The hard-particle model for a dense granular flow down an inclined plane

Perfectly hard particles are those which experience an infinite repulsive force when they overlap, and no force when they do not overlap. In the hard-particle model, the only static state is the isostatic state where the forces between particles are statically determinate. In the flowing state, the interactions between particles are instantaneous because the time of contact approaches zero in the limit of infinite particle stiffness. Here, we discuss the development of a hard particle model for a realistic granular flow down an inclined plane, and examine its utility for predicting the salient features both qualitatively and quantitatively. We first discuss Discrete Element simulations, that even very dense flows of sand or glass beads with volume fraction between 0.5 and 0.58 are in the rapid flow regime, due to the very high particle stiffness. An important length scale in the shear flow of inelastic particles is the `conduction length' delta = (d/(1 - e(2))(1/2)), where d is the particle diameter and e is the coefficient of restitution. When the macroscopic scale h (height of the flowing layer) is larger than the conduction length, the rates of shear production and inelastic dissipation are nearly equal in the bulk of the flow, while the rate of conduction of energy is O((delta/h)(2)) smaller than the rate of dissipation of energy. Energy conduction is important in boundary layers of thickness delta at the top and bottom. The flow in the boundary layer at the top and bottom is examined using asymptotic analysis. We derive an exact relationship showing that the a boundary layer solution exists only if the volume fraction in the bulk decreases as the angle of inclination is increased. In the opposite case, where the volume fraction increases as the angle of inclination is increased, there is no boundary layer solution. The boundary layer theory also provides us with a way of understanding the cessation of flow when at a given angle of inclination when the height of the layer is decreased below a value h(stop), which is a function of the angle of inclination. There is dissipation of energy due to particle collisions in the flow as well as due to particle collisions with the base, and the fraction of energy dissipation in the base increases as the thickness decreases. When the shear production in the flow cannot compensate for the additional energy drawn out of the flow due to the wall collisions, the temperature decreases to zero and the flow stops. Scaling relations can be derived for h(stop) as a function of angle of inclination.

A novel two sources ultrasound modulated optical tomographic system for screening breast cancer through elasticity characterization

The study of non-invasive characterization of elastic properties of soft biological tissues has been a focus of active researches since recent years. Light is highly scattered by biological tissues and hence, sophisticated reconstruction algorithms are required to achieve good imaging depth and a reasonable resolution. Ultrasound (US), on the otherhand, is less scattered by soft tissues and it has been in use for imaging in biomedical ultrasound systems. Combination of the contrast sensitivity of light and good localization of ultrasound provides a challenging technique for characterization of thicker tissues deep inside the body non-invasively. The elasticity of the tissues is characterized by studying the response of tissues to mechanical excitation induced by an acoustic radiation force (remotely) using an optical laser. The US modulated optical signals which traverse the tissue are detected by using a CCD camera as detector array and the pixel map formed on the CCD is used to characterize the embedded inhomogeneities. The use of CCD camera improves the signal-noise-ratio (SNR) by averaging the signals from all of the CCD pixels.

Modified linear prediction method for directions of arrival estimation of narrow-band plane waves

A modified linear prediction (MLP) method is proposed in which the reference sensor is optimally located on the extended line of the array. The criterion of optimality is the minimization of the prediction error power, where the prediction error is defined as the difference between the reference sensor and the weighted array outputs. It is shown that the L2-norm of the least-squares array weights attains a minimum value for the optimum spacing of the reference sensor, subject to some soft constraint on signal-to-noise ratio (SNR). How this minimum norm property can be used for finding the optimum spacing of the reference sensor is described. The performance of the MLP method is studied and compared with that of the linear prediction (LP) method using resolution, detection bias, and variance as the performance measures. The study reveals that the MLP method performs much better than the LP technique.

