Temperature variation of the grüneisen parameter in magnesium oxide

The thermal expansion of magnesium oxide has been measured below room temperature from 140°K to 284.5°K, using an interferometric method. The accuracy of measurement is better than 3% in the temperature range studied. The agreement of these results with Durand's is quite good, but consistently higher over most of the range by 2 or 3%, for the most part within the estimated experimental error. The Grüneisen parameter remains constant at about 1.51 over the present experimental range; but an isolated measurement of Durand at 85°K suggests that at lower temperatures it rises quite sharply above this value. This possibility is therefore investigated theoretically. With a non-central force model to represent MgO, γ(−3) and γ(2) are calculated and it is found that γ(−3) > γ(2), again suggesting that the Grüneisen parameter increases with falling temperature. Of the two reported experimental values for the infra-red absorption frequency, correlation with the heat capacity strongly indicates a wavelength of 25.26μm rather than 17.3μm. Thermal expansion measurements at still lower temperatures must be carried out to confirm definitely the rise in the Grüneisen parameter.

Novel nonlinear opticalphenomenain nematic liquid crystals

In normal materials, the nonlinear optical effects arise from nonlinearities in the polarisabilities of the constituent atoms or molecules. On the other hand the nonlinear optical effects in liquid crystals arise from totally different processes. Also they occur at relatively low laser intensities. In a laser field a liquid crystal exhibits many novel and interesting nonlinear optical effects. In addition we also find laser field induced effects that are peculiar to liquid crystals, like structural transformations, orientational transitions, modulated structures and phase transitions, to name a few. Here we dwell upon a few of these interesting and important nonlinear optical phenomena that exist in nematic liquid crystals.

Smooth DMS-FEM: A new approach to solving nearly incompressible nonlinear elasto-static problems

The DMS-FEM, which enables functional approximations with C(1) or still higher inter-element continuity within an FEM-based meshing of the domain, has recently been proposed by Sunilkumar and Roy [39,40]. Through numerical explorations on linear elasto-static problems, the method was found to have conspicuously superior convergence characteristics as well as higher numerical stability against locking. These observations motivate the present study, which aims at extending and exploring the DMS-FEM to (geometrically) nonlinear elasto-static problems of interest in solid mechanics and assessing its numerical performance vis-a-vis the FEM. In particular, the DMS-FEM is shown to vastly outperform the FEM (presently implemented through the commercial software ANSYS (R)) as the former requires fewer linearization and load steps to achieve convergence. In addition, in the context of nearly incompressible nonlinear systems prone to volumetric locking and with no special numerical artefacts (e.g. stabilized or mixed weak forms) employed to arrest locking, the DMS-FEM is shown to approach the incompressibility limit much more closely and with significantly fewer iterations than the FEM. The numerical findings are suggestive of the important role that higher order (uniform) continuity of the approximated field variables play in overcoming volumetric locking and the great promise that the method holds for a range of other numerically ill-conditioned problems of interest in computational structural mechanics. (C) 2011 Elsevier Ltd. All rights reserved.

Synthesis and nonlinear optical properties of Lead Telluride nanorods

Lead Telluride (PbTe) nanorods have been uniformly grown on silicon substrates, using the thermal evaporation technique under high vacuum conditions. The structural and morphological studies are done using X-ray diffraction and scanning electron microscopy. Optical nonlinearity studies using the open aperture z-scan employing 5 ns and 100 fs laser pulses reveal a three-photon type absorption. For nanosecond excitation the nonlinear absorption coefficients (gamma) are in the order of 10(-22) m(3) W-2 and for femtosecond excitation it is in the order of 10(-29) m(3) W-2. The role of free carriers and excitons in causing the nonlinearity in both excitation time domains is discussed. Results indicate that PbTe nanorods are good optical limiters with potential device applications. (C) 2011 Elsevier B.V. All rights reserved.

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.

