Two-component {CH} system: Inverse Scattering, Peakons and Geometry

An inverse scattering transform method corresponding to a Riemann-Hilbert problem is formulated for CH2, the two-component generalization of the Camassa-Holm (CH) equation. As an illustration of the method, the multi - soliton solutions corresponding to the reflectionless potentials are constructed in terms of the scattering data for CH2.Comment: 22 pages, 3 figures, draft, please send comment

Coupling of nitrogen-vacancy centers in diamond to a GaP waveguide

The optical coupling of guided modes in a GaP waveguide to nitrogen-vacancy (NV) centers in diamond is demonstrated. The electric field penetration into diamond and the loss of the guided mode are measured. The results indicate that the GaP-diamond system could be useful for realizing coupled microcavity-NV devices for quantum information processing in diamond.Comment: 4 pages 4 figure

Frontotemporal Dementia Caused by CHMP2B Mutations

CHMP2B mutations are a rare cause of autosomal dominant frontotemporal dementia (FTD). The best studied example is frontotemporal dementia linked to chromosome 3 (FTD-3) which occurs in a large Danish family, with a further CHMP2B mutation identified in an unrelated Belgian familial FTD patient. These mutations lead to C-terminal truncations of the CHMP2B protein and we will review recent advances in our understanding of the molecular effects of these mutant truncated proteins on vesicular fusion events within the endosome-lysosome and autophagy degradation pathways. We will also review the clinical features of FTD caused by CHMP2B truncation mutations as well as new brain imaging and neuropathological findings. Finally, we collate the current data on CHMP2B missense mutations, which have been reported in FTD and motor neuron disease

A note on multi-dimensional Camassa-Holm type systems on the torus

We present a $2n$-component nonlinear evolutionary PDE which includes the $n$-dimensional versions of the Camassa-Holm and the Hunter-Saxton systems as well as their partially averaged variations. Our goal is to apply Arnold's [V.I. Arnold, Sur la g\'eom\'etrie diff\'erentielle des groupes de Lie de dimension infinie et ses applications \`a l'hydrodynamique des fluides parfaits. Ann. Inst. Fourier (Grenoble) 16 (1966) 319-361], [D.G. Ebin and J.E. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid. Ann. of Math. 92(2) (1970) 102-163] geometric formalism to this general equation in order to obtain results on well-posedness, conservation laws or stability of its solutions. Following the line of arguments of the paper [M. Kohlmann, The two-dimensional periodic $b$-equation on the diffeomorphism group of the torus. J. Phys. A.: Math. Theor. 44 (2011) 465205 (17 pp.)] we present geometric aspects of a two-dimensional periodic $\mu$-$b$-equation on the diffeomorphism group of the torus in this context.Comment: 14 page

Selective decay by Casimir dissipation in fluids

The problem of parameterizing the interactions of larger scales and smaller scales in fluid flows is addressed by considering a property of two-dimensional incompressible turbulence. The property we consider is selective decay, in which a Casimir of the ideal formulation (enstrophy in 2D flows, helicity in 3D flows) decays in time, while the energy stays essentially constant. This paper introduces a mechanism that produces selective decay by enforcing Casimir dissipation in fluid dynamics. This mechanism turns out to be related in certain cases to the numerical method of anticipated vorticity discussed in \cite{SaBa1981,SaBa1985}. Several examples are given and a general theory of selective decay is developed that uses the Lie-Poisson structure of the ideal theory. A scale-selection operator allows the resulting modifications of the fluid motion equations to be interpreted in several examples as parameterizing the nonlinear, dynamical interactions between disparate scales. The type of modified fluid equation systems derived here may be useful in modelling turbulent geophysical flows where it is computationally prohibitive to rely on the slower, indirect effects of a realistic viscosity, such as in large-scale, coherent, oceanic flows interacting with much smaller eddies

Reconstruction of protein structures from a vectorial representation

We show that the contact map of the native structure of globular proteins can be reconstructed starting from the sole knowledge of the contact map's principal eigenvector, and present an exact algorithm for this purpose. Our algorithm yields a unique contact map for all 221 globular structures of PDBselect25 of length $N \le 120$. We also show that the reconstructed contact maps allow in turn for the accurate reconstruction of the three-dimensional structure. These results indicate that the reduced vectorial representation provided by the principal eigenvector of the contact map is equivalent to the protein structure itself. This representation is expected to provide a useful tool in bioinformatics algorithms for protein structure comparison and alignment, as well as a promising intermediate step towards protein structure prediction.Comment: 4 pages, 1 figur

Fluctuation effects of gauge fields in the slave-boson t-J model

We present a quantitative study of the charge-spin separation(CSS) phenomenon in a U(1) gauge theory of the t-J model of high-Tc superconductures. We calculate the critical temperature of confinement-deconfinement phase transition below which the CSS takes place.Comment: Latex, 9 pages, 3 figure

An Integrable Shallow Water Equation with Linear and Nonlinear Dispersion

We study a class of 1+1 quadratically nonlinear water wave equations that combines the linear dispersion of the Korteweg-deVries (KdV) equation with the nonlinear/nonlocal dispersion of the Camassa-Holm (CH) equation, yet still preserves integrability via the inverse scattering transform (IST) method. This IST-integrable class of equations contains both the KdV equation and the CH equation as limiting cases. It arises as the compatibility condition for a second order isospectral eigenvalue problem and a first order equation for the evolution of its eigenfunctions. This integrable equation is shown to be a shallow water wave equation derived by asymptotic expansion at one order higher approximation than KdV. We compare its traveling wave solutions to KdV solitons.Comment: 4 pages, no figure

Calculation of critical exponents by self-similar factor approximants

The method of self-similar factor approximants is applied to calculating the critical exponents of the O(N)-symmetric phi^4 theory and of the Ising glass. It is demonstrated that this method, being much simpler than other known techniques of series summation in calculating the critical exponents, at the same time, yields the results that are in very good agreement with those of other rather complicated numerical methods. The principal advantage of the method of self-similar factor approximants is the combination of its extraordinary simplicity and high accuracy.Comment: 17 pages, 2 table

A tough egg to crack: recreational boats as vectors for invasive goby eggs and transdisciplinary management approaches

Non-native invasive species are a major threat to biodiversity, especially in freshwater ecosystems. Freshwater ecosystems are naturally rather isolated from one another. Nonetheless, invasive species often spread rapidly across water sheds. This spread is to a large extent realized by human activities that provide vectors. For example, recreational boats can carry invasive species propagules as ‘aquatic hitch-hikers’ within and across water sheds. We used invasive gobies in Switzerland as a case study to test the plausibility that recreational boats can serve as vectors for invasive fish and that fish eggs can serve as propagules. We found that the peak season of boat movements across Switzerland and the goby spawning season overlap temporally. It is thus plausible that goby eggs attached to boats, anchors or gear may be transported across watersheds. In experimental trials we found that goby eggs show resistance to physical removal (90mN attachment strength of individual eggs) and stay attached if exposed to rapid water flow (2.8m s-138 for 1h). When exposing the eggs to air, we found that hatching success remained high (>95%) even after eggs had been out of water for up to 24h. It is thus plausible that eggs survive during pick up, within water and overland transport by boats. We complemented the experimental plausibility tests with a survey on how decision makers from inside and outside academia rate the feasibility of managing recreational boats as vectors. We found consensus that an installation of a preventive boat vector management is considered an effective and urgent measure. This study advances our understanding of the potential of recreational boats to serve as vectors for invasive vertebrate species, and demonstrates that preventive management of recreational boats is considered feasible by relevant decision makers in- and outside academia