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Achille Giacometti

Publications and source records attributed to Achille Giacometti.

At least 109 records · Page 6Linked to original sources
arXiv2002

On the compressibility equation of state for multicomponent adhesive hard sphere fluids

The compressibility equation of state for a multicomponent fluid of particles interacting via an infinitely narrow and deep potential, is considered within the mean spherical approximation (MSA). It is shown that for a class of models leading to a particular form of the Baxter functions $q_{ij}(r)$ containing density-independent stickiness coefficient, the compressibility EOS does not exist, unlike the one-component case. The reason for this is that a direct integration of the compressibility at fixed composition, cannot be carried out due to the lack of a reciprocity relation on the second order partial derivatives of the pressure with respect to two different densities. This is, in turn, related to the inadequacy of the MSA. A way out to this drawback is presented in a particular example, leading to a consistent compressibility pressure, and a possible generalization of this result is discussed.

cond-mat.stat-mech↗
arXiv2002

A pseudo-spectral method for the Kardar-Parisi-Zhang equation

We discuss a numerical scheme to solve the continuum Kardar-Parisi-Zhang equation in generic spatial dimensions. It is based on a momentum-space discretization of the continuum equation and on a pseudo-spectral approximation of the non-linear term. The method is tested in (1+1)- and (2+1)- dimensions, where it is shown to reproduce the current most reliable estimates of the critical exponents based on Restricted Solid-on-Solid simulations. In particular it allows the computations of various correlation and structure functions with high degree of numerical accuracy. Some deficiencies which are common to all previously used finite-difference schemes are pointed out and the usefulness of the present approach in this respect is discussed.

cond-mat.stat-mech↗
arXiv2002

Interaction of proteins in solution from small angle scattering: a perturbative approach

In this work, an improved methodology for studying interactions of proteins in solution by small-angle scattering, is presented. Unlike the most common approach, where the protein-protein correlation functions $g_{ij}(r)$ are approximated by their zero-density limit (i.e. the Boltzmann factor), we propose a more accurate representation of $g_{ij}(r)$ which takes into account terms up to the first order in the density expansion of the mean-force potential. This improvement is expected to be particulary effective in the case of strong protein-protein interactions at intermediate concentrations. The method is applied to analyse small angle X-ray scattering data obtained as a function of the ionic strength (from 7 to 507 mM) from acidic solutions of $β$-Lactoglobuline at the fixed concentration of 10 $\rm g L^{-1}$. The results are compared with those obtained using the zero-density approximation and show a significant improvement particularly in the more demanding case of low ionic strength.

cond-mat.stat-mech↗
arXiv2001

Polydisperse fluid mixtures of adhesive colloidal particles

We investigate polydispersity effects on the average structure factor of colloidal suspensions of neutral particles with surface adhesion. A sticky hard sphere model alternative to Baxter's one is considered. The choice of factorizable stickiness parameters in the potential allows a simple analytic solution, within the ``mean spherical approximation'', for any number of components and arbitrary stickiness distribution. Two particular cases are discussed: i) all particles have different sizes but equal stickiness (Model I), and ii) each particle has a stickiness proportional to its size (Model II). The interplay between attraction and polydispersity yields a markedly different behaviour for the two Models in regimes of strong coupling (i.e. strong adhesive forces and low temperature) and large polydispersity. These results are then exploited to reanalyze experimental scattering data on sterically stabilized silica particles.

cond-mat.stat-mech↗
arXiv2000

A pseudo-spectral approach to inverse problems in interface dynamics

An improved scheme for computing coupling parameters of the Kardar-Parisi-Zhang equation from a collection of successive interface profiles, is presented. The approach hinges on a spectral representation of this equation. An appropriate discretization based on a Fourier representation, is discussed as a by-product of the above scheme. Our method is first tested on profiles generated by a one-dimensional Kardar-Parisi-Zhang equation where it is shown to reproduce the input parameters very accurately. When applied to microscopic models of growth, it provides the values of the coupling parameters associated with the corresponding continuum equations. This technique favorably compares with previous methods based on real space schemes.

cond-mat.stat-mech↗
arXiv2000

Structure factors for the simplest solvable model of polydisperse colloidal fluids with surface adhesion

