Projecting low-dimensional chaos from spatiotemporal dynamics in a model for plastic instability

We investigate the possibility of projecting low-dimensional chaos from spatiotemporal dynamics of a model for a kind of plastic instability observed under constant strain rate deformation conditions. We first discuss the relationship between the spatiotemporal patterns of the model reflected in the nature of dislocation bands and the nature of stress serrations. 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 spatiotemporally 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 Role of Strain Rate Response on Tribological Behavior of Metals

In an effort to study the role of strain rate response on the tribological behavior of metals, room temperature experiments were conducted by sliding commercially pure titanium and a-iron pins against an H-11 die steel flats of various surface textures. The steel flat surface textures were specifically prepared to allow for imposing varying amounts of strain rates at the contacting interface during sliding motion. In the experiments, it was observed that titanium (a harder material than iron) formed a transfer layer on H-11 steel surface textures that produced higher strain rates. In contrast, the titanium pins abraded the steel surfaces that produced lower strain rates. The iron pins were found to abrade the H-11 steel surface regardless of the surface texture characteristics. This unique tribological behavior of titanium is likely due to the fact that titanium undergoes adiabatic shear banding at high strain rates, which creates pathways for lower resistance shear planes. These shear planes lead to fracture and transfer layer formation on the surface of the steel flat, which ultimately promotes a higher strain rate of deformation at the asperity level. Iron does not undergo adiabatic shear banding and thus more naturally abrades the surfaces. Overall, the results clear indicated that a materials strain rate response can be an important factor in controlling the tribological behavior of a plastically deforming material at the asperity level. DOI: 10.1115/1.4007675]

Performance of established native seedlings in relation to invasive Lantana camara, rainfall and species' habitat preferences in a seasonally dry tropical forest

Native species' response to the presence of invasive species is context specific. This response cannot be studied in isolation from the prevailing environmental stresses in invaded habitats such as seasonal drought. We investigated the combined effects of an invasive shrub Lantana camara L. (lantana), seasonal rainfall and species' microsite preferences on the growth and survival of 1,105 naturally established seedlings of native trees and shrubs in a seasonally dry tropical forest. Individuals were followed from April 2008 to February 2010, and growth and survival measured in relation to lantana density, seasonality of rainfall and species characteristics in a 50-ha permanent forest plot located in Mudumalai, southern India. We used a mixed effects modelling approach to examine seedling growth and generalized linear models to examine seedling survival. The overall relative height growth rate of established seedlings was found to be very low irrespective of the presence or absence of dense lantana. 22-month growth rate of dry forest species was lower under dense lantana while moist forest species were not affected by the presence of lantana thickets. 4-month growth rates of all species increased with increasing inter-census rainfall. Community results may be influenced by responses of the most abundant species, Catunaregam spinosa, whose growth rates were always lower under dense lantana. Overall seedling survival was high, increased with increasing rainfall and was higher for species with dry forest preference than for species with moist forest preference. The high survival rates of naturally established seedlings combined with their basal sprouting ability in this forest could enable the persistence of woody species in the face of invasive species.

Predicting the lithospheric stress field and plate motions by joint modeling of lithosphere and mantle dynamics

The way in which basal tractions, associated with mantle convection, couples with the lithosphere is a fundamental problem in geodynamics. A successful lithosphere-mantle coupling model for the Earth will satisfy observations of plate motions, intraplate stresses, and the plate boundary zone deformation. We solve the depth integrated three-dimensional force balance equations in a global finite element model that takes into account effects of both topography and shallow lithosphere structure as well as tractions originating from deeper mantle convection. The contribution from topography and lithosphere structure is estimated by calculating gravitational potential energy differences. The basal tractions are derived from a fully dynamic flow model with both radial and lateral viscosity variations. We simultaneously fit stresses and plate motions in order to delineate a best-fit lithosphere-mantle coupling model. We use both the World Stress Map and the Global Strain Rate Model to constrain the models. We find that a strongly coupled model with a stiff lithosphere and 3-4 orders of lateral viscosity variations in the lithosphere are best able to match the observational constraints. Our predicted deviatoric stresses, which are dominated by contribution from mantle tractions, range between 20-70 MPa. The best-fitting coupled models predict strain rates that are consistent with observations. That is, the intraplate areas are nearly rigid whereas plate boundaries and some other continental deformation zones display high strain rates. Comparison of mantle tractions and surface velocities indicate that in most areas tractions are driving, although in a few regions, including western North America, tractions are resistive. Citation: Ghosh, A., W. E. Holt, and L. M. Wen (2013), Predicting the lithospheric stress field and plate motions by joint modeling of lithosphere and mantle dynamics.

