Lagrangian Formalism for nonlinear second-order Riccati Systems: one-dimensional Integrability and two-dimensional Superintegrability

The existence of a Lagrangian description for the second-order Riccati equation is analyzed and the results are applied to the study of two different nonlinear systems both related with the generalized Riccati equation. The Lagrangians are nonnatural and the forces are not derivable from a potential. The constant value $E$ of a preserved energy function can be used as an appropriate parameter for characterizing the behaviour of the solutions of these two systems. In the second part the existence of two--dimensional versions endowed with superintegrability is proved. The explicit expressions of the additional integrals are obtained in both cases. Finally it is proved that the orbits of the second system, that represents a nonlinear oscillator, can be considered as nonlinear Lissajous figuresComment: 25 pages, 7 figure

The pinewood nematode, Bursaphelenchus xylophilus, in Madeira Island

The environmental conditions in Madeira Island are favorable for the presence and dissemination of the pinewood nematode (PWN), Bursaphelenchus xylophilus. Five hundred Pinus pinaster wood samples were collected in several forest areas and PWN was detected in 22.8 % of the samples. Bursaphelenchus xylophilus isolates from Madeira Island displayed the species-specific diagnostic characters. A morphological variation in the female tail terminus was detected. In most females, the tail presented a broadly rounded terminus and, occasionally, a digitate terminus with a terminal nipple-like extension resembling a mucro. PCR ITS-RFLP analysis revealed that Madeira Island isolates exhibited patterns specific to the species B. xylophilus and similar to virulent isolates. Amplified ITS regions were further sequenced and no genetic diversity was found for this genomic region among 17 Portuguese isolates (Madeira Island and Continental Portugal). Phylogenetic analysis revealed that Portuguese isolates grouped with isolates from China, Korea and one isolate from Japa

Optimización de formas en elasticidad bidimensional en medios homogéneos mediante el método de los elementos de contorno

En este trabajo se aborda el problema de la optimización de forma de sólidos elásticos bidimensionales, considerando material isótropo u ortótropo, de cara a obtener una distribución de tensiones lo más uniforme posible en zonas del contorno especificadas. Para ello se calcula la tensión de Von Mises en la zona del contorno a optimizar, y a partir de ésta y de la tensión de referencia especificada se define la función objetivo. Como restricción se impone que el área del sólido en cuestión sea igual a un valor prefijado, aunque se contempla también la posibilidad de que no haya restricciones. Se detalla igualmente el algoritmo utilizado para resolver el problema de optimización no lineal resultante, incluyendo por último algunos ejemplos que ponen de manifiesto la validez de la formulación presentada.Peer Reviewe

Distance constraints on activation of TRPV4 channels by AKAP150-bound PKCα in arterial myocytes.

TRPV4 (transient receptor potential vanilloid 4) channels are Ca2+-permeable channels that play a key role in regulating vascular tone. In arterial myocytes, opening of TRPV4 channels creates local increases in Ca2+ influx, detectable optically as "TRPV4 sparklets." TRPV4 sparklet activity can be enhanced by the action of the vasoconstrictor angiotensin II (AngII). This modulation depends on the activation of subcellular signaling domains that comprise protein kinase C α (PKCα) bound to the anchoring protein AKAP150. Here, we used super-resolution nanoscopy, patch-clamp electrophysiology, Ca2+ imaging, and mathematical modeling approaches to test the hypothesis that AKAP150-dependent modulation of TRPV4 channels is critically dependent on the distance between these two proteins in the sarcolemma of arterial myocytes. Our data show that the distance between AKAP150 and TRPV4 channel clusters varies with sex and arterial bed. Consistent with our hypothesis, we further find that basal and AngII-induced TRPV4 channel activity decays exponentially as the distance between TRPV4 and AKAP150 increases. Our data suggest a maximum radius of action of ∼200 nm for local modulation of TRPV4 channels by AKAP150-associated PKCα

On the Photorefractive Gunn Effect

We present and numerically solve a model of the photorefractive Gunn effect. We find that high field domains can be triggered by phase-locked interference fringes, as it has been recently predicted on the basis of linear stability considerations. Since the Gunn effect is intrinsically nonlinear, we find that such considerations give at best order-of-magnitude estimations of the parameters critical to the photorefractive Gunn effect. The response of the system is much more complex including multiple wave shedding from the injecting contact, wave suppression and chaos with spatial structure.Comment: Revtex, 8 pag., 4 fig. (jpg), submit to Physical Review

Optimización de formas en elasticidad bidimensional en medios homogéneos mediante el método de los elementos de contorno

En este trabajo se aborda el problema de la optimización de forma de sólidos elásticos bidimensionales, considerando material isótropo u ortótropo, de cara a obtener una distribución de tensiones lo más uniforme posible en zonas del contorno especificadas. Para ello se calcula la tensión de Von Mises en la zona del contorno a optimizar, y a partir de ésta y de la tensión de referencia especificada se define la función objetivo. Como restricción se impone que el área del sólido en cuestión sea igual a un valor prefijado, aunque se contempla también la posibilidad de que no haya restricciones. Se detalla igualmente el algoritmo utilizado para resolver el problema de optimización no lineal resultante, incluyendo por último algunos ejemplos que ponen de manifiesto la validez de la formulación presentada.Peer Reviewe

The harmonic oscillator on Riemannian and Lorentzian configuration spaces of constant curvature

The harmonic oscillator as a distinguished dynamical system can be defined not only on the Euclidean plane but also on the sphere and on the hyperbolic plane, and more generally on any configuration space with constant curvature and with a metric of any signature, either Riemannian (definite positive) or Lorentzian (indefinite). In this paper we study the main properties of these `curved' harmonic oscillators simultaneously on any such configuration space, using a Cayley-Klein (CK) type approach, with two free parameters \ki, \kii which altogether correspond to the possible values for curvature and signature type: the generic Riemannian and Lorentzian spaces of constant curvature (sphere ${\bf S}^2$, hyperbolic plane ${\bf H}^2$, AntiDeSitter sphere {\bf AdS}^{\unomasuno} and DeSitter sphere {\bf dS}^{\unomasuno}) appear in this family, with the Euclidean and Minkowski spaces as flat limits. We solve the equations of motion for the `curved' harmonic oscillator and obtain explicit expressions for the orbits by using three different methods: first by direct integration, second by obtaining the general CK version of the Binet's equation and third, as a consequence of its superintegrable character. The orbits are conics with centre at the potential origin in any CK space, thereby extending this well known Euclidean property to any constant curvature configuration space. The final part of the article, that has a more geometric character, presents those results of the theory of conics on spaces of constant curvature which are pertinent.Comment: 29 pages, 6 figure