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Patches of catalyst imprinted on supporting walls induce motion of the fluid around them once they are supplied with the chemical species (``fuel'') that are converted by the catalytic chemical reaction. While the functioning of such chemically active micropumps is conceptually well understood, an in-depth characterization of the induced hydrodynamic flow, and in particular of its possible dependences on parameters such as material properties of the patch and the wall or the geometry of the experimental cell, remains elusive. By using a simple model for the chemical activity of a patch imprinted on a planar wall, we determine analytically the induced hydrodynamic flow in a Newtonian solution that occupies the half space above the wall supporting the patch. This can be seen as an approximation for an experimental-cell geometry with a height much larger than its diameter, the latter, in turn, being much larger than the size of the patch.) The general flow is a linear superposition of a surface-driven and a bulk-driven component; they have different topologies and, generically, each one dominates in distinct regions, with the surface-driven flow being most relevant at small heights above the wall. The surface-driven flows exhibit a somewhat unexpectedly rich behavior, including qualitative changes in the topology of the flow, as a function of the contrast in surface-chemistry (osmotic slip coefficient) between the patch and the support wall. The results are expected to provide guidance for the interpretation of the drift of tracers by the ambient flow, which is the observable usually studied in experimental investigations of chemically active micropumps.

Unlike a classical charged bosonic field, a classical charged fermion field on a static charged black hole does not exhibit superradiant scattering. We demonstrate that the quantum analogue of this classical process is however present. We construct a vacuum state for the fermion field which has no incoming particles from past null infinity, but which contains, at future null infinity, a nonthermal flux of particles. This state describes both the discharge and energy loss of the black hole, and we analyze how the interpretation of this phenomenon depends on the ambiguities inherent in defining the quantum vacuum., Comment: 23 pages, 5 figures

We discuss how the comment by A. Loeb [arXiv:2408.06714] has no bearing on the results of Phys. Rev. Lett. 133, 041401 (2024) [arXiv:2405.02389]., Comment: 2 pages. RevTeX 4.2

When a particle moves in a Newtonian flow at low Reynolds number, inertia is irrelevant and a linear relationship exists between velocities and forces. For incompressible flows, any force distribution $\mathbf{f}(\mathbf{r})$ acting in the fluid bulk induces flow and motion only through its solenoidal component. For force distributions that are spatially localized (i.e., vanish sufficiently fast at infinity), we derive the representation of the rigid body motion as an explicit linear functional of $\nabla\times\mathbf{f}$, which complements the usual representation in terms of $\mathbf{f}$. We illustrate the utility of this alternative representation, which has the advantage of having the incompressibility constraint built-in, in avoiding certain ambiguities that arise, e.g., when implementing approximations for swimmers., Comment: The manuscript proper and the supplemental material have been merged consecutively into a single PDF file

Self-chemophoresis is an appealing and quite successful interpretation of the motility exhibited by certain chemically active colloidal particles suspended in a solution of their "fuel": the particle has a phoretic response to self-generated, rather than externally imposed, inhomogeneities in the chemical composition of the solution. The postulated mechanism of chemophoresis is the interaction of the particle (via an adsorption potential) with the chemical inhomogeneities in the surrounding medium. When the range of this interaction is much smaller than any other relevant scale in the system, the (translational and rotational) phoretic velocities can be described in terms of a phoretic coefficient and a slip fluid velocity at the surface of the particle. Using the case of a spherical particle as a simple and physically insightful example, here we exploit an integral representation of the rigid-body motion to critically re-examine this framework. The systematic analysis highlights two steps in the approximation: first the thin-layer approximation (very large particle size), and subsequently a lubrication approximation (slow variation of the adsorption potential along the tangential direction). We also discuss how these approximations could be relaxed and the effect of this on the particle's motion.

