Pseudo-time marching schemes for inverse problems in structural health assessment and medical imaging

We propose a self-regularized pseudo-time marching strategy for ill-posed, nonlinear inverse problems involving recovery of system parameters given partial and noisy measurements of system response. While various regularized Newton methods are popularly employed to solve these problems, resulting solutions are known to sensitively depend upon the noise intensity in the data and on regularization parameters, an optimal choice for which remains a tricky issue. Through limited numerical experiments on a couple of parameter re-construction problems, one involving the identification of a truss bridge and the other related to imaging soft-tissue organs for early detection of cancer, we demonstrate the superior features of the pseudo-time marching schemes.

Problems and prospects in neurochemistry

The importance of neurochemistry in understanding the functional basis of the nervous system was emphasized. Attention was drawn to the role of lipids, particularly the sphingolipids,whose metabolic abnormalities lead to 'sphingolipidosis' In the brain and to gangliosides, which show growth-promoting and neuritogenic properties. Several questions that remain to be answered in this area were enumerated. It was pointed out that neurons make a large number of proteins, an order of magnitude higher than other cells, and several of these are yet to be characterized and their functional significance established. Myelination and synapto-genesis are two fundamental processes in brain development. Although much is known about myelin lipids and proteins, it is not known what signals the glial cell receives to initiate myelin synthesis around the axon, In fact, the process of myelination provides an excellent system for studying membrane biogenesis and cell-sell interaction. Great strides were made in the understanding of neurotransmitter receptors and their function in synaptic transmission, but how neurons make synapses with other specific neurons in a preprogrammed manner is not known and requires immediate study. In this context, it was stressed that developmental neurobiology of the human brain could be most profitably done in India. The importance and complexity of signal transduction mechanisms in the brain was explained and many fundamental questions that remain to be answered were discussed. In conclusion, several other areas of contemporary research interest in the nervous system were mentioned and it was suggested that a 'National Committee for Brain Research' be constituted to identify and intensify research programmes in this vital field.

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.

Shortcomings of discontinuous-pressure finite element methods on a class of transient problems

Past studies that have compared LBB stable discontinuous- and continuous-pressure finite element formulations on a variety of problems have concluded that both methods yield Solutions of comparable accuracy, and that the choice of interpolation is dictated by which of the two is more efficient. In this work, we show that using discontinuous-pressure interpolations can yield inaccurate solutions at large times on a class of transient problems, while the continuous-pressure formulation yields solutions that are in good agreement with the analytical Solution.

Agents Based Algorithms for Design Parameter Estimation in Contaminant Transport Inverse Problems

A considerable amount of work has been dedicated on the development of analytical solutions for flow of chemical contaminants through soils. Most of the analytical solutions for complex transport problems are closed-form series solutions. The convergence of these solutions depends on the eigen values obtained from a corresponding transcendental equation. Thus, the difficulty in obtaining exact solutions from analytical models encourages the use of numerical solutions for the parameter estimation even though, the later models are computationally expensive. In this paper a combination of two swarm intelligence based algorithms are used for accurate estimation of design transport parameters from the closed-form analytical solutions. Estimation of eigen values from a transcendental equation is treated as a multimodal discontinuous function optimization problem. The eigen values are estimated using an algorithm derived based on glowworm swarm strategy. Parameter estimation of the inverse problem is handled using standard PSO algorithm. Integration of these two algorithms enables an accurate estimation of design parameters using closed-form analytical solutions. The present solver is applied to a real world inverse problem in environmental engineering. The inverse model based on swarm intelligence techniques is validated and the accuracy in parameter estimation is shown. The proposed solver quickly estimates the design parameters with a great precision.

Linear time algorithms for Abelian group isomorphism and related problems

We consider the problem of determining if two finite groups are isomorphic. The groups are assumed to be represented by their multiplication tables. We present an O(n) algorithm that determines if two Abelian groups with n elements each are isomorphic. This improves upon the previous upper bound of O(n log n) [Narayan Vikas, An O(n) algorithm for Abelian p-group isomorphism and an O(n log n) algorithm for Abelian group isomorphism, J. Comput. System Sci. 53 (1996) 1-9] known for this problem. We solve a more general problem of computing the orders of all the elements of any group (not necessarily Abelian) of size n in O(n) time. Our algorithm for isomorphism testing of Abelian groups follows from this result. We use the property that our order finding algorithm works for any group to design a simple O(n) algorithm for testing whether a group of size n, described by its multiplication table, is nilpotent. We also give an O(n) algorithm for determining if a group of size n, described by its multiplication table, is Abelian. (C) 2007 Elsevier Inc. All rights reserved.

Data-aware task scheduling for all-to-all comparison problems in heterogeneous distributed systems

Solving large-scale all-to-all comparison problems using distributed computing is increasingly significant for various applications. Previous efforts to implement distributed all-to-all comparison frameworks have treated the two phases of data distribution and comparison task scheduling separately. This leads to high storage demands as well as poor data locality for the comparison tasks, thus creating a need to redistribute the data at runtime. Furthermore, most previous methods have been developed for homogeneous computing environments, so their overall performance is degraded even further when they are used in heterogeneous distributed systems. To tackle these challenges, this paper presents a data-aware task scheduling approach for solving all-to-all comparison problems in heterogeneous distributed systems. The approach formulates the requirements for data distribution and comparison task scheduling simultaneously as a constrained optimization problem. Then, metaheuristic data pre-scheduling and dynamic task scheduling strategies are developed along with an algorithmic implementation to solve the problem. The approach provides perfect data locality for all comparison tasks, avoiding rearrangement of data at runtime. It achieves load balancing among heterogeneous computing nodes, thus enhancing the overall computation time. It also reduces data storage requirements across the network. The effectiveness of the approach is demonstrated through experimental studies.

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.

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.

A semi-experimental approach to plane problems in elasticity

A semi-experimental approach to solve two-dimensional problems in elasticity is given. The method has been applied to two problems, (i) a square deep beam, and (ii) a bridge pier with a sloping boundary. For the first problem sufficient analytical results are available and hence the accuracy of the method can be verified. Then the method has been extended to the second problem for which sufficient results are not available.

Estimation of the critical viscous sublayer in heat transfer problems

Imagining a disturbance made on a compressible boundary layer with the help of a heat source, the critical viscous sublayer, through which the skin friction at any point on a surface is connected with the heat transferred from a heated element embedded in it, has been estimated. Under similar conditions of external flow (Ray1)) the ratio of the critical viscous sublayer to the undisturbed boundary layer thickness is about one-tenth in the laminar case and one hundredth in the turbulent case. These results are similar to those (cf.1)) found in shock wave boundary layer interaction problems.