Nonlinear Dynamics of Beams with Stochastic Parameter Variations

The aim of this paper is to investigate the steady state response of beams under the action of random support motions. The study is of relevance in the context of earthquake response of extended land based structures such as pipelines and long span bridges, and, secondary systems such as piping networks in nuclear power plant installations. The following complicating features are accounted for in the response analysis: (a) differential support motions: this is characterized in terms of cross power spectral density functions associated with distinct support motions, (b) nonlinear support conditions, and (c) stochastically inhomogeneous stiffness and mass variations of the beam structure; questions on non-Gaussian models for these variations are considered. The method of stochastic finite elements is combined with equivalent linearization technique and Monte Carlo simulations to obtain response moments.

Unsymmetrical aryl disulfides with excellent transparency in the visible region for second order nonlinear optics

Several unsymmetrically substituted aromatic donor acceptor disulfides have been synthesized and analysed for their second order nonlinear optical properties. These molecules exhibit moderately high first hyperpolarizability (beta) with excellent transparency in the visible region. Most of the unsymmetrical disulfides have a cut-off wavelength below 420 nm. Calculations show that the molecules have an asymmetric charge distribution around the disulfide bond which is responsible for their high beta values. These results provide motivation for the design and synthesis of nonlinear optical chromophores with multiple disulfide bonds for large second order nonlinearity and excellent visible transparency.

Geometrically Nonlinear Dynamics of Composite Four-Bar Mechanisms

This work intends to demonstrate the importance of geometrically nonlinear crosssectional analysis of certain composite beam-based four-bar mechanisms in predicting system dynamic characteristics. All component bars of the mechanism are made of fiber reinforced laminates and have thin rectangular cross-sections. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. They are linked to each other by means of revolute joints. We restrict ourselves to linear materials with small strains within each elastic body (beam). Each component of the mechanism is modeled as a beam based on geometrically nonlinear 3-D elasticity theory. The component problems are thus split into 2-D analyses of reference beam cross-sections and nonlinear 1-D analyses along the four beam reference curves. For thin rectangular cross-sections considered here, the 2-D cross-sectional nonlinearity is overwhelming. This can be perceived from the fact that such sections constitute a limiting case between thin-walled open and closed sections, thus inviting the nonlinear phenomena observed in both. The strong elastic couplings of anisotropic composite laminates complicate the model further. However, a powerful mathematical tool called the Variational Asymptotic Method (VAM) not only enables such a dimensional reduction, but also provides asymptotically correct analytical solutions to the nonlinear cross-sectional analysis. Such closed-form solutions are used here in conjunction with numerical techniques for the rest of the problem to predict multi-body dynamic responses, more quickly and accurately than would otherwise be possible. The analysis methodology can be viewed as a three-step procedure: First, the cross-sectional properties of each bar of the mechanism is determined analytically based on an asymptotic procedure, starting from Classical Laminated Shell Theory (CLST) and taking advantage of its thin strip geometry. Second, the dynamic response of the nonlinear, flexible fourbar mechanism is simulated by treating each bar as a 1-D beam, discretized using finite elements, and employing energy-preserving and -decaying time integration schemes for unconditional stability. Finally, local 3-D deformations and stresses in the entire system are recovered, based on the 1-D responses predicted in the previous step. With the model, tools and procedure in place, we shall attempt to identify and investigate a few problems where the cross-sectional nonlinearities are significant. This will be carried out by varying stacking sequences and material properties, and speculating on the dominating diagonal and coupling terms in the closed-form nonlinear beam stiffness matrix. Numerical examples will be presented and results from this analysis will be compared with those available in the literature, for linear cross-sectional analysis and isotropic materials as special cases.

Subdiffusion as a model of transport through the nuclear pore complex

Cargo transport through the nuclear pore complex continues to be a subject of considerable interest to experimentalists and theorists alike. Several recent studies have revealed details of the process that have still to be fully understood, among them the apparent nonlinearity between cargo size and the pore crossing time, the skewed, asymmetric nature of the distribution of such crossing times, and the non-exponentiality in the decay profile of the dynamic autocorrelation function of cargo positions. In this paper, we show that a model of pore transport based on subdiffusive particle motion is in qualitative agreement with many of these observations. The model corresponds to a process of stochastic binding and release of the particle as it moves through the channel. It suggests that the phenylalanine-glycine repeat units that form an entangled polymer mesh across the channel may be involved in translocation, since these units have the potential to intermittently bind to hydrophobic receptor sites on the transporter protein. (C) 2011 American Institute of Physics. [doi:10.1063/1.3651100]

