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.

Temperature dependence of indentation recovery ratios in austenitic and martensitic shape memory alloys

Instrumented microindentation (IM) on two Ni-Ti shape memory alloys (SMAs), where one is austenitic and the other is martensitic at room temperature, were conducted from 40 to 150 degrees C. Results show that the depth and work recovery ratios, eta(d) and eta(w) respectively, are complementary to each other. While eta(d) decreases gradually with temperature for austenite, it drops markedly for the martensite in the martensite-to-austenite transformation regime. These results affirm the utility of IM for characterizing SMAs.

Anomalous piezoelectric response due to stabilization of two ferroelectric phases in Zr-modified BaTiO3

The lead-free Ba (Ti1-xZrx)O-3 ceramic has shown enhanced piezo-response (d(33)) in a narrow composition interval (0.01 <= x <= 0.03) exhibiting the coexistence of two ferroelectric phases. The system presents two electric-field-dependent-property regimes: (i) a low field regime (E < 1.7 kV mm(-1)) where d(33) is nearly independent of the poling field, and (ii) (E > 1.7 kV mm(-1)) for which d(33) drops sharply. X-ray diffraction studies revealed that the later phenomenon is related to field driven irreversible structural transformation, which tends to drive the system away from an equilibrium two phase state to a nearly single phase metastable state.

Design and Evaluation of a Robust Optical Beam-Interruption-Based Vehicle Classifier System

This paper presents the design and development of a novel optical vehicle classifier system, which is based on interruption of laser beams, that is suitable for use in places with poor transportation infrastructure. The system can estimate the speed, axle count, wheelbase, tire diameter, and the lane of motion of a vehicle. The design of the system eliminates the need for careful optical alignment, whereas the proposed estimation strategies render the estimates insensitive to angular mounting errors and to unevenness of the road. Strategies to estimate vehicular parameters are described along with the optimization of the geometry of the system to minimize estimation errors due to quantization. The system is subsequently fabricated, and the proposed features of the system are experimentally demonstrated. The relative errors in the estimation of velocity and tire diameter are shown to be within 0.5% and to change by less than 17% for angular mounting errors up to 30 degrees. In the field, the classifier demonstrates accuracy better than 97.5% and 94%, respectively, in the estimation of the wheelbase and lane of motion and can classify vehicles with an average accuracy of over 89.5%.

Image reconstruction enables high resolution imaging at large penetration depths in fluorescence microscopy

Imaging thick specimen at a large penetration depth is a challenge in biophysics and material science. Refractive index mismatch results in spherical aberration that is responsible for streaking artifacts, while Poissonian nature of photon emission and scattering introduces noise in the acquired three-dimensional image. To overcome these unwanted artifacts, we introduced a two-fold approach: first, point-spread function modeling with correction for spherical aberration and second, employing maximum-likelihood reconstruction technique to eliminate noise. Experimental results on fluorescent nano-beads and fluorescently coated yeast cells (encaged in Agarose gel) shows substantial minimization of artifacts. The noise is substantially suppressed, whereas the side-lobes (generated by streaking effect) drops by 48.6% as compared to raw data at a depth of 150 mu m. Proposed imaging technique can be integrated to sophisticated fluorescence imaging techniques for rendering high resolution beyond 150 mu m mark. (C) 2013 AIP Publishing LLC.

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.

Copula-Based Modeling of TMI Brightness Temperature With Rainfall Type

Overland rain retrieval using spaceborne microwave radiometer offers a myriad of complications as land presents itself as a radiometrically warm and highly variable background. Hence, land rainfall algorithms of the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) have traditionally incorporated empirical relations of microwave brightness temperature (Tb) with rain rate, rather than relying on physically based radiative transfer modeling of rainfall (as implemented in the TMI ocean algorithm). In this paper, sensitivity analysis is conducted using the Spearman rank correlation coefficient as benchmark, to estimate the best combination of TMI low-frequency channels that are highly sensitive to the near surface rainfall rate from the TRMM Precipitation Radar (PR). Results indicate that the TMI channel combinations not only contain information about rainfall wherein liquid water drops are the dominant hydrometeors but also aid in surface noise reduction over a predominantly vegetative land surface background. Furthermore, the variations of rainfall signature in these channel combinations are not understood properly due to their inherent uncertainties and highly nonlinear relationship with rainfall. Copula theory is a powerful tool to characterize the dependence between complex hydrological variables as well as aid in uncertainty modeling by ensemble generation. Hence, this paper proposes a regional model using Archimedean copulas, to study the dependence of TMI channel combinations with respect to precipitation, over the land regions of Mahanadi basin, India, using version 7 orbital data from the passive and active sensors on board TRMM, namely, TMI and PR. Studies conducted for different rainfall regimes over the study area show the suitability of Clayton and Gumbel copulas for modeling convective and stratiform rainfall types for the majority of the intraseasonal months. Furthermore, large ensembles of TMI Tb (from the most sensitive TMI channel combination) were generated conditional on various quantiles (25th, 50th, 75th, and 95th) of the convective and the stratiform rainfall. Comparatively greater ambiguity was observed to model extreme values of the convective rain type. Finally, the efficiency of the proposed model was tested by comparing the results with traditionally employed linear and quadratic models. Results reveal the superior performance of the proposed copula-based technique.

