The effect of boundaries on the plane Couette flow of granular materials: a bifurcation analysis

The tendency of granular materials in rapid shear ow to form non-uniform structures is well documented in the literature. Through a linear stability analysis of the solution of continuum equations for rapid shear flow of a uniform granular material, performed by Savage (1992) and others subsequently, it has been shown that an infinite plane shearing motion may be unstable in the Lyapunov sense, provided the mean volume fraction of particles is above a critical value. This instability leads to the formation of alternating layers of high and low particle concentrations oriented parallel to the plane of shear. Computer simulations, on the other hand, reveal that non-uniform structures are possible even when the mean volume fraction of particles is small. In the present study, we have examined the structure of fully developed layered solutions, by making use of numerical continuation techniques and bifurcation theory. It is shown that the continuum equations do predict the existence of layered solutions of high amplitude even when the uniform state is linearly stable. An analysis of the effect of bounding walls on the bifurcation structure reveals that the nature of the wall boundary conditions plays a pivotal role in selecting that branch of non-uniform solutions which emerges as the primary branch. This demonstrates unequivocally that the results on the stability of bounded shear flow of granular materials presented previously by Wang et al. (1996) are, in general, based on erroneous base states.

Anomalous triple gauge boson couplings in e(-)e(+) -> gamma gamma for noncommutative standard model

We investigate e(+)e(-) -> gamma gamma process within the Seiberg-Witten expanded noncommutative standard model (NCSM) scenario in the presence of anomalous triple gauge boson couplings. This study is done with and without initial beam polarization and we restrict ourselves to leading order effects of noncommutativity i.e. O(Theta). The noncommutative (NC) corrections are sensitive to the electric component ((Theta) over bar (E)) of NC parameter. We include the effects of Earth's rotation in our analysis. This study is done by investigating the effects of noncommutativity on different time averaged cross section observables. We have also defined forward backward asymmetries which will be exclusively sensitive to anomalous couplings. We have looked into the sensitivity of these couplings at future experiments at the International Linear Collider (ILC). This analysis is done under realistic ILC conditions with the center of mass energy (cm.) root s = 800 GeV and integrated luminosity L = 500 fb(-1). The scale of noncommutativity is assumed to be Lambda = 1 TeV. The limits on anomalous couplings of the order 10(-1) from forward backward asymmetries while much stringent limits of the order 10(-2) from total cross section are obtained if no signal beyond SM is seen. (C) 2012 Elsevier B.V. All rights reserved.

A MICROMACHINED WIDE-BAND IN-PLANE SINGLE-AXIS CAPACITIVE ACCELEROMETER WITH A DISPLACEMENT-AMPLIFYING COMPLIANT MECHANISM

With the premise that electronic noise dominates mechanical noise in micromachined accelerometers, we present here a method to enhance the sensitivity and resolution at kHz bandwidth using mechanical amplification. This is achieved by means of a Displacement-amplifying Compliant Mechanism (DaCM) that is appended to the usual sensing element comprising a proof-mass and a suspension. Differential comb-drive arrangement is used for capacitive-sensing. The DaCM is designed to match the stiffness of the suspension so that there is substantial net amplification without compromising the bandwidth. A spring-mass-lever model is used to estimate the lumped parameters of the system. A DaCM-aided accelerometer and another without a DaCM-both occupying the same footprint-are compared to show that the former gives enhanced sensitivity: 8.7 nm/g vs. 1.4 nm/g displacement at the sensing-combs under static conditions. A prototype of the DaCM-aided micromachined acclerometer was fabricated using bulk-micromachining. It was tested at the die-level and then packaged on a printed circuit board with an off-the-shelf integrated chip for measuring change in capacitance. Under dynamic conditions, the measured amplification factor at the output of the DaCM was observed to be about 11 times larger than the displacement of the proof-mass and thus validating the concept of enhancing the sensitivity of accelerometers using mechanical amplifiers. The measured first in-plane natural frequency of the fabricated accelerometer was 6.25 kHz. The packaged accelerometer with the DaCM was measured to have 26.7 mV/g sensitivity at 40 Hz.

