Response of nonlinear systems to narrow-band excitation

The hardening cubic spring oscillator is studied under narrow-band gaussian excitation. Equivalent linearization leads to multiple steady states. The realizability of the solution is discussed through stochastic stability analysis. Theoretical results are supported by numerical simulation.

InMnO3: A biferroic

InMnO3 which has a hexagonal structure similar to that of YMnO3 is found to show a canted antiferromagnetic behavior below 50 K (T-N) and a ferroelectric (FE) transition at 500 K accompanied by hystersis. We have determined the structure, polarization, and energetics of the FE and paraelectric (PE) phases of InMnO3 using first-principles density functional theory calculations based on pseudopotentials and a plane-wave basis, and find the polarization of the PE phase to be a half-integer quantum. The difference in polarization of the FE and PE phases calculated along a simple path is different from the absolute value of polarization of the FE phase. A weak piezoelectric response is exhibited by InMnO3 to uniaxial strain.

Undamped oscillations of homogeneous collisionless stellar systems

The Lewis (1968) invariant of the time-dependent harmonic oscillator is used to construct exact time-dependent, uniform density solutions of the collisionless Boltzmann equation. The spatially bound solutions are time-periodic.

Partially conserved axial-vector current inS-matrix theory

Mandelstam�s argument that PCAC follows from assigning Lorentz quantum numberM=1 to the massless pion is examined in the context of multiparticle dual resonance model. We construct a factorisable dual model for pions which is formulated operatorially on the harmonic oscillator Fock space along the lines of Neveu-Schwarz model. The model has bothm ? andm ? as arbitrary parameters unconstrained by the duality requirement. Adler self-consistency condition is satisfied if and only if the conditionm?2?m?2=1/2 is imposed, in which case the model reduces to the chiral dual pion model of Neveu and Thorn, and Schwarz. The Lorentz quantum number of the pion in the dual model is shown to beM=0.

A matrix identity and perturbation expressions

An identity expressing formally the diagonal and off-diagonal elements of an inverse of a matrix is deduced employing operator techniques. Several well-known perturbation expressions for the self-energy are deduced as special cases. A new approximation and other applications following from the above formalism are briefly indicated through illustrations from a perturbed harmonic oscillator, chemisorption approximations and Kelly's result in the problem of electron correlation.

The behaviour of excited plane jets

A plane subsonic jet can be excited to entrain more fluid from its surroundings by subjecting it to antisymmetric periodic disturbances. The essential feature in this phenomenon is the rolling-up motion of an initially flapping jet to form large vortices which are responsible for greater entrainment. Several methods developed to impart oscillations to the flow at the nozzle, such as the acoustic pressure oscillator, the vibration of a single vane in the potential core region, the reciprocating lip system and the twin vane exciter, are described in this article. A minimum threshold in amplitude is necessary for exciting the flow. However, the frequency of oscillation is much less than that predicted by stability considerations.

Applications of reverse saturable absorbers in laser science

A variety of applications exist for reverse saturable absorbers (RSAs) in the area of optical pulse processing and computing. An RSA can be used as power limiter/pulse smoother and energy limiter/pulse shortner of laser pulses. A combination of RSA and saturable absorber (SA) can be used for mode locking and pulse shaping between high power laser amplifiers in oscillator amplifier chain. Also, an RSA can be used for the construction of a molecular spatial light modulator (SLM) which acts as an input/output device in optical computers. A detailed review of the theoretical studies of these processes is presented. Current efforts to find RSAs at desired wavelength for testing these theoretical predictions are also discussed.

Modelling, Design and Analysis of Low Frequency Platform for Attenuating Micro-Vibration in Spacecraft

One of the most important factors that affect the pointing of precision payloads and devices in space platforms is the vibration generated due to static and dynamic unbalanced forces of rotary equipments placed in the neighborhood of payload. Generally, such disturbances are of low amplitude, less than 1 kHz, and are termed as ‘micro-vibrations’. Due to low damping in the space structure, these vibrations have long decay time and they degrade the performance of payload. This paper addresses the design, modeling and analysis of a low frequency space frame platform for passive and active attenuation of micro-vibrations. This flexible platform has been designed to act as a mount for devices like reaction wheels, and consists of four folded continuous beams arranged in three dimensions. Frequency and response analysis have been carried out by varying the number of folds, and thickness of vertical beam. Results show that lower frequencies can be achieved by increasing the number of folds and by decreasing the thickness of the blade. In addition, active vibration control is studied by incorporating piezoelectric actuators and sensors in the dynamic model. It is shown using simulation that a control strategy using optimal control is effective for vibration suppression under a wide variety of loading conditions.

Characterization of a large-area PVDF thin film for electro-mechanical and ultrasonic sensing applications

Large-area PVDF thin films have been prepared and characterized for quasi-static and high frequency dynamic strain sensing applications. These films are prepared using hot press method and the piezoelectric phase (beta-phase) has been achieved by thermo-mechanical treatment and poling under DC field. The fabricated films have been characterized for quasi-static strain sensing and the linear strain-voltage relationship obtained is promising. In order to evaluate the ultrasonic sensing properties, a PZT wafer has been used to launch Lamb waves in a metal beam on which the PVDF film sensor is bonded at a distance. The voltage signals obtained from the PVDF films have been compared with another PZT wafer sensor placed on the opposite surface of the beam as a reference signal. Due to higher stiffness and higher thickness of the PZT wafer sensors, certain resonance patterns significantly degrade the sensor sensitivity curves. Whereas, the present results show that the large-area PVDF sensors can be superior with the signal amplitude comparable to that of PZT sensors and with no resonance-induced effect, which is due to low mechanical impedance, smaller thickness and larger area of the PVDF film. Moreover, the developed PVDF sensors are able to capture both A(0) and S-0 modes of Lamb wave, whereas the PZT sensors captures only A(0) mode in the same scale of voltage output. This shows promises in using large-area PVDF films with various surface patterns on structures for distributed sensing and structural health monitoring under quasi-static, vibration and ultrasonic situations. (C) 2010 Elsevier B.V. All rights reserved.