Experimental investigation of biofuel drop impact on stainless steel surface

Blends of conventional fuels such as Jet-A1 (aviation kerosene) and diesel with bio-derived components, referred to as biofttels, are gradually replacing the conventional fuels in aircraft and automobile engines. There is a lack of understanding on the interaction of spray drops of such biofuels with solid surfaces. The present study is an experimental investigation on the impact of biofuel drops onto a smooth stainless steel surface. The biofuel is a mixture of 90% commercially available camelina-derived biofuel and 10% aromatics. Biofuel drops were generated using a syringe-hypodermic needle arrangement. On demand, the needle delivers an almost spherical drop with drop diameter in the range 2.05-2.15 mm. Static wetting experiments show that the biofuel drop completely wets the stainless steel surface and exhibits an equilibrium contact angle of 5.6. High speed video camera was used to capture the impact dynamics of biofuel drops with Weber number ranging from 20 to 570. The spreading dynamics and maximum spreading diameter of impacting biofuel drops on the target surface were analyzed. For the impact of high Weber number biofuel drops, the spreading law suggests beta similar to tau(0.5) where beta is the spread factor and tau, the nondimensionalized time. The experimentally observed trend of maximum spread factor, beta(max) of camelina biofuel drop on the target surface with We compares well with the theoretically predicted trend from Ukiwe-Kwok model. After reaching beta(max), the impacting biofuel drop undergoes a prolonged sluggish spreading due to the high wetting nature of the camelina biofuel-stainless steel system. As a result, the final spread factor is found to be a little more than beta(max). (C) 2014 Elsevier Inc. All rights reserved.

Transition from Cassie to impaled state during drop impact on groove-textured solid surfaces

Liquid drops impacted on textured surfaces undergo a transition from the Cassie state characterized by the presence of air pockets inside the roughness valleys below the drop to an impaled state with at least one of the roughness valleys filled with drop liquid. This occurs when the drop impact velocity exceeds a particular value referred to as the critical impact velocity. The present study investigates such a transition process during water drop impact on surfaces textured with unidirectional parallel grooves referred to as groove-textured surfaces. The process of liquid impalement into a groove in the vicinity of drop impact through de-pinning of the three-phase contact line (TPCL) beneath the drop as well as the critical impact velocity were identified experimentally from high speed video recordings of water drop impact on six different groove-textured surfaces made from intrinsically hydrophilic (stainless steel) as well as intrinsically hydrophobic (PDMS and rough aluminum) materials. The surface energy of various 2-D configurations of liquid-vapor interface beneath the drop near the drop impact point was theoretically investigated to identify the locally stable configurations and establish a pathway for the liquid impalement process. A force balance analysis performed on the liquid-vapor interface configuration just prior to TPCL de-pinning provided an expression for the critical drop impact velocity, U-o,U-cr, beyond which the drop state transitions from the Cassie to an impaled state. The theoretical model predicts that Uo, cr increases with the increase in pillar side angle, a, and intrinsic hydrophobicity whereas it decreases with the increase in groove top width, w, of the groove-textured surface. The quantitative predictions of the theoretical model were found to show good agreement with the experimental measurements of U-o,U-cr plotted against the surface texture geometry factor in our model, {tan(alpha/2)/w}(0.5).