Improving the Sensitivity and Bandwidth of In-Plane Capacitive Microaccelerometers Using Compliant Mechanical Amplifiers

This paper presents a method to enhance both the sensitivity and bandwidth of in-plane capacitive micromachined accelerometers by using compliant mechanical amplifiers, and thus obviating the compromise between the sensitivity and bandwidth. Here, we compare one of the most sensitive single-axis capacitive accelerometers and another with large resonant frequency reported in the literature with the modified designs that include displacement-amplifying compliant mechanisms (DaCMs) occupying the same footprint and under identical conditions. We show that 62% improvement in sensitivity and 34% improvement in bandwidth in the former, and 27% and 25% in the latter can be achieved. Also presented here is a dual-axis accelerometer that uses a suspension that decouples and amplifies the displacements along the two in-plane orthogonal axes. The new design was microfabricated, packaged, and tested. The device is 25-mu m thick with the interfinger gap as large as 4 m. Despite the simplicity of the microfabrication process, the measured axial sensitivity (static) of about 0.58 V/g for both the axes was achieved with a cross-axis sensitivity of less than +/- 2%. The measured natural frequency along the two in-plane axes was 920 Hz. Displacement amplification of 6.2 was obtained using the DaCMs in the dual-axis accelerometer. 2013-0083]

Influence of external weld flash on the in-plane plane-strain formability of friction stir welded sheets

The main aim of the present work is to analyze the influence of external weld flash on the formability of friction stir welding sheets through in-plane plane-strain formability tests. The load-extension behavior and forming limit strains are measured to quantify the formability. The influence of friction stir welding parameters on the height of weld flash was also studied. The base materials used for welding trials are AA6061T6 and AA5052H32 alloy sheets of 2.1-mm thickness. It is observed that the influence of external weld flash on the maximum load and total extension for all the friction stir welding conditions is negligible. The effect of weld flash on the limiting major strain is also insignificant. But the presence of weld flash has changed the limiting minor strain, more toward plane-strain condition, indicating the change in strain-path toward plane-strain. This is due to the strain taken by weld flash, along with the major strain, minor strain, and thickness strain in the friction stir welding sheet plane because of constancy of volume. The formation of weld flash and its height are affected synergistically by the axial force and temperature development during friction stir welding. The higher the axial force and temperature, the higher the flash height.

Onset of plane layer magnetoconvection at low Ekman number

We study the onset of magnetoconvection between two infinite horizontal planes subject to a vertical magnetic field aligned with background rotation. In order to gain insight into the convection taking place in the Earth's tangent cylinder, we target regimes of asymptotically strong rotation. The critical Rayleigh number Ra-c and critical wavenumber a(c) are computed numerically by solving the linear stability problem in a systematic way, with either stress-free or no-slip kinematic boundary conditions. A parametric study is conducted, varying the Ekman number E (ratio of viscous to Coriolis forces) and the Elsasser number. (ratio of the Lorentz force to the Coriolis force). E is varied from 10(-9) to 10(-2) and. from 10(-3) to 1. For a wide range of thermal and magnetic Prandtl numbers, our results verify and confirm previous experimental and theoretical results showing the existence of two distinct unstable modes at low values of E-one being controlled by the magnetic field, the other being controlled by viscosity (often called the viscous mode). It is shown that oscillatory onset does not occur in the range of parameters we are interested in. Asymptotic scalings for the onset of these modes are numerically confirmed and their domain of validity is precisely quantified. We show that with no-slip boundary conditions, the asymptotic behavior is reached for E < 10(-6) and establish a map in the (E, Lambda) plane. We distinguish regions where convection sets in either through the magnetic mode or through the viscous mode. Our analysis gives the regime in which the transition between magnetic and viscous modes may be observed. We also show that within the asymptotic regime, the role played by the kinematic boundary conditions is minimal. (C) 2015 AIP Publishing LLC.

