Anomalous Transport And Diffusion Of Inertial Brownian Particles

Einstein’s quantitative study of Brownian motion laid the foundation for non equilibrium statistical theory.Since the end of the last century,a large number of new transport and diffusion phenomena have been discovered in the study of complex fluids and life processes,such as the directional motion of molecular motors at the micro level,and the behavior of bacteria searching for food in solutions.Compared with traditional Brownian particles,these new Brownian particles are often located in complex noise and potential energy surfaces,and the particles themselves also have life activities,the traditional theory of Brownian particle motion encountered fundamental difficulties.This thesis adopts a combination of theoretical analysis and numerical simulation to explore the related problems of typical problems,attempting to provide some cases for understanding these complex phenomena,including:1.The transport and diffusion of active Brownian particles induced by crosscorrelated noises were investigated.It is shown that the cross-correlated noises can lead to abnormal transport of active Brownian particles such as ratchet effect and negative mobility;the diffusion displays hyperdiffusion,superdiffusion,and normal diffusion.For interacting active particles,it is found that cross-correlated noises can lead to the ratchet effect of interacting particles,and interaction between particles can weaken or even eliminate the ratchet effect.The findings are interpreted by the time series,the rectified potential.The research results provide valuable methods for controlling the motion of nanoparticles and particles such as proteins,organelles and cells.2.The transport and diffusion of active Brownian particle in the energy depot were investigated.It is shown that the cross-correlated noises and bias force can lead to a transition from bimodal to unimodal of probability distribution;the cross-correlated noises and bias force can enhance the transport and weaken the diffusion of the particle;the multiplicative noise can facilitate the transport and enhance the diffusion of the particle,and a giant diffusion by a larger multiplicative noise;whereas the additive noise can weaken the transport of the particle.For interacting active particles,we find the cross-correlated noises and bias force can enhance the collective motion of interacting active particles.A physical mechanism for the transport and diffusion of the particle is derived from the effective velocity potential for the above findings.The results will have guiding significance for understanding the motion of atoms and molecules in the microscopic world.3.The effects of stochastic resetting and roughness on the transport and diffusion of an inertial Brownian particle were studied.The results show that stochastic resetting can first lead to the ratchet effect,and the reentrant phenomenon occurs;the roughness and noise intensity do not lead to ratchet effect,but can weaken it;the system undergoes subdiffusion,superdiffusion,and normal diffusion;stochastic resetting can strengthen diffusion,whereas roughness can weaken it.The probability distribution of the Brownian particle velocity is used here to interpret the underlying mechanisms,revealing that stochastic resetting breaks the nature of velocity distribution.The results can be applied to biological,physical systems.4.The transport and diffusion of an inertial Brownian particle with random mass were studied.It is shown that there are multiple current reversals as the mass increases for the deterministic case,which would imply the phenomena of negative mass and mobility,a physical explanation of these phenomena is derived from basins of attraction.For the case of an additional random mass,the results show that the system may be very sensitive to a small change of the strength of dichotomous noise: an increase of the strength of dichotomous noise leads not only to significant decrease of the intervals of negative mass occurs but also to shrink the regions of negative mobility or also diminish the value of negative mobility;the system undergoes subdiffusion,superdiffusion,and normal diffusion,the negative mass and mobility can strengthen the diffusion.The probability distribution of the Brownian particle’ velocity is used to interpret the underlying mechanisms.This thesis investigated the anomalous transport and diffusion of inertial Brownian particles,revealing the basic dynamic mechanism of anomalous transport.The results provide a valuable method of controlling the Brownian particle motion by manipulating cross-correlated noises,stochastic resetting and roughness,enriching the basic research of Brownian motion theory.