A dynamical model for the Portevin-le Chatelier bands

We show that an extension of Ananthakrishna's model to include spatial degrees of freedom produces spatially uncorrelated bands, hopping type and the continuously propagating type with increasing applied strain rate. The velocity of the continuously propagating bands is found to vary linearly with applied strain rate. (C) 2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

Molecular Dynamics in [(CH8)aN]z Cd14 A Proton Magnetic Relaxation Study

second moment measurements are carried out on [(CH,),N], CdI, in the temperature range 77 to 400 K. The results are interpreted based on a molecular dynamical model of randomly reorienting methyl groups and isotropically tumbling tetramethyl ammonium group. The relaxation data show contributions from spin-rotation interaction at high temperatures and presence of inequivalent methyl groups. The correlation times and associated activation energies, connected with this model, are calculated from the data. The structure in the absorption line and in the free-induction decay signal at 77 K indicates the possibility of tunnelling motion of the methyl groups. Im Temperaturbereich 77 bis 400 K werden an [(CH,),N],CdI, Protonen-Spin-Gitter-Relaxationsexperimente (bei Larmorfrequenzen von 10,20 und 30 MHz) und Messungen des zweiten Moments durchgefiihrt. Die Ergebnisse werden an Hand eines molekularen dynamischen Modells sich statistisch umorientierender Methylgruppen und isotrop taumelnder Tetramethyl-Ammoniumgruppen interpretiert. Die Relaxationswerte zeigen Beitriige von Spin-Rotations-Wechselwirkung bei hohen Temperaturen und die Anwesenheit von inaquivalenten Methylgruppen. Die Korrelationszeiten und verknupften Aktivierungsenergien, die mit diesem Model1 verbunden sind, werden am den Werten berechnet. Die Struktur in der Absorptionslinie und im Abklingsignal der freien Induktion bei 77 K zeigt die Moglichkeit einer Tunnelbewegung der Methylgruppen.

On evolutionarily stable compositions of populations of interacting genotypes.

Consider an organism in which the genetic fitness of an individual depends to a large extent on its social interactions. Assuming the genotypes to differ only in the choice of strategies they adopt in social interactions, and equating the variation in genetic fitness to the mean payoff to an individual averaged over all possible encounters, we develop a dynamical model for the evolution of genotypic frequencies in such a population. Such a system is characterised by frequency dependent selection, and depending on the initial composition, the population evolves towards one of several possible compositions. We term as evolutionarily stable compositions (ESC) any such composition towards which a population can evolve and which is stable against small fluctuations in the frequencies of existing genotypes as well as to invasions by any other postulated genotype. We state the necessary and sufficient conditions for the identification of all possible ESC's for any number of interacting genotypes. Our results conform to those derived earlier in connection with the concept of evolutionarily stable strategies only in the case of two interacting genotypes; when more than two genotypes interact the conditions under which various ESC's exist become far richer. We consider interactions with mixed strategists and show that in a conflict with pure strategists the optimal mixed strategist will be the only one to ultimately survive. We illustrate our approach by considering the specific case of a primitively social wasp.

Non-diffusive classical transport in a medium with static randomness

The probability distribution for the displacement x of a particle moving in a one-dimensional continuum is derived exactly for the general case of combined static and dynamic gaussian randomness of the applied force. The dynamics of the particle is governed by the high-friction limit of Brownian motion discussed originally by Einstein and Smoluchowski. In particular, the mean square displacement of the particle varies as t2 for t to infinity . This ballistic motion induced by the disorder does not give rise to a 1/f power spectrum, contrary to recent suggestions based on the above dynamical model.

Chaotic and power law states in the Portevin-Le Chatelier effect

Recent studies on the Portevin-Le Chatelier effect report an intriguing crossover phenomenon from low-dimensional chaotic to an infinite-dimensional scale-invariant power law regime in experiments on CuAl single crystals and AlMg polycrystals, as function of strain rate. We devise fully dynamical model which reproduces these results. At low and medium strain rates, the model is chaotic with the structure of the attractor resembling the reconstructed experimental attractor. At high strain rates, power law statistics for the magnitudes and durations of the stress drops emerge as in experiments and concomitantly, the largest Lyapunov exponent is zero.

