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Identifier

000439203

Title

Approximate Mori-Zwanzig dynamics for star polymers

Alternative Title

Χρήση του φορμαλισμού Mori-Zwanzig για την προσέγγιση της δυναμικής αστεροειδών πολυμερών

Author

Σταυροπούλου, Ελευθερία

Thesis advisor

Χαρμανδάρης, Ευάγγελος
Καλλιγιαννάκη, Ευαγγελία

Reviewer

Πανταζής, Ιωάννης

Abstract

Molecular dynamics (MD) simulations study the physical movement of atoms, provid¬ing valuable insight for a variety of physical systems. In order to study the motion of molecules inside these physical systems we use either classical mechanics, if we want to know the exact location of the particle in the space (determinism) or statistical me¬chanics, if we want to find the probability of the particle being in a particular position. The difficulties due to the temporal and spatial limitations of simulations, lead us to average out the details of atomistic, at the molecular level simulations. This can be achieved by dimensionality reduction. In the current work we adopt coarse graining as a dimensionality reduction approach. Having defined the new coarse grained system, the purpose is to specify structural and dynamical properties of the system. We focus on the equations of motion for the new coarse grained particles. These equations are the known Generalized Langevin Equations (GLE). In this work, we present the derivation of the GLE using the Mori-Zwanzig formalism. Then, we present a Markovian approximation of the GLE based on the constrained dynamics of the microscopic system with respect to the coarsening. This approximation leads to a closed system where the conservative and friction forces can be estimated from data provided by all-atom molecular dynamics simulations. We present the application of the methodology for a high-dimensional system of a star polymer, an 8-arm polystyrene. The coarse-variables are the center of mass of each polystyrene molecule. We perform molecular dynamics simulations for a united-atom system firstly to ensure the system is at thermodynamic equilibrium. Then, we perform molecular dynamics simulations with constrained center of mass in order calculate the average pair force.

Language

English, Greek

Issue date

2021-03-26

Collection

School/Department--School of Sciences and Engineering--Department of Mathematics and Applied Mathematics--Post-graduate theses

Type of Work--Post-graduate theses

Permanent Link

https://elocus.lib.uoc.gr//dlib/2/e/4/metadata-dlib-1618385990-722618-30044.tkl

Views

301

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