An invariant subspace-based approach to the random eigenvalue problem of systems with clustered spectrum

The repeated or closely spaced eigenvalues and corresponding eigenvectors of a matrix are usually very sensitive to a perturbation of the matrix, which makes capturing the behavior of these eigenpairs very difficult. Similar difficulty is encountered in solving the random eigenvalue problem when a matrix with random elements has a set of clustered eigenvalues in its mean. In addition, the methods to solve the random eigenvalue problem often differ in characterizing the problem, which leads to different interpretations of the solution. Thus, the solutions obtained from different methods become mathematically incomparable. These two issues, the difficulty of solving and the non-unique characterization, are addressed here. A different approach is used where instead of tracking a few individual eigenpairs, the corresponding invariant subspace is tracked. The spectral stochastic finite element method is used for analysis, where the polynomial chaos expansion is used to represent the random eigenvalues and eigenvectors. However, the main concept of tracking the invariant subspace remains mostly independent of any such representation. The approach is successfully implemented in response prediction of a system with repeated natural frequencies. It is found that tracking only an invariant subspace could be sufficient to build a modal-based reduced-order model of the system. Copyright (C) 2012 John Wiley & Sons, Ltd.

Pressure-sensitive paint on a truncated cone in hypersonic flow at incidences

The flow over a truncated cone is a classical and fundamental problem for aerodynamic research due to its three-dimensional and complicated characteristics. The flow is made more complex when examining high angles of incidence. Recently these types of flows have drawn more attention for the purposes of drag reduction in supersonic/hypersonic flows. In the present study the flow over a truncated cone at various incidences was experimentally investigated in a Mach 5 flow with a unit Reynolds number of 13.5�10 6m -1. The cone semi-apex angle is 15° and the truncation ratio (truncated length/cone length) is 0.5. The incidence of the model varied from -12° to 12° with 3° intervals relative to the freestream direction. The external flow around the truncated cone was visualised by colour Schlieren photography, while the surface flow pattern was revealed using the oil flow method. The surface pressure distribution was measured using the anodized aluminium pressure-sensitive paint (AA-PSP) technique. Both top and sideviews of the pressure distribution on the model surface were acquired at various incidences. AA-PSP showed high pressure sensitivity and captured the complicated flow structures which correlated well with the colour Schlieren and oil flow visualisation results. © 2012 Elsevier Inc.

Catalysis of tRNA Aminoacylation: Single Turnover to Steady-State Kinetics of tRNA Synthetases

Aminoacyl-tRNA synthetases (aaRS) catalyze the bimolecular association reaction between amino acid and tRNA by specifically and unerringly choosing the cognate amino acid and tRNA. There are two classes of such synthetases that perform tRNA-aminoacylation reaction. Interestingly, these two classes of aminoacyl-tRNA synthetases differ not only in their structures but they also exhibit remarkably distinct kinetics under pre-steady-state condition. The class I synthetases show initial burst of product formation followed by a slower steady-state rate. This has been argued to represent the influence of slow product release. In contrast, there is no burst in the case of class H enzymes. The tight binding of product with enzyme for class I enzymes is correlated with the enhancement of rate in presence of elongation factor. EF-TU. In spite of extensive experimental studies, there is no detailed theoretical analysis that can provide a quantitative understanding of this important problem. In this article, we present a theoretical investigation of enzyme kinetics for both classes of aminoacyl-tRNA synthetases. We present an augmented kinetic scheme and then employ the methods of time-dependent probability statistics to obtain expressions for the first passage time distribution that gives both the time-dependent and the steady-state rates. The present study quantitatively explains all the above experimental observations. We propose an alternative path way in the case of class II enzymes showing the tRNA-dependent amino acid activation and the discrepancy between the single-turnover and steady-state rate.

Complexity of distance paired-domination problem in graphs

Suppose G = (V, E) is a simple graph and k is a fixed positive integer. A subset D subset of V is a distance k-dominating set of G if for every u is an element of V. there exists a vertex v is an element of D such that d(G)(u, v) <= k, where d(G)(u, v) is the distance between u and v in G. A set D subset of V is a distance k-paired-dominating set of G if D is a distance k-dominating set and the induced subgraph GD] contains a perfect matching. Given a graph G = (V, E) and a fixed integer k > 0, the MIN DISTANCE k-PAIRED-DOM SET problem is to find a minimum cardinality distance k-paired-dominating set of G. In this paper, we show that the decision version of MIN DISTANCE k-PAIRED-DOM SET iS NP-complete for undirected path graphs. This strengthens the complexity of decision version Of MIN DISTANCE k-PAIRED-DOM SET problem in chordal graphs. We show that for a given graph G, unless NP subset of DTIME (n(0)((log) (log) (n)) MIN DISTANCE k-PAIRED-Dom SET problem cannot be approximated within a factor of (1 -epsilon ) In n for any epsilon > 0, where n is the number of vertices in G. We also show that MIN DISTANCE k-PAIRED-DOM SET problem is APX-complete for graphs with degree bounded by 3. On the positive side, we present a linear time algorithm to compute the minimum cardinality of a distance k-paired-dominating set of a strongly chordal graph G if a strong elimination ordering of G is provided. We show that for a given graph G, MIN DISTANCE k-PAIRED-DOM SET problem can be approximated with an approximation factor of 1 + In 2 + k . In(Delta(G)), where Delta(G) denotes the maximum degree of G. (C) 2012 Elsevier B.V All rights reserved.

