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International audience; Observations of the interstellar medium (ISM) show a complex density and velocity structure, which is in part attributed to turbulence. Consequently, the multifractal formalism should be applied to observation maps of the ISM in order to characterize its turbulent and multiplicative cascade properties. However, the multifractal formalism, even in its more advanced and recent canonical versions, requires a large number of realizations of the system, which usually cannot be obtained in astronomy. We present a self-contained introduction to the multifractal formalism in a "microcanonical" version, which allows us, for the first time, to compute precise turbulence characteristic parameters from a single observational map without the need for averages in a grand ensemble of statistical observables (e.g., a temporal sequence of images). We compute the singularity exponents and the singularity spectrum for both observations and magnetohydrodynamic simulations, which include key parameters to describe turbulence in the ISM. For the observations we focus on the 250 µm Herschel map of the Musca filament. Scaling properties are investigated using spatial 2D structure functions, and we apply a two-point log-correlation magnitude analysis over various lines of the spatial observation, which is known to be directly related to the existence of a multiplicative cascade under precise conditions. It reveals a clear signature of a multiplicative cascade in Musca with an inertial range from 0.05 to 0.65 pc. We show that the proposed microcanonical approach provides singularity spectra that are truly scale invariant, as required to validate any method used to analyze multifractality. The obtained singularity spectrum of Musca, which is sufficiently precise for the first time, is clearly not as symmetric as usually observed in log-normal behavior. We claim that the singularity spectrum of the ISM toward Musca features a more log-Poisson shape. Since log-Poisson behavior is claimed to exist when dissipation is stronger for rare events in turbulent flows, in contrast to more homogeneous (in volume and time) dissipation events, we suggest that this deviation from log-normality could trace enhanced dissipation in rare events at small scales, which may explain, or is at least consistent with, the dominant filamentary structure in Musca. Moreover, we find that subregions in Musca tend to show different multifractal properties: While a few regions can be described by a log-normal model, other regions have singularity spectra better fitted by a log-Poisson model. This strongly suggests that different types of dynamics exist inside the Musca cloud. We note that this deviation from log-normality and these differences between subregions appear only after reducing noise features, using a sparse edge-aware algorithm, which have the tendency to "log-normalize" an observational map. Implications for the star formation process are discussed. Our study establishes fundamental tools that will be applied to other galactic clouds and simulations in forthcoming studies.

International audience; Cardiac fibrillation a ects the atria or the ventricles and, in both cases, poses major challenges to public health management. Atrial fibrillation is the predominant cause of embolic stroke while ventricular fibrillation leads to sudden cardiac arrest and death. The medical community of cardiac electro-physiologists consider cardiac fibrillation as a disease of known cause, namely a chaotic multiplication of electric pulse reentries, but of unknown trigger. Putative triggers are targeted in an e ort to solve this riddle by a combination of safe therapies including anti-arrhythmic drugs and catheter radio-frequency ablation. In two recent works (10.3389/fphys.2017.01139 and 10.3389/fphys.2019.00480), with Evgeniya Gerasimova Françoise Argoul and Alain Arneodo, we have provided evidence and modeling which clash with the accepted wisdom. We give here the main argument for the incompatibility of the random multifractal scaling, revealed in recordings of the electrical activity of fibrillating human hearts, with the reentry paradigm. In the model, pulse dynamics is akin to a random branching birth and death process due to a highly fluctuating conductance. In this respect, we sketch a calculation of the multifractal spectrum for our cardiac modeling, which underlines how the multifractal parameter is related to the variance of the abnormal capacitive electric field at the gap junction channels. Those new observations and modeling raise a number of theoretical and practical possibilities and new challenges, such as electric recording interpretation from the level of cell-to-cell coupling up to the level of neural modulations. Gray area Is atrial fibrillation characterized only by spatio-temporal irregularity of local beat-to-beat cycles? Figure 1: Left: Atrial fibrillation schematic mechanisms. Right: High density mapping of activation times.