We show that it is not possible to concentrate enough light to precipitate the formation of an event horizon. We argue that the dissipative quantum effects coming from the self-interaction of light (such as vacuum polarization) are enough to prevent any meaningful buildup of energy that could create a black hole in any realistic scenario., Comment: 13 pages. RevTeX 4.2. v2: Updated to match published version

We re-examine the self-phoresis of a particle that releases(removes) pairs of ions into(from) the electrolyte solution. We show analytically that in the linear regime the mathematical description of this system maps onto that of the correlation-induced (self-)chemophoresis (CICP). This connection provides a unifying perspective of the two phenomena, within which one recovers and extends recent predictions as particular instances of CICP. Conversely, ion-phoretic particles are identified as candidates for experimental investigations into the rich variety of motility patterns predicted by CICP., Comment: The manuscript proper and the supplemental material have been merged consecutively into a single PDF file

States of low energy in cosmology minimise the energy density when smeared in a chosen time interval. We extend such construction to generic homogeneous (possibly anisotropic) particle creation settings. Focusing on the Schwinger effect, we study the role played by the support of the smearing function and identify the vacua obtained in the limiting cases of small and large time intervals. We also analyse the spectral properties of the power spectrum and the number of created particles, which are complementary in characterising the vacuum, and investigate the multipolar contributions coming from the anisotropies., Comment: 18 pages, 4 figures

We provide a reinterpretation of the quantum vacuum ambiguities that one encounters when studying particle creation phenomena due to an external and time-dependent agent. We propose a measurement-motivated understanding: Each way of measuring the number of created particles selects a particular vacuum. This point of view gives a clear and physical meaning to the time evolution of the number of particles produced by the agent as the counts in a specific detector and, at the same time relates commonly used quantization prescriptions to particular measurement setups., Comment: 6 pages, 3 figures

The loss of time-translational invariance caused by a time-dependent external agent leads to particle creation effects in quantum field theory. This phenomenon results in ambiguities when selecting the quantum vacuum of the canonical quantization. In this work we analyze how the time evolution of the number of created particles depends on these ambiguities when external agents are spatially homogeneous. In particular, we generalize the standard quantum Vlasov equation in order to accommodate in its formulation the possibility of having different choices of vacuum, including adiabatic vacua. This study leads us to propose a new physical criterion stronger than the unitary implementation of the dynamics in order to reduce the quantization ambiguities., Comment: 14 pages; v2: matches the version published on Phys. Rev. D (additional references added)

In quantum field theory, particle creation occurs, in general, when an intense external field, such as an electromagnetic field, breaks time translational invariance. This leads to an ambiguity in the definition of the vacuum state. In cosmological backgrounds this ambiguity has been reduced by imposing that the quantization preserves the symmetries of the system and that the dynamics is unitarily implemented. In this work, we apply these requirements to the quantization of a massive charged fermionic field coupled to a classical time-dependent homogeneous electric field, extending previous studies done for a scalar field. We characterize the quantizations fulfilling the criteria above and we show that they form a unique equivalence class of unitarily related quantizations, which provide a well-defined number of created particles at all finite times., Comment: 20 pages; v2: matches the version published on J. High Energ. Phys. 2021 (additional clarifications added)

For monolayers of chemically active particles at a fluid interface, collective dynamics are predicted to arise owing to activity-induced Marangoni flow even if the particles are not self-propelled. Here we test this prediction by employing a monolayer of spherically symmetric active TiO_2 particles located at an oil-water interface with or without addition of a non-ionic surfactant. Due to the spherical symmetry, an individual particle does not self-propel. However, the gradients produced by the photochemical fuel degradation give rise to long-ranged Marangoni flows. For the case in which surfactant is added to the system, we indeed observe the emergence of collective motion, with dynamics dependent on the particle coverage of the monolayer. The experimental observations are discussed within the framework of a simple theoretical mean field model., Comment: 12 pages, to be published in EPJ-E

