Instability of Coupled Longitudinal and Transverse Electromagnetic Modes of Wave‐Propagation in Bounded Streaming Plasmas

The instability of coupled longitudinal and transverse electromagnetic modes associated with long wavelengths is studied in bounded streaming plasmas. The main conclusions are as follows: (i) For long waves for which O (k 2)=0, in the absence of relative streaming motion of electrons and ions and aωp/c<0.66, the whole spectrum of harmonic waves is excited due to finite temperature and boundary effects consisting of two subseries. One of these subseries can be identified with Tonks-Dattner resonance oscillations for the electrons, and arises primarily due to the electrons with frequencies greater than the electrostatic plasma frequency corresponding to the electron density in the midplane in the undisturbed state. The other series arises primarily due to ion motion. When aωp/c>0.66, in addition to the above spectrum of harmonic waves, the system admits an infinite number of growing and decaying waves. The instability associated with these modes is found to arise due to the interaction of the waves inside the plasma with the external electromagnetic field. (ii) For modes with comparatively shorter wavelengths for which O (k3)=0, the coupling due to finite temperature sets in, and it is found that the two series of harmonic waves obtained in (i) deriving energy from the transverse modes also become unstable. Thus, for these wavelengths the system admits three sets of growing and decaying modes, first two for all values of aωp/c and the third for (aωp/c) > 0.66. (iii) The presence of streaming velocities introduces various other coupling mechanisms, and we find that even for the wavelengths for which O (k2)=0, we get three sets of growing and decaying waves. The numerical values for the growth rates show that the streaming velocities enhance the growth rates of instability significantly.

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.

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.

Experimental evidence of the cavity theory of sorption-desorption hysteresis by a study of the effect of electric discharge on entrapped water in silica gel

With the use of the quartz fiber spring balance, sorptions and desorptions of water on silica gel at 30°C were studied and the permanent and reproducible hysteresis loop was obtained. At different points on the desorption curve forming the loop, the gel was subjected to high tension glow electric discharge. As a result of the electric discharge, the gel at any point on the desorption curve shifts to a corresponding point on the sorption curve. This is due to the release from the cavities of gel of the entrapped water held in a metastable state. The electric discharge has no effect on the gel at different points on portions of the desorption curve which coincide with the sorption curve and also on the sorption curve itself, indicating the absence of entrapped water in the gel in these regions. The results afford direct experimental evidence of the reality of the cavity theory of sorption-desorption hysteresis.

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.

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.

Wave propagation analysis in carbon nanotube embedded composite using wavelet based spectral finite elements

In this paper, elastic wave propagation is studied in a nanocomposite reinforced with multiwall carbon nanotubes (CNTs). Analysis is performed on a representative volume element of square cross section. The frequency content of the exciting signal is at the terahertz level. Here, the composite is modeled as a higher order shear deformable beam using layerwise theory, to account for partial shear stress transfer between the CNTs and the matrix. The walls of the multiwall CNTs are considered to be connected throughout their length by distributed springs, whose stiffness is governed by the van der Waals force acting between the walls of nanotubes. The analyses in both the frequency and time domains are done using the wavelet-based spectral finite element method (WSFEM). The method uses the Daubechies wavelet basis approximation in time to reduce the governing PDE to a set of ODEs. These transformed ODEs are solved using a finite element (FE) technique by deriving an exact interpolating function in the transformed domain to obtain the exact dynamic stiffness matrix. Numerical analyses are performed to study the spectrum and dispersion relations for different matrix materials and also for different beam models. The effects of partial shear stress transfer between CNTs and matrix on the frequency response function (FRF) and the time response due to broadband impulse loading are investigated for different matrix materials. The simultaneous existence of four coupled propagating modes in a double-walled CNT-composite is also captured using modulated sinusoidal excitation.

Density-wave theory of dislocations in crystals

The density-wave theory of Ramakrishnan and Yussouff is extended to provide a scheme for describing dislocations and other topological defects in crystals. Quantitative calculations are presented for the order-parameter profiles, the atomic configuration, and the free energy of a screw dislocation with Burgers vector b=(a/2, a/2, a/2) in a bcc solid. These calculations are done using a simple parametrization of the direct correlation function and a gradient expansion. It is conventional to express the free energy of the dislocation in a crystal of size R as (λb2/4π)ln(αR/‖b‖), where λ is the shear elastic constant, and α is a measure of the core energy. Our results yield for Na the value α≃1.94a/(‖c1’’‖)1/2 (≃1.85) at the freezing temperature (371 K) and α≃2.48a/(‖c1’’‖)1/2 at 271 K, where c1’’ is the curvature of the first peak of the direct correlation function c(q). Detailed results for the density distribution in the dislocation, particularly the core region, are also presented. These show that the dislocation core has a columnar character. To our knowledge, this study represents the first calculation of dislocation structure, including the core, within the framework of an order-parameter theory and incorporating thermal effects.

Aerodynamic noise from wave-turbulence interaction

Abstract. In order to estimate the acoustic energy scattered when a unit volume of free turbulence, such as in free jets, interacts with a plane steady sound wave, theoretical expressions are derived for two simple models of turbulence: eddy model and isotropic model. The effect of convection by mean motion of the energy-bearing eddies on the incident sound wave and on the sound generated from wave-turbulence interaction is taken into account. Finally, by means of a representative calculation,the directionality pattern and Mach number dependence of the noise so generated is discussed.