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Distributions of the largest fragment charge, Zmax, in multifragmentation reactions around the Fermi energy can be decomposed into a sum of a Gaussian and a Gumbel distribution, whereas at much higher or lower energies one or the other distribution is asymptotically dominant. We demonstrate the same generic behavior for the largest cluster size in critical aggregation models for small systems, in or out of equilibrium, around the critical point. By analogy with the time-dependent irreversible aggregation model, we infer that Zmax distributions are characteristic of the multifragmentation time scale, which is largely determined by the onset of radial expansion in this energy range. [ABSTRACT FROM AUTHOR]

Monte Carlo simulations, fully constrained by experimental parameters, are found to agree well with a measured phase diagram of aqueous dispersions of nanoparticles with a moderate size polydispersity over a broad range of salt concentrations, c_{s}, and volume fractions, ϕ. Upon increasing ϕ, the colloids freeze first into coexisting compact solids then into a body centered cubic phase (bcc) before they melt into a glass forming liquid. The surprising stability of the bcc solid at high ϕ and c_{s} is explained by the interaction (charge) polydispersity and vibrational entropy.

We report small-angle x-ray scattering experiments on aqueous dispersions of colloidal silica with a broad monomodal size distribution (polydispersity, 14%; size, 8 nm). Over a range of volume fractions, the silica particles segregate to build first one, then two distinct sets of colloidal crystals. These dispersions thus demonstrate fractional crystallization and multiple-phase (bcc, Laves AB_{2}, liquid) coexistence. Their remarkable ability to build complex crystal structures from a polydisperse population originates from the intermediate-range nature of interparticle forces, and it suggests routes for designing self-assembling colloidal crystals from the bottom up.

The hydrodynamic properties of rigid fractal aggregates have been investigated by considering their motion in shear flow in the Stokesian dynamics approach. Due to the high fluid viscosity and small particle inertia of colloidal systems, the total force and torque applied to the aggregate reach equilibrium values in a short time. Obtaining equilibrating motions for a number of independent samples, one can extract the average hydrodynamic characteristics of the given fractal aggregates. Despite the geometry of these objects being essentially disordered, the average drag-force distributions for aggregates show symmetric patterns. Moreover, these distributions collapse on a single master curve, characteristic of the nature of the aggregates, provided the positions of the particles are rescaled with the geometric radius of gyration. This result can be used to explain the reason why the stress acting on an aggregate and moments of the forces acting on contact points between particles follow power-law behaviors with the aggregate size. Moreover, the values of the exponents can be explained. As a consequence, considering cohesive force typical for colloidal particles, we find that even aggregates smaller than a few dozen particles must experience restructuring when typical shear flow is applied.

We present the stochastic approach of the polarization state of an electromagnetic wave traveling through randomly twisted optical fiber. We treat the case of the weak randomness. When the geometric torsion of the fiber is distributed as a Gaussian law, we can write explicitly the Fokker-Planck equation for the Stokes parameters of the wave, and find the complete solution of the polarization-state distribution.

We present a framework for the stochastic features of the polarization state of an electromagnetic wave propagating through the optical medium with both deterministic (controlled) and disordered birefringence. In this case, the Stokes parameters obey a Langevin-type equation on the Poincaré sphere. The functional integral method provides for a natural tool to derive the Fokker-Planck equation for the probability distribution of the Stokes parameters. We solve the Fokker-Planck equation in the case of a random anisotropic active medium submitted to a homogeneous electromagnetic field. The possible dissipation and relaxation phenomena are studied in general and in various cases, and we give hints about how to validate experimentally the corresponding phenomenological equations.

We present a numerical study of the effect of interstitial air on a vertically vibrated granular bed within one period of oscillation. We use a three-dimensional molecular-dynamics simulation including air phenomenologically. The simulations are validated with experiments made with spherical glass beads in a rectangular container. After validation, results are reported for a granular column of 9000 grains and approximately 50 layers deep (at rest), agitated with a sinusoidal excitation with maximal acceleration 4.7g at 11.7 Hz. We report the evolution of density, granular temperature, and coordination number within a vibration cycle, and the effect of interstitial air on those parameters. In three-dimensional computer simulations we found that the presence of interstitial air can promote the collective motion of the granular material as a whole.

