Continuum and Spectral Line Radiation from a Random Clumpy Medium

We present a formalism for continuum and line emission from random clumpy media together with its application to problems of current interest, including CO spectral lines from ensembles of clouds and radio emission from HII regions, supernovae and star-forming regions. For line emission we find that the effects of clump opacity on observed line ratios can be indistinguishable from variations of intrinsic line strengths, adding to the difficulties in determining abundances from line observations. Our formalism is applicable to arbitrary distributions of cloud properties, provided the cloud volume filling factor is small; numerical simulations show it to hold up to filling factors of about 10%. We show that irrespective of the complexity of the cloud ensemble, the radiative effect of clumpiness can be parametrized at each frequency by a single multiplicative correction to the overall optical depth; this multiplier is derived from appropriate averaging over individual cloud properties. Our main finding is that cloud shapes have only a negligible effect on radiation propagation in clumpy media; the results of calculations employing point-like clouds are practically indistinguishable from those for finite-size clouds with arbitrary geometrical shapes.Comment: ApJ, to be publishe

A Circumstellar Disc in a High-Mass Star Forming Region

We present an edge-on Keplerian disc model to explain the main component of the 12.2 and 6.7 GHz methanol maser emission detected toward NGC7538-IRS1 N. The brightness distribution and spectrum of the line of bright masers are successfully modeled with high amplification of background radio continuum emission along velocity coherent paths through a maser disc. The bend seen in the position-velocity diagram is a characteristic signature of differentially rotating discs. For a central mass of 30 solar masses, suggested by other observations, our model fixes the masing disc to have inner and outer radii of about 350 AU and 1000 AU.Comment: 11 pages, accepted for publication in ApJ Letter

The decreasing percentile residual life aging notion

Earlier researchers have studied some aspects of the classes of distribution functions with decreasing ?-percentile residual life (DPRL(?)), 0Reliability theory, Hazard rate, Stochastic orders, Aging notions, Nonparametric estimation, Strongly uniform consistency

Upper critical dimension of the KPZ equation

Numerical results for the Directed Polymer model in 1+4 dimensions in various types of disorder are presented. The results are obtained for system size considerably larger than that considered previously. For the extreme strong disorder case (Min-Max system), associated with the Directed Percolation model, the expected value of the meandering exponent, zeta = 0.5 is clearly revealed, with very week finite size effects. For the week disorder case, associated with the KPZ equation, finite size effects are stronger, but the value of seta is clearly seen in the vicinity of 0.57. In systems with "strong disorder" it is expected that the system will cross over sharply from Min-Max behavior at short chains to weak disorder behavior at long chains. This is indeed what we find. These results indicate that 1+4 is not the Upper Critical Dimension (UCD) in the week disorder case, and thus 4+1 does not seem to be the upper critical dimension for the KPZ equation

Significant g-factor values of a two-electron ground state in quantum dots with spin-orbit coupling

The magnetization of semiconductor quantum dots in the presence of spin-orbit coupling and interactions is investigated numerically. When the dot is occupied by two electrons we find that a level crossing between the two lowest many-body eigenstates may occur as a function of the spin-orbit coupling strength. This level crossing is accompanied by a non-vanishing magnetization of the ground-state. Using first order perturbation theory as well as exact numerical diagonalization of small clusters we show that the tendency of interactions to cause Stoner-like instability is enhanced by the SO coupling. The resulting g-factor can have a significant value, and thus may influence g-factor measurements. Finally we propose an experimental method by which the predicted phenomenon can be observed.Comment: 7+ pages, 7 figure

Dynamical Inequality in Growth Models

A recent exponent inequality is applied to a number of dynamical growth models. Many of the known exponents for models such as the Kardar-Parisi-Zhang (KPZ) equation are shown to be consistent with the inequality. In some cases, such as the Molecular Beam Equation, the situation is more interesting, where the exponents saturate the inequality. As the acid test for the relative strength of four popular approximation schemes we apply the inequality to the exponents obtained for two Non Local KPZ systems. We find that all methods but one, the Self Consistent Expansion, violate the inequality in some regions of parameter space. To further demonstrate the usefulness of the inequality, we apply it to a specific model, which belongs to a family of models in which the inequality becomes an equality. We thus show that the inequality can easily yield results, which otherwise have to rely either on approximations or general beliefs.Comment: 6 pages, 4 figure

RANDOM MATRIX THEORY APPROACH TO THE INTENSITY DISTRIBUTIONS OF WAVES PROPAGATING IN A RANDOM MEDIUM

Statistical properties of coherent radiation propagating in a quasi - 1D random media is studied in the framework of random matrix theory. Distribution functions for the total transmission coefficient and the angular transmission coefficient are obtained.Comment: 8 pages, latex, no figures. Submitted to Phys.Rev.

Perturbation of null spaces with application to the eigenvalue problem and generalized inverses

AbstractWe consider properties of a null space of an analytically perturbed matrix. In particular, we obtain Taylor expansions for the eigenvectors which constitute a basis for the perturbed null space. Furthermore, we apply these results to the calculation of Puiseux expansion of the perturbed eigenvectors in the case of general eigenvalue problem as well as to the calculation of Laurent series expansions for the perturbed group inverse and pseudoinverse matrices

Pulsed Adiabatic Photoassociation via Scattering Resonances

We develop the theory for the Adiabatic Raman Photoassociation (ARPA) of ultracold atoms to form ultracold molecules in the presence of scattering resonances. Based on a computational method in which we replace the continuum with a discrete set of "effective modes", we show that the existence of resonances greatly aids in the formation of deeply bound molecular states. We illustrate our general theory by computationally studying the formation of $^{85}$Rb$_2$ molecules from pairs of colliding ultracold $^{85}$Rb atoms. The single-event transfer yield is shown to have a near-unity value for wide resonances, while the ensemble-averaged transfer yield is shown to be higher for narrow resonances. The ARPA yields are compared with that of (the experimentally measured) "Feshbach molecule" magneto-association. Our findings suggest that an experimental investigation of ARPA at sub-$\mu$K temperatures is warranted.Comment: 20 pages, 11 figure

Holography and Fermions at a Finite Chemical Potential

We review the Sakai-Sugimoto model of holographic QCD at zero temperature and finite chemical potential, comparing the results to those expected at large-$N_c$ QCD, and those in a closely related holographic model. We find that as the baryon chemical potential is increased above a critical value, there is a phase transition to a nuclear matter phase, the details of which depend on the model. We argue that the nuclear matter phase is necessarily inhomogeneous to arbitrarily high density, which suggests an explanation of the "chiral density wave" instability of the quark Fermi surface in large-$N_c$ QCD. Some details of the instanton distribution in the holographic dual are reminiscent of a Fermi surface. This short manuscript summarizes a talk given by M.R. at "Theory Canada 4" conference, and is based largely (but not entirely) on the results of \cite{Rozalietal2008}.Comment: 11 pages, 1 figur