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Fulde-Ferrell-Like Molecular States in Spin-Orbit Coupled Ultracold Fermi Gases

Communications in Theoretical Physics 2017年第8期67卷 255-258页

作者：叶冲傅立斌 National Laboratory of Science and Technology on Computational Physics Institute of Applied Physics and Computational Mathematics Graduate School China Academy of Engineering Physics HEDPS CAPTand CICIFSA MoEPeking University

We study the molecular state in three-component Fermi gases with a single impurity of ~6Li immersing in a no-interacting Fermi sea of ^(40)K in the presence of an equal weight combination of Rashba-type and Dresselhaustype spin-orbit coupling. In the region where the Fermi sea has two disjointed Fermi surfaces, we find that there are two Fulde–Ferrell-like molecular states with dominating contributions from the lower helicity branch. Decreasing the scattering length or the spin-orbit coupled Fermi energy, we find the Fulde–Ferrell-like molecular state with small center-of-mass momentum is always energy favored and the other one will suddenly disappear.

关键词： spin-orbit coupling

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A dive into spectral inference networks: improved algorithms for self-supervised learning of continuous spectral representations

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applied mathematics and Mechanics(English Edition) 2023年第7期44卷 1199-1224页

作者： J.WU S.F.WANG P.PERDIKARIS Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA 19104U.S.A. Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania PhiladelphiaPA 19104U.S.A.

We propose a self-supervising learning framework for finding the dominant eigenfunction-eigenvalue pairs of linear and self-adjoint *** represent target eigenfunctions with coordinate-based neural networks and employ the Fourier positional encodings to enable the approximation of high-frequency *** formulate a self-supervised training objective for spectral learning and propose a novel regularization mechanism to ensure that the network finds the exact eigenfunctions instead of a space spanned by the ***,we investigate the effect of weight normalization as a mechanism to alleviate the risk of recovering linear dependent modes,allowing us to accurately recover a large number of *** effectiveness of our methods is demonstrated across a collection of representative benchmarks including both local and non-local diffusion operators,as well as high-dimensional time-series data from a video *** results indicate that the present algorithm can outperform competing approaches in terms of both approximation accuracy and computational cost.

关键词： spectral learning partial differential equation(PDE) neural network slow features analysis

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Channel Dependence of Dielectronic Recombination Rate Coefficients of Fe^(25+) Ion

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Chinese Physics Letters 1998年第4期15卷 263-265页

作者： DONG Chen-zhong WANG Jian-guo QU Yi-zhi Department of Physics Northwest Normal UniversityLanzhou 730070 Institute of Applied Physics and Computational Mathematics Beijing 100088 Graduate School of University of Science and Technology of China Beijing 100039

In the frame of quantum defect theory,the state-testate dielectronic recombination rate coefficients of Fe^(25+) ion are calculated by a simple relativistic configuration interaction *** calculated results are further expressed with a two-parameter fitting formula,and then the dependence of fitting parameters on radiative decay final channel is studied.

关键词： method decay radiative

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A Simple Framework of Conservative Algorithms for the Coupled Nonlinear Schrdinger Equations with Multiply Components

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Communications in Theoretical Physics 2014年第6期61卷 703-709页

作者：钱旭宋松和李伟斌 Department of Mathematics and Systems Science National University of Defense Technology Program in Applied and Computational Mathematics Princeton University State Key Laboratory of High Performance Computing National University of Defense Technology

Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time ***, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.

关键词： conservative algorithm coupled nonlinear SchrSdinger equation multiply components unstablewave

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Fragmentation dynamics of electron-impact double ionization of helium

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Chinese Physics B 2023年第6期32卷 9-15页

作者：刘士炜叶地发刘杰 Beijing Computational Science Research Center Beijing 100193China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing 100088China Graduate School China Academy of Engineering PhysicsBeijing 100193China HEDPS Center for Applied Physics and Technologyand College of EngineeringPeking UniversityBeijing 100871China

