A perturbation procedure for nonlinear oscillations (The dynamics of two oscillators with weak nonlinear coupling)

This thesis considers in detail the dynamics of two oscillators with weak nonlinear coupling. There are three classes of such problems: non-resonant, where the Poincaré procedure is valid to the order considered; weakly resonant, where the Poincaré procedure breaks down because small divisors appear (but do not affect the O(1) term) and strongly resonant, where small divisors appear and lead to O(1) corrections. A perturbation method based on Cole's two-timing procedure is introduced. It avoids the small divisor problem in a straightforward manner, gives accurate answers which are valid for long times, and appears capable of handling all three types of problems with no change in the basic approach.

One example of each type is studied with the aid of this procedure: for the nonresonant case the answer is equivalent to the Poincaré result; for the weakly resonant case the analytic form of the answer is found to depend (smoothly) on the difference between the initial energies of the two oscillators; for the strongly resonant case we find that the amplitudes of the two oscillators vary slowly with time as elliptic functions of ϵ t, where ϵ is the (small) coupling parameter.

Our results suggest that, as one might expect, the dynamical behavior of such systems varies smoothly with changes in the ratio of the fundamental frequencies of the two oscillators. Thus the pathological behavior of Whittaker's adelphic integrals as the frequency ratio is varied appears to be due to the fact that Whittaker ignored the small divisor problem. The energy sharing properties of these systems appear to depend strongly on the initial conditions, so that the systems not ergodic.

The perturbation procedure appears to be applicable to a wide variety of other problems in addition to those considered here.

Studies on the condition factor of the Sierra Leone mangrove oyster (Crassostrea tulipa)

Sierra Leone is a tropical country where water temperatures are high throughout the year. Consequently the local oysters tend to spawn the year round, with one or two spawning peaks. The condition of such tropical oysters may not be as high as those oyesters in temperate countries since the stored glycogen is regularly utilized to form gonads. A high condition factor value indicates that the oysters have accumulated glycogen and or gonads, whereas a low condition factor value indicates that the oysters have spawned and are in the process of accumulating glycogen, which may later be utilized for gonad development. In oyster culture, condition factor studies may be supported by plankton and oyster spat settlement studies in the culture area. These studies give an indication of when oyster larvae and spat settlement are at their peak values. In Sierra Leone studies of the plankton and spat settlement are undertaken every week throughout the year. Conditions factor is obtained from the ratio weight of dry (oyster) meat x 1000/internal volume. Detailed condition factor values are shown in relation to salinity at two stations. Condition factor declines with reducing salinity, which principally occurs during the rainy season. The best times to collect spat are May to June and September to October

ELEBIDUN : un projet de recherche sur l’apprentissage bilingue basque-français

[FR] Depuis plusieurs décennies, il existe une offre de scolarisation en langue basque dans les établissements scolaires du Pays basque nord (Pyrénées Atlantiques). Les élèves qui suivent une scolarité bilingue sont inscrits soit dans un établissement qui pratique la méthode dite immersive (Ikastolak de Seaska) soit dans un modèle à parité horaire dans un établissement public ou privé1. Ainsi, il est possible pour un élève de mener l’apprentissage de la langue basque en parallèle avec celui du français depuis l’école primaire jusqu’au lycée. Cette offre de scolarisation est en développement constant (38 ouvertures sur les 6 dernières années scolaires) et elle concerne aujourd’hui plus d’une école sur deux (58 %), 34 % des élèves du primaire et 43 % des enfants en maternelle.

La estratigrafía analítica: 25 años de ensayo y aprendizaje en el análisis e interpretación del registro arqueológico

Homenaje a Georges Laplace, realizado en Vitoria-Gasteiz el 13,14 y 15 de noviembre de 2012. Edición a cargo de Aitor Calvo, Aitor Sánchez, Maite García-Rojas y Mónica Alonso-Eguíluz.