Third order trace formula

In J. Funct. Anal. 257 (2009) 1092-1132, Dykema and Skripka showed the existence of higher order spectral shift functions when the unperturbed self-adjoint operator is bounded and the perturbation is Hilbert-Schmidt. In this article, we give a different proof for the existence of spectral shift function for the third order when the unperturbed operator is self-adjoint (bounded or unbounded, but bounded below).

Diversity order vs rate in an AWGN channel

We study the diversity order vs rate of an additive white Gaussian noise (AWGN) channel in the whole capacity region. We show that for discrete input as well as for continuous input, Gallager's upper bounds on error probability have exponential diversity in low and high rate region but only subexponential in the mid-rate region. For the best available lower bounds and for the practical codes one observes exponential diversity throughout the capacity region. However we also show that performance of practical codes is close to Gallager's upper bounds and the mid-rate subexponential diversity has a bearing on the performance of the practical codes. Finally we show that the upper bounds with Gaussian input provide good approximation throughout the capacity region even for finite constellation.

Second order transport from anomalies

We study parity odd transport at second order in derivative expansion for a non-conformal charged fluid. We see that there are 27 parity odd transport coefficients, of which 12 are non-vanishing in equilibrium. We use the equilibrium partition function method to express 7 of these in terms of the anomaly, shear viscosity, charge diffusivity and thermodynamic functions. The remaining 5 are constrained by 3 relations which also involve the anomaly. We derive Kubo formulae for 2 of the transport coefficients and show these agree with that derived from the equilibrium partition function.

Quantum Phase Diagram of One-Dimensional Spin and Hubbard Models with Transitions to Bond Order Wave Phases

Similar quantum phase diagrams and transitions are found for three classes of one-dimensional models with equally spaced sites, singlet ground states (GS), inversion symmetry at sites and a bond order wave (BOW) phase in some sectors. The models are frustrated spin-1/2 chains with variable range exchange, half-filled Hubbard models with spin-independent interactions and modified Hubbard models with site energies for describing organic charge transfer salts. In some range of parameters, the models have a first order quantum transition at which the GS expectation value of the sublattice spin < S-A(2)> of odd or even-numbered sites is discontinuous. There is an intermediate BOW phase for other model parameters that lead to two continuous quantum transitions with continuous < S-A(2)>. Exact diagonalization of finite systems and symmetry arguments provide a unified picture of familiar 1D models that have appeared separately in widely different contexts.

Quantum Phase Diagram of One-Dimensional Spin and Hubbard Models with Transitions to Bond Order Wave Phases

Similar quantum phase diagrams and transitions are found for three classes of one-dimensional models with equally spaced sites, singlet ground states (GS), inversion symmetry at sites and a bond order wave (BOW) phase in some sectors. The models are frustrated spin-1/2 chains with variable range exchange, half-filled Hubbard models with spin-independent interactions and modified Hubbard models with site energies for describing organic charge transfer salts. In some range of parameters, the models have a first order quantum transition at which the GS expectation value of the sublattice spin < S-A(2)> of odd or even-numbered sites is discontinuous. There is an intermediate BOW phase for other model parameters that lead to two continuous quantum transitions with continuous < S-A(2)>. Exact diagonalization of finite systems and symmetry arguments provide a unified picture of familiar 1D models that have appeared separately in widely different contexts.

Zero miss distance guidance using feedforward and periodic control

There have been attempts at obtaining robust guidance laws to ensure zero miss distance (ZMD) for interceptors with parametric uncertainties. All these laws require the plant to be of minimum phase type to enable the overall guidance loop transfer function to satisfy strict positive realness (SPR). The SPR property implies absolute stability of the closed loop system, and has been shown in the literature to lead to ZMD because it avoids saturation of lateral acceleration. In these works higher order interceptors are reduced to lower order equivalent models for which control laws are designed to ensure ZMD. However, it has also been shown that when the original system with right half plane (RHP) zeros is considered, the resulting miss distances, using such strategies, can be quite high. In this paper, an alternative approach using the circle criterion establishes the conditions for absolute stability of the guidance loop and relaxes the conservative nature of some earlier results arising from assumption of in�nite engagement time. Further, a feedforward scheme in conjunction with a lead-lag compensator is used as one control strategy while a generalized sampled hold function is used as a second strategy, to shift the RHP transmission zeros, thereby achieving ZMD. It is observed that merely shifting the RHP zero(s) to the left half plane reduces miss distances signi�cantly even when no additional controllers are used to ensure SPR conditions.