Current models of phoretic transport rely on molecular forces creating a "diffuse" particle-fluid interface. We investigate theoretically an alternative mechanism, in which a diffuse interface emerges solely due to a non-vanishing correlation length of the surrounding solution. This mechanism can drive self-motility of a chemically active particle. Numerical estimates indicate that the velocity can reach micrometers per second. The predicted phenomenology includes a bilinear dependence of the velocity on the activity and a possible double velocity reversal upon varying the correlation length., Comment: 6 pages, 2 figures, and 22 pages of supplemental material. To be published as Phys. Rev. Lett

Thermally or chemically active colloids generate thermodynamic gradients in the solution in which they are immersed and thereby induce hydrodynamic flows that affect their dynamical evolution. Here we study a mean-field model for the many-body dynamics of a monolayer of active particles located at a fluid-fluid interface. In this case, the activity of the particles creates long-ranged Marangoni flows due to the response of the interface, which compete with the direct interaction between the particles. For the most interesting case of a $r^{-3}$ soft repulsion that models the electrostatic or magnetic interparticle forces, we show that an "onion-like" density distribution will develop within the monolayer. For a sufficiently large average density, two-dimensional phase transitions (freezing from liquid to hexatic, and melting from solid to hexatic) should be observable in a radially stratified structure. Furthermore, the analysis allows us to conclude that, while the activity may be too weak to allow direct detection of such induced Marangoni flows, it is relevant as a collective effect in the emergence of the experimentally observable spatial structure of phase coexistences noted above. Finally, the relevance of these results for potential experimental realizations is critically discussed., Comment: 11 pages

The formulation of the First and Second Principles of thermodynamics for a particle in contact with a heat bath and submitted to an external force is analyzed, by means of the Boltzmann-Lorentz kinetic equation. The possible definitions of the thermodynamic quantities are discussed in the light of the H theorem verified by the distribution of the particle. The work fluctuation relations formulated by Bochkov and Kuzovlev, and by Jarzynski, respectively, are derived from the kinetic equation. In addition, particle simulations using both the direct simulation Monte Carlo method and Molecular Dynamics, are used to investigate the practical accuracy of the results. Work distributions are also measured, and they turn out to be rather complex. On the other hand, they seem to depend very little, if any, on the interaction potential between the intruder and the bath.

A planar colloidal monolayer exhibits anomalous collective diffusion due to the hydrodynamic interactions. We investigate how this behavior is affected by the curvature of the monolayer when it resides on the interface of a spherical droplet. It is found that the characteristic times of the dynamics still exhibit the same anomalous scaling as in the planar case. The spatial distribution, however, shows a difference due to the relevance of the radius of the droplet. Since for the droplet this is both a global magnitude, i.e., pertaining the spatial extent of the spherical surface, and a local one, i.e., the radius of curvature, the question remains open as to which of these two features actually dominates in the case of a generically curved interface., Comment: 7 pages, 2 figures

It has been recently shown that a colloidal monolayer, e.g., formed at a fluid interface or by means of a suitable confining potential, exhibits anomalous collective diffusion. This is a consequence of the hydrodynamic interactions mediated by the three-dimensional (3D) ambient fluid when the particles are confined to reside on a two-dimensional (2D) manifold. We study theoretically and with numerical simulations the crossover from normal to anomalous diffusion as the particles are, in real systems, confined by a 3D external potential and thus have the possibility to fluctuate out of the 2D manifold, thus forming actually a quasi-monolayer., Comment: 13 pages, 9 figures

Chemically active colloids generate changes in the chemical composition of their surrounding solution and thereby induce flows in the ambient fluid which affect their dynamical evolution. Here we study the many-body dynamics of a monolayer of active particles trapped at a fluid-fluid interface. To this end we consider a mean-field model which incorporates the direct pair interaction (including also the capillary interaction which is caused specifically by the interfacial trapping) as well as the effect of hydrodynamic interactions (including the Marangoni flow induced by the response of the interface to the chemical activity). The values of the relevant physical parameters for typical experimental realizations of such systems are estimated and various scenarios, which are predicted by our approach for the dynamics of the monolayer, are discussed. In particular, we show that the chemically-induced Marangoni flow can prevent the clustering instability driven by the capillary attraction., Comment: 8 pages, 2 figures