Low‐voltage varistors based on zinc antimony spinel Zn7Sb2O12

It is possible to prepare low‐voltage varistors from the zinc antimony spinel Zn7Sb2O12 with breakdown voltages in the range of 3–20 V and nonlinearity coefficient α=7–15. The varistor property is due to the formation of high ohmic potential barriers at the grain boundary regions on low‐ohmic n‐type grain interiors of the polycrystalline samples. The method of preparation of the spinel, synthesized by coprecipitation followed by annealing under restricted partial pressures of oxygen, controls the mixed valence states for antimony, namely, Sb3+ and Sb5+. This is critical in attaining high nonlinearity and lower breakdown voltages.

Leakage current behavior in pulsed laser deposited Ba(Zr0.05Ti0.95)O3 thin films

Barium zirconium titanate [Ba(Zr0.05Ti0.95)O3, BZT] thin films were prepared by pulsed laser ablation technique and dc leakage current conduction behavior was extensively studied. The dc leakage behavior study is essential, as it leads to degradation of the data storage devices. The current-voltage (I-V) of the thin films showed an Ohmic behavior for the electric field strength lower than 7.5 MV/m. Nonlinearity in the current density-voltage (J-V) behavior has been observed at an electric field above 7.5 MV/m. Different conduction mechanisms have been thought to be responsible for the overall I-V characteristics of BZT thin films. The J-V behavior of BZT thin films was found to follow Lampert’s theory of space charge limited conduction similar to what is observed in an insulator with charge trapping moiety. The Ohmic and trap filled limited regions have been explicitly observed in the J-V curves, where the saturation prevailed after a voltage of 6.5 V referring the onset of a trap-free square region. Two different activation energy values of 1.155 and 0.325 eV corresponding to two different regions have been observed in the Arrhenius plot, which was attributed to two different types of trap levels present in the film, namely, deep and shallow traps.

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.

Time and Frequency Domain Finite Element Models for Axial Wave Analysis in Hyperelastic Rods

The propagation of axial waves in hyperelastic rods is studied using both time and frequency domain finite element models. The nonlinearity is introduced using the Murnaghan strain energy function and the equations governing the dynamics of the rod are derived assuming linear kinematics. In the time domain, the standard Galerkin finite element method, spectral element method, and Taylor-Galerkin finite element method are considered. A frequency domain formulation based on the Fourier spectral method is also developed. It is found that the time domain spectral element method provides the most efficient numerical tool for the problem considered.

Basic principles of ultrafast Raman loss spectroscopy

When a light beam passes through any medium, the effects of interaction of light with the material depend on the field intensity. At low light intensities the response of materials remain linear to the amplitude of the applied electromagnetic field. But for sufficiently high intensities, the optical properties of materials are no longer linear to the amplitude of applied electromagnetic field. In such cases, the interaction of light waves with matter can result in the generation of new frequencies due to nonlinear processes such as higher harmonic generation and mixing of incident fields. One such nonlinear process, namely, the third order nonlinear spectroscopy has become a popular tool to study molecular structure. Thus, the spectroscopy based on the third order optical nonlinearity called stimulated Raman spectroscopy (SRS) is a tool to extract the structural and dynamical information about a molecular system. Ultrafast Raman loss spectroscopy (URLS) is analogous to SRS but is more sensitive than SRS. In this paper, we present the theoretical basis of SRS (URLS) techniques which have been developed in our laboratory.

Piecewise Linearization Technique for Compact Charge Modeling of Independent DG MOSFET

Charge linearization techniques have been used over the years in advanced compact models for bulk and double-gate MOSFETs in order to approximate the position along the channel as a quadratic function of the surface potential (or inversion charge densities) so that the terminal charges can be expressed as a compact closed-form function of source and drain end surface potentials (or inversion charge densities). In this paper, in case of the independent double-gate MOSFETs, we show that the same technique could be used to model the terminal charges quite accurately only when the 1-D Poisson solution along the channel is fully hyperbolic in nature or the effective gate voltages are same. However, for other bias conditions, it leads to significant error in terminal charge computation. We further demonstrate that the amount of nonlinearity that prevails between the surface potentials along the channel actually dictates if the conventional charge linearization technique could be applied for a particular bias condition or not. Taking into account this nonlinearity, we propose a compact charge model, which is based on a novel piecewise linearization technique and shows excellent agreement with numerical and Technology Computer-Aided Design (TCAD) simulations for all bias conditions and also preserves the source/drain symmetry which is essential for Radio Frequency (RF) circuit design. The model is implemented in a professional circuit simulator through Verilog-A, and simulation examples for different circuits verify good model convergence.

