Work fluctuations in an elastic dumbbell model of polymers in planar elongational flow

We use a path-integral approach to calculate the distribution P(w, t) of the fluctuations in the work W at time t of a polymer molecule (modeled as an elastic dumbbell in a viscous solvent) that is acted on by an elongational flow field having a flow rate (gamma) over dot. We find that P(w, t) is non-Gaussian and that, at long times, the ratio P(w, t)/ P (-w, t) is equal to expw/(k(B)T)], independent of (gamma) over dot. On the basis of this finding, we suggest that polymers in elongational flows satisfy a fluctuation theorem.

Distribution of transverse chain fluctuations in harmonically confined semiflexible polymers

Two different experimental studies of polymer dynamics based on single-molecule fluorescence imaging have recently found evidence of heterogeneities in the widths of the putative tubes that surround filaments of F-actin during their motion in concentrated solution. In one J. Glaser, D. Chakraborty, K. Kroy, I. Lauter, M. Degawa, N. Kirchesner, B. Hoffmann, R. Merkel, and M. Giesen, Phys. Rev. Lett. 105, 037801 (2010)], the observations were explained in terms of the statistics of a worm-like chain confined to a potential determined self-consistently by a binary collision approximation, and in the other B. Wang, J. Guan, S. M. Anthony, S. C. Bae, K. S. Schweizer, and S. Granick, Phys. Rev. Lett. 104, 118301 (2010)], they were explained in terms of the scaling properties of a random fluid of thin rods. In this paper, we show, using an exact path integral calculation, that the distribution of the length-averaged transverse fluctuations of a harmonically confined weakly bendable rod (one possible realization of a semiflexible chain in a tube), is in good qualitative agreement with the experimental data, although it is qualitatively different in analytic structure from the earlier theoretical predictions. We also show that similar path integral techniques can be used to obtain an exact expression for the time correlation function of fluctuations in the tube cross section. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4712306]

Interfacial growth as a model of tube-width heterogeneities in concentrated solutions of stiff polymers

Recent experimental measurements of the distribution P(w) of transverse chain fluctuations w in concentrated solutions of F-actin filaments B. Wang, J Guan, S. M. Anthony, S. C. Bae, K. S. Schweizer, and S. Granick, Phys. Rev. Lett. 104, 118301 (2010); J. Glaser, D. Chakraborty, K. Kroy, I. Lauter, M. Degawa, N. Kirchgessner, B. Hoffmann, R. Merkel, and M. Giesen, Phys. Rev. Lett. 105, 037801 (2010)] are shown to be well-fit to an expression derived from a model of the conformations of a single harmonically confined weakly bendable rod. The calculation of P(w) is carried out essentially exactly within a path integral approach that was originally applied to the study of one-dimensional randomly growing interfaces. Our results are generally as successful in reproducing experimental trends as earlier approximate results obtained from more elaborate many-chain treatments of the confining tube potential.

Interfacial growth as a model of tube-width heterogeneities in concentrated solutions of stiff polymers

Recent experimental measurements of the distribution P(w) of transverse chain fluctuations w in concentrated solutions of F-actin filaments B. Wang, J Guan, S. M. Anthony, S. C. Bae, K. S. Schweizer, and S. Granick, Phys. Rev. Lett. 104, 118301 (2010); J. Glaser, D. Chakraborty, K. Kroy, I. Lauter, M. Degawa, N. Kirchgessner, B. Hoffmann, R. Merkel, and M. Giesen, Phys. Rev. Lett. 105, 037801 (2010)] are shown to be well-fit to an expression derived from a model of the conformations of a single harmonically confined weakly bendable rod. The calculation of P(w) is carried out essentially exactly within a path integral approach that was originally applied to the study of one-dimensional randomly growing interfaces. Our results are generally as successful in reproducing experimental trends as earlier approximate results obtained from more elaborate many-chain treatments of the confining tube potential. (C) 2013 AIP Publishing LLC.