Interaction Signatures Stabilizing the NAD(P)-Binding Rossmann Fold: A Structure Network Approach

The fidelity of the folding pathways being encoded in the amino acid sequence is met with challenge in instances where proteins with no sequence homology, performing different functions and no apparent evolutionary linkage, adopt a similar fold. The problem stated otherwise is that a limited fold space is available to a repertoire of diverse sequences. The key question is what factors lead to the formation of a fold from diverse sequences. Here, with the NAD(P)-binding Rossmann fold domains as a case study and using the concepts of network theory, we have unveiled the consensus structural features that drive the formation of this fold. We have proposed a graph theoretic formalism to capture the structural details in terms of the conserved atomic interactions in global milieu, and hence extract the essential topological features from diverse sequences. A unified mathematical representation of the different structures together with a judicious concoction of several network parameters enabled us to probe into the structural features driving the adoption of the NAD(P)-binding Rossmann fold. The atomic interactions at key positions seem to be better conserved in proteins, as compared to the residues participating in these interactions. We propose a ``spatial motif'' and several ``fold specific hot spots'' that form the signature structural blueprints of the NAD(P)-binding Rossmann fold domain. Excellent agreement of our data with previous experimental and theoretical studies validates the robustness and validity of the approach. Additionally, comparison of our results with statistical coupling analysis (SCA) provides further support. The methodology proposed here is general and can be applied to similar problems of interest.

A note on the inverse mode shape problem for bars, beams, and plates

Motivated by the idea of designing a structure for a desired mode shape, intended towards applications such as resonant sensors, actuators and vibration confinement, we present the inverse mode shape problem for bars, beams and plates in this work. The objective is to determine the cross-sectional profile of these structures, given a mode shape, boundary condition and the mass. The contribution of this article is twofold: (i) A numerical method to solve this problem when a valid mode shape is provided in the finite element framework for both linear and nonlinear versions of the problem. (ii) An analytical result to prove the uniqueness and existence of the solution in the case of bars. This article also highlights a very important question of the validity of a mode shape for any structure of given boundary conditions.

Active Sequential Hypothesis Testing with Application to a Visual Search Problem

We consider a visual search problem studied by Sripati and Olson where the objective is to identify an oddball image embedded among multiple distractor images as quickly as possible. We model this visual search task as an active sequential hypothesis testing problem (ASHT problem). Chernoff in 1959 proposed a policy in which the expected delay to decision is asymptotically optimal. The asymptotics is under vanishing error probabilities. We first prove a stronger property on the moments of the delay until a decision, under the same asymptotics. Applying the result to the visual search problem, we then propose a ``neuronal metric'' on the measured neuronal responses that captures the discriminability between images. From empirical study we obtain a remarkable correlation (r = 0.90) between the proposed neuronal metric and speed of discrimination between the images. Although this correlation is lower than with the L-1 metric used by Sripati and Olson, this metric has the advantage of being firmly grounded in formal decision theory.

On the Erdos-Szekeres n-interior point problem

The n-interior point variant of the Erdos-Szekeres problem is to show the following: For any n, n-1, every point set in the plane with sufficient number of interior points contains a convex polygon containing exactly n-interior points. This has been proved only for n-3. In this paper, we prove it for pointsets having atmost logarithmic number of convex layers. We also show that any pointset containing atleast n interior points, there exists a 2-convex polygon that contains exactly n-interior points.

Optimal control problem for the time-dependent Kirchhoff-Love plate in a domain with rough boundary

In this paper, we study the asymptotic behavior of an optimal control problem for the time-dependent Kirchhoff-Love plate whose middle surface has a very rough boundary. We identify the limit problem which is an optimal control problem for the limit equation with a different cost functional.

