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.

Role of La0.5Sr0.5COO3 template layers on dielectric and electrical properties of pulsed-laser ablated Pb(Nb2/3Mg1/3)O-3-PbTiO3 thin films

Relaxor ferroelectric thin films of 0.7Pb(Mg1/3Nb2/3)O-3-0.3PbTiO(3) (PMN-PT) deposited on platinized silicon substrates with and without template layers were studied. Perovskite phase (80% by volume) was obtained through proper selection of the processing conditions on bare Pt/Ti/SiO2/Si substrates. The films were initially grown at 300 degreesC using pulsed-laser ablation and subsequently annealed in a rapid thermal annealing furnace in the temperature range of 750-850 degreesC to induce crystallization. Comparison of microstructure of the films annealed at different temperatures showed change in perovskite phase formation and grain size etc. Results from compositional analysis of the films revealed that the films initially possessed high content of lead percentage, which subsequently decreased after annealing at temperature 750-850 degreesC. Films with highest perovskite content were found to form at 820-840 degreesC on Pt substrates where the Pb content was near stoichiometric. Further improvement in the formation of perovskite PMN-PT phase was obtained by using buffer layers of La0.5Sr0.5CoO3 (LSCO) on the Pt substrate. This resulted 100% perovskite phase formation in the films deposited at 650 degreesC. Dielectric studies on the PMN-PT films with LSCO template layers showed high values of relative dielectric constant (3800) with a loss factor (tan delta) of 0.035 at a frequency of 1 kHz at room temperature. (C) 2002 Elsevier Science B.V. All rights reserved.

Right-Definite Multiparameter Sturm–Liouville Problems With Eigenparameter-Dependent Boundary Conditions

We study a system of ordinary differential equations linked by parameters and subject to boundary conditions depending on parameters. We assume certain definiteness conditions on the coefficient functions and on the boundary conditions that yield, in the corresponding abstract setting, a right-definite case. We give results on location of the eigenvalues and oscillation of the eigenfunctions.

Band Structures of Bilayer Graphene Superlattices

We formulate a low energy effective Hamiltonian to study superlattices in bilayer graphene (BLG) using a minimal model which supports quadratic band touching points. We show that a one dimensional (1D) periodic modulation of the chemical potential or the electric field perpendicular to the layers leads to the generation of zero-energy anisotropic massless Dirac fermions and finite energy Dirac points with tunable velocities. The electric field superlattice maps onto a coupled chain model comprised of ``topological'' edge modes. 2D superlattice modulations are shown to lead to gaps on the mini-Brillouin zone boundary but do not, for certain symmetries, gap out the quadratic band touching point. Such potential variations, induced by impurities and rippling in biased BLG, could lead to subgap modes which are argued to be relevant to understanding transport measurements.

Effects of phase inhomogeneity and boundary conditions on the dynamic response of SMA wire actuators

This paper reports the simulation results from the dynamic analysis of a Shape Memory Alloy (SMA) actuator. The emphasis is on understanding the dynamic behavior under various loading rates and boundary conditions, resulting in complex scenarios such as thermal and stress gradients. Also, due to the polycrystalline nature of SMA wires, presence of microstructural inhomogeneity is inevitable. Probing the effect of inhomogeneity on the dynamic behavior can facilitate the prediction of life and characteristics of SMA wire actuator under varieties of boundary and loading conditions. To study the effect of these factors, an initial boundary value problem of SMA wire is formulated. This is subsequently solved using finite element method. The dynamic response of the SMA wire actuator is analyzed under mechanical loading and results are reported. Effect of loading rate, micro-structural inhomogeneity and thermal boundary conditions on the dynamic response of SMA wire actuator is investigated and the simulation results are reported.

Task Dependent Boundary Mannequins in Statistical DHM

The primary objective of the paper is to make use of statistical digital human model to better understand the nature of reach probability of points in the taskspace. The concept of task-dependent boundary manikin is introduced to geometrically characterize the extreme individuals in the given population who would accomplish the task. For a given point of interest and task, the map of the acceptable variation in anthropometric parameters is superimposed with the distribution of the same parameters in the given population to identify the extreme individuals. To illustrate the concept, the task space mapping is done for the reach probability of human arms. Unlike the boundary manikins, who are completely defined by the population, the dimensions of these manikins will vary with task, say, a point to be reached, as in the present case. Hence they are referred to here as the task-dependent boundary manikins. Simulations with these manikins would help designers to visualize how differently the extreme individuals would perform the task. Reach probability at the points in a 3D grid in the operational space is computed; for objects overlaid in this grid, approximate probabilities are derived from the grid for rendering them with colors indicating the reach probability. The method may also help in providing a rational basis for selection of personnel for a given task.

Texture and grain boundary character distribution during Equal Channel Angular Extrusion of some two-phase copper alloys

In the present work, a thorough investigation of evolution of microstructure and texture has been carried out to elucidate the evolution of texture and grain boundary character distribution (GBCD) during Equal Channel Angular Extrusion (ECAE) of some model two-phase materials, namely Cu-0.3Cr and Cu-40Zn. Texture of Cu-0.3Cr alloy is similar to that reported for pure copper. On the other hand, in Cu-40Zn alloy, texture evolution in α and β (B2) phases are interdependent. In Cu-0.3Cr alloy, there is a considerable decreases in volume fraction of low angle boundaries (LAGBs), only a slight increase in CSL boundaries, but increase in high angle grain boundaries (HAGBs) from 1 pass to 4 passes for both the routes. In the case of Cu-40Zn alloy, there is an appreciable increase in CSL volume fraction.

An experimental study of boundary layer transition induced by a cylinder wake

Boundary layer transition induced by the wake of a circular cylinder in the free stream has been investigated using the particle image velocimetry technique. Some differences between simulation and experimental studies have been reported in the literature, and these have motivated the present study. The appearance of spanwise vortices in the early stage is further confirmed here. Lambda spanwise vortex appears to evolve into a Lambda/hairpin vortex; the flow statistics also confirm such vortices. With increasing Reynolds number, based on the cylinder diameter, and with decreasing cylinder height from the plate, the physical size of these hairpin-like structures is found to decrease. Some mean flow characteristics, including the streamwise growth of the disturbance energy, in a wake-induced transition resemble those in bypass transition induced by free stream turbulence. Streamwise velocity streaks that are eventually generated in the late stage often undergo sinuous-type oscillations. Similar to other transitional flows, an inclined shear layer in the wall-normal plane is often seen to oscillate and shed vortices. The normalized shedding frequency of these vortices, estimated from the spatial spacing and the convection velocity of these vortices, is found to be independent of the Reynolds number, similar to that in ribbon-induced transition. Although the nature of free stream disturbance in a wake-induced transition and that in a bypass transition are different, the late-stage features including the flow breakdown characteristics of these two transitions appear to be similar.