Approximate analysis of coupled non-linear non-conservative systems subjected to step-function excitation

The paper deals with the approximate analysis of non-linear non-conservative systems oftwo degrees of freedom subjected to step-function excitation. The method of averaging of Krylov and Bogoliubov is used to arrive at the approximate equations for amplitude and phase. An example of a spring-mass-damper system is presented to illustrate the method and a comparison with numerical results brings out the validity of the approach.

The dynamic stability of degenerate systems under parametric excitation

The parametric resonance in a system having two modes of the same frequency is studied. The simultaneous occurence of the instabilities of the first and second kind is examined, by using a generalized perturbation procedure. The region of instability in the first approximation is obtained by using the Sturm's theorem for the roots of a polynomial equation.

Random vibration of a second order non-linear elastic system

A method is presented for obtaining, approximately, the response covariance and probability distribution of a non-linear oscillator under a Gaussian excitation. The method has similarities with the hierarchy closure and the equivalent linearization approaches, but is different. A Gaussianization technique is used to arrive at the output autocorrelation and the input-output cross-correlation. This along with an energy equivalence criterion is used to estimate the response distribution function. The method is applicable in both the transient and steady state response analysis under either stationary or non-stationary excitations. Good comparison has been observed between the predicted and the exact steady state probability distribution of a Duffing oscillator under a white noise input.

Optimum design of Lanchester damper for a viscously damped single degree of freedom system by using minimum force transmissibility criterion

The problem of optimum design of a Lanchester damper for minimum force transmission from a viscously damped single degree of freedom system subjected to harmonic excitation is investigated. Explicit expressions are developed for determining the optimum absorber parameters. It is shown that for the particular case of the undamped single degree of freedom system the results reduce to the classical ones obtained by using the concept of a fixed point on the transmissibility curves.

GABAa Receptor Mediated Signalling in the Brain: Inhibition, Shunting and Excitation

Within central nervous system, the simple division of chemical synaptic transmission to depolarizing excitation mediated by glutamate and hyperpolarizing inhibition mediated by γ-amino butyric acid (GABA), is evidently an oversimplification. The GABAa receptor (GABAaR) mediated responses can be of opposite sign within a single resting cell, due to the compartmentalized distribution of cation chloride cotransporters (CCCs). The K+/Cl- cotransporter 2 (KCC2), member of the CCC family, promotes K+ fuelled Cl- extrusion and sets the reversal potential of GABA evoked anion currents typically slightly below the resting membrane potential. The interesting ionic plasticity property of GABAergic signalling emerges from the short-term and long-term alterations in the intraneuronal concentrations of GABAaR permeable anions (Cl- and HCO3-). The short-term effects arise rapidly (in the time scale of hundreds of milliseconds) and are due to the GABAaR activation dependent shifts in anion gradients, whereas the changes in expression, distribution and kinetic regulation of CCCs are underlying the long-term effects, which may take minutes or even hours to develop. In this Thesis, the differences in the reversal potential of GABAaR mediated responses between dopaminergic and GABAergic cell types, located in the substantia nigra, were shown to be attributable to the differences in the chloride extrusion mechanisms. The stronger inhibitory effect of GABA on GABAergic neurons was due to the cell type specific expression of KCC2 whereas the KCC2 was absent from dopaminergic neurons, leading to a less prominent inhibition brought by GABAaR activation. The levels of KCC2 protein exhibited activity dependent alterations in hippocampal pyramidal neurons. Intense neuronal activity, leading to a massive release of brain derived neurotrophic factor (BDNF) in vivo, or applications of tyrosine receptor kinase B (TrkB) agonists BDNF or neurotrophin-4 in vitro, were shown to down-regulate KCC2 protein levels which led to a reduction in the efficacy of Cl- extrusion. The GABAergic transmission is interestingly involved in an increase of extracellular K+ concentration. A substantial increase in interstitial K+ tends to depolarize the cell membrane. The effects that varying ion gradients had on the generation of biphasic GABAaR mediated responses were addressed, with particular emphasis on the novel idea that the K+/Cl- extrusion via KCC2 is accelerated in response to a rapid accumulation of intracellular Cl-. The KCC2 inhibitor furosemide produced a large reduction in the GABAaR dependent extracellular K+ transients. Thus, paradoxically, both the inefficient KCC2 activity (via increased intracellular Cl-) and efficient KCC2 activity (via increased extracellular K+) may promote excitation.