Linearization of Drucker-Prager yield criterion for axisymmetric problems: implementation in lower-bound limit analysis

The linearization of the Drucker-Prager yield criterion associated with an axisymmetric problem has been achieved by simulating a sphere with the truncated icosahedron with 32 faces and 60 vertices. On this basis, a numerical formulation has been proposed for solving an axisymmetric stability problem with the usage of the lower-bound limit analysis, finite elements, and linear optimization. To compare the results, the linearization of the Mohr-Coulomb yield criterion, by replacing the three cones with interior polyhedron, as proposed earlier by Pastor and Turgeman for an axisymmetric problem, has also been implemented. The two formulations have been applied for determining the collapse loads for a circular footing resting on a cohesive-friction material with nonzero unit weight. The computational results are found to be quite convincing. (C) 2013 American Society of Civil Engineers.

A multichannel sampling method for 2-D finite-rate-of-innovation signals

We address the problem of sampling and reconstruction of two-dimensional (2-D) finite-rate-of-innovation (FRI) signals. We propose a three-channel sampling method for efficiently solving the problem. We consider the sampling of a stream of 2-D Dirac impulses and a sum of 2-D unit-step functions. We propose a 2-D causal exponential function as the sampling kernel. By causality in 2-D, we mean that the function has its support restricted to the first quadrant. The advantage of using a multichannel sampling method with causal exponential sampling kernel is that standard annihilating filter or root-finding algorithms are not required. Further, the proposed method has inexpensive hardware implementation and is numerically stable as the number of Dirac impulses increases.

Exact internal controllability for a hyperbolic problem in a domain with highly oscillating boundary

In this paper, by using the Hilbert Uniqueness Method (HUM), we study the exact controllability problem described by the wave equation in a three-dimensional horizontal domain bounded at the bottom by a smooth wall and at the top by a rough wall. The latter is assumed to consist in a plane wall covered with periodically distributed asperities whose size depends on a small parameter epsilon > 0, and with a fixed height. Our aim is to obtain the exact controllability for the homogenized equation. In the process, we study the asymptotic analysis of wave equation in two setups, namely solution by standard weak formulation and solution by transposition method.

Analysis of Bandwidth-Unit-Vector-Distortion Tradeoff in PLL During Abnormal Grid Conditions

Phase-locked loops (PLLs) are necessary in applications which require grid synchronization. Presence of unbalance or harmonics in the grid voltage creates errors in the estimated frequency and angle of a PLL. The error in estimated angle has the effect of distorting the unit vectors generated by the PLL. In this paper, analytical expressions are derived which determine the error in the phase angle estimated by a PLL when there is unbalance and harmonics in the grid voltage. By using the derived expressions, the total harmonic distortion (THD) and the fundamental phase error of the unit vectors can be determined for a given PLL topology and a given level of unbalance and distortion in the grid voltage. The accuracy of the results obtained from the analytical expressions is validated with the simulation and experimental results for synchronous reference frame PLL (SRF-PLL). Based on these expressions, a new tuning method for the SRF-PLL is proposed which quantifies the tradeoff between the unit vector THD and the bandwidth of the SRF-PLL. Using this method, the exact value of the bandwidth of the SRF-PLL can be obtained for a given worst case grid voltage unbalance and distortion to have an acceptable level of unit vector THD. The tuning method for SRF-PLL is also validated experimentally.

Inference for the Component and System Lifetime Distribution of a k-unit Parallel System Based on System Data

In this paper, we consider the inference for the component and system lifetime distribution of a k-unit parallel system with independent components based on system data. The components are assumed to have identical Weibull distribution. We obtain the maximum likelihood estimates of the unknown parameters based on system data. The Fisher information matrix has been derived. We propose -expectation tolerance interval and -content -level tolerance interval for the life distribution of the system. Performance of the estimators and tolerance intervals is investigated via simulation study. A simulated dataset is analyzed for illustration.

Application of the random eigenvalue problem in forced response analysis of a linear stochastic structure

The random eigenvalue problem arises in frequency and mode shape determination for a linear system with uncertainties in structural properties. Among several methods of characterizing this random eigenvalue problem, one computationally fast method that gives good accuracy is a weak formulation using polynomial chaos expansion (PCE). In this method, the eigenvalues and eigenvectors are expanded in PCE, and the residual is minimized by a Galerkin projection. The goals of the current work are (i) to implement this PCE-characterized random eigenvalue problem in the dynamic response calculation under random loading and (ii) to explore the computational advantages and challenges. In the proposed method, the response quantities are also expressed in PCE followed by a Galerkin projection. A numerical comparison with a perturbation method and the Monte Carlo simulation shows that when the loading has a random amplitude but deterministic frequency content, the proposed method gives more accurate results than a first-order perturbation method and a comparable accuracy as the Monte Carlo simulation in a lower computational time. However, as the frequency content of the loading becomes random, or for general random process loadings, the method loses its accuracy and computational efficiency. Issues in implementation, limitations, and further challenges are also addressed.