Micro-shock waves generated inside a fluid jet impinging on plane wall

An Nd:glass laser pulse (18 ns, 1.38 J) is focused in a tiny area of about 100-mum diam under ambient conditions to produce micro-shock waves. The laser is focused above a planar surface with a typical standoff distance of about 4 mm, The laser energy is focused inside a supersonic circular jet of carbon dioxide gas produced by a nozzle with internal diameter of 2.9 mm and external diameter of 8 mm, Nominal value of the Mach number of the jet is around 2 with the corresponding pressure ratio of 7.5 (stagnation pressure/static pressure at the exit of the nozzle), The interaction process of the micro-shock wave generated inside the supersonic jet with the plane wall is investigated using double-pulse holographic interferometry. A strong surface vortex field with subsequent generation of a side jet propagating outward along the plane wail is observed. The interaction of the micro-shock wave with the cellular structure of the supersonic jet does not seem to influence the near surface features of the flowfield. The development of the coherent structures near the nozzle exit due to the upstream propagation of pressure waves seems to be affected by the outward propagating micro-shock wave. Mach reflection is observed when the micro-shock wave interacts with the plane wall at a standoff distance of 4 mm, The Mach stem is slightly deflected, indicating strong boundary-layer and viscous effects near the wall. The interaction process is also simulated numerically using an axisymmetric transient laminar Navier-Stokes solver. Qualitative agreement between experimental and numerical results is good.

The scattering of general SH plane wave by interface crack between two dissimilar viscoelastic bodies

The scattering of general SH plane wave by an interface crack between two dissimilar viscoelastic bodies is studied and the dynamic stress,intensity factor at the crack-tip is computed. The scattering problem can be decomposed into two problems: one is the reflection and refraction problem of general SH plane waves at perfect interface (with no crack); another is the scattering problem due to the existence of crack. For the first problem, the viscoelastic wave equation, displacement and stress continuity conditions across the interface are used to obtain the shear stress distribution at the interface. For the second problem, the integral transformation method is used to reduce the scattering problem into dual integral equations. Then, the dual integral equations are transformed into the Cauchy singular integral equation of first kind by introduction of the crack dislocation density function. Finally, the singular integral equation is solved by Kurtz's piecewise continuous function method. As a consequence, the crack opening displacement and dynamic stress intensity factor are obtained. At the end of the paper, a numerical example is given. The effects of incident angle, incident frequency and viscoelastic material parameters are analyzed. It is found that there is a frequency region for viscoelastic material within which the viscoelastic effects cannot be ignored.

Optimization Of Off-Null Ellipsometry For Air/Solid Interfaces

The optimization of off-null ellipsometry is described with emphasis on the improvement of sample thickness sensitivity. Optimal conditions are dependent on azimuth angle settings of the polarizer, compensator, and analyzer in a polarizer-compensator-sample-analyzer ellipsometer arrangement. Numerical simulation utilized offers an approach to present the dependence of the sensitivity on the azimuth angle settings, from which optimal settings corresponding to the best sensitivity are derived. For a series of samples of SiO2 layer (thickness in the range of 1.8-6.5 nm) on silicon substrate, the theory analysis proves that sensitivity at the optimal settings is increased 20 times compared to that at null settings used in most works, and the relationship between intensity and thickness is simplified as a linear type instead of the original nonlinear type, with the relative error reduced to similar to 1/100 at the optimal settings. Furthermore the discussion has been extended toward other factors affecting the sensitivity of the practical system, such as the linear dynamic range of the detector, the signal-to-noise ratio and the intensity from the light source, etc. Experimental results from the investigation Of SiO2 layer on silicon substrate are chosen to verify the optimization. (c) 2007 Optical Society of America.

Complex stress functions and plastic zone sizes for notch cracks subjected to various loading conditions

In this paper, the conformal mapping method is used to solve the plane problem of an infinite plate containing a central lip-shaped notch subjected to biaxial loading at a remote boundary or a surface uniform pressure on the notch. The stress intensity factors KI and KII are obtained by the derived complex stress functions. The simple analytical expressions can be applied to the situation of cracks originating from a circular or an elliptical notch. The plastic zone sizes for such notch cracks are subsequently evaluated in light of the Dugdale strip yield concept. The results are consistent with available numerical data.

