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.

Stochastically driven instability in rotating shear flows

The origin of hydrodynamic turbulence in rotating shear flows is investigated, with particular emphasis on the flows whose angular velocity decreases but whose specific angular momentum increases with the increasing radial coordinate. Such flows are Rayleigh stable, but must be turbulent in order to explain the observed data. Such a mismatch between the linear theory and the observations/experiments is more severe when any hydromagnetic/magnetohydrodynamic instability and then the corresponding turbulence therein is ruled out. This work explores the effect of stochastic noise on such hydrodynamic flows. We essentially concentrate on a small section of such a flow, which is nothing but a plane shear flow supplemented by the Coriolis effect. This also mimics a small section of an astrophysical accretion disc. It is found that such stochastically driven flows exhibit large temporal and spatial correlations of perturbation velocities and hence large energy dissipations of perturbation, which presumably generate the instability. A range of angular velocity (Omega) profiles of the background flow, starting from that of a constant specific angular momentum (lambda = Omega r(2); r being the radial coordinate) to a constant circular velocity (v(phi) = Omega r), is explored. However, all the background angular velocities exhibit identical growth and roughness exponents of their perturbations, revealing a unique universality class for the stochastically forced hydrodynamics of rotating shear flows. This work, to the best of our knowledge, is the first attempt to understand the origin of instability and turbulence in three-dimensional Rayleigh stable rotating shear flows by introducing additive noise to the underlying linearized governing equations. This has important implications to resolve the turbulence problem in astrophysical hydrodynamic flows such as accretion discs.

A THREE-WHEELED MOBILE ROBOT FOR TRAVERSING UNEVEN TERRAIN WITHOUT SLIP: SIMULATION AND EXPERIMENTS

A wheeled mobile robot (WMR) can move on uneven terrains without slip if the wheels are allowed to tilt laterally. This paper deals with the analysis, design and experimentations with a WMR where the wheels can tilt laterally. The wheels of such a WMR must be equipped with two degrees of freedom suspension mechanism. A prototype three-wheeled mobile robot is fabricated with a two degree-of-freedom suspension mechanism. Simulations show that the three-wheeled mobile robot can traverse uneven terrains with very little slip and experiments with the prototype on a representative uneven terrain confirm that the slip is significantly reduced.

Sustainability of apparent slip in micro-channel flows

In the present work, we experimentally study the flow of water over textured hydrophobic surfaces in a micro-channel. Shear stress measurements are done along with direct visualization of trapped air pockets on the hydrophobic surface. The trapped air pockets on such surfaces are known to be responsible for apparent slip at these surfaces and hence in significant drag reduction. In typical circumstances, the apparent slip reduces over time as seen, for example, from our shear stress measurements. This implies that the drag reduction will not be sustained. We have performed extensive visualizations of the trapped air pockets while varying flow parameters like the flow rate and the pressure. We present here direct visualizations that show that under some conditions, the air pockets can grow with time. The variation of the air pocket size with time is found to change qualitatively and quantitatively as the flow rate is varied. These measured changes in the air pocket size with time have a direct bearing on the sustainability of apparent slip in micro-channel flows.

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.

Crow instability in unitary Fermi gas

In this paper, we investigate the initiation and subsequent evolution of Crow instability in an inhomogeneous unitary Fermi gas using zero-temperature Galilei-invariant nonlinear Schrodinger equation. Considering a cigar-shaped unitary Fermi gas, we generate the vortex-antivortex pair either by phase-imprinting or by moving a Gaussian obstacle potential. We observe that the Crow instability in a unitary Fermi gas leads to the decay of the vortex-antivortex pair into multiple vortex rings and ultimately into sound waves.

A multifold reduction in the transition Reynolds number, and ultra-fast mixing, in a micro-channel due to a dynamical instability induced by a soft wall

