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ANALYSIS OF NONEQUILIBRIUM LANGEVIN DYNAMICS FOR STEADY HOMOGENEOUS FLOWS

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dc.contributor.advisorMatthew Dobson
dc.contributor.advisorLuc Rey-Bellet
dc.contributor.advisorHongkun Zhang
dc.contributor.advisorPeng Bai
dc.contributor.authorGeraldo, Abdel Kader A
dc.contributor.departmentUniversity of Massachusetts Amherst
dc.date2024-03-27 19:20:22
dc.date.accessioned2024-04-26T16:00:20Z
dc.date.available2024-04-26T16:00:20Z
dc.date.submittedMay
dc.date.submitted2023
dc.description.abstractFirst, 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.
dc.description.degreeDoctor of Philosophy (PhD)
dc.description.departmentMathematics
dc.identifier.doihttps://doi.org/10.7275/35063641
dc.identifier.orcidhttps://orcid.org/0000-0001-8066-1308
dc.identifier.urihttps://hdl.handle.net/20.500.14394/19186
dc.relation.urlhttps://scholarworks.umass.edu/cgi/viewcontent.cgi?article=3937&context=dissertations_2&unstamped=1
dc.rights.urihttp://creativecommons.org/licenses/by-sa/4.0/
dc.source.statuspublished
dc.subjectnon-equilibrium molecular dynamics
dc.subjectextensional flow
dc.subjectperiodic boundary conditions
dc.subjectNumerical Analysis and Computation
dc.titleANALYSIS OF NONEQUILIBRIUM LANGEVIN DYNAMICS FOR STEADY HOMOGENEOUS FLOWS
dc.typeopenaccess
dc.typedissertation
digcom.contributor.authorisAuthorOfPublication|email:kadergeraldo1@gmail.com|institution:University of Massachusetts Amherst|Geraldo, Abdel Kader A
digcom.identifierdissertations_2/2815
digcom.identifier.contextkey35063641
digcom.identifier.submissionpathdissertations_2/2815
dspace.entity.typePublication
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