Nonclassical Paths in Quantum Interference Experiments

In a double slit interference experiment, the wave function at the screen with both slits open is not exactly equal to the sum of the wave functions with the slits individually open one at a time. The three scenarios represent three different boundary conditions and as such, the superposition principle should not be applicable. However, most well-known text books in quantum mechanics implicitly and/or explicitly use this assumption that is only approximately true. In our present study, we have used the Feynman path integral formalism to quantify contributions from nonclassical paths in quantum interference experiments that provide a measurable deviation from a naive application of the superposition principle. A direct experimental demonstration for the existence of these nonclassical paths is difficult to present. We find that contributions from such paths can be significant and we propose simple three-slit interference experiments to directly confirm their existence.

On the superposition principle in interference experiments

The superposition principle is usually incorrectly applied in interference experiments. This has recently been investigated through numerics based on Finite Difference Time Domain (FDTD) methods as well as the Feynman path integral formalism. In the current work, we have derived an analytic formula for the Sorkin parameter which can be used to determine the deviation from the application of the principle. We have found excellent agreement between the analytic distribution and those that have been earlier estimated by numerical integration as well as resource intensive FDTD simulations. The analytic handle would be useful for comparing theory with future experiments. It is applicable both to physics based on classical wave equations as well as the non-relativistic Schrodinger equation.

A fractional order proportional integral controller for path following and trajectory tracking of miniature air vehicles

In this paper, a fractional order proportional-integral controller is developed for a miniature air vehicle for rectilinear path following and trajectory tracking. The controller is implemented by constructing a vector field surrounding the path to be followed, which is then used to generate course commands for the miniature air vehicle. The fractional order proportional-integral controller is simulated using the fundamentals of fractional calculus, and the results for this controller are compared with those obtained for a proportional controller and a proportional integral controller. In order to analyze the performance of the controllers, four performance metrics, namely (maximum) overshoot, control effort, settling time and integral of the timed absolute error cost, have been selected. A comparison of the nominal as well as the robust performances of these controllers indicates that the fractional order proportional-integral controller exhibits the best performance in terms of ITAE while showing comparable performances in all other aspects.

Comprehensive Path-sensitive Data-flow Analysis

Data-flow analysis is an integral part of any aggressive optimizing compiler. We propose a framework for improving the precision of data-flow analysis in the presence of complex control-flow. W initially perform data-flow analysis to determine those control-flow merges which cause the loss in data-flow analysis precision. The control-flow graph of the program is then restructured such that performing data-flow analysis on the resulting restructured graph gives more precise results. The proposed framework is both simple, involving the familiar notion of product automata, and also general, since it is applicable to any forward data-flow analysis. Apart from proving that our restructuring process is correct, we also show that restructuring is effective in that it necessarily leads to more optimization opportunities. Furthermore, the framework handles the trade-off between the increase in data-flow precision and the code size increase inherent in the restructuring. We show that determining an optimal restructuring is NP-hard, and propose and evaluate a greedy strategy. The framework has been implemented in the Scale research compiler, and instantiated for the specific problem of Constant Propagation. On the SPECINT 2000 benchmark suite we observe an average speedup of 4% in the running times over Wegman-Zadeck conditional constant propagation algorithm and 2% over a purely path profile guided approach.

Impact of Energy Quantization on the Performance of Current-Biased SET Circuits

The current-biased single electron transistor (SET) (CBS) is an integral part of almost all hybrid CMOS SET circuits. In this paper, for the first time, the effects of energy quantization on the performance of CBS-based circuits are studied through analytical modeling and Monte Carlo simulations. It is demonstrated that energy quantization has no impact on the gain of the CBS characteristics, although it changes the output voltage levels and oscillation periodicity. The effects of energy quantization are further studied for two circuits: negative differential resistance (NDR) and neuron cell, which use the CBS. A new model for the conductance of NDR characteristics is also formulated that includes the energy quantization term.