A dynamical instability is observed in experimental studies on micro-channels of rectangular cross-section with smallest dimension 100 and 160 mu m in which one of the walls is made of soft gel. There is a spontaneous transition from an ordered, laminar flow to a chaotic and highly mixed flow state when the Reynolds number increases beyond a critical value. The critical Reynolds number, which decreases as the elasticity modulus of the soft wall is reduced, is as low as 200 for the softest wall used here (in contrast to 1200 for a rigid-walled channel) The instability onset is observed by the breakup of a dye-stream introduced in the centre of the micro-channel, as well as the onset of wall oscillations due to laser scattering from fluorescent beads embedded in the wall of the channel. The mixing time across a channel of width 1.5 mm, measured by dye-stream and outlet conductance experiments, is smaller by a factor of 10(5) than that for a laminar flow. The increased mixing rate comes at very little cost, because the pressure drop (energy requirement to drive the flow) increases continuously and modestly at transition. The deformed shape is reconstructed numerically, and computational fluid dynamics (CFD) simulations are carried out to obtain the pressure gradient and the velocity fields for different flow rates. The pressure difference across the channel predicted by simulations is in agreement with the experiments (within experimental errors) for flow rates where the dye stream is laminar, but the experimental pressure difference is higher than the simulation prediction after dye-stream breakup. A linear stability analysis is carried out using the parallel-flow approximation, in which the wall is modelled as a neo-Hookean elastic solid, and the simulation results for the mean velocity and pressure gradient from the CFD simulations are used as inputs. The stability analysis accurately predicts the Reynolds number (based on flow rate) at which an instability is observed in the dye stream, and it also predicts that the instability first takes place at the downstream converging section of the channel, and not at the upstream diverging section. The stability analysis also indicates that the destabilization is due to the modification of the flow and the local pressure gradient due to the wall deformation; if we assume a parabolic velocity profile with the pressure gradient given by the plane Poiseuille law, the flow is always found to be stable.

Spark plasma sintering may lead to phase instability and inferior mechanical properties: A case study with TiB2

In contrast to the widely reported beneficial aspects of spark plasma sintering in developing materials with better properties, we report here two interesting aspects recorded with difficult-to-sinter titanium diboride: (a) in situ formation of second phase (TiB) and (b) inferior hardness (by similar to 30%) and elastic modulus (by similar to 20%) for spark plasma sintered TiB2, with respect to hot pressed TiB2. The formation of TiB is discussed with reference to the enhanced reaction kinetics in the presence of pulsed electric field. (C) 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Jeans instability criterion modified by external tidal field

The well-known Jeans criterion describes the onset of instabilities in an infinite, homogeneous, self-gravitating medium supported by pressure. Most realistic astrophysical systems, however, are not isolated - instead they are under the influence of an external field such as the tidal field due to a neighbour. Here, we do a linear perturbation analysis for a system in an external field and obtain a generalized dispersion relation that depends on the wavenumber, the sound speed and also the magnitude of the tidal field. A typical, disruptive tidal field is shown to make the system more stable against perturbations, and results in a higher effective Jeans wavelength. The minimum mass that can become unstable is then higher (super-Jeans) than the usual Jeans mass. Conversely, in a compressive tidal field, perturbations can grow even when the mass is lower (sub-Jeans). This approach involving the inclusion of tidal field opens up a new way of looking at instabilities in gravitating systems. The treatment is general and the simple analytical form of the modified Jeans criterion obtained makes it easily accessible.

Micropillar and macropillar compression responses of magnesium single crystals oriented for single slip or extension twinning

Uniaxial compression experiments were conducted on two magnesium (Mg) single crystals whose crystallographic orientations facilitate the deformation either by basal slip or by extension twinning. Specimen size effects were examined by conducting experiments on mu m- and mm-sized samples. A marked specimen size effect was noticed, with micropillars exhibiting significantly higher flow stress than bulk samples. Further, it is observed that the twin nucleation stress exerts strong size dependence, with micropillars requiring substantially higher stress than the bulk samples. The flow curves obtained on the bulk samples are smooth whereas those obtained from micropillars exhibit intermittent and precipitous stress drops. Electron backscattered diffraction and microstructural analyses of the deformed samples reveal that the plastic deformation in basal slip oriented crystals occurs only by slip while twin oriented crystals deform by both slip and twinning modes. The twin oriented crystals exhibit a higher strain hardening during plastic deformation when compared to the single slip oriented crystals. The strain hardening rate, theta, of twin oriented crystals is considerably greater in micropillars compared to the bulk single crystals, suggesting the prevalence of different work hardening mechanisms at these different sample sizes. (C) 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Effect of the Flow Rule on the Bearing Capacity of Strip Foundations on Sand by the Upper-Bound Limit Analysis and Slip Lines

The influence of the flow rule on the bearing capacity of strip foundations placed on sand was investigated using a new kinematic approach of upper-bound limit analysis. The method of stress characteristics was first used to find the mechanism of the failure and to compute the stress field by using the Mohr-Coulomb yield criterion. Once the failure mechanism had been established, the kinematics of the plastic deformation was established, based on the requirements of the upper-bound limit theorem. Both associated and nonassociated plastic flows were considered, and the bearing capacity was obtained by equating the rate of external plastic work to the rate of the internal energy dissipation for both smooth and rough base foundations. The results obtained from the analysis were compared with those available from the literature. (C) 2014 American Society of Civil Engineers.

