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Phase Transitions of Ferromagnetic Potts Models on the Simple Cubic Lattice

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Chinese Physics Letters 2014年第7期31卷 41-45页

作者：王顺谢志远陈靖 Bruce Normand 向涛 Institute of Physics Chinese Academy of Sciences Beijing 100190 Department of Physics Renmin University of China Beijing 100872

We investigate the 2- and 3-state ferromagnetic Ports models on the simple cubic lattice using the tensor renorrealization group method with higher-order singular value decomposition （FIOTRG）. HOTRG works in the thermodynamic limit, where we use the Zq symmetry of the model, combined with a new measure for detecting the transition, to improve the accuracy of the critical point for the 2-state model by two orders of magnitude, obtaining Tc = 4.51152469（1）. The 3-state model is far more complex, and we improve the overall understanding of this case by calculating its thermodynamic quantities with high accuracy. Our results verify that the first-order nature of the phase transition and the HOTRG transition temperature benchmarks the most recent Monte Carlo result.

关键词： PHASE transformations (Physics) FERROMAGNETIC materials CUBIC crystal system CRYSTAL lattices singular value decomposition

Femtosecond time-resolved difference absorption spectroscopy of all-trans-β-Apo-8′-carotenal

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Science China(Physics,Mechanics & Astronomy) 2004年第2期47卷 208-222页

作者： ZHANG Lei QUAN Donghui WANG Li YANG Guozhen WENG Yuxiang Institute of Physics Chinese Academy of Sciences Beijing 100080 China Institute of Physics Chinese Academy of Sciences Beijing 100080 China Institute of Physics Chinese Academy of Sciences Beijing 100080 China Institute of Physics Chinese Academy of Sciences Beijing 100080 China Institute of Physics Chinese Academy of Sciences Beijing 100080 China

The femtosecond time-resolved difference absorption spectra of all-trans-β-Apo-8′-carotenal have been recorded and analyzed by the singular-value decomposition (SVD) method followed by global fitting using a sequential model for the excited-state energy relaxation. With this model, we have obtained the excited-state absorption spectra and the lifetimes of the corresponding excited states both in nonpolar solvent n-hexane and polar solvent methanol. Three excited states, namely S3(170fs), S2(2.32ps) and S1(26ps) in n-hexane, and two excited states S2(190fs) and S1(9.4ps) in methanol have been observed. The excited-state absorption spectra of all-trans-β-Apo-8′-carotenal in methanol display a red shift and broadeness, while the lifetime of S1 state becomes shorter. It is proposed that these effects are related to the presence of a carbonyl functional group that leads to the solvent effect on the excited-state energy level. At the same time, it is shown that the SVD method is a useful tool in resolving the time-resolved absorption spectra.

关键词： singular value decomposition femtosecond time-resolved spectroscopy all-trans-β-Apo-8′-carotenal

Evaluation and Improvement of a SVD-Based Empirical Atmospheric Model

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Advances in Atmospheric Sciences 2011年第3期28卷 636-652页

作者：余嘉裕张振玮涂建翊 Department of Atmospheric Sciences Chinese Culture University Graduate Institute of Earth Science Chinese Culture University

An empirical atmospheric model(EAM) based on the singular value decomposition(SVD) method is evaluated using the composite El Ni(?)o/Southern Oscillation(ENSO) patterns of sea surface temperature (SST) and wind anomalies as the target *** versions of the SVD-based EAM were presented for *** first version estimates the wind anomalies in response to SST variations based on modes that were calculated from a pair of global wind and SST fields(i.e.,conventional EAM or CEAM).The second version utilizes the same model design but is based on modes that were calculated in a region-wise manner by separating the tropical domain from the remaining extratropical regions(i.e.,region-wise EAM or REAM). Our study shows that,while CEAM has shown successful model performance over some tropical areas, such as the equatorial eastern Pacific(EEP),the western North Pacific(WNP),and the tropical Indian Ocean(TIO),its performance over the North Pacific(NP) seems *** REAM is used to estimate the wind anomalies instead of CEAM,a marked improvement over NP readily *** of coupled modes indicate that such an improvement can be attributed to a much stronger coupled variability captured by the first region-wise SVD mode at higher latitudes compared with that captured by the conventional one. The newly proposed way of constructing the EAM(i.e.,REAM) can be very useful in the coupled studies because it gives the model a wider application beyond the commonly accepted tropical domain.

