Large deviation function and fluctuation theorem for classical particle transport

We analytically evaluate the large deviation function in a simple model of classical particle transfer between two reservoirs. We illustrate how the asymptotic long-time regime is reached starting from a special propagating initial condition. We show that the steady-state fluctuation theorem holds provided that the distribution of the particle number decays faster than an exponential, implying analyticity of the generating function and a discrete spectrum for its evolution operator.

Discrete time second order sliding mode observer for uncertain linear multi-output system

This paper presents a second order sliding mode observer (SOSMO) design for discrete time uncertain linear multi-output system. The design procedure is effective for both matched and unmatched bounded uncertainties and/or disturbances. A second order sliding function and corresponding sliding manifold for discrete time system are defined similar to the lines of continuous time counterpart. A boundary layer concept is employed to avoid switching across the defined sliding manifold and the sliding trajectory is confined to a boundary layer once it converges to it. The condition for existence of convergent quasi-sliding mode (QSM) is derived. The observer estimation errors satisfying given stability conditions converge to an ultimate finite bound (within the specified boundary layer) with thickness O(T-2) where T is the sampling period. A relation between sliding mode gain and boundary layer is established for the existence of second order discrete sliding motion. The design strategy is very simple to apply and is demonstrated for three examples with different class of disturbances (matched and unmatched) to show the effectiveness of the design. Simulation results to show the robustness with respect to the measurement noise are given for SOSMO and the performance is compared with pseudo-linear Kalman filter (PLKF). (C) 2013 Published by Elsevier Ltd. on behalf of The Franklin Institute

Correlation between Optical Properties and Nanomorphology of Fluoranthene-Based Conjugated Copolymer

Nanoparticles of conjugated polymers are receiving attention due to their interesting optical properties. Here we report nanoparticles of fluoranthene-based conjugated copolymer prepared by the Suzuki coupling reaction. The copolymer forms nanoparticles by the spontaneous self-assembly after evaporation of organic solvent. The mean diameter of the nanoparticles can be manipulated by varying solvent composition. We investigated the parameters that govern the nanostructured morphology of polymer by systematic variation of good and poor solvent. The UV vis and time-resolved fluorescence spectroscopy measurement reveal the use of poor solvent in the organization of nanostructures. Furthermore, transmission electron microscopy highlights the importance of rigidity of the polymer backbone in morphological development.

Diffusing-wave spectroscopy in an inhomogeneous object: Local viscoelastic spectra from ultrasound-assisted measurement of correlation decay arising from the ultrasound focal volume

We demonstrate diffusing-wave spectroscopy (DWS) in a localized region of a viscoelastically inhomogeneous object by measurement of the intensity autocorrelation g(2)(tau)] that captures only the decay introduced by the temperature-induced Brownian motion in the region. The region is roughly specified by the focal volume of an ultrasound transducer which introduces region specific mechanical vibration owing to insonification. Essential characteristics of the localized non-Markovian dynamics are contained in the decay of the modulation depth M(tau)], introduced by the ultrasound forcing in the focal volume selected, on g(2)(tau). The modulation depth M(tau(i)) at any delay time tau(i) can be measured by short-time Fourier transform of g(2)(tau) and measurement of the magnitude of the spectrum at the ultrasound drive frequency. By following the established theoretical framework of DWS, we are able to connect the decay in M(tau) to the mean-squared displacement (MSD) of scattering centers and the MSD to G*(omega), the complex viscoelastic spectrum. A two-region composite polyvinyl alcohol phantom with different viscoelastic properties is selected for demonstrating local DWS-based recovery of G*(omega) corresponding to these regions from the measured region specific M(tau(i))vs tau(i). The ultrasound-assisted measurement of MSD is verified by simulating, using a generalized Langevin equation (GLE), the dynamics of the particles in the region selected as well as by the usual DWS experiment without the ultrasound. It is shown that whereas the MSD obtained by solving the GLE without the ultrasound forcing agreed with its experimental counterpart covering small and large values of tau, the match was good only in the initial transients in regard to experimental measurements with ultrasound.

