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.

Determination of solid fraction evolution during solidification of aluminum alloy in presence of linear electromagnetic stirring

In many industrial casting processes, knowledge of the solid fraction evolution during the solidification process is a key factor in determining the process parameters such as cooling rate, stirring intensity and in estimating the total solidification time. In the present work, a new method of estimating solid fraction is presented, which is based on calorimetric principles. In this method, the cooling curve data at each point in the melt, along with the thermal boundary conditions, are used to perform energy balance in the mould, from which solid fraction generation during any time interval can be estimated. This method is applied to the case of a rheocasting process, in which Al-Si alloy (A356 alloy) is solidified by stirring in a cylindrical mould placed in the annulus of a linear electromagnetic stirrer. The metal in the mould is simultaneously cooled and stirred to produce a cylindrical billet with non-dendritic globular microstructure. Temperature is measured at key locations in the mould to assess the various heat exchange processes prevalent in the mould and to monitor the solidification rate. The results obtained by energy balance method are compared with those by the conventional procedure of calculating solid fraction using the Schiel equation.

Geothermal reservoirs - A brief review

A brief discussion and review of the geothermal reservoir systems, geothermal energy and modeling and simulation of the geothermal reservoirs has been presented here. Different types of geothermal reservoirs and their governing equations have been discussed first. The conceptual and numerical modeling along with the representation of flow though fractured media, some issues related to non isothermal flow through fractured media, the efficiency of the geothermal reservoir, structure of the numerical models, boundary conditions and calibration procedures have been illustrated. A brief picture of the Indian scenario and some barriers related with geothermal power are discussed and presented thereafter. Finally some gaps of the existing knowledge and recent focuses of research are discussed.

Flavored co-annihilations

Neutralino dark matter in supersymmetric models is revisited in the presence of flavor violation in the soft supersymmetry breaking sector. We focus on flavor violation the sleptonic sector and study the implications for the co-annihilation regions. Flavor is introduced by a single (mu) over tilde (R) - (T) over tilde (R) insertion in the slepton mass matrix. Limits on insertion from BR(tau -> mu + gamma) are weak in some regions of the parameter space where happen within the amplitudes. We look for overlaps in parameter space where the co-annihilation condition as well as the cancellations within the amplitudes occur. mSUGRA, such overlap regions are not existent, whereas they are present in models non-universal Higgs boundary conditions (NUHM). The effect of flavor violation is fold: (a) it shifts the co-annihilation regions towards lighter neutralino masses (b) co-annihilation cross sections would be modified with the inclusion of flavor violating which can contribute significantly. Even if flavor violation is within the presently limits, this is sufficient to modify the thermally averaged cross-sections by about 15)% in mSUGRA and (20{30)% in NUHM, depending on the parameter space. In overlap regions, the flavor violating cross sections become comparable and in some even dominant to the flavor conserving ones. A comparative study of the channels is for mSUGRA and NUHM cases.

Size-dependent free flexural vibration behavior of functionally graded nanoplates

In this paper, size dependent linear free flexural vibration behavior of functionally graded (FG) nanoplates are investigated using the iso-geometric based finite element method. The field variables are approximated by non-uniform rational B-splines. The nonlocal constitutive relation is based on Eringen's differential form of nonlocal elasticity theory. The material properties are assumed to vary only in the thickness direction and the effective properties for the FG plate are computed using Mori-Tanaka homogenization scheme. The accuracy of the present formulation is demonstrated considering the problems for which solutions are available. A detailed numerical study is carried out to examine the effect of material gradient index, the characteristic internal length, the plate thickness, the plate aspect ratio and the boundary conditions on the global response of the FG nanoplate. From the detailed numerical study it is seen that the fundamental frequency decreases with increasing gradient index and characteristic internal length. (c) 2012 Elsevier B.V. All rights reserved.