We show theoretically that near a fluid-fluid interface a single active colloidal particle generating, e.g., chemicals or a temperature gradient experiences an effective force of hydrodynamic origin. This force is due to the fluid flow driven by Marangoni stresses induced by the activity of the particle; it decays very slowly with the distance from the interface, and can be attractive or repulsive depending on how the activity modifies the surface tension. We show that, for typical systems, this interaction can dominate the dynamics of the particle as compared to Brownian motion, dispersion forces, or self-phoretic effects. In the attractive case, the interaction promotes the self-assembly of particles into a crystal-like monolayer at the interface., Comment: The manuscript proper and the supplementary information have been merged consecutively into a single PDF file

It has been shown recently that the coefficient of collective diffusion in a colloidal monolayer is divergent due to the hydrodynamic interactions mediated by the ambient fluid in bulk. The analysis is extended to allow for time--dependent hydrodynamic interactions. Novel observational features specific to this time dependency are predicted. The possible experimental detection in the dynamics of the monolayer is discussed., Comment: 14 pages, 6 figures

We investigate the dynamics of colloids at a fluid interface driven by attractive capillary interactions. At submillimeter length scales, the capillary attraction is formally analogous to two-dimensional gravity. In particular it is a non-integrable interaction and it can be actually relevant for collective phenomena in spite of its weakness at the level of the pair potential. We introduce a mean-field model for the dynamical evolution of the particle number density at the interface. For generic values of the physical parameters the homogeneous distribution is found to be unstable against large-scale clustering driven by the capillary attraction. We also show that for the instability to be observable, the appropriate values for the relevant parameters (colloid radius, surface charge, external electric field, etc.) are experimentally well accessible. Our analysis contributes to current studies of the structure and dynamics of systems governed by long-ranged interactions and points towards their experimental realizations via colloidal suspensions., Comment: Matches version accepted for publication. New refs. added, misprints corrected in figs.6,8,9,10

We present a dynamic density functional theory (dDFT) which takes into accou nt the advection of the particles by a flowing solvent. For potential flows we can use the same closure as in the absence of solvent flow. The structure of the resulting advected dDFT suggests that it could be used for non-potential flows as well. We apply this dDFT to Brownian particles (e.g., polymer coils) in a solvent flowing around a spherical obstacle (e.g., a colloid) and compare the results with direct simulations of the underlying Brownian dynamics. Although numerical limitations do not allow for an accurate quantitative check of the advected dDFT both show the same qualitative features. In contrast to previous works which neglected the deformation of the flow by the obstacle, we find that the bow-wave in the density distribution of particles in front of the obstacle as well as the wake behind it are reduced dramatically. As a consequence the friction force exerted by the (polymer) particles on the colloid can be reduced drastically., Comment: 7 pages, 5 figures, 2 tables, submitted

Within a general theoretical framework we study the effective, deformation-induced interaction between two colloidal particles trapped at a fluid interface in the regime of small deformations. In many studies, this interaction has been computed with the ansatz that the actual interface configuration for the pair is given by the linear superposition of the interface deformations around the single particles. Here we assess the validity of this approach and compute the leading term of the effective interaction for large interparticle separation beyond this so-called superposition approximation. As an application, we consider the experimentally relevant case of interface deformations owing to the electrostatic field emanating from charged colloidal particles. In mechanical isolation, i.e., if the net force acting on the total system consisting of the particles plus the interface vanishes, the superposition approximation is actually invalid. The effective capillary interaction is governed by contributions beyond this approximation and turns out to be attractive. For sufficiently small surface charges on the colloids, such that linearization is strictly valid, and at asymptotically large separations, the effective interaction does not overcome the direct electrostatic repulsion between the colloidal particles., Comment: Minor typos corrected