Landau-Zener problem with waiting at the minimum gap and related quench dynamics of a many-body system

We discuss a technique for solving the Landau-Zener (LZ) problem of finding the probability of excitation in a two-level system. The idea of time reversal for the Schrodinger equation is employed to obtain the state reached at the final time and hence the excitation probability. Using this method, which can reproduce the well-known expression for the LZ transition probability, we solve a variant of the LZ problem, which involves waiting at the minimum gap for a time t(w); we find an exact expression for the excitation probability as a function of t(w). We provide numerical results to support our analytical expressions. We then discuss the problem of waiting at the quantum critical point of a many-body system and calculate the residual energy generated by the time-dependent Hamiltonian. Finally, we discuss possible experimental realizations of this work.

Multiple excitation nano-spot generation and confocal detection for far-field microscopy

An imaging technique is developed for the controlled generation of multiple excitation nano-spots for far-field microscopy. The system point spread function (PSF) is obtained by interfering two counter-propagating extended depth-of-focus PSF (DoF-PSF), resulting in highly localized multiple excitation spots along the optical axis. The technique permits (1) simultaneous excitation of multiple planes in the specimen; (2) control of the number of spots by confocal detection; and (3) overcoming the point-by-point based excitation. Fluorescence detection from the excitation spots can be efficiently achieved by Z-scanning the detector/pinhole assembly. The technique complements most of the bioimaging techniques and may find potential application in high resolution fluorescence microscopy and nanoscale imaging.

An approximate analysis of non-linear non-conservative systems subjected to step function excitation

This paper deals with the approximate analysis of the step response of non-linear nonconservative systems by the application of ultraspherical polynomials. From the differential equations for amplitude and phase, set up by the method of variation of parameters, the approximate solutions are obtained by a generalized averaging technique based on ultraspherical polynomial expansions. The Krylov-Bogoliubov results are given by a particular set of these polynomials. The method has been applied to study the step response of a cubic spring mass system in presence of viscous, material, quadratic, and mixed types of damping. The approximate results are compared with the digital and analogue computer solutions and a close agreement has been found between the analytical and the exact results.

A novel two sources ultrasound modulated optical tomographic system for screening breast cancer through elasticity characterization

The study of non-invasive characterization of elastic properties of soft biological tissues has been a focus of active researches since recent years. Light is highly scattered by biological tissues and hence, sophisticated reconstruction algorithms are required to achieve good imaging depth and a reasonable resolution. Ultrasound (US), on the otherhand, is less scattered by soft tissues and it has been in use for imaging in biomedical ultrasound systems. Combination of the contrast sensitivity of light and good localization of ultrasound provides a challenging technique for characterization of thicker tissues deep inside the body non-invasively. The elasticity of the tissues is characterized by studying the response of tissues to mechanical excitation induced by an acoustic radiation force (remotely) using an optical laser. The US modulated optical signals which traverse the tissue are detected by using a CCD camera as detector array and the pixel map formed on the CCD is used to characterize the embedded inhomogeneities. The use of CCD camera improves the signal-noise-ratio (SNR) by averaging the signals from all of the CCD pixels.

Analysis of grid connected induction generators driven by hydro/wind turbines under realistic system constraints

Results of an investigation dealing with the behaviour of grid-connected induction generators (GCIGs) driven by typical prime movers such as mini-hydro/wind turbines are presented. Certain practical operational problems of such systems are identified. Analytical techniques are developed to study the behavior of such systems. The system consists of the induction generator (IG) feeding a 11 kV grid through a step-up transformer and a transmission line. Terminal capacitors to compensate for the lagging VAr are included in the study. Computer simulation was carried out to predict the system performance at the given input power from the turbine. Effects of variations in grid voltage, frequency, input power, and terminal capacitance on the machine and system performance are studied. An analysis of self-excitation conditions on disconnection of supply was carried out. The behavior of a 220 kW hydel system and 55/11 kW and 22 kW wind driven system corresponding to actual field conditions is discussed

Approximate VB-MO schemes for excitation gaps in Hubbard models

The excitation gaps in the singlet and triplet manifolds for finite Hubbard models in one, two and three dimensions have been obtained using different approximate configuration interaction (CI) schemes, as a function of the correlation strength, by using valence bond (VB) functions constructed over the molecular orbital (MO) basis. These are compared with numerically exact results and it is found that the scheme in which all particle hole excitations below a given threshold are included is the method of choice. The excitation energies are well reproduced, in trend as well as magnitude, particularly when the threshold equals the bandwidth of the corresponding noninteracting system.