Fiber Bragg Gratings, IT Techniques and Strain Gauge Validation for Strain Calculation on Aged Metal Specimens

This paper studies the feasibility of calculating strains in aged F114 steel specimens with Fiber Bragg Grating (FBG) sensors and infrared thermography (IT) techniques. Two specimens have been conditioned under extreme temperature and relative humidity conditions making comparative tests of stress before and after aging using different adhesives. Moreover, a comparison has been made with IT tecniques and conventional methods for calculating stresses in F114 steel. Implementation of Structural Health Monitoring techniques on real aircraft during their life cycle requires a study of the behaviour of FBG sensors and their wiring under real conditions, before using them for a long time. To simulate aging, specimens were stored in a climate chamber at 70 degrees C and 90% RH for 60 days. This study is framed within the Structural Health Monitoring (SHM) and Non Destructuve Evaluation (NDE) research lines, integrated into the avionics area maintained by the Aeronautical Technologies Centre (CTA) and the University of the Basque Country (UPV/EHU).

Studies of Zγ production and constraints on anomalous triple gauge couplings in pp collisions at √s = 7 TeV

In this thesis, we test the electroweak sector of the Standard Model of particle physics through the measurements of the cross section of the simultaneous production of the neutral weak boson Z and photon γ, and the limits on the anomalous Zγγ and ZZγ triple gauge couplings h3 and h4 with the Z decaying to leptons (electrons and muons). We analyze events collected in proton-proton collisions at center of mass energy of sqrt(s) = 7 TeV corresponding to an integrated luminosity of 5.0 inverse femtobarn. The analyzed events were recorded by the Compact Muon Solenoid detector at the Large Hadron Collider in 2011.

The production cross section has been measured for hard photons with transverse momentum greater than 15 GeV that are separated from the the final state leptons in the eta-phi plane by Delta R greater than 0.7, whose sum of the transverse energy of hadrons over the transverse energy of the photon in a cone around the photon with Delta R less than 0.3 is less than 0.5, and with the invariant mass of the dilepton system greater than 50 GeV. The measured cross section value is 5.33 +/- 0.08 (stat.) +/- 0.25 (syst.) +/- 0.12 (lumi.) picobarn. This is compatible with the Standard Model prediction that includes next-to-leading-order QCD contributions: 5.45 +/- 0.27 picobarn.

The measured 95 % confidence-level upper limits on the absolute values of the anomalous couplings h3 and h4 are 0.01 and 8.8E-5 for the Zγγ interactions, and, 8.6E-3 and 8.0E-5 for the ZZγ interactions. These values are also compatible with the Standard Model where they vanish in the tree-level approximation. They extend the sensitivity of the 2012 results from the ATLAS collaboration based on 1.02 inverse femtobarn of data by a factor of 2.4 to 3.1.

Singularities and horizons in the collisions of gravitational waves

This thesis presents a study of the dynamical, nonlinear interaction of colliding gravitational waves, as described by classical general relativity. It is focused mainly on two fundamental questions: First, what is the general structure of the singularities and Killing-Cauchy horizons produced in the collisions of exactly plane-symmetric gravitational waves? Second, under what conditions will the collisions of almost-plane gravitational waves (waves with large but finite transverse sizes) produce singularities?

In the work on the collisions of exactly-plane waves, it is shown that Killing horizons in any plane-symmetric spacetime are unstable against small plane-symmetric perturbations. It is thus concluded that the Killing-Cauchy horizons produced by the collisions of some exactly plane gravitational waves are nongeneric, and that generic initial data for the colliding plane waves always produce "pure" spacetime singularities without such horizons. This conclusion is later proved rigorously (using the full nonlinear theory rather than perturbation theory), in connection with an analysis of the asymptotic singularity structure of a general colliding plane-wave spacetime. This analysis also proves that asymptotically the singularities created by colliding plane waves are of inhomogeneous-Kasner type; the asymptotic Kasner axes and exponents of these singularities in general depend on the spatial coordinate that runs tangentially to the singularity in the non-plane-symmetric direction.