International audience; The formation of stars is intimately linked to the structure and evolution of molecular clouds in the interstellar medium. The French-German (ANR/DFG) collaborative project GENESIS (GENeration and Evolution of Structures in the ISm, http://www.astro.uni-koeln.de/GENESIS), explores this link with a new approach: by combining far-infrared data of dust (Herschel), observations of major cooling lines in the interstellar medium (CII, CI, CO, OI with the Stratospheric Observatory for FIR astronomy SOFIA), and molecular line maps from ground-based telescopes. It is also supported by the German Government funded MOBS (Modelling SOFIA data). We here present results of two workpackages, one showing SOFIA OI observations in the massive star-forming regions S106, and one investigating molecular cloud formation in the diffuse Draco cloud.

International audience; Atrial fibrillation (AF) is a cardiac arrhythmia characterized by rapid and irregular atrial electrical activity with a high clinical impact on stroke incidence. Best available therapeutic strategies combine pharmacological and surgical means. But when successful, they do not always prevent long-term relapses. Initial success becomes all the more tricky to achieve as the arrhythmia maintains itself and the pathology evolves into sustained or chronic AF. This raises the open crucial issue of deciphering the mechanisms that govern the onset of AF as well as its perpetuation. In this study, we develop a wavelet-based multi-scale strategy to analyze the electrical activity of human hearts recorded by catheter electrodes, positioned in the coronary sinus (CS), during episodes of chronic AF. We compute the so-called multifractal spectra using two variants of the wavelet transform modulus maxima method, the moment (partition function) method and the magnitude cumulant method. Application of these methods to long time series recorded in a patient with chronic AF provides quantitative evidence of the multifractal intermittent nature of the electric energy of passing cardiac impulses at low frequencies, i.e. for times (>= 0.5 s) longer than the mean interbeat (10^{-1}s). We also report the results of a two-point magnitude correlation analysis which infers the absence of a multiplicative timescale structure underlying multifractal scaling. The electric energy dynamics looks like a " multifractal white noise " with quadratic (log-normal) multifractal spectra. These observations challenge concepts of functional reentrant circuits in mechanistic theories of AF, still leaving open the role of the autonomic nervous system (ANS). A transition is indeed observed in the computed multifractal spectra which group according to two distinct areas, consistently with the anatomical substrate binding to the CS, namely the left atrial posterior wall, and the ligament of Marshall which is innervated by the ANS. In a companion paper (II. Modeling), we propose a mathematical model of a denervated heart where the kinetics of gap junction conductance alone induces a desynchronization of the myocardial excitable cells, accounting for the multifractal spectra found experimentally in the left atrial posterior wall area.

International audience; Filamentary star formation Herschel observations revealed the ubiquitous presence of interstellar filaments and their importance in star formation (e.g. [1],[2],[3]). It is proposed that they form by dissipation of kinetic energy in large scale magneto-hydrodynamic flows through low-velocity magnetised shocks (C-shocks) and then fragment in prestellar cores after reaching a density threshold of ∼ 16 M /pc [4],[5]. There are indications that these filaments accrete mass through inflow of matter from the sides along the magnetic field (e.g. [6],[7]). However, direct evidence of such shocks is vital to confirm this scenario.

https://statphys26.sciencesconf.org/; International audience; Challenges of C arrhythmias raised by the data:1-Most frequent cause of embolic stroke (AF),with evolution to chronic disease. Major causeof natural death (VF), about 5% only are saved.2-Hysteresis: strike twice and patient resuscitates.3-Most models refer to chaotic dynamics, but thisdoes not describe spontaneous reversions tolesser C arrhythmias.Some features suggest intrinsic disorder:1-The data show intermittency of beat-to-beatintervals and peaks amplitude.2-Slow evolution of vulnerability (thesusceptibility), so called remodeling.Conduction velocity is not known to be very much affected. Intermittency may instead reveal nucleation and contamination processes à laPomeau. However, the medium is excitable and excitability is a robust cycle to any homo- or heteroclinic nucleation. Alteration of conduction, e.g. on a nearly percolating fibrotic substrate, yields fancy anatomical reentries, but no such intermittent behavior. We believe that the data is suggestive of fragmented pulses, following from the desynchronization of the network of electrically coupled excitable cells.

