Microscopic Derivation of Non-Markovian Thermalization of a Brownian Particle

In this paper, the first microscopic approach to the Brownian motion is developed in the case where the mass density of the suspending bath is of the same order of magnitude as that of the Brownian (B) particle. Starting from an extended Boltzmann equation, which describes correctly the interaction with the fluid, we derive systematicaly via the multiple time-scale analysis a reduced equation controlling the thermalization of the B particle, i.e. the relaxation towards the Maxwell distribution in velocity space. In contradistinction to the Fokker-Planck equation, the derived new evolution equation is non-local both in time and in velocity space, owing to correlated recollision events between the fluid and particle B. In the long-time limit, it describes a non-markovian generalized Ornstein-Uhlenbeck process. However, in spite of this complex dynamical behaviour, the Stokes-Einstein law relating the friction and diffusion coefficients is shown to remain valid. A microscopic expression for the friction coefficient is derived, which acquires the form of the Stokes law in the limit where the mean-free in the gas is small compared to the radius of particle B.Comment: 28 pages, no figure, submitted to Journal of Statistical Physic

Slippage of water past superhydrophobic carbon nanotube forests in microchannels

We present in this letter an experimental characterization of liquid flow slippage over superhydrophobic surfaces made of carbon nanotube forests, incorporated in microchannels. We make use of a micro-PIV (Particule Image Velocimetry) technique to achieve the submicrometric resolution on the flow profile necessary for accurate measurement of the surface hydrodynamic properties. We demonstrate boundary slippage on the Cassie superhydrophobic state, associated with slip lengths of a few microns, while a vanishing slip length is found in the Wenzel state, when the liquid impregnates the surface. Varying the lateral roughness scale L of our carbon nanotube forest-based superhydrophobic surfaces, we demonstrate that the slip length varies linearly with L in line with theoretical predictions for slippage on patterned surfaces.Comment: under revie

Impact of Weak Lensing Mass Calibration on eROSITA Galaxy Cluster Cosmological Studies -- a Forecast

We forecast the impact of weak lensing (WL) cluster mass calibration on the cosmological constraints from the X-ray selected galaxy cluster counts in the upcoming eROSITA survey. We employ a prototype cosmology pipeline to analyze mock cluster catalogs. Each cluster is sampled from the mass function in a fiducial cosmology and given an eROSITA count rate and redshift, where count rates are modeled using the eROSITA effective area, a typical exposure time, Poisson noise and the scatter and form of the observed X-ray luminosity-- and temperature--mass--redshift relations. A subset of clusters have mock shear profiles to mimic either those from DES and HSC or from the future Euclid and LSST surveys. Using a count rate selection, we generate a baseline cluster cosmology catalog that contains 13k clusters over 14,892~deg$^2$ of extragalactic sky. Low mass groups are excluded using raised count rate thresholds at low redshift. Forecast parameter uncertainties for $\Omega_\mathrm{M}$, $\sigma_8$ and $w$ are 0.023 (0.016; 0.014), 0.017 (0.012; 0.010), and 0.085 (0.074; 0.071), respectively, when adopting DES+HSC WL (Euclid; LSST), while marginalizing over the sum of the neutrino masses. A degeneracy between the distance--redshift relation and the parameters of the observable--mass scaling relation limits the impact of the WL calibration on the $w$ constraints, but with BAO measurements from DESI an improved determination of $w$ to 0.043 becomes possible. With Planck CMB priors, $\Omega_\text{M}$ ($\sigma_8$) can be determined to $0.005$ ($0.007$), and the summed neutrino mass limited to $\sum m_\nu < 0.241$ eV (at 95\%). If systematics on the group mass scale can be controlled, the eROSITA group and cluster sample with 43k objects and LSST WL could constrain $\Omega_\mathrm{M}$ and $\sigma_8$ to 0.007 and $w$ to 0.050.Comment: 28 pages, 13 figur

Statistical characterization of the forces on spheres in an upflow of air

The dynamics of a sphere fluidized in a nearly-levitating upflow of air were previously found to be identical to those of a Brownian particle in a two-dimensional harmonic trap, consistent with a Langevin equation [Ojha {\it et al.}, Nature {\bf 427}, 521 (2004)]. The random forcing, the drag, and the trapping potential represent different aspects of the interaction of the sphere with the air flow. In this paper we vary the experimental conditions for a single sphere, and report on how the force terms in the Langevin equation scale with air flow speed, sphere radius, sphere density, and system size. We also report on the effective interaction potential between two spheres in an upflow of air.Comment: 7 pages, experimen

