On quasi-degeneracies in plate vibration problems

In plotting the variation of frequencies with geometric parameters such as side ratio, skew angle, thickness taper, etc. in detailed studies of the vibration characteristics of plates, situations are encountered such as crossing of the frequency curves or the tendency of these curves to come close together and veer away from each other. These have been generally referred to as “frequency crossings” and “transitions” respectively. The latter may preferably be referred to as “quasi-degeneracies”. In the literature there appears to be some ambiguity in the analysis and interpretation of these features. In this paper, a clarification of some of these questions as regards rectangular and skew plates is presented by making use of concepts from physics dealing with molecular vibrations.

Multi-channel curve crossing problems: analytically solvable model

We have proposed a general method for finding the exact analytical solution for the multi-channel curve crossing problem in the presence of delta function couplings. We have analysed the case where aa potential energy curve couples to a continuum (in energy) of the potential energy curves.

Design of multiunit electronic exchanges through decomposition

In this paper, we exploit the idea of decomposition to match buyers and sellers in an electronic exchange for trading large volumes of homogeneous goods, where the buyers and sellers specify marginal-decreasing piecewise constant price curves to capture volume discounts. Such exchanges are relevant for automated trading in many e-business applications. The problem of determining winners and Vickrey prices in such exchanges is known to have a worst-case complexity equal to that of as many as (1 + m + n) NP-hard problems, where m is the number of buyers and n is the number of sellers. Our method proposes the overall exchange problem to be solved as two separate and simpler problems: 1) forward auction and 2) reverse auction, which turns out to be generalized knapsack problems. In the proposed approach, we first determine the quantity of units to be traded between the sellers and the buyers using fast heuristics developed by us. Next, we solve a forward auction and a reverse auction using fully polynomial time approximation schemes available in the literature. The proposed approach has worst-case polynomial time complexity. and our experimentation shows that the approach produces good quality solutions to the problem. Note to Practitioners- In recent times, electronic marketplaces have provided an efficient way for businesses and consumers to trade goods and services. The use of innovative mechanisms and algorithms has made it possible to improve the efficiency of electronic marketplaces by enabling optimization of revenues for the marketplace and of utilities for the buyers and sellers. In this paper, we look at single-item, multiunit electronic exchanges. These are electronic marketplaces where buyers submit bids and sellers ask for multiple units of a single item. We allow buyers and sellers to specify volume discounts using suitable functions. Such exchanges are relevant for high-volume business-to-business trading of standard products, such as silicon wafers, very large-scale integrated chips, desktops, telecommunications equipment, commoditized goods, etc. The problem of determining winners and prices in such exchanges is known to involve solving many NP-hard problems. Our paper exploits the familiar idea of decomposition, uses certain algorithms from the literature, and develops two fast heuristics to solve the problem in a near optimal way in worst-case polynomial time.

Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.

Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.

Distributed nonlinear optimization algorithms for general network problems

There are a number of large networks which occur in many problems dealing with the flow of power, communication signals, water, gas, transportable goods, etc. Both design and planning of these networks involve optimization problems. The first part of this paper introduces the common characteristics of a nonlinear network (the network may be linear, the objective function may be non linear, or both may be nonlinear). The second part develops a mathematical model trying to put together some important constraints based on the abstraction for a general network. The third part deals with solution procedures; it converts the network to a matrix based system of equations, gives the characteristics of the matrix and suggests two solution procedures, one of them being a new one. The fourth part handles spatially distributed networks and evolves a number of decomposition techniques so that we can solve the problem with the help of a distributed computer system. Algorithms for parallel processors and spatially distributed systems have been described.There are a number of common features that pertain to networks. A network consists of a set of nodes and arcs. In addition at every node, there is a possibility of an input (like power, water, message, goods etc) or an output or none. Normally, the network equations describe the flows amoungst nodes through the arcs. These network equations couple variables associated with nodes. Invariably, variables pertaining to arcs are constants; the result required will be flows through the arcs. To solve the normal base problem, we are given input flows at nodes, output flows at nodes and certain physical constraints on other variables at nodes and we should find out the flows through the network (variables at nodes will be referred to as across variables).The optimization problem involves in selecting inputs at nodes so as to optimise an objective function; the objective may be a cost function based on the inputs to be minimised or a loss function or an efficiency function. The above mathematical model can be solved using Lagrange Multiplier technique since the equalities are strong compared to inequalities. The Lagrange multiplier technique divides the solution procedure into two stages per iteration. Stage one calculates the problem variables % and stage two the multipliers lambda. It is shown that the Jacobian matrix used in stage one (for solving a nonlinear system of necessary conditions) occurs in the stage two also.A second solution procedure has also been imbedded into the first one. This is called total residue approach. It changes the equality constraints so that we can get faster convergence of the iterations.Both solution procedures are found to coverge in 3 to 7 iterations for a sample network.The availability of distributed computer systems — both LAN and WAN — suggest the need for algorithms to solve the optimization problems. Two types of algorithms have been proposed — one based on the physics of the network and the other on the property of the Jacobian matrix. Three algorithms have been deviced, one of them for the local area case. These algorithms are called as regional distributed algorithm, hierarchical regional distributed algorithm (both using the physics properties of the network), and locally distributed algorithm (a multiprocessor based approach with a local area network configuration). The approach used was to define an algorithm that is faster and uses minimum communications. These algorithms are found to converge at the same rate as the non distributed (unitary) case.