Improved prediction of plane transverse jets in supersonic crossflows

THE flowfield due to transverse injection of a round sonic jet into a supersonic flowis a configuration of interest in the design of supersonic combustors or thrust vector control of supersonic jets. The flow is also of fundamental interest because it presents separation from a smooth surface, embedded subsonic regions, curved shear layers, strong shocks, an unusual development of the injected jet into a kidney-shaped streamwise vortex pair, and a wake behind the jet. Although the geometry is simple, the flow is complex and is a good candidate for assessing the behavior of turbulence models for high-speed flow, beginning with the corresponding two-dimensional flow shown in Fig. 1. At the slot, an underexpanded sonic jet expands rapidly into the supersonic crossflow. Expansion waves reflect at the jet boundary, coalesce, and give rise to a Mach surface (Mach disk for round jets).

Kinetic theory for the density plateau in the granular flow down an inclined plane

The striking lack of observable variation of the volume fraction with height in the center of a granular flow down an inclined plane is analysed using constitutive relations obtained from kinetic theory. It is shown that the rate of conduction in the granular energy balance equation is O(delta(2)) smaller than the rate of production of energy due to mean shear and the rate of dissipation due to inelastic collisions, where the small parameter delta = (d/(1 - e(n))H-1/2), d is the particle diameter, en is the normal coefficient of restitution and H is the thickness of the flowing layer. This implies that the volume fraction is a constant in the leading approximation in an asymptotic analysis in small delta. Numerical estimates of both the parameter delta and its pre-factor are obtained to show that the lack of observable variation of the volume fraction with height can be explained by constitutive relations obtained from kinetic theory.

Investigation of the effect of nonlocal scale on ultrasonic wave dispersion characteristics of a monolayer graphene

In this article, an ultrasonic wave propagation in graphene sheet is studied using nonlocal elasticity theory incorporating small scale effects. The graphene sheet is modeled as an isotropic plate of one-atom thick. For this model, the nonlocal governing differential equations of motion are derived from the minimization of the total potential energy of the entire system. An ultrasonic type of wave propagation model is also derived for the graphene sheet. The nonlocal scale parameter introduces certain band gap region in in-plane and flexural wave modes where no wave propagation occurs. This is manifested in the wavenumber plots as the region where the wavenumber tends to infinite or wave speed tends to zero. The frequency at which this phenomenon occurs is called the escape frequency. The explicit expressions for cutoff frequencies and escape frequencies are derived. The escape frequencies are mainly introduced because of the nonlocal elasticity. Obviously these frequencies are function of nonlocal scaling parameter. It has also been obtained that these frequencies are independent of y-directional wavenumber. It means that for any type of nanostructure, the escape frequencies are purely a function of nonlocal scaling parameter only. It is also independent of the geometry of the structure. It has been found that the cutoff frequencies are function of nonlocal scaling parameter (e(0)a) and the y-directional wavenumber (k(y)). For a given nanostructure, nonlocal small scale coefficient can be obtained by matching the results from molecular dynamics (MD) simulations and the nonlocal elasticity calculations. At that value of the nonlocal scale coefficient, the waves will propagate in the nanostructure at that cut-off frequency. In the present paper, different values of e(o)a are used. One can get the exact e(0)a for a given graphene sheet by matching the MD simulation results of graphene with the results presented in this paper. (C) 2010 Elsevier B.V. All rights reserved.

Simultaneous display of image and spectrum in the same plane: a generalized analysis

A generalized analysis, using the Vander Lugt operational notation, of the building block optical system comprising a single holographic optical element (HOE) for achieving simultaneous display of the spectrum and the image of an object in a single plane, has been carried out. The salient features of this analysis are: (1) it allows comprehensive characterization of the HOE, (2) it provides insights into the many possible configurations for the system, and (3) it explains the existing results in a consistent manner.

