Quantum noise in optical fibers. I. Stochastic equations

We analyze the quantum dynamics of radiation propagating in a single-mode optical fiber with dispersion, nonlinearity, and Raman coupling to thermal phonons. We start from a fundamental Hamiltonian that includes the principal known nonlinear effects and quantum-noise sources, including linear gain and loss. Both Markovian and frequency-dependent, non-Markovian reservoirs are treated. This treatment allows quantum Langevin equations, which have a classical form except for additional quantum-noise terms, to be calculated. In practical calculations, it is more useful to transform to Wigner or 1P quasi-probability operator representations. These transformations result in stochastic equations that can be analyzed by use of perturbation theory or exact numerical techniques. The results have applications to fiber-optics communications, networking, and sensor technology.

A director theory for visco-elastic folding instabilities in multilayered rock

A model for finely layered visco-elastic rock proposed by us in previous papers is revisited and generalized to include couple stresses. We begin with an outline of the governing equations for the standard continuum case and apply a computational simulation scheme suitable for problems involving very large deformations. We then consider buckling instabilities in a finite, rectangular domain. Embedded within this domain, parallel to the longer dimension we consider a stiff, layered beam under compression. We analyse folding up to 40% shortening. The standard continuum solution becomes unstable for extreme values of the shear/normal viscosity ratio. The instability is a consequence of the neglect of the bending stiffness/viscosity in the standard continuum model. We suggest considering these effects within the framework of a couple stress theory. Couple stress theories involve second order spatial derivatives of the velocities/displacements in the virtual work principle. To avoid C-1 continuity in the finite element formulation we introduce the spin of the cross sections of the individual layers as an independent variable and enforce equality to the spin of the unit normal vector to the layers (-the director of the layer system-) by means of a penalty method. We illustrate the convergence of the penalty method by means of numerical solutions of simple shears of an infinite layer for increasing values of the penalty parameter. For the shear problem we present solutions assuming that the internal layering is oriented orthogonal to the surfaces of the shear layer initially. For high values of the ratio of the normal-to the shear viscosity the deformation concentrates in thin bands around to the layer surfaces. The effect of couple stresses on the evolution of folds in layered structures is also investigated. (C) 2002 Elsevier Science Ltd. All rights reserved.

Apparent strain localization and shear wave dispersion in elastic fault gouge with microrotations

Shear deformation of fault gouge or other particulate materials often results in observed strain localization, or more precisely, the localization of measured deformation gradients. In conventional elastic materials the strain localization cannot take place therefore this phenomenon is attributed to special types of non-elastic constitutive behaviour. For particulate materials however the Cosserat continuum which takes care of microrotations independent of displacements is a more appropriate model. In elastic Cosserat continuum the localization in displacement gradients is possible under some combinations of the generalized Cosserat elastic moduli. The same combinations of parameters also correspond to a considerable dispersion in shear wave propagation which can be used for independent experimental verification of the proposed mechanism of apparent strain localization in fault gouge.

Evaluation of elastic modulus and hardness of thin films by nanoindentation

Simple equations are proposed for determining elastic modulus and hardness properties of thin films on substrates from nanoindentation experiments. An empirical formulation relates the modulus E and hardness H of the film/substrate bilayer to corresponding material properties of the constituent materials via a power-law relation. Geometrical dependence of E and H is wholly contained in the power-law exponents, expressed here as sigmoidal functions of indenter penetration relative to film thickness. The formulation may be inverted to enable deconvolution of film properties from data on the film/substrate bilayers. Berkovich nanoindentation data for dense oxide and nitride films on silicon substrates are used to validate the equations and to demonstrate the film property deconvolution. Additional data for less dense nitride films are used to illustrate the extent to which film properties may depend on the method of fabrication.

The intercalated disc of monkey myocardial cells and Purkinje fibers as revealed by scanning electron microscopy

The intercalated discs of working myocardium and Purkinje fibers of the monkey heart were examined by scanning and transmission electron microscopy. The NaOH/ultrasonication technique resulted in the digestion of connective tissue and a separation of the intercellular junctions of intercalated discs, such that these could be visualized three-dimensionally. The intercalated discs of ventricular myocytes, atrial myocytes and Purkinje fibers vary considerably in number and configuration, as do the intercalated discs of the three different layers of the ventricular myocardium. Myocytes in the subepicardial, middle and subendocardial layers of the ventricle have 1-3, 4-5 and 5-6 intercalated discs at the end of these cells, respectively, Those in the endocardial layer are characterized by the presence of small laterally-placed intercalated discs. Atrial myocytes and Purkinje fibers usually only have 1-2 intercalated discs, Individual intercalated discs in ventricular myocytes have complicated stairs with 10-30 steps and corresponding risers, while those of atrial myocytes and Purkinje fibers have simple stairs with 1-3 steps and risers, Steps equivalent to the plicate segments are characterized by densely-packed microplicae and finger-like microprojections which greatly increase surface area in vertricular myocytes, Microprojections in atrial myocytes and Purkinje fibers are sparse by comparison, Risers equivalent to the interplicate segments containing large gap junctional areas are most numerous in left ventricular myocytes, followed by right ventricular myocytes, Purkinje fibers and atrial myocytes in decreasing order. The geometric arrangement of the various types of myocytes may be related with impulse propagation. Large intercalated discs of cell trunks and series branches may participate in longitudinal propagation, while small laterally-placed ones may be the site of transverse propagation.

