to feed the monster'. There has even been speculation that there is an evolutionary link between starbursts and active nuclei, and that possibly active galactic nuclei (AGN's) and QSO's were formed from a starburst. Assuming that the infrared luminosity in merging galaxies is due to star formation, there should be ionizing photons produced from the high mass stars, giving rise to recombination line emission. The objective is to use a simple starburst model to test the hypothesis that the extreme infrared luminosity of merging galaxies is due to a starburst

A method of moments estimator of tail dependence

In the world of multivariate extremes, estimation of the dependence structure still presents a challenge and an interesting problem. A procedure for the bivariate case is presented that opens the road to a similar way of handling the problem in a truly multivariate setting. We consider a semi-parametric model in which the stable tail dependence function is parametrically modeled. Given a random sample from a bivariate distribution function, the problem is to estimate the unknown parameter. A method of moments estimator is proposed where a certain integral of a nonparametric, rank-based estimator of the stable tail dependence function is matched with the corresponding parametric version. Under very weak conditions, the estimator is shown to be consistent and asymptotically normal. Moreover, a comparison between the parametric and nonparametric estimators leads to a goodness-of-fit test for the semiparametric model. The performance of the estimator is illustrated for a discrete spectral measure that arises in a factor-type model and for which likelihood-based methods break down. A second example is that of a family of stable tail dependence functions of certain meta-elliptical distributions.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ130 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients

Elliptic partial differential equations (PDEs) with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electro-magnetic field propagation on heterogeneous media, and diffusion processes on rough surfaces. The standard approach to numerically treating such problems using finite element methods is to assume that the discontinuities lie on the boundaries of the cells in the initial triangulation. However, this does not match applications where discontinuities occur on curves, surfaces, or manifolds, and could even be unknown beforehand. One of the obstacles to treating such discontinuity problems is that the usual perturbation theory for elliptic PDEs assumes bounds for the distortion of the coefficients in the $L_\infty$ norm and this in turn requires that the discontinuities are matched exactly when the coefficients are approximated. We present a new approach based on distortion of the coefficients in an $L_q$ norm with $q<\infty$ which therefore does not require the exact matching of the discontinuities. We then use this new distortion theory to formulate new adaptive finite element methods (AFEMs) for such discontinuity problems. We show that such AFEMs are optimal in the sense of distortion versus number of computations, and report insightful numerical results supporting our analysis.Comment: 24 page

Discontinuous Galerkin Methods for Mass Transfer through Semi-Permeable Membranes

A discontinuous Galerkin (dG) method for the numerical solution of initial/boundary value multi-compartment partial differential equation (PDE) models, interconnected with interface conditions, is presented and analysed. The study of interface problems is motivated by models of mass transfer of solutes through semi-permeable membranes. More specifically, a model problem consisting of a system of semilinear parabolic advection-diffusion-reaction partial differential equations in each compartment, equipped with respective initial and boundary conditions, is considered. Nonlinear interface conditions modelling selective permeability, congestion and partial reflection are applied to the compartment interfaces. An interior penalty dG method is presented for this problem and it is analysed in the space-discrete setting. The a priori analysis shows that the method yields optimal a priori bounds, provided the exact solution is sufficiently smooth. Numerical experiments indicate agreement with the theoretical bounds and highlight the stability of the numerical method in the advection-dominated regime

Distortion Exponent in MIMO Channels with Feedback

The transmission of a Gaussian source over a block-fading multiple antenna channel in the presence of a feedback link is considered. The feedback link is assumed to be an error and delay free link of capacity 1 bit per channel use. Under the short-term power constraint, the optimal exponential behavior of the end-to-end average distortion is characterized for all source-channel bandwidth ratios. It is shown that the optimal transmission strategy is successive refinement source coding followed by progressive transmission over the channel, in which the channel block is allocated dynamically among the layers based on the channel state using the feedback link as an instantaneous automatic repeat request (ARQ) signal.Comment: Presented at the IEEE Information Theory Workshop (ITW), Taormina, Italy, Oct. 200

Mesoscopic model for soft flowing systems with tunable viscosity ratio

We propose a mesoscopic model of binary fluid mixtures with tunable viscosity ratio based on the two-range pseudo-potential lattice Boltzmann method, for the simulation of soft flowing systems. In addition to the short range repulsive interaction between species in the classical single-range model, a competing mechanism between the short range attractive and mid-range repulsive interactions is imposed within each species. Besides extending the range of attainable surface tension as compared with the single-range model, the proposed scheme is also shown to achieve a positive disjoining pressure, independently of the viscosity ratio. The latter property is crucial for many microfluidic applications involving a collection of disperse droplets with a different viscosity from the continuum phase. As a preliminary application, the relative effective viscosity of a pressure-driven emulsion in a planar channel is computed.Comment: 14page

Diversity-Multiplexing Tradeoffs in MIMO Relay Channels

A multi-hop relay channel with multiple antenna terminals in a quasi-static slow fading environment is considered. For both full-duplex and half-duplex relays the fundamental diversity-multiplexing tradeoff (DMT) is analyzed. It is shown that, while decode-and-forward (DF) relaying achieves the optimal DMT in the full-duplex relay scenario, the dynamic decode-and-forward (DDF) protocol is needed to achieve the optimal DMT if the relay is constrained to half-duplex operation. For the latter case, static protocols are considered as well, and the corresponding achievable DMT performance is characterized.Comment: To appear at IEEE Global Communications Conf. (Globecom), New Orleans, LA, Nov. 200

Minimum Sparsity of Unobservable Power Network Attacks

Physical security of power networks under power injection attacks that alter generation and loads is studied. The system operator employs Phasor Measurement Units (PMUs) for detecting such attacks, while attackers devise attacks that are unobservable by such PMU networks. It is shown that, given the PMU locations, the solution to finding the sparsest unobservable attacks has a simple form with probability one, namely, $\kappa(G^M) + 1$, where $\kappa(G^M)$ is defined as the vulnerable vertex connectivity of an augmented graph. The constructive proof allows one to find the entire set of the sparsest unobservable attacks in polynomial time. Furthermore, a notion of the potential impact of unobservable attacks is introduced. With optimized PMU deployment, the sparsest unobservable attacks and their potential impact as functions of the number of PMUs are evaluated numerically for the IEEE 30, 57, 118 and 300-bus systems and the Polish 2383, 2737 and 3012-bus systems. It is observed that, as more PMUs are added, the maximum potential impact among all the sparsest unobservable attacks drops quickly until it reaches the minimum sparsity.Comment: submitted to IEEE Transactions on Automatic Contro