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We discuss the kinetic theory of stellar systems and two-dimensional vortices and stress their analogies. We recall the derivation of the Landau and Lenard–Balescu equations from the Klimontovich formalism. These equations take into account two-body correlations and are valid at the order 1/N, where N is the number of particles in the system. They have the structure of a Fokker–Planck equation involving a diffusion term and a drift term. The systematic drift of a vortex is the counterpart of the dynamical friction experienced by a star. At equilibrium, the diffusion and the drift terms balance each other establishing the Boltzmann distribution of statistical mechanics. We discuss the problem of kinetic blocking in certain cases and how it can be solved at the order by the consideration of three-body correlations. We also consider the behaviour of the system close to the critical point following a recent suggestion by Hamilton and Heinemann (2023). We present a simple calculation, valid for spatially homogeneous systems with long-range interactions described by the Cauchy distribution, showing how the consideration of the Landau modes regularizes the divergence of the friction by polarization at the critical point. We mention, however, that fluctuations may be very important close to the critical point and that deterministic kinetic equations for the mean distribution function (such as the Landau and Lenard–Balescu equations) should be replaced by stochastic kinetic equations.

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We consider an isothermal self-gravitating system surrounding a central body. This model can represent a galaxy or a globular cluster harboring a central black hole. It can also represent a gaseous atmosphere surrounding a protoplanet. In three dimensions, the Boltzmann-Poisson equation must be solved numerically to obtain the density profile of the gas [Chavanis et al., Phys. Rev. E 109, 014118 (2024)]. In one and two dimensions, we show that the Boltzmann-Poisson equation can be solved analytically. We obtain explicit analytical expressions of the density profile around a central body which generalize the analytical solutions found by Camm (1950) and Ostriker (1964) in the absence of a central body. Our results also have applications for self-gravitating Brownian particles (Smoluchowski-Poisson system), for the chemotaxis of bacterial populations in biology (Keller-Segel model), and for two-dimensional point vortices in hydrodynamics (Onsager's model). In the case of bacterial populations, the central body could represent a supply of “food” that attracts the bacteria (chemoattractant). In the case of two-dimensional vortices, the central body could be a central vortex.

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Despite 15 years of extensive investigation, the fabrication and study of nanofluidic devices that incorporate a single carbon nanotube (CNT) still represents a remarkable experimental challenge. In this study, we present the fabrication of nanofluidic devices that integrate an individual single-walled CNT (SWCNT), showcasing a notable reduction in noise by 1 -3 orders of magnitude compared to conventional devices. This achievement was made possible by employing high dielectric constant materials for both the substrate and the CNT-covering layer. Furthermore, we provide a detailed account of the crucial factors contributing to the successful fabrication of SWCNT-based nanofluidic devices that are reliably leak-free, plug-free, and long-lived. Key considerations include the quality of the substrate-layer interface, the nanotube opening, and the effective removal of photoresist residues and trapped microbubbles. We demonstrate that these devices, characterized by a high signal-tonoise ratio, enable spectral noise analysis of ionic transport through an individual SWCNT, thus showing that SWCNTs obey Hooge's law in 1/ f at low frequencies. Beyond advancing our fundamental understanding of ion transport in SWCNTs, these ultralow-noise measurements open avenues for leveraging SWCNTs in nanopore sensing applications for single-molecule detection, offering high sensitivity and identification capabilities.

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Current fluctuations for the one-dimensional totally asymmetric exclusion process (TASEP) connected to reservoirs of particles, and their large scale limit to the KPZ fixed point in finite volume, are studied using exact methods. Focusing on the maximal current phase for TASEP, corresponding to infinite boundary slopes for the KPZ height field, we obtain for general initial condition an exact expression for the late time correction to stationarity, involving extreme value statistics of Brownian paths. In the special cases of stationary and narrow wedge initial conditions, a combination of Bethe ansatz and numerical conjectures alternatively provide fully explicit exact expressions.

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The Riemann surface associated with counting the current between two states of an underlying Markov process is hyperelliptic. We explore the consequences of this property for the time-dependent probability of that current for Markov processes with generic transition rates. When the system is prepared in its stationary state, the relevant meromorphic differential is in particular fully characterized by the precise identification of all its poles and zeroes.

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Sujets

Fermi gas Turbulence Cosmological model Hydrodynamics Smoluchowski equation Statistical mechanics Smoluchowski-Poisson Thermodynamics Gravitation Mesoscale and Nanoscale Physics cond-matmes-hall Cosmological constant Gravitation self-force Collisionless stellar-systems Gravitational collapse Equation of state Computational modelling Entropy Black hole Structure Current fluctuations Dark energy Collective behavior Cosmology Energy density Keller-Segel Model Galaxy Dark matter halo 9880-k Bose–Einstein condensates Rotation Axion star Mass density Scattering length Wisdom of crowds Pressure Dark matter Density Mouvement brownien 9530Sf Physique statistique Collective intelligence Carbon nanotube Critical phenomena Quantum chromodynamics axion Halo Dissipation Catastrophe theory Axion Mass General relativity Phase separation Random walker Nonrelativistic Denaturation Quantum mechanics Condensation Bose-Einstein Brownian motion Dark matter fuzzy Atmosphere Soft Condensed Matter cond-matsoft Chemotaxis Competition Numerical calculations 9862Gq 9536+x Fokker-Planck DNA Dark matter condensation Nonlinear Field theory scalar TASEP Expansion acceleration Kinetic theory Wave function Bethe ansatz Collective behaviour Fermions Bose-Einstein Asymptotic behavior Scalar field Marcheur aléatoire Dark matter density Nanofiltration Dark matter theory Stability FOS Physical sciences Computational modeling Collective motion Chemotaxie 9535+d Evaporation Transition vitreuse Diffusion Gas Chaplygin Collapse Gravitation collapse Effondrement gravitationnel Einstein Formation

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