Muon-spin rotation spectra in the mixed phase of high-T-c superconductors: Thermal fluctuations and disorder effects

We study muon-spin rotation (mu SR) spectra in the mixed phase of highly anisotropic layered superconductors, specifically Bi2+xSr2-xCaCu2O8+delta (BSCCO), by modeling the fluid and solid phases of pancake Vortices using liquid-state and density functional methods. The role of thermal fluctuations in causing motional narrowing of mu SR line shapes is quantified in terms of a first-principles theory of the flux-lattice melting transition. The effects of random point pinning are investigated using a replica treatment of liquid-state correlations and a replicated density functional theory. Our results indicate that motional narrowing in the pure system, although substantial, cannot account for the remarkably small linewidths obtained experimentally at relatively high fields and low temperatures. We find that satisfactory agreement with the mu SR data for BSCCO in this regime can be obtained through the ansatz that this ''phase'' is characterized by frozen short-range positional correlations reflecting the structure of the liquid just above the melting transition. This proposal is consistent with recent suggestions of a ''pinned liquid'' or ''glassy'' state of pancake Vortices in the presence of pinning disorder. Our results for the high-temperature liquid phase indicate that measurable linewidths may be obtained in this phase as a consequence of density inhomogeneities induced by the pinning disorder. The results presented here comprise a unified, first-principles theoretical treatment of mu SR spectra in highly anisotropic layered superconductors in terms of a controlled set of approximations. [S0163-1829(99)08033-9].

Multiple scales without center manifold reductions for delay differential equations near Hopf bifurcations

We study small perturbations of three linear Delay Differential Equations (DDEs) close to Hopf bifurcation points. In analytical treatments of such equations, many authors recommend a center manifold reduction as a first step. We demonstrate that the method of multiple scales, on simply discarding the infinitely many exponentially decaying components of the complementary solutions obtained at each stage of the approximation, can bypass the explicit center manifold calculation. Analytical approximations obtained for the DDEs studied closely match numerical solutions.

Optimum design of a helicopter rotor for low vibration using aeroelastic analysis and response surface methods

An aeroelastic analysis based on finite elements in space and time is used to model the helicopter rotor in forward flight. The rotor blade is represented as an elastic cantilever beam undergoing flap and lag bending, elastic torsion and axial deformations. The objective of the improved design is to reduce vibratory loads at the rotor hub that are the main source of helicopter vibration. Constraints are imposed on aeroelastic stability, and move limits are imposed on the blade elastic stiffness design variables. Using the aeroelastic analysis, response surface approximations are constructed for the objective function (vibratory hub loads). It is found that second order polynomial response surfaces constructed using the central composite design of the theory of design of experiments adequately represents the aeroelastic model in the vicinity of the baseline design. Optimization results show a reduction in the objective function of about 30 per cent. A key accomplishment of this paper is the decoupling of the analysis problem and the optimization problems using response surface methods, which should encourage the use of optimization methods by the helicopter industry. (C) 2002 Elsevier Science Ltd. All rights reserved.

Performance analysis of the random early detection algorithm

In this article we consider a finite queue with its arrivals controlled by the random early detection algorithm. This is one of the most prominent congestion avoidance schemes in the Internet routers. The aggregate arrival stream from the population of transmission control protocol sources is locally considered stationary renewal or Markov modulated Poisson process with general packet length distribution. We study the exact dynamics of this queue and provide the stability and the rates of convergence to the stationary distribution and obtain the packet loss probability and the waiting time distribution. Then we extend these results to a two traffic class case with each arrival stream renewal. However, computing the performance indices for this system becomes computationally prohibitive. Thus, in the latter half of the article, we approximate the dynamics of the average queue length process asymptotically via an ordinary differential equation. We estimate the error term via a diffusion approximation. We use these results to obtain approximate transient and stationary performance of the system. Finally, we provide some computational examples to show the accuracy of these approximations.

