Proterties Of Brownian Particles In Periodic Potential

In this dissertation,the dynamics of Brown particles under periodic potential conditions is studied.In the first chapter,two dynamic equations describing Brownian motion are introduced:(1)Langevin equation;(2)Fokker-Planck equation.By leading random forces into Einstein’s relationship,Langevin explained the randomness in particle motion,then establishing the stochastic dynamic equation of Brown particles.The Fokker-Planck equation is a differential equation about the distribution function of the system.It can describes the statistical law of the system and it shows the evolution of the system.The Fokker-Planck equation is based on the evolution of the distribution function or density function of the system.It describes the statistical law of the system and can show the evolution of the system.Then we give the process of inferring from Langevin equation to Fokker-Planck equation.Finally,the analytical solution of Fokker Planck equation is given.In Chapter 2,We introduce the main theoretical models and numerical calculation methods in the analysis of particle motion.Through the statistical characteristic equation:and the.expression corresponding to the noise,the simulation method of the Lange,equation is obtained.In Chapter 3,we_mainly study the size effect of Brownian particles in the geometric structure.By numerically studying the Langevin equation of particles,we compare the factors such as the noise intensity and particle shape in the equation to the particle transport and diffusion.It is found that in a confined space,the circular shape of the particles is conducive to the movement of the particles,It is found that in the confined space,the circular shape of particles is conducive to the movement of particles,and the speed of particles has a maximum value with the increase of noise intensity.With the increase of external force,there is a maximum of velocity and diffusion coefficient.Finally,in Chapter 4,we studied the transport of Brown particles driven by non-Gaussian noise.We mainly study the effects of noise intensity and correlation coefficient of non-Gaussian noise on the speed and diffusion coefficient of Brown particles.It is found through numerical simulation that there is a maximum value for the velocity and diffusion coefficient of the Brown particles under the influence of noise intensity,and the magnitude of the noise intensity and the correlation time both interfere with the maximum value.In addition,we numerically studied the migration and diffusion of active Brown particles driven by color noise in a two-dimensional asymmetric potential.The results show that the shape of the particles has a great influence on the rectified transport.The ideal spherical shape is conducive to particle transport and diffusion,but the needle-like shape will destroy the directional transmission and diffusion of particles.The maximum value of the particles diffusion coefficient increases as the autocorrelation time increases.As the intensity of the noise increases,the particle velocity gradually decreases and eventually approaches zero.In addition,by applying a finite load(f0＝0.9)in the x direction of the particle,the phenomenon of particle separation can be observed:when the parameter is greater than the critical auto-correlation time,the particle moves to the left,and particles with a parameter less than the critical auto-correlation time move to the right.Figure[23]reference[16]...