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Relevant bibliographies by topics / Explicit symplectic integrator

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Journal articles

Academic literature on the topic 'Explicit symplectic integrator'

Author: Grafiati

Published: 8 February 2025

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Journal articles on the topic "Explicit symplectic integrator"

1

Hu, Ai-Rong, and Guo-Qing Huang. "Application of Explicit Symplectic Integrators in the Magnetized Reissner–Nordström Spacetime." Symmetry 15, no. 5 (2023): 1094. http://dx.doi.org/10.3390/sym15051094.

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In recent works by Wu and Wang a class of explicit symplectic integrators in curved spacetimes was presented. Different splitting forms or appropriate choices of time-transformed Hamiltonians are determined based on specific Hamiltonian problems. As its application, we constructed a suitable explicit symplectic integrator for surveying the dynamics of test particles in a magnetized Reissner–Nordström spacetime. In addition to computational efficiency, the scheme exhibits good stability and high precision for long-term integration. From the global phase-space structure of Poincaré sections, the

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2

Tu, Xiongbiao, Qiao Wang, and Yifa Tang. "Highly Efficient Numerical Integrator for the Circular Restricted Three-Body Problem." Symmetry 14, no. 9 (2022): 1769. http://dx.doi.org/10.3390/sym14091769.

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The dynamic equation of a mass point in the circular restricted three-body problem is governed by Coriolis and centrifugal force, in addition to a co-rotating potential relative to the frame. In this paper, we provide an explicit, symmetric integrator for this problem. Such an integrator is more efficient than the symplectic Euler method and the Gauss Runge–Kutta method as regards this problem. In addition, we proved the integrator is symplectic by the discrete Hamilton’s principle. Several groups of numerical experiments demonstrated the precision and high efficiency of the integrator in the

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3

Nettesheim, Peter, Folkmar A. Bornemann, Burkhard Schmidt, and Christof Schütte. "An explicit and symplectic integrator for quantum-classical molecular dynamics." Chemical Physics Letters 256, no. 6 (1996): 581–88. http://dx.doi.org/10.1016/0009-2614(96)00471-x.

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4

Hu, Airong, and Guoqing Huang. "Chaos in a Magnetized Brane-World Spacetime Using Explicit Symplectic Integrators." Universe 8, no. 7 (2022): 369. http://dx.doi.org/10.3390/universe8070369.

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A brane-world metric with an external magnetic field is a modified theory of gravity. It is suitable for the description of compact sources on the brane such as stars and black holes. We design a class of explicit symplectic integrators for this spacetime and use one of the integrators to investigate how variations of the parameters affect the motion of test particles. When the magnetic field does not vanish, the integrability of the system is destroyed. Thus, the onset of chaos can be allowed under some circumstances. Chaos easily occurs when the electromagnetic parameter becomes large enough

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5

Huang, Zongqiang, Guoqing Huang, and Airong Hu. "Application of Explicit Symplectic Integrators in a Magnetized Deformed Schwarzschild Black Spacetime." Astrophysical Journal 925, no. 2 (2022): 158. http://dx.doi.org/10.3847/1538-4357/ac3edf.

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Abstract Following the latest work of Wu et al., we construct time-transformed explicit symplectic schemes for a Hamiltonian system on the description of charged particles moving around a deformed Schwarzschild black hole with an external magnetic field. Numerical tests show that such schemes have good performance in stabilizing energy errors without secular drift. Meantime, tangent vectors are solved from the variational equations of the system with the aid of an explicit symplectic integrator. The obtained tangent vectors are used to calculate several chaos indicators, including Lyapunov cha

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6

Wang 王, Long 龙. "New Insight of Time-transformed Symplectic Integrator. I. Hybrid Methods for Hierarchical Triples." Astrophysical Journal 978, no. 1 (2024): 65. https://doi.org/10.3847/1538-4357/ad98f3.

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Abstract Accurate N-body simulations of multiple systems such as binaries and triples are essential for understanding the formation and evolution of interacting binaries and binary mergers, including gravitational wave sources, blue stragglers, and X-ray binaries. The logarithmic time-transformed explicit symplectic integrator (LogH), also known as algorithmic regularization, is a state-of-the-art method for this purpose. However, we show that this method is accurate for isolated Kepler orbits because of its ability to trace Keplerian trajectories, but much less accurate for hierarchical tripl

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7

Wang, Long, Keigo Nitadori, and Junichiro Makino. "A slow-down time-transformed symplectic integrator for solving the few-body problem." Monthly Notices of the Royal Astronomical Society 493, no. 3 (2020): 3398–411. http://dx.doi.org/10.1093/mnras/staa480.

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ABSTRACT An accurate and efficient method dealing with the few-body dynamics is important for simulating collisional N-body systems like star clusters and to follow the formation and evolution of compact binaries. We describe such a method which combines the time-transformed explicit symplectic integrator and the slow-down method. The former conserves the Hamiltonian and the angular momentum for a long-term evolution, while the latter significantly reduces the computational cost for a weakly perturbed binary. In this work, the Hamilton equations of this algorithm are analysed in detail. We mat

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8

Pagliantini, Cecilia. "Dynamical reduced basis methods for Hamiltonian systems." Numerische Mathematik 148, no. 2 (2021): 409–48. http://dx.doi.org/10.1007/s00211-021-01211-w.

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AbstractWe consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main factors: the rich geometric structure encoding the physical and stability properties of the dynamics and its local low-rank nature. To address these aspects, we propose a nonlinear structure-preserving model reduction where the reduced phase space evolves in time. In the spirit of dynamical low-rank approximation, the reduced dynamics is obtained by

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9

Cotter, Colin. "Data assimilation on the exponentially accurate slow manifold." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1991 (2013): 20120300. http://dx.doi.org/10.1098/rsta.2012.0300.

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I describe an approach to data assimilation making use of an explicit map that defines a coordinate system on the slow manifold in the semi-geostrophic scaling in Lagrangian coordinates, and apply the approach to a simple toy system that has previously been proposed as a low-dimensional model for the semi-geostrophic scaling. The method can be extended to Lagrangian particle methods such as Hamiltonian particle–mesh and smooth-particle hydrodynamics applied to the rotating shallow-water equations, and many of the properties will remain for more general Eulerian methods. Making use of Hamiltoni

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10

Sun, Xin, Xin Wu, Yu Wang, Chen Deng, Baorong Liu, and Enwei Liang. "Dynamics of Charged Particles Moving around Kerr Black Hole with Inductive Charge and External Magnetic Field." Universe 7, no. 11 (2021): 410. http://dx.doi.org/10.3390/universe7110410.

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We mainly focus on the effects of small changes of parameters on the dynamics of charged particles around Kerr black holes surrounded by an external magnetic field, which can be considered as a tidal environment. The radial motions of charged particles on the equatorial plane are studied via an effective potential. It is found that the particle energies at the local maxima values of the effective potentials increase with an increase in the black hole spin and the particle angular momenta, but decrease with an increase of one of the inductive charge parameter and magnetic field parameter. The r

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