Solution of a hypersingular integral equation of the second kind

A straightforward analysis involving the complex function-theoretic method is employed to determine the closed-form solution of a special hypersingular integral equation of the second kind, and its known solution is recovered.

A fixed-grid finite element based enthalpy formulation for generalized phase change problems: role of superficial mushy region

The enthalpy method is primarily developed for studying phase change in a multicomponent material, characterized by a continuous liquid volume fraction (phi(1)) vs temperature (T) relationship. Using the Galerkin finite element method we obtain solutions to the enthalpy formulation for phase change in 1D slabs of pure material, by assuming a superficial phase change region (linear (phi(1) vs T) around the discontinuity at the melting point. Errors between the computed and analytical solutions are evaluated for the fluxes at, and positions of, the freezing front, for different widths of the superficial phase change region and spatial discretizations with linear and quadratic basis functions. For Stefan number (St) varying between 0.1 and 10 the method is relatively insensitive to spatial discretization and widths of the superficial phase change region. Greater sensitivity is observed at St = 0.01, where the variation in the enthalpy is large. In general the width of the superficial phase change region should span at least 2-3 Gauss quadrature points for the enthalpy to be computed accurately. The method is applied to study conventional melting of slabs of frozen brine and ice. Regardless of the forms for the phi(1) vs T relationships, the thawing times were found to scale as the square of the slab thickness. The ability of the method to efficiently capture multiple thawing fronts which may originate at any spatial location within the sample, is illustrated with the microwave thawing of slabs and 2D cylinders. (C) 2002 Elsevier Science Ltd. All rights reserved.

Generalized model for infrared perception from an engine exhaust

A comprehensive scheme has been developed for the prediction of radiation from engine exhaust and its incidence on an arbitrarily located sensor. Existing codes have been modified for the simulation of flows inside nozzles and jets. A novel view factor computation scheme has been applied for the determination of the radiosities of the discrete panels of a diffuse and gray nozzle surface. The narrowband model has been used to model the radiation from the gas inside the nozzle and the nonhomogeneous jet. The gas radiation from the nozzle inclusive of nozzle surface radiosities have been used as boundary conditions on the jet radiation. Geometric modeling techniques have been developed to identify and isolate nozzle surface panels and gas columns of the nozzle and jet to determine the radiation signals incident on the sensor. The scheme has been validated for intensity and heat flux predictions, and some useful results of practical importance have been generated to establish its viability for infrared signature analysis of jets.

Generalized asymptotic expansions for the wavenumbers in infinite flexible in vacuo orthotropic cylindrical shells

Analytical expressions are found for the wavenumbers and resonance frequencies in flexible, orthotropic shells using the asymptotic methods. These expressions are valid for arbitrary circumferential orders n. The Donnell-Mushtari shell theory is used to model the dynamics of the cylindrical shell. Initially, an in vacuo cylindrical isotropic shell is considered and expressions for all the wavenumbers (bending, near-field bending, longitudinal and torsional) are found. Subsequently, defining a suitable orthotropy parameter epsilon, the problem of wave propagation in an orthotropic shell is posed as a perturbation on the corresponding problem for an isotropic shell. Asymptotic expressions for the wavenumbers in the in vacuo orthotropic shell are then obtained by treating epsilon as an expansion parameter. In both cases (isotropy and orthotropy), a frequency-scaling parameter (eta) and Poisson's ratio (nu) are used to find elegant expansions in the different frequency regimes. The asymptotic expansions are compared with numerical solutions in each of the cases and the match is found to be good. The main contribution of this work lies in the extension of the existing literature by developing closed-form expressions for wavenumbers with arbitrary circumferential orders n in the case of both, isotropic and orthotropic shells. Finally, we present natural frequency expressions in finite shells (isotropic and orthotropic) for the axisymmetric mode and compare them with numerical and ANSYS results. Here also, the comparison is found to be good. (C) 2011 Elsevier Ltd. All rights reserved.

Channel Precoding for STBCs from Generalized Pseudo Orthogonal Designs

Statistical information about the wireless channel can be used at the transmitter side to enhance the performance of MIMO systems. This paper addresses how the concept of channel precoding can be used to enhance the performance of STBCs from Generalized Pseudo Orthogonal Designs which were first introduced by Zhu and Jafarkhani. Such designs include some important classes of STBCs that are directly derivable from Quasi-Orthogonal Designs and Co-ordinate Interleaved Orthogonal Designs.

Two-timescale Q-learning Algorithms with an Application to Routing in Networks

We propose two variants of the Q-learning algorithm that (both) use two timescales. One of these updates Q-values of all feasible state-action pairs at each instant while the other updates Q-values of states with actions chosen according to the ‘current ’ randomized policy updates. A sketch of convergence of the algorithms is shown. Finally, numerical experiments using the proposed algorithms for routing on different network topologies are presented and performance comparisons with the regular Q-learning algorithm are shown.

Bidding Dynamics of Rational Advertisers in Sponsored Search Auctions on the Web

In this paper, we address a key problem faced by advertisers in sponsored search auctions on the web: how much to bid, given the bids of the other advertisers, so as to maximize individual payoffs? Assuming the generalized second price auction as the auction mechanism, we formulate this problem in the framework of an infinite horizon alternative-move game of advertiser bidding behavior. For a sponsored search auction involving two advertisers, we characterize all the pure strategy and mixed strategy Nash equilibria. We also prove that the bid prices will lead to a Nash equilibrium, if the advertisers follow a myopic best response bidding strategy. Following this, we investigate the bidding behavior of the advertisers if they use Q-learning. We discover empirically an interesting trend that the Q-values converge even if both the advertisers learn simultaneously.