A waveguide problem involving a thick iris in the theory of electromagnetism

The problem of electromagnetic wave propagation in a rectangular waveguide containing a thick iris is considered for its complete solution by reducing it to two suitable integral equations, one of which is of the first kind and the other is of the second kind. These integral equations are solved approximately, by using truncated Fourier series for the unknown functions. The reflection coefficient is computed numerically from the two integral equation approaches, and almost the same numerical results are obtained. This is also depicted graphically against the wave number and compared with thin iris results, which are computed by using complementary formulations coupled with Galerkin approximations. While the reflection coefficient for a thin iris steadily increases with the wave number, for a thick iris it fluctuates and zero reflection occurs. The number of zeros of the reflection coefficient for a thick iris increases with the thickness. Thus a thick iris becomes completely transparent for some discrete wave numbers. This phenomenon may be significant in the modelling of rectangular waveguides.

Minimum error solutions of the Boltzmann equation for shock structure

‘Best’ solutions for the shock-structure problem are obtained by solving the Boltzmann equation for a rigid sphere gas by applying minimum error criteria on the Mott-Smith ansatz. The use of two such criteria minimizing respectively the local and total errors, as well as independent computations of the remaining error, establish the high accuracy of the solutions, although it is shown that the Mott-Smith distribution is not an exact solution of the Boltzmann equation even at infinite Mach number. The minimum local error method is found to be particularly simple and efficient. Adopting the present solutions as the standard of comparison, it is found that the widely used v2x-moment solutions can be as much as a third in error, but that results based on Rosen's method provide good approximations. Finally, it is shown that if the Maxwell mean free path on the hot side of the shock is chosen as the scaling length, the value of the density-slope shock thickness is relatively insensitive to the intermolecular potential. A comparison is made on this basis of present results with experiment, and very satisfactory quantitative agreement is obtained.

Peristaltic pumping of a micropolar fluid in a tube

Peristaltic transport of a micropolar fluid in a circular tube is studied under low Reynolds number and long wavelength approximations. The closed form solutions are obtained. for velocity, microrotation components, as well as the stream function and they contain new additional parameters namely, N the coupling number and m the micropolar parameter. In the case of free pumping (pressure difference Deltap = 0) the difference in pumping flux is observed to be very small for Newtonian and micropolar fluids but in the case of pumping (Deltap > 0) the characteristics are significantly altered for different N and m. It is observed that the peristalsis in micropolar fluids works as a pump against a greater pressure rise compared with a Newtonian fluid. Streamline patterns which depict trapping phenomena are presented for different parameter ranges. The limit on the trapping of the center streamline is obtained. The effects of N and m on friction force for different Deltap are discussed.

Tree structure for efficient data mining using rough sets

In data mining, an important goal is to generate an abstraction of the data. Such an abstraction helps in reducing the space and search time requirements of the overall decision making process. Further, it is important that the abstraction is generated from the data with a small number of disk scans. We propose a novel data structure, pattern count tree (PC-tree), that can be built by scanning the database only once. PC-tree is a minimal size complete representation of the data and it can be used to represent dynamic databases with the help of knowledge that is either static or changing. We show that further compactness can be achieved by constructing the PC-tree on segmented patterns. We exploit the flexibility offered by rough sets to realize a rough PC-tree and use it for efficient and effective rough classification. To be consistent with the sizes of the branches of the PC-tree, we use upper and lower approximations of feature sets in a manner different from the conventional rough set theory. We conducted experiments using the proposed classification scheme on a large-scale hand-written digit data set. We use the experimental results to establish the efficacy of the proposed approach. (C) 2002 Elsevier Science B.V. All rights reserved.

Precoder Designs for MIMO Broadcast Channels with Imperfect CSI

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Efficiently Approximating Query Optimizer Plan Diagrams

Given a parametrized n-dimensional SQL query template and a choice of query optimizer, a plan diagram is a color-coded pictorial enumeration of the execution plan choices of the optimizer over the query parameter space. These diagrams have proved to be a powerful metaphor for the analysis and redesign of modern optimizers, and are gaining currency in diverse industrial and academic institutions. However, their utility is adversely impacted by the impractically large computational overheads incurred when standard brute-force exhaustive approaches are used for producing fine-grained diagrams on high-dimensional query templates. In this paper, we investigate strategies for efficiently producing close approximations to complex plan diagrams. Our techniques are customized to the features available in the optimizer's API, ranging from the generic optimizers that provide only the optimal plan for a query, to those that also support costing of sub-optimal plans and enumerating rank-ordered lists of plans. The techniques collectively feature both random and grid sampling, as well as inference techniques based on nearest-neighbor classifiers, parametric query optimization and plan cost monotonicity. Extensive experimentation with a representative set of TPC-H and TPC-DS-based query templates on industrial-strength optimizers indicates that our techniques are capable of delivering 90% accurate diagrams while incurring less than 15% of the computational overheads of the exhaustive approach. In fact, for full-featured optimizers, we can guarantee zero error with less than 10% overheads. These approximation techniques have been implemented in the publicly available Picasso optimizer visualization tool.

