Transient state work fluctuation theorem for a classical harmonic oscillator linearly coupled to a harmonic bath

Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we do not assume anything about the spectral nature of the harmonic bath the derivation is not restricted only to the Ohmic bath, rather it is more general, for a non-Ohmic bath. We also derive expressions of the average work done and the variance of the work done in terms of the two-time correlation function of the fluctuations of the position of the harmonic oscillator. In the case of an Ohmic bath, we use these relations to evaluate the average work done and the variance of the work done analytically and verify the transient state work fluctuation theorem quantitatively. Actually these relations have far-reaching consequences. They can be used to numerically evaluate the average work done and the variance of the work done in the case of a non-Ohmic bath when analytical evaluation is not possible.

Brownian particles in stationary and moving traps: The mean and variance of the heat distribution function

A recent theoretical model developed by Imparato et al. Phys of the experimentally measured heat and work effects produced by the thermal fluctuations of single micron-sized polystyrene beads in stationary and moving optical traps has proved to be quite successful in rationalizing the observed experimental data. The model, based on the overdamped Brownian dynamics of a particle in a harmonic potential that moves at a constant speed under a time-dependent force, is used to obtain an approximate expression for the distribution of the heat dissipated by the particle at long times. In this paper, we generalize the above model to consider particle dynamics in the presence of colored noise, without passing to the overdamped limit, as a way of modeling experimental situations in which the fluctuations of the medium exhibit long-lived temporal correlations, of the kind characteristic of polymeric solutions, for instance, or of similar viscoelastic fluids. Although we have not been able to find an expression for the heat distribution itself, we do obtain exact expressions for its mean and variance, both for the static and for the moving trap cases. These moments are valid for arbitrary times and they also hold in the inertial regime, but they reduce exactly to the results of Imparato et al. in appropriate limits. DOI: 10.1103/PhysRevE.80.011118 PACS.

A Branch and Bound Algorithm for a Transportation Type Problem with Piecewise Linear Convex Objective Function

A branch and bound type algorithm is presented in this paper to the problem of finding a transportation schedule which minimises the total transportation cost, where the transportation cost over each route is assumed to be a piecewice linear continuous convex function with increasing slopes. The algorithm is an extension of the work done by Balachandran and Perry, in which the transportation cost over each route is assumed to beapiecewise linear discontinuous function with decreasing slopes. A numerical example is solved illustrating the algorithm.

Mycobacterial Stress Regulation: The Dps ``Twin Sister'' Defense Mechanism and Structure-Function Relationship

In this work, we have tried to emphasize the connection between mycobacterial growth and regulation of gene expression. Utilization of multiple carbon sources and diauxic growth helps bacteria to regulate gene expression at an optimum level so that the inhospitable conditions encountered during nutrient depletion can be circumvented. These aspects will be discussed with respect to mycobacterial growth in subsequent sections. Identification and characterization of genes induced under such conditions is helpful to understand the physiology of the bacterium. Although it is necessary to compare the total expression profile of proteins as they transit from vegetative growth to stationary phase, at times a lot of insights can be deciphered from the expression pattern of one or two proteins. We have compared the protein expression and sigma factor selectivity of two such proteins in M. smegmatis to understand the differential regulation of genes playing diverse function in the same species. Some newer insights on the structure and function of one of the Dps proteins are also explained.

Rotorcraft parameter estimation using radial basis function neural network

Increased emphasis on rotorcraft performance and perational capabilities has resulted in accurate computation of aerodynamic stability and control parameters. System identification is one such tool in which the model structure and parameters such as aerodynamic stability and control derivatives are derived. In the present work, the rotorcraft aerodynamic parameters are computed using radial basis function neural networks (RBFN) in the presence of both state and measurement noise. The effect of presence of outliers in the data is also considered. RBFN is found to give superior results compared to finite difference derivatives for noisy data. (C) 2010 Elsevier Inc. All rights reserved.

Ring loading of a long, thin, circular cylindrical shell enclosing a soft, solid core: A recalculation by the love function method of elasticity.

The problem is solved using the Love function and Flügge shell theory. Numerical work has been done with a computer for various values of shell geometry parameters and elastic constants.

