An appendix to the paper "approximation of the perturbation equations of a quasi-linear hyperbolic system in the neighborhood of a bicharacteristic"

The theory of Varley and Cumberbatch [l] giving the intensity of discontinuities in the normal derivatives of the dependent variables at a wave front can be deduced from the more general results of Prasad which give the complete history of a disturbance not only at the wave front but also within a short distance behind the wave front. In what follows we omit the index M in Eq. (2.25) of Prasad [2].

Formation of linear plasmid multimers promoted by the phage lambda Red-system in lon mutants of Escherichia coli

We report here the formation of plasmid linear multimers promoted by the Red-system of phage lambda using a multicopy plasmid comprised of lambda red alpha and red beta genes, under the control of the lambda cI857 repressor. Our observations have revealed that the multimerization of plasmid DNA is dependent on the red beta and recA genes, suggesting a concerted role for these functions in the formation of plasmid multimers. The formation of multimers occurred in a recBCD+ sbcB+ xthA+ lon genetic background at a higher frequency than in the isogenic lon+ host cells. The multimers comprised tandem repeats of monomer plasmid DNA. Treatment of purified plasmid DNA with exonuclease III revealed the presence of free double-chain ends in the molecules. Determination of the size of multimeric DNA, by pulse field gel electrophoresis, revealed that the bulk of the DNA was in the range 50-240 kb, representing approximately 5-24 unit lengths of monomeric plasmid DNA. We provide a conceptual framework for Red-system-promoted formation and enhanced accumulation of plasmid linear multimers in lon mutants of E. coli.

A Kalman filter based strategy for linear structural system identification based on multiple static and dynamic test data

The problem of identification of stiffness, mass and damping properties of linear structural systems, based on multiple sets of measurement data originating from static and dynamic tests is considered. A strategy, within the framework of Kalman filter based dynamic state estimation, is proposed to tackle this problem. The static tests consists of measurement of response of the structure to slowly moving loads, and to static loads whose magnitude are varied incrementally; the dynamic tests involve measurement of a few elements of the frequency response function (FRF) matrix. These measurements are taken to be contaminated by additive Gaussian noise. An artificial independent variable τ, that simultaneously parameterizes the point of application of the moving load, the magnitude of the incrementally varied static load and the driving frequency in the FRFs, is introduced. The state vector is taken to consist of system parameters to be identified. The fact that these parameters are independent of the variable τ is taken to constitute the set of ‘process’ equations. The measurement equations are derived based on the mechanics of the problem and, quantities, such as displacements and/or strains, are taken to be measured. A recursive algorithm that employs a linearization strategy based on Neumann’s expansion of structural static and dynamic stiffness matrices, and, which provides posterior estimates of the mean and covariance of the unknown system parameters, is developed. The satisfactory performance of the proposed approach is illustrated by considering the problem of the identification of the dynamic properties of an inhomogeneous beam and the axial rigidities of members of a truss structure.

Linear time algorithms for Abelian group isomorphism and related problems

We consider the problem of determining if two finite groups are isomorphic. The groups are assumed to be represented by their multiplication tables. We present an O(n) algorithm that determines if two Abelian groups with n elements each are isomorphic. This improves upon the previous upper bound of O(n log n) [Narayan Vikas, An O(n) algorithm for Abelian p-group isomorphism and an O(n log n) algorithm for Abelian group isomorphism, J. Comput. System Sci. 53 (1996) 1-9] known for this problem. We solve a more general problem of computing the orders of all the elements of any group (not necessarily Abelian) of size n in O(n) time. Our algorithm for isomorphism testing of Abelian groups follows from this result. We use the property that our order finding algorithm works for any group to design a simple O(n) algorithm for testing whether a group of size n, described by its multiplication table, is nilpotent. We also give an O(n) algorithm for determining if a group of size n, described by its multiplication table, is Abelian. (C) 2007 Elsevier Inc. All rights reserved.

Effect of static deflection on natural frequency of non-linear spring mass system by direct linearization method

An exact expression for the frequency of a non-linear cubic spring mass system is obtained considering the effect of static deflection. An alternative expression for the approximate frequency is also obtained by the direct linearization procedure; it is shown that this is very accurate as compared with the exact method. This approximate frequency equation is used to explain a “dual behaviour” of the frequency amplitude curves.

Response spectrum of non-linear spring mass system subjected to transient disturbances

The transient response spectrum of a cubic spring mass system subjected to a step function input is obtained. An approximate method is adopted where non-linear restoring force characteristic is replaced by two linear segments, so that the mean square error between them is a minimum. The effect of viscous damping on the peak response is also discussed for various values of the damping constant and the non-linearity restoring force parameter.