We study the double ionization dynamics of a helium atom impacted by electrons with full-dimensional classical trajectory Monte Carlo simulation. The excess energy is chosen to cover a wide range of values from 5 e V to 1 ke V for comparative study. At the lowest excess energy, i.e., close to the double-ionization threshold, it is found that the projectile momentum is totally transferred to the recoil-ion while the residual energy is randomly partitioned among the three outgoing electrons, which are then most probably emitted with an equilateral triangle configuration. Our results agree well with experiments as compared with early quantum-mechanical calculation as well as classical simulation based on a two-dimensional Bohr's model. Furthermore, by mapping the final momentum vectors event by event into a Dalitz plot,we unambiguously demonstrate that the ergodicity has been reached and thus confirm a long-term scenario conceived by Wannier. The time scale for such few-body thermalization, from the initial nonequilibrium state to the final microcanonical distribution, is only about 100 attoseconds. Finally, we predict that, with the increase of the excess energy, the dominant emission configuration undergoes a transition from equilateral triangle to T-shape and finally to a co-linear mode. The associated signatures of such configuration transition in the electron–ion joint momentum spectrum and triple-electron angular distribution are also demonstrated.

关键词： double ionization classical trajectory Monte Carlo simulation Wannier threshold law ergodicity

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Absolute change pivot rule for the simplex algorithm

Absolute change pivot rule for the simplex algorithm

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International MultiConference of Engineers and Computer Scientists, IMECS 2014

作者： Chankong, Kittiphong Intiyot, Boonyarit Sinapiromsaran, Krung Applied Mathematics and Computational Science Program Department of Mathematics and Computer Science Faculty of Science Chulalongkorn University Bangkok Thailand

ISBN: (纸本)9789881925336

The simplex algorithm is a widely used method for solving a linear programming problem (LP) which is first presented by George B. Dantzig. One of the important steps of the simplex algorithm is applying an appropriate pivot rule, the rule to select the entering variable. An effective pivot rule can lead to the optimal solution of LP with the small number of iterations. In a minimization problem, Dantzig's pivot rule selects an entering variable corresponding to the most negative reduced cost. The concept is to have the maximum improvement in the objective value per unit step of the entering variable. However, in some problems, Dantzig's rule may visit a large number of extreme points before reaching the optimal solution. In this paper, we propose a pivot rule that could reduce the number of such iterations over the Dantzig's pivot rule. The idea is to have the maximum improvement in the objective value function by trying to block a leaving variable that makes a little change in the objective function value as much as possible. Then we test and compare the efficacy of this rule with Dantzig' original rule.

关键词： Linear programming

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Blind recognition of k/n rate convolutional encoders from noisy observation

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Journal of Systems Engineering and Electronics 2017年第2期28卷 235-243页

作者： Li Huang Wengu Chen Enhong Chen Hong Chen Computer Science and Technology University of Science and Technology of China Hefei 230026 China Graduate School China Academy of Engineering Physics Beijing 100088 China Institute of Applied Physics and Computational Mathematics Beijing 100088 China

Blind recognition of convolutional codes is not only essential for cognitive radio, but also for non-cooperative context. This paper is dedicated to the blind identification of rate k/n convolutional encoders in a noisy context based on Walsh-Hadamard transformation and block matrix (WHT-BM). The proposed algorithm constructs a system of noisy linear equations and utilizes all its coefficients to recover parity check matrix. It is able to make use of fault-tolerant feature of WHT, thus providing more accurate results and achieving better error performance in high raw bit error rate (BER) regions. Moreover, it is more computationally efficient with the use of the block matrix (BM) method. © 2017 Beijing Institute of Aerospace Information.

关键词： Cognitive radio Convolution Convolutional codes Error correction Hadamard matrices Hadamard transforms Linear transformations Mathematical transformations Matrix algebra Signal encoding

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Prediction of methylene blue dye sorption to sulfonated date palm kernel biochar using statistical regression and machine learning methods and DFT studies

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Journal of Molecular Liquids 2025年 429卷

作者： Aigbe, Uyiosa Osagie Ukhurebor, Kingsley Eghonghon Onyancha, Robert Birundu Osibote, Adelaja Otolorin Hassaan, Mohamed A. ElKatory, Marwa R. Nemr, Ahmed El Center for Space Research North-West University Private Bag X6001 Potchefstroom2531 South Africa National Institute of Theoretical and Computational Science Johannesburg2000 South Africa School of Chemistry & Physics University of KwaZulu-Natal Pietermaritzburg Campus Private Bag X01 Scottsville3209 South Africa Department of Physics Faculty of Science Edo State University Uzairue Edo State Nigeria School of Physics and Earth Science Faculty of Applied Science and Technology Technical University of Kenya Nairobi Kenya College of Graduate Studies School of Interdisciplinary Research and Graduate Studies Muckleneuk Campus University of South Africa Pretoria0003 South Africa Department of Mathematics and Physics Cape Peninsula University of Technology Cape Town South Africa Kayet Bey Alexandria Elanfoushy Egypt Advanced Technology and New Materials Research Institute SRTA-City New Borg El-Arab City 21934 Alexandria Egypt