Adaptive constellation rotation scheme for two-user fading MAC with quantized fade state feedback

With no Channel State Information (CSI) at the users, transmission over the two-user Gaussian Multiple Access Channel with fading and finite constellation at the input, will have high error rates due to multiple access interference (MAI). However, perfect CSI at the users is an unrealistic assumption in the wireless scenario, as it would involve extremely large feedback overheads. In this paper we propose a scheme which removes the adverse effect of MAI using only quantized knowledge of fade state at the transmitters such that the associated overhead is nominal. One of the users rotates its constellation relative to the other without varying the transmit power to adapt to the existing channel conditions, in order to meet certain predetermined minimum Euclidean distance requirement in the equivalent constellation at the destination. The optimal rotation scheme is described for the case when both the users use symmetric M-PSK constellations at the input, where M = 2(gimel), gimel being a positive integer. The strategy is illustrated by considering the example where both the users use QPSK signal sets at the input. The case when the users use PSK constellations of different sizes is also considered. It is shown that the proposed scheme has considerable better error performance compared to the conventional non-adaptive scheme, at the cost of a feedback overhead of just log log(2) (M-2/8 - M/4 + 2)] + 1 bits, for the M-PSK case.

Influence of system size on spatiotemporal dynamics of a model for plastic instability: Projecting low-dimensional and extensive chaos

This work is a continuation of our efforts to quantify the irregular scalar stress signals from the Ananthakrishna model for the Portevin-Le Chatelier instability observed under constant strain rate deformation conditions. Stress related to the spatial average of the dislocation activity is a dynamical variable that also determines the time evolution of dislocation densities. We carry out detailed investigations on the nature of spatiotemporal patterns of the model realized in the form of different types of dislocation bands seen in the entire instability domain and establish their connection to the nature of stress serrations. We then characterize the spatiotemporal dynamics of the model equations by computing the Lyapunov dimension as a function of the drive parameter. The latter scales with the system size only for low strain rates, where isolated dislocation bands are seen, and at high strain rates, where fully propagating bands are seen. At intermediate applied strain rates corresponding to the partially propagating bands, the Lyapunov dimension exhibits two distinct slopes, one for small system sizes and another for large. This feature is rationalized by demonstrating that the spatiotemporal patterns for small system sizes are altered from the partially propagating band types to isolated burst type. This in turn allows us to reconfirm that low-dimensional chaos is projected from the stress signals as long as there is a one-to-one correspondence between the bursts of dislocation bands and the stress drops. We then show that the stress signals in the regime of partially to fully propagative bands have features of extensive chaos by calculating the correlation dimension density. We also show that the correlation dimension density also depends on the system size. A number of issues related to the system size dependence of the Lyapunov dimension density and the correlation dimension density are discussed.

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.

Effect of steady rotation on low Reynolds number vortex shedding behind a circular cylinder

In this paper control of oblique vortex shedding in the wake behind a straight circular cylinder is explored experimentally and computationally. Towards this, steady rotation of the cylinder about its axis is used as a control device. Some limited studies are also performed with a stepped circular cylinder, where at the step the flow is inevitably three-dimensional irrespective of the rotation rate. When there is no rotation, the vortex shedding pattern is three dimensional as described in many previous studies. With a non-zero rotation rate, it is demonstrated experimentally as well as numerically that the shedding pattern becomes more and more two-dimensional. At sufficiently high rotation rates, the vortex shedding is completely suppressed.

Total internal reflection Raman spectroscopy of poly(alpha-olefin) oils in a lubricated contact

The rheology of a poly(alpha-olefin) base oil (PAO) in a sliding point contact has been investigated by total internal reflection (TIR) Raman spectroscopy. TIR Raman has the sensitivity to analyse nanometer-thick lubricant films in a tribological contact. The Raman signal generated from the sliding contact was used to determine the lubricant film thickness. The experimentally obtained film thicknesses were compared with theoretical calculations and a transition from Newtonian to non-Newtonian behaviour was observed at high shear rates. The Raman spectra showed no significant changes in the conformation of the PAO chains under the applied conditions of pressure and shear, but the polarisation dependence of the spectra revealed a preferred orientation of the hydrocarbon side chains in the shear-thinned region. Monolayers formed by a boundary lubricant, arachidic acid, dissolved in the PAO could be detected on the surfaces in the elastohydrodynamic regime.

Strategic Marketing and Innovation Performance of Indian MSMEs

Micro Small and Medium Enterprises (MSMEs) is an integral part of the Indian industrial sector. The distinctive features of MSMEs are less capital investment and high labour absorption which has created unprecedented importance to this sector. As per the Development Commissioner of MSME, the sector has the credit of being the second highest in employment in India, which stands next to agricultural sector. The MSMEs are very much needed in efficiently allocating the enormous labour supply and scarce capital by implementing labour intensive production processes. Associated with this high growth rates, MSMEs are also facing a number of problems like sub-optimal scale of operation, technological obsolescence, supply chain inefficiencies, increasing domestic and global competition, fund shortages, change in manufacturing & marketing strategies, turbulent and uncertain market scenario. To survive with such issues and compete with large and global enterprises, MSMEs need to adopt innovative approaches in their regular business operations. Among the manufacturing sectors, we find that they are unable to focus themselves in the present competition. This paper presents a brief literature of work done in MSMEs, Innovation and Strategic marketing with reference to Indian manufacturing firms.