Suboptimal reentry guidance of a reusable launch vehicle using pitch plane maneuver

Using the recently developed model predictive static programming (MPSP) technique, a nonlinear suboptimal reentry guidance scheme is presented in this paper for a reusable launch vehicle (RLV). Unlike traditional RLV guidance, the problem considered over here is restricted only to pitch plane maneuver of the vehicle, which allows simpler mission planning and vehicle load management. The computationally efficient MPSP technique brings in the philosophy of trajectory optimization into the framework of guidance design, which in turn results in very effective guidance schemes in general. In the problem addressed in this paper, it successfully guides the RLV through the critical reentry phase both by constraining it to the allowable narrow flight corridor as well as by meeting the terminal constraints at the end of the reentry segment. The guidance design is validated by considering possible aerodynamic uncertainties as well as dispersions in the initial conditions. (C) 2010 Elsevier Masson SAS. All rights reserved.

The behaviour of excited plane jets

A plane subsonic jet can be excited to entrain more fluid from its surroundings by subjecting it to antisymmetric periodic disturbances. The essential feature in this phenomenon is the rolling-up motion of an initially flapping jet to form large vortices which are responsible for greater entrainment. Several methods developed to impart oscillations to the flow at the nozzle, such as the acoustic pressure oscillator, the vibration of a single vane in the potential core region, the reciprocating lip system and the twin vane exciter, are described in this article. A minimum threshold in amplitude is necessary for exciting the flow. However, the frequency of oscillation is much less than that predicted by stability considerations.

A Direct Approach to the Problem of Diffraction by a Half-Plane under Mixed Boundary Conditions

A general direct technique of solving a mixed boundary value problem in the theory of diffraction by a semi-infinite plane is presented. Taking account of the correct edge-conditions, the unique solution of the problem is derived, by means of Jones' method in the theory of Wiener-Hopf technique, in the case of incident plane wave. The solution of the half-plane problem is found out in exact form. (The far-field is derived by the method of steepest descent.) It is observed that it is not the Wiener-Hopf technique which really needs any modification but a new technique is certainly required to handle the peculiar type of coupled integral equations which the Wiener-Hopf technique leads to. Eine allgemeine direkte Technik zur Lösung eines gemischten Randwertproblems in der Theorie der Beugung an einer halbunendlichen Ebene wird vorgestellt. Unter Berücksichtigung der korrekten Eckbedingungen wird mit der Methode von Jones aus der Theorie der Wiener-Hopf-Technik die eindeutige Lösung für den Fall der einfallenden ebenen Welle hergeleitet. Die Lösung des Halbebenenproblems wird in exakter Form angegeben. (Das Fernfeld wurde mit der Methode des steilsten Abstiegs bestimmt.) Es wurde bemerkt, daß es nicht die Wiener-Hopf-Technik ist, die wirklich irgend welcher Modifikationen bedurfte. Gewiß aber wird eine neue Technik zur Behandlung des besonderen Typs gekoppelter Integralgleichungen benötigt, auf die die Wiener-Hopf-Technik führt.

Diffraction of a cylindrical pulse by a half plane under mixed boundary conditions

The general time dependent source problem has been solved by the method of transforms (Laplace, Lebedev–Kontorovich in succession) and the solution is obtained in the form of an infinite series involving Legendre functions. The solutions in the case of harmonic time dependence and the incident plane wave have been derived from the above solution and are presented in the form of an infinite series. In the case of an incident plane wave, the series has been summed and the final solution involves an improper integral which behaves like a complementary error function for large values of the argument. Finally, the far field evaluation has been shown. The results are compared with those of Sommerfeld's half-plane diffraction problem with unmixed boundary conditions.

Diffraction of a cylindrical pulse by a metallic half plane

A direct transform technique is applied to the initial and boundary value problem involving diffraction of a cylindrical pulse by a half plane, on which impedance type of boundary conditions must be met by the total field. The solution to the time harmonic incident plane wave is deduced as a particular case of the general time-dependent problem considered here and we avoid the Wiener–Hopf technique which leads to very complicated factorization and which masks the role of the impedance factor Z′ (a small quantity) in the expression for the scattered field.