Channel estimation relying on the minimum bit-error-ratio criterion for BPSK and QPSK signals

The authors consider the channel estimation problem in the context of a linear equaliser designed for a frequency selective channel, which relies on the minimum bit-error-ratio (MBER) optimisation framework. Previous literature has shown that the MBER-based signal detection may outperform its minimum-mean-square-error (MMSE) counterpart in the bit-error-ratio performance sense. In this study, they develop a framework for channel estimation by first discretising the parameter space and then posing it as a detection problem. Explicitly, the MBER cost function (CF) is derived and its performance studied, when transmitting binary phase shift keying (BPSK) and quadrature phase shift keying (QPSK) signals. It is demonstrated that the MBER based CF aided scheme is capable of outperforming existing MMSE, least square-based solutions.

A 5th and 7th Order Harmonic Suppression Scheme for Open-end Winding Asymmetrical Six-phase IM Drive Using Capacitor-fed Inverter

Voltage source inverter (VSI) fed six-phase induction motor drives have high 6n +/- 1; n = odd order harmonic currents, due to absence of back emf for these currents. To suppress these harmonic currents, either bulky inductive harmonic filters or complex pulse width modulation (PWM) techniques have to be used. This paper proposes a simple harmonic elimination scheme using capacitor fed inverters, for an asymmetrical six-phase induction motor VSI fed drive. Two three phase inverters fed from a single capacitor is used on the open-end side of the motor, to suppress 6n +/- 1; n = odd order harmonics. A PWM scheme that can suppress the harmonics, as well as balance the capacitor voltage is also proposed. The capacitor fed inverters are switched so that the fundamental voltage is not affected. The proposed scheme is verified using MATLAB Simulink simulation at different speeds. The effectiveness of the scheme is demonstrated by comparing the results with those obtained by disabling the capacitor fed inverters. Experimental results are also provided to validate the functionality of the proposed controller.

Elliptical tracers in two-dimensional, homogeneous, isotropic fluid turbulence: The statistics of alignment, rotation, and nematic order

We study the statistical properties of orientation and rotation dynamics of elliptical tracer particles in two-dimensional, homogeneous, and isotropic turbulence by direct numerical simulations. We consider both the cases in which the turbulent flow is generated by forcing at large and intermediate length scales. We show that the two cases are qualitatively different. For large-scale forcing, the spatial distribution of particle orientations forms large-scale structures, which are absent for intermediate-scale forcing. The alignment with the local directions of the flow is much weaker in the latter case than in the former. For intermediate-scale forcing, the statistics of rotation rates depends weakly on the Reynolds number and on the aspect ratio of particles. In contrast with what is observed in three-dimensional turbulence, in two dimensions the mean-square rotation rate increases as the aspect ratio increases.

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

CONVERGENCE ANALYSIS OF THE LOWEST ORDER WEAKLY PENALIZED ADAPTIVE DISCONTINUOUS GALERKIN METHODS

In this article, we prove convergence of the weakly penalized adaptive discontinuous Galerkin methods. Unlike other works, we derive the contraction property for various discontinuous Galerkin methods only assuming the stabilizing parameters are large enough to stabilize the method. A central idea in the analysis is to construct an auxiliary solution from the discontinuous Galerkin solution by a simple post processing. Based on the auxiliary solution, we define the adaptive algorithm which guides to the convergence of adaptive discontinuous Galerkin methods.

Minimum switching loss pulse width modulation for reduced power conversion loss in reactive power compensators

Advanced bus-clamping switching sequences, which employ an active vector twice in a subcycle, are used to reduce line current distortion and switching loss in a space vector modulated voltage source converter. This study evaluates minimum switching loss pulse width modulation (MSLPWM), which is a combination of such sequences, for static reactive power compensator (STATCOM) application. It is shown that MSLPWM results in a significant reduction in device loss over conventional space vector pulse width modulation. Experimental verification is presented at different power levels of up to 150 kVA.

