Projecting low and extensive dimensional chaos from spatio-temporal dynamics

We review the spatio-temporal dynamical features of the Ananthakrishna model for the Portevin-Le Chatelier effect, a kind of plastic instability observed under constant strain rate deformation conditions. We then establish a qualitative correspondence between the spatio-temporal structures that evolve continuously in the instability domain and the nature of the irregularity of the scalar stress signal. Rest of the study is on quantifying the dynamical information contained in the stress signals about the spatio-temporal dynamics of the model. We show that at low applied strain rates, there is a one-to-one correspondence with the randomly nucleated isolated bursts of mobile dislocation density and the stress drops. We then show that the model equations are spatio-temporally chaotic by demonstrating the number of positive Lyapunov exponents and Lyapunov dimension scale with the system size at low and high strain rates. Using a modified algorithm for calculating correlation dimension density, we show that the stress-strain signals at low applied strain rates corresponding to spatially uncorrelated dislocation bands exhibit features of low dimensional chaos. This is made quantitative by demonstrating that the model equations can be approximately reduced to space independent model equations for the average dislocation densities, which is known to be low-dimensionally chaotic. However, the scaling regime for the correlation dimension shrinks with increasing applied strain rate due to increasing propensity for propagation of the dislocation bands. The stress signals in the partially propagating to fully propagating bands turn to have features of extensive chaos.

Solvation dynamics of tryptophan in water-dimethyl sulfoxide binary mixture: In search of molecular origin of composition dependent multiple anomalies

Experimental and simulation studies have uncovered at least two anomalous concentration regimes in water-dimethyl sulfoxide (DMSO) binary mixture whose precise origin has remained a subject of debate. In order to facilitate time domain experimental investigation of the dynamics of such binary mixtures, we explore strength or extent of influence of these anomalies in dipolar solvation dynamics by carrying out long molecular dynamics simulations over a wide range of DMSO concentration. The solvation time correlation function so calculated indeed displays strong composition dependent anomalies, reflected in pronounced non-exponential kinetics and non-monotonous composition dependence of the average solvation time constant. In particular, we find remarkable slow-down in the solvation dynamics around 10%-20% and 35%-50% mole percentage. We investigate microscopic origin of these two anomalies. The population distribution analyses of different structural morphology elucidate that these two slowing down are reflections of intriguing structural transformations in water-DMSO mixture. The structural transformations themselves can be explained in terms of a change in the relative coordination number of DMSO and water molecules, from 1DMSO:2H(2)O to 1H(2)O:1DMSO and 1H(2)O:2DMSO complex formation. Thus, while the emergence of first slow down (at 15% DMSO mole percentage) is due to the percolation among DMSO molecules supported by the water molecules (whose percolating network remains largely unaffected), the 2nd anomaly (centered on 40%-50%) is due to the formation of the network structure where the unit of 1DMSO:1H(2)O and 2DMSO:1H(2)O dominates to give rise to rich dynamical features. Through an analysis of partial solvation dynamics an interesting negative cross-correlation between water and DMSO is observed that makes an important contribution to relaxation at intermediate to longer times.

Effect of electro-mechanical coupling on actuation behavior of a carbon nanotube cellular structure

We demonstrate the effect of mechanical strain on the electrostrictive behavior of catalytically grown cellular structure of carbon nanotube (CNT). In the small strain regime, where the stress-strain behavior of the material is linear, application of an electric-field along the mechanical loading direction induces an instantaneous increase in the stress and causes an increase in the apparent Young's modulus. The instantaneous increase in the stress shows a cubic-polynomial dependence on the electric-field, which is attributed to the non-linear coupling of the mechanical strain and the electric-field induced polarization of the CNT. The electrostriction induced actuation becomes >100 times larger if the CNT sample is pre-deformed to a small strain. However, in the non-linear stress-strain regime, although a sharp increase in the apparent Young's modulus is observed upon application of an electric-field, no instantaneous increase in the stress occurs. This characteristic suggests that the softening due to the buckling of individual CNT compensates for any instantaneous rise in the electrostriction induced stress at the higher strains. We also present an analytical model to elucidate the experimental observations. (C) 2013 Elsevier Ltd. All rights reserved.

