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Alexakis A.,CNRS ENS Statistical Physics Laboratory
Physical Review Letters

High Reynolds number magnetohydrodynamic turbulence in the presence of zero-flux large-scale magnetic fields is investigated as a function of the magnetic field strength. For a variety of flow configurations, the energy dissipation rate Ïμ follows the scaling Urms3/ℓ even when the large-scale magnetic field energy is twenty times larger than the kinetic energy. A further increase of the magnetic energy showed a transition to the Urms2Brms/ℓ scaling implying that magnetic shear becomes more efficient at this point at cascading the energy than the velocity fluctuations. Strongly helical configurations form nonturbulent helicity condensates that deviate from these scalings. Weak turbulence scaling was absent from the investigation. Finally, the magnetic energy spectra support the Kolmogorov spectrum k-5/3 while kinetic energy spectra are closer to the Iroshnikov-Kraichnan spectrum k-3/2 as observed in the solar wind. © 2013 American Physical Society. Source

Cocco S.,CNRS ENS Statistical Physics Laboratory | Monasson R.,CNRS Physics Laboratory | Weigt M.,University Pierre and Marie Curie
PLoS Computational Biology

Various approaches have explored the covariation of residues in multiple-sequence alignments of homologous proteins to extract functional and structural information. Among those are principal component analysis (PCA), which identifies the most correlated groups of residues, and direct coupling analysis (DCA), a global inference method based on the maximum entropy principle, which aims at predicting residue-residue contacts. In this paper, inspired by the statistical physics of disordered systems, we introduce the Hopfield-Potts model to naturally interpolate between these two approaches. The Hopfield-Potts model allows us to identify relevant 'patterns' of residues from the knowledge of the eigenmodes and eigenvalues of the residue-residue correlation matrix. We show how the computation of such statistical patterns makes it possible to accurately predict residue-residue contacts with a much smaller number of parameters than DCA. This dimensional reduction allows us to avoid overfitting and to extract contact information from multiple-sequence alignments of reduced size. In addition, we show that low-eigenvalue correlation modes, discarded by PCA, are important to recover structural information: the corresponding patterns are highly localized, that is, they are concentrated in few sites, which we find to be in close contact in the three-dimensional protein fold. © 2013 Cocco et al. Source

Mora T.,Princeton University | Mora T.,CNRS ENS Statistical Physics Laboratory | Bialek W.,Princeton University
Journal of Statistical Physics

Many of life's most fascinating phenomena emerge from interactions among many elements-many amino acids determine the structure of a single protein, many genes determine the fate of a cell, many neurons are involved in shaping our thoughts and memories. Physicists have long hoped that these collective behaviors could be described using the ideas and methods of statistical mechanics. In the past few years, new, larger scale experiments have made it possible to construct statistical mechanics models of biological systems directly from real data. We review the surprising successes of this "inverse" approach, using examples from families of proteins, networks of neurons, and flocks of birds. Remarkably, in all these cases the models that emerge from the data are poised near a very special point in their parameter space-a critical point. This suggests there may be some deeper theoretical principle behind the behavior of these diverse systems. © 2011 Springer Science+Business Media, LLC. Source

Maimbourg T.,Ecole Normale Superieure de Paris | Kurchan J.,CNRS ENS Statistical Physics Laboratory | Zamponi F.,Ecole Normale Superieure de Paris
Physical Review Letters

We obtain analytic expressions for the time correlation functions of a liquid of spherical particles, exact in the limit of high dimensions d. The derivation is long but straightforward: a dynamic virial expansion for which only the first two terms survive, followed by a change to generalized spherical coordinates in the dynamic variables leading to saddle-point evaluation of integrals for large d. The problem is, thus, mapped onto a one-dimensional diffusion in a perturbed harmonic potential with colored noise. At high density, an ergodicity-breaking glass transition is found. In this regime, our results agree with thermodynamics, consistently with the general random first order transition scenario. The glass transition density is higher than the best known lower bound for hard sphere packings in large d. Because our calculation is, if not rigorous, elementary, an improvement in the bound for sphere packings in large dimensions is at hand. © 2016 American Physical Society. Source

Alexakis A.,CNRS ENS Statistical Physics Laboratory
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

The dynamo instability is investigated in the limit of infinite magnetic Prandtl number. In this limit the fluid is assumed to be very viscous so that the inertial terms can be neglected and the flow is enslaved to the forcing. The forcing consist of an external forcing function that drives the dynamo flow and the resulting Lorentz force caused by the back reaction of the magnetic field. The flows under investigation are the Archontis flow and the ABC flow forced at two different scales. The investigation covers roughly 3 orders of magnitude of the magnetic Reynolds number above onset. All flows show a weak increase of the averaged magnetic energy as the magnetic Reynolds number is increased. Most of the magnetic energy is concentrated in flat elongated structures that produce a Lorentz force with small solenoidal projection so that the resulting magnetic field configuration is almost force free. Although the examined system has zero kinetic Reynolds number at sufficiently large magnetic Reynolds number the structures are unstable to small scale fluctuations that result in a chaotic temporal behavior. © 2011 American Physical Society. Source

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