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DYNAMIC BIFURCATION OF NONLINEAR EVOLUTION EQUATIONS

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Chinese Annals of Mathematics,Series B 2005年第2期26卷 185-206页

作者： MA Tian WANG Shouhong Department of Mathematics Sichuan UniversityChengdu 610064China Department of Mathematics Indiana UniversityBloomingtonIN 47405USA.

The authors introduce a notion of dynamic bifurcation for nonlinear evolution equa- tions, which can be called attractor bifurcation. It is proved that as the control pa- rameter crosses certain critical value, the system bifurcates from a trivial steady state solution to an attractor with dimension between m and m + 1, where m + 1 is the number of eigenvalues crossing the imaginary axis. The attractor bifurcation theory presented in this article generalizes the existing steady state bifurcations and the Hopf bifurcations. It provides a uni?ed point of view on dynamic bifurcation and can be applied to many problems in physics and mechanics.

关键词： Attractor bifurcation Steady state bifurcation Dynamic bifurcation Hopf bifurcation Nonlinear evolution equation

Evaluating acoustic communication performance of micro autonomous underwater vehicles in confined spaces

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Frontiers of Information Technology & Electronic Engineering 2018年第8期19卷 1013-1023页

作者： Qiu-yang TAO Yue-hai ZHOU Feng TONG Ai-jun SONG Fumin ZHANG School of Electrical and Computer Engineering Georgia Institute of Technology College of Ocean and Earth Sciences Xiamen University Department of Electrical and Computer Engineering The University of Alabama

Micro-sized autonomous underwater vehicles(μAUVs) are well suited to various applications in confined underwater spaces. Acoustic communication is required for many application scenarios of μAUVs to enable data transmission without surfacing. This paper presents the integration of a compact acoustic communication device with a μAUV prototype. Packet reception rate(PRR) and bit error rate(BER) of the acoustic communication link are evaluated in a confined pool environment through experiments while the μAUV is either stationary or *** pinpoint several major factors that impact the communication performance. Experimental results show that the multi-path effect significantly affects the synchronization signals of the communication device. The relative motion between the vehicle and the base station also degrades the communication performance. These results suggest future methods towards improvements.

关键词： Autonomous underwater vehicles Underwater acoustic communications Confined water space

Short-Time Linear Response with Reduced-Rank Tangent Map

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Chinese Annals of Mathematics,Series B 2009年第5期30卷 447-462页

作者： Rafail V. ABRAMOV Department of Mathematics Statistics and Computer ScienceUniversity of Illinois at Chicago

The recently developed short-time linear response algorithm,which predicts the response of a nonlinear chaotic forced-dissipative system to small external perturbation,yields high precision of the response ***,the computation of the short-time linear response formula with the full rank tangent map can be ***,a numerical method to potentially overcome the increasing numerical complexity for large scale models with many variables by using the reduced-rank tangent map in the computation is *** conditions for which the short-time linear response approximation with the reduced-rank tangent map is valid are established,and two practical situations are examined,where the response to small external perturbations is predicted for nonlinear chaotic forced-dissipative systems with different dynamical properties.

关键词： Fluctuation-dissipation theorem Linear response

Invariant Measures and Asymptotic Gaussian Bounds for Normal Forms of Stochastic Climate Model

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Chinese Annals of Mathematics,Series B 2011年第3期32卷 343-368页

作者： Yuan YUAN Andrew J. MAJDA Department of Mathematics Courant Institute New York University 251 Mercer Street New York NY 10012 USA Department of Mathematics and Center for Atmospheric Ocean Sciences Courant Institute New York University 251 Mercer Street New York NY 10012 USA

The systematic development of reduced low-dimensional stochastic climate models from observations or comprehensive high dimensional climate models is an important topic for atmospheric low-frequency variability,climate sensitivity,and improved extended range ***,techniques from applied mathematics have been utilized to systematically derive normal forms for reduced stochastic climate models for low-frequency *** was shown that dyad and multiplicative triad interactions combine with the climatological linear operator interactions to produce a normal form with both strong nonlinear cubic dissipation and Correlated Additive and Multiplicative(CAM) stochastic *** probability distribution functions(PDFs) of low frequency climate variables exhibit small but significant departure from Gaussianity but have asymptotic tails which decay at most like a ***,rigorous upper bounds with Gaussian decay are proved for the invariant measure of general normal form stochastic *** Gaussian lower bounds are also established under suitable hypotheses.

关键词： Reduced stochastic climate model Invariant measure Fokker-Planck equation Comparison principle Global estimates of probability density function

ASYMPTOTIC NORMALITY OF MINIMUML_1-NORM ESTIMATES IN LINEAR MODELS

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Science China Mathematics 1990年第11期33卷 1311-1328页

作者：陈希孺白志东赵林城吴月华 University of Science and Technology of China Hofei 230026PRC Southeast University Nanjing 210018 PRC

Consider the standard linear model where x_x,x_2… are assumed to be the known p-vectors, β the unknown p-vector of regression coefficients, and e_1, e_2, …the independent random error sequence, each having a median zero. Define the minimum L_1norm estimator as,the solution of the minimization problem inf It is proved in this paper that is asymptotically normal under very weak conditions. In particular, the condition imposed on {xi} is exactly the same which ensures the asymptotic normality of least-squares estimate:

关键词： linear model minimum L_1-norm estimate asymptotic normality.

