The sputtering temperature of a cooling cylindrical rod without and with an insulated core in a two-fluid medium

Utilising Jones' method associated with the Wiener-Hopf technique, explicit solutions are obtained for the temperature distributions on the surface of a cylindrical rod without an insulated core as well as that inside a cylindrical rod with an insulated inner core when the rod, in either of the two cases, is allowed to enter, with a uniform speed, into two different layers of fluid with different cooling abilities. Simple expressions are derived for the values of the sputtering temperatures of the rod at the points of entry into the respective layers, assuming the upper layer of the fluid to be of finite depth and the lower of infinite extent. Both the problems are solved through a three-part Wiener-Hopf problem of special type and the numerical results under certain special circumstances are obtained and presented in tabular forms.

Chordal Bipartite Graphs with High Boxicity

The boxicity of a graph G is defined as the minimum integer k such that G is an intersection graph of axis-parallel k-dimensional boxes. Chordal bipartite graphs are bipartite graphs that do not contain an induced cycle of length greater than 4. It was conjectured by Otachi, Okamoto and Yamazaki that chordal bipartite graphs have boxicity at most 2. We disprove this conjecture by exhibiting an infinite family of chordal bipartite graphs that have unbounded boxicity.

Exact free-surface flows for shallow-water equations .2. the compressible case

Exact free surface flows with shear in a compressible barotropic medium are found, extending the authors' earlier work for the incompressible medium. The barotropic medium is of finite extent in the vertical direction, while it is infinite in the horizontal direction. The ''shallow water'' equations for a compressible barotropic medium, subject to boundary conditions at the free surface and at the bottom, are solved in terms of double psi-series, Simple wave and time-dependent solutions are found; for the former the free surface is of arbitrary shape while for the latter it is a damping traveling wave in the horizontal direction, For other types of solutions, the height of the free surface is constant either on lines of constant acceleration or on lines of constant speed. In the case of an isothermal medium, when gamma = 1, we again find simple wave and time-dependent solutions.

Vortex sheet simulation of a plane �canonical� mixing layer

Discrete vortex simulations of the mixing layer carried out in the past have usually involved large induced velocity fluctuations, and thus demanded rather long time-averaging to obtain satisfactory values of Reynolds stresses and third-order moments. This difficulty has been traced here, in part, to the use of discrete vortices to model what in actuality are continuous vortex sheets. We propose here a novel two-dimensional vortex sheet technique for computing mixing layer flow in the limit of infinite Reynolds number. The method divides the vortex sheet into constant-strength linear elements, whose motions are computed using the Biot-Savart law. The downstream far-field is modelled by a steady vorticity distribution derived by application of conical similarity from the solution obtained in a finite computational domain. The boundary condition on the splitter plate is satisfied rigorously using a doublet sheet. The computed large-scale roll-up of the vortex sheet is qualitatively similar to experimentally obtained shadow-graphs of the plane turbulent mixing layer. The mean streamwise velocity profile and the growth rate agree well with experimental data. The presently computed Reynolds stresses and third-order moments are comparable with experimental and previous vortex-dynamical results, without using any external parameter (such as the vortex core-size) of the kind often used in the latter. The computed autocorrelations are qualitatively similar to experimental results along the top and bottom edges of the mixing layer, and show a well-defined periodicity along the centreline. The accuracy of the present computation is independently established by demonstrating negligibly small changes in the five invariants (including the Hamiltonian) in vortex dynamics.

On Walkup's class K (d) and a minimal triangulation of (S-3 (sic) S-1)(#3)

For d >= 2, Walkup's class K (d) consists of the d-dimensional simplicial complexes all whose vertex-links are stacked (d - 1)-spheres. Kalai showed that for d >= 4, all connected members of K (d) are obtained from stacked d-spheres by finitely many elementary handle additions. According to a result of Walkup, the face vector of any triangulated 4-manifold X with Euler characteristic chi satisfies f(1) >= 5f(0) - 15/2 chi, with equality only for X is an element of K(4). Kuhnel observed that this implies f(0)(f(0) - 11) >= -15 chi, with equality only for 2-neighborly members of K(4). Kuhnel also asked if there is a triangulated 4-manifold with f(0) = 15, chi = -4 (attaining equality in his lower bound). In this paper, guided by Kalai's theorem, we show that indeed there is such a triangulation. It triangulates the connected sum of three copies of the twisted sphere product S-3 (sic) S-1. Because of Kuhnel's inequality, the given triangulation of this manifold is a vertex-minimal triangulation. By a recent result of Effenberger, the triangulation constructed here is tight. Apart from the neighborly 2-manifolds and the infinite family of (2d + 3)-vertex sphere products Sd-1 X S-1 (twisted for d odd), only fourteen tight triangulated manifolds were known so far. The present construction yields a new member of this sporadic family. We also present a self-contained proof of Kalai's result. (C) 2011 Elsevier B.V. All rights reserved.

