A parallel Jacobson-Oksman optimization algorithm

A gradient-dependent optimization technique which exploits the vector-streaming or parallel-computing capabilities of some modern computers is presented. The algorithm, derived by assuming that the function to be minimized is homogeneous, is a modification of the Jacobson-Oksman serial minimization method. In addition to describing the algorithm, conditions insuring the convergence of the iterates of the algorithm and the results of numerical experiments on a group of sample test functions are presented. The results of these experiments indicate that this algorithm will solve optimization problems in less computing time than conventional serial methods on machines having vector-streaming or parallel-computing capabilities

Goal-oriented sensitivity analysis for lattice kinetic Monte Carlo simulations

In this paper we propose a new class of coupling methods for the sensitivity analysis of high dimensional stochastic systems and in particular for lattice Kinetic Monte Carlo. Sensitivity analysis for stochastic systems is typically based on approximating continuous derivatives with respect to model parameters by the mean value of samples from a finite difference scheme. Instead of using independent samples the proposed algorithm reduces the variance of the estimator by developing a strongly correlated-"coupled"- stochastic process for both the perturbed and unperturbed stochastic processes, defined in a common state space. The novelty of our construction is that the new coupled process depends on the targeted observables, e.g. coverage, Hamiltonian, spatial correlations, surface roughness, etc., hence we refer to the proposed method as em goal-oriented sensitivity analysis. In particular, the rates of the coupled Continuous Time Markov Chain are obtained as solutions to a goal-oriented optimization problem, depending on the observable of interest, by considering the minimization functional of the corresponding variance. We show that this functional can be used as a diagnostic tool for the design and evaluation of different classes of couplings. Furthermore the resulting KMC sensitivity algorithm has an easy implementation that is based on the Bortz-Kalos-Lebowitz algorithm's philosophy, where here events are divided in classes depending on level sets of the observable of interest. Finally, we demonstrate in several examples including adsorption, desorption and diffusion Kinetic Monte Carlo that for the same confidence interval and observable, the proposed goal-oriented algorithm can be two orders of magnitude faster than existing coupling algorithms for spatial KMC such as the Common Random Number approach

Metal-insulator transition in three dimensional Anderson model: universal scaling of higher Lyapunov exponents

Numerical studies of the Anderson transition are based on the finite-size scaling analysis of the smallest positive Lyapunov exponent. We prove numerically that the same scaling holds also for higher Lyapunov exponents. This scaling supports the hypothesis of the one-parameter scaling of the conductance distribution. From the collected numerical data for quasi one dimensional systems up to the system size 24 x 24 x infinity we found the critical disorder 16.50 < Wc < 16.53 and the critical exponent 1.50 < \nu < 1.54. Finite-size effects and the role of irrelevant scaling parameters are discussed.Comment: 4 pages, 2 figure

Noise regularization and computations for the 1-dimensional stochastic Allen-Cahn problem

We address the numerical discretization of the Allen-Cahn prob- lem with additive white noise in one-dimensional space. The discretization is conducted in two stages: (1) regularize the white noise and study the regularized problem, (2) approximate the regularized problem. We address (1) by introducing a piecewise constant random approximation of the white noise with respect to a space-time mesh. We analyze the regularized problem and study its relation to both the original problem and the deterministic Allen-Cahn problem. Step (2) is then performed leading to a practical Monte-Carlo method combined with a Finite Element-Implicit Euler scheme. The resulting numerical scheme is tested against theoretical benchmark results.Comment: 28 pages, 16 (4x4) figures, published in 2007; Interfaces and Free Boundaries 2007 vol. 9 (1

Implicit prices of indigenous cattle traits in central Ethiopia: Application of revealed and stated preference approaches

The diversity of animal genetic resources has a quasi-public good nature that makes market prices inadequate indicator of its economic worth. Applying the characteristics theory of value, this research estimated the relative economic worth of the attributes of cattle genetic resources in central Ethiopia. Transaction level data were collected over four seasons in a year and choice experiment survey was done in five markets to generate data on both revealed and stated preferences of cattle buyers. Heteroscedasticity efficient estimation and random parameters logit were employed to analyse the data. The results essentially show that attributes related to the subsistence functions of cattle are more valued than attributes that directly influence marketable products of the animals. The findings imply the strong need to invest on improvement of attributes of cattle in the study area that enhance the subsistence functions of cattle that their owners accord higher priority to support their livelihoods than they do to tradable products

Finite-length Lyapunov exponents and conductance for quasi-1D disordered solids

The transfer matrix method is applied to finite quasi-1D disordered samples attached to perfect leads. The model is described by structured band matrices with random and regular entries. We investigate numerically the level spacing distribution for finite-length Lyapunov exponents as well as the conductance and its fluctuations for different channel numbers and sample sizes. A comparison is made with theoretical predictions and with numerical results recently obtained with the scattering matrix approach. The role of the coupling and finite size effects is also discussed.Comment: 19 pages in LaTex and 8 Postscript figure

Anisotropy and oblique total transmission at a planar negative-index interface

We show that a class of negative index (n) materials has interesting anisotropic optical properties, manifest in the effective refraction index that can be positive, negative, or purely imaginary under different incidence conditions. With dispersion taken into account, reflection at a planar negative-index interface exhibits frequency selective total oblique transmission that is distinct from the Brewster effect. Finite-difference-time-domain simulation of realistic negative-n structures confirms the analytic results based on effective indices.Comment: to appear in Phys. Rev.

Topology dependent quantities at the Anderson transition

The boundary condition dependence of the critical behavior for the three dimensional Anderson transition is investigated. A strong dependence of the scaling function and the critical conductance distribution on the boundary conditions is found, while the critical disorder and critical exponent are found to be independent of the boundary conditions

Finite-size scaling from self-consistent theory of localization

Accepting validity of self-consistent theory of localization by Vollhardt and Woelfle, we derive the finite-size scaling procedure used for studies of the critical behavior in d-dimensional case and based on the use of auxiliary quasi-1D systems. The obtained scaling functions for d=2 and d=3 are in good agreement with numerical results: it signifies the absence of essential contradictions with the Vollhardt and Woelfle theory on the level of raw data. The results \nu=1.3-1.6, usually obtained at d=3 for the critical exponent of the correlation length, are explained by the fact that dependence L+L_0 with L_0>0 (L is the transversal size of the system) is interpreted as L^{1/\nu} with \nu>1. For dimensions d\ge 4, the modified scaling relations are derived; it demonstrates incorrectness of the conventional treatment of data for d=4 and d=5, but establishes the constructive procedure for such a treatment. Consequences for other variants of finite-size scaling are discussed.Comment: Latex, 23 pages, figures included; additional Fig.8 is added with high precision data by Kramer et a