An Optimizing Code Generator for a Class of Lattice-Boltzmann Computations

The Lattice-Boltzmann method (LBM), a promising new particle-based simulation technique for complex and multiscale fluid flows, has seen tremendous adoption in recent years in computational fluid dynamics. Even with a state-of-the-art LBM solver such as Palabos, a user has to still manually write the program using library-supplied primitives. We propose an automated code generator for a class of LBM computations with the objective to achieve high performance on modern architectures. Few studies have looked at time tiling for LBM codes. We exploit a key similarity between stencils and LBM to enable polyhedral optimizations and in turn time tiling for LBM. We also characterize the performance of LBM with the Roofline performance model. Experimental results for standard LBM simulations like Lid Driven Cavity, Flow Past Cylinder, and Poiseuille Flow show that our scheme consistently outperforms Palabos-on average by up to 3x while running on 16 cores of an Intel Xeon (Sandybridge). We also obtain an improvement of 2.47x on the SPEC LBM benchmark.

Broadcast Control Mechanism for Positional Consensus in Multiagent Systems

In this paper, a strategy for controlling a group of agents to achieve positional consensus is presented. The problem is constrained by the requirement that every agent must be given the same control input through a broadcast communication mechanism. Although the control command is computed using state information in a global framework, the control input is implemented by the agents in a local coordinate frame. We propose a novel linear programming (LP) formulation that is computationally less intensive than earlier proposed methods. Moreover, a random perturbation input in the control command that helps the agents to come close to each other even for a large number of agents, which was not possible with an existing strategy in the literature, is introduced. The method is extended to achieve positional consensus at a prespecified location. The effectiveness of the approach is illustrated through simulation results. A comparison between the LP approach and the existing second-order cone programming-based approach is also presented. The algorithm was successfully implemented on a robotic platform with three robots.

Energy Harvesting WSNs for Accurately Estimating the Maximum Sensor Reading: Trade-Offs and Optimal Design

Computing the maximum of sensor readings arises in several environmental, health, and industrial monitoring applications of wireless sensor networks (WSNs). We characterize the several novel design trade-offs that arise when green energy harvesting (EH) WSNs, which promise perpetual lifetimes, are deployed for this purpose. The nodes harvest renewable energy from the environment for communicating their readings to a fusion node, which then periodically estimates the maximum. For a randomized transmission schedule in which a pre-specified number of randomly selected nodes transmit in a sensor data collection round, we analyze the mean absolute error (MAE), which is defined as the mean of the absolute difference between the maximum and that estimated by the fusion node in each round. We optimize the transmit power and the number of scheduled nodes to minimize the MAE, both when the nodes have channel state information (CSI) and when they do not. Our results highlight how the optimal system operation depends on the EH rate, availability and cost of acquiring CSI, quantization, and size of the scheduled subset. Our analysis applies to a general class of sensor reading and EH random processes.

Investigation of schemes for incorporating generator Q limits in the fast decoupled load flow method

Fast Decoupled Load Flow (FDLF) is a very popular and widely used power flow analysis method because of its simplicity and efficiency. Even though the basic FDLF algorithm is well investigated, the same is not true in the case of additional schemes/modifications required to obtain adjusted load flow solutions using the FDLF method. Handling generator Q limits is one such important feature needed in any practical load flow method. This paper presents a comprehensive investigation of two classes of schemes intended to handle this aspect i.e. the bus type switching scheme and the sensitivity scheme. We propose two new sensitivity based schemes and assess their performance in comparison with the existing schemes. In addition, a new scheme to avoid the possibility of anomalous solutions encountered while using the conventional schemes is also proposed and evaluated. Results from extensive simulation studies are provided to highlight the strengths and weaknesses of these existing and proposed schemes, especially from the point of view of reliability.

