Diffusion of rays in random media.
Fokker-Planck equation applied to probability density for finding rays larger than correlation distance during propagation in random medium
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Fokker-Planck equation applied to probability density for finding rays larger than correlation distance during propagation in random medium
Absolute value type of early-late gate bit synchronizer phase noise performance determined by Fokker-Planck method, comparing results with different circuits performance
Digital data transition tracking loop mean square phase noise computed as function of input SNR by Fokker-Planck technique
Hybrid phase lock loop model derived by Fokker-Planck technique
Tracking systems synthesis and performance analysis based on continuous Markov processes theory, particularly Fokker-Planck equation
Brownian motion for large viscosity, deriving modified Fokker-Planck equation based on quasi- Huygens relation
Model probability distribution for hybrid phase locked loop derived by Fokker-Planck techniques, providing superior performance for all SNR
Transient behavior of first order phase locked loop in presence of noise, solving Fokker-Planck equation for loop dynamics by numerical integration
Absolute value type early-late gate bit synchronizer steady state phase noise performance evaluation by Fokker-Planck method
Fokker-Planck boundary value solutions to transient phase error response of nonlinear phase locked tracking systems
Dark matter density spikes forming around adiabatically growing black holes can dramatically enhance indirect and direct detection signals. Canonical predictions, however, assume a zero-mass seed in a purely dark matter environment and do not track the long-term dynamical impact of surrounding stars. We present a semi-analytic framework that first generalizes adiabatic spike formation to include finite seed masses, stellar cusps, and non-circular orbits, and then studies the subsequent cosmic evolution by solving coupled Fokker-Planck equations for the dark matter and stellar phase-space distributions, with a heating rate modulated by the cosmic star formation rate. Starting conservatively from canonical Gondolo-Silk spikes and marginalizing over astrophysical uncertainties, we find that stellar gravitational heating drives the inner slope towards $γ_χ\simeq 1.5$ within a few Gyrs (e.g by $z \lesssim 2$ for spikes formed at $z\simeq 10$), yielding overdensities two to four orders of magnitude below canonical expectations but still well above an NFW-like cusp. We provide redshift-dependent benchmarks for the column density and $J$-factor relevant to scattering, decay and annihilation signatures. Any robust interpretation of indirect dark matter signals from galactic nuclei must account for this evolution.
Recent experimental demonstrations of ignition and target gain in inertial confinement fusion (ICF) have stimulated interest in exploring the fundamental physics of violent deuterium-tritium (DT) burn in high-gain ICF targets. A significant DT-burn fraction is a necessary condition for high energy gain and large neutron yields (>100MJ). Using classical molecular-dynamics (MD) simulations and a hybrid fluid-kinetic model, we examine how a large fraction of low-energy 𝛼 particles can kick D and T ions out of equilibrium in high-gain ICF targets. The MD results suggest that (1) temperatures of 𝑇 𝐷 and 𝑇 𝑇 can differ by as much as ∼20% of their mean temperature and (2) the deviation of the DT energy distribution from the Maxwell-Boltzmann function can exceed ∼30%. Some of these MD observations, such as the preferential heating of D ions by low-energy 𝛼 particles and the temperature separation, can be explained by a proposed hybrid fluid-kinetic model. Furthermore, the implication of such nonequilibrium effects on the DT reactivity is also discussed.
Diffusion of protons in outer radiation belt due to violation of third adiabatic invariant for trapped particles
Scattering of test particle by enhanced electric field fluctuations in plamsa containing nonthermal electrons
Diffusion of protons in outer radiation belt due to violation of third adiabatic invariant for trapped particles
Longitude dependence of geomagnetically trapped electrons
Charged particle motion in random magnetic field, describing time evolution of particle distribution in pitch angle and position in terms of Fokker- Planck coefficients
Chandrasekhar dynamical friction theory for star in cluster adapted to Fokker-Plank electron in two-component plasma theory and including multiple encounters