Frequency-dependent (ac) Conduction in Disordered Composites: a Percolative Study

In a recent paper [Phys. Rev. B{\bf57}, 3375 (1998)], we examined in detail the nonlinear (electrical) dc response of a random resistor cum tunneling bond network ($RRTN$, introduced by us elsewhere to explain nonlinear response of metal-insulator type mixtures). In this work which is a sequel to that paper, we consider the ac response of the $RRTN$-based correlated $RC$ ($CRC$) model. Numerical solutions of the Kirchoff's laws for the $CRC$ model give a power-law exponent (= 0.7 near $p = p_c$) of the modulus of the complex ac conductance at moderately low frequencies, in conformity with experiments on various types of disordered systems. But, at very low frequencies, it gives a simple quadratic or linear dependence on the frequency depending upon whether the system is percolating or not. We do also discuss the effective medium approximation ($EMA$) of our $CRC$ and the traditional random $RC$ network model, and discuss their comparative successes and shortcomings.Comment: Revised and reduced version with 17 LaTeX pages plus 8 JPEG figure

Dephasing via stochastic absorption: A case study in Aharonov-Bohm oscillations

The Aharonov-Bohm ring has been the mainstay of mesoscopic physics research since its inception. In this paper we have dwelt on the problem of dephasing of AB oscillations using a phenomenological model based on stochastic absorption. To calculate the conductance in the presence of inelastic scattering we have used the method due to Brouwer and Beenakker. We have shown that conductance is symmetric under flux reversal and visibility of AB oscillations decay to zero as a function of the incoherence parameter thus signalling dephasing in the system. Some comments are made on the relative merits of stochastic absorption with respect to optical potential model, which have been used to mimic dephasing.Comment: 4 pages, 4 figures Minor corrections made and journal reference adde

Neural network trigger algorithms for heavy quark event selection in a fixed target high energy physics experiment

Abstract The study of particles containing heavy quarks is currently a major topic in high energy physics. In this paper, neural net trigger algorithms are developed to distinghish heavy quark (signal) events from light quark (background) events in a fixed target experiment. The event tracks which are parametrized by the impact parameter D and the angle Φ of the track with respect to the beam line, vary in number and in position in the Φ - D plane. An invariant second-order moment feature set and an invariant D -sequence representation are derived to characterize the signal and background event track patterns in the Φ - D plane. A three-layer perceptron is trained to classify events as signal/background via the moments and D -sequences. A nearest neighbor classifier is also developed to serve as a benchmark for comparing the performance of the neural net triggers. Results indicate that the selected moment feature set and the D -sequence representation contain essential signal/background discriminatory information. The results also show that the neural network trigger algorithms are superior to the nearest neighbor trigger algorithms. A very high discrimination against background events and a very high efficiency for selecting signal events is obtained with the D -sequence neural net trigger algorithm

Goodness-of-Fit Tests to study the Gaussianity of the MAXIMA data

Goodness-of-Fit tests, including Smooth ones, are introduced and applied to detect non-Gaussianity in Cosmic Microwave Background simulations. We study the power of three different tests: the Shapiro-Francia test (1972), the uncategorised smooth test developed by Rayner and Best(1990) and the Neyman's Smooth Goodness-of-fit test for composite hypotheses (Thomas and Pierce 1979). The Smooth Goodness-of-Fit tests are designed to be sensitive to the presence of ``smooth'' deviations from a given distribution. We study the power of these tests based on the discrimination between Gaussian and non-Gaussian simulations. Non-Gaussian cases are simulated using the Edgeworth expansion and assuming pixel-to-pixel independence. Results show these tests behave similarly and are more powerful than tests directly based on cumulants of order 3, 4, 5 and 6. We have applied these tests to the released MAXIMA data. The applied tests are built to be powerful against detecting deviations from univariate Gaussianity. The Cholesky matrix corresponding to signal (based on an assumed cosmological model) plus noise is used to decorrelate the observations previous to the analysis. Results indicate that the MAXIMA data are compatible with Gaussianity.Comment: MNRAS, in pres

Survival of Φ0/2\Phi_{0}/2 periodicity in presence of incoherence in asymmetric Aharonov-Bohm rings

