Dynamics of sheared inelastic dumbbells

We study the dynamical properties of the homogeneous shear flow of inelastic dumbbells in two dimensions as a first step towards examining the effect of shape on the properties of flowing granular materials. The dumbbells are modelled as smooth fused disks characterized by the ratio of the distance between centres (L) and the disk diameter (D), with an aspect ratio (L/D) varying between 0 and 1 in our simulations. Area fractions studied are in the range 0.1-0.7, while coefficients of normal restitution (e(n)) from 0.99 to 0.7 are considered. The simulations use a modified form of the event-driven methodology for circular disks. The average orientation is characterized by an order parameter S, which varies between 0 (for a perfectly disordered fluid) and 1 (for a fluid with the axes of all dumbbells in the same direction). We investigate power-law fits of S as a function of (L D) and (1 - e(n)(2)) There is a gradual increase in ordering as the area fraction is increased, as the aspect ratio is increased or as the coefficient of restitution is decreased. The order parameter has a maximum value of about 0.5 for the highest area fraction and lowest coefficient of restitution considered here. The mean energy of the velocity fluctuations in the flow direction is higher than that in the gradient direction and the rotational energy, though the difference decreases as the area fraction increases, due to the efficient collisional transfer of energy between the three directions. The distributions of the translational and rotational velocities are Gaussian to a very good approximation. The pressure is found to be remarkably independent of the coefficient of restitution. The pressure and dissipation rate show relatively little variation when scaled by the collision frequency for all the area fractions studied here, indicating that the collision frequency determines the momentum transport and energy dissipation, even at the lowest area fractions studied here. The mean angular velocity of the particles is equal to half the vorticity at low area fractions, but the magnitude systematically decreases to less than half the vorticity as the area fraction is increased, even though the stress tensor is symmetric.

Scaling theory of quantum resistance distributions in disordered systems

We have derived explicitly, the large scale distribution of quantum Ohmic resistance of a disordered one-dimensional conductor. We show that in the thermodynamic limit this distribution is characterized by two independent parameters for strong disorder, leading to a two-parameter scaling theory of localization. Only in the limit of weak disorder we recover single parameter scaling, consistent with existing theoretical treatments.

The velocity dispersion of giant molecular clouds. II - Mathematical and numerical refinements

The energy input to giant molecular clouds is recalculated, using the proper linearized equations of motion, including the Coriolis force and allowing for changes in the guiding center. Perturbation theory yields a result in the limit of distant encounters and small initial epicyclic amplitudes. Direct integration of the motion equations allows the strong encounter regime to be studied. The present perturbation theory result differs by a factor of order unity from that of Jog and Ostriker (1988). The result of present numerical integrations for the 2D (planar) velocity dispersion is presented. The accretion rate for a molecular cloud in the Galactic disk is calculated.

Biorthogonal series method for Oseen type flows

A biorthogonal series method is developed to solve Oseen type flow problems. The theory leads to a new set of eigenfunctions for a specific class of linear non-selfadjoint operators containing the biharmonic one. These eigenfunctions differ from those given earlier in the literature for the biharmonic operator. The method is applied to the problem of thermocapillary flow in a cylindrical liquid bridge of finite length with axial through flow. Flow and temperature distributions are obtained at leading order of an expansion for small surface tension Reynolds number and Prandtl number. Another related problem considered is that of cylindrical cavity flow. Solutions for both cases are presented in terms of biorthogonal series. The effect of axial through flow on velocity and temperature fields is discussed by numerical evaluation of the truncated analytical series. The presence of axial through flow not only convectively shifts the vortices induced by surface forces in the direction of the through flow, but also moves their centers toward the outer cylindrical boundary. This process can lead to significantly asymmetric flow structures.

Squeezed states, photon-number distributions, and U(l) invariance

We study the photon-number distribution in squeezed states of a single-mode radiation field. A U(l)-invariant squeezing criterion is compared and contrasted with a more restrictive criterion, with the help of suggestive geometric representations. The U(l) invariance of the photon-number distribution in a squeezed coherent state, with arbitrary complex squeeze and displacement parameters, is explicitly demonstrated. The behavior of the photon-number distribution for a representative value of the displacement and various values of the squeeze parameter is numerically investigated. A new kind of giant oscillation riding as an envelope over more rapid oscillations in this distribution is demonstrated.

Evolution in the time series of vortex velocity fluctuations across different regimes of vortex flow

Investigations of vortex velocity fluctuation in time domain have revealed a presence of low frequency velocity fluctuations which evolve with the different driven phases of the vortex state in a single crystal of 2H-NbSe2. The observation of velocity fluctuations with a characteristic low frequency is associated with the onset of nonlinear nature of vortex flow deep in the driven elastic vortex state. (C) 2009 Elsevier B.V. All rights reserved.