Diffusion in pores and its dependence on boundary conditions

We study the influence of the boundary conditions at the solid liquid interface on diffusion in a confined fluid. Using an hydrodynamic approach, we compute numerical estimates for the diffusion of a particle confined between two planes. Partial slip is shown to significantly influence the diffusion coefficient near a wall. Analytical expressions are derived in the low and high confinement limits, and are in good agreement with numerical results. These calculations indicate that diffusion of tagged particles could be used as a sensitive probe of the solid-liquid boundary conditions.Comment: soumis \`a J.Phys. Cond. Matt. special issue on "Diffusion in Liquids, Polymers, Biophysics and Chemical Dynamics

A Hydrodynamic model for a dynamical jammed-to-flowing transition in gravity driven granular media

Granular material on an inclined plane will flow like a fluid if the angle $\theta$ the plane makes with the horizontal is large enough. We employ a modification of a hydrodynamic model introduced previously to describe Couette flow experiments to describe chute flow down a plane. In this geometry, our model predicts a jammed-to-flowing transition as $\theta$ is increased even though it does not include solid friction, which might seem necessary to stabilize a state without flow. The transition is driven by coupling between mean and fluctuating velocity. In agreement with experiments and simulations, it predicts flow for layers with a thickness H larger than a critical value $H_{\rm stop}(\theta)$ and absence of flow for $H<H_{\rm stop}(\theta)$

Possibility to study eta-mesic nuclei and photoproduction of slow eta-mesons at the GRAAL facility

A new experiment is proposed with the aim to study eta-mesic nuclei and low-energy interactions of eta with nuclei. Two decay modes of eta produced by a photon beam inside a nucleus will be observed, namely a collisional decay \eta N \to \pi N inside the nucleus and the radiative decay \eta \to \gamma \gamma outside. In addition, a collisional decay of stopped S_{11}(1535) resonance inside the nucleus, S_{11}(1535) N \to N N, will be studied. The experiment can be performed using the tagged photon beam at ESRF with the end-point energy 1000 MeV and the GRAAL detector which includes a high-resolution BGO calorimeter and a large acceptance lead-scintillator time-of-flight wall. Some results of simulation and estimates of yields are given.Comment: 20 pages, 19 figure

The Diffusion of Humans and Cultures in the Course of the Spread of Farming

The most profound change in the relationship between humans and their environment was the introduction of agriculture and pastoralism. [....] For an understanding of the expansion process, it appears appropriate to apply a diffusive model. Broadly, these numerical modeling approaches can be catego- rized in correlative, continuous and discrete. Common to all approaches is the comparison to collections of radiocarbon data that show the apparent wave of advance of the transition to farming. However, these data sets differ in entry density and data quality. Often they disregard local and regional specifics and research gaps, or dating uncertainties. Thus, most of these data bases may only be used on a very general, broad scale. One of the pitfalls of using irregularly spaced or irregularly documented radiocarbon data becomes evident from the map generated by Fort (this volume, Chapter 16): while the general east-west and south-north trends become evident, some areas appear as having undergone anomalously early transitions to farming. This may be due to faulty entries into the data base or regional problems with radiocarbon dating, if not unnoticed or undocumented laboratory mistakes.Comment: 20 pages, 5 figures, submitted to Diffusive Spreading in Nature, Technology and Society, edited by Armin Bunde, J\"urgen Caro, J\"org K\"arger, Gero Vogl, Chapter 1

Equilibrium Configurations of Strongly Magnetized Neutron Stars with Realistic Equations of State

We investigate equilibrium sequences of magnetized rotating stars with four kinds of realistic equations of state (EOSs) of SLy (Douchin et al.), FPS (Pandharipande et al.), Shen (Shen et al.), and LS (Lattimer & Swesty). Employing the Tomimura-Eriguchi scheme to construct the equilibrium configurations. we study the basic physical properties of the sequences in the framework of Newton gravity. In addition we newly take into account a general relativistic effect to the magnetized rotating configurations. With these computations, we find that the properties of the Newtonian magnetized stars, e.g., structure of magnetic field, highly depends on the EOSs. The toroidal magnetic fields concentrate rather near the surface for Shen and LS EOSs than those for SLy and FPS EOSs. The poloidal fields are also affected by the toroidal configurations. Paying attention to the stiffness of the EOSs, we analyze this tendency in detail. In the general relativistic stars, we find that the difference due to the EOSs becomes small because all the employed EOSs become sufficiently stiff for the large maximum density, typically greater than $10^{15}\rm{g} \rm{cm}^{-3}$. The maximum baryon mass of the magnetized stars with axis ratio $q\sim 0.7$ increases about up to twenty percents for that of spherical stars. We furthermore compute equilibrium sequences at finite temperature, which should serve as an initial condition for the hydrodynamic study of newly-born magnetars. Our results suggest that we may obtain information about the EOSs from the observation of the masses of magnetars.Comment: submitted to MNRA