Risk-sensitive control of continuous time Markov chains

We study risk-sensitive control of continuous time Markov chains taking values in discrete state space. We study both finite and infinite horizon problems. In the finite horizon problem we characterize the value function via Hamilton Jacobi Bellman equation and obtain an optimal Markov control. We do the same for infinite horizon discounted cost case. In the infinite horizon average cost case we establish the existence of an optimal stationary control under certain Lyapunov condition. We also develop a policy iteration algorithm for finding an optimal control.

Dynamic Site Characterization and Correlation of Shear Wave Velocity with Standard Penetration Test `N' Values for the City of Agartala, Tripura State, India

Seismic site characterization is the basic requirement for seismic microzonation and site response studies of an area. Site characterization helps to gauge the average dynamic properties of soil deposits and thus helps to evaluate the surface level response. This paper presents a seismic site characterization of Agartala city, the capital of Tripura state, in the northeast of India. Seismically, Agartala city is situated in the Bengal Basin zone which is classified as a highly active seismic zone, assigned by Indian seismic code BIS-1893, Indian Standard Criteria for Earthquake Resistant Design of Structures, Part-1 General Provisions and Buildings. According to the Bureau of Indian Standards, New Delhi (2002), it is the highest seismic level (zone-V) in the country. The city is very close to the Sylhet fault (Bangladesh) where two major earthquakes (M (w) > 7) have occurred in the past and affected severely this city and the whole of northeast India. In order to perform site response evaluation, a series of geophysical tests at 27 locations were conducted using the multichannel analysis of surface waves (MASW) technique, which is an advanced method for obtaining shear wave velocity (V (s)) profiles from in situ measurements. Similarly, standard penetration test (SPT-N) bore log data sets have been obtained from the Urban Development Department, Govt. of Tripura. In the collected data sets, out of 50 bore logs, 27 were selected which are close to the MASW test locations and used for further study. Both the data sets (V (s) profiles with depth and SPT-N bore log profiles) have been used to calculate the average shear wave velocity (V (s)30) and average SPT-N values for the upper 30 m depth of the subsurface soil profiles. These were used for site classification of the study area recommended by the National Earthquake Hazard Reduction Program (NEHRP) manual. The average V (s)30 and SPT-N classified the study area as seismic site class D and E categories, indicating that the city is susceptible to site effects and liquefaction. Further, the different data set combinations between V (s) and SPT-N (corrected and uncorrected) values have been used to develop site-specific correlation equations by statistical regression, as `V (s)' is a function of SPT-N value (corrected and uncorrected), considered with or without depth. However, after considering the data set pairs, a probabilistic approach has also been presented to develop a correlation using a quantile-quantile (Q-Q) plot. A comparison has also been made with the well known published correlations (for all soils) available in the literature. The present correlations closely agree with the other equations, but, comparatively, the correlation of shear wave velocity with the variation of depth and uncorrected SPT-N values provides a more suitable predicting model. Also the Q-Q plot agrees with all the other equations. In the absence of in situ measurements, the present correlations could be used to measure V (s) profiles of the study area for site response studies.

TIME VARYING LINEAR PREDICTION USING SPARSITY CONSTRAINTS

Time-varying linear prediction has been studied in the context of speech signals, in which the auto-regressive (AR) coefficients of the system function are modeled as a linear combination of a set of known bases. Traditionally, least squares minimization is used for the estimation of model parameters of the system. Motivated by the sparse nature of the excitation signal for voiced sounds, we explore the time-varying linear prediction modeling of speech signals using sparsity constraints. Parameter estimation is posed as a 0-norm minimization problem. The re-weighted 1-norm minimization technique is used to estimate the model parameters. We show that for sparsely excited time-varying systems, the formulation models the underlying system function better than the least squares error minimization approach. Evaluation with synthetic and real speech examples show that the estimated model parameters track the formant trajectories closer than the least squares approach.