Automatic energy-momentum conserving time integrators for hyperelastic waves

An energy-momentum conserving time integrator coupled with an automatic finite element algorithm is developed to study longitudinal wave propagation in hyperelastic layers. The Murnaghan strain energy function is used to model material nonlinearity and full geometric nonlinearity is considered. An automatic assembly algorithm using algorithmic differentiation is developed within a discrete Hamiltonian framework to directly formulate the finite element matrices without recourse to an explicit derivation of their algebraic form or the governing equations. The algorithm is illustrated with applications to longitudinal wave propagation in a thin hyperelastic layer modeled with a two-mode kinematic model. Solution obtained using a standard nonlinear finite element model with Newmark time stepping is provided for comparison. (C) 2012 Elsevier B.V. All rights reserved.

Urea-based constructs readily amplify and attenuate nonlinear optical activity in response to H-bonding and anion recognition

Urea-based molecular constructs are shown for the first time to be nonlinear optically (NLO) active in solution. We demonstrate self-assembly triggered large amplification and specific anion recognition driven attenuation of the NLO activity. This orthogonal modulation along with an excellent nonlinearity-transparency trade-off makes them attractive NLO probes for studies related to weak self-assembly and anion transportation by second harmonic microscopy.

Radial Deformation of Cylinders Due to Torsion

Classical literature on solid mechanics claims existence of radial deformation due to torsion but there is hardly any literature on analytic solutions capturing this phenomenon. This paper tries to solve this problem in an asymptotic sense using the variational asymptotic method (VAM). The method makes no ad hoc assumptions and hence asymptotic correctness is assured. The VAM splits the 3D elasticity problem into two parts: A 1D problem along the length of the cylinder which gives the twist and a 2D cross-sectional problem which gives the radial deformation. This enables closed form solutions, even for some complex problems. Starting with a hollow cylinder, made up of orthotropic but transversely isotropic material, the 3D problem has been formulated and solved analytically despite the presence of geometric nonlinearity. The general results have been specialized for particularly useful cases, such as solid cylinders and/or cylinders with isotropic material. DOI: 10.1115/1.4006803]

SURE-FAST BILATERAL FILTERS

Edge-preserving smoothing is widely used in image processing and bilateral filtering is one way to achieve it. Bilateral filter is a nonlinear combination of domain and range filters. Implementing the classical bilateral filter is computationally intensive, owing to the nonlinearity of the range filter. In the standard form, the domain and range filters are Gaussian functions and the performance depends on the choice of the filter parameters. Recently, a constant time implementation of the bilateral filter has been proposed based on raisedcosine approximation to the Gaussian to facilitate fast implementation of the bilateral filter. We address the problem of determining the optimal parameters for raised-cosine-based constant time implementation of the bilateral filter. To determine the optimal parameters, we propose the use of Stein's unbiased risk estimator (SURE). The fast bilateral filter accelerates the search for optimal parameters by faster optimization of the SURE cost. Experimental results show that the SURE-optimal raised-cosine-based bilateral filter has nearly the same performance as the SURE-optimal standard Gaussian bilateral filter and the Oracle mean squared error (MSE)-based optimal bilateral filter.

On the Compatibility of a Flux Transport Dynamo with a Fast Tachocline Scenario

The compatibility of the fast-tachocline scenario with a flux-transport dynamo model is explored. We employ a flux-transport dynamo model coupled with simple feedback formulae relating the thickness of the tachocline to the amplitude of the magnetic field or to the Maxwell stress. The dynamo model is found to be robust against the nonlinearity introduced by this simplified fast-tachocline mechanism. Solar-like butterfly diagrams are found to persist and, even without any parameter fitting, the overall thickness of the tachocline is well within the range admitted by helioseismic constraints. In the most realistic case of a time-and latitude-dependent tachocline thickness linked to the value of the Maxwell stress, both the thickness and its latitudinal dependence are in excellent agreement with seismic results. In nonparametric models, cycle-related temporal variations in tachocline thickness are somewhat larger than admitted by helioseismic constraints; we find, however, that introducing a further parameter into our feedback formula readily allows further fine tuning of the thickness variations.