Self-regularized pseudo time-marching schemes for structural system identification with static measurements

We explore the application of pseudo time marching schemes, involving either deterministic integration or stochastic filtering, to solve the inverse problem of parameter identification of large dimensional structural systems from partial and noisy measurements of strictly static response. Solutions of such non-linear inverse problems could provide useful local stiffness variations and do not have to confront modeling uncertainties in damping, an important, yet inadequately understood, aspect in dynamic system identification problems. The usual method of least-square solution is through a regularized Gauss-Newton method (GNM) whose results are known to be sensitively dependent on the regularization parameter and data noise intensity. Finite time,recursive integration of the pseudo-dynamical GNM (PD-GNM) update equation addresses the major numerical difficulty associated with the near-zero singular values of the linearized operator and gives results that are not sensitive to the time step of integration. Therefore, we also propose a pseudo-dynamic stochastic filtering approach for the same problem using a parsimonious representation of states and specifically solve the linearized filtering equations through a pseudo-dynamic ensemble Kalman filter (PD-EnKF). For multiple sets of measurements involving various load cases, we expedite the speed of thePD-EnKF by proposing an inner iteration within every time step. Results using the pseudo-dynamic strategy obtained through PD-EnKF and recursive integration are compared with those from the conventional GNM, which prove that the PD-EnKF is the best performer showing little sensitivity to process noise covariance and yielding reconstructions with less artifacts even when the ensemble size is small.

Self-regularized pseudo time-marching schemes for structural system identification with static measurements

We explore the application of pseudo time marching schemes, involving either deterministic integration or stochastic filtering, to solve the inverse problem of parameter identification of large dimensional structural systems from partial and noisy measurements of strictly static response. Solutions of such non-linear inverse problems could provide useful local stiffness variations and do not have to confront modeling uncertainties in damping, an important, yet inadequately understood, aspect in dynamic system identification problems. The usual method of least-square solution is through a regularized Gauss-Newton method (GNM) whose results are known to be sensitively dependent on the regularization parameter and data noise intensity. Finite time, recursive integration of the pseudo-dynamical GNM (PD-GNM) update equation addresses the major numerical difficulty associated with the near-zero singular values of the linearized operator and gives results that are not sensitive to the time step of integration. Therefore, we also propose a pseudo-dynamic stochastic filtering approach for the same problem using a parsimonious representation of states and specifically solve the linearized filtering equations through apseudo-dynamic ensemble Kalman filter (PD-EnKF). For multiple sets ofmeasurements involving various load cases, we expedite the speed of the PD-EnKF by proposing an inner iteration within every time step. Results using the pseudo-dynamic strategy obtained through PD-EnKF and recursive integration are compared with those from the conventional GNM, which prove that the PD-EnKF is the best performer showing little sensitivity to process noise covariance and yielding reconstructions with less artifacts even when the ensemble size is small. Copyright (C) 2009 John Wiley & Sons, Ltd.

Points-to Analysis as a System of Linear Equations

We propose a novel formulation of the points-to analysis as a system of linear equations. With this, the efficiency of the points-to analysis can be significantly improved by leveraging the advances in solution procedures for solving the systems of linear equations. However, such a formulation is non-trivial and becomes challenging due to various facts, namely, multiple pointer indirections, address-of operators and multiple assignments to the same variable. Further, the problem is exacerbated by the need to keep the transformed equations linear. Despite this, we successfully model all the pointer operations. We propose a novel inclusion-based context-sensitive points-to analysis algorithm based on prime factorization, which can model all the pointer operations. Experimental evaluation on SPEC 2000 benchmarks and two large open source programs reveals that our approach is competitive to the state-of-the-art algorithms. With an average memory requirement of mere 21MB, our context-sensitive points-to analysis algorithm analyzes each benchmark in 55 seconds on an average.

Analysis of a linear one-dimensional active noise control system by means of block diagrams and transfer functions

In arriving at the ideal filter transfer function for an active noise control system in a duct, the effect of the auxiliary sources (generally loudspeakers) on the waves generated by the primary source has invariably been neglected in the existing literature, implying a rigid wall or infinite impedance. The present paper presents a fairly general analysis of a linear one-dimensional noise control system by means of block diagrams and transfer functions. It takes into account the passive as well as active role of a terminal primary source, wall-mounted auxiliary source, open duct radiation impedance, and the effects of mean flow and damping. It is proved that the pressure generated by a source against a load impedance can be looked upon as a sum of two pressure waves, one generated by the source against an anechoic termination and the other by reflecting the rearward wave (incident on the source) off the passive source impedance. Application of this concept is illustrated for both the types of sources. A concise closed-form expression for the ideal filter transfer function is thus derived and discussed. Finally, the dynamics of an adaptive noise control system is discussed briefly, relating its standing-wave variables and transfer functions with those of the progressive-wave model presented here.

