Yonathan Shapir

Sociophysics: A new approach of sociological collective behaviour. I. mean‐behaviour description of a strike

A new approach to the understanding of sociological collective behaviour, based on the framework of critical phenomena in physics, is presented. The first step consists of constructing a simple mean‐behaviour model and applying it to a strike process in a plant. The model comprises only a limited number of parameters characteristic of the plant considered and of the society. A dissatisfaction function is introduced with a basic principle stating that the stable state of the plant is a state which minimizes this function. It is found that the plant can be in one of two phases: the “collective phase” and the “individual phase.” These two phases are separated by a critical point, in the neighbourhood of which the system is very sensitive to small changes in the parameters. The collective phase includes a region of parameters for which the system has two possible states: a “work state” and a “strike state.” The actual state of the system depends on the parameters and on the “history of the system.” The irreve...

Improved kinetic renormalisation group approach to diffusion-limited aggregation

An improved kinetic renormalisation group approach to diffusion-limited aggregation is presented. This approach is based on the growth process itself and accounts for the dispersity in the growth probabilities. It yields the multifractal spectrum D(q) with better values at smaller q. On the 2D square lattice the authors find Df=1.694 for the fractal dimensions of the cluster and that of its interface, and D(1)=1.01 for the information dimension. The former agrees with the simulation results (Df approximately=1.70) and the latter compares very well with the exact value D(1)=1.

Maximal height scaling of kinetically growing surfaces.

The scaling properties of the maximal height of a growing self-affine surface with a lateral extent L are considered. In the late-time regime its value measured relative to the evolving average height scales like the roughness: h*(L) approximately L alpha. For large values its distribution obeys logP(h*(L)) approximately (-)A(h*(L)/L(alpha))(a). In the early-time regime where the roughness grows as t(beta), we find h*(L) approximately t(beta)[lnL-(beta/alpha)lnt+C](1/b), where either b = a or b is the corresponding exponent of the velocity distribution. These properties are derived from scaling and extreme-value arguments. They are corroborated by numerical simulations and supported by exact results for surfaces in 1D with the asymptotic behavior of a Brownian path.

Fractal-mound growth of pentacene thin films

The growth mechanism of pentacene film formation on

Scaling of Roughness in Silver Electrodeposition

\mathrm{Si}{\mathrm{O}}_{2}

Excitonic Funneling in Extended Dendrimers with Nonlinear and Random Potentials

substrate was investigated with a combination of atomic force microscopy measurements and numerical modeling. In addition to the diffusion-limited aggregation (DLA) that has already been shown to govern the growth of the ordered pentacene thin films, it is shown here that the Schwoebel barrier effect steps in and disrupts the desired epitaxial growth for the subsequent layers, leading to mound growth. The terraces of the growing mounds have a fractal dimension of 1.6, indicating a lateral DLA shape. This growth morphology thus combines horizontal DLA-like growth with vertical mound growth.

Scaling of self and Fickian diffusion coefficients in the critical region

The electrodeposition of silver from thiosulfate solutions and its surface roughness are studied using scaling methods. Although silver electrodeposition from photographic fixing baths containing thiosulfate has been done successfully for many years, the vast majority of information about this process remains empirical. A comparison is made between plating silver from ammonium- and sodium-thiosulfate-containing solutions. Atomic force microscopy is used to study surface roughness, which is then analyzed by scaling methods. Silver electrodeposition from sodium-thiosulfate-containing solutions was found to be smoother than from ammonium-thiosulfate-containing solutions. The obtained scaling exponents, found after correction for local effects, depend strongly on the nature of the electrolyte; the growth exponents β are 0.13 and 0.71 for sodium and ammonium thiosulfate solutions, respectively. Local effects are observed only for the sodium but not for the ammonium thiosulfate solution.

Ground-state roughness of the disordered substrate and flux lines in d = 2

The mean first passage time (MFPT) for photoexcitations diffusion in a funneling potential of artificial treelike light-harvesting antennas (phenylacetylene dendrimers with generation-dependent segment lengths) is computed. Effects of the nonlinearity of the realistic funneling potential and slow random solvent fluctuations considerably slow down the center-bound diffusion beyond a temperature-dependent optimal size. Diffusion on a disordered Cayley tree with a linear potential is investigated analytically. At low temperatures we predict a phase in which the MFPT is dominated by a few paths.

