The Experts below are selected from a list of 58461 Experts worldwide ranked by ideXlab platform
Ruili Zhang - One of the best experts on this subject based on the ideXlab platform.
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local energy Conservation Law for a spatially discretized hamiltonian vlasov maxwell system
Physics of Plasmas, 2017Co-Authors: Jianyuan Xiao, Hong Qin, Jian Liu, Ruili ZhangAbstract:Because of the unparalleled long-term conservative property, the structure-preserving geometric algorithm for the Vlasov-Maxwell (VM) equations is currently an active research topic. We show that spatially discretized Hamiltonian systems for the VM equations admit a local energy Conservation Law in space-time. This is accomplished by proving that a sum-free and only locally non-zero scalar field can always be written as the divergence of a vector field that is only locally non-zero. The result demonstrates that the Hamiltonian discretization of Vlasov-Maxwell system can preserve local Conservation Laws, in addition to the symplectic structure, both of which are the intrinsic physical properties of infinite dimensional Hamiltonian systems in physics.
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local energy Conservation Law for spatially discretized hamiltonian vlasov maxwell system
arXiv: Computational Physics, 2016Co-Authors: Jianyuan Xiao, Hong Qin, Jian Liu, Ruili ZhangAbstract:Structure-preserving geometric algorithm for the Vlasov-Maxwell (VM) equations is currently an active research topic. We show that spatially-discretized Hamiltonian systems for the VM equations admit a local energy Conservation Law in space-time. This is accomplished by proving that for a general spatially-discretized system, a global Conservation Law always implies a discrete local Conservation Law in space-time when the algorithm is local. This general result demonstrates that Hamiltonian discretizations can preserve local Conservation Laws, in addition to the symplectic structure, both of which are the intrinsic physical properties of infinite dimensional Hamiltonian systems in physics.
Hong Qian - One of the best experts on this subject based on the ideXlab platform.
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a thermodynamic theory of ecology helmholtz theorem for lotka volterra equation extended Conservation Law and stochastic predator prey dynamics
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2015Co-Authors: Hong QianAbstract:We carry out mathematical analyses, a la Helmholtz’s and Boltzmann’s 1884 studies of monocyclic Newtonian dynamics, for the Lotka–Volterra (LV) equation exhibiting predator–prey oscillations. In doing so, a novel ‘thermodynamic theory’ of ecology is introduced. An important feature, absent in the classical mechanics, of ecological systems is a natural stochastic population dynamic formulation of which the deterministic equation (e.g. the LV equation studied) is the infinite population limit. Invariant density for the stochastic dynamics plays a central role in the deterministic LV dynamics. We show how the Conservation Law along a single trajectory extends to incorporate both variations in a model parameter α and in initial conditions: Helmholtz’s theorem establishes a broadly valid Conservation Law in a class of ecological dynamics. We analyse the relationships among mean ecological activeness θ , quantities characterizing dynamic ranges of populations A and α , and the ecological force F α . The analyses identify an entire orbit as a stationary ecology, and establish the notion of an ‘equation of ecological states’. Studies of the stochastic dynamics with finite populations show the LV equation as the robust, fast cyclic underlying behaviour. The mathematical narrative provides a novel way of capturing long-term dynamical behaviours with an emergent conservative ecology .
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a thermodynamic theory of ecology helmholtz theorem for lotka volterra equation extended Conservation Law and stochastic predator prey dynamics
arXiv: Mathematical Physics, 2014Co-Authors: Hong QianAbstract:We carry out mathematical analyses, {\em \`{a} la} Helmholtz's and Boltzmann's 1884 studies of monocyclic Newtonian dynamics, for the Lotka-Volterra (LV) equation exhibiting predator-prey oscillations. In doing so a novel "thermodynamic theory" of ecology is introduced. An important feature, absent in the classical mechanics, of ecological systems is a natural stochastic population dynamic formulation of which the deterministic equation (e.g., the LV equation studied) is the infinite population limit. Invariant density for the stochastic dynamics plays a central role in the deterministic LV dynamics. We show how the Conservation Law along a single trajectory extends to incorporate both variations in a model parameter $\alpha$ and in initial conditions: Helmholtz's theorem establishes a broadly valid Conservation Law in a class of ecological dynamics. We analyze the relationships among mean ecological activeness $\theta$, quantities characterizing dynamic ranges of populations $\mathcal{A}$ and $\alpha$, and the ecological force $F_{\alpha}$. The analyses identify an entire orbit as a stationary ecology, and establish the notion of "equation of ecological states". Studies of the stochastic dynamics with finite populations show the LV equation as the robust, fast cyclic underlying behavior. The mathematical narrative provides a novel way of capturing long-term dynamical behaviors with an emergent {\em conservative ecology}.
Hong Qin - One of the best experts on this subject based on the ideXlab platform.
