Activated escape of periodically driven systems

We discuss activated escape from a metastable state of a system driven by a time-periodic force. We show that the escape probabilities can be changed very strongly even by a comparatively weak force. In a broad parameter range, the activation energy of escape depends linearly on the force amplitude. This dependence is described by the logarithmic susceptibility, which is analyzed theoretically and through analog and digital simulations. A closed-form explicit expression for the escape rate of an overdamped Brownian particle is presented and shown to be in quantitative agreement with the simulations. We also describe experiments on a Brownian particle optically trapped in a double-well potential. A suitable periodic modulation of the optical intensity breaks the spatio-temporal symmetry of an otherwise spatially symmetric system. This has allowed us to localize a particle in one of the symmetric wells. (c) 2001 American Institute of Physics.     

An algorithm for the fast solution of symmetric linear complementarity problems

This paper studies algorithms for the solution of mixed symmetric linear complementarity problems. The goal is to compute fast and approximate solutions of medium to large sized problems, such as those arising in computer game simulations and American options pricing. The paper proposes an improvement of a method described by Kocvara and Zowe (Numer Math 68:95–106, 1994) that combines projected Gauss–Seidel iterations with subspace minimization steps. The proposed algorithm employs a recursive subspace minimization designed to handle severely ill-conditioned problems. Numerical tests indicate that the approach is more efficient than interior-point and gradient projection methods on some physical simulation problems that arise in computer game scenarios. The research of J. L. Morales was supported by Asociación Mexicana de Cultura AC and CONACyT-NSF grant J110.388/2006. The research of J. Nocedal was supported by National Science Foundation grant CCF-0514772, Department of Energy grant DE-FG02-87ER25047-A004 and a grant from the Intel Corporation.     

Dynamical inference of hidden biological populations

Population fluctuations in a predator-prey system are analyzed for the case where the number of prey could be determined, subject to measurement noise, but the number of predators was unknown. The problem of how to infer the unmeasured predator dynamics, as well as the model parameters, is addressed. Two solutions are suggested. In the first of these, measurement noise and the dynamical noise in the equation for predator population are neglected; the problem is reduced to a one-dimensional case, and a Bayesian dynamical inference algorithm is employed to reconstruct the model parameters. In the second solution a full-scale Markov Chain Monte Carlo simulation is used to infer both the unknown predator trajectory, and also the model parameters, using the one-dimensional solution as an initial guess.     

Quantifying uncertainty in the measurement of arsenic in suspended particulate matter by Atomic Absorption Spectrometry with hydride generator

Arsenic is the toxic element, which creates several problems in human being specially when inhaled through air. So the accurate and precise measurement of arsenic in suspended particulate matter (SPM) is of prime importance as it gives information about the level of toxicity in the environment, and preventive measures could be taken in the effective areas. Quality assurance is equally important in the measurement of arsenic in SPM samples before making any decision. The quality and reliability of the data of such volatile elements depends upon the measurement of uncertainty of each step involved from sampling to analysis. The analytical results quantifying uncertainty gives a measure of the confidence level of the concerned laboratory. So the main objective of this study was to determine arsenic content in SPM samples with uncertainty budget and to find out various potential sources of uncertainty, which affects the results. Keeping these facts, we have selected seven diverse sites of Delhi (National Capital of India) for quantification of arsenic content in SPM samples with uncertainty budget following sampling by HVS to analysis by Atomic Absorption Spectrometer-Hydride Generator (AAS-HG). In the measurement of arsenic in SPM samples so many steps are involved from sampling to final result and we have considered various potential sources of uncertainties. The calculation of uncertainty is based on ISO/IEC17025: 2005 document and EURACHEM guideline. It has been found that the final results mostly depend on the uncertainty in measurement mainly due to repeatability, final volume prepared for analysis, weighing balance and sampling by HVS. After the analysis of data of seven diverse sites of Delhi, it has been concluded that during the period from 31^st Jan. 2008 to 7^th Feb. 2008 the arsenic concentration varies from 1.44 ± 0.25 to 5.58 ± 0.55 ng/m³ with 95% confidence level (k = 2).     

Size dependence of the minimum excitation gap in the quantum adiabatic algorithm

We study the typical (median) value of the minimum gap in the quantum version of the exact cover problem using quantum Monte Carlo simulations, in order to understand the complexity of the quantum adiabatic algorithm for much larger sizes than before. For a range of sizes N< or =128, where the classical Davis-Putnam algorithm shows exponential median complexity, the quantum adiabatic algorithm shows polynomial median complexity. The bottleneck of the algorithm is an isolated avoided-crossing point of a Landau-Zener type (collision between the two lowest energy levels only).     

Inference of a nonlinear stochastic model of the cardiorespiratory interaction

We reconstruct a nonlinear stochastic model of the cardiorespiratory interaction in terms of a set of polynomial basis functions representing the nonlinear force governing system oscillations. The strength and direction of coupling and noise intensity are simultaneously inferred from a univariate blood pressure signal. Our new inference technique does not require extensive global optimization, and it is applicable to a wide range of complex dynamical systems subject to noise.     

Structural characteristics of different types of nanoparticles synthesised in mesomorphic metal alkanoates

The class of thermotropic ionic liquid crystals (LCs) of the metal alkanoates possesses a number of unique properties, such as intrinsic ionic conductivity, high dissolving ability and ability to form time-stable mesomorphic glasses. These ionic LCs can be used as nanoreactors for the synthesis and stabilisation of different types of nanoparticles (NPs). Thus, some semiconductors, metals and core/shell NPs were chemically synthesised in the thermotropic ionic liquid crystalline phase (smectic A) of the cadmium octanoate (CdC₈) and of the cobalt octanoate (CoC₈). By applying the scanning electron microscopy, the cadmium and cobalt octanoate composites containing CdS, Au, Ag and core/shell Au/CdS NPs have been studied. NPs’ sizes and dispersion distribution of the NPs’ size in the nanocomposites have been obtained.