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A novel class of energy-preserving Runge-Kutta methods for the Korteweg-de Vries equation

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arXiv 2021年

作者： Chen, Yue Gong, Yuezheng Hong, Qi Wang, Chunwu Department of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing211106 China MIIT Nanjing211106 China Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing210023 China

In this paper, we present a quadratic auxiliary variable approach to develop a new class of energy-preserving Runge-Kutta methods for the Korteweg-de Vries equation. The quadratic auxiliary variable approach is first proposed to reformulate the original model into an equivalent system, which transforms the energy conservation law of the Korteweg-de Vries equation into two quadratic invariants of the reformulated system. Then the symplectic Runge-Kutta methods are directly employed for the reformulated model to arrive at a new kind of time semi-discrete schemes for the original problem. Under the consistent initial condition, the proposed methods are rigorously proved to maintain the original energy conservation law of the Korteweg-de Vries equation. In addition, the Fourier pseudo-spectral method is used for spatial discretization, resulting in fully discrete energy-preserving schemes. To implement the proposed methods effectively, we present a very efficient iterative technique, which not only greatly saves the calculation cost, but also achieves the purpose of practically preserving structure. Ample numerical results are addressed to confirm the expected order of accuracy, conservative property and efficiency of the proposed algorithms. Copyright © 2021, The Authors. All rights reserved.

关键词： Runge Kutta methods

Bottomoniumlike tetraquarks in a chiral quark model

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Physical Review D 2022年第1期106卷 014021-014021页

作者： Gang Yang Jialun Ping Jorge Segovia Department of Physics Zhejiang Normal University Jinhua 321004 China Department of Physics and Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal University Nanjing 210023 People’s Republic of China Departamento de Sistemas Físicos Químicos y Naturales Universidad Pablo de Olavide E-41013 Sevilla Spain

The low-lying bottomoniumlike tetraquarks bb¯qq¯ (q=u, d, s) with spin-parity JP=0+, 1+, and 2+, and isospin I=0, 1, or 12, are systematically investigated within the theoretical framework of real- and complex-scaling range of a chiral quark model, which has already been successfully applied in analysis of several multiquark systems. A complete four-body S-wave function, which includes meson-meson, diquark-antidiquark and K-type arrangements of quarks, along with all possible color configurations are considered. In the bb¯qq¯ (q=u, d) tetraquark system, we found resonance states of B(*)B¯(*), ϒω, ϒρ, and ηbρ nature with all possible I(JP) quantum numbers. Their masses are generally located in the energy range 11.0–11.3 GeV and their widths are less than 10 MeV. In addition, extremely narrow resonances, with two-meson strong decay widths less than 1.5 MeV, are obtained in both bb¯us¯ and bb¯ss¯ tetraquark systems. Particularly, four radial excitations of ϒK* and ηbK* are found at ∼11.1 GeV in JP=0+, 1+, and 2+ channels of bb¯us¯ system. One ϒ(1S)ϕ(2S) resonance state is obtained at 11.28 GeV in the JP=1+ sector.

关键词： Quantum chromodynamics Quark model Strong interaction

numerical Validations of the Tangent Linear Model for the Lorenz Equations

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Computer Modeling in Engineering & Sciences 2019年第7期120卷 83-104页

作者： Tengjin Zhao Jing Zhang Zhilin Li Zhiyue Zhang School of Mathematical Sciences Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex SystemsNanjing Normal UniversityNanjing210023China Department of Mathematics North Carolina State UniversityRaleighNC 27695-8205USA

The validity of the tangent linear model(TLM)is studied numerically using the example of the Lorenz equations in this *** relationship between the limit of the validity time of the TLM and initial perturbations for the Lorenz equations is investigated using the Monte Carlo sampling method.A new error function between the nonlinear and the linear evolution of the perturbations is ***,numerical sensitivity analysis is carried to establish the relationship between parameters and the validity of the TLM,such as the initial perturbation,the prediction time,the time step size and so on,by the method of mathematical statistics.