Performance analysis of a fluid queue with random service rate in discrete time

We consider a fluid queue in discrete time with random service rate. Such a queue has been used in several recent studies on wireless networks where the packets can be arbitrarily fragmented. We provide conditions on finiteness of moments of stationary delay, its Laplace-Stieltjes transform and various approximations under heavy traffic. Results are extended to the case where the wireless link can transmit in only a few slots during a frame.

Opportunistic scheduling of wireless links

We consider the problem of scheduling of a wireless channel (server) to several queues. Each queue has its own link (transmission) rate. The link rate of a queue can vary randomly from slot to slot. The queue lengths and channel states of all users are known at the beginning of each slot. We show the existence of an optimal policy that minimizes the long term (discounted) average sum of queue lengths. The optimal policy, in general needs to be computed numerically. Then we identify a greedy (one step optimal) policy, MAX-TRANS which is easy to implement and does not require the channel and traffic statistics. The cost of this policy is close to optimal and better than other well-known policies (when stable) although it is not throughput optimal for asymmetric systems. We (approximately) identify its stability region and obtain approximations for its mean queue lengths and mean delays. We also modify this policy to make it throughput optimal while retaining good performance.

Incremental natural-gradient actor-critic algorithms

We present four new reinforcement learning algorithms based on actor-critic and natural-gradient ideas, and provide their convergence proofs. Actor-critic rein- forcement learning methods are online approximations to policy iteration in which the value-function parameters are estimated using temporal difference learning and the policy parameters are updated by stochastic gradient descent. Methods based on policy gradients in this way are of special interest because of their com- patibility with function approximation methods, which are needed to handle large or infinite state spaces. The use of temporal difference learning in this way is of interest because in many applications it dramatically reduces the variance of the gradient estimates. The use of the natural gradient is of interest because it can produce better conditioned parameterizations and has been shown to further re- duce variance in some cases. Our results extend prior two-timescale convergence results for actor-critic methods by Konda and Tsitsiklis by using temporal differ- ence learning in the actor and by incorporating natural gradients, and they extend prior empirical studies of natural actor-critic methods by Peters, Vijayakumar and Schaal by providing the first convergence proofs and the first fully incremental algorithms.

WCET Estimation for Executables in the Presence of Data Caches

This paper describes techniques to estimate the worst case execution time of executable code on architectures with data caches. The underlying mechanism is Abstract Interpretation, which is used for the dual purposes of tracking address computations and cache behavior. A simultaneous numeric and pointer analysis using an abstraction for discrete sets of values computes safe approximations of access addresses which are then used to predict cache behavior using Must Analysis. A heuristic is also proposed which generates likely worst case estimates. It can be used in soft real time systems and also for reasoning about the tightness of the safe estimate. The analysis methods can handle programs with non-affine access patterns, for which conventional Presburger Arithmetic formulations or Cache Miss Equations do not apply. The precision of the estimates is user-controlled and can be traded off against analysis time. Executables are analyzed directly, which, apart from enhancing precision, renders the method language independent.

Extrinsic Analog Synthesis using Piecewise Linear Current-Mode Circuits

A methodology is presented for the synthesis of analog circuits using piecewise linear (PWL) approximations. The function to be synthesized is divided into PWL segments such that each segment can be realized using elementary MOS current-mode programmable-gain circuits. A number of these elementary current-mode circuits when connected in parallel, it is possible to realize piecewise linear approximation of any arbitrary analog function with in the allowed approximation error bounds. Simulation results show a close agreement between the desired function and the synthesized output. The number of PWL segments used for approximation and hence the circuit area is determined by the required accuracy and the smoothness of the resulting function.