Studies On The Collective Diffusion Characteristics Of Two-dimensional Self-propelled Particles

Active particles have the ability to obtain energy from the environment and consume it to drive themselves to move forward.Active particles are different from passive particles on the pattern of motion.In recent years,the study on its physical properties has become an important subject of non-equilibrium statistical mechanics.At present,there are many studies on the equilibrium state properties of active particles,but less on the collective diffusion transport of non-equilibrium properties.In addition,the relationship between the activity and the passivity of the particle is still an unsolved problem.In this thesis,a study will be carried on the collective diffusion coefficient and the potential factors influencing the propelled particles in the two-dimensional channel.The main approaches are molecular dynamics and Monte Carlo method.The results maybe provide an illumination for the definition of particle activity.Firstly,this work has studied the relationship between the collective diffusion coefficient of propelled particles and particle concentration,propelled velocity,channel length,temperature and mass,and found that the collective diffusion coefficient was positively correlated with particle concentration,propelled velocity and channel length.The collective diffusion coefficient of active particles can be expressed as D^*=D₀^*+(bV^*e)/?T^*?,where e is a parameter greater than 1,and its value increases with the channel length.When the channel is long enough,e will tend to 2.The activity of particles can be defined by the relationship between the collective diffusion coefficient and temperature or mass.The collective diffusion coefficient determined by temperature can be divided into three regions:passive,transition and active region.The phase diagram composed of the critical temperature and critical momentum of propelled particles has showed that the activity of the particles depends on the competition between the momentum of the propelled particles and the environmental temperature.Secondly,the relationship between the particle rotation velocity and the collective diffusion coefficient have been studied,and it is found that the rotational friction coefficient is not depended on the collective diffusion coefficient of the passive particles.However,for the active particles,it is shown that it increases first and then keeps unchanged.In addition,the rotation velocity of the particles themselves has no effect on the collective diffusion coefficient of the passive particles.For the active particles,the faster the rotation,the smaller the collective diffusion coefficient,the more unfavorable to the collective diffusion of the active particles.The relationship between the active particle diffusion coefficient and the rotation velocity can be expressed as a power exponential relationship:D^*?w^B.Under different temperature conditions,the rotation velocity does not affect diffusion for passive particles,but the higher the temperature,the faster the diffusion,which means the positive correlation;for active particles,when the rotation velocity is less than 1×10^-4,the propelled velocity mainly affects the diffusion factor and the collective diffusion coefficient is basically unchanged;however,when the rotation is greater than 1×10^-4,temperature is the main factor.The higher the temperature,the larger the collective diffusion coefficient.Finally,the collective diffusion behavior of active particles under different propelled velocity distributions are studied.It is found that if the propelled velocity is a normally distribution,average random distribution and constant,it basically does not affect the collective diffusion coefficient.When the propelled velocity of the active particles is distributed as a Boltzmann like distribution,the collective diffusion coefficient of the active particles is larger and increases with the distribution width.According to the reverse Boltzmann distribution,the collective diffusion coefficient of the active particles is small,and decreases with the distribution width.The results show that the active particles are unique from the passive particles,that is,the particles with higher velocity contribute more to the diffusion coefficient than a larger number particles with close to the average velocity,increasing the collective diffusion coefficient.