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.Comment: 20 pages, Revtex 3.0, 13 figures in compressed format using uufiles command, to appear in Phys. Rev. E, for an hard copy or problems e-mail to: [email protected]

Thermodynamic consistency of energy and virial routes: An exact proof within the linearized Debye-H\"uckel theory

The linearized Debye-H\"uckel theory for liquid state is shown to provide thermodynamically consistent virial and energy routes for any potential and for any dimensionality. The importance of this result for bounded potentials is discussed.Comment: 4 pages, 1 figure; v2: minor change

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.Comment: 12 pages, 9 figures, revtex 3.0 with epsf style, to appear in Phys. Rev.

Diffusion with critically correlated traps and the slow relaxation of the longest wavelength mode

We study diffusion on a substrate with permanent traps distributed with critical positional correlation, modeled by their placement on the perimeters of a critical percolation cluster. We perform a numerical analysis of the vibrational density of states and the largest eigenvalue of the equivalent scalar elasticity problem using the method of Arnoldi and Saad. We show that the critical trap correlation increases the exponent appearing in the stretched exponential behavior of the low frequency density of states by approximately a factor of two as compared to the case of no correlations. A finite size scaling hypothesis of the largest eigenvalue is proposed and its relation to the density of states is given. The numerical analysis of this scaling postulate leads to the estimation of the stretch exponent in good agreement with the density of states result.Comment: 15 pages, LaTeX (RevTeX

Phase diagram and structural properties of a simple model for one-patch particles

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 square-well 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.Comment: 27 pages, 10 figures, J. Chem. Phys. in pres

Phase diagrams of Janus fluids with up-down constrained orientations

A class of binary mixtures of Janus fluids formed by colloidal spheres with the hydrophobic hemispheres constrained to point either up or down are studied by means of Gibbs ensemble Monte Carlo simulations and simple analytical approximations. These fluids can be experimentally realized by the application of an external static electrical field. The gas-liquid and demixing phase transitions in five specific models with different patch-patch affinities are analyzed. It is found that a gas-liquid transition is present in all the models, even if only one of the four possible patch-patch interactions is attractive. Moreover, provided the attraction between like particles is stronger than between unlike particles, the system demixes into two subsystems with different composition at sufficiently low temperatures and high densities.Comment: 10 pages, 6 figure

Phase behavior of weakly polydisperse sticky hard spheres: Perturbation theory for the Percus-Yevick solution

We study the effects of size polydispersity on the gas-liquid phase behaviour of mixtures of sticky hard spheres. To achieve this, the system of coupled quadratic equations for the contact values of the partial cavity functions of the Percus-Yevick solution is solved within a perturbation expansion in the polydispersity, i.e. the normalized width of the size distribution. This allows us to make predictions for various thermodynamic quantities which can be tested against numerical simulations and experiments. In particular, we determine the leading-order effects of size polydispersity on the cloud curve delimiting the region of two-phase coexistence and on the associated shadow curve; we also study the extent of size fractionation between the coexisting phases. Different choices for the size-dependence of the adhesion strengths are examined carefully; the Asakura-Oosawa model of a mixture of polydisperse colloids and small polymers is studied as a specific example.Comment: 43 pages, 12 figures, and 1 tabl

From rods to helices: evidence of a screw-like nematic phase

Evidence of a special chiral nematic phase is provided using numerical simulation and Onsager theory for systems of hard helical particles. This phase appears at the high density end of the nematic phase, when helices are well aligned, and is characterized by the C$_2$ symmetry axes of the helices spiraling around the nematic director with periodicity equal to the particle pitch. This coupling between translational and rotational degrees of freedom allows a more efficient packing and hence an increase of translational entropy. Suitable order parameters and correlation functions are introduced to identify this screw-like phase, whose main features are then studied as a function of radius and pitch of the helical particles. Our study highlights the physical mechanism underlying a similar ordering observed in colloidal helical flagella [E. Barry et al. \textit{Phys. Rev. Lett.} \textbf{96}, 018305 (2006)] and raises the question of whether it could be observed in other helical particle systems, such as DNA, at sufficiently high densities.Comment: List of authors correcte

Thermal stability and long term hydrogen/deuterium release from soft to hard amorphous carbon layers analyzed using in-situ Raman spectroscopy. Comparison with Tore Supra deposits

The thermal stability of 200 nm thick plasma enhanced chemical vapor deposited a-C:H and a-C:D layers ranging from soft to hard layers has been studied and compared to that of deposits collected on the Tore Supra tokamak plasma facing components by means of in-situ Raman spectroscopy. Linear ramp heating and long term isotherms (from several minutes to 21 days) have been performed and correlations between spectrometric parameters have been found. The information obtained on the sp 2 clustering has been investigated by comparing the G band shift and the 514 nm photon absorption evolution due to the thermal treatment of the layer. The effects of isotopic substitution have also been investigated.Comment: appears in Thin Solid Films, Elsevier, 201

A numerical study of a binary Yukawa model in regimes characteristic of globular proteins in solutions

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 ($\beta$-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. The relevance of our findings for interpreting SAS results is also discussed.Comment: Physical Review E, in press (2005