Filter design using radial basis function neural network and genetic algorithm for improved operational health monitoring

The problem of denoising damage indicator signals for improved operational health monitoring of systems is addressed by applying soft computing methods to design filters. Since measured data in operational settings is contaminated with noise and outliers, pattern recognition algorithms for fault detection and isolation can give false alarms. A direct approach to improving the fault detection and isolation is to remove noise and outliers from time series of measured data or damage indicators before performing fault detection and isolation. Many popular signal-processing approaches do not work well with damage indicator signals, which can contain sudden changes due to abrupt faults and non-Gaussian outliers. Signal-processing algorithms based on radial basis function (RBF) neural network and weighted recursive median (WRM) filters are explored for denoising simulated time series. The RBF neural network filter is developed using a K-means clustering algorithm and is much less computationally expensive to develop than feedforward neural networks trained using backpropagation. The nonlinear multimodal integer-programming problem of selecting optimal integer weights of the WRM filter is solved using genetic algorithm. Numerical results are obtained for helicopter rotor structural damage indicators based on simulated frequencies. Test signals consider low order polynomial growth of damage indicators with time to simulate gradual or incipient faults and step changes in the signal to simulate abrupt faults. Noise and outliers are added to the test signals. The WRM and RBF filters result in a noise reduction of 54 - 71 and 59 - 73% for the test signals considered in this study, respectively. Their performance is much better than the moving average FIR filter, which causes significant feature distortion and has poor outlier removal capabilities and shows the potential of soft computing methods for specific signal-processing applications.

Filter design using radial basis function neural network and genetic algorithm for improved operational health monitoring

The problem of denoising damage indicator signals for improved operational health monitoring of systems is addressed by applying soft computing methods to design filters. Since measured data in operational settings is contaminated with noise and outliers, pattern recognition algorithms for fault detection and isolation can give false alarms. A direct approach to improving the fault detection and isolation is to remove noise and outliers from time series of measured data or damage indicators before performing fault detection and isolation. Many popular signal-processing approaches do not work well with damage indicator signals, which can contain sudden changes due to abrupt faults and non-Gaussian outliers. Signal-processing algorithms based on radial basis function (RBF) neural network and weighted recursive median (WRM) filters are explored for denoising simulated time series. The RBF neural network filter is developed using a K-means clustering algorithm and is much less computationally expensive to develop than feedforward neural networks trained using backpropagation. The nonlinear multimodal integer-programming problem of selecting optimal integer weights of the WRM filter is solved using genetic algorithm. Numerical results are obtained for helicopter rotor structural damage indicators based on simulated frequencies. Test signals consider low order polynomial growth of damage indicators with time to simulate gradual or incipient faults and step changes in the signal to simulate abrupt faults. Noise and outliers are added to the test signals. The WRM and RBF filters result in a noise reduction of 54 - 71 and 59 - 73% for the test signals considered in this study, respectively. Their performance is much better than the moving average FIR filter, which causes significant feature distortion and has poor outlier removal capabilities and shows the potential of soft computing methods for specific signal-processing applications. (C) 2005 Elsevier B. V. All rights reserved.

Single-molecule thermodynamics: the heat distribution function of a charged particle in a static magnetic field

Interest in the applicability of fluctuation theorems to the thermodynamics of single molecules in external potentials has recently led to calculations of the work and total entropy distributions of Brownian oscillators in static and time-dependent electromagnetic fields. These calculations, which are based on solutions to a Smoluchowski equation, are not easily extended to a consideration of the other thermodynamic quantity of interest in such systems-the heat exchanges of the particle alone-because of the nonlinear dependence of the heat on a particle's stochastic trajectory. In this paper, we show that a path integral approach provides an exact expression for the distribution of the heat fluctuations of a charged Brownian oscillator in a static magnetic field. This approach is an extension of a similar path integral approach applied earlier by our group to the calculation of the heat distribution function of a trapped Brownian particle, which was found, in the limit of long times, to be consistent with experimental data on the thermal interactions of single micron-sized colloids in a viscous solvent.

Reinforcement Learning With Function Approximation for Traffic Signal Control

We propose, for the first time, a reinforcement learning (RL) algorithm with function approximation for traffic signal control. Our algorithm incorporates state-action features and is easily implementable in high-dimensional settings. Prior work, e. g., the work of Abdulhai et al., on the application of RL to traffic signal control requires full-state representations and cannot be implemented, even in moderate-sized road networks, because the computational complexity exponentially grows in the numbers of lanes and junctions. We tackle this problem of the curse of dimensionality by effectively using feature-based state representations that use a broad characterization of the level of congestion as low, medium, or high. One advantage of our algorithm is that, unlike prior work based on RL, it does not require precise information on queue lengths and elapsed times at each lane but instead works with the aforementioned described features. The number of features that our algorithm requires is linear to the number of signaled lanes, thereby leading to several orders of magnitude reduction in the computational complexity. We perform implementations of our algorithm on various settings and show performance comparisons with other algorithms in the literature, including the works of Abdulhai et al. and Cools et al., as well as the fixed-timing and the longest queue algorithms. For comparison, we also develop an RL algorithm that uses full-state representation and incorporates prioritization of traffic, unlike the work of Abdulhai et al. We observe that our algorithm outperforms all the other algorithms on all the road network settings that we consider.

