Numerical procedure for second order non-linear ordinary differential equations and application to heat transfer problem

In this paper, we have first given a numerical procedure for the solution of second order non-linear ordinary differential equations of the type y″ = f (x;y, y′) with given initial conditions. The method is based on geometrical interpretation of the equation, which suggests a simple geometrical construction of the integral curve. We then translate this geometrical method to the numerical procedure adaptable to desk calculators and digital computers. We have studied the efficacy of this method with the help of an illustrative example with known exact solution. We have also compared it with Runge-Kutta method. We have then applied this method to a physical problem, namely, the study of the temperature distribution in a semi-infinite solid homogeneous medium for temperature-dependent conductivity coefficient.

Quantum kinematics of Fermi-Dirac vacuum-plus-one-electron problem

Following Weisskopf, the kinematics of quantum mechanics is shown to lead to a modified charge distribution for a test electron embedded in the Fermi-Dirac vacuum with interesting consequences.

An auction algorithm for procuring wireless channel in a heterogenous wireless network

In this paper, we develop a novel auction algorithm for procuring wireless channel by a wireless node in a heterogeneous wireless network. We assume that the service providers of the heterogeneous wireless network are selfish and non-cooperative in the sense that they are only interested in maximizing their own utilities. The wireless user needs to procure wireless channels to execute multiple tasks. To solve the problem of the wireless user, we propose a reverse optimal (REVOPT) auction and derive an expression for the expected payment by the wireless user. The proposed auction mechanism REVOPT satisfies important game theoretic properties such as Bayesian incentive compatibility and individual rationality.

A generalized Linear Programming based approach to optimal divisible load scheduling

In this paper we propose a general Linear Programming (LP) based formulation and solution methodology for obtaining optimal solution to the load distribution problem in divisible load scheduling. We exploit the power of the versatile LP formulation to propose algorithms that yield exact solutions to several very general load distribution problems for which either no solutions or only heuristic solutions were available. We consider both star (single-level tree) networks and linear daisy chain networks, having processors equipped with front-ends, that form the generic models for several important network topologies. We consider arbitrary processing node availability or release times and general models for communication delays and computation time that account for constant overheads such as start up times in communication and computation. The optimality of the LP based algorithms is proved rigorously.

Transient signal detection using wigner-ville distribution and wavelet denoising

The problem of detecting an unknown transient signal in noise is considered. The SNR of the observed data is first enhanced using wavelet domain filter The output of the wavelet domain filter is then transformed using a Wigner-Ville transform,which separates the spectrum of the observed signal into narrow frequency bands. Each subband signal at the output of the Wigner-ville block is subjected kto wavelet based level dependent denoising (WBLDD)to supress colored noise A weighted sum of the absolute value of outputs of WBLDD is passed through an energy detector, whose output is used as test statistic to take the final decision. By assigning weights proportional to the energy of the corresponding subband signals, the proposed detector approximates a frequency domain matched filter Simulation results are presented to show that the performance of the proposed detector is better than that of the wavelet packet transform based detector.

A neural network based CBIR system using STI features and relevance feedback

Multimedia mining primarily involves, information analysis and retrieval based on implicit knowledge. The ever increasing digital image databases on the Internet has created a need for using multimedia mining on these databases for effective and efficient retrieval of images. Contents of an image can be expressed in different features such as Shape, Texture and Intensity-distribution(STI). Content Based Image Retrieval(CBIR) is an efficient retrieval of relevant images from large databases based on features extracted from the image. Most of the existing systems either concentrate on a single representation of all features or linear combination of these features. The paper proposes a CBIR System named STIRF (Shape, Texture, Intensity-distribution with Relevance Feedback) that uses a neural network for nonlinear combination of the heterogenous STI features. Further the system is self-adaptable to different applications and users based upon relevance feedback. Prior to retrieval of relevant images, each feature is first clustered independent of the other in its own space and this helps in matching of similar images. Testing the system on a database of images with varied contents and intensive backgrounds showed good results with most relevant images being retrieved for a image query. The system showed better and more robust performance compared to existing CBIR systems

Lessons from the Sparse Sensor Network Deployment in Rural India

We discuss the key issues in the deployment of sparse sensor networks. The network monitors several environment parameters and is deployed in a semi-arid region for the benefit of small and marginal farmers. We begin by discussing the problems of an existing unreliable 1 sq km sparse network deployed in a village. The proposed solutions are implemented in a new cluster. The new cluster is a reliable 5 sq km network. Our contributions are two fold. Firstly, we describe a. novel methodology to deploy a sparse reliable data gathering sensor network and evaluate the ``safe distance'' or ``reliable'' distance between nodes using propagation models. Secondly, we address the problem of transporting data from rural aggregation servers to urban data centres. This paper tracks our steps in deploying a sensor network in a village,in India, trying to provide better diagnosis for better crop management. Keywords - Rural, Agriculture, CTRS, Sparse.

Filter design using radial basis function neural network and genetic algorithm for improved operational health monitoring

The problem of denoising damage indicator signals for improved operational health monitoring of systems is addressed by applying soft computing methods to design filters. Since measured data in operational settings is contaminated with noise and outliers, pattern recognition algorithms for fault detection and isolation can give false alarms. A direct approach to improving the fault detection and isolation is to remove noise and outliers from time series of measured data or damage indicators before performing fault detection and isolation. Many popular signal-processing approaches do not work well with damage indicator signals, which can contain sudden changes due to abrupt faults and non-Gaussian outliers. Signal-processing algorithms based on radial basis function (RBF) neural network and weighted recursive median (WRM) filters are explored for denoising simulated time series. The RBF neural network filter is developed using a K-means clustering algorithm and is much less computationally expensive to develop than feedforward neural networks trained using backpropagation. The nonlinear multimodal integer-programming problem of selecting optimal integer weights of the WRM filter is solved using genetic algorithm. Numerical results are obtained for helicopter rotor structural damage indicators based on simulated frequencies. Test signals consider low order polynomial growth of damage indicators with time to simulate gradual or incipient faults and step changes in the signal to simulate abrupt faults. Noise and outliers are added to the test signals. The WRM and RBF filters result in a noise reduction of 54 - 71 and 59 - 73% for the test signals considered in this study, respectively. Their performance is much better than the moving average FIR filter, which causes significant feature distortion and has poor outlier removal capabilities and shows the potential of soft computing methods for specific signal-processing applications.

