Ultrasound-modulated optical tomography: recovery of amplitude of vibration in the insonified region from boundary measurement of light correlation

We address a certain inverse problem in ultrasound-modulated optical tomography: the recovery of the amplitude of vibration of scatterers [p(r)] in the ultrasound focal volume in a diffusive object from boundary measurement of the modulation depth (M) of the amplitude autocorrelation of light [phi(r, tau)] traversing through it. Since M is dependent on the stiffness of the material, this is the precursor to elasticity imaging. The propagation of phi(r, tau) is described by a diffusion equation from which we have derived a nonlinear perturbation equation connecting p(r) and refractive index modulation [Delta n(r)] in the region of interest to M measured on the boundary. The nonlinear perturbation equation and its approximate linear counterpart are solved for the recovery of p(r). The numerical results reveal regions of different stiffness, proving that the present method recovers p(r) with reasonable quantitative accuracy and spatial resolution. (C) 2011 Optical Society of America

Laser damage threshold studies on urea L-malic acid: A nonlinear optical crystal

A detailed study of surface laser damage performed on a nonlinear optical crystal, urea L-malic acid, using 7 ns laser pulses at 10 Hz repetition rate from a Q-switched Nd:YAG laser at wavelengths of 532 and 1064 nm is reported. The single shot and multiple shot surface laser damage threshold values are determined to be 26.64±0.19 and 20.60±0.36 GW cm−2 at 1064 nm and 18.44±0.31 and 7.52±0.22 GW cm−2 at 532 nm laser radiation, respectively. The laser damage anisotropy is consistent with the Vickers mechanical hardness measurement performed along three crystallographic directions. The Knoop polar plot also reflects the damage morphology. Our investigation reveals a direct correlation between the laser damage profile and hardness anisotropy. Thermal breakdown of the crystal is identified as the possible mechanism of laser induced surface damage.

Dynamical behavior in the nonlinear rheology of surfactant solutions

Several surfactant molecules self-assemble in solution to form long, flexible wormlike micelles which get entangled with each other, leading to viscoelastic gel phases. We discuss our recent work on the rheology of such a gel formed in the dilute aqueous solutions of a surfactant CTAT. In the linear rheology regime, the storage modulus G′(ω) and loss modulus G″(ω) have been measured over a wide frequency range. In the nonlinear regime, the shear stress σ shows a plateau as a function of the shear rate math above a certain cutoff shear rate mathc. Under controlled shear rate conditions in the plateau regime, the shear stress and the first normal stress difference show oscillatory time-dependence. The analysis of the measured time series of shear stress and normal stress has been done using several methods incorporating state space reconstruction by embedding of time delay vectors. The analysis shows the existence of a finite correlation dimension and a positive Lyapunov exponent, unambiguously implying that the dynamics of the observed mechanical instability can be described by that of a dynamical system with a strange attractor of dimension varying from 2.4 to 2.9.

Studies on lithium L-ascorbate dihydrate: An interesting chiral nonlinear optical crystal

Lithium L-Ascorbate dihydrate (LLA) is a new metal organic nonlinear optical crystal belonging to the saccharide family. Single crystals of LLA were grown from aqueous solution. Solubility of the crystal has a positive temperature coefficient facilitating growth by slow cooling. Rietveld refinement was used to confirm the phase formation. The crystal has prismatic habit with (010), (001) and (10-1) prominent faces. Thermal analysis shows that the crystal is stable up to 102 degrees C. Transmission spectrum of the crystal extends from 302 nm to 1600 nm. Dielectric spectroscopic analysis revealed Cole Cole behaviour and prominent piezoelectric resonance peaks were observed in the range of 100-200 kHz. Second harmonic generation (SHG) conversion efficiency of up to 2.56 times that of a phase matched KDP crystal was achieved when the (010) plate of LLA single crystal was rotated about the +ve c axis, by 9.4 degrees in the clockwise direction. We also observed SHG conical sections which were attributed to noncollinear phase matching. The observation of the third conical section suggests very high birefringence and large nonlinear coefficients. A detailed study of surface laser damage showed that the crystal has high multiple damage thresholds of 9.7 GW cm(-2) and 42 GW cm(-2) at 1064 nm and 532 nm radiation respectively. (C) 2012 Elsevier B.V. All rights reserved.