Identification of dominant modes in random dynamical and aeroelastic systems

Identification of dominant modes is an important step in studying linearly vibrating systems, including flow-induced vibrations. In the presence of uncertainty, when some of the system parameters and the external excitation are modeled as random quantities, this step becomes more difficult. This work is aimed at giving a systematic treatment to this end. The ability to capture the time averaged kinetic energy is chosen as the primary criterion for selection of modes. Accordingly, a methodology is proposed based on the overlap of probability density functions (pdf) of the natural and excitation frequencies, proximity of the natural frequencies of the mean or baseline system, modal participation factor, and stochastic variation of mode shapes in terms of the modes of the baseline system - termed here as statistical modal overlapping. The probabilistic descriptors of the natural frequencies and mode shapes are found by solving a random eigenvalue problem. Three distinct vibration scenarios are considered: (i) undamped arid damped free vibrations of a bladed disk assembly, (ii) forced vibration of a building, and (iii) flutter of a bridge model. Through numerical studies, it is observed that the proposed methodology gives an accurate selection of modes. (C) 2015 Elsevier Ltd. All rights reserved.

A Zero-Crossing Rate Property of Power Complementary Analysis Filterbank Outputs

We establish zero-crossing rate (ZCR) relations between the input and the subbands of a maximally decimated M-channel power complementary analysis filterbank when the input is a stationary Gaussian process. The ZCR at lag is defined as the number of sign changes between the samples of a sequence and its 1-sample shifted version, normalized by the sequence length. We derive the relationship between the ZCR of the Gaussian process at lags that are integer multiples of Al and the subband ZCRs. Based on this result, we propose a robust iterative autocorrelation estimator for a signal consisting of a sum of sinusoids of fixed amplitudes and uniformly distributed random phases. Simulation results show that the performance of the proposed estimator is better than the sample autocorrelation over the SNR range of -6 to 15 dB. Validation on a segment of a trumpet signal showed similar performance gains.

A hybrid method for stochastic response analysis of a vibrating structure

Response analysis of a linear structure with uncertainties in both structural parameters and external excitation is considered here. When such an analysis is carried out using the spectral stochastic finite element method (SSFEM), often the computational cost tends to be prohibitive due to the rapid growth of the number of spectral bases with the number of random variables and the order of expansion. For instance, if the excitation contains a random frequency, or if it is a general random process, then a good approximation of these excitations using polynomial chaos expansion (PCE) involves a large number of terms, which leads to very high cost. To address this issue of high computational cost, a hybrid method is proposed in this work. In this method, first the random eigenvalue problem is solved using the weak formulation of SSFEM, which involves solving a system of deterministic nonlinear algebraic equations to estimate the PCE coefficients of the random eigenvalues and eigenvectors. Then the response is estimated using a Monte Carlo (MC) simulation, where the modal bases are sampled from the PCE of the random eigenvectors estimated in the previous step, followed by a numerical time integration. It is observed through numerical studies that this proposed method successfully reduces the computational burden compared with either a pure SSFEM of a pure MC simulation and more accurate than a perturbation method. The computational gain improves as the problem size in terms of degrees of freedom grows. It also improves as the timespan of interest reduces.

Asymptotic Bounds on the Power-Delay Tradeoff for Fading Point-to-Point Links From Geometric Bounds on the Stationary Distribution of the Queue Length

The optimal power-delay tradeoff is studied for a time-slotted independently and identically distributed fading point-to-point link, with perfect channel state information at both transmitter and receiver, and with random packet arrivals to the transmitter queue. It is assumed that the transmitter can control the number of packets served by controlling the transmit power in the slot. The optimal tradeoff between average power and average delay is analyzed for stationary and monotone transmitter policies. For such policies, an asymptotic lower bound on the minimum average delay of the packets is obtained, when average transmitter power approaches the minimum average power required for transmitter queue stability. The asymptotic lower bound on the minimum average delay is obtained from geometric upper bounds on the stationary distribution of the queue length. This approach, which uses geometric upper bounds, also leads to an intuitive explanation of the asymptotic behavior of average delay. The asymptotic lower bounds, along with previously known asymptotic upper bounds, are used to identify three new cases where the order of the asymptotic behavior differs from that obtained from a previously considered approximate model, in which the transmit power is a strictly convex function of real valued service batch size for every fade state.

