Possibility of chaos in interval friction experiments of martensites

Wuttig and Suzuki's model on anelastic nonlinearities in solids in the vicinity of martensite transformations is analysed numerically. This model shows chaos even in the absence of applied forcing field as a function of a temperature dependent parameter. Even though the model exhibits sustained oscillations as a function of the amplitude of the forcing term, it does not exactly capture the features of the experimental time series. We have improved the model by adding a symmetry breaking term. The improved model shows period doubling bifurcation as a function of the amplitude of the forcing term. The solutions of our improved model shows good resemblance with the nonsymmetric period four oscillation seen in the experiment. (C) 1999 Elsevier Science B.V. All rights reserved.

Carbon Nanotube based Composite Fibers for Strain Sensing, Signal Processing and Computing

Carbon nanotubes dispersed in polymer matrix have been aligned in the form of fibers and interconnects and cured electrically and by UV light. Conductivity and effective semiconductor tunneling against reverse to forward bias field have been designed to have differentiable current-voltage response of each of the fiber/channel. The current-voltage response is a function of the strain applied to the fibers along axial direction. Biaxial and shear strains are correlated by differentiating signals from the aligned fibers/channels. Using a small doping of magnetic nanoparticles in these composite fibers, magneto-resistance properties are realized which are strong enough to use the resulting magnetostriction as a state variable for signal processing and computing. Various basic analog signal processing tasks such as addition, convolution and filtering etc. can be performed. These preliminary study shows promising application of the concept in combined analog-digital computation in carbon nanotube based fibers. Various dynamic effects such as relaxation, electric field dependent nonlinearities and hysteresis on the output signals are studied using experimental data and analytical model.

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.

Nonlinear dynamic state estimation in instrumented structures with conditionally linear Gaussian substructures

Many problems of state estimation in structural dynamics permit a partitioning of system states into nonlinear and conditionally linear substructures. This enables a part of the problem to be solved exactly, using the Kalman filter, and the remainder using Monte Carlo simulations. The present study develops an algorithm that combines sequential importance sampling based particle filtering with Kalman filtering to a fairly general form of process equations and demonstrates the application of a substructuring scheme to problems of hidden state estimation in structures with local nonlinearities, response sensitivity model updating in nonlinear systems, and characterization of residual displacements in instrumented inelastic structures. The paper also theoretically demonstrates that the sampling variance associated with the substructuring scheme used does not exceed the sampling variance corresponding to the Monte Carlo filtering without substructuring. (C) 2012 Elsevier Ltd. All rights reserved.

Large nonlinear refraction and two photon absorption in ferroelectric Bi2VO5.5 thin films

Ferroelectric c-oriented Bi2VO5.5 (BVO) thin films (thickness approximate to 300 nm) were fabricated by pulsed laser deposition on corning glass substrates. Nonlinear refractive index (n(2)) and two photon absorption coefficient (beta) were measured by Z-scan technique at 532 nm wavelength delivering pulses with 10 ns duration. Relatively large values of n(2) = 2.05 +/- 0.2 x 10(-10) cm(2)/W and beta = 9.36 +/- 0.3 cm/MW were obtained for BVO thin films. Origin of the large optical nonlinearities in BVO thin films was discussed based on bond-orbital theory of transition metal oxides. (c) 2012 Elsevier B.V. All rights reserved.

A two-axis in-plane motion measurement system based on optical beam deflection

Measurement of in-plane motion with high resolution and large bandwidth enables model-identification and real-time control of motion-stages. This paper presents an optical beam deflection based system for measurement of in-plane motion of both macro- and micro-scale motion stages. A curved reflector is integrated with the motion stage to achieve sensitivity to in-plane translational motion along two axes. Under optimal settings, the measurement system is shown to theoretically achieve sub-angstrom measurement resolution over a bandwidth in excess of 1 kHz and negligible cross-sensitivity to linear motion. Subsequently, the proposed technique is experimentally demonstrated by measuring the in-plane motion of a piezo flexure stage and a scanning probe microcantilever. For the former case, reflective spherical balls of different radii are employed to measure the in-plane motion and the measured sensitivities are shown to agree with theoretical values, on average, to within 8.3%. For the latter case, a prototype polydimethylsiloxane micro-reflector is integrated with the microcantilever. The measured in-plane motion of the microcantilever probe is used to identify nonlinearities and the transient dynamics of the piezo-stage upon which the probe is mounted. These are subsequently compensated by means of feedback control. (C) 2013 AIP Publishing LLC.