Tensile flow and work hardening behavior of hot cross-rolled AA7010 aluminum alloy sheets

The present work describes the tensile flow and work hardening behavior of a high strength 7010 aluminum alloy by constitutive relations. The alloy has been hot rolled by three different cross-rolling schedules. Room temperature tensile properties have been evaluated as a function of tensile axis orientation in the as-hot rolled as well as peak aged conditions. It is found that both the Ludwigson and a generalized Voce-Bergstrom relation adequately describe the tensile flow behavior of the present alloy in all conditions compared to the Hollomon relation. The variation in the Ludwigson fitting parameter could be correlated well with the microstructural features and anisotropic contribution of strengthening precipitates in the as-rolled and peak aged conditions, respectively. The hardening rate and the saturation stress of the first Voce-Bergstrom parameter, on the other hand, depend mainly on the crystallographic texture of the specimens. It is further shown that for the peak aged specimens the uniform elongation (epsilon(u)) derived from the Ludwigson relation matches well with the measured epsilon(u) irrespective of processing and loading directions. However, the Ludwigson fit overestimates the epsilon(u) in case of the as-rolled specimens. The Hollomon fit, on the other hand, predicts well the measured epsilon(u), of the as-rolled specimens but severely underestimates the epsilon(u), for the peak aged specimens. Contrarily, both the relations significantly overestimate the UTS of the as-rolled and the peak aged specimens. The Voce-Bergstrom parameters define the slope of e Theta-sigma plots in the stage-III regime when the specimens show a classical linear decrease in hardening rate in stage-III. Further analysis of work hardening behavior throws some light on the effect of texture on the dislocation storage and dynamic recovery.

Synthesis and application of weight function for edge cracked semicircular disk (ECSD)

We analyze the utility of edge cracked semicircular disk (ECSD) for rapid assessment of fracture toughness using compressive loading. Continuing our earlier work on ECSD, a theoretical examination here leads to a novel way for synthesizing weight functions using two distinct form factors. The efficacy of ECSD mode-I weight function synthesized using displacement and form factor methods is demonstrated by comparing with finite element results. Theory of elasticity in conjunction with finite element method is utilized to analyze crack opening potency of ECSD under eccentric compression to explore newer configurations of ECSD for fracture testing.

Form and Function of Proteins. Historical Background and the Indian Effort in Macromolecular Crystallography

Global efforts in macromolecular crystallography started in the thirties of the last century. However, definitive results began to emerge only in the late fifties and the early sixties. India has a long tradition in crystallography. The country had a head start in theoretical and computational structural biology, thanks to the efforts of G.N. Ramachandran and his colleagues in the fifties and the sixties. However, macromolecular crystallography got off the ground in India only in the eighties, particularly after the Bangalore group received adequate support from the Department of Science and Technology under their Thrust Area Programme. The Bangalore centre was also identified as a national nucleus for the development of the area in the country. Since then work in the area has spread widely and is being carried out by several groups, mainly led by scientists trained at Bangalore or their descendents, in about thirty institutions in India. In addition to the Department of Science and Technology, the effort is now supported by other agencies like the Department of Biotechnology and the Council of Scientific and Industrial Research. The problems addressed by macromolecular crystallographers in India encompass almost all aspects of modern biology. Indian efforts in macromolecular crystallography have also become an important component of the international efforts in the area.

Structure-function hierarchies and von Karman-Howarth relations for turbulence in magnetohydrodynamical equations

We generalize the method of A. M. Polyakov, Phys. Rev. E 52, 6183 (1995)] for obtaining structure-function relations in turbulence in the stochastically forced Burgers equation, to develop structure-function hierarchies for turbulence in three models for magnetohydrodynamics (MHD). These are the Burgers analogs of MHD in one dimension Eur. Phys. J.B 9, 725 (1999)], and in three dimensions (3DMHD and 3D Hall MHD). Our study provides a convenient and unified scheme for the development of structure-function hierarchies for turbulence in a variety of coupled hydrodynamical equations. For turbulence in the three sets of MHD equations mentioned above, we obtain exact relations for third-order structure functions and their derivatives; these expressions are the analogs of the von Karman-Howarth relations for fluid turbulence. We compare our work with earlier studies of such relations in 3DMHD and 3D Hall MHD.