A numerical study of effect of grain boundaries on elastic and plastic properties in nanocomposite materials

Nanocomposite materials have received considerable attention in recent years due to their novel properties. Grain boundaries are considered to play an important role in nanostructured materials. This work focuses on the finite element analysis of the effect of grain boundaries on the overall mechanical properties of aluminium/alumina composites. A grain boundary is incorporated into the commonly used unit cell model to investigate its effect on material properties. By combining the unit cell model with an indentation model, coupled with experimental indentation measurements, the ''effective'' plastic property of the grain boundary is estimated. In addition, the strengthening mechanism is also discussed based on the Estrin-Mecking model.

Elastic moduli of model random three-dimensional closed-cell cellular solids

Most cellular solids are random materials, while practically all theoretical structure-property results are for periodic models. To be able to generate theoretical results for random models, the finite element method (FEM) was used to study the elastic properties of solids with a closed-cell cellular structure. We have computed the density (rho) and microstructure dependence of the Young's modulus (E) and Poisson's ratio (PR) for several different isotropic random models based on Voronoi tessellations and level-cut Gaussian random fields. The effect of partially open cells is also considered. The results, which are best described by a power law E infinity rho (n) (1<n<2), show the influence of randomness and isotropy on the properties of closed-cell cellular materials, and are found to be in good agreement with experimental data. (C) 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

The plausibility of long-wavelength stress correlation or stress magnitude as a mechanism for precursory seismicity: Results from two simple elastic models

Observations of accelerating seismic activity prior to large earthquakes in natural fault systems have raised hopes for intermediate-term eartquake forecasting. If this phenomena does exist, then what causes it to occur? Recent theoretical work suggests that the accelerating seismic release sequence is a symptom of increasing long-wavelength stress correlation in the fault region. A more traditional explanation, based on Reid's elastic rebound theory, argues that an accelerating sequence of seismic energy release could be a consequence of increasing stress in a fault system whose stress moment release is dominated by large events. Both of these theories are examined using two discrete models of seismicity: a Burridge-Knopoff block-slider model and an elastic continuum based model. Both models display an accelerating release of seismic energy prior to large simulated earthquakes. In both models there is a correlation between the rate of seismic energy release with the total root-mean-squared stress and the level of long-wavelength stress correlation. Furthermore, both models exhibit a systematic increase in the number of large events at high stress and high long-wavelength stress correlation levels. These results suggest that either explanation is plausible for the accelerating moment release in the models examined. A statistical model based on the Burridge-Knopoff block-slider is constructed which indicates that stress alone is sufficient to produce accelerating release of seismic energy with time prior to a large earthquake.

Computation of the linear elastic properties of random porous materials with a wide variety of microstructure

A finite-element method is used to study the elastic properties of random three-dimensional porous materials with highly interconnected pores. We show that Young's modulus, E, is practically independent of Poisson's ratio of the solid phase, nu(s), over the entire solid fraction range, and Poisson's ratio, nu, becomes independent of nu(s) as the percolation threshold is approached. We represent this behaviour of nu in a flow diagram. This interesting but approximate behaviour is very similar to the exactly known behaviour in two-dimensional porous materials. In addition, the behaviour of nu versus nu(s) appears to imply that information in the dilute porosity limit can affect behaviour in the percolation threshold limit. We summarize the finite-element results in terms of simple structure-property relations, instead of tables of data, to make it easier to apply the computational results. Without using accurate numerical computations, one is limited to various effective medium theories and rigorous approximations like bounds and expansions. The accuracy of these equations is unknown for general porous media. To verify a particular theory it is important to check that it predicts both isotropic elastic moduli, i.e. prediction of Young's modulus alone is necessary but not sufficient. The subtleties of Poisson's ratio behaviour actually provide a very effective method for showing differences between the theories and demonstrating their ranges of validity. We find that for moderate- to high-porosity materials, none of the analytical theories is accurate and, at present, numerical techniques must be relied upon.

