Localization versus subradiance in three-dimensional scattering of light

We study the scattering modes of light in a three-dimensional disordered medium, in the scalar approximation and above the critical density for Anderson localization. Localized modes represent a minority of the total number of modes, even well above the threshold density, whereas spatially extended subradiant modes predominate. For specific energy ranges however, almost all modes are localized, yet adjusting accordingly the probe frequency does not allow to address these only in the regime accessible numerically. Finally, their lifetime is observed to be dominated by finite-size effects, and more specifically by the ratio of the localization length to their distance to the system boundaries.Comment: Add figure comparing localization percentage via frequency, fixed text, addition of Ioffe-Regel criterion limits, figure axis were normalize

Counterions at charge-modulated substrates

We consider counterions in the presence of a single planar surface with a spatially inhomogeneous charge distribution using Monte-Carlo simulations and strong-coupling theory. For high surface charges, multivalent counterions, or pronounced substrate charge modulation the counterions are laterally correlated with the surface charges and their density profile deviates strongly from the limit of a smeared-out substrate charge distribution, in particular exhibiting a much increased laterally averaged density at the surface.Comment: 7 page

Singular diffusion and criticality in a confined sandpile

We investigate the behavior of a two-state sandpile model subjected to a confining potential in one and two dimensions. From the microdynamical description of this simple model with its intrinsic exclusion mechanism, it is possible to derive a continuum nonlinear diffusion equation that displays singularities in both the diffusion and drift terms. The stationary-state solutions of this equation, which maximizes the Fermi-Dirac entropy, are in perfect agreement with the spatial profiles of time-averaged occupancy obtained from model numerical simulations in one as well as in two dimensions. Surprisingly, our results also show that, regardless of dimensionality, the presence of a confining potential can lead to the emergence of typical attributes of critical behavior in the two-state sandpile model, namely, a power-law tail in the distribution of avalanche sizes.Comment: 5 pages, 5 figure

Greedy randomized dispatching heuristics for the single machine scheduling problem with quadratic earliness and tardiness penalties

In this paper, we present greedy randomized dispatching heuristics for the single machine scheduling problem with quadratic earliness and tardiness costs, and no machine idle time. The several heuristic versions differ, on the one hand, on the strategies involved in the construction of the greedy randomized schedules. On the other hand, these versions also differ on whether they employ only a final improvement step, or perform a local search after each greedy randomized construction. The proposed heuristics were compared with existing procedures, as well as with optimum solutions for some instance sizes. The computational results show that the proposed procedures clearly outperform their underlying dispatching heuristic, and the best of these procedures provide results that are quite close to the optimum. The best of the proposed algorithms is the new recommended heuristic for large instances, as well as a suitable alternative to the best existing procedure for the larger of the middle size instances.scheduling, single machine, early/tardy, quadratic penalties, greedy randomized dispatching rules

Irreversibility line and low-field grain-boundary pinning in electron-doped superconducting thin films

AC magnetic susceptibilities of electron-doped Pr_{1.85}Ce_{0.15}CuO_4 (PCCO) and Sm_{1.85}Ce_{0.15}CuO_4 (SCCO) granular thin films have been measured as a function of temperature and magnetic-field strength. Depending on the level of homogeneity of our films, two different types of the irreversibility line (IL) defined as the intergrain-loss peak temperature in the imaginary part of susceptibility have been found. The obtained results are described via the critical-state model taking into account the low-field grain-boundary pinning. The extracted pinning-force densities in more granular SCCO films turn out to be four times larger than their counterparts in less granular PCCO films

Bootstrap and Higher-Order Expansion Validity When Instruments May Be Weak

It is well-known that size-adjustments based on Edgeworth expansions for the t-statistic perform poorly when instruments are weakly correlated with the endogenous explanatory variable. This paper shows, however, that the lack of Edgeworth expansions and bootstrap validity are not tied to the weak instrument framework, but instead depends on which test statistic is examined. In particular, Edgeworth expansions are valid for the score and conditional likelihood ratio approaches, even when the instruments are uncorrelated with the endogenous explanatory variable. Furthermore, there is a belief that the bootstrap method fails when instruments are weak, since it replaces parameters with inconsistent estimators. Contrary to this notion, we provide a theoretical proof that guarantees the validity of the bootstrap for the score test, as well as the validity of the conditional bootstrap for many conditional tests. Monte Carlo simulations show that the bootstrap actually decreases size distortions in both cases.

Bootstrap and Higher-Order Expansion Validity When Instruments May Be Weak

It is well-known that size-adjustments based on Edgeworth expansions for the t-statistic perform poorly when instruments are weakly correlated with the endogenous explanatory variable. This paper shows, however, that the lack of Edgeworth expansions and bootstrap validity are not tied to the weak instrument framework, but instead depends on which test statistic is examined. In particular, Edgeworth expansions are valid for the score and conditional likelihood ratio approaches, even when the instruments are uncorrelated with the endogenous explanatory variable. Furthermore, there is a belief that the bootstrap method fails when instruments are weak, since it replaces parameters with inconsistent estimators. Contrary to this notion, we provide a theoretical proof that guarantees the validity of the bootstrap for the score test, as well as the validity of the conditional bootstrap for many conditional tests. Monte Carlo simulations show that the bootstrap actually decreases size distortions in both cases.