Symmetric periodic orbits near a heteroclinic loop in R3 formed by two singular points, a semistable periodic orbit and their invariant manifolds

In this paper we consider C1 vector fields X in R3 having a “generalized heteroclinic loop” L which is topologically homeomorphic to the union of a 2–dimensional sphere S2 and a diameter connecting the north with the south pole. The north pole is an attractor on S2 and a repeller on . The equator of the sphere is a periodic orbit unstable in the north hemisphere and stable in the south one. The full space is topologically homeomorphic to the closed ball having as boundary the sphere S2. We also assume that the flow of X is invariant under a topological straight line symmetry on the equator plane of the ball. For each n ∈ N, by means of a convenient Poincar´e map, we prove the existence of infinitely many symmetric periodic orbits of X near L that gives n turns around L in a period. We also exhibit a class of polynomial vector fields of degree 4 in R3 satisfying this dynamics.

Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

In this paper we consider vector fields in R3 that are invariant under a suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two singular points (e+ and e −) and their invariant manifolds: one of dimension 2 (a sphere minus the points e+ and e −) and one of dimension 1 (the open diameter of the sphere having endpoints e+ and e −). In particular, we analyze the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar´e map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R3, and the second one is the charged rhomboidal four body problem.

Percolation and three-dimensional structure of supercritical water

It is well established that at ambient and supercooled conditions water can be described as a percolating network of H bonds. This work is aimed at identifying, by neutron diffraction experiments combined with computer simulations, a percolation line in supercritical water, where the extension of the H-bond network is in question. It is found that in real supercritical water liquidlike states are observed at or above the percolation threshold, while below this threshold gaslike water forms small, sheetlike configurations. Inspection of the three-dimensional arrangement of water molecules suggests that crossing of this percolation line is accompa- nied by a change of symmetry in the first neighboring shell of molecules from trigonal below the line to tetrahedral above.

Oral findings in Midline Syndrome: a case report and literature review

We describe a female patient with a midline syndrome. The patient presents agenesis of the corpus callosum, encephalocele, iris coloboma, hypertelorism, submucosal cleft palate and dental anomalies. Despite being very characteristic, her phenotypical traits do not coincide exactly with those reported to date in the literature. The karyotype and the molecular cytogenetic study do not show mutations. We identify the presence of dental anomalies in the mother and other family members, not being identified MSX1 and PAX9 mutations that could the related with their etiology. Despite the fact that dental agenesis has been related to a large number of other malformation syndromes and congenital conditions, dental anomalies have only rarely been mentioned when reporting midline syndromes. These dental phenotypical traits, present in the patient and her family, could be considered part of the midline syndrome in carriers as well as in the patients.

Viral self-assembly as a thermodynamic process

The protein shells, or capsids, of nearly all spherelike viruses adopt icosahedral symmetry. In the present Letter, we propose a statistical thermodynamic model for viral self-assembly. We find that icosahedral symmetry is not expected for viral capsids constructed from structurally identical protein subunits and that this symmetry requires (at least) two internal switching configurations of the protein. Our results indicate that icosahedral symmetry is not a generic consequence of free energy minimization but requires optimization of internal structural parameters of the capsid proteins

Sedimentation of pairs of hydrodynamically interacting semiflexible filaments

We describe the effect of hydrodynamic interactions in the sedimentation of a pair of inextensible semiflexible filaments under a uniform constant force at low Reynolds numbers. We have analyzed the different regimes and the morphology of such polymers in simple geometries, which allow us to highlight the peculiarities of the interplay between elastic and hydrodynamic stresses. Cooperative and symmetry breaking effects associated to the geometry of the fibers gives rise to characteristic motion which give them distinct properties from rigid and elastic filaments.

Fluctuation relation for weakly ergodic aging systems

A fluctuation relation for aging systems is introduced and verified by extensive numerical simulations. It is based on the hypothesis of partial equilibration over phase-space regions in a scenario of entropy-driven relaxation. The relation provides a simple alternative method, amenable of experimental implementation, to measure replica symmetry breaking parameters in aging systems. The connection with the effective temperatures obtained from the fluctuation-dissipation theorem is discussed

Topological phases in small quantum Hall samples

Topological order has proven a useful concept to describe quantum phase transitions which are not captured by the Ginzburg-Landau type of symmetry-breaking order. However, lacking a local order parameter, topological order is hard to detect. One way to detect it is via direct observation of anyonic properties of excitations which are usually discussed in the thermodynamic limit, but so far has not been realized in macroscopic quantum Hall samples. Here we consider a system of few interacting bosons subjected to the lowest Landau level by a gauge potential, and theoretically investigate vortex excitations in order to identify topological properties of different ground states. Our investigation demonstrates that even in surprisingly small systems anyonic properties are able to characterize the topological order. In addition, focusing on a system in the Laughlin state, we study the robustness of its anyonic behavior in the presence of tunable finite-range interactions acting as a perturbation. A clear signal of a transition to a different state is reflected by the system's anyonic properties.