Decentralized linear quadratic power system stabilizers for multi-machine power systems

Linear quadratic stabilizers are well-known for their superior control capabilities when compared to the conventional lead-lag power system stabilizers. However, they have not seen much of practical importance as the state variables are generally not measurable; especially the generator rotor angle measurement is not available in most of the power plants. Full state feedback controllers require feedback of other machine states in a multi-machine power system and necessitate block diagonal structure constraints for decentralized implementation. This paper investigates the design of Linear Quadratic Power System Stabilizers using a recently proposed modified Heffron-Phillip's model. This model is derived by taking the secondary bus voltage of the step-up transformer as reference instead of the infinite bus. The state variables of this model can be obtained by local measurements. This model allows a coordinated linear quadratic control design in multi machine systems. The performance of the proposed controller has been evaluated on two widely used multi-machine power systems, 4 generator 10 bus and 10 generator 39 bus systems. It has been observed that the performance of the proposed controller is superior to that of the conventional Power System Stabilizers (PSS) over a wide range of operating and system conditions.

Discrete time second order sliding mode observer for uncertain linear multi-output system

This paper presents a second order sliding mode observer (SOSMO) design for discrete time uncertain linear multi-output system. The design procedure is effective for both matched and unmatched bounded uncertainties and/or disturbances. A second order sliding function and corresponding sliding manifold for discrete time system are defined similar to the lines of continuous time counterpart. A boundary layer concept is employed to avoid switching across the defined sliding manifold and the sliding trajectory is confined to a boundary layer once it converges to it. The condition for existence of convergent quasi-sliding mode (QSM) is derived. The observer estimation errors satisfying given stability conditions converge to an ultimate finite bound (within the specified boundary layer) with thickness O(T-2) where T is the sampling period. A relation between sliding mode gain and boundary layer is established for the existence of second order discrete sliding motion. The design strategy is very simple to apply and is demonstrated for three examples with different class of disturbances (matched and unmatched) to show the effectiveness of the design. Simulation results to show the robustness with respect to the measurement noise are given for SOSMO and the performance is compared with pseudo-linear Kalman filter (PLKF). (C) 2013 Published by Elsevier Ltd. on behalf of The Franklin Institute

An out-of-plane linear motion measurement system based on optical beam deflection

Measurement of out-of-plane linear motion with high precision and bandwidth is indispensable for development of precision motion stages and for dynamic characterization of mechanical structures. This paper presents an optical beam deflection (OBD) based system for measurement of out-of-plane linear motion for fully reflective samples. The system also achieves nearly zero cross-sensitivity to angular motion, and a large working distance. The sensitivities to linear and angular motion are analytically obtained and employed to optimize the system design. The optimal shot-noise limited resolution is shown to be less than one angstrom over a bandwidth in excess of 1 kHz. Subsequently, the system is experimentally realized and the sensitivities to out-of-plane motions are calibrated using a novel strategy. The linear sensitivity is found to be in agreement with theory. The angular sensitivity is shown to be over 7.5-times smaller than that of conventional OBD. Finally, the measurement system is employed to measure the transient response of a piezo-positioner, and, with the aid of an open-loop controller, reduce the settling time by about 90%. It is also employed to operate the positioner in closed-loop and demonstrate significant minimization of hysteresis and positioning error.

Finite Element Solution Of Surface-Tension Driven Flows In Laser Surface-Melting

Lasers are very efficient in heating localized regions and hence they find a wide application in surface treatment processes. The surface of a material can be selectively modified to give superior wear and corrosion resistance. In laser surface-melting and welding problems, the high temperature gradient prevailing in the free surface induces a surface-tension gradient which is the dominant driving force for convection (known as thermo-capillary or Marangoni convection). It has been reported that the surface-tension driven convection plays a dominant role in determining the melt pool shape. In most of the earlier works on laser-melting and related problems, the finite difference method (FDM) has been used to solve the Navier Stokes equations [1]. Since the Reynolds number is quite high in these cases, upwinding has been used. Though upwinding gives physically realistic solutions even on a coarse grid, the results are inaccurate. McLay and Carey have solved the thermo-capillary flow in welding problems by an implicit finite element method [2]. They used the conventional Galerkin finite element method (FEM) which requires that the pressure be interpolated by one order lower than velocity (mixed interpolation). This restricts the choice of elements to certain higher order elements which need numerical integration for evaluation of element matrices. The implicit algorithm yields a system of nonlinear, unsymmetric equations which are not positive definite. Computations would be possible only with large mainframe computers.Sluzalec [3] has modeled the pulsed laser-melting problem by an explicit method (FEM). He has used the six-node triangular element with mixed interpolation. Since he has considered the buoyancy induced flow only, the velocity values are small. In the present work, an equal order explicit FEM is used to compute the thermo-capillary flow in the laser surface-melting problem. As this method permits equal order interpolation, there is no restriction in the choice of elements. Even linear elements such as the three-node triangular elements can be used. As the governing equations are solved in a sequential manner, the computer memory requirement is less. The finite element formulation is discussed in this paper along with typical numerical results.