Intermittent Dynamics, Stochastic Resonance and Dynamical Heterogeneity in Supercooled Liquid Water

Here we find through computer simulations and theoretical analysis that the low temperature thermodynamic anomalies of liquid water arises from the intermittent fluctuation between its high density and low density forms, consisting largely of 5-coordinated and 4-coordinated water molecules, respectively. The fluctuations exhibit strong dynamic heterogeneity (defined by the four point time correlation function), accompanied by a divergence like growth of the dynamic correlation length, of the type encountered in fragile supercooled liquids. The intermittency has been explained by invoking a two state model often employed to understand stochastic resonance, with the relevant periodic perturbation provided here by the fluctuation of the total volume of the system.

Dynamical Transition of Water in the Grooves of DNA Duplex at Low Temperature

At low temperature (below its freezing/melting temperature), liquid water under confinement is known to exhibit anomalous dynamical features. Here we study structure and dynamics of water in the grooves of a long DNA duplex using molecular dynamics simulations with TIP5P potential at low temperature. We find signatures of a dynamical transition in both translational and orientational dynamics of water molecules in both the major and the minor grooves of a DNA duplex. The transition occurs at a slightly higher temperature (TGL ≈ 255 K) than the temperature at which the bulk water is found to undergo a dynamical transition, which for the TIP5P potential is at 247 K. Groove water, however, exhibits markedly different temperature dependence of its properties from the bulk. Entropy calculations reveal that the minor groove water is ordered even at room temperature, and the transition at T ≈ 255 K can be characterized as a strong-to-strong dynamical transition. Confinement of water in the grooves of DNA favors the formation of a low density four-coordinated state (as a consequence of enthalpy−entropy balance) that makes the liquid−liquid transition stronger. The low temperature water is characterized by pronounced tetrahedral order, as manifested in the sharp rise near 109° in the O−O−O angle distribution. We find that the Adams−Gibbs relation between configurational entropy and translational diffusion holds quite well when the two quantities are plotted together in a master plot for different region of aqueous DNA duplex (bulk, major, and minor grooves) at different temperatures. The activation energy for the transfer of water molecules between different regions of DNA is found to be weakly dependent on temperature.

Unusual dynamical arrest in polymer grafted nanoparticles

We present results of temperature dependent measurements of dynamics of polymer grafted nanoparticles with high grafting density with star polymerlike morphology. We observed for the low grafting density and hence low functionality sample, a dynamically arrested state with lowering of temperature, similar to what was conjectured earlier. However the high grafting density sample shows liquidlike relaxation at all measured temperatures. Possible origin of dynamical arrest in the two grafting density sample is discussed.

A pseudo-dynamical systems approach to a class of inverse problems in engineering

A pseudo-dynamical approach for a class of inverse problems involving static measurements is proposed and explored. Following linearization of the minimizing functional associated with the underlying optimization problem, the new strategy results in a system of linearized ordinary differential equations (ODEs) whose steady-state solutions yield the desired reconstruction. We consider some explicit and implicit schemes for integrating the ODEs and thus establish a deterministic reconstruction strategy without an explicit use of regularization. A stochastic reconstruction strategy is then developed making use of an ensemble Kalman filter wherein these ODEs serve as the measurement model. Finally, we assess the numerical efficacy of the developed tools against a few linear and nonlinear inverse problems of engineering interest.

Identification of dynamical systems with fractional derivative damping models using inverse sensitivity analysis

The problem of identifying parameters of time invariant linear dynamical systems with fractional derivative damping models, based on a spatially incomplete set of measured frequency response functions and experimentally determined eigensolutions, is considered. Methods based on inverse sensitivity analysis of damped eigensolutions and frequency response functions are developed. It is shown that the eigensensitivity method requires the development of derivatives of solutions of an asymmetric generalized eigenvalue problem. Both the first and second order inverse sensitivity analyses are considered. The study demonstrates the successful performance of the identification algorithms developed based on synthetic data on one, two and a 33 degrees of freedom vibrating systems with fractional dampers. Limited studies have also been conducted by combining finite element modeling with experimental data on accelerances measured in laboratory conditions on a system consisting of two steel beams rigidly joined together by a rubber hose. The method based on sensitivity of frequency response functions is shown to be more efficient than the eigensensitivity based method in identifying system parameters, especially for large scale systems.

Stabilization of linear and nonlinear dynamical systems using an observer-controller configuration

In this paper the problem of stabilization of systems by means of stable compensations is considered, and results are derived for systems using observer�controller structures, for systems using a cascade structure, and for nonlinear systems

Velocity ratio in the analysis of linear dynamical systems

The transfer matrix method is known to be well suited for a complete analysis of a lumped as well as distributed element, one-dimensional, linear dynamical system with a marked chain topology. However, general subroutines of the type available for classical matrix methods are not available in the current literature on transfer matrix methods. In the present article, general expressions for various aspects of analysis-viz., natural frequency equation, modal vectors, forced response and filter performance—have been evaluated in terms of a single parameter, referred to as velocity ratio. Subprograms have been developed for use with the transfer matrix method for the evaluation of velocity ratio and related parameters. It is shown that a given system, branched or straight-through, can be completely analysed in terms of these basic subprograms, on a stored program digital computer. It is observed that the transfer matrix method with the velocity ratio approach has certain advantages over the existing general matrix methods in the analysis of one-dimensional systems.

