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We discuss the occurrence of gravitational phase transitions and instabilities in a gas of self-gravitating fermions within the framework of general relativity. In the classical (nondegenerate) limit, the system undergoes a gravitational collapse at low energies E<Ec and low temperatures T<Tc . This is called “gravothermal catastrophe” in the microcanonical ensemble and “isothermal collapse” in the canonical ensemble. When quantum mechanics is taken into account and when the particle number is below the Oppenheimer-Volkoff limit ( N<NOV ), complete gravitational collapse is prevented by the Pauli exclusion principle. In that case, the Fermi gas undergoes a gravitational phase transition from a gaseous phase to a condensed phase. The condensed phase represents a compact object like a white dwarf, a neutron star, or a dark matter fermion ball. When N>NOV , there can be a subsequent gravitational collapse below a lower critical energy E<Ec″ or a lower critical temperature T<Tc′ leading presumably to the formation of a black hole. The evolution of the system is different in the microcanonical and canonical ensembles. In the microcanonical ensemble, the system takes a “core-halo” structure. The core consists in a compact quantum object or a black hole while the hot halo is expelled at large distances. This is reminiscent of the red giant structure of low-mass stars or the implosion-explosion of massive stars (supernova). In the canonical ensemble, the system collapses as a whole towards a compact object or a black hole. This is reminiscent of the implosion of supermassive stars (hypernova).

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In a previous paper (Chavanis, 2015) we have introduced a new cosmological model that we called the logotropic model. This model involves a fundamental constant Λ which is the counterpart of Einstein’s cosmological constant in the Λ CDM model. The logotropic model is able to account, without free parameter, for the constant surface density of the dark matter halos, for their mass–radius relation, and for the Tully-Fisher relation. In this paper, we explore other consequences of this model. By advocating a form of “strong cosmic coincidence” we predict that the present proportion of dark energy in the Universe is Ωde,0=e∕(1+e)≃0.731 which is close to the observed value. We also remark that the surface density of dark matter halos and the surface density of the Universe are of the same order as the surface density of the electron. This makes a curious connection between cosmological and atomic scales. Using these coincidences, we can relate the Hubble constant, the electron mass and the electron charge to the cosmological constant. We also suggest that the famous numbers 137 (fine-structure constant) and 123 (logotropic constant) may actually represent the same thing. This could unify microphysics and cosmophysics. We study the thermodynamics of the logotropic model and find a connection with the Bekenstein-Hawking entropy of black holes if we assume that the logotropic dark fluid is made of particles of mass mΛ∼ħΛ∕c2=2.08×10−33eV∕c2 (cosmons). In that case, the universality of the surface density of the dark matter halos may be related to a form of holographic principle (the fact that their entropy scales like their area). We use similar arguments to explain why the surface density of the electron and the surface density of the Universe are of the same order and justify the empirical Weinberg relation. Finally, we combine the results of our approach with the quantum Jeans instability theory to predict the order of magnitude of the mass of ultralight axions m∼10−23eV∕c2 in the Bose–Einstein condensate dark matter paradigm.

We employ a field-theoretical variational approach to study the behavior of ionic solutions in the grand canonical ensemble. To describe properly the hardcore interactions between ions, we use a cutoff in Fourier space for the electrostatic contribution of the grand potential and the Carnahan-Starling equation of state with a modified chemical potential for the pressure one. We first calibrate our method by comparing its predictions at room temperature with Monte Carlo results for excess chemical potential and energy. We then validate our approach in the bulk phase by describing the classical “ionic liquid-vapor” phase transition induced by ionic correlations at low temperature, before applying it to electrolytes at room temperature confined to nanopores embedded in a low dielectric medium and coupled to an external reservoir of ions. The ionic concentration in the nanopore is then correctly described from very low bulk concentrations, where dielectric exclusion shifts the transition up to room temperature for sufficiently tight nanopores, to high concentrations where hardcore interactions dominate which, as expected, modify only slightly this ionic “capillary evaporation.”

Being capable of characterizing DNA local bending is essential to understand thoroughly many biological processes because they involve a local bending of the double helix axis, either intrinsic to the sequence or induced by the binding of proteins. Developing a method to measure DNA bend angles that does not perturb the conformation of the DNA itself or the DNA-protein complex is a challenging task. Here, we propose a joint theory-experiment high throughput approach to rigorously measure such bend angles using the Tethered Particle Motion (TPM) technique. By carefully modeling the TPM geometry, we propose a simple formula based on a kinked Worm-Like Chain model to extract the bend angle from TPM measurements. Using constructs made of 575 base-pair DNAs with in-phase assemblies of 1 to 7 6A-tracts, we find that the sequence CA6CGG induces a bend angle of 19 [4] {\deg}. Our method is successfully compared to more theoretically complex or experimentally invasive ones such as cyclization, NMR, FRET or AFM. We further apply our procedure to TPM measurements from the literature and demonstrate that the angles of bends induced by proteins, such as Integration Host Factor (IHF) can be reliably evaluated as well.

The double stranded DNA molecule undergoes drastic structural changes during biological processes such as transcription during which it opens locally under the action of RNA polymerases. Local spontaneous denaturation could contribute to this mechanism by promoting it. Supporting this idea, different biophysical studies have found an unexpected increase in the flexibility of DNA molecules with various sequences as a function of the temperature, which would be consistent with the formation of a growing number of locally denatured sequences. Here, we take advantage of our capacity to detect subtle changes occurring on DNA by using high throughput tethered particle motion to question the existence of bubbles in double stranded DNA under physiological salt conditions through their conformational impact on DNA molecules ranging from several hundreds to thousands of base pairs. Our results strikingly differ from previously published ones, as we do not detect any unexpected change in DNA flexibility below melting temperature. Instead, we measure a bending modulus that remains stable with temperature as expected for intact double stranded DNA.