The Effect of Rate of Surface Growth on Roughness Scaling

Abstract The behavior of diffusion coefficients in the critical region is important to understanding transport phenomena in supercritical fluids. For example, it is often claimed that mass transfer rates are high in the critical region. However, it is also generally accepted that diffusion processes slow down dramatically as the critical point is approached, although there appear to be conflicting results on this point in the literature. From published experimental data for the self-diffusion constant of pure fluids in the critical region one could conclude that this property: (1) approaches zero at the critical point (Cini-Castagnoli et al. Physica 48 (1970) 153), (2) remains finite there, showing no anomalous behavior (Etesse et al. Physica B 183 (1993) 45) or (3) displays singular behavior, approaching infinity, at the critical point itself (Duffield and Harris, Ber.Bunsenges-Gesellschaft 80 (1976) 157). We discuss these and related issues from the vantage point of dynamic scaling theory and the Onsager regression hypothesis. We conclude that while self-diffusion coefficients are not predicted to show anomalous behavior at the critical point, consistent with much of the available data, Fickian (transport) diffusion coefficients are predicted to approach zero there. We are unaware of any measurements of this latter property in a pure fluid consistent with scaling predictions.

Monte Carlo simulation of Fickian diffusion in the critical region

We apply optimization algorithms to the problem of finding ground states for crystalline surfaces and flux-line arrays in the presence of disorder. The algorithms provide ground states in polynomial time, which provides for a more precise study of the interface widths than from Monte Carlo simulations at finite temperature. Using d › 2 systems up to size 420 2 , with a minimum of 2 3 10 3 realizations at each size, we find very strong evidence for a ln 2 sLd super-rough state at low The flux-line arrays formed in a 2D type-II dirty superconductor with the magnetic field parallel to the plane and the surface configurations of a crystalline defect-free material deposited on a disordered substrate (DS) are closely related systems. They have been studied for both the intrinsic interest and because they serve as prototypical models for elastic media in a disordered environment. Both have low temperature glassy phases in which equilibrium and dynamic properties are dominated by the disorder. In the continuum limit they are both described by the random-phase sine-Gordon model (RSGM). However, analytic attempts at understanding the equilibrium properties of the glassy phase based on the RSGM have yielded conflicting results [1,2]. Finite-temperature simulations of the RSGM or the corresponding discrete Gaussian model for the disordered substrate have also been ambiguous [3 ‐7]. Moreover, it is not clear to what extent universality arguments, which yield the RSGM as the continuum limit, can be trusted at temperatures well below the glass transition. The aim of the present work is to address both issues by finding the exact minimum energy configurations in discrete models of the DS surface and that of the fluxline arrays. This yields their T › 0 shapes for any given disorder realization; averaging over disorder allows for the evaluation of their averaged physical properties. In particular, the quantities that theory and simulation have focused on are the height-height correlations in the disordered substrate model and the line-line correlations in the flux-line model. The flux-line system is discretized by its mapping to a surface model (see below), and one may observe the transition by inspecting the roughness scaling of the respective surfaces instead. The transition into the glassy phase is exhibited by a change in these height-height correlations in both models. The predictions from the analytic studies of the RSGM are as follows: Above the transition temperature T › Tg the surface is always logarithmically rough, with a prefactor proportional to T . Below the transition temperature, renormalization group (RG) calculations [1] predict a ln 2 sLd behavior, while variational approaches [2] predict the persistence of the lnsLd behavior but with the prefactor unchanging for T # Tg. Numerical simulations have differed in their results as well. Simulations of the RSGM with weak coupling have shown no transition at all [3]. Others have shown a transition with a lnsLd [4] or a ln 2 sLd behavior [5]. Monte Carlo simulations of the discrete Gaussian version of the model have exhibited the transition, but the behavior of the roughness could better fit the ln sLd [6] or the ln 2 sLd