Ultrasonic wave characteristics of nanorods via nonlocal strain gradient models

This paper studies an ultrasonic wave dispersion characteristics of a nanorod. Nonlocal strain gradient models (both second and fourth order) are introduced to analyze the ultrasonic wave behavior in nanorod. Explicit expressions are derived for wave numbers and the wave speeds of the nanorod. The analysis shows that the fourth order strain gradient model gives approximate results over the second order strain gradient model for dynamic analysis. The second order strain gradient model gives a critical wave number at certain wave frequency, where the wave speeds are zero. A relation among the number of waves along the nanorod, the nonlocal scaling parameter (e(0)a), and the length of the nanorod is obtained from the nonlocal second order strain gradient model. The ultrasonic wave characteristics of the nanorod obtained from the nonlocal strain gradient models are compared with the classical continuum model. The dynamic response behavior of nanorods is explained from both the strain gradient models. The effect of e(0)a on the ultrasonic wave behavior of the nanorods is also observed. (C) 2010 American Institute of Physics.

Wave propagation in a micropolar fluid contained in a visco-elastic membrane

The aim of the paper is to investigate the propagation of a pulse in a micropolar fluid contained in a visco-elastic membrane. It was undertaken with a view to study how closely we can approximate the flow of blood in arteries by the above model. We find that for large Reynolds number, the effect of micropolarity is hardly perceptible, whereas for small Reynolds numbers it is of considerable importance.

Use of Abel integral equations in water wave scattering by two surface-piercing barriers

In this paper the classical problem of water wave scattering by two partially immersed plane vertical barriers submerged in deep water up to the same depth is investigated. This problem has an exact but complicated solution and an approximate solution in the literature of linearised theory of water waves. Using the Havelock expansion for the water wave potential, the problem is reduced here to solving Abel integral equations having exact solutions. Utilising these solutions,two sets of expressions for the reflection and transmission coefficients are obtained in closed forms in terms of computable integrals in contrast to the results given in the literature which,involved six complicated integrals in terms of elliptic functions. The two different expressions for each coefficient produce almost the same numerical results although it has not been possible to prove their equivalence analytically. The reflection coefficient is depicted against the wave number in a number of figures which almost coincide with the figures available in the literature wherein the problem was solved approximately by employing complementary approximations. (C) 2009 Elsevier B.V. All rights reserved.

Multi-criteria seismic hazard evaluation for Bangalore city, India

Different seismic hazard components pertaining to Bangalore city,namely soil overburden thickness, effective shear-wave velocity, factor of safety against liquefaction potential, peak ground acceleration at the seismic bedrock, site response in terms of amplification factor, and the predominant frequency, has been individually evaluated. The overburden thickness distribution, predominantly in the range of 5-10 m in the city, has been estimated through a sub-surface model from geotechnical bore-log data. The effective shear-wave velocity distribution, established through Multi-channel Analysis of Surface Wave (MASW) survey and subsequent data interpretation through dispersion analysis, exhibits site class D (180-360 m/s), site class C (360-760 m/s), and site class B (760-1500 m/s) in compliance to the National Earthquake Hazard Reduction Program (NEHRP) nomenclature. The peak ground acceleration has been estimated through deterministic approach, based on the maximum credible earthquake of M-W = 5.1 assumed to be nucleating from the closest active seismic source (Mandya-Channapatna-Bangalore Lineament). The 1-D site response factor, computed at each borehole through geotechnical analysis across the study region, is seen to be ranging from around amplification of one to as high as four times. Correspondingly, the predominant frequency estimated from the Fourier spectrum is found to be predominantly in range of 3.5-5.0 Hz. The soil liquefaction hazard assessment has been estimated in terms of factor of safety against liquefaction potential using standard penetration test data and the underlying soil properties that indicates 90% of the study region to be non-liquefiable. The spatial distributions of the different hazard entities are placed on a GIS platform and subsequently, integrated through analytical hierarchal process. The accomplished deterministic hazard map shows high hazard coverage in the western areas. The microzonation, thus, achieved is envisaged as a first-cut assessment of the site specific hazard in laying out a framework for higher order seismic microzonation as well as a useful decision support tool in overall land-use planning, and hazard management. (C) 2010 Elsevier Ltd. All rights reserved.

Analysis of Ridge-Loaded Folded-Waveguide Slow-Wave Structures for Broadband Traveling-Wave Tubes

An E-plane serpentine folded-waveguide slow-wave structure with ridge loading on one of its broad walls is proposed for broadband traveling-wave tubes (TWTs) and studied using a simple quasi-transverse-electromagnetic analysis for the dispersion and interaction impedance characteristics, including the effects of the beam-hole discontinuity. The results are validated against cold test measurements, an approximate transmission-line parametric analysis, an equivalent circuit analysis, and 3-D electromagnetic modeling using CST Microwave Studio. The effect of the structure parameters on widening the bandwidth of a TWT is also studied.

Free energy of mixing of divalent basic oxides with silica

An expression derived for the free energy of mixing of a divalent basic oxide (MO) with SiO2 based on a model of silicate structure, takes into account the distribution of O2- (from MO) into the silica network, the mixing of silicate ions with O2- and the enthalpy of mixing. The resulting expression is ΔGmix=RT{N11n (2N1-N)2/4N1(1-N)+N21n N 2-N/1-N}, where N={(β+N1)-√(β+N 1)2-8βN1N2}/2β β=characteristic constant for the system N1=mol fraction of silica N2=mol fraction of MO. For the proper choice of β, calculated values of the activity of MO for the system PbO-SiO2, MnO-SiO2, FeO-SiO2 and CaO-SiO2 are in good agreement with experiment. The model predicts that the activity of the basic oxide decreases with increase in temperature.