A QFT-based robust SVC controller for improving the dynamic stability of power systems

A new design technique for an SVC-based power system damping controller has been proposed. The controller attempts to place all plant poles within a specified region on the s-plane to guarantee the desired closed loop performance. The use of Horowitz's quantitative feedback theory (QFT) permits the design of a 'fixed gain controller' that maintains its performance in spite of large variations in the plant parameters during its normal course of operation. The required controller parameters are arrived at by solving an optimization problem that incorporates the control specifications. The performance of this robust controller has been evaluated on a single machine infinite bus system equipped with a mid point SVC, and the results are shown to be consistent with the expected performance of the stabilizer. (C) 1998 Elsevier Science S.A. All rights reserved.

On the incoming water waves against a vertical cliff

The problems of obliquely incident surface water waves against a vertical cliff have been handled in both the cases of water of infinite as well as finite depth by straightforward uses of appropriate Havelock-type expansion theorems. The logarithmic singularity along the shore-line has been incorporated in a direct manner, by suitably representing the Dirac's delta function.

On the optimality of exhaustive service policies in multiclass queueing systems with modulated arrivals and switchovers

Consider a single-server multiclass queueing system with K classes where the individual queues are fed by K-correlated interrupted Poisson streams generated in the states of a K-state stationary modulating Markov chain. The service times for all the classes are drawn independently from the same distribution. There is a setup time (and/or a setup cost) incurred whenever the server switches from one queue to another. It is required to minimize the sum of discounted inventory and setup costs over an infinite horizon. We provide sufficient conditions under which exhaustive service policies are optimal. We then present some simulation results for a two-class queueing system to show that exhaustive, threshold policies outperform non-exhaustive policies.

Representation of thermodynamic properties of quaternary systems using interaction parameters

Integral excess free energy of a quaternary system has been expressed in terms of the MacLaurin infinite series. The series is subjected to appropriate boundary conditions and each of the derivatives correlated to the corresponding interaction coefficients. The derivation of the partial functions involves extensive summation of various infinite series pertaining to the first order and quaternary parameters to remove any truncational error. The thermodynamic consistency of the derived partials has been established based on the Gibbs-Duhem relations. The equations are used to interpret the thermodynamic properties of the Fe-Cr-Ni-N system.

Spin state and exchange in the quasi-one-dimensional antiferromagnet KFeS2

We report the optical spectra and single crystal magnetic susceptibility of the one-dimensional antiferromagnet KFeS2. Measurements have been carried out to ascertain the spin state of Fe3+ and the nature of the magnetic interactions in this compound. The optical spectra and magnetic susceptibility could be consistently interpreted using a S = 1/2 spin ground state for the Fe3+ ion. The features in the optical spectra have been assigned to transitions within the d-electron manifold of the Fe3+ ion, and analysed in the strong field limit of the ligand field theory. The high temperature isotropic magnetic susceptibility is typical of a low-dimensional system and exhibits a broad maximum at similar to 565 K. The susceptibility shows a well defined transition to a three dimensionally ordered antiferromagnetic state at T-N = 250 K. The intra and interchain exchange constants, J and J', have been evaluated from the experimental susceptibilities using the relationship between these quantities, and chi(max), T-max, and T-N for a spin 1/2 one-dimensional chain. The values are J = -440.71 K, and J' = 53.94 K. Using these values of J and J', the susceptibility of a spin 1/2 Heisenberg chain was calculated. A non-interacting spin wave model was used below T-N. The susceptibility in the paramagnetic region was calculated from the theoretical curves for an infinite S = 1/2 chain. The calculated susceptibility compares well with the experimental data of KFeS2. Further support for a one-dimensional spin 1/2 model comes from the fact that the calculated perpendicular susceptibility at 0K (2.75 x 10(-4) emu/mol) evaluated considering the zero point reduction in magnetization from spin wave theory is close to the projected value (2.7 x 10(-4) emu/mol) obtained from the experimental data.