In the work on collisions of almost-plane gravitational waves, first some general properties of single almost-plane gravitational-wave spacetimes are explored. It is shown that, by contrast with an exact plane wave, an almost-plane gravitational wave cannot have a propagation direction that is Killing; i.e., it must diffract and disperse as it propagates. It is also shown that an almost-plane wave cannot be precisely sandwiched between two null wavefronts; i.e., it must leave behind tails in the spacetime region through which it passes. Next, the occurrence of spacetime singularities in the collisions of almost-plane waves is investigated. It is proved that if two colliding, almost-plane gravitational waves are initially exactly plane-symmetric across a central region of sufficiently large but finite transverse dimensions, then their collision produces a spacetime singularity with the same local structure as in the exact-plane-wave collision. Finally, it is shown that a singularity still forms when the central regions are only approximately plane-symmetric initially. Stated more precisely, it is proved that if the colliding almost-plane waves are initially sufficiently close to being exactly plane-symmetric across a bounded central region of sufficiently large transverse dimensions, then their collision necessarily produces spacetime singularities. In this case, nothing is now known about the local and global structures of the singularities.

Gauge Invariant Spectral Cauchy Characteristic Extraction of Gravitational Waves in Computational General Relativity

We present a complete system for Spectral Cauchy characteristic extraction (Spectral CCE). Implemented in C++ within the Spectral Einstein Code (SpEC), the method employs numerous innovative algorithms to efficiently calculate the Bondi strain, news, and flux.

Spectral CCE was envisioned to ensure physically accurate gravitational wave-forms computed for the Laser Interferometer Gravitational wave Observatory (LIGO) and similar experiments, while working toward a template bank with more than a thousand waveforms to span the binary black hole (BBH) problem’s seven-dimensional parameter space.

The Bondi strain, news, and flux are physical quantities central to efforts to understand and detect astrophysical gravitational wave sources within the Simulations of eXtreme Spacetime (SXS) collaboration, with the ultimate aim of providing the first strong field probe of the Einstein field equation.

In a series of included papers, we demonstrate stability, convergence, and gauge invariance. We also demonstrate agreement between Spectral CCE and the legacy Pitt null code, while achieving a factor of 200 improvement in computational efficiency.

Spectral CCE represents a significant computational advance. It is the foundation upon which further capability will be built, specifically enabling the complete calculation of junk-free, gauge-free, and physically valid waveform data on the fly within SpEC.

Plane-strain discrete dislocation plasticity with climb-assisted glide motion of dislocations

A small-strain two-dimensional discrete dislocation plasticity (DDP) framework is developed wherein dislocation motion is caused by climb-assisted glide. The climb motion of the dislocations is assumed to be governed by a drag-type relation similar to the glide-only motion of dislocations: such a relation is valid when vacancy kinetics is either diffusion limited or sink limited. The DDP framework is employed to predict the effect of dislocation climb on the uniaxial tensile and pure bending response of single crystals. Under uniaxial tensile loading conditions, the ability of dislocations to bypass obstacles by climb results in a reduced dislocation density over a wide range of specimen sizes in the climb-assisted glide case compared to when dislocation motion is only by glide. A consequence is that, at least in a single slip situation, size effects due to dislocation starvation are reduced. By contrast, under pure bending loading conditions, the dislocation density is unaffected by dislocation climb as geometrically necessary dislocations (GNDs) dominate. However, climb enables the dislocations to arrange themselves into lower energy configurations which significantly reduces the predicted bending size effect as well as the amount of reverse plasticity observed during unloading. The results indicate that the intrinsic plasticity material length scale associated with GNDs is strongly affected by thermally activated processes and will be a function of temperature. © 2013 IOP Publishing Ltd.