On the Dynamics of solitons in the nonlinear Schroedinger equation

We study the behavior of the soliton solutions of the equation i((\partial{\psi})/(\partialt))=-(1/(2m)){\Delta}{\psi}+(1/2)W_{{\epsilon}}'({\psi})+V(x){\psi} where W_{{\epsilon}}' is a suitable nonlinear term which is singular for {\epsilon}=0. We use the "strong" nonlinearity to obtain results on existence, shape, stability and dynamics of the soliton. The main result of this paper (Theorem 1) shows that for {\epsilon}\to0 the orbit of our soliton approaches the orbit of a classical particle in a potential V(x).Comment: 29 page

Calibrated Surfaces and Supersymmetric Wilson Loops

We study the dual gravity description of supersymmetric Wilson loops whose expectation value is unity. They are described by calibrated surfaces that end on the boundary of anti de-Sitter space and are pseudo-holomorphic with respect to an almost complex structure on an eight-dimensional slice of AdS_5 x S^5. The regularized area of these surfaces vanishes, in agreement with field theory non-renormalization theorems for the corresponding operators.Comment: 28 pages, 2 figure

Location of the Energy Levels of the Rare-Earth Ion in BaF2 and CdF2

The location of the energy levels of rare-earth (RE) elements in the energy band diagram of BaF2 and CdF2 crystals is determined. The role of RE3+ and RE2+ ions in the capture of charge carriers, luminescence, and the formation of radiation defects is evaluated. It is shown that the substantial difference in the luminescence properties of BaF2:RE and CdF2:RE is associated with the location of the excited energy levels in the band diagram of the crystals

Complexity for extended dynamical systems

We consider dynamical systems for which the spatial extension plays an important role. For these systems, the notions of attractor, epsilon-entropy and topological entropy per unit time and volume have been introduced previously. In this paper we use the notion of Kolmogorov complexity to introduce, for extended dynamical systems, a notion of complexity per unit time and volume which plays the same role as the metric entropy for classical dynamical systems. We introduce this notion as an almost sure limit on orbits of the system. Moreover we prove a kind of variational principle for this complexity.Comment: 29 page

The tale of two centres

We study motion in the field of two fixed centres described by a family of Einstein-dilaton-Maxwell theories. Transitions between regular and chaotic motion are observed as the dilaton coupling is varied.Comment: 20 pages, RevTeX, 7 figures included, TeX format change

Detoxification of Multiple Heavy Metals by a Half-Molecule ABC Transporter, HMT-1, and Coelomocytes of Caenorhabditis elegans

Developing methods for protecting organisms in metal-polluted environments is contingent upon our understanding of cellular detoxification mechanisms. In this regard, half-molecule ATP-binding cassette (ABC) transporters of the HMT-1 subfamily are required for cadmium (Cd) detoxification. HMTs have conserved structural architecture that distinguishes them from other ABC transporters and allows the identification of homologs in genomes of different species including humans. We recently discovered that HMT-1 from the simple, unicellular organism, Schizosaccharomyces pombe, SpHMT1, acts independently of phytochelatin synthase (PCS) and detoxifies Cd, but not other heavy metals. Whether HMTs from multicellular organisms confer tolerance only to Cd or also to other heavy metals is not known.Using molecular genetics approaches and functional in vivo assays we showed that HMT-1 from a multicellular organism, Caenorhabditis elegans, functions distinctly from its S. pombe counterpart in that in addition to Cd it confers tolerance to arsenic (As) and copper (Cu) while acting independently of pcs-1. Further investigation of hmt-1 and pcs-1 revealed that these genes are expressed in different cell types, supporting the notion that hmt-1 and pcs-1 operate in distinct detoxification pathways. Interestingly, pcs-1 and hmt-1 are co-expressed in highly endocytic C. elegans cells with unknown function, the coelomocytes. By analyzing heavy metal and oxidative stress sensitivities of the coelomocyte-deficient C. elegans strain we discovered that coelomocytes are essential mainly for detoxification of heavy metals, but not of oxidative stress, a by-product of heavy metal toxicity.We established that HMT-1 from the multicellular organism confers tolerance to multiple heavy metals and is expressed in liver-like cells, the coelomocytes, as well as head neurons and intestinal cells, which are cell types that are affected by heavy metal poisoning in humans. We also showed that coelomocytes are involved in detoxification of heavy metals. Therefore, the HMT-1-dependent detoxification pathway and coelomocytes of C. elegans emerge as novel models for studies of heavy metal-promoted diseases

Compactness and existence results in weighted Sobolev spaces of radial functions. Part II: Existence

We prove existence and multiplicity results for finite energy solutions to the nonlinear elliptic equation $$-\triangle u+V\left( \left| x\right| \right) u=g\left( \left| x\right| ,u\right) \quad \textrm{in }\Omega \subseteq \mathbb{R}^{N},\ N\geq 3,$$ where $\Omega$ is a radial domain (bounded or unbounded) and $u$ satisfies $u=0$ on $\partial \Omega$ if $\Omega \neq \mathbb{R}^{N}$ and $u\rightarrow 0$ as $\left| x\right| \rightarrow \infty$ if $\Omega$ is unbounded. The potential $V$ may be vanishing or unbounded at zero or at infinity and the nonlinearity $g$ may be superlinear or sublinear. If $g$ is sublinear, the case with $g\left( \left| \cdot \right| ,0\right) \neq 0$ is also considered.Comment: 29 pages, 8 figure

Multimode Free Space Optical Link Enabled by SiP Integrated Meshes

A silicon photonic mesh of tuneable Mach-Zehnder Interferometers (MZIs) is employed to receive two spatially-overlapped Hermite-Gaussian beams modulated at 10 Gbit/s, sharing the same wavelength and state of polarization. The mesh automatically self-configures, separating and sorting the two beams out without any excess loss