Wormlike Chain Model Statistics (wlcstat)

This python repository contains functions to predict the equilibrium and dynamic behavior of polymeric fluids and materials, particularly focusing on semiflexible polymers modeled using the wormlike chain model and several related models. Theoretical background for these functions is systematically developed in the associated pages, including derivations and example calculations. These theoretical developments represent an overview of analytical theory developed in the Spakowitz lab at Stanford University (Spakowitz lab website).

All microscopic polymer models exhibit an intermediate-scale semiflexible behavior before trending towards the Gaussian Chain Model. Demonstration of a microscopic model (Freely Rotating Chain Model) behaving as the Effective Elastic Chain at intermediate scales before approaching the Gaussian Chain Model.

Contents:

• Gaussian Chain Theory
  • Gaussian Chain model Green function—explicit path integration
  • Gaussian Chain model Green function—Schrödinger equation
• Wormlike Chain Theory
  • Wormlike Chain model Green function—Path integral formulation and the Diffusion equation
  • Orientation statistics
• Average Quantities
  • Functions contained with the ‘wlcave’ module
  • Example usage of ‘r2_ave’
  • Example usage of ‘rg2_ave’
  • Example usage of ‘rz4_ave’
• Wormlike Chain Green's Function
  • Methods to Evaluate the Wormlike Chain Green’s Function
  • Functions contained with the ‘wlcgreen’ module
  • Example usage of ‘eval_poles_and_residues’
• Structure Factor
  • Two-point Structure Factor
  • Three-point and Four-point Density Correlation Functions
  • Functions contained with the ‘wlcstruc’ module
  • Example usage of ‘s2_wlc’
• Polymer Confinement
  • Chain segmental density and average position for free ends
  • Chain segmental density and average position for attached ends
• Polymer Liquid Crystalline Solutions
  • Functions contained with the ‘wlc_lcpoly’ module
  • Example usage of ‘q_lcpoly’
• Semiflexible Copolymers
  • Diblock Copolymer Multi-point Structure Factor
  • Two-point Structure Factor for a Diblock Copolymer
• Wormlike Chains with Twist, Helices, and Ribbons
  • Polymer chain representations
  • Geometry and topology of space curves
  • Models for the deformation energy
  • Wormlike Ribbons: Chain Statistics and Averages
• Chromosomal DNA
  • Functions contained with the ‘chromo’ module
  • Example usage of ‘r2_kinked_twlc’
  • Example usage of ‘gen_chromo_conf’ and ‘gen_chromo_pymol_file’
• Polymer Dynamics
  • Dynamics of a linear and ring flexible Gaussian chains (Rouse model)
  • Functions contained with the ‘poly_dyn’ module
  • Example usage of ‘linear_mscd’ and ‘ring_mscd’
  • Application of ‘linear_mscd’ and ‘ring_mscd’ to homologue pairing in meiosis
• Active-Brownian Dynamics
  • Dynamic behavior of an Active-Brownian polymer
  • Functions contained with the ‘active_brown’ module
• Appendix
  • Coordinate Definitions
  • Spherical Harmonics
• References

Indices and tables

• Index

• Module Index

• Search Page