关键词： Lorenz model tangent linear model nonlinear model Monte Carlo

A hybrid phase field method for fluid-structure interactions in viscous fluids

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arXiv 2021年

作者： Hong, Qi Wang, Qi College of Science Nanjing University of Aeronautics and Astronautics Nanjing210016 China MIIT Nanjing211106 China Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex System Department of Mathematics University of South Carolina ColumbiaSC29208 United States

We present a novel computational modeling framework to numerically investigate fluid-structure interaction in viscous fluids using the phase field embedding method. Each rigid body or elastic structure immersed in the incompressible viscous fluid matrix, grossly referred to as the particle in this paper, is identified by a volume preserving phase field. The motion of the particle is driven by the fluid velocity in the matrix for passive particles or combined with its self-propelling velocity for active particles. The excluded volume effect between a pair of particles or between a particle and the boundary is modeled by a repulsive potential force. The drag exerted to the fluid by a particle is assumed proportional to its velocity. When the particle is rigid, its state is described by a zero velocity gradient tensor within the nonzero phase field that defines its profile and a constraining stress exists therein. While the particle is elastic, a linear constitutive equation for the elastic stress is provided within the particle domain. A hybrid, thermodynamically consistent hydrodynamic model valid in the entire computational domain is then derived for the fluid-particle ensemble using the generalized Onsager principle accounting for both rigid and elastic particles. Structure-preserving numerical algorithms are subsequently developed for the thermodynamically consistent model. numerical tests in 2D and 3D space are carried out to verify the rate of convergence and numerical examples are given to demonstrate the usefulness of the computational framework for simulating fluid-structure interactions for passive as well as self-propelling active particles in a viscous fluid matrix. Copyright © 2021, The Authors. All rights reserved.

关键词： Hydrodynamics

Bottomonium-like tetraquarks in a chiral quark model

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arXiv 2022年

作者： Yang, Gang Ping, Jialun Segovia, Jorge Department of Physics Zhejiang Normal University Jinhua321004 China Department of Physics Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal University Nanjing210023 China Departamento de Sistemas Físicos Químicos y Naturales Universidad Pablo de Olavide SevillaE-41013 Spain

The low-lying bottomonium-like tetraquarks b(Equation presented)q(Equation presented) (q = u, d, s) with spin-parity JP = 0+, 1+ and 2+, and isospin I = 0, 1 or 1/2, are systematically investigated within the theoretical framework of real- and complex-scaling range of a chiral quark model, which has already been successfully applied in analysis of several multiquark systems. A complete four-body S-wave function, which includes meson-meson, diquark-antidiquark and K-type arrangements of quarks, along with all possible color configurations are considered. In the b(Equation presented)q(Equation presented) (q = u, d) tetraquark system, we found resonance states of B(*)(Equation presented)(*), Υω, Υρ and ηbρ nature with all possible I(JP) quantum numbers. Their masses are generally located in the energy range 11.0 − 11.3 GeV and their widths are less than 10 MeV. In addition, extremely narrow resonances, with two-meson strong decay widths less than 1.5 MeV, are obtained in both b(Equation presented)u(Equation presented) and b(Equation presented)s(Equation presented) tetraquark systems. Particularly, four radial excitations of ΥK∗ and ηbK∗ are found at ∼ 11.1 GeV in JP = 0+, 1+ and 2+ channels of b(Equation presented)u(Equation presented) system. One Υ(1S)φ(2S) resonance state is obtained at 11.28 GeV in the JP = 1+ sector. Copyright © 2022, The Authors. All rights reserved.

