Perturbative Analysis of Spectral Singularities and Their Optical Realizations

We develop a perturbative method of computing spectral singularities of a Schreodinger operator defined by a general complex potential that vanishes outside a closed interval. These can be realized as zero-width resonances in optical gain media and correspond to a lasing effect that occurs at the threshold gain. Their time-reversed copies yield coherent perfect absorption of light that is also known as an antilaser. We use our general results to establish the exactness of the n-th order perturbation theory for an arbitrary complex potential consisting of n delta-functions, obtain an exact expression for the transfer matrix of these potentials, and examine spectral singularities of complex barrier potentials of arbitrary shape. In the context of optical spectral singularities, these correspond to inhomogeneous gain media.Comment: 13 pages, 2 figures, one table, a reference added, typos correcte

DETERMINING BILATERAL TRADE PATTERNS USING A DYNAMIC GRAVITY EQUATION

Using a dynamic gravity equation, we show that the national product differentiation model explains food and agricultural trade more properly, while the product differentiation model is more appropriate to explain large-scale manufacturing trade. In this context, our result is not consistent with the one found by Head and Ries (2001) in the short-run. The intuitive explanation for this result is that inward foreign direct investment can occur through either merger or acquisition in the short-run. Second, the pattern of bilateral trade could quickly adjust to changes in relative income between countries. Furthermore, we illustrate the positive impacts of world income growth on bilateral trade, which is in sharp contrast with the conventional analysis. This reveals yet another way to test the pattern of bilateral trade.dynamic gravity equation, national product differentiation, product differentiation, world income growth, International Relations/Trade,

Lower order terms for the moments of symplectic and orthogonal families of LL-functions

We derive formulas for the terms in the conjectured asymptotic expansions of the moments, at the central point, of quadratic Dirichlet $L$-functions, $L(1/2,\chi_d)$, and also of the $L$-functions associated to quadratic twists of an elliptic curve over \Q. In so doing, we are led to study determinants of binomial coefficients of the form $\det (\binom{2k-i-\lambda_{k-i+1}}{2k-2j})$.Comment: 34 pages, 4 table

Comparison of acoustic travel-time measurement of solar meridional circulation from SDO/HMI and SOHO/MDI

Time-distance helioseismology is one of the primary tools for studying the solar meridional circulation. However, travel-time measurements of the subsurface meridional flow suffer from a variety of systematic errors, such as a center-to-limb variation and an offset due to the P-angle uncertainty of solar images. Here we apply the time-distance technique to contemporaneous medium-degree Dopplergrams produced by SOHO/MDI and SDO/HMI to obtain the travel-time difference caused by meridional circulation throughout the solar convection zone. The P-angle offset in MDI images is measured by cross-correlating MDI and HMI images. The travel-time measurements in the south-north and east-west directions are averaged over the same observation period for the two data sets and then compared to examine the consistency of MDI and HMI travel times after correcting the systematic errors. The offsets in the south-north travel-time difference from MDI data induced by the P-angle error gradually diminish with increasing travel distance. However, these offsets become noisy for travel distances corresponding to waves that reach the base of the convection zone. This suggests that a careful treatment of the P-angle problem is required when studying a deep meridional flow. After correcting the P-angle and the removal of the center-to-limb effect, the travel-time measurements from MDI and HMI are consistent within the error bars for meridional circulation covering the entire convection zone. The fluctuations observed in both data sets are highly correlated and thus indicate their solar origin rather than an instrumental origin. Although our results demonstrate that the ad hoc correction is capable of reducing the wide discrepancy in the travel-time measurements from MDI and HMI, we cannot exclude the possibility that there exist other systematic effects acting on the two data sets in the same way.Comment: accepted for publication in A&

Modelling distributed lag effects in mortality and air pollution studies: the case of Santiago

Most of the epidemiological literature on air pollution and mortality deals only with single or dual pollutant models whose results are hard to interpret and of questionable value from the policy perspective. In addition, much of the existing literature deals only with the very short-term effects of air pollution whereas policy makers need to know when, whether and to what extent pollution-induced increases in mortality counts are reversed. This involves modelling the infinite distributed lag effects of air pollution. Borrowing from econometrics this paper presents a method by which the infinite distributed lag effects can be estimated parsimoniously but plausibly estimated. The paper presents a time series study into the relationship between ambient levels of air pollution and daily mortality counts for Santiago employing this technique which confirms that the infinite lag effects are highly significant. It is also shown that day to day variations in NO2 concentrations and in the concentrations of both fine and coarse particulates are associated with short-term variations in death rates. These findings are made in the context of a model that simultaneously includes six different pollutants. Evidence is found pointing to the operation of a very short term harvesting effect

Three Lectures: Nemd, Spam, and Shockwaves

We discuss three related subjects well suited to graduate research. The first, Nonequilibrium molecular dynamics or "NEMD", makes possible the simulation of atomistic systems driven by external fields, subject to dynamic constraints, and thermostated so as to yield stationary nonequilibrium states. The second subject, Smooth Particle Applied Mechanics or "SPAM", provides a particle method, resembling molecular dynamics, but designed to solve continuum problems. The numerical work is simplified because the SPAM particles obey ordinary, rather than partial, differential equations. The interpolation method used with SPAM is a powerful interpretive tool converting point particle variables to twice-differentiable field variables. This interpolation method is vital to the study and understanding of the third research topic we discuss, strong shockwaves in dense fluids. Such shockwaves exhibit stationary far-from-equilibrium states obtained with purely reversible Hamiltonian mechanics. The SPAM interpolation method, applied to this molecular dynamics problem, clearly demonstrates both the tensor character of kinetic temperature and the time-delayed response of stress and heat flux to the strain rate and temperature gradients. The dynamic Lyapunov instability of the shockwave problem can be analyzed in a variety of ways, both with and without symmetry in time. These three subjects suggest many topics suitable for graduate research in nonlinear nonequilibrium problems.Comment: 40 pages, with 21 figures, as presented at the Granada Seminar on the Foundations of Nonequilibrium Statistical Physics, 13-17 September, as three lecture