Narrowband random excitation of a limit cycle system

The response of the Van der Pol oscillator to stationary narrowband Gaussian excitation is considered. The central frequency of excitation is taken to be in the neighborhood of the system limit cycle frequency. The solution is obtained using a non-Gaussian closure approximation on the probability density function of the response. The validity of the solution is examined with the help of a stochastic stability analysis. Solution based on Stratonovich''s quasistatic averaging technique is also obtained. The comparison of the theoretical solutions with the digital simulations shows that the theoretical estimates are reasonably good.

A New Liquid Level Sensor for Process-Control Applications

Many process-control systems are air-operated. In such an environment, it would be desirable and economical to use pneumatic sensors. Bubble-back pressure sensors perform quite satisfactorily, but in case of viscous inflammable and slurry-like liquids with a tendency to froth, this level sensor is inadequate. The method suggested in this paper utilizes a pneumatic capacitor, one boundary of which is formed by the liquid level, to modulate a fluid amplifier feedback oscillator. The absence of moving parts and economy obtained makes this method attractive for process-control applications. The system has been mathematically modeled and simulated on an IBM 360/44 digital computer. Experimental values compare fairly well with the theoretical results. For the range tested, the sensor is found to have a linear frequency variation with the liquid level Extended running in the laboratory shows that the system is very reliable. This system has been found insensitive to temperature variations of up to 15ðC.

Second harmonic generation in some donor-acceptor ethylenes—I

We report the absorption spectra, oscillator strengths, ground state and excited state dipole moments, and molecular second order polarizability coefficients (βCT) due to donor—acceptor charge transfer in four trisubstituted ethylenes, namely 1,1-bisdimethylamino-2-nitroethylene, 1,1-bispyrolidino-2-nitroethylene, 1,1-bispiperidino-2-nitroethylene and 1,1-bismorpholino-2-nitroethylene. The results are compared with that of trans-N,N-dimethylamino-nitroethylene, which has a large βCT. The powder second harmonic generation (SHG) intensity of all these molecules is also measured and only 1,1-bispiperidino-2-nitroethylene is found to possess an efficiency of 20% of that of urea under the same conditions. The SHG efficiency of this compound and deficiency in the other molecules in the powdered state is discussed in terms of their arrangements in the unit cell. The crystal structure of the active molecule is also presented and the structure—property relationship is critically examined in all these molecules.

Exact nonlinear travelling hydromagnetic wave solutions

Exact travelling wave solutions for hydromagnetic waves in an exponentially stratified incompressible medium are obtained. With the help of two integrals it becomes possible to reduce the system of seven nonlinear PDE's to a second order nonlinear ODE which describes an one dimensional harmonic oscillator with a nonlinear friction term. This equation is studied in detail in the phase plane. The travelling waves are periodic only when they propagate either horizontally or vertically. The reduced second order nonlinear differential equation describing the travelling waves in inhomogeneous conducting media has rather ubiquitous nature in that it also appears in other geophysical systems such as internal waves, Rossby waves and topographic Rossby waves in the ocean.

Mechanisms of variability and predictability of the tropical coupled ocean-atmosphere system

A conceptual model is proposed to explain the observed aperiodicity in the short term climate fluctuations of the tropical coupled ocean-atmosphere system. This is based on the evidence presented here that the tropical coupled ocean-atmosphere system sustains a low frequency inter-annual mode and a host of higher frequency intra-seasonal unstable modes. At long wavelengths, the low frequency mode is dominant while at short wavelengths, the high frequency modes are dominant resulting in the co-existence of a long wave low frequency mode with some short wave intra-seasonal modes in the tropical coupled system. It is argued that due to its long wavelength, the low frequency mode would behave like a linear oscillator while the higher frequency short wave modes would be nonlinear. The conceptual model envisages that an interaction between the low frequency linear oscillator and the high frequency nonlinear oscillations results in the observed aperiodicity of the tropical coupled system. This is illustrated by representing the higher frequency intra-seasonal oscillations by a nonlinear low order model which is then coupled to a linear oscillator with a periodicity of four years. The physical mechanism resulting in the aperiodicity in the low frequency oscillations and implications of these results on the predictability of the coupled system are discussed.

NDDO-based CI methods for the prediction of electronic spectra and sum-over-states molecular hyperpolarization

NDDO-based (AM1) configuration interaction (CI) calculations have been used to calculate the wavelength and oscillator strengths of electronic absorptions in organic molecules and the results used in a sum-over-states treatment to calculate second-order-hyperpolarizabilities. The results for both spectra and hyperpolarizabilities are of acceptable quality as long as a suitable CI-expansion is used. We have found that using an active space of eight electrons in eight orbitals and including all single and pair-double excitations in the CI leads to results that agree well with experiment and that do not change significantly with increasing active space for most organic molecules. Calculated second-order hyperpolarizabilities using this type of CI within a sum-over-states calculation appear to be of useful accuracy.