关键词： Hadrons

Fully-charm and -bottom pentaquarks in a Lattice-QCD inspired quark model

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arXiv 2022年

The fully-charm and -bottom pentaquarks, i.e. ccccc¯ and bbbb¯b, with spin-parity quantum numbers JP = 1/2− , 3/2− and 5/2−, are investigated within a Lattice-QCD inspired quark model, which has already successfully described the recently announced fully-charm tetraquark candidate X(6900), and has also predicted several other fully-heavy tetraquarks. A powerful computational technique, based on the Gaussian expansion method combined with a complex-scaling range approach, is employed to predict, and distinguish, bound, resonance and scattering states of the mentioned five-body system. Both baryon-meson and diquark-diquark-antiquark configurations, along with all of their possible color channels are comprehensively considered. Narrow resonances are obtained in each spin-parity channel for the fully-charm and -bottom systems. Moreover, most of them seems to be compact multiquarks whose wave-functions are dominated by either hidden-color baryon-meson or diquark-diquark-antiquark structure, or by the coupling between them. Copyright © 2022, The Authors. All rights reserved.

关键词： Hadrons

Y(4626) in a chiral constituent quark model

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Physical Review D 2020年第5期101卷 054010-054010页

作者： Yue Tan Jialun Ping Department of Physics and Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal University Nanjing 210023 People's Republic of China

Recently, the Belle Collaboration reported a new exotic state Y(4620) with mass at 4625.9 MeV in the positronium annihilation process. Inspired by experiment, we study the tetraquark system cs¯sc¯ with quantum numbers JP=1− in the framework of chiral constituent quark model with the help of Gaussian expansion method. Two structures, diquark-antidiquark and meson-meson, with all possible color and spin configurations are considered. The result shows that no bound state can be formed. To investigate the possible resonance states, the real scaling method is employed. Several resonance states with energies 4354, 4408, 4469, 4497, and 4531 MeV are proposed. Taking into account the errors in calculating the qq¯ mesons, the system errors in the calculation of four-quark system are around 60–100 MeV. The resonance with energy 4531 MeV is possible the candidate of the newly found state Y(4620).

关键词： Hadron-hadron interactions Quark model

Investigation of qqqsq¯ pentaquarks in a chiral quark model

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arXiv 2020年

作者： Qin, Liting Tan, Yue Hu, Xiaohuang Ping, Jialun Department of Physics Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal University Nanjing210023 China

We investigate the pentaquark system qqqsq¯in a framework of chiral quark model. Two structures, (qqq)(sq¯) and (qqs)(qq¯), with all possible color, spin, flavor configurations are considered. The calculations show that there are several possible resonance states, Sigmaπ and NK¯ state with IJP = 012−, Σ∗π with IJP = 032−, Σ∗ρ with IJP = 025 −, ∆K¯ with IJP = 132− and ∆K¯ ∗ with IJP = 152−. Where the NK¯ state with IJP = 012− can be used to explain the Λ(1405), and together with another state Σπ is related to the two-pole structure of the scattering amplitude proposed before. The decay properties of Λ(1520) prevent the assignment of Σ∗π with IJP = 023 − to Λ(1520), although the energy ∼ 1518 MeV of Σ∗π is close to experimental value of Λ(1520). Other resonance states generally have a large width. Copyright © 2020, The Authors. All rights reserved.

关键词： Hadrons

QQqq in a chiral constituent quark model

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arXiv 2020年

作者： Tan, Yue Lu, Weichang Ping, Jialun Dept. of Physics and Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal University Nanjing210023 China

Inspired by Ξccreported by LHCb Collaboration and X(5568) reported by D0 Collaboration, the QQqq (Q = c, b, q = u, d) tetraquark states, are studied in the present work. With the help of Gaussian expansion method, two structures, diquark-antiquark and meson-meson, with all possible color configurations are investigated systematically in a chiral quark model to search for the possible stable states. The results show that there is no bound state in the isovector QQqq system, while there are rather deep bound states in the isoscalar bbqq, ccqq and bcqq systems. Mixing two structures of diquark-antidiquark and meson-meson can introduce more attractions and convert some unbound isoscalar states into shallow bound states. The large mass of the heavy quark is beneficial to the formation of the bound state. The separations between quarks are calculated to unravel the spacial structure of the system. Copyright © 2020, The Authors. All rights reserved.

关键词： Hadrons