Solution of the symmetric eigenproblem AX=lambda BX by delayed division

Delayed division is an iterative method for solving the linear eigenvalue problem AX = lambda BX for a limited number of small eigenvalues and their corresponding eigenvectors. The distinctive feature of the method is the reduction of the problem to an approximate triangular form by systematically dropping quadratic terms in the eigenvalue lambda. The report describes the pivoting strategy in the reduction and the method for preserving symmetry in submatrices at each reduction step. Along with the approximate triangular reduction, the report extends some techniques used in the method of inverse subspace iteration. Examples are included for problems of varying complexity

The Essential Role and the Continuous Evolution of Modulation Techniques for Voltage-Source Inverters in the Past, Present, and Future Power Electronics

The cost reduction of power-electronic devices, the increase in their reliability, efficiency, and power capability, and lower development times, together with more demanding application requirements, has driven the development of several new inverter topologies recently introduced in the industry, particularly medium-voltage converters. New more complex inverter topologies and new application fields come along with additional control challenges, such as voltage imbalances, power-quality issues, higher efficiency needs, and fault-tolerant operation, which necessarily requires the parallel development of modulation schemes. Therefore, recently, there have been significant advances in the field of modulation of dc/ac converters, which conceptually has been dominated during the last several decades almost exclusively by classic pulse-width modulation (PWM) methods. This paper aims to concentrate and discuss the latest developments on this exciting technology, to provide insight on where the state-of-the-art stands today, and analyze the trends and challenges driving its future

Constraint handling strategies in Genetic Algorithms application to optimal batch plant design

Optimal batch plant design is a recurrent issue in Process Engineering, which can be formulated as a Mixed Integer Non-Linear Programming(MINLP) optimisation problem involving specific constraints, which can be, typically, the respect of a time horizon for the synthesis of various products. Genetic Algorithms constitute a common option for the solution of these problems, but their basic operating mode is not always wellsuited to any kind of constraint treatment: if those cannot be integrated in variable encoding or accounted for through adapted genetic operators, their handling turns to be a thorny issue. The point of this study is thus to test a few constraint handling techniques on a mid-size example in order to determine which one is the best fitted, in the framework of one particular problem formulation. The investigated methods are the elimination of infeasible individuals, the use of a penalty term added in the minimized criterion, the relaxation of the discrete variables upper bounds, dominancebased tournaments and, finally, a multiobjective strategy. The numerical computations, analysed in terms of result quality and of computational time, show the superiority of elimination technique for the former criterion only when the latter one does not become a bottleneck. Besides, when the problem complexity makes the random location of feasible space too difficult, a single tournament technique proves to be the most efficient one

On measuring the covariance matrix of the nonlinear power spectrum from simulations

We show how to estimate the covariance of the power spectrum of a statistically homogeneous and isotropic density field from a single periodic simulation, by applying a set of weightings to the density field, and by measuring the scatter in power spectra between different weightings. We recommend a specific set of 52 weightings containing only combinations of fundamental modes, constructed to yield a minimum variance estimate of the covariance of power. Numerical tests reveal that at nonlinear scales the variance of power estimated by the weightings method substantially exceeds that estimated from a simple ensemble method. We argue that the discrepancy is caused by beat-coupling, in which products of closely spaced Fourier modes couple by nonlinear gravitational growth to the beat mode between them. Beat-coupling appears whenever nonlinear power is measured from Fourier modes with a finite spread of wavevector, and is therefore present in the weightings method but not the ensemble method. Beat-coupling inevitably affects real galaxy surveys, whose Fourier modes have finite width. Surprisingly, the beat-coupling contribution dominates the covariance of power at nonlinear scales, so that, counter-intuitively, it is expected that the covariance of nonlinear power in galaxy surveys is dominated not by small scale structure, but rather by beat-coupling to the largest scales of the survey.Comment: 19 pages, 4 figures. To appear in Monthly Notices of the Royal Astronomical Society. Revised to match accepted versio

Recursive Stochastic Effects in Valley Hybrid Inflation

Hybrid Inflation is a two-field model where inflation ends by a tachyonic instability, the duration of which is determined by stochastic effects and has important observational implications. Making use of the recursive approach to the stochastic formalism presented in Ref. [1], these effects are consistently computed. Through an analysis of back-reaction, this method is shown to converge in the valley but points toward an (expected) instability in the waterfall. It is further shown that quasi-stationarity of the auxiliary field distribution breaks down in the case of a short-lived waterfall. It is found that the typical dispersion of the waterfall field at the critical point is then diminished, thus increasing the duration of the waterfall phase and jeopardizing the possibility of a short transition. Finally, it is found that stochastic effects worsen the blue tilt of the curvature perturbations by an order one factor when compared with the usual slow-roll contribution.Comment: 26 pages, 6 figure

Leveraging Continuous Material Averaging for Inverse Electromagnetic Design

Inverse electromagnetic design has emerged as a way of efficiently designing active and passive electromagnetic devices. This maturing strategy involves optimizing the shape or topology of a device in order to improve a figure of merit--a process which is typically performed using some form of steepest descent algorithm. Naturally, this requires that we compute the gradient of a figure of merit which describes device performance, potentially with respect to many design variables. In this paper, we introduce a new strategy based on smoothing abrupt material interfaces which enables us to efficiently compute these gradients with high accuracy irrespective of the resolution of the underlying simulation. This has advantages over previous approaches to shape and topology optimization in nanophotonics which are either prone to gradient errors or place important constraints on the shape of the device. As a demonstration of this new strategy, we optimize a non-adiabatic waveguide taper between a narrow and wide waveguide. This optimization leads to a non-intuitive design with a very low insertion loss of only 0.041 dB at 1550 nm.Comment: 20 pages, 9 figure