Stability and throughput analysis of unslotted CDMA-ALOHA with finite number of users and code sharing

We consider a system comprising a finite number of nodes, with infinite packet buffers, that use unslotted ALOHA with Code Division Multiple Access (CDMA) to share a channel for transmitting packetised data. We propose a simple model for packet transmission and retransmission at each node, and show that saturation throughput in this model yields a sufficient condition for the stability of the packet buffers; we interpret this as the capacity of the access method. We calculate and compare the capacities of CDMA-ALOHA (with and without code sharing) and TDMA-ALOHA; we also consider carrier sensing and collision detection versions of these protocols. In each case, saturation throughput can be obtained via analysis pf a continuous time Markov chain. Our results show how saturation throughput degrades with code-sharing. Finally, we also present some simulation results for mean packet delay. Our work is motivated by optical CDMA in which "chips" can be optically generated, and hence the achievable chip rate can exceed the achievable TDMA bit rate which is limited by electronics. Code sharing may be useful in the optical CDMA context as it reduces the number of optical correlators at the receivers. Our throughput results help to quantify by how much the CDMA chip rate should exceed the TDMA bit rate so that CDMA-ALOHA yields better capacity than TDMA-ALOHA.

Optimal control of a stochastic hybrid system with discounted cost

We address the optimal control problem of a very general stochastic hybrid system with both autonomous and impulsive jumps. The planning horizon is infinite and we use the discounted-cost criterion for performance evaluation. Under certain assumptions, we show the existence of an optimal control. We then derive the quasivariational inequalities satisfied by the value function and establish well-posedness. Finally, we prove the usual verification theorem of dynamic programming.

The effect of boundaries on the plane Couette flow of granular materials: a bifurcation analysis

The tendency of granular materials in rapid shear flow to form non-uniform structures is well documented in the literature. Through a linear stability analysis of the solution of continuum equations for rapid shear flow of a uniform granular material, performed by Savage (1992) and others subsequently, it has been shown that an infinite plane shearing motion may be unstable in the Lyapunov sense, provided the mean volume fraction of particles is above a critical value. This instability leads to the formation of alternating layers of high and low particle concentrations oriented parallel to the plane of shear. Computer simulations, on the other hand, reveal that non-uniform structures are possible even when the mean volume fraction of particles is small. In the present study, we have examined the structure of fully developed layered solutions, by making use of numerical continuation techniques and bifurcation theory. It is shown that the continuum equations do predict the existence of layered solutions of high amplitude even when the uniform state is linearly stable. An analysis of the effect of bounding walls on the bifurcation structure reveals that the nature of the wall boundary conditions plays a pivotal role in selecting that branch of non-uniform solutions which emerges as the primary branch. This demonstrates unequivocally that the results on the stability of bounded shear how of granular materials presented previously by Wang et al. (1996) are, in general, based on erroneous base states.

Unsteady axisymmetric stagnation-point flow of a viscous fluid on a cylinder

The unsteady viscous flow in the vicinity of an axisymmetric stagnation point of an infinite circular cylinder is investigated when both the free stream velocity and the velocity of the cylinder vary arbitrarily with time. The cylinder moves either in the same direction as that of the free stream or in the opposite direction. The flow is initially (t = 0) steady and then at t > 0 it becomes unsteady. The semi-similar solution of the unsteady Navier-Stokes equations has been obtained numerically using an implicit finite-difference scheme. Also the self-similar solution of the Navier-Stokes equations is obtained when the velocity of the cylinder and the free stream velocity vary inversely as a linear function of time. For small Reynolds number, a closed form solution is obtained. When the Reynolds number tends to infinity, the Navier-Stokes equations reduce to those of the two-dimensional stagnation-point flow. The shear stresses corresponding to stationary and the moving cylinder increase with the Reynolds number. The shear stresses increase with time for the accelerating flow but decrease with increasing time for the decelerating flow. For the decelerating case flow reversal occurs in the velocity profiles after a certain instant of time. (C) 1999 Elsevier Science Ltd. All rights reserved.

Chaotic and power law states in the Portevin-Le Chatelier effect

Recent studies on the Portevin-Le Chatelier effect report an intriguing crossover phenomenon from low-dimensional chaotic to an infinite-dimensional scale-invariant power law regime in experiments on CuAl single crystals and AlMg polycrystals, as function of strain rate. We devise fully dynamical model which reproduces these results. At low and medium strain rates, the model is chaotic with the structure of the attractor resembling the reconstructed experimental attractor. At high strain rates, power law statistics for the magnitudes and durations of the stress drops emerge as in experiments and concomitantly, the largest Lyapunov exponent is zero.