Brownian Motion In Confined Systems

In this thesis, the dynamics of Brownian particles in confined systems is stud-ied, which include the geometry-induced stochastic resonance and gravity separa-tion by entropic transport. First, the development of the stochastic dynamics is introduced, from the fluctuation-dissipation theory to the transport and diffusion of Brownian particles in one dimensional energetic potential and then the study of particles in confined geometry. Second, the traditional double-well model of stochastic resonance is introduced. Comparing with the entropic stochastic reso-nance and geometric stochastic resonance developed in recent years, a new model where the switching between these two kinds of resonances can be observed is pro-posed. Through tuning the geometric parameters of the system, the mechanism of the resonance and the switching are studied. Moreover, a new separation method is proposed according to the symmetry-breaking context of the geometric confine-ment and the external forces, leading to the effective separation of the particles with the same size but with different weights. The separation purity can reach to99%in the context of entropic splitter method.