Large D gravity and low D strings

We show that in the limit of a large number of dimensions a wide class of nonextremal neutral black holes has a universal near-horizon limit. The limiting geometry is the two-dimensional black hole of string theory with a two-dimensional target space. Its conformal symmetry explains the properties of massless scalars found recently in the large-D limit. For black branes with string charges, the near-horizon geometry is that of the three-dimensional black strings of Horne and Horowitz. The analogies between the α′ expansion in string theory and the large-D expansion in gravity suggest a possible effective string description of the large-D limit of black holes. We comment on applications to several subjects, in particular to the problem of critical collapse.

Synchronization of symmetric chaotic systems

This paper contains a study of the synchronization by homogeneous nonlinear driving of systems that are symmetric in phase space. The main consequence of this symmetry is the ability of the response to synchronize in more than just one way to the driving systems. These different forms of synchronization are to be understood as generalized synchronization states in which the motions of drive and response are in complete correlation, but the phase space distance between them does not converge to zero. In this case the synchronization phenomenon becomes enriched because there is multistability. As a consequence, there appear multiple basins of attraction and special responses to external noise. It is shown, by means of a computer simulation of various nonlinear systems, that: (i) the decay to the generalized synchronization states is exponential, (ii) the basins of attraction are symmetric, usually complicated, frequently fractal, and robust under the changes in the parameters, and (iii) the effect of external noise is to weaken the synchronization, and in some cases to produce jumps between the various synchronization states available

Dynamical sectors of a relativistic two particle model

We reconsider a model of two relativistic particles interacting via a multiplicative potential, as an example of a simple dynamical system with sectors, or branches, with different dynamics and degrees of freedom. The presence or absence of sectors depends on the values of rest masses. Some aspects of the canonical quantization are described. The model could be interpreted as a bigravity model in one dimension.

Symmetries of the free Schrödinger equation in the non-commutative plane

We study all the symmetries of the free Schr odinger equation in the non-commu- tative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schröodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.

Symmetries of the free Schrödinger equation in the non-commutative plane

We study all the symmetries of the free Schrödinger equation in the non-commu- tative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schröodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.

Plantas hospedantes de Rhopalosiphum maidis (Fitch) (Homoptera: Aphididae) y su papel en el ciclo biológico del pulgón en Cataluña

Se evaluó el papel de las distintas plantas hospedantes de Rhopalosiphum maidis (Fitch) en el ciclo biológico anual de los dos cariotipos más comunes en Cataluña (2n = 8 y 2n = 10 cromosomas) mediante el seguimiento de poblaciones de pulgones en cereales de invierno y verano y en gramíneas espontáneas. Asimismo se registró la densidad de R. maidis en parcelas comerciales de maíz y se determinó el periodo de colonización mediante la instalación de una trampa de succión. Las gramíneas espontáneas juegan un papel fundamental en el ciclo biológico anual de ambos cariotipos. Los pulgones de cariotipo 2n = 10 pueden vivir sobre cebada durante el otoño, invierno y primavera, y sobre gramíneas adventicias, como Setaria sp. y Echinochloa crus-galli ((L.) P. Beauv.), en verano e inicios de otoño; la superposición del ciclo de estas gramíneas permite a los pulgones con este cariotipo cerrar su ciclo anual en ellas. En el caso de los pulgones de cariotipo 2n = 8, el sorgo es el principal hospedante de verano; la cañota constituye un hospedante básico en primavera y otoño, pudiendo actuar como hospedante en inviernos extremadamente cálidos. El periodo primaveral de colonización del maíz por R. maidis se produjo principalmente en mayo y duró hasta mediados de junio. El número de alados capturados en la trampa de succión, así como el de individuos hallados sobre plantas, fue muy bajo tanto en mayo como en junio. Los resultados obtenidos sugieren que el maíz no juega un papel relevante en el ciclo de R. maidis. Se analizan algunas de las posibles causas de este fenómeno.

Ensayo de preferencia de individuos alados de Rhopalosiphum maidis (Fitch) (Homoptera: Aphididae) sobre siete gramíneas cultivadas

Se evaluó en laboratorio la preferencia de dos poblaciones leridanas de Rhopalosiphum maidis (Fitch) en la colonización de siete gramíneas cultivadas. Una de las poblaciones fue recogida sobre cañota (Sorghum halepense C. (L.) Pers.) y su cariotipo era 2n = 8. Los individuos de la otra población presentaban un cariotipo 2n = 10 y procedían de cebada. Las gramíneas testadas fueron: sorgo, maíz, trigo, trigo duro, cebada, triticale y avena. Los individuos alados de ambas poblaciones colonizaron los siete cereales aunque de distinta manera. El sorgo fue preferentemente colonizado por los pulgones con cariotipo 2n = 8 y el número de ninfas producidas en 48 horas fue mayor que en el resto de las gramíneas testadas. Los pulgones con cariotipo 2n = 10 mostraron preferencia por la cebada. Los alados de ambas poblaciones fueron incapaces de reproducirse sobre las plantas de maíz.