Base Triggered Enhancement of First Hyperpolarizability of a Keto-Enol Tautomer

This work describes the base triggered enhancement of first hyperpolarizability of a tautomeric organic molecule, namely, benzoylacetanilide (BA). We have used the hyper-Rayleigh scattering technique to measure the first hyperpolarizability (beta) of BA which exists in the pure keto form in water and as a keto-enol tautomer in ethanol. Its anion exists in equilibrium with the keto and enol forms at pH 11 in aqueous solution. The beta value of the anion form is 709 X 10(-30) esu, whereas that of the enol is 232 x 10(-3) esu and of the keto is 88 X 10(-30) esu. There is an enhancement of beta by similar to 8 times for the anion and similar to 3 times for the enol compared to the keto form. All these are achieved by altering the equilibrium between the three forms of BA by simple means. MP2 calculations reproduce the experimental trend, but the computed beta values are much lower than the measured values. DFT calculations with the standard B3LYP functional could not predict the right order in the beta values. The difference between experimental and calculated values is, perhaps, due to the fact that electron correlation effects are important in computing optical nonlinearities of large organic molecules and MP2 and B3LYP calculations done here for different forms of BA could not account for such effects adequately.

The irregularities of the sunspot cycle and their theoretical modelling

The 11-year sunspot cycle has many irregularities, the most prominent amongst them being the grand minima when sunspots may not be seen for several cycles. After summarizing the relevant observational data about the irregularities, we introduce the flux transport dynamo model, the currently most successful theoretical model for explaining the 11-year sunspot cycle. Then we analyze the respective roles of nonlinearities and random fluctuations in creating the irregularities. We also discuss how it has recently been realized that the fluctuations in meridional circulation also can be a source of irregularities. We end by pointing out that fluctuations in the poloidal field generation and fluctuations in meridional circulation together can explain the occurrences of grand minima.

CROSS-SECTIONAL ANALYSIS OF PRE-TWISTED THICK BEAMS USING VARIATIONAL ASYMPTOTIC METHOD

An asymptotically-exact methodology is presented for obtaining the cross-sectional stiffness matrix of a pre-twisted moderately-thick beam having rectangular cross sections and made of transversely isotropic materials. The anisotropic beam is modeled from 3-D elasticity, without any further assumptions. The beam is allowed to have large displacements and rotations, but small strain is assumed. The strain energy of the beam is computed making use of the constitutive law and the kinematical relations derived with the inclusion of geometrical nonlinearities and initial twist. Large displacements and rotations are allowed, but small strain is assumed. The Variational Asymptotic Method is used to minimize the energy functional, thereby reducing the cross section to a point on the reference line with appropriate properties, yielding a 1-D constitutive law. In this method as applied herein, the 2-D cross-sectional analysis is performed asymptotically by taking advantage of a material small parameter and two geometric small parameters. 3-D strain components are derived using kinematics and arranged as orders of the small parameters. Warping functions are obtained by the minimization of strain energy subject to certain set of constraints that renders the 1-D strain measures well-defined. Closed-form expressions are derived for the 3-D non-linear warping and stress fields. The model is capable of predicting interlaminar and transverse shear stresses accurately up to first order.

Analysis of Transverse Shear Strains in Pre-Twisted Thick Beams using Variational Asymptotic Method

The cross-sectional stiffness matrix is derived for a pre-twisted, moderately thick beam made of transversely isotropic materials and having rectangular cross sections. An asymptotically-exact methodology is used to model the anisotropic beam from 3-D elasticity, without any further assumptions. The beam is allowed to have large displacements and rotations, but small strain is assumed. The strain energy is computed making use of the beam constitutive law and kinematical relations derived with the inclusion of geometrical nonlinearities and an initial twist. The energy functional is minimized making use of the Variational Asymptotic Method (VAM), thereby reducing the cross section to a point on the beam reference line with appropriate properties, forming a 1-D constitutive law. VAM is a mathematical technique employed in the current problem to rigorously split the 3-D analysis of beams into two: a 2-D analysis over the beam cross-sectional domain, which provides a compact semi-analytical form of the properties of the cross sections, and a nonlinear 1-D analysis of the beam reference curve. In this method, as applied herein, the cross-sectional analysis is performed asymptotically by taking advantage of a material small parameter and two geometric small parameters. 3-D strain components are derived using kinematics and arranged in orders of the small parameters. Closed-form expressions are derived for the 3-D non-linear warping and stress fields. Warping functions are obtained by the minimization of strain energy subject to certain set of constraints that render the 1-D strain measures well-defined. The zeroth-order 3-D warping field thus yielded is then used to integrate the 3-D strain energy density over the cross section, resulting in the 1-D strain energy density, which in turn helps identify the corresponding cross-sectional stiffness matrix. The model is capable of predicting interlaminar and transverse shear stresses accurately up to first order.

