The Decoupled Potential Integral Equation for Time-Harmonic Electromagnetic Scattering

We present a new formulation for the problem of electromagnetic scattering from perfect electric conductors. While our representation for the electric and magnetic fields is based on the standard vector and scalar potentials ${\bf A},\phi$ in the Lorenz gauge, we establish boundary conditions on the potentials themselves, rather than on the field quantities. This permits the development of a well-conditioned second kind Fredholm integral equation which has no spurious resonances, avoids low frequency breakdown, and is insensitive to the genus of the scatterer. The equations for the vector and scalar potentials are decoupled. That is, the unknown scalar potential defining the scattered field, $\phi^{Sc}$, is determined entirely by the incident scalar potential $\phi^{In}$. Likewise, the unknown vector potential defining the scattered field, ${\bf A}^{Sc}$, is determined entirely by the incident vector potential ${\bf A}^{In}$. This decoupled formulation is valid not only in the static limit but for arbitrary $\omega\ge 0$.Comment: 33 pages, 7 figure

The key role of off-axis singularities in free-space vortex transmutation

We experimentally demonstrate the generation of off-axis phase singularities in a vortex transmutation process induced by the breaking of rotational symmetry. The process takes place in free space by launching a highly-charged vortex, owning full rotational symmetry, into a linear thin diffractive element presenting discrete rotational symmetry. It is shown that off-axis phase singularities follow straight dark rays bifurcating from the symmetry axis. This phenomenon may provide new routes towards the spatial control of multiple phase singularities for applications in atom trapping and particle manipulation.Comment: 4 pages, 4 figures, to appear in Applied Physics B: Lasers and Optic

Vorticity cutoff in nonlinear photonic crystals

Using group theory arguments, we demonstrate that, unlike in homogeneous media, no symmetric vortices of arbitrary order can be generated in two-dimensional (2D) nonlinear systems possessing a discrete-point symmetry. The only condition needed is that the non-linearity term exclusively depends on the modulus of the field. In the particular case of 2D periodic systems, such as nonlinear photonic crystals or Bose-Einstein condensates in periodic potentials, it is shown that the realization of discrete symmetry forbids the existence of symmetric vortex solutions with vorticity higher than two.Comment: 4 pages, 5 figures; minor changes in address and reference

Symmetry, winding number and topological charge of vortex solitons in discrete-symmetry media

We determine the functional behavior near the discrete rotational symmetry axis of discrete vortices of the nonlinear Schr\"odinger equation. We show that these solutions present a central phase singularity whose charge is restricted by symmetry arguments. Consequently, we demonstrate that the existence of high-charged discrete vortices is related to the presence of other off-axis phase singularities, whose positions and charges are also restricted by symmetry arguments. To illustrate our theoretical results, we offer two numerical examples of high-charged discrete vortices in photonic crystal fibers showing hexagonal discrete rotational invariance.Comment: 6 pages, 2 figure

Vortex transmutation

Using group theory arguments and numerical simulations, we demonstrate the possibility of changing the vorticity or topological charge of an individual vortex by means of the action of a system possessing a discrete rotational symmetry of finite order. We establish on theoretical grounds a "transmutation pass rule'' determining the conditions for this phenomenon to occur and numerically analize it in the context of two-dimensional optical lattices or, equivalently, in that of Bose-Einstein condensates in periodic potentials.Comment: 4 pages, 4 figure

Microbenthic Net Metabolism Along Intertidal Gradients (Cadiz Bay, SW Spain): Spatio-Temporal Patterns and Environmental Factors

Microphytobenthos (MPB), the photosynthetic primary producing component of microbenthos, shows variable patterns in its biomass distribution along the intertidal gradient as a result of the interactions of factors such as light, tides, temperature, and grazing pressure. These patterns have been studied more extensively in northern European estuaries than southern European coastal systems. Even less information is available regarding temporal changes in MPB primary production rates in these systems. For this reason, we followed the seasonal changes in net production in light and dark respiration rates (determined by oxygen microelectrodes) and MPB biomass (estimated by sediment chlorophyll a) along the intertidal gradient of the inner Cadiz Bay during a year. Sediment cores were collected along two transects (five sampling stations per transect) with distinct sediment granulometry: one muddy [Puerto Real (PR)] and one muddy-sandy transect [San Fernando (SF)]. Our results show that MPB biomass and net production increased seawards reaching their maxima in winter. In contrast to what is observed in northern European systems, the higher solar irradiance and temperatures occurring in summer in southern Spain likely inhibit MPB production. In Cadiz Bay, spatial patterns of MPB biomass and net production depended on season and location due to the environmental heterogeneity observed. Environmental variables, analyzed by principal component analysis (PCA), were used to explain the variability of MPB metabolism by multiple regression. Selected principal component (PC) axes explained 60% of the net production in light and 41% of the dark respiration rates variability in PR, while they only accounted for 25% of the same rates in SF. The differences observed between transects and the variability in the environmental variables explaining them highlight the importance of considering the spatial heterogeneity of our system to estimate the contribution of MPB to the inner Cadiz Bay productivity. In our case, this contribution is significant accounting for up to 49% of the total benthic production of the inner Cadiz Bay intertidal sediments, confirming previous global estimates

Una herramienta para la caracterización de modelos producidos en la resolución de problemas de Fermi

En este trabajo presentamos una herramienta de caracterización de los modelos matemáticos que producen los alumnos de Educación Secundaria. En concreto, utilizamos esta herramienta para analizar las producciones de los estudiantes de 16 años de dos centros diferentes al resolver problemas de estimación de grandes cantidades, que son un tipo de problemas de Fermi. Los resultados muestran que la herramienta propuesta permite distinguir aspectos diferenciadores entre los modelos producidos por alumnos sin experiencia modelizadora, de los producidos por alumnos con experiencia previa