Magneto conductance oscillations periodic in flux with periodicity $\Phi_{0}$ and $\Phi_{0}/2$ are seen in asymmetric Aharonov-Bohm rings as a function of density of electrons or Fermi wave vector. Dephasing of these oscillations is incorporated using a simple approach of wave attenuation. In this work we study how the excitation of the $\Phi_{0}/2$ oscillations and the accompanying phase change of $\pi$ are affected by dephasing. Our results show that the $\Phi_{0}/2$ oscillations survive incoherence, i.e., dephasing, albeit with reduced visibility while incoherence is also unable to obliterate the phase change of $\pi$.Comment: 4 pages, 3 figure

Monopole Percolation in pure gauge compact QED

The role of monopoles in quenched compact QED has been studied by measuring the cluster susceptibility and the order parameter $n_{max}/n_{tot}$ previously introduced by Hands and Wensley in the study of the percolation transition observed in non-compact QED. A correlation between these parameters and the energy (action) at the phase transition has been observed. We conclude that the order parameter $n_{max}/n_{tot}$ is a sensitive probe for studying the phase transition of pure gauge compact QED.Comment: LaTeX file + 4 PS figures, 12 pag., Pre-UAB-FT-308 ILL-(TH)-94-1

Stochastic Vehicle Routing with Recourse

We study the classic Vehicle Routing Problem in the setting of stochastic optimization with recourse. StochVRP is a two-stage optimization problem, where demand is satisfied using two routes: fixed and recourse. The fixed route is computed using only a demand distribution. Then after observing the demand instantiations, a recourse route is computed -- but costs here become more expensive by a factor lambda. We present an O(log^2 n log(n lambda))-approximation algorithm for this stochastic routing problem, under arbitrary distributions. The main idea in this result is relating StochVRP to a special case of submodular orienteering, called knapsack rank-function orienteering. We also give a better approximation ratio for knapsack rank-function orienteering than what follows from prior work. Finally, we provide a Unique Games Conjecture based omega(1) hardness of approximation for StochVRP, even on star-like metrics on which our algorithm achieves a logarithmic approximation.Comment: 20 Pages, 1 figure Revision corrects the statement and proof of Theorem 1.

Pairwise Relative Distance (PRED) is an intuitive and robust metric for assessing vector similarity and class separability

Scientific studies often require assessment of similarity between ordered sets of values. Each set, containing one value for every dimension or class of data, can be conveniently represented as a vector. The commonly used metrics for vector similarity include angle-based metrics, such as cosine similarity or Pearson correlation, which compare the relative patterns of values, and distance-based metrics, such as the Euclidean distance, which compare the magnitudes of values. Here we evaluate a newly proposed metric, pairwise relative distance (PRED), which considers both relative patterns and magnitudes to provide a single measure of vector similarity. PRED essentially reveals whether the vectors are so similar that their values across the classes are separable. By comparing PRED to other common metrics in a variety of applications, we show that PRED provides a stable chance level irrespective of the number of classes, is invariant to global translation and scaling operations on data, has high dynamic range and low variability in handling noisy data, and can handle multi-dimensional data, as in the case of vectors containing temporal or population responses for each class. We also found that PRED can be adapted to function as a reliable metric of class separability even for datasets that lack the vector structure and simply contain multiple values for each class

The Matter and the Pseudoscalar Densities in Lattice QCD

The matter and the pseudoscalar densities inside a hadron are calculated via gauge-invariant equal-time correlation functions. A comparison is made between the charge charge and the matter density distributions for the pion, the rho, the nucleon and the $\Delta^+$ within the quenched theory, and with two flavours of dynamical quarks.Comment: Typos corrected; 13 pages, 16 figure

Vortex dynamics and upper critical fields in ultrathin Bi films

Current-voltage (I-V) characteristics of quench condensed, superconducting, ultrathin $Bi$ films in a magnetic field are reported. These I-V's show hysteresis for all films, grown both with and without thin $Ge$ underlayers. Films on Ge underlayers, close to superconductor-insulator transition (SIT), show a peak in the critical current, indicating a structural transformation of the vortex solid (VS). These underlayers, used to make the films more homogeneous, are found to be more effective in pinning the vortices. The upper critical fields (B$_{c2}$) of these films are determined from the resistive transitions in perpendicular magnetic field. The temperature dependence of the upper critical field is found to differ significantly from Ginzburg-Landau theory, after modifications for disorder.Comment: Phys Rev B, to be published Figure 6 replaced with correct figur