Handling large variations in mechanics: Some applications

There is a need to use probability distributions with power-law decaying tails to describe the large variations exhibited by some of the physical phenomena. The Weierstrass Random Walk (WRW) shows promise for modeling such phenomena. The theory of anomalous diffusion is now well established. It has found number of applications in Physics, Chemistry and Biology. However, its applications are limited in structural mechanics in general, and structural engineering in particular. The aim of this paper is to present some mathematical preliminaries related to WRW that would help in possible applications. In the limiting case, it represents a diffusion process whose evolution is governed by a fractional partial differential equation. Three applications of superdiffusion processes in mechanics, illustrating their effectiveness in handling large variations, are presented.

Onset of plane layer magnetoconvection at low Ekman number

We study the onset of magnetoconvection between two infinite horizontal planes subject to a vertical magnetic field aligned with background rotation. In order to gain insight into the convection taking place in the Earth's tangent cylinder, we target regimes of asymptotically strong rotation. The critical Rayleigh number Ra-c and critical wavenumber a(c) are computed numerically by solving the linear stability problem in a systematic way, with either stress-free or no-slip kinematic boundary conditions. A parametric study is conducted, varying the Ekman number E (ratio of viscous to Coriolis forces) and the Elsasser number. (ratio of the Lorentz force to the Coriolis force). E is varied from 10(-9) to 10(-2) and. from 10(-3) to 1. For a wide range of thermal and magnetic Prandtl numbers, our results verify and confirm previous experimental and theoretical results showing the existence of two distinct unstable modes at low values of E-one being controlled by the magnetic field, the other being controlled by viscosity (often called the viscous mode). It is shown that oscillatory onset does not occur in the range of parameters we are interested in. Asymptotic scalings for the onset of these modes are numerically confirmed and their domain of validity is precisely quantified. We show that with no-slip boundary conditions, the asymptotic behavior is reached for E < 10(-6) and establish a map in the (E, Lambda) plane. We distinguish regions where convection sets in either through the magnetic mode or through the viscous mode. Our analysis gives the regime in which the transition between magnetic and viscous modes may be observed. We also show that within the asymptotic regime, the role played by the kinematic boundary conditions is minimal. (C) 2015 AIP Publishing LLC.

Length scales in glass-forming liquids and related systems: a review

The central problem in the study of glass-forming liquids and other glassy systems is the understanding of the complex structural relaxation and rapid growth of relaxation times seen on approaching the glass transition. A central conceptual question is whether one can identify one or more growing length scale(s) associated with this behavior. Given the diversity of molecular glass-formers and a vast body of experimental, computational and theoretical work addressing glassy behavior, a number of ideas and observations pertaining to growing length scales have been presented over the past few decades, but there is as yet no consensus view on this question. In this review, we will summarize the salient results and the state of our understanding of length scales associated with dynamical slow down. After a review of slow dynamics and the glass transition, pertinent theories of the glass transition will be summarized and a survey of ideas relating to length scales in glassy systems will be presented. A number of studies have focused on the emergence of preferred packing arrangements and discussed their role in glassy dynamics. More recently, a central object of attention has been the study of spatially correlated, heterogeneous dynamics and the associated length scale, studied in computer simulations and theoretical analysis such as inhomogeneous mode coupling theory. A number of static length scales have been proposed and studied recently, such as the mosaic length scale discussed in the random first-order transition theory and the related point-to-set correlation length. We will discuss these, elaborating on key results, along with a critical appraisal of the state of the art. Finally we will discuss length scales in driven soft matter, granular fluids and amorphous solids, and give a brief description of length scales in aging systems. Possible relations of these length scales with those in glass-forming liquids will be discussed.