Evaluation of kissing bond in composite adhesive lap joints using digital image correlation: Preliminary studies

The assembly of aerospace and automotive structures in recent years is increasingly carried out using adhesives. Adhesive joints have advantages of uniform stress distribution and less stress concentration in the bonded region. Nevertheless, they may suffer due to the presence of defects in bond line and at the interface or due to improper curing process. While defects like voids, cracks and delaminations present in the adhesive bond line may be detected using different NDE methods, interfacial defects in the form of kissing bond may go undetected. Attempts using advanced ultrasonic methods like nonlinear ultrasound and guided wave inspection to detect kissing bond have met with limited success stressing the need for alternate methods. This paper concerns the preliminary studies carried out on detectability of dry contact kissing bonds in adhesive joints using the Digital Image Correlation (DIC) technique. In this attempt, adhesive joint samples containing varied area of kissing bond were prepared using the glass fiber reinforced composite (GFRP) as substrates and epoxy resin as the adhesive layer joining them. The samples were also subjected to conventional and high power ultrasonic inspection. Further, these samples were loaded till failure to determine the bond strength during which digital images were recorded and analyzed using the DIC method. This noncontact method could indicate the existence of kissing bonds at less than 50% failure load. Finite element studies carried out showed a similar trend. Results obtained from these preliminary studies are encouraging and further tests need to be done on a larger set of samples to study experimental uncertainties and scatter associated with the method. (C) 2013 Elsevier Ltd. All rights reserved.

Experimental analysis of composite single-lap joints using digital image correlation and comparison with theoretical models

The demand for energy efficient, low weight structures has boosted the use of composite structures assembled using increased quantities of structural adhesives. Bonded structures may be subjected to severe working environments such as high temperature and moisture due to which the adhesive gets degraded over a period of time. This reduces the strength of a joint and leads to premature failure. Measurement of strains in the adhesive bondline at any point of time during service may be beneficial as an assessment can be made on the integrity of a joint and necessary preventive actions may be taken before failure. This paper presents an experimental approach of measuring peel and shear strains in the adhesive bondline of composite single-lap joints using digital image correlation. Different sets of composite adhesive joints with varied bond quality were prepared and subjected to tensile load during which digital images were taken and processed using digital image correlation software. The measured peel strain at the joint edge showed a rapid increase with the initiation of a crack till failure of the joint. The measured strains were used to compute the corresponding stresses assuming a plane strain condition and the results were compared with stresses predicted using theoretical models, namely linear and nonlinear adhesive beam models. A similar trend in stress distribution was observed. Further comparison of peel and shear strains also exhibited similar trend for both healthy and degraded joints. Maximum peel stress failure criterion was used to predict the failure load of a composite adhesive joint and a comparison was made between predicted and actual failure loads. The predicted failure loads from theoretical models were found to be higher than the actual failure load for all the joints.

Study of phase synchronization in multichannel seizure EEG using nonlinear recurrence measure

Complex biological systems such as the human brain can be expected to be inherently nonlinear and hence difficult to model. Most of the previous studies on investigations of brain function have either used linear models or parametric nonlinear models. In this paper, we propose a novel application of a nonlinear measure of phase synchronization based on recurrences, correlation between probabilities of recurrence (CPR), to study seizures in the brain. The advantage of this nonparametric method is that it makes very few assumptions thus making it possible to investigate brain functioning in a data-driven way. We have demonstrated the utility of CPR measure for the study of phase synchronization in multichannel seizure EEG recorded from patients with global as well as focal epilepsy. For the case of global epilepsy, brain synchronization using thresholded CPR matrix of multichannel EEG signals showed clear differences in results obtained for epileptic seizure and pre-seizure. Brain headmaps obtained for seizure and preseizure cases provide meaningful insights about synchronization in the brain in those states. The headmap in the case of focal epilepsy clearly enables us to identify the focus of the epilepsy which provides certain diagnostic value. Comparative studies with linear correlation have shown that the nonlinear measure CPR outperforms the linear correlation measure. (C) 2014 Elsevier Ltd. All rights reserved.

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.

