Deformation of geometry and bifurcation of vortex rings

We construct a smooth family of Hamiltonian systems, together with a family of group symmetries and momentum maps, for the dynamics of point vortices on surfaces parametrized by the curvature of the surface. Equivariant bifurcations in this family are characterized, whence the stability of the Thomson heptagon is deduced without recourse to the Birkhoff normal form, which has hitherto been a necessary tool.Comment: 26 page

Stability of relative equilibria with singular momentum values in simple mechanical systems

A method for testing $G_\mu$-stability of relative equilibria in Hamiltonian systems of the form "kinetic + potential energy" is presented. This method extends the Reduced Energy-Momentum Method of Simo et al. to the case of non-free group actions and singular momentum values. A normal form for the symplectic matrix at a relative equilibrium is also obtained.Comment: Partially rewritten. Some mistakes fixed. Exposition improve

Memory for single items, word pairs, and temporal order of different kinds in a patient with selective hippocampal lesions

One kind of between-list and two kinds of within-list temporal order memory were examined in a patient with selective bilateral hippocampal lesions. This damage disrupted memory for all three kinds of temporal order memory, but left item and word pair recognition relatively intact. These findings are inconsistent with claims that (1) hippocampal lesions, like those of the medial temporal lobe (MTL) cortex, disrupt item and word pair recognition, and that (2) hippocampal lesions disrupt temporal order memory and item recognition to the same degree. Not only was word pair recognition intact in the patient, but further evidence indicates that her recognition of other associations between items of the same kind is also spared so retrieval of such associations cannot be sufficient to support within-list temporal order recognition. Rather, as other evidence indicates that the patient is impaired at recogni-tion of associations between different kinds of information, within-list (and possibly between-list) temporal order memory may be impaired by hippocampal lesions because it critically depends on re-trieving associations between different kinds of information

The effect of two planting dates on the physiological age and yielding potential of seed potatoes grown in a warm temperate climate in Argentina

The effect of two planting dates upon the physiological age of seed tubers, measured by their incubation period, and their yielding potential was studied during a three-year period with two medium-early and one medium-late cultivar. Although seed tubers of the December planting were physiologically significantly younger than those obtained from the November planting in two of the three seasons studied, no reliable effect upon tuber yield was found. Reasons for this lack of relation are discussed. The accumulated day-degrees above 17°C (daily mean temperature) during the bulking period of the seed crop modified the incubation period of the tubers clearly.Der Einfluss zweier Pflanztermine auf das physiologische Alter von Pflanzkartoffeln und ihr Ertragspotential wurde während einer Dreijahresperiode an zwei mittelfrühen Sorten, Spunta und Kennebec, und einer mittelspäten Sorte, Bonaerense la Ballenera MAA, in warmer gemässigter Klimazone in Argentinien geprüft. Saatbestände aus November- und Dezemberpflanzungen von 1979, 1980 und 1981 wurden im November 1980, 1981 und 1982 in vergleichenden Ertragsversuchen gepflanzt. Das physiologische Alter der Knollen wurde bei der Pflanzung durch die Inkubationsperiode (Claver, 1973, 1975) gemessen. Abb. 1 zeigt die meteorologischen Daten der vier Vegetationsperioden. Es ergaben sich signifikante Unterschiede im physiologischen Alter zwischen den Sorten und den Pflanzterminen (Tab. 1). Bei Lagerung der Saatkartoffeln in Mieten im Feld beschleunigte sich das physiologische Alter (Tab. lc). Die Gesamtknollenerträge schwankten zwischen den Sorten in 1980/81 und 1982/83 (Tab. 2a und 2c), es ergaben sich jedoch keine signifikanten Unterschiede zwischen Pflanzgut der beiden Pflanztermine, obwohl sich zwischen beiden Pflanzterminen Unterschiede im physiologischen Alter ergaben. Der Gesamtknollenertrag war 1982/83 am höchsten (Tab. 2c), obwohl die Pflanzknollen physiologisch die Ältesten waren. Es ist unwahrscheinlich, dass eine hohe prozentuale Infektionsrate mit PLRV und PVY der Pflanzknollen von Spunta und Kennebec aus der Dezemberflanzung den Einfluss des physiologischen Alters auf den Ertrag derart überdeckte, dass keine signifikanten Unterschiede mehr gefunden werden konnten (Abb. 2). Weil die Unterschiede im physiologischen Alter innerhalb einer Sorte jedoch klein waren, waren andere ertragsbestimmende Faktoren offensichtlich wichtiger als die Unterschiede im Alter. Die akkumulierten Tagesgrade über einer täglichen Temperatur von 17°C während der Periode des Knollenansatzes hatten eine klare Änderung der Inkubationsperiode zur Folge.L'effet de deux dates de plantation sur l'âge physiologique de tubercules de semence et sur leur rendement potentiel a été étudié durant une période de trois années avec deux variétés demi-hâtives, Spunta et Kennebec, et une demi-tardive, Bonaerense la Ballenera MAA, cultivées dans un climat chaud d'Argentine. Les plants récoltés en novembre et décembre des années 1979, 1980 et 1981 ont été plantés en novembre 1980, 1981 et 1982 selon des essais comparables de rendement. L'âge physiologique des tubercules était évalué à la plantation par la période d'incubation (Claver, 1973, 1975). Les relevés météorologiques pour les quatres saisons sont donnés dans la fig. 1. On observait des différences significatives dans l'âge physiologique entre les variétés et les dates de plantation (tabl. 1). Quand les tubercules de semence étaient conservés en silo au champ, l'âge physiologique était avancé (tabl. lc). Le rendement total en tubercules était différent entre variétés pour 1980/81 et 1982/83 (tabl. 2a et 2c) mais il n'y avait pas de différences significatives entre les plants des deux dates de plantation bien qu'il y ait des différences significatives dans leur âge physiologique. Le rendement total en tubercules était plus élevé en 1982/83 (tabl. 2c) malgré des tubercules de semence physiologiquement plus vieux. Il est peu probable que le taux important d'infection par les virus de l'enroulement et Y des semences de Spunta et Kennebec observé de l'âge physiologique des plants sur les rendements, ceux-ci ne présentant aucune différence significative (fig. 2). De plus, parce que les différences d'âge physiologique des semences au sein d'une variété sont-faibles, d'autres facteurs déterminants que le rendement doivent avoir été plus importants que la différence d'âge. Le cumul jour-degrés au-dessus de la température journalière de 17°C durant la période de tubérisation des tubercules de semence modifie sensiblement la durée d'incubation des plants (fig. 3).Instituto de Fisiología Vegeta