Polynomial Decompositions in Polynomial Time

Fix a prime p. Given a positive integer k, a vector of positive integers Delta = (Delta(1), Delta(2), ... , Delta(k)) and a function Gamma : F-p(k) -> F-p, we say that a function P : F-p(n) -> F-p is (k, Delta, Gamma)-structured if there exist polynomials P-1, P-2, ..., P-k : F-p(n) -> F-p with each deg(P-i) <= Delta(i) such that for all x is an element of F-p(n), P(x) = Gamma(P-1(x), P-2(x), ..., P-k(x)). For instance, an n-variate polynomial over the field Fp of total degree d factors nontrivially exactly when it is (2, (d - 1, d - 1), prod)- structured where prod(a, b) = a . b. We show that if p > d, then for any fixed k, Delta, Gamma, we can decide whether a given polynomial P(x(1), x(2), ..., x(n)) of degree d is (k, Delta, Gamma)-structured and if so, find a witnessing decomposition. The algorithm takes poly(n) time. Our approach is based on higher-order Fourier analysis.

Cross-correlation-aided transport in stochastically driven accretion flows

The origin of linear instability resulting in rotating sheared accretion flows has remained a controversial subject for a long time. While some explanations of such non-normal transient growth of disturbances in the Rayleigh stable limit were available for magnetized accretion flows, similar instabilities in the absence of magnetic perturbations remained unexplained. This dichotomy was resolved in two recent publications by Chattopadhyay and co-workers Mukhopadhyay and Chattopadhyay, J. Phys. A 46, 035501 (2013); Nath et al., Phys. Rev. E 88, 013010 (2013)] where it was shown that such instabilities, especially for nonmagnetized accretion flows, were introduced through interaction of the inherent stochastic noise in the system (even a ``cold'' accretion flow at 3000Kis too ``hot'' in the statistical parlance and is capable of inducing strong thermal modes) with the underlying Taylor-Couette flow profiles. Both studies, however, excluded the additional energy influx (or efflux) that could result from nonzero cross correlation of a noise perturbing the velocity flow, say, with the noise that is driving the vorticity flow (or equivalently the magnetic field and magnetic vorticity flow dynamics). Through the introduction of such a time symmetry violating effect, in this article we show that nonzero noise cross correlations essentially renormalize the strength of temporal correlations. Apart from an overall boost in the energy rate (both for spatial and temporal correlations, and hence in the ensemble averaged energy spectra), this results in mutual competition in growth rates of affected variables often resulting in suppression of oscillating Alfven waves at small times while leading to faster saturations at relatively longer time scales. The effects are seen to be more pronounced with magnetic field fluxes where the noise cross correlation magnifies the strength of the field concerned. Another remarkable feature noted specifically for the autocorrelation functions is the removal of energy degeneracy in the temporal profiles of fast growing non-normal modes leading to faster saturation with minimum oscillations. These results, including those presented in the previous two publications, now convincingly explain subcritical transition to turbulence in the linear limit for all possible situations that could now serve as the benchmark for nonlinear stability studies in Keplerian accretion disks.

Using long time series of agricultural-derived nitrates for estimating catchment transit times

