We derive a set of phase field models for biofilms using the
one-fluid two-component formulation in which the combination of
extracellular polymeric substances (EPS) and the bacteria are
effectively modeled as one fluid component while the collective
ensemble of nutrient and the solvent are modeled as the other. The
biofilm is assumed an incompressible continuum. Two growth modes
are identified in linearized analysis. Numerical simulations are
carried out in one and two space dimension using a
velocity-corrected projection method for incompressible flows.
Biofilm growth, expansion, streaming, rippling, and detachment are
simulated in shear cells numerically. Viscoelastic properties of
the biofilm is investigated as well.

Superconductivity in two dimensions provides a unique area in which a fascinating variety of novel and fundamental phenomena occur. In this talk, I will review recent theoretical and experimental results on disordered films, which undergo a magnetic-field-tuned superconducting-insulator transition at low temperatures. I will focus on the unusual phases and fluctuation phenomena evident in the experimental studies of the field-tuned transition. First, I will explain how rare disorder fluctuations can enhance global superconductivity and increase the critical magnetic field at which samples become superconducting. Next, I will briefly summarize the recently developed theory of quantum superconducting fluctuations, which explains transport properties above the transition. At the end of my talk, I will focus on the low-temperature metallic phase observed in certain materials. This metallic state is truly mysterious and can not be explained by any conventional theory (in! ! volving bosonic vortices as basic excitations). I will argue that under certain circumstances the statistics of the vortices can change from bosonic to fermionic. Such a statistical transmutation may explain the nature of the metallic state. I will discuss possible experimental signatures of the resulting vortex Fermi liquid.