Self-adjoint and Markovian extensions of infinite quantum graphs.

We investigate the relationship between one of the classical notions of boundaries for infinite graphs, , and self-adjoint extensions of the minimal Kirchhoff Laplacian on a metric graph. We introduce the notion of for ends of a metric graph and show that finite volume graph ends is the proper notion of a boundary for Markovian extensions of the Kirchhoff Laplacian. In contrast to manifolds and weighted graphs, this provides a transparent geometric characterization of the uniqueness of Markovian extensions, as well as of the self-adjointness of the Gaffney Laplacian - the underlying metric graph does not have finite volume ends.

Estimating Subseasonal Variability and Trends in Global Atmosphere Using Reanalysis Data.

A new measure of subseasonal variability is introduced that provides a scale-dependent estimation of vertically and meridionally integrated atmospheric variability in terms of the normal modes of linearized primitive equations. Applied to the ERA-Interim data, the new measure shows that subseasonal variability decreases for larger zonal wave numbers. Most of variability is due to balanced (Rossby mode) dynamics but the portion associated with the inertio-gravity (IG) modes increases as the scale reduces.

Surface Tension of Acid Solutions: Fluctuations beyond the Nonlinear Poisson-Boltzmann Theory.

We extend our previous study of surface tension of ionic solutions and apply it to acids (and salts) with strong ion-surface interactions, as described by a single adhesivity parameter for the ionic species interacting with the interface. We derive the appropriate nonlinear boundary condition with an effective surface charge due to the adsorption of ions from the bulk onto the interface. The calculation is done using the loop-expansion technique, where the zero loop (mean field) corresponds of the full nonlinear Poisson-Boltzmann equation.