We study the effective forces acting between colloidal particles trapped at a fluid interface which itself is exposed to a pressure field. To this end we apply what we call the ``force approach'', which relies solely on the condition of mechanical equilibrium and turns to be in a certain sense less restrictive than the more frequently used ``energy approach'', which is based on the minimization of a free energy functional. The main goal is to elucidate the advantages and disadvantages of the force approach as compared to the energy approach. First, we derive a general stress-tensor formulation of the forces at the interface and work out a useful analogy with 2D electrostatics in the particular case of small deformations of the interface relative to its flat configuration. We apply this analogy to compute the asymptotic decay of the effective force between particles trapped at a fluid interface, extending the validity of previous results. Second, we address the case of deformations of a non-flat interface. We compute the deformation of a spherical droplet due to the electric field of a charged particle trapped at its surface and conclude that the interparticle capillary force is unlikely to explain certain recent experimental observations. Finally we discuss the application to a generally curved interface and show as an illustrative example that a nonspherical particle deposited on an interface forming a minimal surface is pulled to regions of larger curvature., Comment: 17 pages, 5 eps-figures. In this new version, the order of sections has been reshuffled and a new subsection has been added

We pinpoint and correct several mathematical errors in EPL 75(2006)978. As a consequence, we conclude that there is no logarithmically varying interfacial deformation, contrary to the claim in the EPL., Comment: Comment to EPL 75 (2006) 978

There is evidence of a scale-invariant matter distribution up to scales over 10 Megaparsecs. We review scaling (fractal or multifractal) models of large scale structure and their observational evidence. We conclude that the dynamics of cosmological structure formation seems to be driven to a multifractal attractor. This supports previous studies, which we review, of structure formation by means of the renormalization group within a hydrodynamic formulation., Comment: 8 pages, IOP LaTeX

We present a series of cosmological N-body simulations which make use of the hydrodynamic approach to the evolution of structures (Dominguez 2000). This approach addresses explicitly the existence of a finite spatial resolution and the dynamical effect of subresolution degrees of freedom. We adapt this method to cosmological simulations of the standard LCDM structure formation scenario and study the effects induced at redshift z=0 by this novel approach on the large-scale clustering patterns as well as (individual) dark matter halos. Comparing these simulations to usual N-body simulations, we find that (i) the new (hydrodynamic) model entails a proliferation of low--mass halos, and (ii) dark matter halos have a higher degree of rotational support. These results agree with the theoretical expectation about the qualitative behaviour of the "correction terms" introduced by the hydrodynamic approach: these terms act as a drain of inflow kinetic energy and a source of vorticity by the small-scale tidal torques and shear stresses., Comment: 18 pages, 17 figs, MNRAS in press, article with full resolution figures avaialble at http://www.aip.de/People/AKnebe/page2/page2.html

Within a general framework we study the effective, deformation-induced interaction between two colloids trapped at a fluid interface. As an application, we consider the interface deformation owing to the electrostatic field of charged colloids. The effective interaction is attractive and overcomes the direct electrostatic repulsion at large separations if the system is not mechanically isolated. Otherwise, a net attraction seems possible only for large enough colloidal charges., Comment: Contribution to the proceedings of the 6th Liquid Matter Conference

