The Hamiltonian structure and Euler-Poincaré formulation of the Vlasov-Maxwell and gyrokinetic systems
暂无分享,去创建一个
H. Qin | W. Tang | C. Chandre | W. M. Tang | J. Squire | H. Qin | W. Tang | J. Squire | C. Chandre
[1] S. Reich,et al. Numerical methods for Hamiltonian PDEs , 2006 .
[2] Hong Qin,et al. Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme , 2012, 1401.6723.
[3] Keenan Crane,et al. Energy-preserving integrators for fluid animation , 2009, SIGGRAPH 2009.
[4] R. McLachlan,et al. Explicit Lie-Poisson integration and the Euler equations. , 1993, Physical review letters.
[5] Morrison,et al. Local conservation laws for the Maxwell-Vlasov and collisionless kinetic guiding-center theories. , 1985, Physical review. A, General physics.
[6] J. Marsden,et al. Structure-preserving discretization of incompressible fluids , 2009, 0912.3989.
[7] Philip J. Morrison,et al. Poisson brackets for fluids and plasmas , 1982 .
[8] William McCay Nevins,et al. Geometric gyrokinetic theory for edge plasmasa) , 2007 .
[9] Darryl D. Holm,et al. The Euler–Poincaré Equations and Semidirect Products with Applications to Continuum Theories , 1998, chao-dyn/9801015.
[10] A. Brizard,et al. Hamiltonian formulation of reduced Vlasov-Maxwell equations , 2008, 1211.0850.
[11] Darryl D. Holm,et al. Direct numerical simulations of the Navier–Stokes alpha model , 1999, Physica D: Nonlinear Phenomena.
[12] Darryl D. Holm,et al. Euler-Poincare Formulation Of Hybrid Plasma Models , 2010, 1012.0999.
[13] M. Kruskal,et al. On the Stability of Plasma in Static Equilibrium , 1958 .
[14] P. Similon. Conservation laws for relativistic guiding-center plasma , 1985 .
[15] Darryl D. Holm,et al. Multisymplectic formulation of fluid dynamics using the inverse map , 2007, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[16] New method of deriving local energy- and momentum-conserving Maxwell-collisionless drift-kinetic and gyrokinetic theories: basic theory , 2004, Journal of Plasma Physics.
[17] Alain J. Brizard,et al. Variational principle for nonlinear gyrokinetic Vlasov–Maxwell equations , 2000 .
[18] J. Marsden,et al. Discrete mechanics and variational integrators , 2001, Acta Numerica.
[19] D. Schmidt,et al. Accuracy and conservation properties of a three-dimensional unstructured staggered mesh scheme for fluid dynamics , 2002 .
[20] P. Morrison,et al. Noncanonical Hamiltonian Density Formulation of Hydrodynamics and Ideal Magnetohydrodynamics. , 1980 .
[21] F. Jenko,et al. Gyrokinetic Large Eddy Simulations , 2011, 1104.2422.
[22] P. Morrison,et al. The energy-momentum tensor for the linearized Maxwell-Vlasov and kinetic guiding center theories , 1991 .
[23] A. Brizard,et al. New variational principle for the Vlasov-Maxwell equations. , 2000, Physical review letters.
[24] T. Flå. Action principle and the Hamiltonian formulation for the Maxwell–Vlasov equations on a symplectic leaf , 1994 .
[25] Noether formalism with gauge-invariant variations , 2004 .
[26] F. Low,et al. A Lagrangian formulation of the Boltzmann-Vlasov equation for plasmas , 1958, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.
[27] J. Krommes,et al. Nonlinear gyrokinetic equations , 1983 .
[28] R. Littlejohn. Hamiltonian perturbation theory in noncanonical coordinates , 1982 .
[29] B. Scott,et al. Energetic consistency and momentum conservation in the gyrokinetic description of tokamak plasmas , 2010, 1008.1244.
[30] P. Morrison,et al. The Maxwell-Vlasov equations as a continuous hamiltonian system , 1980 .
[31] H. Gümral. Geometry of plasma dynamics. I. Group of canonical diffeomorphisms , 2010 .
[32] Jerrold E. Marsden,et al. Geometric Computational Electrodynamics with Variational Integrators and Discrete Differential Forms , 2007, 0707.4470.