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.

Filter design using radial basis function neural network and genetic algorithm for improved operational health monitoring

The problem of denoising damage indicator signals for improved operational health monitoring of systems is addressed by applying soft computing methods to design filters. Since measured data in operational settings is contaminated with noise and outliers, pattern recognition algorithms for fault detection and isolation can give false alarms. A direct approach to improving the fault detection and isolation is to remove noise and outliers from time series of measured data or damage indicators before performing fault detection and isolation. Many popular signal-processing approaches do not work well with damage indicator signals, which can contain sudden changes due to abrupt faults and non-Gaussian outliers. Signal-processing algorithms based on radial basis function (RBF) neural network and weighted recursive median (WRM) filters are explored for denoising simulated time series. The RBF neural network filter is developed using a K-means clustering algorithm and is much less computationally expensive to develop than feedforward neural networks trained using backpropagation. The nonlinear multimodal integer-programming problem of selecting optimal integer weights of the WRM filter is solved using genetic algorithm. Numerical results are obtained for helicopter rotor structural damage indicators based on simulated frequencies. Test signals consider low order polynomial growth of damage indicators with time to simulate gradual or incipient faults and step changes in the signal to simulate abrupt faults. Noise and outliers are added to the test signals. The WRM and RBF filters result in a noise reduction of 54 - 71 and 59 - 73% for the test signals considered in this study, respectively. Their performance is much better than the moving average FIR filter, which causes significant feature distortion and has poor outlier removal capabilities and shows the potential of soft computing methods for specific signal-processing applications. (C) 2005 Elsevier B. V. All rights reserved.

Neural network based approach to standard cell placement

We propose a novel algorithm for placement of standard cells in VLSI circuits based on an analogy of this problem with neural networks. By employing some of the organising principles of these nets, we have attempted to improve the behaviour of the bipartitioning method as proposed by Kernighan and Lin. Our algorithm yields better quality placements compared with the above method, and also makes the final placement independent of the initial partition.

Probability Distribution of the Eigenvalues of the Random String Equation

The probability distribution of the eigenvalues of a second-order stochastic boundary value problem is considered. The solution is characterized in terms of the zeros of an associated initial value problem. It is further shown that the probability distribution is related to the solution of a first-order nonlinear stochastic differential equation. Solutions of this equation based on the theory of Markov processes and also on the closure approximation are presented. A string with stochastic mass distribution is considered as an example for numerical work. The theoretical probability distribution functions are compared with digital simulation results. The comparison is found to be reasonably good.

Analysis of transients in a canal network

A generalised formulation of the mathematical model developed for the analysis of transients in a canal network, under subcritical flow, with any realistic combination of control structures and their multiple operations, has been presented. The model accounts for a large variety of control structures such as weirs, gates, notches etc. discharging under different conditions, namely submerged and unsubmerged. A numerical scheme to compute and approximate steady state flow condition as the initial condition has also been presented. The model can handle complex situations that may arise from multiple gate operations. This has been demonstrated with a problem wherein the boundary conditions change from a gate discharge equation to an energy equation and back to a gate discharge equation. In such a situation the wave strikes a fixed gate and leads to large and rapid fluctuations in both discharge and depth.

Numerical Electromagnetic Analysis of Current and Voltage Distribution along Down Conductors and Towers Hit by Direct Lightning

In order to answer the practically important question of whether the down conductors of lightning protection systems to tall towers and buildings can be electrically isolated from the structure itself, this work is conducted. As a first step in this regard, it is presumed that the down conductor placed on metallic tower will be a pessimistic representation of the actual problem. This opinion was based on the fact that the proximity of heavy metallic structure will have a large damping effect. The post-stroke current distributions along the down conductors and towers, which can be quite different from that in the lightning channel, govern the post-stroke near field and the resulting gradient in the soil. Also, for a reliable estimation of the actual stroke current from the measured down conductor currents, it is essential to know the current distribution characteristics along the down conductors. In view of these, the present work attempts to deduce the post-stroke current and voltage distribution along typical down conductors and towers. A solution of the governing field equations on an electromagnetic model of the system is sought for the investigation. Simulation results providing the spatio-temporal distribution of the post-stroke current and voltage has provided very interesting results. It is concluded that it is almost impossible to achieve electrical isolation between the structure and the down conductor. Furthermore, there will be significant induction into the steel matrix of the supporting structure.

Persistence Problem in Two-Dimensional Fluid Turbulence

We present a natural framework for studying the persistence problem in two-dimensional fluid turbulence by using the Okubo-Weiss parameter Lambda to distinguish between vortical and extensional regions. We then use a direct numerical simulation of the two-dimensional, incompressible Navier-Stokes equation with Ekman friction to study probability distribution functions (PDFs) of the persistence times of vortical and extensional regions by employing both Eulerian and Lagrangian measurements. We find that, in the Eulerian case, the persistence-time PDFs have exponential tails; by contrast, this PDF for Lagrangian particles, in vortical regions, has a power-law tail with an exponent theta = 2.9 +/- 0.2.