Alexandria Digital Research Library

Level set strategy for SCFT

Author:
Ouaknin, Gaddiel
Degree Grantor:
University of California, Santa Barbara. Mechanical Engineering
Degree Supervisor:
Frederic G. Gibou
Place of Publication:
[Santa Barbara, Calif.]
Publisher:
University of California, Santa Barbara
Creation Date:
2016
Issued Date:
2016
Topics:
Materials science, Applied mathematics, and Mechanical engineering
Keywords:
Quad/Oct Tree
Level-Set
Inverse Problem
DSA
Shape Optimization
SCFT
Genres:
Dissertations, Academic and Online resources
Dissertation:
Ph.D.--University of California, Santa Barbara, 2016
Description:

This thesis investigates the design of sharp in terface level set methods in the context of self-consistent field theory (SCFT) in polymer physics. SCFT computes the structure and energy of inhomogeneous self-assembling polymers at thermodynamic equilibrium. Level set methods are based on an implicit representation of free boundaries, which enable motions with arbitrary change in topology. In addition, recent advances on how to impose Robin boundary conditions enables the study of free boundary problems of interest in the community interested in self-assembly.

We first present a computational framework, encoded on a forest of quad/oct-trees in a parallel environment. We then present results of imposing sharp Neumann boundary conditions as was first proposed by de Gennes, which enables SCFT computations of meaningful quantities at the boundary of irregular geometries. We then introduce the concept of functional level-set derivative in the context of SCFT and rigorously derive expressions for the change of energy of a diblock copolymer with respect to an enclosing shape. The level-set derivative is then used to embed SCFT into a variable shape simulator, where the internal structure and the enclosing shape are coupled together and evolve in tandem in order to reduce the energy of the diblock copolymer. Finally an algorithm for solving the inverse problem for directed self-assembly is presented.

Physical Description:
1 online resource (180 pages)
Format:
Text
Collection(s):
UCSB electronic theses and dissertations
ARK:
ark:/48907/f3gx4bm5
ISBN:
9781369147032
Catalog System Number:
990046968930203776
Rights:
Inc.icon only.dark In Copyright
Copyright Holder:
Gaddiel Ouaknin
File Description
Access: Public access
Ouaknin_ucsb_0035D_13053.pdf pdf (Portable Document Format)