International audience; We elaborate on quite a surprising mapping between plasma excitation Landau damping to a«quantum statistical» perturbative treatment of Schrödinger equation in a nonlinear potential.Firstly, the setting for this mapping is to assume spatially inhomogeneous stable modes, such asBernstein Green Kruskal modes. Bulk plasma frequency is then locally slightly altered by those.From a low frequency approximation of Bohm and Gross dispersion relation, we write a nonlinearSchrödinger equation for fluctuating macroscopic quantities, like the density of trapped particles.Naïvely, a statistical time dependant perturbative treatment of the relaxation of excitations comesfrom self-scattering. Dyson’s equation accounts for the renormalised bulk plasma frequency. Thissetting also predicts a Lamb shift for the only remaining ground state energy mode. Landaudamping is retrieved when one estimates the energy spectrum from local equilibrium, which showsa condensation at Debye’s wavelength. Or in other words, a gap has opened.It is in full agreement with the fluctuation-dissipation theorem and holds for all time.This mapping seems to be a natural continuum limit for a statistical treatment of bulk plasmaperturbations. It can be extended to the non perturbative case of Lynden-Bell violent relaxation.Secondly, wediscuss the justification of renormalisation in this context. Naturally, the statisticaltreatment is traced back to the presence of intrinsic disorder from the wild oscillations in phasespace. Precisely, a minimal mean field model is written for the coarse grained dynamics. It isinstructive to draw an illustration from the idea of a hierarchy of KAM tori and the emergence offrustration for the oscillations of trapped particles. Based on ideas by D. Escande and S. McKay,we arrive at an effective coupling between neighbouring clusters of trapped particles which isrenormalised chaotically. Thus, defining a local phase for the spatially inhomogeneous oscillationsof macroscopic quantities, it is possible to «geometrize» their symplectic dynamics, therebyjustifying the initially intuitive «quantum statistical» treatment of the Schrödinger equation.For driven systems, the chaotic parameter further forces large deviations on the dynamics, withnon-Maxwellian stationary distributions, or strong turbulence. Therefore, since at large scalesexchange entropy with bulk plasma and (KS-)entropy production rates are high, a comparison withcoupled chaotic map lattices for coarse grained observables is qualitatively worthy. This implies arich structure of phase space diagram, where many transitions are to be expected between stableor metastable states (phases), related to QSSs (quasi stationary states).

International audience; The noisy aspect of data recorded by electrodes, on the inner surface of human atria during episodes of atrial fibrillation, exhibit intriguing features for excitable media. Instead of phase chaos as typically expected, it shares many common traits of non-equilibrium fluctuations in disordered systems or strong turbulence. To assess those peculiar observations we investigate a synaptic plasticity that affects conduction properties. Electrical synapses comprise many different kinds of connexins, which may be affected by diverse factors, so we use a generic approach. Slight detuning of their linear response leads to an instability of the modulating agents, here an excess charge. Acting on slow time scales of repolarisation, it is understood as collective modes propagating through and retroacting on each synapse: The medium is desynchronised. It is not a syncytium. Transient states are here associated with a phenomenon called electrical remodelling, which has not received any accepted description thus far. Moreover, from the properties of the model it is possible to start exploring phase space. Transitions between different regimes could help decipher stages in the evolution of the disease from acute to chronic, one main goal of cardiovascular research.

Ma thèse développe essentiellement la phénoménologie d'une forme particulière de relaxation pour le non équilibre ; d'abord dans le cas du plasma magnétisé, où il est identifié en un sens précis un point critique, autour duquel la relaxation est intermittente, puis dans un cadre plus général. Est reconsidéré la résonance entre ondes de Langmuir et particules : "l'amortissement Landau" n'est pas de nature cinétique, pour la simple raison que le champ est moyen. La preuve est apportée par le calcul des susceptibilités. Etablir cette preuve nécessite de recourir à l'hypothèse de linéarité thermodynamique, or l'instabilité est du type Rayleigh, qui développe une turbulence loin de l'équilibre. Il s'avère que dans une description de type Van der Waals, la définition de l'énergie libre est compromise par des coefficients fluctuants : des cycles s'effectuent entre les régions sur-critique et métastable. Par extrapolation de la théorie de Landau, ou avec l'argument d'une orbite de renormalisation chaotique,à cause de la présence d'un champ extérieur, intrinsèque et non nul, on détermine les exposants critiques. Ils sont notoirement différentes de ceux que livrent la théorie statique ou même la théorie dynamique critique. En particulier, z=1. Dans le régime stationnaire, l'hypothèse d'invariance d'échelle permet d'associer une généralisation de la relation de fluctuation-dissipation. Il y a l'amorce de la détermination, assez universelle, des distributions non maxwelliennes.