Dynamic range tuning of graphene nanoresonators

From sensing perspective, smaller electromechanical devices, in general, are expected to be more responsive to the stimuli. This enhanced performance, however, is contingent upon the noise sources remaining unchanged and the onset of nonlinear behavior not being precipitated by miniaturization. In this paper, we study the effect of strain on the nonlinearities and dynamic range in graphene nanoresonators. The dynamic response and the onset of nonlinearity in these devices are sensitive both to the electrostatic field used to actuate the device and the strain. By tuning the strain of the device by two orders of magnitude, we observe an enhancement of 25 dB in the dynamic range leading to a mass resolution of 100 yoctogram. The increase in dynamic range in our devices is modeled as a combined effect of strain and partial cancellation of elastic and electrostatic nonlinearities. (C) 2015 AIP Publishing LLC.

Nonlinear Dynamics of a Rotating Flexible Link

This paper deals with the study of the nonlinear dynamics of a rotating flexible link modeled as a one dimensional beam, undergoing large deformation and with geometric nonlinearities. The partial differential equation of motion is discretized using a finite element approach to yield four nonlinear, nonautonomous and coupled ordinary differential equations (ODEs). The equations are nondimensionalized using two characteristic velocities-the speed of sound in the material and a velocity associated with the transverse bending vibration of the beam. The method of multiple scales is used to perform a detailed study of the system. A set of four autonomous equations of the first-order are derived considering primary resonances of the external excitation and one-to-one internal resonances between the natural frequencies of the equations. Numerical simulations show that for certain ranges of values of these characteristic velocities, the slow flow equations can exhibit chaotic motions. The numerical simulations and the results are related to a rotating wind turbine blade and the approach can be used for the study of the nonlinear dynamics of a single link flexible manipulator.

Fabrication and Nonlinear Thermomechanical Analysis of SU8 Thermal Actuator

SU8-based micromechanical structures are widely used as thermal actuators in the development of compliant micromanipulation tools. This paper reports the design, nonlinear thermomechanical analysis, fabrication, and thermal actuation of SU8 actuators. The thermomechanical analysis of the actuator incorporates nonlinear temperature-dependent properties of SU8 polymer to accurately model its thermal response during actuation. The designed SU8 thermal actuators are fabricated using surface micromachining techniques and the electrical interconnects are made to them using flip-chip bonding. The issues due to thermal stress during fabrication are discussed and a novel strategy is proposed to release the thermal stress in the fabricated actuators. Subsequent characterization of the actuator using an optical profilometer reveals excellent thermal response, good repeatability, and low hysteresis. The average deflection is similar to 8.5 mu m for an actuation current of similar to 5 mA. The experimentally obtained deflection profile and the tip deflection at different currents are both shown to be in good agreement with the predictions of the nonlinear thermomechanical model. This underscores the need to consider nonlinearities when modeling the response of SU8 thermal actuators. 2015-0087]

Simulated long-term climate response to idealized solar geoengineering

Solar geoengineering has been proposed as a potential means to counteract anthropogenic climate change, yet it is unknown how such climate intervention might affect the Earth's climate on the millennial time scale. Here we use the HadCM3L model to conduct a 1000year sunshade geoengineering simulation in which solar irradiance is uniformly reduced by 4% to approximately offset global mean warming from an abrupt quadrupling of atmospheric CO2. During the 1000year period, modeled global climate, including temperature, hydrological cycle, and ocean circulation of the high-CO2 simulation departs substantially from that of the control preindustrial simulation, whereas the climate of the geoengineering simulation remains much closer to that of the preindustrial state with little drift. The results of our study do not support the hypothesis that nonlinearities in the climate system would cause substantial drift in the climate system if solar geoengineering was to be deployed on the timescale of a millennium.