Nonlinear viscoelasticity of entangled wormlike micellar fluid under large-amplitude oscillatory shear: Role of elastic Taylor-Couette instability

The role of elastic Taylor-Couette flow instabilities in the dynamic nonlinear viscoelastic response of an entangled wormlike micellar fluid is studied by large-amplitude oscillatory shear (LAOS) rheology and in situ polarized light scattering over a wide range of strain and angular frequency values, both above and below the linear crossover point. Well inside the nonlinear regime, higher harmonic decomposition of the resulting stress signal reveals that the normalized third harmonic I-3/I-1 shows a power-law behavior with strain amplitude. In addition, I-3/I-1 and the elastic component of stress amplitude sigma(E)(0) show a very prominent maximum at the strain value where the number density (n(v)) of the Taylor vortices is maximum. A subsequent increase in applied strain (gamma) results in the distortions of the vortices and a concomitant decrease in n(v), accompanied by a sharp drop in I-3 and sigma(E)(0). The peak position of the spatial correlation function of the scattered intensity along the vorticity direction also captures the crossover. Lissajous plots indicate an intracycle strain hardening for the values of gamma corresponding to the peak of I-3, similar to that observed for hard-sphere glasses.

Slow Slip Acceleration beneath Andaman Islands Triggered by the 11 April 2012 Indian Ocean Earthquakes

The M-w 8.6 and 8.2 strike-slip earthquakes that struck the northeast Indian Ocean on 11 April 2012 resulted in coseismic deformation both at near and distant sites. The slip distribution, deduced using seismic-wave analysis for the orthogonal faults that ruptured during these earthquakes, is sufficient to predict the coseismic displacements at the Global Positioning System (GPS) sites, such as NTUS, PALK, and CUSV, but fall short at four continuous sites in the Andaman Islands region. Slip modeling, for times prior to the events, suggests that the lower portion of the thrust fault beneath the Andaman Islands has been slipping at least at the rate of 40 cm/yr, in response to the 2004 Sumatra-Andaman coseismic stress change. Modeling of GPS displacements suggests that the en echelon and orthogonal fault ruptures of the 2012 intraplate oceanic earthquakes could have possibly accelerated the ongoing slow slip, along the lower portion of the thrust fault beneath the islands with a month-long slip of 4-10 cm. The misfit to the coseismic GPS displacements along the Andaman Islands could be improved with a better source model, assuming that no local process contributed to this anomaly.

Effect of surfactants on the instability of a two-layer film flow down an inclined plane

The effect of insoluble surfactants on the instability of a two-layer film flow down an inclined plane is investigated based on the Orr-Sommerfeld boundary value problem. The study, focusing on Stokes flow P. Gao and X.-Y. Lu, ``Effect of surfactants on the inertialess instability of a two-layer film flow,'' J. Fluid Mech. 591, 495-507 (2007)], is further extended by including the inertial effect. The surface mode is recognized along with the interface mode. The initial growth rate corresponding to the interface mode accelerates at sufficiently long-wave regime in the presence of surface surfactant. However, the maximum growth rate corresponding to both interface and surface modes decelerates in the presence of surface surfactant when the upper layer is more viscous than the lower layer. On the other hand, when the upper layer is less viscous than the lower layer, a new interfacial instability develops due to the inertial effect and becomes weaker in the presence of interfacial surfactant. In the limit of negligible surface and interfacial tensions, respectively, two successive peaks of temporal growth rate appear in the long-wave and short-wave regimes when the interface mode is analyzed. However, in the case of the surface mode, only the long-wave peak appears. (C) 2014 AIP Publishing LLC.

Secondary instability as a possible mechanism for clear-air turbulence: a case study

Many theories and mechanisms have been proposed to explain the phenomenon of clear-air turbulence (CAT), and some of them have been successful in predicting light, moderate and, in some cases, severe turbulence. It is only recently that skill in the forecasting of the severe form of CAT, which could lead to injuries to passengers and damage to aircraft, has improved. Recent observations and simulations suggest that some severe to extreme turbulence could be caused by horizontal vortex tubes resulting from secondary instabilities of regions of high shear in the atmosphere. We have conducted direct numerical simulations to understand the scale relationship between primary structures (larger-scale structures related to one of the causes mentioned above) and secondary structures (smaller-sized, shear structures of the size of aircraft). From shear layer simulations, we find that the ratio of sizes of primary and secondary vortices is of the right order to generate aircraft-scale vortex tubes from typical atmospheric shear layers. We have also conducted simulations with a mesoscale atmospheric model, to understand possible causes of turbulence experienced by a flight off the west coast of India. Our simulations show the occurrence of primary flow structures related to synoptic conditions around the time of the incident. The evidence presented for this mechanism also has implications for possible methods of detection and avoidance of severe CAT.