The estimation of water and solute transit times in catchments is crucial for predicting the response of hydrosystems to external forcings (climatic or anthropogenic). The hydrogeochemical signatures of tracers (either natural or anthropogenic) in streams have been widely used to estimate transit times in catchments as they integrate the various processes at stake. However, most of these tracers are well suited for catchments with mean transit times lower than about 4-5 years. Since the second half of the 20th century, the intensification of agriculture led to a general increase of the nitrogen load in rivers. As nitrate is mainly transported by groundwater in agricultural catchments, this signal can be used to estimate transit times greater than several years, even if nitrate is not a conservative tracer. Conceptual hydrological models can be used to estimate catchment transit times provided their consistency is demonstrated, based on their ability to simulate the stream chemical signatures at various time scales and catchment internal processes such as N storage in groundwater. The objective of this study was to assess if a conceptual lumped model was able to simulate the observed patterns of nitrogen concentration, at various time scales, from seasonal to pluriannual and thus if it was relevant to estimate the nitrogen transit times in headwater catchments. A conceptual lumped model, representing shallow groundwater flow as two parallel linear stores with double porosity, and riparian processes by a constant nitrogen removal function, was applied on two paired agricultural catchments which belong to the Research Observatory ORE AgrHys. The Global Likelihood Uncertainty Estimation (GLUE) approach was used to estimate parameter values and uncertainties. The model performance was assessed on (i) its ability to simulate the contrasted patterns of stream flow and stream nitrate concentrations at seasonal and inter-annual time scales, (ii) its ability to simulate the patterns observed in groundwater at the same temporal scales, and (iii) the consistency of long-term simulations using the calibrated model and the general pattern of the nitrate concentration increase in the region since the beginning of the intensification of agriculture in the 1960s. The simulated nitrate transit times were found more sensitive to climate variability than to parameter uncertainty, and average values were found to be consistent with results from others studies in the same region involving modeling and groundwater dating. This study shows that a simple model can be used to simulate the main dynamics of nitrogen in an intensively polluted catchment and then be used to estimate the transit times of these pollutants in the system which is crucial to guide mitigation plans design and assessment. (C) 2015 Elsevier B.V. All rights reserved.

Quick, Decentralized, Energy-Efficient One-Shot Max Function Computation Using Timer-Based Selection

In several wireless sensor networks, it is of interest to determine the maximum of the sensor readings and identify the sensor responsible for it. We propose a novel, decentralized, scalable, energy-efficient, timer-based, one-shot max function computation (TMC) algorithm. In it, the sensor nodes do not transmit their readings in a centrally pre-defined sequence. Instead, the nodes are grouped into clusters, and computation occurs over two contention stages. First, the nodes in each cluster contend with each other using the timer scheme to transmit their reading to their cluster-heads. Thereafter, the cluster-heads use the timer scheme to transmit the highest sensor reading in their cluster to the fusion node. One new challenge is that the use of the timer scheme leads to collisions, which can make the algorithm fail. We optimize the algorithm to minimize the average time required to determine the maximum subject to a constraint on the probability that it fails to find the maximum. TMC significantly lowers average function computation time, average number of transmissions, and average energy consumption compared to approaches proposed in the literature.

Phase space path integral approach to harmonic oscillator with a time-dependent force constant

The quantum statistical mechanical propagator for a harmonic oscillator with a time-dependent force constant, m omega(2)(t), has been investigated in the past and was found to have only a formal solution in terms of the solutions of certain ordinary differential equations. Such path integrals are frequently encountered in semiclassical path integral evaluations and having exact analytical expressions for such path integrals is of great interest. In a previous work, we had obtained the exact propagator for motion in an arbitrary time-dependent harmonic potential in the overdamped limit of friction using phase space path integrals in the context of Levy flights - a result that can be easily extended to Brownian motion. In this paper, we make a connection between the overdamped Brownian motion and the imaginary time propagator of quantum mechanics and thereby get yet another way to evaluate the latter exactly. We find that explicit analytic solution for the quantum statistical mechanical propagator can be written when the time-dependent force constant has the form omega(2)(t) = lambda(2)(t) - d lambda(t)/dt where lambda(t) is any arbitrary function of t and use it to evaluate path integrals which have not been evaluated previously. We also employ this method to arrive at a formal solution of the propagator for both Levy flights and Brownian subjected to a time-dependent harmonic potential in the underdamped limit of friction. (C) 2015 Elsevier B.V. All rights reserved.