A kinetic Ising model study of dynamical correlations in confined fluids: Emergence of both fast and slow time scales

Experiments and computer simulation studies have revealed existence of rich dynamics in the orientational relaxation of molecules in confined systems such as water in reverse micelles, cyclodextrin cavities, and nanotubes. Here we introduce a novel finite length one dimensional Ising model to investigate the propagation and the annihilation of dynamical correlations in finite systems and to understand the intriguing shortening of the orientational relaxation time that has been reported for small sized reverse micelles. In our finite sized model, the two spins at the two end cells are oriented in the opposite directions to mimic the effects of surface that in real system fixes water orientation in the opposite directions. This produces opposite polarizations to propagate inside from the surface and to produce bulklike condition at the center. This model can be solved analytically for short chains. For long chains, we solve the model numerically with Glauber spin flip dynamics (and also with Metropolis single-spin flip Monte Carlo algorithm). We show that model nicely reproduces many of the features observed in experiments. Due to the destructive interference among correlations that propagate from the surface to the core, one of the rotational relaxation time components decays faster than the bulk. In general, the relaxation of spins is nonexponential due to the interplay between various interactions. In the limit of strong coupling between the spins or in the limit of low temperature, the nature of relaxation of the spins undergoes a qualitative change with the emergence of a homogeneous dynamics where decay is predominantly exponential, again in agreement with experiments. (C) 2010 American Institute of Physics. doi: 10.1063/1.3474948]

Phase separation in a simple model with dynamical asymmetry

We perform computer simulations of a Cahn-Hilliard model of phase separation that has dynamical asymmetry between the two coexisting phases. The dynamical asymmetry is incorporated by considering a mobility function that is order parameter dependent. Simulations of this model reveal morphological features similar to those observed in viscoelastic phase separation. In the early stages, the minority phase domains form a percolating structure that shrinks with time, eventually leading to the formation of disconnected regions that are characterized by the presence of random interfaces as well as isolated droplets. The domains grow as L(t)similar to t(1/3) in the very late stages. Although dynamical scaling is violated in the area shrinking regime, it is restored at late times. However, the form of the scaling function is found to depend on the extent of dynamical asymmetry. [S1063-651X(99)12101-9].

Time variant reliability model updating in instrumented dynamical systems based on Girsanov's transformation

The problem of updating the reliability of instrumented structures based on measured response under random dynamic loading is considered. A solution strategy within the framework of Monte Carlo simulation based dynamic state estimation method and Girsanov's transformation for variance reduction is developed. For linear Gaussian state space models, the solution is developed based on continuous version of the Kalman filter, while, for non-linear and (or) non-Gaussian state space models, bootstrap particle filters are adopted. The controls to implement the Girsanov transformation are developed by solving a constrained non-linear optimization problem. Numerical illustrations include studies on a multi degree of freedom linear system and non-linear systems with geometric and (or) hereditary non-linearities and non-stationary random excitations.

Time variant reliability model updating in instrumented dynamical systems based on Girsanov’s transformation

The problem of updating the reliability of instrumented structures based on measured response under random dynamic loading is considered. A solution strategy within the framework of Monte Carlo simulation based dynamic state estimation method and Girsanov’s transformation for variance reduction is developed. For linear Gaussian state space models, the solution is developed based on continuous version of the Kalman filter, while, for non-linear and (or) non-Gaussian state space models, bootstrap particle filters are adopted. The controls to implement the Girsanov transformation are developed by solving a constrained non-linear optimization problem. Numerical illustrations include studies on a multi degree of freedom linear system and non-linear systems with geometric and (or) hereditary non-linearities and non-stationary random excitations.

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.

Gaussian Schell-model beams and general shape invariance

We present two six-parameter families of anisotropic Gaussian Schell-model beams that propagate in a shape-invariant manner, with the intensity distribution continuously twisting about the beam axis. The two families differ in the sense or helicity of this beam twist. The propagation characteristics of these shape-invariant beams are studied, and the restrictions on the beam parameters that arise from the optical uncertainty principle are brought out. Shape invariance is traced to a fundamental dynamical symmetry that underlies these beams. This symmetry is the product of spatial rotation and fractional Fourier transformation.

Infinite Dimensional Slow Modulations In A Delayed Model For Orthogonal Cutting Vibrations

We apply the method of multiple scales (MMS) to a well known model of regenerative cutting vibrations in the large delay regime. By ``large'' we mean the delay is much larger than the time scale of typical cutting tool oscillations. The MMS upto second order for such systems has been developed recently, and is applied here to study tool dynamics in the large delay regime. The second order analysis is found to be much more accurate than first order analysis. Numerical integration of the MMS slow flow is much faster than for the original equation, yet shows excellent accuracy. The main advantage of the present analysis is that infinite dimensional dynamics is retained in the slow flow, while the more usual center manifold reduction gives a planar phase space. Lower-dimensional dynamical features, such as Hopf bifurcations and families of periodic solutions, are also captured by the MMS. Finally, the strong sensitivity of the dynamics to small changes in parameter values is seen clearly.

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.

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.

Optimal resource allocation in conflicts with the Lanchester linear law (2,1) model

This paper presents a detailed analysis of a model for military conflicts where the defending forces have to determine an optimal partitioning of available resources to counter attacks from an adversary in two different fronts in an area fire situation. Lanchester linear law attrition model is used to develop the dynamical equations governing the variation in force strength. Here we address a static resource allocation problem namely, Time-Zero-Allocation (TZA) where the resource allocation is done only at the initial time. Numerical examples are given to support the analytical results.