Systems with global symmetry group O(2) experience topological transition in the two-dimensional space. But there is controversy about such a transition for systems with global symmetry group O(3). As an example of the latter case, we study the Lebwohl-Lasher model for the two-dimensional liquid crystal, using three different methods independent of the proper values of possible critical exponents. Namely, we analyze the at-equilibrium order parameter distribution function with (1) the hyperscaling relation; (2) the first-scaling collapse for the probability distribution function; and (3) the Binder's cumulant. We give strong evidence for definite lack of a line of critical points at low temperatures in the Lebwohl-Lasher model, contrary to conclusions of a number of previous numerical studies.

We show how applying field conjugated to the order parameter may act as a very precise probe to explore the probability distribution function of the order parameter. Using this "magnetic-field scanning" on large-scale numerical simulations of the critical two-dimensional XY model, we are able to discard the conjectured double-exponential form of the large-magnetization asymptote.

We show that the order-parameter distribution for the mean-field percolation at the critical point is the Kolmogorov-Smirnov distribution and that it coincides with the corresponding distribution for a mean-field aggregation process at the critical time. Both processes are known to belong to the same universality class in the sense that they share the same set of critical exponents, but percolation is at the equilibrium while the aggregation is a dynamical critical process. This shows that, in this case, the probability density for order-parameter fluctuations is universal at the critical point of the infinite lattice, independent of the hypothesis of thermodynamic equilibrium.

We present a theoretical model for the compaction of a colloidal sediment under uniaxial mechanical pressure in the continuous three-dimensional space. The initial system is formed with aggregated particles dispersed in a fluid, and softly sedimented in a vessel. When a uniform pressure is applied, it evolves irreversibly through successive creation and destruction of bonds between the particles. The rules governing the bonds depend on both geometrical constraints and current stresses. Numerical simulations of such systems exhibit three different scenarios, corresponding, respectively, to the fragile, elastic, and plastic behaviors. In the elastic regime, where most bonds are permanent, the pressure scales as a power law of the volume fraction of particles, with a numerical exponent equal to 4.4. In the plastic regime, where many bonds are broken and many others created, the pressure also scales with volume fraction, but the exponent is much lower, equal to 1.7. These scaling behaviors agree remarkably well with recent experiments realized on the compaction of systems with aggregated silica particles in the oedometer cell. They also can be explained with simple theoretical arguments using a plausible morphology of the resistant paths acting throughout the system. Finally, at very large applied pressures, all these regimes converge to the random close packing of spheres.

The spherical spin model with infinite-range ferromagnetic interactions is investigated analytically in the framework of nonextensive thermostatics generalizing the Boltzmann-Gibbs statistical mechanics. We show that for repulsive correlations, a weak-ferromagnetic phase develops. There is a tricritical point separating para-, weak-ferro, and ferro regimes. The transition from paramagnetic to weak-ferromagnetic phase is an unusual first-order phase transition in which a discontinuity of the averaged order parameter appears, even for finite number of spins. This result puts in a different way the question of the stability of critical phenomena with respect to the long-ranged correlations.

Since statistically isotropic fractal aggregates of particles are a particular case of self-organized critical systems, we describe formally field-induced behaviors of aggregated ferrofluids as responses of regular at-equilibrium critical systems at the critical point to the small field conjugated to its order parameter. This leads us to expect some general scaling laws, which are checked numerically on two examples: the magnetic susceptibility and the magneto-optical linear dichroism of two-dimensional aggregated ferrofluids. This is performed by numerical simulations of such an aggregating system under weak magnetic field applied in the plane of the aggregates.

We discuss the scaling laws of both the charged fragments multiplicity n fluctuations and the charge of the largest fragment Z(max) fluctuations for Xe + Sn collisions in the range of bombarding energies between 25A MeV and 50A MeV. We show at E(lab) > or similar to 32 MeV/A the transition in the fluctuation regime of Z(max) which is compatible with the transition from the ordered to disordered phase of excited nuclear matter. The size (charge) of the largest fragment is closely related to the order parameter characterizing this process.