Structural instability of vortices in Bose-Einstein condensates

In this paper we study a gaseous Bose-Einstein condensate (BEC) and show that: (i) A minimum value of the interaction is needed for the existence of stable persistent currents. (ii) Vorticity is not a fundamental invariant of the system, as there exists a conservative mechanism which can destroy a vortex and change its sign. (iii) This mechanism is suppressed by strong interactions.Comment: 4 pages with 3 figures. Submitted to Phys. Rev. Let

Testing the Reliability of Financial Sustainability. The Case of Spanish Local Governments

Local Governments (LGs) have strengthened the financial control as a consequence of mandatory requirements to ensure financial sustainability in their management. The aim of this study is to determine whether financial indicators about financial conditions defined in Spanish regulation are backed by worldwide generally accepted financial benchmarking indicators. For this purpose, we analyze the relationship between Spanish indicators of financial sustainability based on European Union (EU) regulations and Financial Trends Monitoring System Indicators (FTMS) of the International City/County Management Association (ICMA). For this purpose, two methodologies are applied: discriminant analysis and logistic regression, where the dependent variables are each of the Spanish financial indicators and the independent variables are ICMA indicators. The evidence supports that variables that are related to the control of expenditures, debt and the revenues show a greater explanatory power of financial sustainability, being the most important elements which offer relevant information about the financial sustainability measurement of LGs

Bis[(E)-4-(hydroxy­imino­meth­yl)pyridinium] oxalate

The formula unit of the title compound, 2C6H7N2O+·C2O4 2−, comprises two symmetry-equivalent 4-(hydroxy­imino­meth­yl)­pyridinium cations on general positions, linked through hydrogen bonding via an oxalate anion that resides on a crystallographic centre of symmetry. The crystal structure consists of infinite chains of cations and oxalate anions directed by O—H⋯O and multicentre N—H⋯O inter­molecular hydrogen-bonding inter­actions

Dipole-Mode Vector Solitons

We find a new type of optical vector soliton that originates from trapping of a dipole mode by a soliton-induced waveguide. These solitons, which appear as a consequence of the vector nature of the two component system, are more stable than the previously found optical vortex-mode solitons and represent a new type of extremely robust nonlinear vector structure.Comment: Four pages with five eps figure

Unleashing Optics and Optoacoustics for Developmental Biology

The past decade marked an optical revolution in biology: an unprecedented number of optical techniques were developed and adopted for biological exploration, demonstrating increasing interest in optical imaging and in vivo interrogations. Optical methods have become faster and have reached nanoscale resolution, and are now complemented by optoacoustic (photoacoustic) methods capable of imaging whole specimens in vivo. Never before were so many optical imaging barriers broken in such a short time-frame: with new approaches to optical microscopy and mesoscopy came an increased ability to image biology at unprecedented speed, resolution, and depth. This review covers the most relevant techniques for imaging in developmental biology, and offers an outlook on the next steps for these technologies and their applications.The work on this review article has received funding from the Deutsche Forschungsgemeinschaft (DFG), Germany (Leibniz Prize 2013; NT 3/10 1) and the Federal Ministry of Education and Research (BMBF), Photonic Science Germany, Tech2See 13N12623/ 4. J.R. acknowledges support from the European Commission FP7 CIG grant HIGH THROUGH PUT TOMO, and Spanish MINECO grant MESO IMAGING FIS2013 41802 R

Resonant nonlinearity management for nonlinear-Schr\"{o}dinger solitons

We consider effects of a periodic modulation of the nonlinearity coefficient on fundamental and higher-order solitons in the one-dimensional NLS equation, which is an issue of direct interest to Bose-Einstein condensates in the context of the Feshbach-resonance control, and fiber-optic telecommunications as concerns periodic compensation of the nonlinearity. We find from simulations, and explain by means of a straightforward analysis, that the response of a fundamental soliton to the weak perturbation is resonant, if the modulation frequency $\omega$ is close to the intrinsic frequency of the soliton. For higher-order $n$-solitons with $n=2$ and 3, the response to an extremely weak perturbation is also resonant, if $\omega$ is close to the corresponding intrinsic frequency. More importantly, a slightly stronger drive splits the 2- or 3-soliton, respectively, into a set of two or three moving fundamental solitons. The dependence of the threshold perturbation amplitude, necessary for the splitting, on $\omega$ has a resonant character too. Amplitudes and velocities of the emerging fundamental solitons are accurately predicted, using exact and approximate conservation laws of the perturbed NLS equation.Comment: 14 pages, 6 figure

Lyashko-Looijenga morphisms and submaximal factorisations of a Coxeter element

When W is a finite reflection group, the noncrossing partition lattice NCP_W of type W is a rich combinatorial object, extending the notion of noncrossing partitions of an n-gon. A formula (for which the only known proofs are case-by-case) expresses the number of multichains of a given length in NCP_W as a generalised Fuss-Catalan number, depending on the invariant degrees of W. We describe how to understand some specifications of this formula in a case-free way, using an interpretation of the chains of NCP_W as fibers of a Lyashko-Looijenga covering (LL), constructed from the geometry of the discriminant hypersurface of W. We study algebraically the map LL, describing the factorisations of its discriminant and its Jacobian. As byproducts, we generalise a formula stated by K. Saito for real reflection groups, and we deduce new enumeration formulas for certain factorisations of a Coxeter element of W.Comment: 18 pages. Version 2 : corrected typos and improved presentation. Version 3 : corrected typos, added illustrated example. To appear in Journal of Algebraic Combinatoric