Department of Molecular Sciences and Nanosystems

The principle of reparametrization invariance is used to derive a dynamical equation for the erosion of the landscape of the drainage basin of river networks. The stationary solutions of the equation are found to have scaling behavior that is consistent with observational data. Our analytic prediction of the main stream profile is confirmed by numerical results and is amenable to direct observational verification. [S0031-9007(97)

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) that 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 analyze small-angle x-ray scattering data obtained as a function of the ionic strength (from 7 to 507 mM) from acidic solutions of ␤-lactoglobulin at the fixed concentration of 10 gl Ϫ1 . The results are compared with those obtained using the zero-density approximation and show significant improvement, particularly in the more demanding case of low ionic strength.

The main goal of this paper is to assess the limits of validity, in the regime of low concentration and strong Coulomb coupling (high molecular charges), for a simple perturbative approximation to the radial distribution functions (RDF), based upon a low-density expansion of the potential of mean force and proposed to describe protein-protein interactions in a recent Small-Angle-Scattering (SAS) experimental study. A highly simplified Yukawa (screened Coulomb) model of monomers and dimers of a charged globular protein (β-lactoglobulin) in solution is considered. We test the accuracy of the RDF approximation, as a necessary complementary part of the previous experimental investigation, by comparison with the fluid structure predicted by approximate integral equations and exact Monte Carlo (MC) simulations. In the MC calculations, an Ewald construction for Yukawa potentials has been used to take into account the long-range part of the interactions in the weakly screened cases. Our results confirm that the perturbative first-order approximation is valid for this system even at strong Coulomb coupling, provided that the screening is not too weak (i.e., for Debye length smaller than monomer radius). A comparison of the MC results with integral equation calculations shows that both the hypernetted-chain (HNC) and the Percus-Yevick (PY) closures have a satisfactory behavior under these regimes, with the HNC being superior throughout.

We study the thermodynamic and structural properties of a simple, one-patch fluid model using the reference hypernetted-chain (RHNC) integral equation and specialized Monte Carlo simulations. In this model, the interacting particles are hard spheres, each of which carries a single identical, arbitrarily-oriented, attractive circular patch on its surface; two spheres attract via a simple squarewell potential only if the two patches on the spheres face each other within a specific angular range dictated by the size of the patch. For a ratio of attractive to repulsive surface of 0.8, we construct the RHNC fluid-fluid separation curve and compare with that obtained by Gibbs ensemble and grand canonical Monte Carlo simulations. We find that RHNC provides a quick and highly reliable estimate for the position of the fluid-fluid critical line. In addition, it gives a detailed (though approximate) description of all structural properties and their dependence on patch size.

We perform numerical simulations of a simple model of one-patch colloidal particles to investigate: (i) the behavior of the gas-liquid phase diagram on moving from a spherical attractive potential to a Janus potential and (ii) the collective structure of a system of Janus particles. We show that, for the case where one of the two hemispheres is attractive and one is repulsive, the system organizes into a dispersion of orientational ordered micelles and vesicles and, at low T , the system can be approximated as a fluid of such clusters, interacting essentially via excluded volume. The stability of this cluster phase generates a very peculiar shape of the gas and liquid coexisting densities, with a gas coexistence density which increases on cooling, approaching the liquid coexistence density at very low T .

We introduce a model of attractive penetrable spheres by adding a short range attractive square well outside a penetrable core, and we provide a detailed analysis of structural and thermodynamical properties in one dimension using the exact impenetrable counterpart as a starting point. The model is expected to describe star polymers in regimes of good and moderate solvent under dilute conditions. We derive the exact coefficients of a low density expansion up to second order for the radial distribution function and up to fourth order in the virial expansion. These exact results are used as a benchmark to test the reliability of approximate theories (Percus-Yevick and hypernetted chain). Notwithstanding the lack of an exact solution for arbitrary densities, our results are expected to be rather precise within a wide range of temperatures and densities. A detailed analysis of some limiting cases is carried out. In particular we provide a complete solution of the sticky penetrablesphere model in one dimension up to the same order in density. The issue of Ruelle's thermodynamics stability is analyzed and the region of a well defined thermodynamic limit is identified.

A relation between two exponents characterizing the scaling behavior of random agglomeration models with particle injection is proposed and verified by numerical simulations. This relation, and a link between diffusion-limited agglomeration models with and without injection combined with an exact solution of the latter, leads to a solution of the former in arbitrary dimensionality. [S0031-9007(97)04406-2] PACS numbers: 82.20. -w

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.

We study structural and thermophysical properties of a one-dimensional classical fluid made of penetrable spheres interacting via an attractive square-well potential. Penetrability of the spheres is enforced by reducing from infinite to finite the repulsive energy barrier in the pair potentials As a consequence, an exact analytical solution is lacking even in one dimension. Building upon previous exact analytical work in the low-density limit [Santos et al., Phys. Rev. E 77, 051206 (2008)], we propose an approximate theory valid at any density and in the low-penetrable regime.

The one-dimensional penetrable-square-well fluid is studied using both analytical tools and specialized Monte Carlo simulations. The model consists of a penetrable core characterized by a finite repulsive energy combined with a short-range attractive well. This is a many-body one-dimensional problem, lacking an exact analytical solution, for which the usual van Hove theorem on the absence of phase transition does not apply. We determine a high-penetrability approximation complementing a similar low-penetrability approximation presented in previous work. This is shown to be equivalent to the usual Debye-Hückel theory for simple charged fluids for which the virial and energy routes are identical. The internal thermodynamic consistency with the compressibility route and the validity of the approximation in describing the radial distribution function is assessed by a comparison against numerical simulations. The Fisher-Widom line separating the oscillatory and monotonic large-distance behavior of the radial distribution function is computed within the high-penetrability approximation and compared with the opposite regime, thus providing a strong indication of the location of the line in all possible regimes. The high-penetrability approximation predicts the existence of a critical point and a spinodal line, but this occurs outside the applicability domain of the theory. We investigate the possibility of a fluid-fluid transition by Gibbs ensemble Monte Carlo techniques, not finding any evidence of such a transition. Additional analytical arguments are given to support this claim. Finally, we find a clustering transition when Ruelle's stability criterion is not fulfilled. The consequences of these findings on the three-dimensional phase diagrams are also discussed.

We consider an anisotropic version of Baxter's model of 'sticky hard spheres', where a nonuniform adhesion is implemented by adding, to an isotropic surface attraction, an appropriate 'dipolar sticky' correction (positive or negative, depending on the mutual orientation of the molecules). The resulting nonuniform adhesion varies continuously, in such a way that in each molecule one hemisphere is 'stickier' than the other.