Nonlinear analysis of a thin pre-twisted and delaminated anisotropic strip

The present work is aimed at the development of an efficient mathematical model to assess the degradation in the stiffness properties of an anisotropic strip due to delamination. In particular, the motive is to capture those nonlinear effects in a strip that arise due to the geometry of the structure, in the presence of delamination. The variational asymptotic method (VAM) is used as a mathematical tool to simplify the original 3D problem to a 1D problem. Further simplification is achieved by modeling the delaminated structure by a sublaminate approach. By VAM, a 2D nonlinear sectional analysis is carried out to determine compact expression for the stiffness terms. The stiffness terms, both linear and nonlinear, are derived as functions of delamination length and location in closed form. In general, the results from the analysis include fully coupled nonlinear 1D stiffness coefficients, 3D strain field, 3D stress field, and in-plane and warping fields. In this work, the utility of the model is demonstrated for a static case, and its capability to capture the trapeze effect in the presence of delamination is investigated and compared with results available in the literature.

Cross-correlation-aided transport in stochastically driven accretion flows

The origin of linear instability resulting in rotating sheared accretion flows has remained a controversial subject for a long time. While some explanations of such non-normal transient growth of disturbances in the Rayleigh stable limit were available for magnetized accretion flows, similar instabilities in the absence of magnetic perturbations remained unexplained. This dichotomy was resolved in two recent publications by Chattopadhyay and co-workers Mukhopadhyay and Chattopadhyay, J. Phys. A 46, 035501 (2013); Nath et al., Phys. Rev. E 88, 013010 (2013)] where it was shown that such instabilities, especially for nonmagnetized accretion flows, were introduced through interaction of the inherent stochastic noise in the system (even a ``cold'' accretion flow at 3000Kis too ``hot'' in the statistical parlance and is capable of inducing strong thermal modes) with the underlying Taylor-Couette flow profiles. Both studies, however, excluded the additional energy influx (or efflux) that could result from nonzero cross correlation of a noise perturbing the velocity flow, say, with the noise that is driving the vorticity flow (or equivalently the magnetic field and magnetic vorticity flow dynamics). Through the introduction of such a time symmetry violating effect, in this article we show that nonzero noise cross correlations essentially renormalize the strength of temporal correlations. Apart from an overall boost in the energy rate (both for spatial and temporal correlations, and hence in the ensemble averaged energy spectra), this results in mutual competition in growth rates of affected variables often resulting in suppression of oscillating Alfven waves at small times while leading to faster saturations at relatively longer time scales. The effects are seen to be more pronounced with magnetic field fluxes where the noise cross correlation magnifies the strength of the field concerned. Another remarkable feature noted specifically for the autocorrelation functions is the removal of energy degeneracy in the temporal profiles of fast growing non-normal modes leading to faster saturation with minimum oscillations. These results, including those presented in the previous two publications, now convincingly explain subcritical transition to turbulence in the linear limit for all possible situations that could now serve as the benchmark for nonlinear stability studies in Keplerian accretion disks.

VAM Applied to Dimensional Reduction of Nonlinear Multifunctional Film-fabric Laminates

This work aims at asymptotically accurate dimensional reduction of non-linear multi-functional film-fabric laminates having specific application in design of envelopes for High Altitude Airships (HAA). The film-fabric laminate for airship envelope consists of a woven fabric core coated with thin films on each face. These films provide UV protection and Helium leakage prevention, while the core provides required structural strength. This problem is both geometrically and materially non-linear. To incorporate the geometric non-linearity, generalized warping functions are used and finite deformations are allowed. The material non-linearity is handled by using hyper-elastic material models for each layer. The development begins with three-dimensional (3-D) nonlinear elasticity and mathematically splits the analysis into a one-dimensional through-the-thickness analysis and a two-dimensional (2-D) plate analysis. The through-the-thickness analysis provides the 2-D constitutive law which is then given as an input to the 2-D reference surface analysis. The dimensional reduction is carried out using Variational Asymptotic Method (VAM) for moderate strains and very small thickness-to-wavelength ratio. It features the identification and utilization of additional small parameters such as ratio of thicknesses and stiffness coefficients of core and films. Closed form analytical expressions for warping functions and 2-D constitutive law of the film-fabric laminate are obtained.