Superfine Structure Of The Elastic Rod Model And Numerical Simulation Algorithm

In recent years, great progress has been made in modeling, numericalsimulating and analyzing a super slender elastic rod as an importantstructural model for studying DNA structure. Based on the achievements andthe fact that the electrostatic repulsion in DNA can notably affects itsstructure, a Kirchhoff equation and its Euler quaternion representation aregiven in this paper as structural models for studying the super slender elasticrods with electrostatic repulsion.Since the new models are complicated differential/integral equations withunknown integral paths, computation techniques are designed in numericalsimulation. To initial problems, an iterative method is introduced to deal withunknown integral paths, and a recursive formula is designed to reduce theamount of computation. To boundary problems, an algorithm based on finiteelement method is given.In addition, by using the Kirchhoff's dynamical analog technique, adifferential equation system is set up to describe the surface of the elasticrod.As a model study for DNA structures, we expect our results can findfurther applications in forecasting the super-helix properties and the affectionof electrostatic repulsion.