Role of multicritical points in addressing some key problems concerning condensed matter science

We illustrate the potential of using higher order critical points in the deeper understanding of several interesting problems of condensed matter science, e.g. critical adsorption, finite size effects, morphology of critical fluctuations, reversible aggregation of colloids, dynamics of the ordering process, etc.

Synthetic aperture radar: A focus on current problems

Synthetic aperture radar (SAR) is a powerful tool for mapping and remote sensing. The theory and operation of SAR have seen a period of intense activity in recent years. This paper attempts to review some of the more advanced topics studied in connection with modern SAR systems based on digital processing. Following a brief review of the principles involved in the operation of SAR, attention is focussed on special topics such as advanced SAR modelling and focussing techniques, in particular clutterlock and autofocus, Doppler centroid (DC) estimation methods involving seismic migration technique, moving target imaging, bistatic radar imaging, effects of system nonlinearities, etc.

Modelling electricity demand with representative load curves

Models for electricity planning require inclusion of demand. Depending on the type of planning, the demand is usually represented as an annual demand for electricity (GWh), a peak demand (MW) or in the form of annual load-duration curves. The demand for electricity varies with the seasons, economic activities, etc. Existing schemes do not capture the dynamics of demand variations that are important for planning. For this purpose, we introduce the concept of representative load curves (RLCs). Advantages of RLCs are demonstrated in a case study for the state of Karnataka in India. Multiple discriminant analysis is used to cluster the 365 daily load curves for 1993-94 into nine RLCs. Further analyses of these RLCs help to identify important factors, namely, seasonal, industrial, agricultural, and residential (water heating and air-cooling) demand variations besides rationing by the utility. (C) 1999 Elsevier Science Ltd. All rights reserved.

Studies of the specific gravity of some Indian coal ashes

One of the major problems faced by coal based thermal power stations is handling and disposal of ash. Among the various uses of fly ash, the major quantity of ash produced is used in geotechnical engineering applications such as construction of embankments, as a backfill material, etc. The generally low specific gravity of fly ash resulting in low unit weight as compared to soils is an attractive property for its use in geotechnical applications. In general, specific gravity of coal ash lies around 2.0 but can vary to a large extent (1.6 to 3.1). The variation of specific gravity of coal ash is due to the combination of various factors like gradation, particle shape, and chemical composition. Since specific gravity is an important physical property, it has been studied in depth for three Indian coal ashes and reported in this paper.

The effect of surface tension in porous wave maker problems

Using a mixed-type Fourier transform of a general form in the case of water of infinite depth and the method of eigenfunction expansion in the case of water of finite depth, several boundary-value problems involving the propagation and scattering of time harmonic surface water waves by vertical porous walls have been fully investigated, taking into account the effect of surface tension also. Known results are recovered either directly or as particular cases of the general problems under consideration.

Problems with geoengineering schemes to combat climate change

The accelerated rate of increase in atmospheric CO2 concentration in recent years has revived the idea of stabilizing the global climate through geoengineering schemes. Majority of the proposed geoengineering schemes will attempt to reduce the amount of solar radiation absorbed by our planet. Climate modelling studies of these so called 'sunshade geoengineering schemes' show that global warming from increasing concentrations of CO2 can be mitigated by intentionally manipulating the amount of sunlight absorbed by the climate system. These studies also suggest that the residual changes could be large on regional scales, so that climate change may not be mitigated on a local basis. More recent modelling studies have shown that these schemes could lead to a slow-down in the global hydrological cycle. Other problems such as changes in the terrestrial carbon cycle and ocean acidification remain unsolved by sunshade geoengineering schemes. In this article, I review the proposed geoengineering schemes, results from climate models and discuss why geoengineering is not the best option to deal with climate change.

Equivariant Birch-Swinnerton-Dyer Conjecture for the Base Change of Elliptic Curves: An Example

Let E be an elliptic curve defined over Q and let K/Q be a finite Galois extension with Galois group G. The equivariant Birch-Swinnerton-Dyer conjecture for h(1)(E x(Q) K)(1) viewed as amotive over Q with coefficients in Q[G] relates the twisted L-values associated with E with the arithmetic invariants of the same. In this paper I prescribe an approach to verify this conjecture for a given data. Using this approach, we verify the conjecture for an elliptic curve of conductor 11 and an S-3-extension of Q.

Estimation of mineral-adhered biomass of Thiobacillusferrooxidans by protein assay-some problems and remedies

Enumeration of adhered cells of Thiobacillus ferrooxidans on sulphide minerals through protein assay poses problems due to interference from dissolved mineral constituents. The manner in which sulphide minerals such as pyrite, chalcopyrite, sphalerite, arsenopyrite and pyrrhotite interfere with bacterial protein estimation is demonstrated. Such interferences can be minimised either through dilution or addition of H2O2 to the filtrate after hot alkaline digestion of the biotreated mineral samples.

Maximal regularity for second order non-autonomous Cauchy problems

We consider some non-autonomous second order Cauchy problems of the form u + B(t)(u) over dot + A(t)u = f (t is an element of [0, T]), u(0) = (u) over dot(0) = 0. We assume that the first order problem (u) over dot + B(t)u = f (t is an element of [0, T]), u(0) = 0, has L-p-maximal regularity. Then we establish L-p-maximal regularity of the second order problem in situations when the domains of B(t(1)) and A(t(2)) always coincide, or when A(t) = kappa B(t).