Relation Between the Diffusivity, Viscosity, and Ionic Radius of LiCl in Water, Methanol, and Ethylene Glycol: A Molecular Dynamics Simulation

A molecular dynamics (MD) investigation of LiCl in water, methanol, and ethylene glycol (EG) at 298 K is reported. Several; structural and dynamical properties of the ions as well as the solvent such as self-diffusivity, radial distribution functions, void and neck distributions, velocity autocorrelation functions, and mean residence times of solvent in the first solvation shell have been computed. The results show that the reciprocal relationship between the self-diffusivity of the ions and the viscosity is valid in almost all solvents with the exception of water. From an analysis of radial distribution functions and coordination numbers the nature of hydrogen bonding within the solvent and its influence on the void and neck distribution becomes evident. It is seen that the solvent solvent interaction is important in EG while solute solvent interactions dominate in water and methanol. From Voronoi tessellation, it is seen that the voids and necks within methanol are larger as compared to those within water or EG. On the basis of the void and neck distributions obtained from MD simulations and literature experimental data of limiting ion conductivity for various ions of different sizes we show that there is a relation between the void and neck radius on e one hand and dependence of conductivity on the ionic radius on the other. It is shown that the presence of large diameter voids and necks in methanol is responsible for maximum in limiting ion conductivity (lambda(0)) of TMA(+), while in water in EG, the maximum is seen for Rb+. In the case of monovalent anions, maximum in lambda(0) as a function ionic radius is seen for Br- in water EG but for the larger ClO4- ion in methanol. The relation between the void and neck distribution and the variation in lambda(0) with ionic radius arises via the Levitation effect which is discussed. These studies show the importance of the solvent structure and the associated void structure.

Dynamics of prolate spheroidal mass distributions with varying eccentricity

In this paper we calculate the potential for a prolate spheroidal distribution as in a dark matter halo with a radially varying eccentricity. This is obtained by summing up the shell-by-shell contributions of isodensity surfaces, which are taken to be concentric and with a common polar axis and with an axis ratio that varies with radius. Interestingly, the constancy of potential inside a shell is shown to be a good approximation even when the isodensity contours are dissimilar spheroids, as long as the radial variation in eccentricity is small as seen in realistic systems. We consider three cases where the isodensity contours are more prolate at large radii, or are less prolate or have a constant eccentricity. Other relevant physical quantities like the rotation velocity, the net orbital and vertical frequency due to the halo and an exponential disc of finite thickness embedded in it are obtained. We apply this to the kinematical origin of Galactic warp, and show that a prolate-shaped halo is not conducive to making long-lived warps - contrary to what has been proposed in the literature. The results for a prolate mass distribution with a variable axis ratio obtained are general, and can be applied to other astrophysical systems, such as prolate bars, for a more realistic treatment.

Dynamics and fracture of ligaments from a droplet on a vibrating surface

A droplet residing on a vibrating surface and in the pressure antinode of an asymmetric standing wave can spread radially outward and atomize. In this work, proper orthogonal decomposition through high speed imaging is shown to predict the likelihood of atomization for various viscous fluids based on prior information in the droplet spreading phase. Capillary instabilities are seen to affect ligament rupture. Viscous dissipation plays an important role in determining the wavelength of the most unstable mode during the inception phase of the ligaments. However, the highest ligament capillary number achieved was less than 1, and the influence of viscosity in the ligament growth and breakup phases is quite minimal. It is inferred from the data that the growth of a typical ligament is governed by a balance between the inertial force obtained from the inception phase and capillary forces. By including the effect of acoustic pressure field around the droplet, the dynamics of the ligament growth phase is revealed and the ligament growth profiles for different fluids are shown to collapse on a straight line using a new characteristic time scale.

Dynamics of a flexible splitter plate in the wake of a circular cylinder

Rigid splitter plates in the wake of bluff bodies are known to suppress the primary vortex shedding. In the present work, we experimentally study the problem of a flexible splitter plate in the wake of a circular cylinder. In this case, the splitter plate is free to continuously deform along its length due to the fluid forces acting on it; the flexural rigidity (EI) of the plate being an important parameter. Direct visualizations of the splitter plate motions, for very low values of flexural rigidity (EI), indicate periodic traveling wave type deformations of the splitter plate with maximum tip amplitudes of the order of I cylinder diameter. As the Reynolds number based on cylinder diameter is varied, two regimes of periodic splitter plate motions are found that are referred to as mode I and mode II, with a regime of aperiodic motions between them. The frequency of plate motions in both periodic modes is found to be close to the plane cylinder Strouhal number of about 0.2, while the average frequencies in the non-periodic regime are substantially lower. The measured normalized phase speed of the traveling wave for both periodic modes is also close to the convection speed of vortices in the plane cylinder wake. As the flexural rigidity of the plate (EI) is increased, the response of the plate was found to shift to the right when plotted with flow speed or Re. To better capture the effect of varying EI, we define and use a non-dimensional bending stiffness, K*, similar to the ones used in the flag flutter problem, K*=EI/(0.5 rho(UL3)-L-2), where U is the free-stream velocity and L is the splitter plate length. Amplitude data for different EI cases when plotted against this parameter appear to collapse on to a single curve for a given splitter plate length. Measurements of the splitter plate motions for varying splitter plate lengths indicate that plates that are substantially larger than the formation length of the plane cylinder wake have similar responses, while shorter plates show significant differences.