Enhancing von Neumann entropy by chaos in spin–orbit entanglement

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Chinese Physics B 2019年第10期28卷 153-159页

作者： Chen-Rong Liu Pei Yu Xian-Zhang Chen Hong-Ya Xu Liang Huang Ying-Cheng Lai School of Physical Science and Technology and Key Laboratory for Magnetism and Magnetic Materials of MOELanzhou UniversityLanzhou 730000China School of Electrical Computerand Energy EngineeringArizona State UniversityTempeAZ 85287USA Department of Physics Arizona State UniversityTempeAZ 85287USA

For a quantum system with multiple degrees of freedom or subspaces, loss of coherence in a certain subspace is intimately related to the enhancement of entanglement between this subspace and another one. We investigate intra-particle entanglement in two-dimensional mesoscopic systems, where an electron has both spin and orbital degrees of freedom and the interaction between them is enabled by Rashba type of spin-orbit coupling. The geometric shape of the scattering region can be adjusted to produce a continuous spectrum of classical dynamics with different degree of chaos. Focusing on the spin degree of freedom in the weak spin-orbit coupling regime, we find that classical chaos can significantly enhance spin-orbit entanglement at the expense of spin coherence. Our finding that classical chaos can be beneficial to intra-particle entanglement may have potential applications such as enhancing the bandwidth of quantum communications.

关键词： spin-orbit entanglement chaos von Neumann entropy spin decoherence

A perspective on high-order methods in computational fluid dynamics

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Science China(Physics,Mechanics & Astronomy) 2016年第1期59卷 1-6页

作者： ZhiJian Wang Department of Aerospace Engineering University of Kansas

There has been an intensive international effort to develop high-order Computational Fluid Dynamics(CFD) methods into design tools in aerospace engineering during the last one and half decades. These methods offer the potential to significantly improve solution accuracy and efficiency for vortex dominated turbulent flows. Enough progresses have been made in algorithm development, mesh generation and parallel computing that these methods are on the verge of being applied in a production design environment. Since many review papers have been written on the subject, I decide to offer a personal perspective on the state-of-the-art in high-order CFD methods and the challenges that must be overcome.

关键词： CFD high-order large eddy simulation aerospace engineering

WAVE PROPAGATION IN ELECTROSTRICTIVE MATERIALS UNDER BIASED FIELDS

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Acta Mechanica Solida Sinica 2004年第3期17卷 209-217页

作者： Hu Yuantai Yang Jiashi Jiang Qing Department of Mechanics Huazhong University of Science and TechnologyWuhan 430074China Department of Engineering Mechanics University of NebraskaLincolnNE 68588USA Department of Mechanical Engineering University of CaliforniaRiversideCA 92521USA

Constitutive relations for nonlinear, isotropic, electroelastic solids quadratic in the ?nite strain tensor and the referential electric ?eld are derived from the full nonlinearity theory of electroelasticity by tensor invariants, which can describe the behavior of electrostrictive ma- terials. The equations are linearized for small, dynamic ?elds superposed on ?nite, static biased ?elds. These linear equations are used to study plane waves propagating in an electroelastic body under various mechanical and/or electric biased ?elds. It is shown that the speed of the acoustic waves exhibits a strong dependence upon those material parameters in the nonlinear constitu- tive relations. Experimental determination of these material parameters using this dependence is discussed.

关键词： electrostrictive materials biased fields incremental fields acoustic waves

Autonomous flying blimp interaction with human in an indoor space

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Frontiers of Information Technology & Electronic Engineering 2019年第1期20卷 45-59页

作者： Ning-shi YAO Qiu-yang TAO Wei-yu LIU Zhen LIU Ye TIAN Pei-yu WANG Timothy LI Fumin ZHANG School of Electrical and Computer Engineering Georgia Institute of Technology College of Computing Georgia Institute of Technology

We present the Georgia Tech Miniature Autonomous Blimp(GT-MAB), which is designed to support human-robot interaction experiments in an indoor space for up to two hours. GT-MAB is safe while flying in close proximity to humans. It is able to detect the face of a human subject, follow the human, and recognize hand gestures. GT-MAB employs a deep neural network based on the single shot multibox detector to jointly detect a human user's face and hands in a real-time video stream collected by the onboard camera. A human-robot interaction procedure is designed and tested with various human users. The learning algorithms recognize two hand waving gestures. The human user does not need to wear any additional tracking device when interacting with the flying blimp. Vision-based feedback controllers are designed to control the blimp to follow the human and fly in one of two distinguishable patterns in response to each of the two hand gestures. The blimp communicates its intentions to the human user by displaying visual symbols. The collected experimental data show that the visual feedback from the blimp in reaction to the human user significantly improves the interactive experience between blimp and *** demonstrated success of this procedure indicates that GT-MAB could serve as a flying robot that is able to collect human data safely in an indoor environment.

关键词： Robotic blimp Human-robot interaction Deep learning Face detection Gesture recognition