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.

Robust Relay Precoder Design for MIMO-Relay Networks

In this paper, we consider a robust design of MIMO-relay precoder and receive filter for the destination nodes in a non-regenerative multiple-input multiple-output (MIMO) relay network. The network consists of multiple source-destination node pairs assisted by a single MIMO-relay node. The source and destination nodes are single antenna nodes, whereas the MIMO-relay node has multiple transmit and multiple receive antennas. The channel state information (CSI) available at the MIMO-relay node for precoding purpose is assumed to be imperfect. We assume that the norms of errors in CSI are upper-bounded, and the MIMO-relay node knows these bounds. We consider the robust design of the MIMO-relay precoder and receive filter based on the minimization of the total MIMO-relay transmit power with constraints on the mean square error (MSE) at the destination nodes. We show that this design problem can be solved by solving an alternating sequence of minimization and worst-case analysis problems. The minimization problem is formulated as a convex optimization problem that can be solved efficiently using interior-point methods. The worst-case analysis problem can be solved analytically using an approximation for the MSEs at the destination nodes. We demonstrate the robust performance of the proposed design through simulations.

Analysing Message Sequence Graph Specifications

We give a detailed construction of a finite-state transition system for a com-connected Message Sequence Graph. Though this result is well-known in the literature and forms the basis for the solution to several analysis and verification problems concerning MSG specifications, the constructions given in the literature are either not amenable to implementation, or imprecise, or simply incorrect. In contrast we give a detailed construction along with a proof of its correctness. Our transition system is amenable to implementation, and can also be used for a bounded analysis of general (not necessarily com-connected) MSG specifications.

Tatonnement Mechanisms for Combinatorial Exchanges

Combinatorial exchanges are double sided marketplaces with multiple sellers and multiple buyers trading with the help of combinatorial bids. The allocation and other associated problems in such exchanges are known to be among the hardest to solve among all economic mechanisms. It has been shown that the problems of surplus maximization or volume maximization in combinatorial exchanges are inapproximable even with free disposal. In this paper, the surplus maximization problem is formulated as an integer linear programming problem and we propose a Lagrangian relaxation based heuristic to find a near optimal solution. We develop computationally efficient tâtonnement mechanisms for clearing combinatorial exchanges where the Lagrangian multipliers can be interpreted as the prices of the items set by the exchange in each iteration. Our mechanisms satisfy Individual-rationality and Budget-nonnegativity properties. The computational experiments performed on representative data sets show that the proposed heuristic produces a feasible solution with negligible optimality gap.

Weakly non-linear stability of a hydrodynamic accretion disc

When the cold accretion disc coupling between neutral gas and a magnetic field is so weak that the magnetorotational instability is less effective or even stops working, it is of prime interest to investigate the pure hydrodynamic origin of turbulence and transport phenomena. As the Reynolds number increases, the relative importance of the non-linear term in the hydrodynamic equation increases. In an accretion disc where the molecular viscosity is too small, the Reynolds number is large enough for the non-linear term to have new effects. We investigate the scenario of the `weakly non-linear' evolution of the amplitude of the linear mode when the flow is bounded by two parallel walls. The unperturbed flow is similar to the plane Couette flow, but with the Coriolis force included in the hydrodynamic equation. Although there is no exponentially growing eigenmode, because of the self-interaction, the least stable eigenmode will grow in an intermediate phase. Later, this will lead to higher-order non-linearity and plausible turbulence. Although the non-linear term in the hydrodynamic equation is energy-conserving, within the weakly non-linear analysis it is possible to define a lower bound of the energy (alpha A(c)(2), where A(c) is the threshold amplitude) needed for the flow to transform to the turbulent phase. Such an unstable phase is possible only if the Reynolds number >= 10(3-4). The numerical difficulties in obtaining such a large Reynolds number might be the reason for the negative result of numerical simulations on a pure hydrodynamic Keplerian accretion disc.