Retrieval and Multi-scale Validation of Soil Moisture from Multi-temporal SAR Data in a Semi-Arid Tropical Region

The current study presents an algorithm to retrieve surface Soil Moisture (SM) from multi-temporal Synthetic Aperture Radar (SAR) data. The developed algorithm is based on the Cumulative Density Function (CDF) transformation of multi-temporal RADARSAT-2 backscatter coefficient (BC) to obtain relative SM values, and then converts relative SM values into absolute SM values using soil information. The algorithm is tested in a semi-arid tropical region in South India using 30 satellite images of RADARSAT-2, SMOS L2 SM products, and 1262 SM field measurements in 50 plots spanning over 4 years. The validation with the field data showed the ability of the developed algorithm to retrieve SM with RMSE ranging from 0.02 to 0.06 m(3)/m(3) for the majority of plots. Comparison with the SMOS SM showed a good temporal behaviour with RMSE of approximately 0.05 m(3)/m(3) and a correlation coefficient of approximately 0.9. The developed model is compared and found to be better than the change detection and delta index model. The approach does not require calibration of any parameter to obtain relative SM and hence can easily be extended to any region having time series of SAR data available.

De-DUFing the DUFs: Deciphering distant evolutionary relationships of Domains of Unknown Function using sensitive homology detection methods

Background: In the post-genomic era where sequences are being determined at a rapid rate, we are highly reliant on computational methods for their tentative biochemical characterization. The Pfam database currently contains 3,786 families corresponding to ``Domains of Unknown Function'' (DUF) or ``Uncharacterized Protein Family'' (UPF), of which 3,087 families have no reported three-dimensional structure, constituting almost one-fourth of the known protein families in search for both structure and function. Results: We applied a `computational structural genomics' approach using five state-of-the-art remote similarity detection methods to detect the relationship between uncharacterized DUFs and domain families of known structures. The association with a structural domain family could serve as a start point in elucidating the function of a DUF. Amongst these five methods, searches in SCOP-NrichD database have been applied for the first time. Predictions were classified into high, medium and low-confidence based on the consensus of results from various approaches and also annotated with enzyme and Gene ontology terms. 614 uncharacterized DUFs could be associated with a known structural domain, of which high confidence predictions, involving at least four methods, were made for 54 families. These structure-function relationships for the 614 DUF families can be accessed on-line at http://proline.biochem.iisc.ernet.in/RHD_DUFS/. For potential enzymes in this set, we assessed their compatibility with the associated fold and performed detailed structural and functional annotation by examining alignments and extent of conservation of functional residues. Detailed discussion is provided for interesting assignments for DUF3050, DUF1636, DUF1572, DUF2092 and DUF659. Conclusions: This study provides insights into the structure and potential function for nearly 20 % of the DUFs. Use of different computational approaches enables us to reliably recognize distant relationships, especially when they converge to a common assignment because the methods are often complementary. We observe that while pointers to the structural domain can offer the right clues to the function of a protein, recognition of its precise functional role is still `non-trivial' with many DUF domains conserving only some of the critical residues. It is not clear whether these are functional vestiges or instances involving alternate substrates and interacting partners. Reviewers: This article was reviewed by Drs Eugene Koonin, Frank Eisenhaber and Srikrishna Subramanian.

A Few Case Studies on the Correlation of Particle Network and Its Stability on the Ionic Conductivity of Solid-Liquid Composite Electrolytes

We discuss here the crucial role of the particle network and its stability on the long-range ion transport in solid liquid composite electrolytes. The solid liquid composite electrolytes chosen for the study here comprise nanometer sized silica (SiO2) particles having various surface chemical functionalities dispersed in nonaqueous lithium salt solutions, viz, lithium perchlorate (LiClO4) in two different polyethylene glycol based solvents. These systems constitute representative examples of an independent class of soft matter electrolytes known as ``soggy sand'' electrolytes, which have tremendous potential in diverse electrochemical devices. The oxide additive acts as a heterogeneous dopant creating free charge carriers and enhancing the local ion transport. For long-range transport, however, a stable spanning particle network is needed. Systematic experimental investigations here reveal that the spatial and time dependent characteristics of the particle network in the liquid solution are nontrivial. The network characteristics are predominantly determined by the chemical makeup of the electrolyte components and the chemical interactions between them. It is noteworthy that in this study the steady state macroscopic ionic conductivity and viscosity of the solid liquid composite electrolyte are observed to be greatly determined by the additive oxide surface chemical functionality, solvent chemical composition, and solvent dielectric constant.