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Author ORCID Identifier

https://orcid.org/0000-0001-8066-1308

AccessType

Open Access Dissertation

Document Type

dissertation

Degree Name

Doctor of Philosophy (PhD)

Degree Program

Mathematics

Year Degree Awarded

2023

Month Degree Awarded

May

First Advisor

Matthew Dobson

Second Advisor

Luc Rey-Bellet

Third Advisor

Hongkun Zhang

Fourth Advisor

Peng Bai

Subject Categories

Numerical Analysis and Computation

Abstract

First, we propose using rotating periodic boundary conditions (PBCs) [13] to simulate nonequilibrium molecular dynamics (NEMD) in uniaxial or biaxial stretching flow. These specialized PBCs are required because the simulation box deforms with the flow. The method extends previous models with one or two lattice remappings and is simpler to implement than PBCs proposed by Dobson [10] and Hunt [24].

Then, using automorphism remapping PBC techniques such as Lees-Edwards for shear flow and Kraynik-Reinelt for planar elongational flow, we demonstrate expo-nential convergence to a steady-state limit cycle of incompressible two-dimensional
NELD. To demonstrate convergence [12], we use a technique similar to [R. Joubaud, G. A. Pavliotis, and G. Stoltz, 2014] after converting NELD to Lagrangian coordi-nates.

Finally, we propose a number of numerical schemes for solving Nonequilibrium Langevin Dynamics (NELD) [11], and we examine the strong rate of convergence for each scheme. Lees-Edwards and Kraynik-Reinelt boundary conditions, as well as their generalizations, are used in the schemes considered here. We demonstrate that when implementing standard stochastic integration schemes with these boundary conditions, care must be taken to avoid a breakdown in the strong order of convergence.

DOI

https://doi.org/10.7275/35063641

Creative Commons License

Creative Commons Attribution-Share Alike 4.0 License
This work is licensed under a Creative Commons Attribution-Share Alike 4.0 License.

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