An adaptive cascade compensator for a wide class of stable minimum or nonminimum phase plants through time moment estimation

Model Reference Adaptive Control (MRAC) of a wide repertoire of stable Linear Time Invariant (LTI) systems is addressed here. Even an upper bound on the order of the finite-dimensional system is unavailable. Further, the unknown plant is permitted to have both minimum phase and nonminimum phase zeros. Model following with reference to a completely specified reference model excited by a class of piecewise continuous bounded signals is the goal. The problem is approached by taking recourse to the time moments representation of an LTI system. The treatment here is confined to Single-Input Single-Output (SISO) systems. The adaptive controller is built upon an on-line scheme for time moment estimation of a system given no more than its input and output. As a first step, a cascade compensator is devised. The primary contribution lies in developing a unified framework to eventually address with more finesse the problem of adaptive control of a large family of plants allowed to be minimum or nonminimum phase. Thus, the scheme presented in this paper is confined to lay the basis for more refined compensators-cascade, feedback and both-initially for SISO systems and progressively for Multi-Input Multi-Output (MIMO) systems. Simulations are presented.

On an oscillatory point force in a rotating stratified fluid

The forced oscillations due to a point forcing effect in an infinite or contained, inviscid, incompressible, rotating, stratified fluid are investigated taking into account the density variation in the inertia terms in the linearized equations of motion. The solutions are obtained in closed form using generalized Fourier transforms. Solutions are presented for a medium bounded by a finite cylinder when the oscillatory forcing effect is acting at a point on the axis of the cylinder. In both the unbounded and bounded case, there exist characteristic cones emanating from the point of application of the force on which either the pressure or its derivatives are discontinuous. The perfect resonance existing at certain frequencies in an unbounded or bounded homogeneous fluid is avoided in the case of a confined stratified fluid.

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

The tendency of granular materials in rapid shear ow 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 flow of granular materials presented previously by Wang et al. (1996) are, in general, based on erroneous base states.

N-gamma for rough strip footing using the method of characteristics

By using the method of characteristics, the bearing capacity factor N-gamma was computed for a rough strip footing. The analysis was performed by considering a curved nonplastic wedge under the foundation base bounded by curved slip lines being tangential to the base of the footing at its either edge and inclined at an angle pi/4 - phi/2 with the vertical axis of symmetry. The existing theories in the literature for rough footings, which usually employ a triangular wedge below the footing base, were generally found to provide greater values of N-gamma as compared with the results obtained in this contribution.

Two new families of low-correlation interleaved QAM sequence

Two families of low correlation QAM sequences are presented here. In a CDMA setting, these sequences have the ability to transport a large amount of data as well as enable variable-rate signaling on the reverse link. The first family Á2SQ - B2− is constructed by interleaving 2 selected QAM sequences. This family is defined over M 2-QAM, where M = 2 m , m ≥ 2. Over 16-QAM, the normalized maximum correlation [`(q)]maxmax is bounded above by <~1.17 ÖNUnknown control sequence '\lesssim' , where N is the period of the sequences in the family. This upper bound on [`(q)]maxmax is the lowest among all known sequence families over 16-QAM.The second family Á4SQ4 is constructed by interleaving 4 selected QAM sequences. This family is defined over M 2-QAM, where M = 2 m , m ≥ 3, i.e., 64-QAM and beyond. The [`(q)]maxmax for sequences in this family over 64-QAM is upper bounded by <~1.60 ÖNUnknown control sequence '\lesssim' . For large M, [`(q)]max <~1.64 ÖNUnknown control sequence '\lesssim' . These upper bounds on [`(q)]maxmax are the lowest among all known sequence families over M 2-QAM, M = 2 m , m ≥ 3.

Low correlation interleaved QAM sequences

A low correlation interleaved QAM sequence family is presented here. In a CDMA setting, these sequences have the ability to transport a large amount of data as well as enable variable-rate signaling on the reverse link. The new interleaved selected family INQ has period N, normalized maximum correlation parameter thetasmacrmax bounded above by lsim a radicN, where a ranges from 1.17 in the 16-QAM case to 1.99 for large M2-QAM, where M = 2m, m ges 2. Each user is enabled to transfer m + 1 bits of data per period of the spreading sequence. These constructions have the lowest known value of maximum correlation of any sequence family with the same alphabet.