We study the Jeans instability of an infinite homogeneous dissipative self-gravitating Bose–Einstein condensate described by generalized Gross–Pitaevskii–Poisson equations [Chavanis, P.H. Eur. Phys. J. Plus 2017, 132, 248]. This problem has applications in relation to the formation of dark matter halos in cosmology. We consider the case of a static and an expanding universe. We take into account an arbitrary form of repulsive or attractive self-interaction between the bosons (an attractive self-interaction being particularly relevant for the axion). We consider both gravitational and hydrodynamical (tachyonic) instabilities and determine the maximum growth rate of the instability and the corresponding wave number. We study how they depend on the scattering length of the bosons (or more generally on the squared speed of sound) and on the friction coefficient. Previously obtained results (notably in the dissipationless case) are recovered in particular limits of our study.

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A major problem that resulted from the massive use of social media networks is the diffusion of incorrect information. However, very few studies have investigated the impact of incorrect information on individual and collective decisions. We performed experiments in which participants had to estimate a series of quantities before and after receiving social information. Unbeknownst to them, we controlled the degree of inaccuracy of the social information through "virtual influencers", who provided some incorrect information. We find that a large proportion of individuals only partially follow the social information, thus resisting incorrect information. Moreover, we find that incorrect social information can help a group perform better when it overestimates the true value, by partly compensating a human underestimation bias. Overall, our results suggest that incorrect information does not necessarily impair the collective wisdom of groups, and can even be used to dampen the negative effects of known cognitive biases.

A discrete self-gravitating quasi-Keplerian razor-thin axisymmetric stellar disc orbiting a massive black hole sees its orbital structure diffuse on secular timescales as a result of a self-induced resonant relaxation. In the absence of collective effects, such a process is described by the recently derived inhomogeneous multi-mass degenerate Landau equation. Relying on Gauss’ method, we computed the associated drift and diffusion coefficients to characterise the properties of the resonant relaxation of razor-thin discs. For a disc-like configuration in our Galactic centre, we showed how this secular diffusion induces an adiabatic distortion of orbits and estimate the typical timescale of resonant relaxation. When considering a disc composed of multiple masses similarly distributed, we have illustrated how the population of lighter stars will gain eccentricity, driving it closer to the central black hole, provided the distribution function increases with angular momentum. The kinetic equation recovers as well the quenching of the resonant diffusion of a test star in the vicinity of the black hole (the “Schwarzschild barrier”) as a result of the divergence of the relativistic precessions. The dual stochastic Langevin formulation yields consistent results and offers a versatile framework in which to incorporate other stochastic processes.

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We study spectral gaps of the one-dimensional totally asymmetric simple exclusion process (TASEP) with open boundaries in the maximal current phase. Earlier results for the model with periodic boundaries suggest that the gaps contributing to the universal KPZ regime may be understood as points on an infinite genus Riemann surface built from a parametric representation of the cumulant generating function of the current. We perform explicit analytic continuations from the known large deviations of the current for open TASEP, and confirm the results for the gaps by an exact Bethe ansatz calculation, with additional checks using high precision extrapolation numerics.

Social media filters combined with recommender systems can lead to the emergence of filter bubbles and polarized groups. In addition, segregation processes of human groups in certain social contexts have been shown to share some similarities with phase separation phenomena in physics. Here, we study the impact of information filtering on collective segregation behavior. We report a series of experiments where groups of 22 subjects have to perform a collective segregation task that mimics the tendency of individuals to bond with other similar individuals. More precisely, the participants are each assigned a color (red or blue) unknown to them, and have to regroup with other subjects sharing the same color. To assist them, they are equipped with an artificial sensory device capable of detecting the majority color in their ``environment'' (defined as their k nearest neighbors, unbeknownst to them), for which we control the perception range, k=1,3,5,7,9,11,13. We study the separation dynamics (emergence of unicolor groups) and the properties of the final state, and show that the value of k controls the quality of the segregation, although the subjects are totally unaware of the precise definition of the ``environment''. We also find that there is a perception range k=7 above which the ability of the group to segregate does not improve. We introduce a model that precisely describes the random motion of a group of pedestrians in a confined space, and which faithfully reproduces and allows to interpret the results of the segregation experiments. Finally, we discuss the strong and precise analogy between our experiment and the phase separation of two immiscible materials at very low temperature.

We examine the behavior of supercoiled DNA minicircles containing between 200 and 400 base-pairs, also named microDNA, in which supercoiling favors thermally assisted DNA denaturation bubbles of nanometer size and controls their lifetime. Mesoscopic modeling and accelerated dynamics simulations allow us to overcome the limitations of atomistic simulations encountered in such systems, and offer detailed insight into the thermodynamic and dynamical properties associated with the nucleation and closure mechanisms of long-lived thermally assisted denaturation bubbles which do not stem from bending-or torque-driven stress. Suitable tuning of the degree of supercoiling and size of specifically designed microDNA is observed to lead to the control of opening characteristic times in the millisecond range, and closure characteristic times ranging over well distinct timescales, from microseconds to several minutes. We discuss how our results can be seen as a dynamical bandwidth which might enhance selectivity for specific DNA binding proteins.

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