Flows to Schrodinger Geometries

We construct RG flow solutions interpolating AdS and Schrodinger geometries in Abelian Higgs models obtained from consistent reductions of type IIB supergravity and M-theory. We find that z=2 Schrodinger geometries can be realized at the minima of scalar potentials of these models, where a scalar charged under U(1) gauge symmetry obtains a nonzero vacuum expectation value. The RG flows are induced by an operator deformation of the dual CFT. The flows are captured by fake superpotentials of the theories.Comment: 19 pages, 5 figures, v2: typos corrected, references added, published version in PR

Initial Conditions of Planet Formation: Lifetimes of Primordial Disks

The statistical properties of circumstellar disks around young stars are important for constraining theoretical models for the formation and early evolution of planetary systems. In this brief review, I survey the literature related to ground-based and Spitzer-based infrared (IR) studies of young stellar clusters, with particular emphasis on tracing the evolution of primordial (``protoplanetary'') disks through spectroscopic and photometric diagnostics. The available data demonstrate that the fraction of young stars with optically thick primordial disks and/or those which show spectroscopic evidence for accretion appears to approximately follow an exponential decay with characteristic time ~2.5 Myr (half-life = 1.7 Myr). Large IR surveys of ~2-5 Myr-old stellar samples show that there is real cluster-by-cluster scatter in the observed disk fractions as a function of age. Recent Spitzer surveys have found convincing evidence that disk evolution varies by stellar mass and environment (binarity, proximity to massive stars, and cluster density). Perhaps most significantly for understanding the planeticity of stars, the disk fraction decay timescale appears to vary by stellar mass, ranging from ~1 Myr for >1.3 Msun stars to ~3 Myr for <0.08 Msun brown dwarfs. The exponential decay function may provide a useful empirical formalism for estimating very rough ages for YSO populations and for modeling the effects of disk-locking on the angular momentum of young stars.Comment: 8 pages, 1 figure, invited review, Proceedings of the 2nd Subaru International Conference "Exoplanets and Disks: Their Formation and Diversity", Keauhou - Hawaii - USA, 9-12 March 200

Plasmonic waveguides cladded by hyperbolic metamaterials

Strongly anisotropic media with hyperbolic dispersion can be used for claddings of plasmonic waveguides. In order to analyze the fundamental properties of such waveguides, we analytically study 1D waveguides arranged of a hyperbolic metamaterial (HMM) in a HMM-Insulator-HMM (HIH) structure. We show that hyperbolic metamaterial claddings give flexibility in designing the properties of HIH waveguides. Our comparative study on 1D plasmonic waveguides reveals that HIH-type waveguides can have a higher performance than MIM or IMI waveguides

On Myosin II dynamics in the presence of external loads

We address the controversial hot question concerning the validity of the loose coupling versus the lever-arm theories in the actomyosin dynamics by re-interpreting and extending the phenomenological washboard potential model proposed by some of us in a previous paper. In this new model a Brownian motion harnessing thermal energy is assumed to co-exist with the deterministic swing of the lever-arm, to yield an excellent fit of the set of data obtained by some of us on the sliding of Myosin II heads on immobilized actin filaments under various load conditions. Our theoretical arguments are complemented by accurate numerical simulations, and the robustness of the model is tested via different choices of parameters and potential profiles.Comment: 6 figures, 8 tables, to appear on Biosystem

On the Large Time Behavior of Solutions of Hamilton-Jacobi Equations Associated with Nonlinear Boundary Conditions

In this article, we study the large time behavior of solutions of first-order Hamilton-Jacobi Equations, set in a bounded domain with nonlinear Neumann boundary conditions, including the case of dynamical boundary conditions. We establish general convergence results for viscosity solutions of these Cauchy-Neumann problems by using two fairly different methods : the first one relies only on partial differential equations methods, which provides results even when the Hamiltonians are not convex, and the second one is an optimal control/dynamical system approach, named the "weak KAM approach" which requires the convexity of Hamiltonians and gives formulas for asymptotic solutions based on Aubry-Mather sets

Weak KAM aspects of convex Hamilton-Jacobi equations with Neumann type boundary conditions

We establish the stability under the formations of infimum and of convex combinations of subsolutions of convex Hamilton-Jacobi equations, some comparison and existence results for convex and coercive Hamilton-Jacobi equations with the Neumann type boundary condition as well as existence results for the Skorokhod problem. We define the Aubry-Mather set associated with the Neumann type boundary problem and establish some properties of the Aubry-Mather set including the existence results for the ``calibrated'' extremals for the corresponding action functional (or variational problem).Comment: 39 pages, 1 figur