Random sequential adsorption on a dashed line

We study analytically and numerically a model of random sequential adsorption (RSA) of segments on a line, subject to some constraints suggested by two kinds of physical situations: - deposition of dimers on a lattice where the sites have a spatial extension; - deposition of extended particles which must overlap one (or several) adsorbing sites on the substrate. Both systems involve discrete and continuous degrees of freedom, and, in one dimension, are equivalent to our model, which depends on one length parameter. When this parameter is varied, the model interpolates between a variety of known situations : monomers on a lattice, "car-parking" problem, dimers on a lattice. An analysis of the long-time behaviour of the coverage as a function of the parameter exhibits an anomalous 1/t^2 approach to the jamming limit at the transition point between the fast exponential kinetics, characteristic of the lattice model, and the 1/t law of the continuous one.Comment: 14 pages (Latex) + 4 Postscript figure

Irreversible Deposition of Line Segment Mixtures on a Square Lattice: Monte Carlo Study

We have studied kinetics of random sequential adsorption of mixtures on a square lattice using Monte Carlo method. Mixtures of linear short segments and long segments were deposited with the probability $p$ and $1-p$, respectively. For fixed lengths of each segment in the mixture, the jamming limits decrease when $p$ increases. The jamming limits of mixtures always are greater than those of the pure short- or long-segment deposition. For fixed $p$ and fixed length of the short segments, the jamming limits have a maximum when the length of the long segment increases. We conjectured a kinetic equation for the jamming coverage based on the data fitting.Comment: 7 pages, latex, 5 postscript figure

La forêt méditerranéenne en tant que paysage : patrimoine naturel, cadre de vie ou espace social ? -

Chacun, de nos jours, fait référence au paysage, comme si ce concept allait de soi ! Pourtant, si à ce terme on rajoute "forestier" et, en plus, "méditerranéen", on entre dans une sorte de labyrinthe dans lequel les auteurs s'efforcent de nous guider. Eclaircissant les différentes approches du paysage forestier méditerranéen, l'article montre que s'agissant d'écologie, de sylviculture, d'aménagement et de développement durable des territoires, voire d'esthétique, la préoccupation et la pratique paysagère ne sont pas qu'utiles (outil), elles sont sans doute recommandées

Critical Behavior of the Ferromagnetic Ising Model on a Sierpinski Carpet: Monte Carlo Renormalization Group Study

We perform a Monte Carlo Renormalization Group analysis of the critical behavior of the ferromagnetic Ising model on a Sierpi\'nski fractal with Hausdorff dimension $d_f\simeq 1.8928$. This method is shown to be relevant to the calculation of the critical temperature $T_c$ and the magnetic eigen-exponent $y_h$ on such structures. On the other hand, scaling corrections hinder the calculation of the temperature eigen-exponent $y_t$. At last, the results are shown to be consistent with a finite size scaling analysis.Comment: 16 pages, 7 figure

Adsorption of Line Segments on a Square Lattice

We study the deposition of line segments on a two-dimensional square lattice. The estimates for the coverage at jamming obtained by Monte-Carlo simulations and by $7^{th}$-order time-series expansion are successfully compared. The non-trivial limit of adsorption of infinitely long segments is studied, and the lattice coverage is consistently obtained using these two approaches.Comment: 19 pages in Latex+5 postscript files sent upon request ; PTB93_

Jamming coverage in competitive random sequential adsorption of binary mixture

We propose a generalized car parking problem where cars of two different sizes are sequentially parked on a line with a given probability $q$. The free parameter $q$ interpolates between the classical car parking problem of only one car size and the competitive random sequential adsorption (CRSA) of a binary mixture. We give an exact solution to the CRSA rate equations and find that the final coverage, the jamming limit, of the line is always larger for a binary mixture than for the uni-sized case. The analytical results are in good agreement with our direct numerical simulations of the problem.Comment: 4 pages 2-column RevTeX, Four figures, (there was an error in the previous version. We replaced it (including figures) with corrected and improved version that lead to new results and conclusions

Cell viability assessment using the Alamar blue assay: A comparison of 2D and 3D cell culture models

Comparisons of 2D and 3D cell culture models in literature have indicated differences in cellular morphology and metabolism, commonly attributed the better representation of in vivo conditions of the latter cell culture environment. Thus, interest in the use of 3D collagen gels for in vitro analysis has been growing. Although comparative studies to date have indicated an enhanced resistance of cells on collagen matrices against different toxicants, in the present study it is demonstrated that non-adapted protocols can lead to misinterpretation of results obtained from classical colorometric dye-based cytotoxic assays. Using the well established Alamar Blue assay, the study demonstrates how the transfer from 2D substrates to 3D collagen matrices can affect the uptake of the resazurin itself, affecting the outcome of the assay. Using flow cytometry, it is demonstrated that the cell viability is unaffected when cells are grown on collagen matrices, thus the difference seen in the fluorescence is a result of a dilution of the resazurin dye in the collagen matrix, and an increased uptake rate due to the larger cell surface exposed to the surrounding environment, facilitating more effective diffusion through the cellular membrane. The results are supported by a rate equation based simulation, verifying that differing uptake kinetics can result in apparently different cell viability. Finally, this work highlights the feasibility to apply classical dye-based assays on collagen based 3D cell culture models. However, the diffusion and bioavailbility of test substances in 3D matrices used in in vitro toxicological assays must be considered and adaption of the protocols is necessary for direct comparison with the traditional 2D models. Moreover, the observations made based on the resazurin dye can be applied to drugs or nanoparticles which freely diffuse through the collagen matrices, thus affecting the effective concentration exposed to the cells

Fractal formation and ordering in random sequential adsorption

We reveal the fractal nature of patterns arising in random sequential adsorption of particles with continuum power-law size distribution, $P(R)\sim R^{\alpha-1}$, $R \le R_{\rm max}$. We find that the patterns become more and more ordered as $\alpha$ increases, and that the Apollonian packing is obtained at $\alpha \to \infty$ limit. We introduce the entropy production rate as a quantitative criteria of regularity and observe a transition from an irregular regime of the pattern formation to a regular one. We develop a scaling theory that relates kinetic and structural properties of the system.Comment: 4 pages, RevTex, 4 postscript figures. To appear in Phys.Rev.Let