Nonlinear cyclic load analysis for lateral response of batter piles in soft clay with a rigorous degradation model

Nonlinear analysis of batter piles in soft clay is performed using the finite element technique. As the batter piles are not only governed by lateral load but also axial load, the effect of P- Delta moment and geometric stiffness matrix is included in the analysis. For implementing the nonlinear soil behavior, reduction in soil strength (degradation), and formation of gap with number of load cycles, a numerical model is developed where a hyperbolic relation is adopted for the soil in static condition and hyperbolic relation considering degradation and gap for cyclic load condition. The numerical model is validated with published experimental results for cyclic lateral loading and the hysteresis loops are developed to predict the load-deflection behavior and soil resistance behavior during consecutive cycles of loading. This paper highlights the importance of a rigorous degradation model for subsequent cycles of loading on the pile-soil system by a hysteretic representation.

Structural, vibrational and thermal studies of a new nonlinear optical material: L-Asparagine-L-tartaric acid

Crystals of a new nonlinear optical (NLO) material, viz., L-asparagine-L-tartaric acid (LALT)(1) were grown by slow evaporation of an aqueous solution containing equimolar concentrations of L-asparagine and t-tartaric acid. The structure of the title compound which crystallizes in the non-centrosymmetric monoclinic space group P2(1) consists of a molecule of L-asparagine and a molecule of free L-tartaric acid both of which are interlinked by three varieties of H-bonding interactions namely O-H center dot center dot center dot O, N-H center dot center dot center dot O and C-H center dot center dot center dot O. The UV-Vis-NIR spectrum of 1 reveals its transparent nature while the vibrational spectra confirm the presence of the functional groups in 1. The thermal stability and second harmonic generation (SHG) conversion efficiency of 1 were investigated. (C) 2012 Elsevier B.V. All rights reserved.

Solvent effect on the fluorescence quenching of biologically active carboxamide by aniline and carbon tetrachloride in different solvents using S-V plots

The fluorescence quenching studies of carboxamide namely (E)-N-(3-Chlorophenyl)-2-(3,4,5-trimethoxybenzylideneamino)-4,5,6,7 tetrahydrobenzob]thiophene-3-carboxamide ENCTTTC] by aniline and carbon tetrachloride in six different solvents namely toluene, cyclohexane, n-hexane, n-heptane, n-decane and n-pentane have been carried out at room temperature with a view to understand the quenching mechanisms. The Stern-Volmer (S-V) plots have been found to be nonlinear with a positive deviation for all the solvents studied. In order to interpret these results we have invoked the ground state complex formation and sphere of action static quenching models. Using these models various quenching rate parameters have been determined. The magnitudes of these parameters suggest that sphere of action static quenching model agrees well with the experimental results. Hence the positive deviation is attributed to the static and dynamic quenching. Further, with the use of Finite Sink approximation model, it was possible to check these bimolecular reactions as diffusion-limited and to estimate independently distance parameter R' and mutual diffusion coefficient D. Finally an effort has been made to correlate the values of R' and D with the values of the encounter distance R and the mutual coefficient D determined using the Edward's empirical relation and Stokes Einstein relation. (C) 2011 Elsevier B.V. All rights reserved.

Nonlinear viscoelasticity of freestanding and polymer-anchored vertically aligned carbon nanotube foams

Vertical arrays of carbon nanotubes (VACNTs) show unique mechanical behavior in compression, with a highly nonlinear response similar to that of open cell foams and the ability to recover large deformations. Here, we study the viscoelastic response of both freestanding VACNT arrays and sandwich structures composed of a VACNT array partially embedded between two layers of poly(dimethylsiloxane) (PDMS) and bucky paper. The VACNTs tested are similar to 2 mm thick foams grown via an injection chemical vapor deposition method. Both freestanding and sandwich structures exhibit a time-dependent behavior under compression. A power-law function of time is used to describe the main features observed in creep and stress-relaxation tests. The power-law exponents show nonlinear viscoelastic behavior in which the rate of creep is dependent upon the stress level and the rate of stress relaxation is dependent upon the strain level. The results show a marginal effect of the thin PDMS/bucky paper layers on the viscoelastic responses. At high strain levels (epsilon - 0.8), the peak stress for the anchored CNTs reaches similar to 45 MPa, whereas it is only similar to 15MPa for freestanding CNTs, suggesting a large effect of PDMS on the structural response of the sandwich structures. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.3699184]

