Matching with shift for one-dimensional Gibbs measures

We consider matching with shifts for Gibbsian sequences. We prove that the maximal overlap behaves as $c\log n$, where $c$ is explicitly identified in terms of the thermodynamic quantities (pressure) of the underlying potential. Our approach is based on the analysis of the first and second moment of the number of overlaps of a given size. We treat both the case of equal sequences (and nonzero shifts) and independent sequences.Comment: Published in at http://dx.doi.org/10.1214/08-AAP588 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

A numerical study of infinitely renormalizable area-preserving maps

It has been shown in (Gaidashev et al, 2010) and (Gaidashev et al, 2011) that infinitely renormalizable area-preserving maps admit invariant Cantor sets with a maximal Lyapunov exponent equal to zero. Furthermore, the dynamics on these Cantor sets for any two infinitely renormalizable maps is conjugated by a transformation that extends to a differentiable function whose derivative is Holder continuous of exponent alpha>0. In this paper we investigate numerically the specific value of alpha. We also present numerical evidence that the normalized derivative cocycle with the base dynamics in the Cantor set is ergodic. Finally, we compute renormalization eigenvalues to a high accuracy to support a conjecture that the renormalization spectrum is real

Spectral degeneracy and escape dynamics for intermittent maps with a hole

We study intermittent maps from the point of view of metastability. Small neighbourhoods of an intermittent fixed point and their complements form pairs of almost-invariant sets. Treating the small neighbourhood as a hole, we first show that the absolutely continuous conditional invariant measures (ACCIMs) converge to the ACIM as the length of the small neighbourhood shrinks to zero. We then quantify how the escape dynamics from these almost-invariant sets are connected with the second eigenfunctions of Perron-Frobenius (transfer) operators when a small perturbation is applied near the intermittent fixed point. In particular, we describe precisely the scaling of the second eigenvalue with the perturbation size, provide upper and lower bounds, and demonstrate $L^1$ convergence of the positive part of the second eigenfunction to the ACIM as the perturbation goes to zero. This perturbation and associated eigenvalue scalings and convergence results are all compatible with Ulam's method and provide a formal explanation for the numerical behaviour of Ulam's method in this nonuniformly hyperbolic setting. The main results of the paper are illustrated with numerical computations.Comment: 34 page

A Numerical Study of the Hierarchical Ising Model: High Temperature Versus Epsilon Expansion

We study numerically the magnetic susceptibility of the hierarchical model with Ising spins ($\sigma =\pm 1$) above the critical temperature and for two values of the epsilon parameter. The integrations are performed exactly, using recursive methods which exploit the symmetries of the model. Lattices with up to $2^18$ sites have been used. Surprisingly, the numerical data can be fitted very well with a simple power law of the form $(1- \beta /\beta _c )^{- \gamma}$for the {\it whole} temperature range. The numerical values for $\gamma$ agree within a few percent with the values calculated with a high-temperature expansion but show significant discrepancies with the epsilon-expansion. We would appreciate comments about these results.Comment: 15 Pages, 12 Figures not included (hard copies available on request), uses phyzzx.te

Warm and Cold Denaturation in the Phase Diagram of a Protein Lattice Model

Studying the properties of the solvent around proteins, we propose a much more sophisticated model of solvation than temperature-independent pairwise interactions between monomers, as is used commonly in lattice representations. We applied our model of solvation to a 16-monomer chain constrained on a two-dimensional lattice. We compute a phase diagram function of the temperature and a solvent parameter which is related to the pH of the solution. It exhibits a native state in which the chain coalesces into a unique compact conformation as well as a denatured state. Under certain solvation conditions, both warm and cold denaturations occur between the native and the denatured states. A good agreement is found with the data obtained from calorimetric experiments, thereby validating the proposed model.Comment: 7 pages, 2 figure

The Hierarchical Random Energy Model

We introduce a Random Energy Model on a hierarchical lattice where the interaction strength between variables is a decreasing function of their mutual hierarchical distance, making it a non-mean field model. Through small coupling series expansion and a direct numerical solution of the model, we provide evidence for a spin glass condensation transition similar to the one occuring in the usual mean field Random Energy Model. At variance with mean field, the high temperature branch of the free-energy is non-analytic at the transition point

Dual Fronts Propagating into an Unstable State

The interface between an unstable state and a stable state usually develops a single confined front travelling with constant velocity into the unstable state. Recently, the splitting of such an interface into {\em two} fronts propagating with {\em different} velocities was observed numerically in a magnetic system. The intermediate state is unstable and grows linearly in time. We first establish rigorously the existence of this phenomenon, called ``dual front,'' for a class of structurally unstable one-component models. Then we use this insight to explain dual fronts for a generic two-component reaction-diffusion system, and for the magnetic system.Comment: 19 pages, Postscript, A

A new view on exoplanet transits: Transit of Venus described using three-dimensional solar atmosphere Stagger-grid simulations

Stellar activity and, in particular, convection-related surface structures, potentially cause fluctuations that can affect the transit light curves. Surface convection simulations can help the interpretation of ToV. We used realistic three-dimensional radiative hydrodynamical simulation of the Sun from the Stagger-grid and synthetic images computed with the radiative transfer code Optim3D to provide predictions for the transit of Venus in 2004 observed by the satellite ACRIMSAT. We computed intensity maps from RHD simulation of the Sun and produced synthetic stellar disk image. We computed the light curve and compared it to the ACRIMSAT observations and also to the light curves obtained with solar surface representations carried out using radial profiles with different limb-darkening laws. We also applied the same spherical tile imaging method to the observations of center-to-limb Sun granulation with HINODE. We managed to explain ACRIMSAT observations of 2004 ToV and showed that the granulation pattern causes fluctuations in the transit light curve. We evaluated the contribution of the granulation to the ToV. We showed that the granulation pattern can partially explain the observed discrepancies between models and data. This confirms that the limb-darkening and the granulation pattern simulated in 3D RHD Sun represent well what is imaged by HINODE. In the end, we found that the Venus's aureole contribution during ToV is less intense than the solar photosphere, and thus negligible. Being able to explain consistently the data of 2004 ToV is a new step forward for 3D RHD simulations that are becoming essential for the detection and characterization of exoplanets. They show that the granulation have to be considered as an intrinsic incertitude, due to the stellar variability, on precise measurements of exoplanet transits of, most likely, planets with small diameters.Comment: Accepted for publication in Astronomy and Astrophysic