In this study, methylene blue (MB) dye adsorption to synthesised sulfonated date palm kernel biochar (SDPKB) was predicted and optimized using statistical-based regression approach (response surface methodology (RSM), machine-learning algorithms (artificial-neural-network (ANN), and adaptive-neuro-fuzzy-inference-system (ANFIS) models), and quantum chemistry calculations performed using density function theory (DFT) to link the electrical properties of the MB dye with the experimental findings. The percentage (%) of MB dye removed using SDPKB was found to be proportional to the biosorbent dosage and interaction time and inversely proportional to the solution pH and initial concentrations based on different used models results. It was observed that these models were accurate and comparable for the prediction of the removal of MB with coefficient of regression (R2) values of 0.9174, 0.9742, and 0.9999, mean square error (MSE) values of 181.71, 94.50, and 0.00000049, and root MSE (RMSE) values of 13.48, 9.72, and 0.0007 for the RSM, ANN, and ANFIS, respectively. The ANFIS model was found to be more effective in the prediction of MB sorption to SDPKB than the other models (ANFIS > ANN > RSM), and it was highly applicable in the sorption process. This study has revealed that the SDPKB can serve as a better biosorbent for MB adsorption. Therefore, this study will serve as a first reference point data that will be of great assistance in industrial effluent management as well as decision-making on the adoption of statistical and machine learning models for adsorption study. © 2025 Elsevier B.V.

关键词： Adversarial machine learning

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Error Estimate of a New Conservative Finite Difference Scheme for the Klein-Gordon-Dirac System

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Numerical mathematics(Theory,Methods and Applications) 2023年第1期16卷 140-164页

作者： Shasha Bian Yue Cheng Boling Guo Tingchun Wang The Graduate School of China Academy of Engineering Physics Beijing 100088China School of Mathematics and Statistics Nanjing University of Information Science and TechnologyNanjing 210044China Institute of Applied Physics and Computational Mathematics Beijing 100088China

In this paper,we derive and analyze a conservative Crank-Nicolson-type finite difference scheme for the Klein-Gordon-Dirac(KGD)*** from the derivation of the existing numerical methods given in literature where the numerical schemes are proposed by directly discretizing the KGD system,we translate the KGD equations into an equivalent system by introducing an auxiliary function,then derive a nonlinear Crank-Nicolson-type finite difference scheme for solving the equivalent *** scheme perfectly inherits the mass and energy conservative properties possessed by the KGD,while the energy preserved by the existing conservative numerical schemes expressed by two-level’s solution at each time *** using energy method together with the‘cut-off’function technique,we establish the optimal error estimate of the numerical solution,and the convergence rate is O(τ^(2)+h^(2))in l∞-norm with time stepτand mesh size *** experiments are carried out to support our theoretical conclusions.

关键词： Klein-Gordon-Dirac equation nonlinear finite difference scheme conservation error analysis

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A Gas-Kinetic Scheme for Collisional Vlasov-Poisson Equations in Cylindrical Coordinates

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Communications in computational Physics 2022年第8期32卷 779-809页

作者： Yi Wang Jiexing Zhang Guoxi Ni University of Science and Technology of China HefeiChina Graduate school of China Academy of Engineering Physics BeijingChina Institute of Applied Physics and computational mathematics BeijingChina

Many configurations in plasma physics are axisymmetric,it will be more convenient to depict them in cylindrical coordinates compared with Cartesian *** this paper,a gas-kinetic scheme for collisional Vlasov-Poisson equations in cylindrical coordinates is proposed,our algorithm is based on Strang *** equation is divided into two parts,one is the kinetic transport-collision part solved by multiscale gas-kinetic scheme,and the other is the acceleration part solved by a Runge-Kutta *** asymptotic preserving property of whole algorithm is proved and it’s applied on the study of charge separation problem in plasma edge and 1D Z-pinch *** results show it can capture the process fromnon-equilibrium to equilibrium state by Coulomb collisions,and numerical accuracy is obtained.

关键词： Vlasov-BGK-Poisson equations cylindrical coordinates gas-kinetic scheme asymptotic preserving property Coulomb collisions

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