Wrinkled and slack membranes: nonlinear 3D elasticity solutions via smooth DMS-FEM and experiment

The smooth DMS-FEM, recently proposed by the authors, is extended and applied to the geometrically nonlinear and ill-posed problem of a deformed and wrinkled/slack membrane. A key feature of this work is that three-dimensional nonlinear elasticity equations corresponding to linear momentum balance, without any dimensional reduction and the associated approximations, directly serve as the membrane governing equations. Domain discretization is performed with triangular prism elements and the higher order (C1 or more) interelement continuity of the shape functions ensures that the errors arising from possible jumps in the first derivatives of the conventional C0 shape functions do not propagate because the ill-conditioned tangent stiffness matrices are iteratively inverted. The present scheme employs no regularization and exhibits little sensitivity to h-refinement. Although the numerically computed deformed membrane profiles do show some sensitivity to initial imperfections (nonplanarity) in the membrane profile needed to initiate transverse deformations, the overall patterns of the wrinkles and the deformed shapes appear to be less so. Finally, the deformed profiles, computed through the DMS FEM-based weak formulation, are compared with those obtained through an experiment on an ultrathin Kapton membrane, wherein wrinkles form because of the applied boundary displacement conditions. Comparisons with a reported experiment on a rectangular membrane are also provided. These exercises lend credence to the feasibility of the DMS FEM-based numerical route to computing post-wrinkled membrane shapes. Copyright (c) 2012 John Wiley & Sons, Ltd.

Linearization and Reconstruction of Non-linear Diffuse Optical Tomographic Image

Diffuse optical tomography (DOT) is one of the ways to probe highly scattering media such as tissue using low-energy near infra-red light (NIR) to reconstruct a map of the optical property distribution. The interaction of the photons in biological tissue is a non-linear process and the phton transport through the tissue is modelled using diffusion theory. The inversion problem is often solved through iterative methods based on nonlinear optimization for the minimization of a data-model misfit function. The solution of the non-linear problem can be improved by modeling and optimizing the cost functional. The cost functional is f(x) = x(T)Ax - b(T)x + c and after minimization, the cost functional reduces to Ax = b. The spatial distribution of optical parameter can be obtained by solving the above equation iteratively for x. As the problem is non-linear, ill-posed and ill-conditioned, there will be an error or correction term for x at each iteration. A linearization strategy is proposed for the solution of the nonlinear ill-posed inverse problem by linear combination of system matrix and error in solution. By propagating the error (e) information (obtained from previous iteration) to the minimization function f(x), we can rewrite the minimization function as f(x; e) = (x + e)(T) A(x + e) - b(T)(x + e) + c. The revised cost functional is f(x; e) = f(x) + e(T)Ae. The self guided spatial weighted prior (e(T)Ae) error (e, error in estimating x) information along the principal nodes facilitates a well resolved dominant solution over the region of interest. The local minimization reduces the spreading of inclusion and removes the side lobes, thereby improving the contrast, localization and resolution of reconstructed image which has not been possible with conventional linear and regularization algorithm.

Analysis of Parameter Values in the van der Waals and Platteeuw Theory for Methane Hydrates Using Monte Carlo Molecular Simulations

The van der Waals and Platteuw (vdVVP) theory has been successfully used to model the thermodynamics of gas hydrates. However, earlier studies have shown that this could be due to the presence of a large number of adjustable parameters whose values are obtained through regression with experimental data. To test this assertion, we carry out a systematic and rigorous study of the performance of various models of vdWP theory that have been proposed over the years. The hydrate phase equilibrium data used for this study is obtained from Monte Carlo molecular simulations of methane hydrates. The parameters of the vdWP theory are regressed from this equilibrium data and compared with their true values obtained directly from simulations. This comparison reveals that (i) methane-water interactions beyond the first cage and methane-methane interactions make a significant contribution to the partition function and thus cannot be neglected, (ii) the rigorous Monte Carlo integration should be used to evaluate the Langmuir constant instead of the spherical smoothed cell approximation, (iii) the parameter values describing the methane-water interactions cannot be correctly regressed from the equilibrium data using the vdVVP theory in its present form, (iv) the regressed empty hydrate property values closely match their true values irrespective of the level of rigor in the theory, and (v) the flexibility of the water lattice forming the hydrate phase needs to be incorporated in the vdWP theory. Since methane is among the simplest of hydrate forming molecules, the conclusions from this study should also hold true for more complicated hydrate guest molecules.