The notion of `adhesion' has been advanced for the phenomenon of stabilization of large-scale structure emerging from gravitational instability of a cold medium. Recently, the physical origin of adhesion has been identified: a systematic derivation of the equations of motion for the density and the velocity fields leads naturally to the key equation of the `adhesion approximation' - however, under a set of strongly simplifying assumptions. In this work, we provide an evaluation of the current status of adhesive gravitational clustering and a clear explanation of the assumptions involved. Furthermore, we propose systematic generalizations with the aim to relax some of the simplifying assumptions. We start from the general Newtonian evolution equations for self-gravitating particles on an expanding Friedmann background and recover the popular `dust model' (pressureless fluid), which breaks down after the formation of density singularities; then we investigate, in a unified framework, two other models which, under the restrictions referred to above, lead to the `adhesion approximation'. We apply the Eulerian and Lagrangian perturbative expansions to these new models and, finally, we discuss some non-perturbative results that may serve as starting points for workable approximations of non-linear structure formation in the multi-stream regime. In particular, we propose a new approximation that includes, in limiting cases, the standard `adhesion model' and the Eulerian as well as Lagrangian first-order approximations., Comment: LateX, 23 pages, uses A&A documentclass, matches published version in Astronomy & Astrophysics; appendices published online

We report on a new study of the velocity distribution in N-body simulations. We investigate the center-of-mass and internal kinetic energies of coarsening cells as a function of time, cell size and cell mass. By using self-similar cosmological models, we are able to derive theoretical predictions for comparison and to assess the influence of finite-size and resolution effects. The most interesting result is the discovery of a polytropic-like relationship between the average velocity dispersion (internal kinetic energy) and the mass density in an intermediate range of densities, K ~ rho^{2-eta}. The exponent eta measures the deviations from the virial prediction, eta_virial=0. For self-similar models, eta depends only on the spectral index of the initial power spectrum. We also study CDM models and confirm a previous result that the same polytropic-like dependence exists (astro-ph/0103313), with a time and coarsening length dependent eta. The dependence K(rho) is an important input for a recently proposed theoretical model of cosmological structure formation which improves over the standard dust model (pressureless fluid) by regularizing the density singularities., Comment: Version accepted by A&A (in press). One paragraph added toward the end of Sec. 5

In astro-ph/0109199, the initial conditions (IC's) of cosmological N-body simulations by the Virgo Consortium are analyzed and it is concluded that the density fluctuations are rather different from the desired ones. We have repeated the analysis of the IC's using our own code and the code provided by the authors of astro-ph/0109199, obtaining results that disprove the criticisms., Comment: 2 pages, 4 eps figures, epl.cls style file

In thermal equilibrium, a colloidal particle between two parallel plates immersed in a fluid which partially wets both the particle and the plates, is attracted by the walls. However, if the particle moves parallel to the plates, a hydrodynamic lift force away from the plates arises in the limit of low Reynolds number. We study theoretically the competition of these two effects and identify the range of velocity in which the velocity may serve as a parameter controlling the adsorption in microflows., Comment: Poster contribution to the EURESCO conference "Solid/fluid interfaces", April 2003

We present the study of ten random realizations of a density field characterized by a cosmological power spectrum P(k) at redshift z=50. The reliability of such initial conditions for n-body simulations are tested with respect to their correlation properties. The power spectrum P(k), and the mass variance sigmaM(r) do not show detectable deviations from the desired behavior in the intermediate range of scales between the mean interparticle distance and the simulation volume. The estimator for xi(r) is too noisy to detect any reliable signal at the initial redshift z=50. The particle distributions are then evolved forward until z=0. This allows us to explore the cosmic variance stemming from the random nature of the initial conditions. With cosmic variance we mean the fact that a simulation represents a single realization of the stochastic initial conditions whereas the real Universe contains many realizations of regions of the size of the box; this problem affects most importantly the scales at about the fundamental mode. We study morphological descriptors of the matter distribution such as the genus, as well as the internal properties of the largest object(s) forming in the box. We find that the scatter is at least comparable to the scatter in the fundamental mode., Comment: 22 pages, 12 figures, replaced with major revision to previous submission, PASA in press