A fractional order proportional integral controller for path following and trajectory tracking of miniature air vehicles

In this paper, a fractional order proportional-integral controller is developed for a miniature air vehicle for rectilinear path following and trajectory tracking. The controller is implemented by constructing a vector field surrounding the path to be followed, which is then used to generate course commands for the miniature air vehicle. The fractional order proportional-integral controller is simulated using the fundamentals of fractional calculus, and the results for this controller are compared with those obtained for a proportional controller and a proportional integral controller. In order to analyze the performance of the controllers, four performance metrics, namely (maximum) overshoot, control effort, settling time and integral of the timed absolute error cost, have been selected. A comparison of the nominal as well as the robust performances of these controllers indicates that the fractional order proportional-integral controller exhibits the best performance in terms of ITAE while showing comparable performances in all other aspects.

Multi-site downscaling of maximum and minimum daily temperature using support vector machine

Climate change impact assessment studies involve downscaling large-scale atmospheric predictor variables (LSAPVs) simulated by general circulation models (GCMs) to site-scale meteorological variables. This article presents a least-square support vector machine (LS-SVM)-based methodology for multi-site downscaling of maximum and minimum daily temperature series. The methodology involves (1) delineation of sites in the study area into clusters based on correlation structure of predictands, (2) downscaling LSAPVs to monthly time series of predictands at a representative site identified in each of the clusters, (3) translation of the downscaled information in each cluster from the representative site to that at other sites using LS-SVM inter-site regression relationships, and (4) disaggregation of the information at each site from monthly to daily time scale using k-nearest neighbour disaggregation methodology. Effectiveness of the methodology is demonstrated by application to data pertaining to four sites in the catchment of Beas river basin, India. Simulations of Canadian coupled global climate model (CGCM3.1/T63) for four IPCC SRES scenarios namely A1B, A2, B1 and COMMIT were downscaled to future projections of the predictands in the study area. Comparison of results with those based on recently proposed multivariate multiple linear regression (MMLR) based downscaling method and multi-site multivariate statistical downscaling (MMSD) method indicate that the proposed method is promising and it can be considered as a feasible choice in statistical downscaling studies. The performance of the method in downscaling daily minimum temperature was found to be better when compared with that in downscaling daily maximum temperature. Results indicate an increase in annual average maximum and minimum temperatures at all the sites for A1B, A2 and B1 scenarios. The projected increment is high for A2 scenario, and it is followed by that for A1B, B1 and COMMIT scenarios. Projections, in general, indicated an increase in mean monthly maximum and minimum temperatures during January to February and October to December.

Design of fully rotatable, roller-crank-driven, cam mechanisms for arbitrary motion specifications

The design of a non-traditional cam and roller-follower mechanism is described here. In this mechanism, the roller-crank rather than the cam is used as the continuous input member, while both complete a full rotation in each revolution and remain in contact throughout. It is noted that in order to have the cam fully rotate for every full rotation of the roller-crank, the cam cannot be a closed profile, rather the roller traverses the open cam profile twice in each cycle. Using kinematic analysis, the angular velocity of the cam when the roller traverses the cam profile in one direction, is related to the angular velocity of the cam when the roller retraces its path on the cam in the other direction. Thus, one can specify any arbitrary function relating the motion of the cam to the motion of the roller-crank for only 180 degrees of rotation in the angular velocity space. The motion of the cam in the remaining portion is then automatically determined. In specifying the arbitrary motion, many desirable characteristics such as multiple dwells, low acceleration and jerk, etc., can be obtained. Useful design equations are derived for this purpose. Using the kinematic inversion technique, the cam profile is readily obtained once the motion is specified in the angular velocity space. The only limitation to the arbitrary motion specification is making sure that the transmission angle never gets too low, so that the force will be transmitted efficiently from roller to cam. This is addressed by incorporating a transmission index into the motion specification in the synthesis process. Consequently, in this method we can specify any arbitrary motion within a permissible rone, such that the transmission index is higher than the specified minimum value. Single-dwell, double-dwell and a long hesitation motion are used as examples to demonstrate the ffectiveness of the design method. Force closure using an optimally located spring and quasi-kinetostatic analysis are also discussed. (C) 2001 Elsevier Science Ltd. All rights reserved.