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We study the nature of phase transitions in a self-gravitating classical gas in the presence of a central body. The central body can mimic a black hole at the center of a galaxy or a rocky core (protoplanet) in the context of planetary formation. In the chemotaxis of bacterial populations, sharing formal analogies with self-gravitating systems, the central body can be a supply of ``food'' (chemoattractant). We consider both microcanonical (fixed energy) and canonical (fixed temperature) descriptions and study the inequivalence of statistical ensembles. At high energies (resp. high temperatures), the system is in a ``gaseous'' phase and at low energies (resp. low temperatures) it is in a condensed phase with a ``cusp-halo'' structure, where the cusp corresponds to the rapid increase of the density of the gas at the contact with the central body. For a fixed density $\rho_{*}$ of the central body, we show the existence of two critical points in the phase diagram, one in each ensemble, depending on the core radius $R_{*}$: for small radii $R_{*}<R_{*}^{\rm MCP}$, there exist both microcanonical and canonical phase transitions (that are zeroth and first order); for intermediate radii $R_{*}^{\rm MCP}<R_{*}<R_{*}^{\rm CCP}$, only canonical phase transitions are present; and for large radii $R_{*}>R_{*}^{\rm CCP}$, there is no phase transition at all. We study how the nature of these phase transitions changes as a function of the dimension of space. We also discuss the analogies and the differences with phase transitions in the self-gravitating Fermi gas [P.H. Chavanis, Phys. Rev. E 65, 056123 (2002)].

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In cell membranes, proteins and lipids are organized into submicrometric nanodomains of varying sizes, shapes, and compositions, performing specific functions. Despite their biological importance, the detailed morphology of these nanodomains remains unknown. Not only can they hardly be observed by conventional microscopy due to their small size, but there is no full consensus on the theoretical models to describe their structuring and their shapes. Here, we use a combination of analytical calculations and Monte Carlo simulations based upon a model coupling membrane composition and shape to show that increasing protein concentration leads to an elongation of membrane nanodomains. The results are corroborated by single-particle tracking measurements on HIV receptors, whose level of expression in the membrane of specifically designed living cells can be tuned. These findings highlight that protein abundance can modulate nanodomain shape and potentially their biological function. Beyond biomembranes, this mesopatterning mechanism is of relevance in several soft-matter systems because it relies on generic physical arguments.

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Abstract Coarse-grained descriptions of collective motion of flocking systems are often derived for the macroscopic or the thermodynamic limit. However, many real flocks are small sized (10 to 100 individuals), called the mesoscopic scales, where stochasticity arising from the finite flock sizes is important. Developing mesoscopic scale equations, typically in the form of stochastic differential equations, can be challenging even for the simplest of the collective motion models. Here, we take a novel data-driven equation learning approach to construct the stochastic mesoscopic descriptions of a simple self-propelled particle (SPP) model of collective motion. In our SPP model, a focal individual can interact with k randomly chosen neighbours within an interaction radius. We consider k = 1 (called stochastic pairwise interactions), k = 2 (stochastic ternary interactions), and k equalling all available neighbours within the interaction radius (equivalent to Vicsek-like local averaging). The data-driven mesoscopic equations reveal that the stochastic pairwise interaction model produces a novel form of collective motion driven by a multiplicative noise term (hence termed, noise-induced flocking). In contrast, for higher order interactions (k > 1), including Vicsek-like averaging interactions, yield collective motion driven primarily by the deterministic forces. We find that the relation between the parameters of the mesoscopic equations describing the dynamics and the population size are sensitive to the density and to the interaction radius, exhibiting deviations from mean-field theoretical expectations. We provide semi-analytic arguments potentially explaining these observed deviations. In summary, our study emphasizes the importance of mesoscopic descriptions of flocking systems and demonstrates the potential of the data-driven equation discovery methods for complex systems studies.