Support vector machine for evaluating seismic-liquefaction potential using shear wave velocity

The use of the shear wave velocity data as a field index for evaluating the liquefaction potential of sands is receiving increased attention because both shear wave velocity and liquefaction resistance are similarly influenced by many of the same factors such as void ratio, state of stress, stress history and geologic age. In this paper, the potential of support vector machine (SVM) based classification approach has been used to assess the liquefaction potential from actual shear wave velocity data. In this approach, an approximate implementation of a structural risk minimization (SRM) induction principle is done, which aims at minimizing a bound on the generalization error of a model rather than minimizing only the mean square error over the data set. Here SVM has been used as a classification tool to predict liquefaction potential of a soil based on shear wave velocity. The dataset consists the information of soil characteristics such as effective vertical stress (sigma'(v0)), soil type, shear wave velocity (V-s) and earthquake parameters such as peak horizontal acceleration (a(max)) and earthquake magnitude (M). Out of the available 186 datasets, 130 are considered for training and remaining 56 are used for testing the model. The study indicated that SVM can successfully model the complex relationship between seismic parameters, soil parameters and the liquefaction potential. In the model based on soil characteristics, the input parameters used are sigma'(v0), soil type. V-s, a(max) and M. In the other model based on shear wave velocity alone uses V-s, a(max) and M as input parameters. In this paper, it has been demonstrated that Vs alone can be used to predict the liquefaction potential of a soil using a support vector machine model. (C) 2010 Elsevier B.V. All rights reserved.

Symmetry Properties of the Large-Deviation Function of the Velocity of a Self-Propelled Polar Particle

A geometrically polar granular rod confined in 2D geometry, subjected to a sinusoidal vertical oscillation, undergoes noisy self-propulsion in a direction determined by its polarity. When surrounded by a medium of crystalline spherical beads, it displays substantial negative fluctuations in its velocity. We find that the large-deviation function (LDF) for the normalized velocity is strongly non-Gaussian with a kink at zero velocity, and that the antisymmetric part of the LDF is linear, resembling the fluctuation relation known for entropy production, even when the velocity distribution is clearly non-Gaussian. We extract an analogue of the phase-space contraction rate and find that it compares well with an independent estimate based on the persistence of forward and reverse velocities.

Improved velocity method for the determination of coefficient of consolidation

Parkin (1978) suggested the velocity method based on the observation that the theoretical rate of consolidation and time factor plot on a log-log scale yields an initial slope of 1:2 up to 50% consolidation. A new method is proposed that is an improvement over Parkin's velocity method because it minimizes the problems encountered in using that method. The results obtained agree with the other methods in use.

Self-similar solutions of laser produced blast waves

The aerodynamics of the blast wave produced by laser ablation is studied using the piston analogy. The unsteady one-dimensional gasdynamic equations governing the flow an solved under assumption of self-similarity. The solutions are utilized to obtain analytical expressions for the velocity, density, pressure and temperature distributions. The results predict. all the experimentally observed features of the laser produced blast waves.

Estimation of low-velocity impact damage in laminated composite circular plates using nonlinear finite element analysis

Nonlinear finite element analysis is used for the estimation of damage due to low-velocity impact loading of laminated composite circular plates. The impact loading is treated as an equivalent static loading by assuming the impactor to be spherical and the contact to obey Hertzian law. The stresses in the laminate are calculated using a 48 d.o.f. laminated composite sector element. Subsequently, the Tsai-Wu criterion is used to detect the zones of failure and the maximum stress criterion is used to identify the mode of failure. Then the material properties of the laminate are degraded in the failed regions. The stress analysis is performed again using the degraded properties of the plies. The iterative process is repeated until no more failure is detected in the laminate. The problem of a typical T300/N5208 composite [45 degrees/0 degrees/-45 degrees/90 degrees](s) circular plate being impacted by a spherical impactor is solved and the results are compared with experimental and analytical results available in the literature. The method proposed and the computer code developed can handle symmetric, as well as unsymmetric, laminates. It can be easily extended to cover the impact of composite rectangular plates, shell panels and shells.

Translational velocity oscillations of piston generated vortex rings

Experimental results are presented that show that the translational velocities of piston generated vortex rings often undergo oscillations, similar to those recently discovered for drop generated rings. An attempt has been made to minimize uncertainties by utilizing both dye and hydrogen bubbles for visualization and carefully repeating measurements on the same ring and on different realizations under the same nominal piston conditions. The results unambiguously show that under most conditions, both for laminar and turbulent rings and for rings generated from pipes and orifices, the oscillations are present. The present results, together with the earlier results on drop generated rings, give support to the view that translational velocity oscillations are probably an inherent feature of translating vortex ring fields. (C) 1995 American Institute of Physics.