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An entropy scheme for the FokkerPlanck collision operator of plasma kinetic theory
, 1994
"... this paper is to propose a finite difference sheme for the FokkerPlanck equation (1.1)(1.3) which preserves the conservation laws of mass, momentum and energy. Previous finite difference conservative schemes have been proposed in [3] for the isotropic case and in [1214] for the azimuthal symmetr ..."
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Cited by 24 (1 self)
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this paper is to propose a finite difference sheme for the FokkerPlanck equation (1.1)(1.3) which preserves the conservation laws of mass, momentum and energy. Previous finite difference conservative schemes have been proposed in [3] for the isotropic case and in [1214] for the azimuthal
A guidingcenter FokkerPlanck collision operator for nonuniform magnetic fields, Phys. Plasmas 11
, 2004
"... A new formulation for collisional kinetic theory is presented based on the use of Lietransform methods to eliminate fast orbital time scales from a general bilinear collision operator. As an application of this new formalism, a general guidingcenter bilinear FokkerPlanck (FP) collision operator is ..."
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Cited by 6 (0 self)
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A new formulation for collisional kinetic theory is presented based on the use of Lietransform methods to eliminate fast orbital time scales from a general bilinear collision operator. As an application of this new formalism, a general guidingcenter bilinear FokkerPlanck (FP) collision operator
An implicit energyconservative 2D Fokker–Planck algorithm
 II. Jacobianfree Newton–Krylov solver, J. Comput. Phys
, 2000
"... Numerical energy conservation in Fokker–Planck problems requires the energy moment of the Fokker–Planck equation to cancel exactly. However, standard discretization techniques not only do not observe this requirement (thus precluding exact energy conservation), but they also demand very refined mes ..."
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Cited by 5 (2 self)
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collision operator using Maxwell stress tensor formalism. As a result, the Fokker–Planck collision operator takes the form of a double divergence operating on a tensor, which is suitable for particle and energy conservative differencing. Numerical results show that the new discretization scheme improves
The FokkerPlanck operator as . . .
, 2001
"... We derive the FokkerPlanck operator describing a highly forward peaked scattering process in the linear transport equation, in anisotropic media, as a formal asymptotic limit of the exact integral operator. The resulting operator, being both convective and diffusive in angle and energy variables ..."
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We derive the FokkerPlanck operator describing a highly forward peaked scattering process in the linear transport equation, in anisotropic media, as a formal asymptotic limit of the exact integral operator. The resulting operator, being both convective and diffusive in angle and energy
FokkerPlanck and quasilinear codes
 Comp. Phys. Rep
, 1986
"... The interaction of radiofrequency waves with a plasma is described by a Fokker–Planck equation with an added quasilinear term. Methods for solving this equation on a computer are discussed. ..."
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Cited by 2 (0 self)
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The interaction of radiofrequency waves with a plasma is described by a Fokker–Planck equation with an added quasilinear term. Methods for solving this equation on a computer are discussed.
Local and global Fokker–Planck
, 2012
"... neoclassical calculations showing flow and bootstrap current modification in a pedestal ..."
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neoclassical calculations showing flow and bootstrap current modification in a pedestal
The Variational Formulation of the FokkerPlanck Equation
 SIAM J. Math. Anal
, 1999
"... The FokkerPlanck equation, or forward Kolmogorov equation, describes the evolution of the probability density for a stochastic process associated with an Ito stochastic differential equation. It pertains to a wide variety of timedependent systems in which randomness plays a role. In this paper, ..."
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Cited by 285 (22 self)
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The FokkerPlanck equation, or forward Kolmogorov equation, describes the evolution of the probability density for a stochastic process associated with an Ito stochastic differential equation. It pertains to a wide variety of timedependent systems in which randomness plays a role. In this paper
Multipole expansions for the FokkerPlanck equation
"... We give a sequence of operators approximating the FokkerPlanckLandau collision operator. This sequence is obtained by aplying the fast multipole method based on the work by Greengard and Rocklin [17], and tends to the exact FokkerPlanckLandau operator with an arbitrary accuracy. These operators s ..."
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Cited by 4 (2 self)
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We give a sequence of operators approximating the FokkerPlanckLandau collision operator. This sequence is obtained by aplying the fast multipole method based on the work by Greengard and Rocklin [17], and tends to the exact FokkerPlanckLandau operator with an arbitrary accuracy. These operators
Numerical Solution of the FokkerPlanck Approximation of the
, 2005
"... The chemical master equation (CME) describes the probability for the discrete molecular copy numbers that define the state of a chemical system. Each molecular species in the chemical model adds a dimension to the state space. The CME is a differencedifferential equation which can be solved numeric ..."
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numerically if the state space is truncated at an upper limit of the copy number in each dimension. The size of the truncated CME suffers from an exponential growth for an increasing number of chemical species. In this thesis the CME is approximated by a continuous FokkerPlanck equation (FPE) which makes
Results 1  10
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245,453