Excitation and relaxation energies of trans-stilbene: Confined singlet, triplet, and charged bipolarons

The π-electronic excitations and excited-state geometries of trans-stilbene (tS) are found by combining exact solutions of the Pariser-Parr-Pople (PPP) model and semiempirical Parametric Method 3 (PM3) calculations. Comprehensive comparisons with tS spectra are obtained and related to the fluorescence and topological alternation of poly(paraphenylenevinylene) (PPV). The one-photon absorption and triplet of tS correspond, respectively, to singlet and triplet bipolarons confined to two phenyls, while the tS2- ground state is a confined charged bipolaron. Independent estimates of the relaxation energy between vertical and adiabatic excitation show the bipolaron binding energy to depend on both charge and spin, as expected for interacting π electrons in correlated or molecular states. Complete configuration interaction within the PPP model of tS accounts for the singlet-triplet gap, for the fine-structure constants and triplet-triplet spectra, for two-photon transitions and intensities, and for one-photon spectra and the radiative lifetime, although the relative position of nearly degenerate covalent and ionic singlets is not resolved. The planar PM3 geometry and low rotational barrier of tS agree with resolved rotational and vibrational spectra in molecular beams. PM3 excitation and relaxation energies for tS bipolarons are consistent with experiment and with PPP results. Instead of the exciton model, we interpret tS excitations in terms of states that are localized on each ring or extended over an alternating chain, as found exactly in Hückel theory, and find nearly degenerate transitions between extended and localized states in the singlet, triplet, and dianion manifolds. The large topological alternation of the extended system increases the ionicity and interchanges the order of the lowest one- and two-photon absorption of PPV relative to polyenes.

Cascades of Selective Pulses on Connected Single-Quantum Transitions Leading to the Selective Excitation of Multiple-Quantum Coherences

A symmetric cascade of selective pulses applied on connected transitions leads to the excitation of a selected multiple-quantum coherence by a well-defined angle. This cascade selectively operates on the subspace of the multiple-quantum coherence and acts as a generator of rotation selectively on the multiple-quantum subspace. Single-transition operator algebra has been used to explain these experiments. Experiments have been performed on two- and three-spin systems. It is shown that such experiments can be utilized to measure the relaxation times of selected multiple-quantum coherences or of a specifically prepared initial longitudinal state of the spin system.

Seismic Hazard and Microzonation Studies using Geographic Information System - A Case Study of Bangalore city

Seismic hazard and microzonation of cities enable to characterize the potential seismic areas that need to be taken into account when designing new structures or retrofitting the existing ones. Study of seismic hazard and preparation of geotechnical microzonation maps has been attempted using Geographical Information System (GIS). GIS will provide an effective solution for integrating different layers of information thus providing a useful input for city planning and in particular input to earthquake resistant design of structures in an area. Seismic hazard is the study of expected earthquake ground motions at any point on the earth. Microzonation is the process of sub division of region in to number of zones based on the earthquake effects in the local scale. Seismic microzonation is the process of estimating response of soil layers under earthquake excitation and thus the variation of ground motion characteristic on the ground surface. For the seismic microzonation, geotechnical site characterization need to be assessed at local scale (micro level), which is further used to assess of the site response and liquefaction susceptibility of the sites. Seismotectonic atlas of the area having a radius of 350km around Bangalore has been prepared with all the seismogenic sources and historic earthquake events (a catalogue of about 1400 events since 1906). We have attempted to carryout the site characterization of Bangalore by collating conventional geotechnical boreholes data (about 900 borehole data with depth) and integrated in GIS. 3-D subsurface model of Bangalore prepared using GIS is shown in Figure 1.Further, Shear wave velocity survey based on geophysical method at about 60 locations in the city has been carried out in 220 square Kms area. Site response and local site effects have been evaluated using 1-dimensional ground response analysis. Spatial variability of soil overburden depths, ground surface Peak Ground Acceleration’s(PGA), spectral acceleration for different frequencies, liquefaction susceptibility have been mapped in the 220 sq km area using GIS.ArcInfo software has been used for this purpose. These maps can be used for the city planning and risk & vulnerability studies. Figure 2 shows a map of peak ground acceleration at rock level for Bangalore city. Microtremor experiments were jointly carried out with NGRI scientists at about 55 locations in the city and the predominant frequency of the overburden soil columns were evaluated.

Spin State Selective Excitation of Single Quantum Transitions Using Multiple Quantum Spectroscopy- an Aid to Analyse Complex Proton NMR spectra of Oriented Molecules

NMR spectra of molecules oriented in liquid-crystalline matrix provide information on the structure and orientation of the molecules. Thermotropic liquid crystals used as an orienting media result in the spectra of spins that are generally strongly coupled. The number of allowed transitions increases rapidly with the increase in the number of interacting spins. Furthermore, the number of single quantum transitions required for analysis is highly redundant. In the present study, we have demonstrated that it is possible to separate the subspectra of a homonuclear dipolar coupled spin system on the basis of the spin states of the coupled heteronuclei by multiple quantum (MQ)−single quantum (SQ) correlation experiments. This significantly reduces the number of redundant transitions, thereby simplifying the analysis of the complex spectrum. The methodology has been demonstrated on the doubly 13C labeled acetonitrile aligned in the liquid-crystal matrix and has been applied to analyze the complex spectrum of an oriented six spin system.