Exclusion and multiplicity for stable communities in Lotka-Volterra systems.

For classic Lotka-Volterra systems governing many interacting species, we establish an exclusion principle that rules out the existence of linearly asymptotically stable steady states in subcommunities of communities that admit a stable state which is internally D-stable. This type of stability is known to be ensured, e.g.

Analysis of binding at a single spatially localized cluster of binding sites by fluorescence recovery after photobleaching.

Cells contain many subcellular structures in which specialized proteins locally cluster. Binding interactions within such clusters may be analyzed in live cells using models for fluorescence recovery after photobleaching (FRAP). Here we analyze a three-dimensional FRAP model that accounts for a single spatially localized cluster of binding sites in the presence of both diffusion and impermeable boundaries.

Analysis of binding reactions by fluorescence recovery after photobleaching.

Fluorescence recovery after photobleaching (FRAP) is now widely used to investigate binding interactions in live cells. Although various idealized solutions have been identified for the reaction-diffusion equations that govern FRAP, there has been no comprehensive analysis or systematic approach to serve as a guide for extracting binding information from an arbitrary FRAP curve. Here we present a complete solution to the FRAP reaction-diffusion equations for either single or multiple independent binding interactions, and then relate our solution to the various idealized cases.

Decay rates of internal waves in a fluid near the liquid-vapor critical point.

We study the damping of internal waves in a viscous fluid near the liquid-vapor critical point. Such a fluid becomes strongly stratified by gravity due to its large compressibility. Using the variable-density incompressible Navier-Stokes equations, we model an infinite fluid layer with rigid horizontal boundaries and periodic side boundary conditions.