Design of fully rotatable, roller-crank-driven, cam mechanisms for arbitrary motion specifications

The design of a non-traditional cam and roller-follower mechanism is described here. In this mechanism, the roller-crank rather than the cam is used as the continuous input member, while both complete a full rotation in each revolution and remain in contact throughout. It is noted that in order to have the cam fully rotate for every full rotation of the roller-crank, the cam cannot be a closed profile, rather the roller traverses the open cam profile twice in each cycle. Using kinematic analysis, the angular velocity of the cam when the roller traverses the cam profile in one direction, is related to the angular velocity of the cam when the roller retraces its path on the cam in the other direction. Thus, one can specify any arbitrary function relating the motion of the cam to the motion of the roller-crank for only 180 degrees of rotation in the angular velocity space. The motion of the cam in the remaining portion is then automatically determined. In specifying the arbitrary motion, many desirable characteristics such as multiple dwells, low acceleration and jerk, etc., can be obtained. Useful design equations are derived for this purpose. Using the kinematic inversion technique, the cam profile is readily obtained once the motion is specified in the angular velocity space. The only limitation to the arbitrary motion specification is making sure that the transmission angle never gets too low, so that the force will be transmitted efficiently from roller to cam. This is addressed by incorporating a transmission index into the motion specification in the synthesis process. Consequently, in this method we can specify any arbitrary motion within a permissible rone, such that the transmission index is higher than the specified minimum value. Single-dwell, double-dwell and a long hesitation motion are used as examples to demonstrate the ffectiveness of the design method. Force closure using an optimally located spring and quasi-kinetostatic analysis are also discussed. (C) 2001 Elsevier Science Ltd. All rights reserved.

Dislocation dynamical approach to force fluctuations in nanoindentation experiments

We develop an approach that combines the power of nonlinear dynamics with the evolution equations for the mobile and immobile dislocation densities and force to explain force fluctuations in nanoindentation experiments. The model includes nucleation, multiplication, and propagation thresholds for mobile dislocations, and other well known dislocation transformation mechanisms. The model predicts all the generic features of nanoindentation such as the Hertzian elastic branch followed by several force drops of decreasing magnitudes, and residual plasticity after unloading. The stress corresponding to the elastic force maximum is close to the yield stress of an ideal solid. The predicted values for all the quantities are close to those reported by experiments. Our model allows us to address the indentation-size effect including the ambiguity in defining the hardness in the force drop dominated regime. At large indentation depths, the hardness remains nearly constant with a marginal decreasing trend.

An experimental study on loading rate effect on acoustic emission based b-values related to reinforced concrete fracture

This article reports on analysis of fracture processes in reinforced concrete (RC) beams with acoustic emission (AE) technique. An emphasis was given to study the effect of loading rate on variation in AE based b-values with the development of cracks in RC structures. RC beams of length 3.2 m were tested under load control at a rate of 4 kN/s, 5 kN/s and 6 kN/s and the b-value analysis available in seismology was used to study the fracture process in RC structures. Moreover, the b-value is related to the strain in steel to assess the damage state. It is observed that when the loading rate is higher, quick cracking development lead to rapid fluctuations and drops in the b-values. Also it is observed that concrete behaves relatively more brittle at higher loading rates (or at higher strain rates). The average b-values are lower as a few but larger amplitudes of AE events occur in contrast to more number of low amplitude AE events occur at low loading rates (or at low strain rates). (C) 2014 Elsevier Ltd. All rights reserved.

Dynamics of intermittent force fluctuations in vesicular nanotubulation

Irregular force fluctuations are seen in most nanotubulation experiments. The dynamics behind their presence has, however, been neither commented upon nor modeled. A simple estimate of the mean energy dissipated in force drops turns out to be several times the thermal energy. This coupled with the rate dependent nature of the deformation reported in several experiments point to a dynamical origin of the serrations. We simplify the whole process of tether formation through a three-stage model of successive deformations of sphere to ellipsoid, neck-formation, and tubule birth and extension. Based on this, we envisage a rate-softening frictional force at the neck that must be overcome before a nanotube can be pulled out. Our minimal model includes elastic and visco-elastic deformation of the vesicle, and has built-in dependence on pull velocity, vesicle radius, and other material parameters, enabling us to capture various kinds of serrated force-extension curves for different parameter choices. Serrations are predicted in the nanotubulation region. Other features of force-extension plots reported in the literature such as a plateauing serrated region beyond a force drop, serrated flow region with a small positive slope, an increase in the elastic threshold with pull velocity, force-extension curves for vesicles with larger radius lying lower than those for smaller radius, are all also predicted by the model. A toy model is introduced to demonstrate that the role of the friction law is limited to inducing stick-slip oscillations in the force, and all other qualitative and quantitative features emerging from the model can only be attributed to other physical mechanisms included in the deformation dynamics of the vesicle. (C) 2014 AIP Publishing LLC.