Spectral Methods for Self-Assembly
Licentiate thesis, 2011

Conventional manufacturing relies on robotics and chemistry to create, shape and combine components into products. Nature shows us an alternative route: by carefully designing interactions between components, they can be made to spontaneously self-assemble into complex arrangements. The field of self-assembly has seen a series of experimental triumphs, but there is a relative dearth of theoretical results of the kind expected in physics. This thesis present some analytical results and their connection to self-assembly. The common theme is a focus on the energy spectrum of the (isotropic) interactions of a given model. Paper I solves an adaptation of the spherical spin model, demonstrating the centrality of the energy spectrum and predicting universal striped behavior. Paper II derives an alternative set of solutions, relevant for aggregating particle systems, and predicts a large but limited morphological alphabet. They both describe what happens typically, in systems with general interactions. Paper III represents a different take on the spectral picture, not trying to understand general interactions but to design specific ones. It presents a method that allows us to self-assemble complex crystal structures by matching an energy spectrum to the Fourier spectrum of the target structure. Interestingly, the method produces interactions for which we can prove that the target structure is a ground state.

classical spin models


isotropic interactions



ML11, Hörsalsvägen 5, Maskinteknik, Chalmers
Opponent: Stellan Östlund


Erik Edlund

SuMo Biomaterials

Chalmers, Energy and Environment, Physical Resource Theory

Designing Isotropic Interactions for Self-Assembly of Complex Lattices

Physical Review Letters,; Vol. 107(2011)p. 085503-

Journal article

Novel Self-Assembled Morphologies from Isotropic Interactions

Physical Review Letters,; Vol. 107(2011)p. 085501-

Journal article

Universality of Striped Morphologies

Physical Review Letters,; Vol. 105(2010)p. 137203-

Journal article

Subject Categories

Physical Sciences


Basic sciences

ML11, Hörsalsvägen 5, Maskinteknik, Chalmers

Opponent: Stellan Östlund

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