Self assembly phenomenon at different scales has inspired the scientific community to understand and design many physical and engineering systems. Making effective use of the fine resolution experimental data available today is not a trivial task. In this study, we develop and propose amicable analytic and geometric methods that helps to make coarse grained models for self-assembling systems. The necessary information that dictates the evolution of a self assembling system is inscribed in the various interacting components. This information is encrypted via the physical properties of the interacting components (e.g., their mass, surface properties etc), their interaction with each other (e.g., electro-magnetic properties, i.e., potential energy functions) and their local environment. We introduce two new tools (1) Local minimal structures (LMS) and (2) Programmable potentials for Hamiltonian systems. The topological tool LMS, helps us understand the effect of the morphology of the interacting components on the global topology of a two-dimensional self-assembly system with only short range interactions. The second tool, programmable potentials, helps us to obtain physical Hamiltonian models by coupling interaction properties and local information. This allows us to construct Hamiltonian models which encodes the observed qualitative behavior of a given system.

The efficacy of LMS is illustrated with a coarse grained model mimicking previous experiments on the transition of the random network structures of cytosine molecule to a glassy structure over a gold surface. The identification of the LMS generated by the favored interactions not only provides a complete finite set of local structures possible, but may also provide an interesting viewpoint to understand the formation of amorphous and glassy (covalent) systems.

Using the concept of programmable potentials, we define a new class of potentials that allow interacting entities to self assemble into a prescribed configuration governed by operational logic. We show how a sequence of logical statements that govern the system evolution, can be used to construct physical Hamiltonian model. We present several simple examples that illustrate this formalism. Specifically, we give examples from signal transduction, pathway selection and self-assembly of fifteen north-eastern states of United States starting from an initially disordered configuration. This approach is general in nature and can be used for other complex systems. Towards the end of the talk, we demonstrate numerically (using molecular dynamics simulations) the motility of Kinesin motor proteins. Kinesin are essential nanoscale motors found in Eukaryotic cell and are responsible for intracellular transportation, mitosis, etc. We develop a ten dimensional reduced order model that allows us to include the various (experimentally known) physical and chemical aspects of Kinesin motion in a simple way.