An ultrametric state space with a dense discrete overlap distribution: Paperfolding sequences

We compute the Parisi overlap distribution for paperfolding sequences. It turns out to be discrete, and to live on the dyadic rationals. Hence it is a pure point measure whose support is the full interval [-1; +1]. The space of paperfolding sequences has an ultrametric structure. Our example provides an illustration of some properties which were suggested to occur for pure states in spin glass models

Coarsening in 2D slabs

We study coarsening; that is, the zero-temperature limit of Glauber dynamics in the standard Ising model on slabs S_k = Z^2 x {0, ..., k-1} of all thicknesses k \geq 2 (with free and periodic boundary conditions in the third coordinate). We show that with free boundary conditions, for k \geq 3, some sites fixate for large times and some do not, whereas for k=2, all sites fixate. With periodic boundary conditions, for k \geq 4, some sites fixate and others do not, while for k=2 and 3, all sites fixate.Comment: 8 pages, 2 figure

On Bootstrap Percolation in Living Neural Networks

Recent experimental studies of living neural networks reveal that their global activation induced by electrical stimulation can be explained using the concept of bootstrap percolation on a directed random network. The experiment consists in activating externally an initial random fraction of the neurons and observe the process of firing until its equilibrium. The final portion of neurons that are active depends in a non linear way on the initial fraction. The main result of this paper is a theorem which enables us to find the asymptotic of final proportion of the fired neurons in the case of random directed graphs with given node degrees as the model for interacting network. This gives a rigorous mathematical proof of a phenomena observed by physicists in neural networks

Metastable States in Spin Glasses and Disordered Ferromagnets

We study analytically M-spin-flip stable states in disordered short-ranged Ising models (spin glasses and ferromagnets) in all dimensions and for all M. Our approach is primarily dynamical and is based on the convergence of a zero-temperature dynamical process with flips of lattice animals up to size M and starting from a deep quench, to a metastable limit. The results (rigorous and nonrigorous, in infinite and finite volumes) concern many aspects of metastable states: their numbers, basins of attraction, energy densities, overlaps, remanent magnetizations and relations to thermodynamic states. For example, we show that their overlap distribution is a delta-function at zero. We also define a dynamics for M=infinity, which provides a potential tool for investigating ground state structure.Comment: 34 pages (LaTeX); to appear in Physical Review

Changes in meltwater chemistry over a 20-year period following a thermal regime switch from polythermal to cold-based glaciation at Austre Broggerbreen, Svalbard

Our long-term study gives a rare insight into meltwater hydrochemistry following the transition of Austre Brøggerbreen from polythermal to cold-based glaciation and its continued retreat. We find that the processes responsible for ion acquisition did not change throughout the period of records but became more productive. Two regimes before and after July/August 2000 were identified from changes in solute concentrations and pH. They resulted from increased chemical weathering occurring in ice-marginal and proglacial environments that have become progressively exposed by glacier retreat. Carbonate carbonation nearly doubled between 2000 and 2010, whilst increases in the weathering of silicate minerals were also marked. In addition, the end of ablation season chemistry was characterized by reactions in long residence time flow paths like those in subglacial environments, in spite of their absence in the watershed. Furthermore, the retreat of the glacier caused the sudden re-routing of meltwaters through its immediate forefield during 2009, which more than doubled crustal ion yields in this particular year and influenced chemical weathering in 2010 regardless of a low water flux. Such a “flush” of crustally derived ions can be meaningful for downstream terrestrial and marine ecosystems. We therefore find that, during glacier retreat, the recently exposed forefield is the most chemically active part of the watershed, making high rates of weathering possible, even when ice losses have caused a switch to cold-based conditions with no delayed subglacial drainage flowpaths. In addition, the drainage system reorganization events result in significant pCO2 depletion in an otherwise high pCO2 system

Chemistry of clays and clay minerals

Les réactions de défense du palmier à huile contre la fusariose vasculaire sont stimulées de façon identique par la prémunition à l'aide d'une souche avirulente de FUSARIUM OXYSPORUM et par l'application d'éliciteurs fongiques. Les mécanismes physiologiques impliqués paraissent similaires TYPBIB