关键词： singular value decomposition empirical atmospheric model coupled variability

A novel single-trial event-related potential estimation method based on compressed sensing

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Neuroscience Bulletin 2013年第6期29卷 788-797页

作者： Zhihua Huang Minghong Li Shangchuan Yang Yuanye Ma Changle Zhou College of Mathematics and Computer Science Fuzhou University Kunming Institute of Zoology CAS Cognitive Science Department Xiamen University

Cognitive functions are often studied using eventrelated potentials（ERPs）that are usually estimated by an averaging ***,estimation of single-trial ERPs can provide researchers with many more details of cognitive activity than the averaging algorithm.A novel method to estimate single-trial ERPs is proposed in this *** method includes two key ***,singular value decomposition was used to construct a matrix,which mapped singletrial electroencephalographic recordings（EEG）into a low-dimensional vector that contained little information from the spontaneous ***,we used the theory of compressed sensing to build a procedure to restore single-trial ERPs from this low-dimensional *** are sparse or approximately sparse in the frequency *** fact allowed us to use the theory of compressed *** verified this method in simulated and real *** method and dVCA（differentially variable component analysis）,another method of single-trial ERPs estimation,were both used to estimate single-trial ERPs from the same simulated *** demonstrated that our method significantly outperforms dVCA under various conditions of signal-to-noise ***,the single-trial ERPs estimated from the real data by our method are statistically consistent with the theories of cognitive science.

关键词： compressed sensing event-related potentials single-trial electroencephalography singular value decomposition

Image restoration with shifting reflective boundary conditions

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Science China(Information Sciences) 2013年第6期56卷 45-59页

作者： HUANG Jie HUANG TingZhu ZHAO XiLe XU ZongBen School of Mathematical Sciences University of Electronic Science and Technology of China Institute of Information and System Sciences Xi'an Jiaotong University

In signal and image processing,we want to recover a faithful representation of an original scene from blurred,noisy image *** process can be transformed mathematically into solving a linear system with a blurring ***,the blurring matrix is determined from not only a point spread function(PSF),which defines how each pixel is blurred,but also boundary conditions(BCs),which specify our assumptions on the data outside the domain of *** this paper,we first propose shifting reflective BCs which preserve the continuity at the boundaries and,therefore,reduce ringing effects in the restored image.A Kronecker product approximation of the corresponding blurring matrix is then provided,regardless of symmetry requirement of the ***,we demonstrate the efficiency of our approximation in an SVD-based regularization method by several numerical examples.

关键词： Image restoration boundary conditions Kronecker product singular value decomposition

Method for obtaining high-resolution velocity spectrum based on weighted similarity

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Applied Geophysics 2020年第2期17卷 221-232,315页

作者： Xu Xing-Rong Su Qin Xie Jun-Fa Wang Jing Kou Long-Jiang Liu Meng-Li Research Institute of Petroleum Exploration&Development-Northwest(NWGI) PetrochinaLanzhou 730020china

Seismic wave velocity is one of the most important processing parameters of seismic data,which also determines the accuracy of *** conventional method of velocity analysis involves scanning through a series of equal intervals of velocity,producing the velocity spectrum by superposing energy or similarity *** this method,however,the sensitivity of the semblance spectrum to change of velocity is weak,so the resolution is *** this paper,to solve the above deficiencies of conventional velocity analysis,a method for obtaining a high-resolution velocity spectrum based on weighted similarity is *** introducing two weighting functions,the resolution of the similarity spectrum in time and velocity is *** examples and real seismic data indicate that the proposed method provides a velocity spectrum with higher resolution than conventional methods and can separate cross reflectors which are aliased in conventional semblance spectrums;at the same time,the method shows good noise-resistibility.