Closed analytical expressions for scattering intensity and other global structure factors are derived for a new solvable model of polydisperse sticky hard spheres. The starting point is the exact solution of the ``mean spherical approximation'' for hard core plus Yukawa potentials, in the limit of infinite amplitude and vanishing range of the attractive tail, with their product remaining constant. The choice of factorizable coupling (stickiness) parameters in the Yukawa term yields a simpler ``dyadic structure'' in the Fourier transform of the Baxter factor correlation function $q_{ij}(r)$, with a remarkable simplification in all structure functions with respect to previous works. The effect of size and stickiness polydispersity is analyzed and numerical results are presented for two particular versions of the model: i) when all polydisperse particles have a single, size-independent, stickiness parameter, and ii) when the stickiness parameters are proportional to the diameters. The existence of two different regimes for the average structure factor, respectively above and below a generalized Boyle temperature which depends on size polydispersity, is recognized and discussed. Because of its analycity and simplicity, the model may be useful in the interpretation of small-angle scattering experimental data for polydisperse colloidal fluids of neutral particles with surface adhesion.

cond-mat.stat-mech↗
arXiv2000

Small Angle Scattering data analysis for dense polydisperse systems: the FLAC program

FLAC is a program to calculate the small-angle neutron scattering intensity of highly packed polydisperse systems of neutral or charged hard spheres within the Percus-Yevick and the Mean Spherical Approximation closures, respectively. The polydisperse system is defined by a size distribution function and the macro-particles have hard sphere radii which may differ from the size of their scattering cores. With FLAC, one can either simulate scattering intensities or fit experimental small angle neutron scattering data. In output scattering intensities, structure factors and pair correlation functions are provided. Smearing effects due to instrumental resolution, vertical slit, primary beam width and multiple scattering effects are also included on the basis of the existing theories. Possible form factors are those of filled or two-shell spheres.

cond-mat.stat-mech↗
arXiv2000

Local minimal energy landscapes in river networks

The existence and stability of the universality class associated to local minimal energy landscapes is investigated. Using extensive numerical simulations, we first study the dependence on a parameter $γ$ of a partial differential equation which was proposed to describe the evolution of a rugged landscape toward a local minimum of the dissipated energy. We then compare the results with those obtained by an evolution scheme based on a variational principle (the optimal channel networks). It is found that both models yield qualitatively similar river patterns and similar dependence on $γ$. The aggregation mechanism is however strongly dependent on the value of $γ$. A careful analysis suggests that scaling behaviors may weakly depend both on $γ$ and on initial condition, but in all cases it is within observational data predictions. Consequences of our results

cond-mat.stat-mech↗
arXiv2000

Interface dynamics from experimental data

A novel algorithm is envisaged to extract the coupling parameters of the Kardar-Parisi-Zhang (KPZ) equation from experimental data. The method hinges on the Fokker-Planck equation combined with a classical least-square error procedure. It takes properly into account the fluctuations of surface height through a deterministic equation for space correlations. We apply it to the 1+1 KPZ equation and carefully compare its results with those obtained by previous investigations. Unlike previous approaches, our method does not require large sizes and is stable under a modification of sampling time of observations. Shortcomings associated to standard discretizations of the continuous KPZ equation are also pointed out and possible future perspectives are finally analyzed.

cond-mat.stat-mech↗
arXiv1999

A scaling approximation for structure factors in the integral equation theory of polydisperse nonionic colloidal fluids

Integral equation of pure liquids, combined with a new "scaling approximation" based on a corresponding states treatment of pair correlation functions, is used to evaluate approximate structure factors for colloidal fluids constituted of uncharged particles with polydispersity in size and energy parameters. Both hard spheres and Lennard-Jones interactions are considered. For polydisperse hard spheres, the scaling approximation is compared to theories utilized by small angle scattering experimentalists (decoupling approximation, local monodisperse approximation)and to the van der Waals one-fluid theory. The results are tested against predictions from analytical expressions, exact within the Percus-Yevick approximation. For polydisperse Lennard-Jones particles, the scaling approximation combined with a "modified hypernetted chain" integral equation, is tested against molecular dynamics data generated for the present work. Despite ist simplicity, the scaling approximation exhibits a satisfactory performance for both potentials and represents a considerable improvement over the above mentioned theories. Shortcomings of the proposed theory, its applicability to the analysis of experimental scattering data, and its possible extensions to different potentials are finally discussed.

cond-mat.stat-mech↗
arXiv1999

A corresponding states approach to Small-Angle-Scattering for polydisperse ionic colloidal fluids