Upper bound on cubicity in terms of boxicity for graphs of low chromatic number

The boxicity (respectively cubicity) of a graph G is the least integer k such that G can be represented as an intersection graph of axis-parallel k-dimensional boxes (respectively k-dimensional unit cubes) and is denoted by box(G) (respectively cub(G)). It was shown by Adiga and Chandran (2010) that for any graph G, cub(G) <= box(G) log(2) alpha(G], where alpha(G) is the maximum size of an independent set in G. In this note we show that cub(G) <= 2 log(2) X (G)] box(G) + X (G) log(2) alpha(G)], where x (G) is the chromatic number of G. This result can provide a much better upper bound than that of Adiga and Chandran for graph classes with bounded chromatic number. For example, for bipartite graphs we obtain cub(G) <= 2(box(G) + log(2) alpha(G)] Moreover, we show that for every positive integer k, there exist graphs with chromatic number k such that for every epsilon > 0, the value given by our upper bound is at most (1 + epsilon) times their cubicity. Thus, our upper bound is almost tight. (c) 2015 Elsevier B.V. All rights reserved.

Determinantal point processes in the plane from products of random matrices

We show that the density of eigenvalues for three classes of random matrix ensembles is determinantal. First we derive the density of eigenvalues of product of k independent n x n matrices with i.i.d. complex Gaussian entries with a few of matrices being inverted. In second example we calculate the same for (compatible) product of rectangular matrices with i.i.d. Gaussian entries and in last example we calculate for product of independent truncated unitary random matrices. We derive exact expressions for limiting expected empirical spectral distributions of above mentioned ensembles.

SPEECH ENHANCEMENT USING DISCRIMINATIVE RANDOM FIELDS

Speech enhancement in stationary noise is addressed using the ideal channel selection framework. In order to estimate the binary mask, we propose to classify each time-frequency (T-F) bin of the noisy signal as speech or noise using Discriminative Random Fields (DRF). The DRF function contains two terms - an enhancement function and a smoothing term. On each T-F bin, we propose to use an enhancement function based on likelihood ratio test for speech presence, while Ising model is used as smoothing function for spectro-temporal continuity in the estimated binary mask. The effect of the smoothing function over successive iterations is found to reduce musical noise as opposed to using only enhancement function. The binary mask is inferred from the noisy signal using Iterated Conditional Modes (ICM) algorithm. Sentences from NOIZEUS corpus are evaluated from 0 dB to 15 dB Signal to Noise Ratio (SNR) in 4 kinds of additive noise settings: additive white Gaussian noise, car noise, street noise and pink noise. The reconstructed speech using the proposed technique is evaluated in terms of average segmental SNR, Perceptual Evaluation of Speech Quality (PESQ) and Mean opinion Score (MOS).

Percolative switching in transition metal dichalcogenide field-effect transistors at room temperature

We have addressed the microscopic transport mechanism at the switching or `on-off' transition in transition metal dichalcogenide (TMDC) field-effect transistors (FETs), which has been a controversial topic in TMDC electronics, especially at room temperature. With simultaneous measurement of channel conductivity and its slow time-dependent fluctuation (or noise) in ultrathin WSe2 and MoS2 FETs on insulating SiO2 substrates where noise arises from McWhorter-type carrier number fluctuations, we establish that the switching in conventional backgated TMDC FETs is a classical percolation transition in a medium of inhomogeneous carrier density distribution. From the experimentally observed exponents in the scaling of noise magnitude with conductivity, we observe unambiguous signatures of percolation in a random resistor network, particularly, in WSe2 FETs close to switching, which crosses over to continuum percolation at a higher doping level. We demonstrate a powerful experimental probe to the microscopic nature of near-threshold electrical transport in TMDC FETs, irrespective of the material detail, device geometry, or carrier mobility, which can be extended to other classes of 2D material-based devices as well.