关键词： Weighted function similarity high resolution velocity spectrum singular value decomposition wavelet

SOME PROBLEMS WITH THE METHOD OF FUNDAMENTAL SOLUTION USING RADIAL BASIS FUNCTIONS

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Acta Mechanica Solida Sinica 2007年第1期20卷 21-29页

作者： Wang Hui Qin Qinghua College of Civil Engineering and Architecture Henan University of Technology Zhengzhou 450052 China Department of Mechanics Tianjin University Tianjin 300072 China Department of Engineering Australian National University Canberra ACT 0200 Austrulia

The present work describes the application of the method of fundamental solutions （MFS） along with the analog equation method （AEM） and radial basis function （RBF） approximation for solving the 2D isotropic and anisotropic Helmholtz problems with different wave numbers. The AEM is used to convert the original governing equation into the classical Poisson＇s equation, and the MFS and RBF approximations are used to derive the homogeneous and particular solutions, respectively. Finally, the satisfaction of the solution consisting of the homogeneous and particular parts to the related governing equation and boundary conditions can produce a system of linear equations, which can be solved with the singular value decomposition （SVD） technique. In the computation, such crucial factors related to the MFS-RBF as the location of the virtual boundary, the differential and integrating strategies, and the variation of shape parameters in multi-quadric （MQ） are fully analyzed to provide useful reference.

关键词： meshless method analog equation method method of fundamental solution radial basis function singular value decomposition Helmholtz equation

Calculation method of the signal-to-noise ratio attribute of seismic data based on structural orientation

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Applied Geophysics 2019年第4期16卷 455-462,560页

作者： Zhao Yan Mao Ning-Bo Chen Xu Key Laboratory of Exploration Technologies for Oil and Gas Resources(Yangtze University) Ministry of EducationWuhanHubei 430100China School of Geophysics and Oil Resources Yangtze UniversityWuhanHubei 430100China Institute of Mud Logging Technology and Engineering Yangtze UniversityJingzhou 434023China.

At present,most signal-to-noise ratio(SNR)estimation methods can only calculate the global and not the local SNR of seismic *** paper proposes a calculation method of a structure-oriented-based seismic SNR *** purpose is to characterize the temporal and spatial variation of the seismic data ***,the local slope parameters of the seismic events are calculated using a plane wave decomposition ***,the singular value decomposition method is used to calculate the local seismic data SNR,thereby obtaining it in time and *** proposed method overcomes the insufficiency of a conventional global SNR to characterize any local seismic data features and uses the SNR as an attribute of seismic data to more accurately describe the signal-noise energy distribution characteristics of seismic data in time and *** results of a theoretical model test and real data processing show that the SNR attribute can be used not only for seismic data quality evaluation but also for analysis and evaluation of denoising methods.

关键词： Seismic data signal-to-noise ratio attribute local slope singular value decomposition structure-oriented

Spacecraft Attitude Tracking and Energy Storage Using Flywheels

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Chinese Journal of Aeronautics 2005年第1期18卷 1-7页

作者：贾英宏徐世杰 Department of Astronautic Engineering and Mechanics Harbin Institute of TechnologyHarbin 150001China School of Astronautics Beijing University of Aeronautics and Astronautics Beijing 100083China

The control law of the flywheel in an integrated power and attitude control system （IPACS） for a spacecraft is investigated. The flywheels are used as attitude control actuators as well as energy storage device. A feedback control law for attitude tracking is firstly developed by using Lyapunov approach, and then a torque based control law of the flywheel is studied. The control torque vector of the flywheel is decomposed into three parts which are orthogonal to one another by using the method of singularity value decomposition （SVD）. One part is used to provide the attitude control torque, another part is used to store energy with given power, and the last part is used to accomplish wheel speed equalization to avoid wheel saturation caused by large difference among the wheel spin rates. A management scheme for energy storage power using kinetic energy feedback is proposed to keep energy balance, which can avoid wheel saturation caused by superfluous energy. Numerical simulation results demonstrate the effectiveness of the control scheme.

关键词： integrated power and attitude control attitude tracking singular value decomposition energy storage flywheel