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local energy Conservation Law for a spatially discretized hamiltonian vlasov maxwell system
Physics of Plasmas, 2017Co-Authors: Jianyuan Xiao, Hong Qin, Jian Liu, Ruili ZhangAbstract:Because of the unparalleled long-term conservative property, the structure-preserving geometric algorithm for the Vlasov-Maxwell (VM) equations is currently an active research topic. We show that spatially discretized Hamiltonian systems for the VM equations admit a local energy Conservation Law in space-time. This is accomplished by proving that a sum-free and only locally non-zero scalar field can always be written as the divergence of a vector field that is only locally non-zero. The result demonstrates that the Hamiltonian discretization of Vlasov-Maxwell system can preserve local Conservation Laws, in addition to the symplectic structure, both of which are the intrinsic physical properties of infinite dimensional Hamiltonian systems in physics.
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local energy Conservation Law for spatially discretized hamiltonian vlasov maxwell system
arXiv: Computational Physics, 2016Co-Authors: Jianyuan Xiao, Hong Qin, Jian Liu, Ruili ZhangAbstract:Structure-preserving geometric algorithm for the Vlasov-Maxwell (VM) equations is currently an active research topic. We show that spatially-discretized Hamiltonian systems for the VM equations admit a local energy Conservation Law in space-time. This is accomplished by proving that for a general spatially-discretized system, a global Conservation Law always implies a discrete local Conservation Law in space-time when the algorithm is local. This general result demonstrates that Hamiltonian discretizations can preserve local Conservation Laws, in addition to the symplectic structure, both of which are the intrinsic physical properties of infinite dimensional Hamiltonian systems in physics.
Jianyuan Xiao - One of the best experts on this subject based on the ideXlab platform.
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local energy Conservation Law for a spatially discretized hamiltonian vlasov maxwell system
Physics of Plasmas, 2017Co-Authors: Jianyuan Xiao, Hong Qin, Jian Liu, Ruili ZhangAbstract:Because of the unparalleled long-term conservative property, the structure-preserving geometric algorithm for the Vlasov-Maxwell (VM) equations is currently an active research topic. We show that spatially discretized Hamiltonian systems for the VM equations admit a local energy Conservation Law in space-time. This is accomplished by proving that a sum-free and only locally non-zero scalar field can always be written as the divergence of a vector field that is only locally non-zero. The result demonstrates that the Hamiltonian discretization of Vlasov-Maxwell system can preserve local Conservation Laws, in addition to the symplectic structure, both of which are the intrinsic physical properties of infinite dimensional Hamiltonian systems in physics.
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local energy Conservation Law for spatially discretized hamiltonian vlasov maxwell system
arXiv: Computational Physics, 2016Co-Authors: Jianyuan Xiao, Hong Qin, Jian Liu, Ruili ZhangAbstract:Structure-preserving geometric algorithm for the Vlasov-Maxwell (VM) equations is currently an active research topic. We show that spatially-discretized Hamiltonian systems for the VM equations admit a local energy Conservation Law in space-time. This is accomplished by proving that for a general spatially-discretized system, a global Conservation Law always implies a discrete local Conservation Law in space-time when the algorithm is local. This general result demonstrates that Hamiltonian discretizations can preserve local Conservation Laws, in addition to the symplectic structure, both of which are the intrinsic physical properties of infinite dimensional Hamiltonian systems in physics.
Jian Liu - One of the best experts on this subject based on the ideXlab platform.
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local energy Conservation Law for a spatially discretized hamiltonian vlasov maxwell system
Physics of Plasmas, 2017Co-Authors: Jianyuan Xiao, Hong Qin, Jian Liu, Ruili ZhangAbstract:Because of the unparalleled long-term conservative property, the structure-preserving geometric algorithm for the Vlasov-Maxwell (VM) equations is currently an active research topic. We show that spatially discretized Hamiltonian systems for the VM equations admit a local energy Conservation Law in space-time. This is accomplished by proving that a sum-free and only locally non-zero scalar field can always be written as the divergence of a vector field that is only locally non-zero. The result demonstrates that the Hamiltonian discretization of Vlasov-Maxwell system can preserve local Conservation Laws, in addition to the symplectic structure, both of which are the intrinsic physical properties of infinite dimensional Hamiltonian systems in physics.
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local energy Conservation Law for spatially discretized hamiltonian vlasov maxwell system
arXiv: Computational Physics, 2016Co-Authors: Jianyuan Xiao, Hong Qin, Jian Liu, Ruili ZhangAbstract:Structure-preserving geometric algorithm for the Vlasov-Maxwell (VM) equations is currently an active research topic. We show that spatially-discretized Hamiltonian systems for the VM equations admit a local energy Conservation Law in space-time. This is accomplished by proving that for a general spatially-discretized system, a global Conservation Law always implies a discrete local Conservation Law in space-time when the algorithm is local. This general result demonstrates that Hamiltonian discretizations can preserve local Conservation Laws, in addition to the symplectic structure, both of which are the intrinsic physical properties of infinite dimensional Hamiltonian systems in physics.