Study On Anomalous Diffusion In Fluctuating Potential Field

In recent years,the study of anomalous diffusion has attracted extensive attention.In recent years,studies on anomalous diffusion and transport have been more mature in free field,linear field and harmonic potential field,and there are still some shortcomings in studies on fluctuating potential field.In this paper,the probability of particle passing through periodic modulation and the probability of particle passing through normal distribution function under general damping is studied in detail.It is found that the probability of particle passing through saddle point is significantly affected by the modulation factor,and the relationship between the probability of particle passing through and the modulation factor is obtained.The first chapter mainly introduces the background of anomalous diffusion,including Brownian motion,the types and expressions of anomalous diffusion,and the research progress of anomalous diffusion.In the second chapter,several numerical simulation methods are introduced,the process of differential treatment of Langevin equation is given,and the discrete form of the equation is given.The third chapter studies the particles through general damping cases periodic modulation of the probability of potential field potential barrier in the saddle points,and introduces the numerical simulation of the programming ideas,a detailed analysis of the particles by probability and the relationship between the modulation factor,and with damping case particles through probability to do the contrast,the particle is obtained under the condition of general damping crossing probability of the results of numerical simulation.In chapter 4,the probability of a particle passing through a barrier saddle point in a potential field modulated by a normal distribution function under general damping is studied.The differences between the passing probabilities of the potential field particles in the periodic modulation and the normal distribution modulation are compared,and the idea of using the normal distribution function to replace the inverted harmonic oscillator potential for simulation research is proposed,which provides a new research idea for the follow-up research.The fifth chapter is a summary of the work of this paper,and to the future work,make a prospect.