Calculating the bound spectrum by path summation in action-angle variables

The density of states n(E) is calculated for a bound system whose classical motion is integrable, starting from an expression in terms of the trace of the time-dependent Green function. The novel feature is the use of action-angle variables. This has the advantages that the trace operation reduces to a trivial multiplication and the dependence of n(E) on all classical closed orbits with different topologies appears naturally. The method is contrasted with another, not applicable to integrable systems except in special cases, in which quantization arises from a single closed orbit which is assumed isolated and the trace taken by the method of stationary phase.

Computation of Thermal Stress Intensity Factors for Bimaterial Interface Cracks Using Domain Integral Method

The concept of domain integral used extensively for J integral has been applied in this work for the formulation of J(2) integral for linear elastic bimaterial body containing a crack at the interface and subjected to thermal loading. It is shown that, in the presence of thermal stresses, the J(k) domain integral over a closed path, which does not enclose singularities, is a function of temperature and body force. A method is proposed to compute the stress intensity factors for bimaterial interface crack subjected to thermal loading by combining this domain integral with the J(k) integral. The proposed method is validated by solving standard problems with known solutions.

Relation between integral and partial properties of ternary solutions along different composition trajectories

The relations between partial and integral properties of ternary solutions along composition trajectories suggested by Kohler, Colinet and Jacob, and along an arbitrary path are derived. The chemical potentials of the components are related to the slope of integral free energy by expressions involving the binary compositions generated by the intersections of the composition trajectory with the sides of the ternary triangle. Only along the Kohler composition trajectory it is possible to derive the integral free energy from the variation of the chemical potential of a single component with composition or vice versa. Along all other paths the differential of the integral free energy is related to two chemical potentials. The Gibbs-Duhem integration proposed by Darken for the ternary system uses the Kohler isogram. The relative merits of different limits for integration are discussed.

The estimation of the thermodynamic properties of ternary alloys from binary data using the shortest distance composition path

A new composition path, Xi-Xj=constant, is suggested for the semi-empirical calculation of the thermodynamic properties of ternary ‘substitutional’ solutions from binary data, when the binary systems show deviations from the regular solution model. A comparison is made between the results obtained for integral and partial properties using this composition path and those calculated employing other composition paths suggested in literature. It appears that the best estimate of the ternary properties is obtained when binary data at compositions closest to the ternary composition are used.

Time-Optimal Convergence to a Rectilinear Path in the Presence of Wind

This paper considers the problem of determining the time-optimal path of a fixed-wing Miniature Air Vehicle (MAV), in the presence of wind. The MAV, which is subject to a bounded turn rate, is required to eventually converge to a straight line starting from a known initial position and orientation. Earlier work in the literature uses Pontryagin's Minimum Principle (PMP) to solve this problem only for the no-wind case. In contrast, the present work uses a geometric approach to solve the problem completely in the presence of wind. In addition, it also shows how PMP can be used to partially solve the problem. Using a 6-DOF model of a MAV the generated optimal path is tracked by an autopilot consisting of proportional-integral-derivative (PID) controllers. The simulation results show the path generation and tracking for cases with steady and time-varying wind. Some issues on real-time path planning are also addressed.

Optimal Trajectory Generation for Convergence to a Rectilinear Path

This paper presents a strategy to determine the shortest path of a fixed-wing Miniature Air Vehicle (MAV), constrained by a bounded turning rate, to eventually fly along a given straight line, starting from an arbitrary but known initial position and orientation. Unlike the work available in the literature that solves the problem using the Pontryagin's Minimum Principle (PMP) the trajectory generation algorithm presented here considers a geometrical approach which is intuitive and easy to understand. This also computes the explicit solution for the length of the optimal path as a function of the initial configuration. Further, using a 6-DOF model of a MAV the generated optimal path is tracked by an autopilot consisting of proportional-integral-derivative (PID) controllers. The simulation results show the path generation and tracking for different cases.