Forced Oscillations of a Contained Rotating Stratified Fluid

The motion generated by forced oscillations in an incompressible inviscid rotating and/or stratified fluid is examined under linear theory taking the density variation on the inertia terms. The solution consists of numerous internal modes in addition to the mode which oscillates with forcing frequency. Resonance occurs when the forcing frequency is equal to one of the frequencies of the internal modes. Some of these modes grow linearly or exponentially with time rendering the motion unstable and eventually may lead to turbulence. Most of the results discussed here will be missed under Boussinesq approximation.

Negative resistance mode of forced oscillations of a string

A new mode of driven nonlinear vibrations of a stretched string is investigated with reference to conditions of existence, properties, and regions of stability. It is shown that this mode exhibits negative resistance properties at all frequencies and driving force amplitudes. Discovery of this mode helps to fill certain gaps in the theory of forced nonlinear vibrations of strings.

Application of ultraspherical polynomials to forced oscillations of a third-order non-linear system

In this paper the method of ultraspherical polynomial approximation is applied to study the steady-state response in forced oscillations of a third-order non-linear system. The non-linear function is expanded in ultraspherical polynomials and the expansion is restricted to the linear term. The equation for the response curve is obtained by using the linearized equation and the results are presented graphically. The agreement between the approximate solution and the analog computer solution is satisfactory. The problem of stability is not dealt with in this paper.

Rocket Propellant Combustion Studies in a Constant Volume Bomb

A constant volume window bomb has been used to measure the characteristic velocity (c*) of rocket propellants. Analysis of the combustion process inside the bomb including heat losses has been made. The experiments on double base and composite propellants have revealed some (i) basic heat transfer aspects inside the bomb and (ii) combustion characteristics of Ammonium Perchlorate-Polyester propellants. It has been found that combustion continues even beyond the peak pressure and temperature points. Lithium Fluoride mixed propellants do not seem to indicate significant differences in c*) though the low pressure deflagration limit is increased with percentage of Lithium Fluoride.

Coupled Solution for Forced Recharge in Confined Aquifers

Analytical solutions for forced well recharge currently in use were initially developed for pumping scenarios and applied for recharge cases assuming that radial flow in the recharge well replicates a mirror image of that in to a pumping well. Moreover these solutions were not extended to multiaquifer systems. Well bore numerical solutions were generally not considering the effect of well bore interaction, which has a significant effect in the case of a recharge well. In the present paper, improved analytical solutions are developed for a well fully penetrating either single or multiaquifers in respect.to of well storage, well loss, and interactions between the individual aquifers through well bore. The solution developed for constant and variable rates of injection and well loss is applied to the experimental data of the Hansol well injection project near the city of Ahmedabad in the Gujarat state in India. The paper also discusses the difference in well hydraulics of recharge and recovery wells.

Vitrification, relaxation and free volume in glycerol-water binary liquid mixture:Spin probe ESR studies

Glass transition and relaxation of the glycerol-water (G-W) binary mixture system have been studied over the glycerol concentration range of 5-85 mol% by using the highly sensitive technique of electron spin resonance (ESR). For the water rich mixture the glass transition,sensed by the dissolved spin probe, arises from the vitrified mesoscopic portion of the binary system. The concentration dependence of the glass transition temperature manifests a closely related molecular level cooperativity in the system. A drastic change in the mesoscopic structure of the system at the critical concentration of 40 mol is confirmed by an estimation of the spin probe effective volume in a temperature range where the tracer reorientation is strongly coupled to the system dynamics.

Free-volume dependent pressure sensitivity of Zr-based bulk metallic glass

Instrumented indentation experiments on a Zr-based bulk metallic glass (BMG) in as-cast, shot-peened and structurally relaxed conditions were conducted to examine the dependence of plastic deformation on its structural state. Results show significant differences in hardness, H, with structural relaxation increasing it and shot peening markedly reducing it, and slightly changed morphology of shear bands around the indents. This is in contrast to uniaxial compressive yield strength, sigma(y), which remains invariant with the change in the structural state of the alloys investigated. The plastic constraint factor, C = H/sigma(y), of the relaxed BMG increases compared with that of the as-cast glass, indicating enhanced pressure sensitivity upon annealing. In contrast, C of the shot-peened layer was found to be similar to that observed in crystalline metals, indicating that severe plastic deformation could eliminate pressure sensitivity. Microscopic origins for this result, in terms of shear transformation zones and free volume, are discussed.

Efficient computation of volume fractions for multi-material cell complexes in a grid by slicing

The paper presents a novel slicing based method for computation of volume fractions in multi-material solids given as a B-rep whose faces are triangulated and shared by either one or two materials. Such objects occur naturally in geoscience applications and the said computation is necessary for property estimation problems and iterative forward modeling. Each facet in the model is cut by the planes delineating the given grid structure or grid cells. The method, instead of classifying the points or cells with respect to the solid, exploits the convexity of triangles and the simple axis-oriented disposition of the cutting surfaces to construct a novel intermediate space enumeration representation called slice-representation, from which both the cell containment test and the volume-fraction computation are done easily. Cartesian and cylindrical grids with uniform and non-uniform spacings have been dealt with in this paper. After slicing, each triangle contributes polygonal facets, with potential elliptical edges, to the grid cells through which it passes. The volume fractions of different materials in a grid cell that is in interaction with the material interfaces are obtained by accumulating the volume contributions computed from each facet in the grid cell. The method is fast, accurate, robust and memory efficient. Examples illustrating the method and performance are included in the paper.