Status of supersymmetric type-I seesaw in SO(10) inspired models

We report on the status of supersymmetric seesaw models in the light of recent experimental results on mu -> e + gamma, theta(13) and the light Higgs mass at the LHC. SO(10)-like relations are assumed for neutrino Dirac Yukawa couplings and two cases of mixing, one large, PMNS-like, and another small, CKM-like, are considered. It is shown that for the large mixing case, only a small range of parameter space with moderate tan beta is still allowed. This remaining region can be ruled out by an order of magnitude improvement in the current limit on BR(mu -> e + gamma). We also explore a model with non-universal Higgs mass boundary conditions at the high scale. It is shown that the renormalization group induced flavor violating slepton mass terms are highly sensitive to the Higgs boundary conditions. Depending on the choice of the parameters, they can either lead to strong enhancements or cancellations within the flavor violating terms. Such cancellations might relax the severe constraints imposed by lepton flavor violation compared to mSUGRA. Nevertheless for a large region of parameter space the predicted rates lie within the reach of future experiments once the light Higgs mass constraint is imposed. We also update the potential of the ongoing and future experimental searches for lepton flavor violation in constraining the supersymmetric parameter space.

Automatic finite element formulation and assembly of hyperelastic higher order structural models

The formulation of higher order structural models and their discretization using the finite element method is difficult owing to their complexity, especially in the presence of non-linearities. In this work a new algorithm for automating the formulation and assembly of hyperelastic higher-order structural finite elements is developed. A hierarchic series of kinematic models is proposed for modeling structures with special geometries and the algorithm is formulated to automate the study of this class of higher order structural models. The algorithm developed in this work sidesteps the need for an explicit derivation of the governing equations for the individual kinematic modes. Using a novel procedure involving a nodal degree-of-freedom based automatic assembly algorithm, automatic differentiation and higher dimensional quadrature, the relevant finite element matrices are directly computed from the variational statement of elasticity and the higher order kinematic model. Another significant feature of the proposed algorithm is that natural boundary conditions are implicitly handled for arbitrary higher order kinematic models. The validity algorithm is illustrated with examples involving linear elasticity and hyperelasticity. (C) 2013 Elsevier Inc. All rights reserved.

Boundary perturbations and the Helmholtz equation in three dimensions

We propose an analytic perturbative scheme in the spirit of Lord Rayleigh's work for determining the eigenvalues of the Helmholtz equation in three dimensions inside an arbitrary boundary where the eigenfunction satisfies either the Dirichlet boundary condition or the Neumann boundary condition. Although numerous works are available in the literature for arbitrary boundaries in two dimensions, to the best of our knowledge the formulation in three dimensions is proposed for the first time. In this novel prescription, we have expanded the arbitrary boundary in terms of spherical harmonics about an equivalent sphere and obtained perturbative closed-form solutions at each order for the problem in terms of corrections to the equivalent spherical boundary for both the boundary conditions. This formulation is in parallel with the standard time-independent Rayleigh-Schrodinger perturbation theory. The efficacy of the method is tested by comparing the perturbative values against the numerically calculated eigenvalues for spheroidal, superegg and superquadric shaped boundaries. It is shown that this perturbation works quite well even for wide departure from spherical shape and for higher excited states too. We believe this formulation would find applications in the field of quantum dots and acoustical cavities.

Tailoring the second mode of Euler-Bernoulli beams: an analytical approach

In this paper, we study the inverse mode shape problem for an Euler-Bernoulli beam, using an analytical approach. The mass and stiffness variations are determined for a beam, having various boundary conditions, which has a prescribed polynomial second mode shape with an internal node. It is found that physically feasible rectangular cross-section beams which satisfy the inverse problem exist for a variety of boundary conditions. The effect of the location of the internal node on the mass and stiffness variations and on the deflection of the beam is studied. The derived functions are used to verify the p-version finite element code, for the cantilever boundary condition. The paper also presents the bounds on the location of the internal node, for a valid mass and stiffness variation, for any given boundary condition. The derived property variations, corresponding to a given mode shape and boundary condition, also provides a simple closed-form solution for a class of non-uniform Euler-Bernoulli beams. These closed-form solutions can also be used to check optimization algorithms proposed for modal tailoring.

Spin populations in one-dimensional alternant spin systems: A theoretical approach

Spin-density maps, deduced from polarized neutron diffraction experiments, for both the pair and chain compounds of the system Mn2+Cu2+ have been reported recently. These results have motivated us to investigate theoretically the spin populations in such alternant mixed-spin systems. In this paper, we report our studies on the one-dimensional ferrimagnetic systems (S-A,S-B)(N) where hi is the number of AB pairs. We have considered all cases in which the spin Sri takes on allowed values in the range I to 7/2 while the spin S-B is held fixed at 1/2. The theoretical studies have been carried out on the isotropic Heisenberg model, using the density matrix renormalization group method. The effect of the magnitude of the larger spin SA On the quantum fluctuations in both A and B sublattices has been studied as a function of the system size N. We have investigated systems with both periodic and open boundary conditions, the latter with a view to understanding end-of-chain effects. The spin populations have been followed as a function of temperature as well as an applied magnetic field. High-magnetic fields are found to lead to interesting re-entrant behavior. The ratio of spin populations P-A-P-B is not sensitive to temperature at low temperatures.