Dynamics of strain bifurcations in a magnetostrictive ribbon

We develop a coupled nonlinear oscillator model involving magnetization and strain to explain several experimentally observed dynamical features exhibited by forced magnetostrictive ribbon. Here we show that the model recovers the observed period-doubling route to chaos as function of the dc field for a fixed ac field and quasiperiodic route to chaos as a function of the ac field, keeping the dc field constant. The model also predicts induced and suppressed chaos under the influence of an additional small-amplitude near-resonant ac field. Our analysis suggests rich dynamics in coupled order-parameter systems such as magnetomartensitic and magnetoelectric materials.

Estimation of heavy rainfall during cyclonic storms from microwave observations using nonlinear approach over Indian Ocean

In this study, an effort has been made to study heavy rainfall events during cyclonic storms over Indian Ocean. This estimate is based on microwave observations from tropical rainfall measuring mission (TRMM) Microwave Imager (TMI). Regional scattering index (SI) developed for Indian region based on measurements at 19-, 21- and 85-GHz brightness temperature and polarization corrected temperature (PCT) at 85 GHz have been utilized in this study. These PCT and SI are collocated against Precipitation Radar (PR) onboard TRMM to establish a relationship between rainfall rate, PCT and SI. The retrieval technique using both linear and nonlinear regressions has been developed utilizing SI, PCT and the combination of SI and PCT. The results have been compared with the observations from PR. It was found that a nonlinear algorithm using combination of SI and PCT is more accurate than linear algorithm or nonlinear algorithm using either SI or PCT. Statistical comparison with PR exhibits the correlation coefficients (CC) of 0.68, 0.66 and 0.70, and root mean square error (RMSE) of 1.78, 1.96 and 1.68 mm/h from the observations of SI, PCT and combination of SI and PCT respectively using linear regressions. When nonlinear regression is used, the CC of 0.73, 0.71, 0.79 and RMSE of 1.64, 1.95, 1.54 mm/h are observed from the observations of SI, PCT and combination of SI and PCT, respectively. The error statistics for high rain events (above 10 mm/h) shows the CC of 0.58, 0.59, 0.60 and RMSE of 5.07, 5.47, 5.03 mm/h from the observations of SI, PCT and combination of SI and PCT, respectively, using linear regression, and on the other hand, use of nonlinear regression yields the CC of 0.66, 0.64, 0.71 and RMSE of 4.68, 5.78 and 4.02 mm/h from the observations of SI, PCT and combined SI and PCT, respectively.

Nonlinear Refraction and Two-Photon Absorption in Dense 2Bi(2)O(3)-B2O3 Glasses

High density transparent glasses (7.86 g/cc) were fabricated in the 2Bi(2)O(3)-B2O3 (BBO) system. Optical band gap of the obtained glasses was found to be 2.6eV. The refractive index measured for these glasses was 2.25 +/- 0.05 at lambda=543 nm. Nonlinear refraction and absorption studies were carried out on the BBO glasses using z-scan technique a lambda=532 nm of 10 ns pulse width. The nonlinear refractive index obtained was n(2)=12.1x10(-14) cm(2)/W and nonlinear absorption coefficient was beta=15.2 cm/GW. The n(2) and beta values of the BBO glasses were large compared to the other reported high index bismuth based oxide glass systems in the literature. These were attributed to the high density, high linear refractive index, low band gap and two photon absorption associated with these glasses. The electronic origin of large nonlinearities was discussed based on bond-orbital theory.