The influence of adiabatic focusing on particle diffusion is an important topic in astrophysics and plasma physics. In the past several authors have explored the influence of along-field adiabatic focusing on parallel diffusion of charged energetic particles. In this paper by using the Unified NonLinear Transport (UNLT) theory developed by Shalchi (SH2010) and the method of He and Schlickeiser (HS2014) we derive a new nonlinear perpendicular diffusion coefficient for nonuniform background magnetic field. This formula demonstrates that particle perpendicular diffusion coefficient is modified by along-field adiabatic focusing.For isotropic pitch-angle scattering and weak adiabatic focusing limit the derived perpendicular diffusion coefficient is independent of the sign of adiabatic focusing characteristic length. For two-component model we simplify the perpendicular diffusion coefficient up to second order of the power series of adiabatic focusing characteristic quantity. We find that the first order modifying factor is equal to zero and the sign of the second one is determined by the energy of particles.
Social networks are an important infrastructure for information, the paper present a information diffusion model with random perturbation in social networks, which is based on SIR deterministic epidemic diseases. We prove that there exists a unique nonnegative solution to the stochastic information diffusion model for any positive initial value, investigate the stochastic asymptotic behavior of the information diffusion model, give the stability condition by the construction of the Lyapunov function, i.e. the conditions of the information diffusion will die out and be persistent in social networks.
The field line random walk (FLRW) of magnetic turbulence is one of the
important topics in plasma physics and astrophysics. In this article by using
the field line tracing method mean square displacements (MSD) of FLRW is
calculated in all possible length scales for pure two-dimensional turbulence
with damping dynamical model. We demonstrate that in order to describe FLRW
with damping dynamical model a new dimensionless quantity $R$ is needed to be
introduced. In different length scales dimensionless MSD shows different
relationship with the dimensionless quantity $R$. Although temporal effect
impacts MSD of FLRW and even changes regimes of FLRW, it dose not affect the
relationship between the dimensionless MSD and dimensionless quantity $R$ in
all possible length scales
Abstract. The paper explore an information diffusion models with random perturbation in social network. First, we show the models exit the unique global positive solution. By the construction of the Lyapunov function, we give the positive solution is stochastically asymptotically stable in the large around disease-free equilibrium, i.e. the conditions of the information diffusion will die out, investigate the stochastic asymptotic behavior of the positive solution around endemic equilibrium of the deterministic models, obtain the stochastic asymptotic stability condition, i.e. the conditions of the information diffusion will be persistent in social networks.
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