Static analysis of infinite laminated cylindrical shell panel

This paper presents an approximate three-dimensional elasticity solution for an infinitely long, cross-ply laminated circular cylindrical shell panel with simply supported boundary conditions, subjected to an arbitrary discontinuous transverse loading. The solution is based on the principal assumption that the ratio of the thickness of the lamina to its middle surface radius is negligible compared to unity. The validity of this assumption and the range of application of this approximate solution have been established through a comparison with an exact solution. Results of classical and first-order shear deformation shell theories have been compared with the results of the present solution to bring out the accuracy of these theories. It is also shown that for very shallow shell panels the definition of a thin shell should be based on the ratio of thickness to chord width rather than the ratio of thickness to mean radius.

Transonic Properties of Accretion Disk Around Compact Objects

An accretion flow is necessarily transonic around a black hole.However, around a neutron star it may or may not be transonic, depending on the inner disk boundary conditions influenced by the neutron star. I will discuss various transonic behavior of the disk fluid in general relativistic (or pseudo general relativistic) framework. I will address that there are four types of sonic/critical point. possible to form in an accretion disk. It will be shown that how the fluid properties including location of sonic point's vary with angular momentum of the compact object which controls the overall disk dynamics and outflows.

Analysis of a finite composite plate with smooth rigid pin

A continuum method of analysis is presented in this paper for the problem of a smooth rigid pin in a finite composite plate subjected to uniaxial loading. The pin could be of interference, push or clearance fit. The plate is idealized to an orthotropic sheet. As the load on the plate is progressively increased, the contact along the pin-hole interface is partial above certain load levels in all three types of fit. In misfit pins (interference or clearance), such situations result in mixed boundary value problems with moving boundaries and in all of them the arc of contact and the stress and displacement fields vary nonlinearly with the applied load. In infinite domains similar problems were analysed earlier by ‘inverse formulation’ and, now, the same approach is selected for finite plates. Finite outer domains introduce analytical complexities in the satisfaction of boundary conditions. These problems are circumvented by adopting a method in which the successive integrals of boundary error functions are equated to zero. Numerical results are presented which bring out the effects of the rectangular geometry and the orthotropic property of the plate. The present solutions are the first step towards the development of special finite elements for fastener joints.

Flow through a plateau border of cellular foam

Experimentally measured average velocities through plateau borders of stationary cellular foam, when compared with those calculated with the assumption of rigid Plateau Border walls, show that the assumption of rigid walls severely underestimates the velocities. An analysis of the situation wherein plateau border walls have velocities, as decided by the surface viscosity of the system, is presented here. The plateau border is idealized as a pipe of equilateral triangular cross-section with vertices of the triangle having zero velocity. The pertinent form of Navier-Stoke's equations with inhomogeneous boundary conditions and its solution through a procedure of successive approximations is presented in dimensionless form. The solution reduces to the known solution of slow steady flow through a triangular pipe, when surface viscosity is infinite. Results indicate that the assumption of rigid plateau border walls is valid only when value of the inverse of dimensionless surface viscosity is less than 0.044. Beyond that the assumption severely underestimates the flow and the effect of nonrigidity of the wall must be considered.

On an analytical-numerical procedure for the analysis of cylindrical shells with arbitrarily oriented cracks

An analytical-numerical procedure for obtaining stress intensity factor solutions for an arbitrarily oriented crack in a long, thin circular cylindrical shell is presented. The method of analysis involves obtaining a series solution to the governing shell equation in terms of Mathieu and modified Mathieu functions by the method of separation of variables and satisfying the crack surface boundary conditions numerically using collocation. The solution is then transformed from elliptic coordinates to polar coordinates with crack tip as the origin through a Taylor series expansion and membrane and bending stress intensity factors are computed. Numerical results are presented and discussed for the pressure loading case.