Modal stability theory

This article contains a review of modal stability theory. It covers local stability analysis of parallel flows including temporal stability, spatial stability, phase velocity, group velocity, spatio-temporal stability, the linearized Navier-Stokes equations, the Orr-Sommerfeld equation, the Rayleigh equation, the Briggs-Bers criterion, Poiseuille flow, free shear flows, and secondary modal instability. It also covers the parabolized stability equation (PSE), temporal and spatial biglobal theory, 2D eigenvalue problems, 3D eigenvalue problems, spectral collocation methods, and other numerical solution methods. Computer codes are provided for tutorials described in the article. These tutorials cover the main topics of the article and can be adapted to form the basis of research codes. Copyright © 2014 by ASME.

Global modes with multiple saddle points

Significant progress has been made towards understanding the global stability of slowly-developing shear flows. The WKBJ theory developed by Patrick Huerre and his co-authors has proved absolutely central, with the result that both the linear and the nonlinear stability of a wide range of flows can now be understood in terms of their local absolute/convective instability properties. In many situations, the local absolute frequency possesses a single dominant saddle point in complex X-space (where X is the slow streamwise coordinate of the base flow), which then acts as a single wavemaker driving the entire global linear dynamics. In this paper we consider the more complicated case in which multiple saddles may act as the wavemaker for different values of some control parameter. We derive a frequency selection criterion in the general case, which is then validated against numerical results for the linearized third-order Ginzburg-Landau equation (which possesses two saddle points). We believe that this theory may be relevant to a number of flows, including the boundary layer on a rotating disk and the eccentric Taylor-Couette-Poiseuille flow. © 2014 Elsevier Masson SAS. All rights reserved.

Standing up with motor primitives

As observed in nature, complex locomotion can be generated based on an adequate combination of motor primitives. In this context, the paper focused on experiments which result in the development of a quality criterion for the design and analysis of motor primitives. First, the impact of different vocabularies on behavioural diversity, robustness of prelearned behaviours and learning process is elaborated. The experiments are performed with the quadruped robot MiniDog6M for which a running and standing up behaviour is implemented. Further, a reinforcement learning approach based on Q-learning is introduced which is used to select an adequate sequence of motor primitives. © 2006 Springer-Verlag Berlin Heidelberg.

Lineshape Analysis of the Beat Signal Between Optical Carrier and Delayed Sidebands

This paper presents the lineshape analysis of the beat signal between the optical carrier and the shifted and delayed side-bands produced by sinusoidal amplitude modulation. It is shown that the beat signal has a typical lineshape with a very narrow delta-peak superposed on a quasi-Lorentzian profile. Theoretical explanation for the appearance of this peak has been given based on optical spectral structure constructed by a large number of optical wave trains. It is predicted that the delta-peak is originated from the beat between the wave trains in the carrier and those in the delayed sidebands when their average coherence length is longer than the delay line. Experiments carried out using different delay lines clearly show that the delta-peak is always located at the modulation frequency and decreases with the increasing delay line. Our analysis explicitly indicates that the linewidth is related to the observation time. It is also suggested that the disappearance of the delta-peak can be used as the criterion of coherence elimination.

An investigation of the mode characteristics of SOI submicron rib waveguides using the film mode matching method

The mode characteristics of SOI (silicon-on-insulator) submicron rib waveguides are very different from those of micrometer-sized ones. Using the full-vector film mode matching method, we propose a simple criterion to determine whether a waveguide mode is guided or not. The single-mode condition for deep-etched waveguides is obtained using this criterion. We also obtain the inherent TM mode leakage and sharp cancelation effects due to TE-TM mode coupling in shallow-etched rib waveguides from numerical simulations, which agree well with the analytical results based on total internal reflection and interference theories.

Detecting a set of entanglement measures in an unknown tripartite quantum state by local operations and classical communication

We propose a more general method for detecting a set of entanglement measures, i.e., negativities, in an arbitrary tripartite quantum state by local operations and classical communication. To accomplish the detection task using this method, three observers do not need to perform partial transposition maps by the structural physical approximation; instead, they only need to collectively measure some functions via three local networks supplemented by a classical communication. With these functions, they are able to determine the set of negativities related to the tripartite quantum state.

Study on text-dependent speaker recognition based on Biomimetic Pattern Recognition

We studied the application of Biomimetic Pattern Recognition to speaker recognition. A speaker recognition neural network using network matching degree as criterion is proposed. It has been used in the system of text-dependent speaker recognition. Experimental results show that good effect could be obtained even with lesser samples. Furthermore, the misrecognition caused by untrained speakers occurring in testing could be controlled effectively. In addition, the basic idea "cognition" of Biomimetic Pattern Recognition results in no requirement of retraining the old system for enrolling new speakers.