Approximate scattering functions for polydisperse ionic colloidal fluids are obtained by a corresponding states approach. This assumes that all pair correlation functions $g_{αβ}(r)$ of a polydisperse fluid are conformal to those of an appropriate monodisperse binary fluid (reference system) and can be generated from them by scaling transformations. The correspondence law extends to ionic fluids a {\it scaling approximation} (SA) successfully proposed for nonionic colloids in a recent paper. For the primitive model of charged hard spheres in a continuum solvent, the partial structure factors of the monodisperse binary reference system are evaluated by solving the Orstein-Zernike (OZ) integral equations coupled with an approximate closure. The SA is first tested within the mean spherical approximation (MSA) closure, which allows analytical solutions. The results are found in good overall agreement with exact MSA predictions up to relevant polidispersity. The SA is shown to be an improvement over the ``decoupling approximation'' extended to the ionic case. The simplicity of the SA scheme allows its application also when the OZ equations can be solved only numerically. An example is then given by using the hypernetted chain (HNC) closure. Shortcomings of the SA approach, its possible use in the analysis of experimental scattering data and other related points are also briefly addressed.

cond-mat.stat-mech↗
arXiv1998

Dynamical properties of the Zhang model of Self-Organized Criticality

Critical exponents of the infinitely slowly driven Zhang model of self-organized criticality are computed for $d=2,3$ with particular emphasis devoted to the various roughening exponents. Besides confirming recent estimates of some exponents, new quantities are monitored and their critical exponents computed. Among other results, it is shown that the three dimensional exponents do not coincide with the Bak, Tang, and Wiesenfeld (abelian) model and that the dynamical exponent as computed from the correlation length and from the roughness of the energy profile do not necessarily coincide as it is usually implicitly assumed. An explanation for this is provided. The possibility of comparing these results with those obtained from Renormalization Group arguments is also briefly addressed.

cond-mat.stat-mech↗
arXiv1998

Models of Fractal River Basins

Two distinct models for self-similar and self-affine river basins are numerically investigated. They yield fractal aggregation patterns following non-trivial power laws in experimentally relevant distributions. Previous numerical estimates on the critical exponents, when existing, are confirmed and superseded. A physical motivation for both models in the present framework is also discussed.

cond-mat.stat-mech↗
arXiv1997

Scattering functions for multicomponent mixtures of charged hard spheres, including the polydisperse limit. Analytic expressions in the Mean Spherical Approximation

We present a closed analytical formula for the scattering intensity from charged hard sphere fluids with any arbitrary number of components. Our result is an extension to ionic systems of Vrij's analogous expression for uncharged hard sphere mixtures. Use is made of Baxter's factor correlation functions within the Mean Spherical Approximation (MSA). The polydisperse case of an infinite number of species with a continuous distribution of hard sphere diameters and charges is also considered. As an important by-product of our investigation, we present some properties of a particular kind of matrices (sum of the identity matrix with a dyadic matrix) appearing in the solution of the MSA integral equations for both uncharged and charged hard sphere mixtures. This analysis provides a general framework to deal with a wide class of MSA solutions having dyadic structure and allows an easy extension of our formula for the scattering intensity to different potential models. Finally, the relevance of our results for the interpretation of small angle neutron scattering experimental data is briefly discussed.

cond-mat.stat-mech↗
arXiv1996

Diffusion and Trapping on a one-dimensional lattice

The properties of a particle diffusing on a one-dimensional lattice where at each site a random barrier and a random trap act simultaneously on the particle are investigated by numerical and analytical techniques. The combined effect of disorder and traps yields a decreasing survival probability with broad distribution (log-normal). Exact enumerations, effective-medium approximation and spectral analysis are employed. This one-dimensional model shows rather rich behaviours which were previously believed to exist only in higher dimensionality. The possibility of a trapping-dominated super universal class is suggested.

cond-mat↗
arXiv1995

Continuum Model for River Networks

The effects of erosion, avalanching and random precipitation are captured in a simple stochastic partial differential equation for modelling the evolution of river networks. Our model leads to a self-organized structured landscape and to abstraction and piracy of the smaller tributaries as the evolution proceeds. An algebraic distribution of the average basin areas and a power law relationship between the drainage basin area and the river length are found.

cond-mat↗
arXiv1995

Iterated Function System and Diffusion in the Presence of Disorder and Traps

The escape probability $ξ_{x}$ from a site $x$ of a one-dimensional disordered lattice with trapping is treated as a discrete dynamical evolution by random iterations over nonlinear maps parametrized by the right and left jump probabilities. The invariant measure of the dynamics is found to be a multifractal. However the measure becomes uniform over the support when the disorder becomes weak for any non-zero trapping probability. Implications of our findings in terms of diffusion are discussed.

cond-mat↗