Golden gaskets: variations on the Sierpi\'nski sieve

We consider the iterated function systems (IFSs) that consist of three general similitudes in the plane with centres at three non-collinear points, and with a common contraction factor \la\in(0,1). As is well known, for \la=1/2 the invariant set, \S_\la, is a fractal called the Sierpi\'nski sieve, and for \la<1/2 it is also a fractal. Our goal is to study \S_\la for this IFS for 1/2<\la<2/3, i.e., when there are "overlaps" in \S_\la as well as "holes". In this introductory paper we show that despite the overlaps (i.e., the Open Set Condition breaking down completely), the attractor can still be a totally self-similar fractal, although this happens only for a very special family of algebraic \la's (so-called "multinacci numbers"). We evaluate \dim_H(\S_\la) for these special values by showing that \S_\la is essentially the attractor for an infinite IFS which does satisfy the Open Set Condition. We also show that the set of points in the attractor with a unique ``address'' is self-similar, and compute its dimension. For ``non-multinacci'' values of \la we show that if \la is close to 2/3, then \S_\la has a nonempty interior and that if \la<1/\sqrt{3} then \S_\la$ has zero Lebesgue measure. Finally we discuss higher-dimensional analogues of the model in question.Comment: 27 pages, 10 figure

Equivalent forms of Dirac equations in curved spacetimes and generalized de Broglie relations

One may ask whether the relations between energy and frequency and between momentum and wave vector, introduced for matter waves by de Broglie, are rigorously valid in the presence of gravity. In this paper, we show this to be true for Dirac equations in a background of gravitational and electromagnetic fields. We first transform any Dirac equation into an equivalent canonical form, sometimes used in particular cases to solve Dirac equations in a curved spacetime. This canonical form is needed to apply the Whitham Lagrangian method. The latter method, unlike the WKB method, places no restriction on the magnitude of Planck's constant to obtain wave packets, and furthermore preserves the symmetries of the Dirac Lagrangian. We show using canonical Dirac fields in a curved spacetime, that the probability current has a Gordon decomposition into a convection current and a spin current, and that the spin current vanishes in the Whitham approximation, which explains the negligible effect of spin on wave packet solutions, independent of the size of Planck's constant. We further discuss the classical-quantum correspondence in a curved spacetime based on both Lagrangian and Hamiltonian formulations of the Whitham equations. We show that the generalized de Broglie relations in a curved spacetime are a direct consequence of Whitham's Lagrangian method, and not just a physical hypothesis as introduced by Einstein and de Broglie, and by many quantum mechanics textbooks.Comment: PDF, 32 pages in referee format. Added significant material on canonical forms of Dirac equations. Simplified Theorem 1 for normal Dirac equations. Added section on Gordon decomposition of the probability current. Encapsulated main results in the statement of Theorem

Resonances in a spring-pendulum: algorithms for equivariant singularity theory

A spring-pendulum in resonance is a time-independent Hamiltonian model system for formal reduction to one degree of freedom, where some symmetry (reversibility) is maintained. The reduction is handled by equivariant singularity theory with a distinguished parameter, yielding an integrable approximation of the Poincaré map. This makes a concise description of certain bifurcations possible. The computation of reparametrizations from normal form to the actual system is performed by Gröbner basis techniques.