Ordering and finite-size effects in the dynamics of one-dimensional transient patterns

We introduce and analyze a general one-dimensional model for the description of transient patterns which occur in the evolution between two spatially homogeneous states. This phenomenon occurs, for example, during the Freedericksz transition in nematic liquid crystals.The dynamics leads to the emergence of finite domains which are locally periodic and independent of each other. This picture is substantiated by a finite-size scaling law for the structure factor. The mechanism of evolution towards the final homogeneous state is by local roll destruction and associated reduction of local wavenumber. The scaling law breaks down for systems of size comparable to the size of the locally periodic domains. For systems of this size or smaller, an apparent nonlinear selection of a global wavelength holds, giving rise to long lived periodic configurations which do not occur for large systems. We also make explicit the unsuitability of a description of transient pattern dynamics in terms of a few Fourier mode amplitudes, even for small systems with a few linearly unstable modes.Comment: 18 pages (REVTEX) + 10 postscript figures appende

Singularities and Topology of Meromorphic Functions

We present several aspects of the "topology of meromorphic functions", which we conceive as a general theory which includes the topology of holomorphic functions, the topology of pencils on quasi-projective spaces and the topology of polynomial functions.Comment: 21 pages, 1 figur

Stability of Spatial Optical Solitons

We present a brief overview of the basic concepts of the soliton stability theory and discuss some characteristic examples of the instability-induced soliton dynamics, in application to spatial optical solitons described by the NLS-type nonlinear models and their generalizations. In particular, we demonstrate that the soliton internal modes are responsible for the appearance of the soliton instability, and outline an analytical approach based on a multi-scale asymptotic technique that allows to analyze the soliton dynamics near the marginal stability point. We also discuss some results of the rigorous linear stability analysis of fundamental solitary waves and nonlinear impurity modes. Finally, we demonstrate that multi-hump vector solitary waves may become stable in some nonlinear models, and discuss the examples of stable (1+1)-dimensional composite solitons and (2+1)-dimensional dipole-mode solitons in a model of two incoherently interacting optical beams.Comment: 34 pages, 9 figures; to be published in: "Spatial Optical Solitons", Eds. W. Torruellas and S. Trillo (Springer, New York

Unusual magneto-optical behavior induced by local dielectric variations under localized surface plasmon excitations

We study the effect of global and local dielectric variations on the polarization conversion rps response of ordered nickel nanowires embedded in an alumina matrix. When considering local changes, we observe a non-monotonous behavior of the rps, its intensity unusually modified far beyond to what it is expected for a monotonous change of the whole refractive index of the embedding medium. This is related to the local redistribution of the electromagnetic field when a localized surface plasmon is excited. This finding may be employed to develop and improve new biosensing magnetoplasmonic devices

Molecular Phylogeny of the Acanthocephala (Class Palaeacanthocephala) with a Paraphyletic Assemblage of the Orders Polymorphida and Echinorhynchida

Acanthocephalans are attractive candidates as model organisms for studying the ecology and co-evolutionary history of parasitic life cycles in the marine ecosystem. Adding to earlier molecular analyses of this taxon, a total of 36 acanthocephalans belonging to the classes Archiacanthocephala (3 species), Eoacanthocephala (3 species), Palaeacanthocephala (29 species), Polyacanthocephala (1 species) and Rotifera as outgroup (3 species) were analyzed by using Bayesian Inference and Maximum Likelihood analyses of nuclear 18S rDNA sequence. This data set included three re-collected and six newly collected taxa, Bolbosoma vasculosum from Lepturacanthus savala, Filisoma rizalinum from Scatophagus argus, Rhadinorhynchus pristis from Gempylus serpens, R. lintoni from Selar crumenophthalmus, Serrasentis sagittifer from Johnius coitor, and Southwellina hispida from Epinephelus coioides, representing 5 new host and 3 new locality records. The resulting trees suggest a paraphyletic arrangement of the Echinorhynchida and Polymorphida inside the Palaeacanthocephala. This questions the placement of the genera Serrasentis and Gorgorhynchoides within the Echinorhynchida and not the Polymorphida, necessitating further insights into the systematic position of these taxa based on morphology

Cooperation of decay-accelerating factor and membrane cofactor protein in regulating survival of human cervical cancer cells

<p>Abstract</p> <p>Background</p> <p>Decay-accelerating factor (DAF) and membrane cofactor protein (MCP) are the key molecules involved in cell protection against autologus complement, which restricts the action of complement at critical stages of the cascade reaction. The cooperative effect of DAF and MCP on the survival of human cervical cancer cell (ME180) has not been demonstrated.</p> <p>Methods</p> <p>In this study we applied, for the first time, short hairpin RNA (shRNA) to knock down the expression of the DAF and MCP with the aim of exploiting complement more effectively for tumor cell damage. Meanwhile, we investigated the cooperative effects of DAF and MCP on the viability and migration, moreover the proliferation of ME180 cell.</p> <p>Results</p> <p>The results showed that shRNA inhibition of DAF and MCP expression enhanced complement-dependent cytolysis (CDC) up to 39% for MCP and up to 36% for DAF, and the combined inhibition of both regulators yielded further additive effects in ME180 cells. Thus, the activities of DAF and MCP, when present together, are greater than the sum of the two protein individually.</p> <p>Conclusion</p> <p>These data indicated that combined DAF and MCP shRNA described in this study may offer an additional alternative to improve the efficacy of antibody-and complement-based cancer immunotherapy.</p

Continuous-wave biexciton lasing at room temperature using solution-processed quantum wells

