Hamiltonian model of capture into mean motion resonance

Mean motion resonances are a common feature of both our own Solar System and of extrasolar planetary systems. Bodies can be trapped in resonance when their orbital semi-major axes change, for instance when they migrate through a protoplanetary disc. We use a Hamiltonian model to thoroughly investigate the capture behaviour for first and second order resonances. Using this method, all resonances of the same order can be described by one equation, with applications to specific resonances by appropriate scaling. We focus on the limit where one body is a massless test particle and the other a massive planet. We quantify how the the probability of capture into a resonance depends on the relative migration rate of the planet and particle, and the particle's eccentricity. Resonant capture fails for high migration rates, and has decreasing probability for higher eccentricities, although for certain migration rates, capture probability peaks at a finite eccentricity. We also calculate libration amplitudes and the offset of the libration centres for captured particles, and the change in eccentricity if capture does not occur. Libration amplitudes are higher for larger initial eccentricity. The model allows for a complete description of a particle's behaviour as it successively encounters several resonances. The model is applicable to many scenarios, including (i) Planet migration through gas discs trapping other planets or planetesimals in resonances; (ii) Planet migration through a debris disc; (iii) Dust migration through PR drag. Full details can be found in \cite{2010submitted}. (Abridged)Comment: 4 pages, Proceedings of IAUS276 "The Astrophysics of Planetary Systems: Formation, Structure, and Dynamical Evolution

Modelling fungal colonies and communities:challenges and opportunities

This contribution, based on a Special Interest Group session held during IMC9, focuses on physiological based models of filamentous fungal colony growth and interactions. Fungi are known to be an important component of ecosystems, in terms of colony dynamics and interactions within and between trophic levels. We outline some of the essential components necessary to develop a fungal ecology: a mechanistic model of fungal colony growth and interactions, where observed behaviour can be linked to underlying function; a model of how fungi can cooperate at larger scales; and novel techniques for both exploring quantitatively the scales at which fungi operate; and addressing the computational challenges arising from this highly detailed quantification. We also propose a novel application area for fungi which may provide alternate routes for supporting scientific study of colony behaviour. This synthesis offers new potential to explore fungal community dynamics and the impact on ecosystem functioning

Hercynian Metamorphism in the Catalonian Coastel Ranges

Paleozoic rocks in the Catalonian Coastal Ranges are in their largest part affectedby alow- tovery-low grade Hercynian metamorphism. Amphibolite facies conditions are only found in restricted areas such as the southwestern part of the Guilleries massif where upper amphibolite facies conditions are reached. Metamorphic grade increases from top to bottom of the Paleozoic stratigraphic sequence and the metamorphic peak is diachronous, being progressively older in the lower grade metamorphic zones. The isograd pattern, mineral assemblages, mineral chemistry and preserved reaction textures are consistent with a low pressure metamorphism possibly evolving from a previous Barrovian type event. The metamorphic climax in the high grade zone was reached after the seconddeformational phase. Calculatedpeak P-Tconditions are 620-640 OC and around 3.5 Kb . A latter episode of decompression from the maximum conditions to 1-2 Kb, with an associated temperature decrease to 530-550 OC, is recognized. The intrusion of late Hercynian granitoids produced contact metamorphic aureoles where the pyroxene-hornfels facies is locally reached

Stable, metastable and unstable states in the mean-field RFIM at T=0

We compute the probability of finding metastable states at a given field in the mean-field random field Ising model at T=0. Remarkably, this probability is finite in the thermodynamic limit, even on the so-called ``unstable'' branch of the magnetization curve. This implies that the branch is reachable when the magnetization is controlled instead of the magnetic field, in contrast with the situation in the pure system.Comment: 10 pages, 3 figure

Capillary condensation in one-dimensional irregular confinement

Peer reviewedPublisher PD