Distributed Source Coding for Sensor Data Model and Estimation of Cluster Head Errors Using Bayesian and K-Near Neighborhood Classifiers in Deployment of Dense Wireless Sensor Networks

The lifetime calculation of large dense sensor networks with fixed energy resources and the remaining residual energy have shown that for a constant energy resource in a sensor network the fault rate at the cluster head is network size invariant when using the network layer with no MAC losses.Even after increasing the battery capacities in the nodes the total lifetime does not increase after a max limit of 8 times. As this is a serious limitation lots of research has been done at the MAC layer which allows to adapt to the specific connectivity, traffic and channel polling needs for sensor networks. There have been lots of MAC protocols which allow to control the channel polling of new radios which are available to sensor nodes to communicate. This further reduces the communication overhead by idling and sleep scheduling thus extending the lifetime of the monitoring application. We address the two issues which effects the distributed characteristics and performance of connected MAC nodes. (1) To determine the theoretical minimum rate based on joint coding for a correlated data source at the singlehop, (2a) to estimate cluster head errors using Bayesian rule for routing using persistence clustering when node densities are the same and stored using prior probability at the network layer, (2b) to estimate the upper bound of routing errors when using passive clustering were the node densities at the multi-hop MACS are unknown and not stored at the multi-hop nodes a priori. In this paper we evaluate many MAC based sensor network protocols and study the effects on sensor network lifetime. A renewable energy MAC routing protocol is designed when the probabilities of active nodes are not known a priori. From theoretical derivations we show that for a Bayesian rule with known class densities of omega1, omega2 with expected error P* is bounded by max error rate of P=2P* for single-hop. We study the effects of energy losses using cross-layer simulation of - large sensor network MACS setup, the error rate which effect finding sufficient node densities to have reliable multi-hop communications due to unknown node densities. The simulation results show that even though the lifetime is comparable the expected Bayesian posterior probability error bound is close or higher than Pges2P*.

On the Limits of Spatial Reuse and Cooperative Communication for Dense Wireless Networks

We consider a dense ad hoc wireless network comprising n nodes confined to a given two dimensional region of fixed area. For the Gupta-Kumar random traffic model and a realistic interference and path loss model (i.e., the channel power gains are bounded above, and are bounded below by a strictly positive number), we study the scaling of the aggregate end-to-end throughput with respect to the network average power constraint, P macr, and the number of nodes, n. The network power constraint P macr is related to the per node power constraint, P macr, as P macr = np. For large P, we show that the throughput saturates as Theta(log(P macr)), irrespective of the number of nodes in the network. For moderate P, which can accommodate spatial reuse to improve end-to-end throughput, we observe that the amount of spatial reuse feasible in the network is limited by the diameter of the network. In fact, we observe that the end-to-end path loss in the network and the amount of spatial reuse feasible in the network are inversely proportional. This puts a restriction on the gains achievable using the cooperative communication techniques studied in and, as these rely on direct long distance communication over the network.

Incentive Compatible Mechanisms for Resource Procurement in Computational Grids with Rational resource Providers

In a computational grid, the presence of grid resource providers who are rational and intelligent could lead to an overall degradation in the efficiency of the grid. In this paper, we design incentive compatible grid resource procurement mechanisms which ensure that the efficiency of the grid is not affected by the rational behavior of resource providers.In particular, we offer three elegant incentive compatible mechanisms for this purpose: (1) G-DSIC (Grid-Dominant Strategy Incentive Compatible) mechanism (2) G-BIC (Grid-Bayesian Nash Incentive Compatible) mechanism (3) G-OPT(Grid-Optimal) mechanism which minimizes the cost to the grid user, satisfying at the same time, (a) Bayesian incentive compatibility and (b) individual rationality. We evaluate the relative merits and demerits of the above three mechanisms using game theoretical analysis and numerical experiments.

Incentive compatible mechanisms for group ticket allocation in software maintenance services

A customer reported problem (or Trouble Ticket) in software maintenance is typically solved by one or more maintenance engineers. The decision of allocating the ticket to one or more engineers is generally taken by the lead, based on customer delivery deadlines and a guided complexity assessment from each maintenance engineer. The key challenge in such a scenario is two folds, un-truthful (hiked up) elicitation of ticket complexity by each engineer to the lead and the decision of allocating the ticket to a group of engineers who will solve the ticket with in customer deadline. The decision of allocation should ensure Individual and Coalitional Rationality along with Coalitional Stability. In this paper we use game theory to examine the issue of truthful elicitation of ticket complexities by engineers for solving ticket as a group given a specific customer delivery deadline. We formulate this problem as strategic form game and propose two mechanisms, (1) Division of Labor (DOL) and (2) Extended Second Price (ESP). In the proposed mechanisms we show that truth telling by each engineer constitutes a Dominant Strategy Nash Equilibrium of the underlying game. Also we analyze the existence of Individual Rationality (IR) and Coalitional Rationality (CR) properties to motivate voluntary and group participation. We use Core, solution concept from co-operative game theory to analyze the stability of the proposed group based on the allocation and payments.