Deep and superficial fibers of the lumbar multifidus muscle are differentially active during voluntary arm movements

AB Study Design. A cross-sectional study was conducted. Objective. To determine the activity of the deep and superficial fibers of the lumbar multifidus during voluntary movement of the arm. Summary of Background Data. The multifidus contributes to stability of the lumbar spine. Because the deep and superficial parts of the multifidus are near the center of lumbar joint rotation, the superficial fibers are well suited to control spine orientation, and the deep fibers to control intervertebral movement. However, there currently are limited in vivo data to support this distinction. Methods. Electromyographic activity was recorded in both the deep and superficial multifidus, transversus abdominis, erector spinae, and deltoid using selective intramuscular electrodes and surface electrodes during single and repetitive arm movements. The latency of electromyographic onset in each muscle during single movements and the pattern of electromyographic activity during repetitive movements were compared between muscles. Results. With single arm movements, the onset of electromyography in the erector spinae and superficial multifidus relative to the deltoid was dependent on the direction of movement, but the onset in the deep multifidus and transversus abdominis was not. With repetitive arm movements, peaks in superficial multifidus and erector spinae electromyography occurred only during flexion for most subjects, whereas peaks in deep multifidus electromyography occurred during movement in both directions. Conclusions. The deep and superficial fibers of the multifidus are differentially active during single and repetitive movements of the arm. The data from this study support the hypothesis that the superficial multifidus contributes to the control of spine orientation, and that the deep multifidus has a role in controlling intersegmental motion. (C) 2002 Lippincott Williams & Wilkins, Inc.

The comparative characterization of structural heterogeneity of mesoporous activated carbon fibers (ACFs)

The comparative analysis of the most widely used methods of mesoporosity characterization of two activated carbon fibers is presented. Not only the older methods are used, i.e. Barrett, Joyner and Halenda (BJH), Dubinin (the so-called first variant-D-1ST and the so-called second variant-D-2ND), Dollimore and Heal (DH), and Pierce (P) but the recently developed ones, i.e. the method of Nguyen and Do (ND) and that developed by Do (Do) are also applied. Additionally, the method of the characterization of fractality is put to use (fractal analog of FHH isotherm). The results are compared and discussed. (C) 2002 Elsevier Science B.V. All fights reserved.

An Analytical Solution for the Elastic Lateral-Distortional Buckling of I-section Beams

Lateral-distortional buckling may occur in I-section beams with slender webs and stocky flanges. A computationally efficient method is presented in this paper to study this phenomenon. Previous studies on distortional buckling have been on the use of 3(rd) and 5(th) order polynomials to model the displacements. The present study provides an alternative way, using Fourier Series, to model the behaviour. Beams of different cross-sectional dimensions, load cases and restraint conditions are examined and compared. The accuracy and versatility of the method are verified by calibrating against the results of other published studies. The present method is believed to be a simple and efficient way of determining the buckling load and mode shapes of I-section beams that are susceptible to lateral-distortional buckling modes.

On the possibility of elastic strain localisation in a fault

The phenomenon of strain localisation is often observed in shear deformation of particulate materials, e.g., fault gouge. This phenomenon is usually attributed to special types of plastic behaviour of the material (e.g., strain softening or mismatch between dilatancy and pressure sensitivity or both). Observations of strain localisation in situ or in experiments are usually based on displacement measurements and subsequent computation of the displacement gradient. While in conventional continua the symmetric part of the displacement gradient is equal to the strain, it is no longer the case in the more realistic descriptions within the framework of generalised continua. In such models the rotations of the gouge particles are considered as independent degrees of freedom the values of which usually differ from the rotation of an infinitesimal volume element of the continuum, the latter being described for infinitesimal deformations by the non-symmetric part of the displacement gradient. As a model for gouge material we propose a continuum description for an assembly of spherical particles of equal radius in which the particle rotation is treated as an independent degree of freedom. Based on this model we consider simple shear deformations of the fault gouge. We show that there exist values of the model parameters for which the displacement gradient exhibits a pronounced localisation at the mid-layers of the fault, even in the absence of inelasticity. Inelastic effects are neglected in order to highlight the role of the independent rotations and the associated additional parameters. The localisation-like behaviour occurs if (a) the particle rotations on the boundary of the shear layer are constrained (this type of boundary condition does not exist in a standard continuum) and (b) the contact moment-or bending stiffness is much smaller than the product of the effective shear modulus of the granulate and the square of the width of the gouge layer. It should be noted however that the virtual work functional is positive definite over the range of physically meaningful parameters (here: contact stiffnesses, solid volume fraction and coordination number) so that strictly speaking we are not dealing with a material instability.

Characterization of activated carbon fibers using argon adsorption

In this paper, we present results of the internal structure (pore size and pore wall thickness distributions) of a series of activated carbon fibers with different degrees of burn-off, determined from interpretation of argon adsorption data at 87 K using infinite and finite wall thickness models. The latter approach has recently been developed in our laboratory. The results show that while the low bun-off samples have nearly uniform pore size (