Energy-Driven Pattern Formation in Planar Dipole-Dipole Systems

A variety of two-dimensional fluid systems, known as dipole-mediated systems, exhibit a dipole-dipole interaction between their fluid constituents. The competition of this repulsive dipolar force with the cohesive fluid forces cause these systems to form intricate and patterned structures in their boundaries. In this thesis, we show that the microscopic details of any such system are irrelevant in the macroscopic limit and contribute only to a constant offset in the system’s energy. A numeric model is developed, and some important stable domain morphologies are characterized. Previously unresolved bifurcating branches are explored. Finally, by applying a random energy background to the numerics, we recover the smörgåsbord of diverse domain morphologies that are seen in experiment. We develop an empirical description of these domains and use it to demonstrate that the nondimensional parameter, , which is the ratio of the line tension to the dipole–dipole density, can be extracted for any domain using only its shape.