Date of Thesis

Spring 2020


Many biological structures can be modeled as a system of interacting particles moving on a two-dimensional elastic membrane, for instance, protein clusters on cell-membranes and capsids of immature enveloped viruses. In this work, we present a model for such systems. We adopt the combination of the Helfrich model and the Lennard-Jones model as our energy representation of the particle-membrane system. The nonlinearity of the model gives rise to a complex competition of equilibrium states of the energy with symmetric features. We implement group-theoretic techniques to examine symmetric states and develop an automated computer program that systematically catalogs the symmetric equilibrium configurations for varying numbers of particles and model parameters.


Membrane Elasticity, Group Representation

Access Type

Honors Thesis (Bucknell Access Only)

Degree Type

Bachelor of Science



First Advisor

Sanjay Dharmavaram

Second Advisor

Peter Brooksbank