Method for detecting concurrence without the structural physical approximation by local operations and classical communication

We present a modified method for detecting the concurrence in an arbitrary two-qubit quantum state rho(AB) with local operations and classical communication. In this method, it is not necessary for the two observers to prepare the quantum state rho(AB) by the structural physical approximation. Their main task is to measure four specific functions via two local quantum networks. With these functions they can determine the concurrence and then the entanglement of formation.

Entanglement in a spin-one spin chain

The thermal entanglement in a two-spin-qutrit system with two spins coupled by exchange interaction is investigated in terms of the measure of entanglement called 'negativity'. We strictly show that for any temperature the entanglement is symmetric with respect to zero magnetic field. The behavior of negativity is presented for four different cases. We find that the entanglement may be enhanced under a nonuniform magnetic field. Because there is not any necessary and sufficient condition for quantum separability in systems of dimension 3 circle times 3, our results are qualitative, not quantitative. (c) 2006 Elsevier Ltd. All rights reserved.

The effects of nonlinear couplings and external magnetic field on the thermal entanglement in a two-spin-qutrit system

We investigate the effects of nonlinear couplings and external magnetic field on the thermal entanglement in a two-spin-qutrit system by applying the concept of negativity. It is found that the nonlinear couplings favor the thermal entanglement creating. Only when the nonlinear couplings vertical bar K vertical bar are larger than a certain critical value does the entanglement exist. The dependence of the thermal entanglement in this system on the magnetic field and temperature is also presented. The critical magnetic field increases with the increasing nonlinear couplings constant vertical bar K vertical bar. And for a fixed nonlinear couplings constant, the critical temperature is independent of the magnetic field B. (c) 2005 Elsevier B.V. All rights reserved.

Thermal entanglement in a two-spin-qutrit system under a nonuniform external magnetic field

The thermal entanglement in a two-spin-qutrit system with two spins coupled by exchange interaction under a magnetic field in an arbitrary direction is investigated. Negativity, the measurement of entanglement is calculated. We find that for any temperature the evolvement of negativity is symmetric with respect to magnetic field. The behavior of negativity is presented for four different cases. The results show that for different temperature; different magnetic field give maximum entanglement. Both the parallel and antiparallel magnetic field cases are investigated qualitatively (not quantitatively) in detail, we find that the entanglement may be enhanced under an antiparallel magnetic field.

Conditions for the local manipulation of all bipartite Gaussian states

We provide a general, necessary, and sufficient condition for the possibility of transforming a mixed bipartite Gaussian state with arbitrarily many modes to another one under arbitrary local Gaussian channels, which do not include classical communication. Moreover, by means of this condition we present a necessary criterion that can be used to check the possibility of a state transformation between two mixed Gaussian states. At the same time, we prove that our criterion can be reduced to the Eisert-Plenio criterion when the mode number is chosen as 1 per side.

Conditions for the local manipulation of tripartite Gaussian states

We present the normal form of the covariance matrix for three-mode tripartite Gaussian states. By means of this result, the general form of a necessary and sufficient criterion for the possibility of a state transformation from one tripartite entangled Gaussian state to another with three modes is found. Moreover, we show that the conditions presented include not only inequalities but equalities as well.

An adaptive controller for a class of nonlinear system using direction basis function

For a class of nonlinear dynamical systems, the adaptive controllers are investigated using direction basis function (DBF) in this paper. Based on the criterion of Lyapunov' stability, DBF is designed which guarantees that the output of the controlled system asymptotically tracks the reference signals. Finally, the simulation shows the good tracking effectiveness of the adaptive controller.

X-ray double-crystal characterization of the strain relaxation in GaAs/GaNxAs1-x/GaAs(001) sandwiched structures

An X-ray diffraction method, estimating the strain relaxation in an ultrathin layer, has been discussed by using kinematic and dynamical X-ray diffraction (XRD) theory. The characteristic parameter Delta Omega, used as the criterion of the strain relaxation in ultrathin layers, is deduced theoretically. It reveals that Delta Omega should be independent of the layer thickness in a coherently strained layer. By this method, we characterized our ultrathin GaNxAs1-x samples with N contents up to 5%. XRD measurements show that our GaNxAs1-x layers are coherently strained on GaAs even for such a large amount of N. Furthermore, a series of GaNxAs1-x samples with same N contents but different layer thicknesses were also characterized. It was found that the critical thickness (L-c) of GaNAs in the GaAs/GaNAs/GaAs structures determined by XRD measurement was 10 times smaller than the theoretical predictions based on the Matthews and Blakeslee model. This result was also confirmed by in situ observation of reflection high-energy electron diffraction (RHEED) and photoluminescence (PL) measurements. RHEED observation showed that the growth mode of GaNAs layer changed from 2D- to 3D-mode as the layer thickness exceeded L-c. PL measurements showed that the optical properties of GaNAs layers deteriorated rapidly as the layer thickness exceeded L-c. (C) 2000 Elsevier Science B.V. All rights reserved.