Equivalent constitutive model-based design of wave-absorbing material system and controller

A design methodology for wave-absorbing active material system is reported. The design enforces equivalence between an assumed material model having wave-absorbing behavior and a set of target feedback controllers for an array of microelectro-mechanical transducers which are integral part of the active material system. The proposed methodology is applicable to problems involving the control of acoustic waves in passive-active material system with complex constitutive behavior at different length-scales. A stress relaxation type one-dimensional constitutive model involving viscous damping mechanism is considered, which shows asymmetric wave dispersion characteristics about the half-line. The acoustic power flow and asymptotic stability of such material system are studied. A single sensor non-collocated linear feedback control system in a one-dimensional finite waveguide, which is a representative volume element in an active material system, is considered. Equivalence between the exact dynamic equilibrium of these two systems is imposed. It results in the solution space of the design variables, namely the equivalent damping coefficient, the wavelength(s) to be controlled and the location of the sensor. The characteristics of the controller transfer functions and their pole-placement problem are studied. (c) 2005 Elsevier Ltd. All rights reserved.

Four-dimensional current algebra from Chern-Simons theory

We study an abelian Chern-Simons theory on a five-dimensional manifold with boundary. We find it to be equivalent to a higher-derivative generalization of the abelian Wess-Zumino-Witten model on the boundary. It contains a U(1) current algebra with an operational extension.

A four-timescale algorithm for constrained stochastic optimization of RED

The overall performance of random early detection (RED) routers in the Internet is determined by the settings of their associated parameters. The non-availability of a functional relationship between the RED performance and its parameters makes it difficult to implement optimization techniques directly in order to optimize the RED parameters. In this paper, we formulate a generic optimization framework using a stochastically bounded delay metric to dynamically adapt the RED parameters. The constrained optimization problem thus formulated is solved using traditional nonlinear programming techniques. Here, we implement the barrier and penalty function approaches, respectively. We adopt a second-order nonlinear optimization framework and propose a novel four-timescale stochastic approximation algorithm to estimate the gradient and Hessian of the barrier and penalty objectives and update the RED parameters. A convergence analysis of the proposed algorithm is briefly sketched. We perform simulations to evaluate the performance of our algorithm with both barrier and penalty objectives and compare these with RED and a variant of it in the literature. We observe an improvement in performance using our proposed algorithm over RED, and the above variant of it.

Wave algorithms:Optimal database search and catalysis

Grover's database search algorithm, although discovered in the context of quantum computation, can be implemented using any physical system that allows superposition of states. A physical realization of this algorithm is described using coupled simple harmonic oscillators, which can be exactly solved in both classical and quantum domains. Classical wave algorithms are far more stable against decoherence compared to their quantum counterparts. In addition to providing convenient demonstration models, they may have a role in practical situations, such as catalysis.

Detection of Tsunami Wave Generation and Propagation Using Fiber Bragg Grating Sensors

This paper describes the design and development of a Fiber Bragg Grating (FBG) sensor system for monitoring tsunami waves generated in the deep ocean. An experimental setup was designed and fabricated to simulate the generation and propagation of a tsunami wave. The characteristics and efficiency of the developed FBG sensor was evaluated with a standard commercial Digiquartz sensor. For real time monitoring of tsunami waves, FBG sensors bonded to a cantilever is used and the wavelength shifts (Delta lambda(B)) in the reflected spectra resulting from the strain/pressure imparted on the FBGs have been recorded using a high-speed Micron Optics FBG interrogation system. The parameters sensed are the signal burst during tsunami generation and pressure variations at different places as the tsunami wave propagates away from the source of generation. The results obtained were compared with the standard commercial sensor used in tsunami detection. The observations suggest that the FBG sensor was highly sensitive and free from many of the constraints associated with the commercial tsunameter.

A molecular theory of collective orientational relaxation in pure and binary dipolar liquids

A molecular theory of collective orientational relaxation of dipolar molecules in a dense liquid is presented. Our work is based on a generalized, nonlinear, Smoluchowski equation (GSE) that includes the effects of intermolecular interactions through a mean‐field force term. The effects of translational motion of the liquid molecules on the orientational relaxation is also included self‐consistently in the GSE. Analytic expressions for the wave‐vector‐dependent orientational correlation functions are obtained for one component, pure liquid and also for binary mixtures. We find that for a dipolar liquid of spherical molecules, the correlation function ϕ(k,t) for l=1, where l is the rank of the spherical harmonics, is biexponential. At zero wave‐vector, one time constant becomes identical with the dielectric relaxation time of the polar liquid. The second time constant is the longitudinal relaxation time, but the contribution of this second component is small. We find that polar forces do not affect the higher order correlation functions (l>1) of spherical dipolar molecules in a linearized theory. The expression of ϕ(k,t) for a binary liquid is a sum of four exponential terms. We also find that the wave‐vector‐dependent relaxation times depend strongly on the microscopic structure of the dense liquid. At intermediate wave vectors, the translational diffusion greatly accelerates the rate of orientational relaxation. The present study indicates that one must pay proper attention to the microscopic structure of the liquid while treating the translational effects. An analysis of the nonlinear terms of the GSE is also presented. An interesting coupling between the number density fluctuation and the orientational fluctuation is uncovered.