| Popis: |
The Rouse models are designed to understand the dynamics of a polymer in a dilute solvent. The discrete model is described by a stochastic differential equation while the continuum one is by a stochastic heat equation. When a polymer resides in a polymeric liquid, its motion undergoes obstruction from neighboring polymers. The neighboring polymers build a region where the polymer is able to move. And the polymer makes a reptile-like move. We propose polymer models in a polymeric liquid based on the Rouse models, called by the reflected Rouse models. The dynamics of the reflected Rouse models are described by stochastic equations. We investigate the reflected continuum Rouse model in the upper-half space ℝ3+ the dynamics of which is described by a reflected stochastic partial differential equation and prove the existence and uniqueness problems of the reflected stochastic differential equation. And we discuss the curves in ℝ3 driven by a random curvature and a random torsion and the physical Brownian motion in ℝ. |