This work reports on the application of the Eulerian perturbation theory to a recently proposed model of cosmological structure formation by gravitational instability (astro-ph/0009414). Its physical meaning is discussed in detail and put in perspective of previous works. The model incorporates in a systematic fashion corrections to the popular dust model due to multistreaming and, more generally, the small-scale, virialized degrees of freedom. It features a time-dependent length scale L(t) estimated to be L/r0 ~ 0.1 (r0(t) is the nonlinear scale, at which the density variance =1). The model provides a new angle on the dust model and allows to overcome some of its limitations. Thus, the scale L(t) works as a physically meaningful short-distance cutoff for the divergences appearing in the perturbation expansion of the dust model when there is too much initial power on small scales. The model also incorporates the generation of vorticity by tidal forces; according to the perturbational result, the filtered vorticity for standard CDM initial conditions should be significant today only at scales below ~ 1 Mpc/h., Comment: 9 pages, coincides with the published version

The effect of the large-scale cosmological expansion on small systems is studied in the light of modern cosmological models of large-scale structure. We identify certain assumptions of earlier works which render them unrealistic regarding these cosmological models. The question is reanalyzed by dropping these assumptions to conclude that a given small system can experience either an expansion or a contraction of cosmological origin., Comment: 7 pages. Accepted for publication in Europhysics Letters

This work reports on a study of the spatially coarse-grained velocity dispersion in cosmological N-body simulations (OCDM and Lambda-CDM models) as a function of time (redshifts z=0-4) and of the coarsening length (0.6-20 Mpc/h). The main result is the discovery of a polytropic relationship I_1 ~ rho^{2-eta} between the velocity-dispersion kinetic energy density of the coarsening cells, I_1, and their mass density, rho. The exponent eta, dependent on time and coarsening scale, is a compact measure of the deviations from the naive virial prediction eta_virial=0. This relationship supports the ``polytropic assumption'' which has been employed in theoretical models for the growth of cosmological structure by gravitational instability., Comment: Minor, unimportant changes. Matches published version

The Minkowski functionals are a mathematical tool to quantify morphological features of patterns. Some applications to the matter distribution in galaxy catalogues and N-body simulations are reviewed, with an emphasis on the effects of cosmic variance. The conclusions are that (i) the observed large-scale morphology is sensitive to cosmic variance on scales much larger than the nonlinear length (approx. 8 Mpc/h), and (ii) the large-scale morphology predicted by simulations is thus affected by finite-size effects, but nonetheless a Lambda-CDM model is favored., Comment: Contribution to the proceedings of the 4th German-Chinese Joint Miniworkshop on Cosmology. 6 pages, 8 EPS figures, uses a World Scientific style file

A hydrodynamic formulation of the evolution of large-scale structure in the Universe is presented. It relies on the spatially coarse-grained description of the dynamical evolution of a many-body gravitating system. Because of the assumed irrelevance of short-range (``collisional'') interactions, the way to tackle the hydrodynamic equations is essentially different from the usual case. The main assumption is that the influence of the small scales over the large-scale evolution is weak: this idea is implemented in the form of a large-scale expansion for the coarse-grained equations. This expansion builds a framework in which to derive in a controlled manner the popular ``dust'' model (as the lowest-order term) and the ``adhesion'' model (as the first-order correction). It provides a clear physical interpretation of the assumptions involved in these models and also the possibility to improve over them., Comment: 14 pages, 3 figures. Version to appear in Phys. Rev. D

There is an ongoing debate in cosmology about the value of the length scale at which ``homogeneity'' in the matter distribution is reached or even if such a scale exists. In the wake of this debate, we intend in this letter to clarify the meaning of the statement transition to homogeneity and of the concept of correlation length. We show that there are two scales each associated to the fractal and to the homogeneous regimes of the matter distribution, respectively. The distinction between both scales has deep consequences, for there can be a regime which despite having small fluctuations around the average density exhibits large clusters of galaxies., Comment: 10 pages, 2 large PS figures, AAS macros. Substantial additions as regards the implications for cosmology, including the prospective observation of critical phenomena, and new references. Version to appear in ApJL