Solution-processed inorganic and organic materials have been pursued for more than a decade as low-threshold, high-gain lasing media, motivated in large part by their tunable optoelectronic properties and ease of synthesis and processing. Although both have demonstrated stimulated emission and lasing, they have not yet approached the continuous-wave pumping regime. Two-dimensional CdSe colloidal nanosheets combine the advantage of solution synthesis with the optoelectronic properties of epitaxial two-dimensional quantum wells. Here, we show that these colloidal quantum wells possess large exciton and biexciton binding energies of 132 meV and 30 meV, respectively, giving rise to stimulated emission from biexcitons at room temperature. Under femtosecond pulsed excitation, close-packed thin films yield an ultralow stimulated emission threshold of 6 μJ cm(-2), sufficient to achieve continuous-wave pumped stimulated emission, and lasing when these layers are embedded in surface-emitting microcavities

The Taylor expansion of the exponential map and geometric applications

The final publication is available at Springer via http://dx.doi.org/10.1007/s13398-013-0149-zIn this work we consider the Taylor expansion of the exponential map of a submanifold immersed in Rn up to order three, in order to introduce the concepts of lateral and frontal deviation. We compute the directions of extreme lateral and frontal deviation for surfaces in R3. Also we compute, by using the Taylor expansion, the directions of high contact with hyperspheres of a surface immersed in R4 and the asymptotic directions of a surface immersed in RnThis work was partially supported by DGCYT grant no. MTM2009-08933.Monera, M.; Montesinos Amilibia, Á.; Sanabria Codesal, E. (2014). The Taylor expansion of the exponential map and geometric applications. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas (RACSAM). 108(2):881-906. https://doi.org/10.1007/s13398-013-0149-zS8819061082Arnol’d, V.I., Gusein-zade, V.I., Varchenko, A.N.: Singularities of Differentiable Maps. Monographs in Mathematics, vol. 82. Birkhäuser, Boston (1985)Chen, B.-Y., Li, S.-J.: The contact number of a Euclidean submanifold. Proc. Edinburgh Math. Soc. 47, 69–100 (2004)Fessler, W.: $$\ddot{U}$$ U ¨ ber die normaltorsion von Fl $$\ddot{a}$$ a ¨ chen im vierdimensionalen euklidischen. Raum. Comm. Math. Helv. 33(2), 89–108 (1959)García, R., Sotomayor, J.: Geometric mean curvature lines on surfaces immersed in $$\mathbb{R}^3$$ R 3 . Annales de la faculté des sciences de Toulouse, $$6^e$$ 6 e ser, vol. 11, No. 3, pp. 377–401 (2002)García, R., Sotomayor, J.: Lines of axial curvature on surfaces immersed in $$R^4$$ R 4 . Differ. Geom. Appl. 12, 253–269 (2000)Golubitsky, M., Gillemin, V.: Stable Mappings and their Singularities. Springer, Berlin (1973)Hartmann, F., Hanzen, R.: Apollonius’s Ellipse and Evolute Revisited–The Discriminant of the Related Quartic. http://www3.villanova.edu/maple/misc/ellipse/Apollonius2004.pdfLlibre, J., Yanquian, Y.: On the dynamics of surface vector fields and homeomofphisms (preprint)Looijenga, E.J.N.: Structural stability of smooth families of $$C^{\infty }$$ C ∞ -functions. University of Amsterdam, Doctoral Thesis (1974)Mochida, D.K.H., Romero-Fuster, M.C., Ruas, M.A.S.: Inflection points and nonsingular embeddings of surfaces in $$\mathbb{R}^5$$ R 5 . Rocky Mt. J. Math. 33, 3 (2003)Mochida, D.K.H., Romero-Fuster, M.C., Ruas, M.A.S.: Osculating hyperplanes and asymptotic directions of codimension two submanifolds of Euclidean spaces. Geom. Dedicata 77(3), 305–315 (1999)Mochida, D.K.H., Romero Fuster, M.C., Ruas, M.A.S.: The geometry of surfaces in 4-space from a contact viewpoint. Geom. Dedicata 54, 323–332 (1995)Monera, G.M., Montesinos-Amilibia, A., Moraes, S.M., Sanabria-Codesal, E.: Critical points of higher order for the normal map of immersions in $$\mathbb{R}^d$$ R d . Topol. Appl. 159, 537–544 (2012)Montaldi, J.A.: Contact with application to submanifolds, PhD Thesis, University of Liverpool (1983)Montaldi, J.A.: On contact between submanifolds. Michigan Math. J. 33, 195–199 (1986)Montesinos-Amilibia, A.: Parametricas4, computer program freely available from http://www.uv.es/montesinMontesinos-Amilibia, A.: Parametricas5, computer program freely available from http://www.uv.es/montesinMoraes, S., Romero-Fuster, M.C., Sánchez-Bringas, F.: Principal configurations and umbilicity of submanifolds in $$I\!\! R^n$$ I R n . Bull. Bel. Math. Soc. 10, 227–245 (2003)Porteous, I.R.: The normal singularities of a submanifold. J. Differ. Geom. 5, 543–564 (1971)Romero-Fuster, M.C., Ruas, M.A.S., Tari, F.: Asymptotic curves on surfaces in $$R^5$$ R 5 . Commun. Contemp. Math. 10, 309–335 (2008)Romero-Fuster, M.C., Sánchez-Bringas, F.: Umbilicity of surfaces with orthogonal asymptotiv lines in $$R^4$$ R 4 . Differ. Geom. Appl. 16, 213–224 (2002)Tari, F.: On pairs of geometric foliations on a cross-cap. Tohoku Math. J. 59(2), 233–258 (2007