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Les enjeux modernes de filtration de l’eau, de production d’énergie à partir de l’eau salée, et de stockage d’énergie avec des liquides ioniques nécessitent une description des phénomènes physiques à l’échelle du nanomètre, à l’interface entre la description continue des fluides et de la description particulaire de la matière. Cette thèse se concentre sur les phénomènes physiques qui ont cours lors du transport des ions en solution dans l’eau à travers les nanotubes en se concentrant sur l’interaction entre les ions et la surface des nanopores, et plus spécifiquement des nanotubes de carbone. Ceux-ci semblent prometteurs d’un point de vue technologique. Ce travail adopte une approche théorique mais nous comparons nos résultats aux données expérimentales lorsqu’elles existent. Dans un premier temps, après avoir passé en revue les mécanismes connus du transport des ions, nous nous intéressons à l’origine de la charge de surface du nanotube de carbone qui participe grandement aux grandes conductivités ioniques de l’électrolyte confiné dans le tube. Pour cela, nous explorons d’abord un mécanisme de régulation de charges des groupements chimiques de la surface, pour ensuite étudier la charge surfacique du nanotube de carbone quand il est soumis à une tension de grille par une électrode apposée au pore. Pour cela, nous avons exploré les propriétés intrinsèques de ce matériau et les inclure dans notre modèle théorique pour la conductivité. Ensuite, nous étudions les effets spécifiques aux ions pour analyser leur impact possible sur cette conductivité. En effet, en plus des effets purement électrostatiques, il existe d’autres effets non-décrits en champ moyen comme la répulsion diélectrique de la surface et le déficit de solvatation, déjà étudiés en partie pour un modèle d’ions ponctuels. De plus de récentes études expérimentales montrent que l’eau confinée à l’échelle nanométrique voit sa permittivité diélectrique diminuer drastiquement, ouvrant la possibilité qu’une énergie de Born intervienne également dans la barrière d’énergie d’entrée des ions dans le pore. Nous développons pour cela une approche variationnelle de théorie des champs pour des ions de taille finie et montrons à la fois l’impact de la taille des ions et de l’énergie de Born sur la concentration en ions dans la nanopore, directement reliée à la conductivité. Dans un dernier chapitre, nous développons au deuxième ordre notre approche variationnelle dans le but d’inclure la formation de paires d’ions dans la théorie.

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A single logotropic fluid, responsible for the existence of the whole dark sector, is here extensively revised at intermediate redshifts. In particular, by investigating possible generalizations that conceptually overcome previous issues of standard logotropic scenarios, we fix bound over classes of logotropic models that exhibit additional terms in the equation of state. Employing <math altimg="si1.svg" display="inline" id="d1e2965"><msub><mrow><mi>σ</mi></mrow><mrow><mn>8</mn></mrow></msub></math> measurements combined with low redshift data sets of Supernovae and Hubble observational data, we show the statistical significance of those extensions and their departure from the standard cosmological model. Evidences against generalized versions of logotropic models are, in particular, prompted. Our outcomes definitively show that any departure from the original logotropic model, including the Anton–Schmidt dark energy, are clearly disfavored at the level of perturbations and/or background cosmology. This indicates that, in order to have a logotropic fluid, plausible generalized versions of it would point out to reduce the complexity of the fluid itself, instead of adding extra terms.

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Fokker-Planck Cosmology Chemotaxis Galaxy Statistical mechanics Phase separation Axion star Equation of state Expansion acceleration Computational modeling Feedback Field theory scalar Marcheur aléatoire Brownian motion Mouvement brownien Wave function Axion Quantum chromodynamics axion 9530Sf Density Diffusion Numerical calculations 9862Gq Energy density Hydrodynamics Dark matter halo General relativity Chemotaxie Effondrement gravitationnel Gas Chaplygin Entropy Bose–Einstein condensates Scalar field Collapse Collective motion Halo Turbulence Einstein Nonrelativistic Cosmological model Fermi gas Critical phenomena Euler-Maclaurin Ions close to interfaces Dissipation Stability Formation Fuzzy Dark matter density Nanofiltration Denaturation Structure 9535+d Galaxies kinematics and dynamics Evaporation Gravitation self-force Dark energy Catastrophe theory DNA TASEP Pressure Interacting agents Generalized thermodynamics Dark matter fuzzy Cosmological constant Gravitation collapse Energy high Collisionless stellar-systems Energy internal Black hole Asymptotic behavior Competition Field theory scalar complex Gas Galaxies nuclei Dark matter condensation Rotation Game theory Gravitation Thermodynamics Fermions Smoluchowski equation Dark matter theory Kinetic theory Atmosphere Gravitational collapse Condensation Bose-Einstein Mass density Current fluctuations 9536+x Smoluchowski-Poisson Fermion 9880-k Bose-Einstein Computational modelling Glass transition Keller-Segel Bethe ansatz Dark matter Random walker


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