Fokker-Planck equation with arbitrary dc and ac fields: Continued fraction method

Abstract

The continued fraction method (CFM) is used to solve the Fokker-Planck equation with arbitrary dc and ac fields. With an appropriate choice of basis functions, the Fokker-Planck equation is converted into a set of linear algebraic equations with short-ranged coupling and then CFM is implemented to obtain numerical solutions with high efficiency. Both a proposed perturbative CFM and the numerically exact matrix CFM are used to study the nonlinear response of driven systems, with their results compared to assess the validity regime of the perturbative approach. The proposed perturbative CFM approach needs scalar quantities only and hence is more efficient within its validity regime. Two nonlinear systems of different nature are used as examples: molecular dipole (rotational Brownian motion) and particle in a periodic potential (translational Brownian motion). The associated full dynamics is presented in the compact form of hysteresis loops. It is observed that as the strength of an AC driving field increases, pronounced nonlinear effects are manifested in the deformation of the hysteresis loops.

Timing theory continuous nursing, resistance training: Rehabilitation and mental health of caregivers and stroke patients with traumatic fractures

“…The goal is to improve caregivers’ ability to provide care, the quality of care, and the effectiveness of patients’ rehabilitation[ 9 ]. A continuous nursing care plan, guided by post-discharge timing theory, can reduce the pressure on caregivers’ through the application of a variety of intervention tools and measures, ensuring the effectiveness of post-discharge patient rehabilitation[ 12 ]. The continuous nursing model based on timing theory and combined with resistance training was used for patients with stroke that had been complicated with a traumatic fracture and incorporated both patients and caregivers.…”