Turbulence-induced melting of a nonequilibrium vortex crystal in a forced thin fluid film

To gain a better understanding of recent experiments on the turbulence-induced melting of a periodic array of vortices in a thin fluid film, we perform a direct numerical simulation of the two-dimensional Navier-Stokes equations forced such that, at low Reynolds numbers, the steady state of the film is a square lattice of vortices. We find that as we increase the Reynolds number, this lattice undergoes a series of nonequilibrium phase transitions, first to a crystal with a different reciprocal lattice and then to a sequence of crystals that oscillate in time. Initially, the temporal oscillations are periodic; this periodic behaviour becoming more and more complicated with increasing Reynolds number until the film enters a spatially disordered nonequilibrium statistical steady state that is turbulent. We study this sequence of transitions using fluid-dynamics measures, such as the Okubo-Weiss parameter that distinguishes between vortical and extensional regions in the flow, ideas from nonlinear dynamics, e.g. Poincare maps, and theoretical methods that have been developed to study the melting of an equilibrium crystal or the freezing of a liquid and that lead to a natural set of order parameters for the crystalline phases and spatial autocorrelation functions that characterize short- and long-range order in the turbulent and crystalline phases, respectively.

Optimal auctions for multi-unit procurement with volume discount bids

Our attention, is focused on designing an optimal procurement mechanism which a buyer can use for procuring multiple units of a homogeneous item based on bids submitted by autonomous, rational, and intelligent suppliers. We design elegant optimal procurement mechanisms for two different situations. In the first situation, each supplier specifies the maximum quantity that can be supplied together with a per unit price. For this situation, we design an optimal mechanism S-OPT (Optimal with Simple bids). In the more generalized case, each supplier specifies discounts based on the volume of supply. In this case, we design an optimal mechanism VD-OPT (Optimal with Volume Discount, bids). The VD-OPT mechanism uses the S-OPT mechanism as a building block. The proposed mechanisms minimize the cost to the buyer, satisfying at the same time, (a) Bayesian, incentive compatibility and (b) interim individual rationality.

Volume change behaviour of fine grained solis

Soils in and and semi-arid zones undergoes volume changes due to wetting. Depending upon the type of clay minerals present, degree of saturation, externally applied load and bonding, the fine grained soils either swells or compresses. One of the parameter that affects the volume change behaviour is the primary clay mineral present in their clay size fraction. A simple method of identifying the same has been presented. It has been brought out that in an expansive unsaturated undisturbed soil, the diffuse double layer repulsion, the stress state and the bonding play significant role in their volume change behaviour. In non-expansive fine grained unsaturated undisturbed soils, the shearing resistance at particle level (including the matrix suction and bonding) and fabric play a significant role in influencing the volume change behaviour. While both the mechanism co-exist, one of them play a dominant role depending upon the primary clay mineral is swelling or non swelling.

Handling sectional views in volume-based approach to automatically construct 3D solid from 2D views

This paper presents an algorithm for solid model reconstruction from 2D sectional views based on volume-based approach. None of the existing work in automatic reconstruction from 2D orthographic views have addressed sectional views in detail. It is believed that the volume-based approach is better suited to handle different types of sectional views. The volume-based approach constructs the 3D solid by a boolean combination of elementary solids. The elementary solids are formed by sweep operation on loops identified in the input views. The only adjustment to be made for the presence of sectional views is in the identification of loops that would form the elemental solids. In the algorithm, the conventions of engineering drawing for sectional views, are used to identify the loops correctly. The algorithm is simple and intuitive in nature. Results have been obtained for full sections, offset sections and half sections. Future work will address other types of sectional views such as removed and revolved sections and broken-out sections. (C) 2004 Elsevier Ltd. All rights reserved.

On the ignition and extinction problems in forced convection systems

In this paper the problem of ignition and extinction has been formulated for the flow of a compressible fluid with Prandtl and Schmidt numbers taken as unity. In particular, the problems of (i) a jet impinging on a wall of combustible material and (ii) the opposed jet diffusion flame have been studied. In the wall jet case, three approximations in the momentum equation namely, (i) potential flow, (ii) viscous flow, (ii) viscous incompressible with k = 1 and (iii) Lees' approximation (taking pressure gradient terms zero) are studied. It is shown that the predictions of the mass flow rates at extinction are not very sensitive to the approximations made in the momentum equation. The effects of varying the wall temperature in the case (i) and the jet temperature in the case (ii) on the extinction speeds have been studied. The effects of varying the activation energy and the free stream oxidant concentration in case (ii), have also been investigated.