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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
Recommended Citation
Geraldo, Abdel Kader A., "ANALYSIS OF NONEQUILIBRIUM LANGEVIN DYNAMICS FOR STEADY HOMOGENEOUS FLOWS" (2023). Doctoral Dissertations. 2815.
https://doi.org/10.7275/35063641
https://scholarworks.umass.edu/dissertations_2/2815
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