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Showing 1 to 20 of 44 for “"Fokker-Planck Equation"”.
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Relaxation to equilibrium for kinetic Fokker-Planck equation
… behaviour of solutions $f_t$ of kinetic Fokker-Planck equation in $\mathbb{R}^d$, namely their convergence towards equilibrium $f_\infty$ in the form \[ \textrm{d}(f_t,f_\infty)\leq C_1 e^{-C_2 t}\textrm{d}(f_0,\mu) \] for appropriate distances $\textit{d}$ and constants $C_1 \geq 1$, …
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Solution of the Fokker-Planck Equation by Sequentially Optimized Meshfree Approximation
This thesis presents a technique to solve the Fokker-Planck equation by applica- tion of the Sequentially Optimized Meshfree Approximation (SOMA) method. It is well known that numerical solution of the Fokker-Planck equation is made di cult by the challenges of positivity enforcement, in nite …
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Efficient solution of the Fokker-Planck Equation via smooth particle hydrodynamics for nonlinear estimation
… systems is to solve the system's corresponding Fokker-Planck equation. The Fokker-Planck Equation (FPE) is the degenerate parabolic partial differential continuity equation that fully defines the evolution of the states' transition probability density function (PDF) over time. This also makes …
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Drift-diffusion of a vacancy in inhomogeneous media and its material constants : a Fokker-Planck equation approach with an application to foreign exchange data
… the mobility and diffusion coefficients of a Fokker-Planck equation describing a vacancy hopping in inhomogeneous media in one dimension under a directed stress. The study used the general master equation as a basis for a physical model because of the mesoscopic view that the change in average …
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Stochastic Averaging for Mechanical Systems
… method to reduce the number of differential equations required to describe the long term evolution of dynamical systems forced by small amplitude stochastic forces. There are three novelties in the work presented in this thesis. First, and perhaps most importantly, the systems studied exhibit …
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Modeling nonlinear stochastic ocean loads as diffusive stochastic differential equations to derive the dynamic responses of offshore wind turbines
… wind loads as diffusive stochastic differential equations (SDE) in a state space form to derive the response statistics of offshore structures, specifically wind turbines. Often, severe wind and wave systems are highly nonlinear and thus treatment as linear systems is not applicable, leading to …
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Deterministic and Stochastic Approaches to Relaxation to Equilibrium for Particle Systems
… is about convergence to equilibrium problems for equations coming from kinetic theory. The bulk of the work is about Hypocoercivity. Hypocoercivity is the phenomenon when a semigroup shows exponentially relaxation towards equilibrium without the corresponding coercivity (dissipativity) inequality …
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The Fokker-Planck and Related Equations in Theoretical Population Dynamics
… of a single species is modeled by a differential equation with initial condition(s) so that the number of organisms in the population is derived using some mechanism of growth, i.e. a growth rate function. However, such deterministic models are often highly unrealistic in population dynamics …
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Conformation and Rheology of Semiflexible Macromolecules Using Non-Equilibrium Brownian Dynamics and Monte Carlo Simulations
… Debye-Huckel potential is also present. The Fokker-Planck equation describing this chain is converted to a Stochastic Differential Equation (SDE) from which the simulation algorithm for the NEBD is obtained. In steady, potential flows, the solution of the Fokker-Planck equation exists and is …
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Fokker -Planck Modeling of Spherical Inertial Electrostatic, Virtual -Cathode Fusion Systems
… steady-state solutions of the bounce-averaged Fokker-Planck equation in which the Maxwellian ion population---absolutely confined in the electrostatic well---is dominant correspond to lowest ion recirculation powers (and hence highest fusion energy gains). Also, it is shown that the square-well …
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Probabilistic methods applied to fluctuating systems
… efficiency. In all three stochastic systems a Fokker-Planck equation is used to describe how the scale-dependent measure is correlated across nested scales.
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A Framework for Solving Parabolic Partial Differential Equations on Discrete Domains
… a class of parabolic partial differential equations on triangle mesh surfaces, including the Hamilton-Jacobi equation and the Fokker- Planck equation. Certain PDE in this class often have nonlinear or stiff terms that cannot be resolved with standard methods on triangle mesh surfaces. To …
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Transition Flow in Edge Plasmas: Solution of the Two-Fluid Region With Sources
… plasma and collisionless sheath, the linearized Fokker-Planck equation for the ions, in an intermediate collisionality region, is generalized to include an arbitrary source function. Nonisentropic effects due to the source function impact the isotropic part of the distribution function. A …
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Orbital effects on pitch angle diffusion of injected fast-ion beams in tokamaks
… a priori. In both cases an orbit average of the Fokker-Planck equation is taken, yielding a solution in velocity space variables velocity and pitch angle. In the first case, conditions in the form of a linear combination of co, counter, and trapped distributions or fluxes are matched at the orbit …
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Nonequilibrium transitions in quantum optical systems
… development is described by a Markovian master equation in the interaction picture. This is equivalent to a corresponding time development equation or Fokker-Planck equation in a vector space of c-numbers. In order to deal with the type of Fokker-Planck equation that results, we introduce a …
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Fokker-Planck models and globular cluster evolution
… cluster evolution using the orbit-averaged Fokker-Planck equation are compared with observations of the globular clusters M71 and NGC 6397. The first set of models studied includes a mass spectrum, a tidal boundary and allows for a central energy source from the formation, hardening and …
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The required ansatz to construct Lie point transformations and the symmetries of a first-order stochastic differential equation
… Lie point transformations of evolution-type equations from the contact transformation approach. We indicate that the Lie point transformations of the Fokker-Planck equation (FPE), which is a second-order linear parabolic partial differential equation (PDE), are projectable by using the …
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A Problem From Hamiltonian Mechanics With Time -Periodic Coefficients, Small Noise, and Degeneracy
… process can also be understood through the Fokker-Planck equation, and the gluing coefficients arise in the corresponding conservation of flux and in the continuity equation.
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