An algebraic algorithm for the design and analysis of linear dynamical systems

In an earlier paper [1], it has been shown that velocity ratio, defined with reference to the analogous circuit, is a basic parameter in the complete analysis of a linear one-dimensional dynamical system. In this paper it is shown that the terms constituting velocity ratio can be readily determined by means of an algebraic algorithm developed from a heuristic study of the process of transfer matrix multiplication. The algorithm permits the set of most significant terms at a particular frequency of interest to be identified from a knowledge of the relative magnitudes of the impedances of the constituent elements of a proposed configuration. This feature makes the algorithm a potential tool in a first approach to a rational design of a complex dynamical filter. This algorithm is particularly suited for the desk analysis of a medium size system with lumped as well as distributed elements.

A Note on Easily Testable Realizations for Logic Functions

It is shown that at most, n + 3 tests are required to detect any single stuck-at fault in an AND gate or a single faulty EXCLUSIVE OR (EOR) gate in a Reed-Muller canonical form realization of a switching function.

L_{2}- stability of a class of nonstationary feedback systems with dynamical nonlinear subsystems

A class of feedback systems, consisting of dynamical non-linear subsystems which arise in many diverse control applications, is analyzed for L2-stability. It is shown that, although a transformation of these systems to the familiar Lur'e configuration does not seem to be possible, a one-to-one correspondence may be effected between the stability properties of these and the Lur'e systems. Interesting stability criteria are developed by exploiting this characteristic.

Anomalous dynamical charges, phonons, and the origin of negative thermal expansion in Y2W3O12

We use a combination of classical model and first-principles density functional theory calculations to study lattice dynamics of Y2W3O12 and identify phonons responsible for its negative thermal expansion (NTE). Born dynamical charges of various atoms are found to deviate anomalously from their nominal values. We find that the phonons with energy from 4 to 10 meV are the primary contributors to its NTE. These phonons involve rotations of the YO6 octahedra and WO4 tetrahedra in mutually opposite sense and collective translational atomic displacements, reflecting a strong mixing between acoustic and optic modes.

Nonlinear structural dynamical system identification using adaptive particle filters

The problem of identifying parameters of nonlinear vibrating systems using spatially incomplete, noisy, time-domain measurements is considered. The problem is formulated within the framework of dynamic state estimation formalisms that employ particle filters. The parameters of the system, which are to be identified, are treated as a set of random variables with finite number of discrete states. The study develops a procedure that combines a bank of self-learning particle filters with a global iteration strategy to estimate the probability distribution of the system parameters to be identified. Individual particle filters are based on the sequential importance sampling filter algorithm that is readily available in the existing literature. The paper develops the requisite recursive formulary for evaluating the evolution of weights associated with system parameter states. The correctness of the formulations developed is demonstrated first by applying the proposed procedure to a few linear vibrating systems for which an alternative solution using adaptive Kalman filter method is possible. Subsequently, illustrative examples on three nonlinear vibrating systems, using synthetic vibration data, are presented to reveal the correct functioning of the method. (c) 2007 Elsevier Ltd. All rights reserved.

Dynamical processes in the stratosphere and upper troposphere and their influence on the distribution of trace gases in the polar atmosphere

Transport plays an important role in the distribution of long-lived gases such as ozone and water vapour in the atmosphere. Understanding of observed variability in these gases as well as prediction of the future changes depends therefore on our knowledge of the relevant atmospheric dynamics. This dissertation studies certain dynamical processes in the stratosphere and upper troposphere which influence the distribution of ozone and water vapour in the atmosphere. The planetary waves that originate in the troposphere drive the stratospheric circulation. They influence both the meridional transport of substances as well as parameters of the polar vortices. In turn, temperatures inside the polar vortices influence abundance of the Polar Stratospheric Clouds (PSC) and therefore the chemical ozone destruction. Wave forcing of the stratospheric circulation is not uniform during winter. The November-December averaged stratospheric eddy heat flux shows a significant anticorrelation with the January-February averaged eddy heat flux in the midlatitude stratosphere and troposphere. These intraseasonal variations are attributable to the internal stratospheric vacillations. In the period 1979-2002, the wave forcing exhibited a negative trend which was confined to the second half of winter only. In the period 1958-2002, area, strength and longevity of the Arctic polar vortices do not exhibit significant long-term changes while the area with temperatures lower than the threshold temperature for PSC formation shows statistically significant increase. However, the Arctic vortex parameters show significant decadal changes which are mirrored in the ozone variability. Monthly ozone tendencies in the Northern Hemisphere show significant correlations (|r|=0.7) with proxies of the stratospheric circulation. In the Antarctic, the springtime vortex in the lower stratosphere shows statistically significant trends in temperature, longevity and strength (but not in area) in the period 1979-2001. Analysis of the ozone and water vapour vertical distributions in the Arctic UTLS shows that layering below and above the tropopause is often associated with poleward Rossby wave-breaking. These observations together with calculations of cross-tropopause fluxes emphasize the importance of poleward Rossby wave breaking for the stratosphere-troposphere exchange in the Arctic.

A dynamical approach to the spatio-temporal features of the Portevin-Le Chatelier effect

We show that the extended Ananthakrishna's model exhibits all the features of the Portevin - Le Chatelier effect including the three types of bands. The model reproduces the recently observed crossover from a low dimensional chaotic state at low and medium strain rates to a high dimensional power law state of stress drops at high strain rates. The dynamics of crossover is elucidated through a study of the Lyapunov spectrum.