[33] P. Morrison,et al. The Hamiltonian description of incompressible fluid ellipsoids , 2008, 0811.4439.
[34] Darryl D. Holm,et al. The Effect of Subfilter-Scale Physics on Regularization Models , 2010, J. Sci. Comput..
[35] Hong Qin,et al. Variational symplectic algorithm for guiding center dynamics in the inner magnetosphere , 2011 .
[36] J. Krommes,et al. The Gyrokinetic Description of Microturbulence in Magnetized Plasmas , 2012 .
[37] Cristel Chandre,et al. On the use of projectors for Hamiltonian systems and their relationship with Dirac brackets , 2012, 1205.2347.
[38] Alain J. Brizard,et al. Foundations of Nonlinear Gyrokinetic Theory , 2007 .
[39] J. Marsden,et al. Asynchronous Variational Integrators , 2003 .
[40] F. Jenko,et al. Dynamic procedure for filtered gyrokinetic simulations , 2011, 1110.0747.
[41] Jerrold E. Marsden,et al. Lagrangian Averaging for Compressible Fluids , 2005, Multiscale Model. Simul..
[42] Hong Qin,et al. Variational symplectic integrator for long-time simulations of the guiding-center motion of charged particles in general magnetic fields. , 2008, Physical review letters.
[43] H. Sugama. Gyrokinetic field theory , 2000 .
[44] Jerrold E. Marsden,et al. The Hamiltonian structure of the Maxwell-Vlasov equations , 1982 .
[45] Margaret H. Wright,et al. The opportunities and challenges of exascale computing , 2010 .
[46] Evan S. Gawlik,et al. Geometric, variational discretization of continuum theories , 2010, 1010.4851.
[47] Derivation of reduced two-dimensional fluid models via Dirac’s theory of constrained Hamiltonian systems , 2010, 1001.4629.
[48] Yiying Tong,et al. Stable, circulation-preserving, simplicial fluids , 2007, TOGS.
[49] Jerrold E. Marsden,et al. Nonlinear stability of fluid and plasma equilibria , 1985 .
[50] P. Morrison,et al. On the Hamiltonian formulation of incompressible ideal fluids and magnetohydrodynamics via Dirac's theory of constraints , 2011, 1110.6891.
[51] D. Pfirsch,et al. Poisson brackets for guiding-centre and gyrocentre theories , 2005, Journal of Plasma Physics.
[52] C. Tronci. A Lagrangian kinetic model for collisionless magnetic reconnection , 2012, 1208.5674.
[53] J. Marsden,et al. Multisymplectic Geometry, Variational Integrators, and Nonlinear PDEs , 1998, math/9807080.
[54] Alain J. Brizard,et al. Nonlinear gyrokinetic theory for finite‐beta plasmas , 1988 .
[55] Jerrold E. Marsden,et al. Hamilton–Pontryagin Integrators on Lie Groups Part I: Introduction and Structure-Preserving Properties , 2008, Found. Comput. Math..
[56] Darryl D. Holm. Lagrangian averages, averaged Lagrangians, and the mean effects of fluctuations in fluid dynamics. , 2002, Chaos.
[57] P. Morrison,et al. A general theory for gauge-free lifting , 2010, 1210.6564.
[58] Darryl D. Holm,et al. Camassa-Holm Equations as a Closure Model for Turbulent Channel and Pipe Flow , 1998, chao-dyn/9804026.
[59] T. Hahm,et al. Turbulent transport reduction by zonal flows: massively parallel simulations , 1998, Science.
[60] Huanchun Ye,et al. Action principles for the Vlasov equation , 1992 .
[61] Paul Adrien Maurice Dirac. Generalized Hamiltonian dynamics , 1950 .
[62] Noether methods for fluids and plasmas , 2004, Journal of Plasma Physics.
[63] T. Ribeiro,et al. Nonlinear Dynamics in the Tokamak Edge , 2010 .
[64] Covariant Lagrangian Methods of Relativistic Plasma Theory , 2003, physics/0307148.
[65] H. Qin,et al. Gauge properties of the guiding center variational symplectic integrator , 2012, 1401.6725.