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Alvaro Dominguez

Publications and source records attributed to Alvaro Dominguez.

At least 19 recordsLinked to original sources
arXiv2017

Work fluctuation theorems and free energy from kinetic theory

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.

cond-mat.stat-mech↗
arXiv2010

Dynamics of colloidal particles with capillary interactions

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.

cond-mat.soft↗
arXiv2008

Force balance of particles trapped at fluid interfaces

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.

cond-mat.soft↗
arXiv2008

Theory of capillary-induced interactions beyond the superposition approximation

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.

cond-mat.soft↗
arXiv2007

A dynamic density functional theory for particles in a flowing solvent

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.

cond-mat.soft↗
arXiv2006

Scaling Laws in the Cosmic Structure and Renormalization Group

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.

astro-ph↗
arXiv2006

Hydrodynamic Approach to the Evolution of Cosmic Structures II: Study of N-body Simulations at z=0

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.

astro-ph↗
arXiv2005

Capillary-induced interactions between colloids at an interface

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.

cond-mat.soft↗
arXiv2005

Adhesive Gravitational Clustering

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.

astro-ph↗
arXiv2004

Numerical study of the cosmological velocity field as a function of density

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.

astro-ph↗
arXiv2003

Velocity dispersion in N-body simulations of CDM models

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.

astro-ph↗
arXiv2003

Comment on ''On the problem of initial conditions in cosmological N-body simulations'' (Europhys. Lett. 57, 322)

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.

astro-ph↗
arXiv2003

Wall adsorption of a colloidal particle moving in a quiescent partially wetting fluid

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.

cond-mat.soft↗
arXiv2003

On the reliability of initial conditions for dissipationless cosmological simulations

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.

astro-ph↗
arXiv2002

Study of corrections to the dust model via perturbation theory

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.

astro-ph↗
arXiv2001

Influence of the cosmological expansion on small systems

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.

astro-ph↗
arXiv2001

Morphology of the large-scale structure

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.

astro-ph↗