Robert Botet

A new interpretation of scattered light measurements at Titan's limb

Images of Titan, taken by Voyager 2 at phase angles Φ=140° and Φ=155° have provided radial intensity profiles at the bright and dark limbs, which provide information on the vertical and latitudinal distribution of organic hazes. In previous work, the deduced extinction coefficient, using ad hoc particle sizes, was obtained without help of microphysics, and it appeared difficult to compare it with coefficients computed from theoretical models. We use here our fractal approach of microphysical modeling and optics of agregates to compute intensity profiles of the main haze at the bright limb, and compare to the Voyager observations. Fractal aerosol distributions are obtained using different production altitudes and rates. Scattering and absorption of light are described by an improved model, based on the use of fractal aggregates made of spherical (Mie) particles. We show that the fractal dimension of aggregates has to be Df≈2, as predicted by microphysical arguments. Only a production altitude z0≈385±60 km, corresponding to a monomer radius rm≈0.066 μm, is fully consistent with both phase angle data. We also point out that the production rate of the aerosols decreases by a factor ≈2 between 30°S and the midnorthern latitude and further, increases up to 80°N. The average value of the production rate is Q≈1.4×10−13 kg/m2/s; we give arguments in favor of dynamical processes rather than of a purely microphysical mechanisms to explain such latitudinal variations.

Hierarchical model for irreversible kinetic cluster formation

A model is proposed to describe the growth of clusters by a mechanism of irreversible clustering of clusters. The fractal exponent is extracted by means of numerical simulations on small systems, both directly and in the form of a renormalisation-group analysis. The results are in excellent agreement with previous Monte Carlo simulations. The numerical precision is better due to the simpler (hierarchical) formulation of the model. In the present form the model looks like the diffusion limited aggregation model, which for the sake of comparison is treated by the same renormalisation-group method.

Mean-field approximation of Mie scattering by fractal aggregates of identical spheres

We apply the recent exact theory of multiple electromagnetic scattering by sphere aggregates to statistically isotropic finite fractal clusters of identical spheres. In the mean-field approximation the usual Mie expansion of the scattered wave is shown to be still valid, with renormalized Mie coefficients as the multipolar terms. We give an efficient method of computing these coefficients, and we compare this mean-field approach with exact results for silica aggregates of fractal dimension 2.

Semi-empirical model of absorption and scattering by isotropic fractal aggregates of spheres

Abstract Existing models of scattering by fractal aggregates of spheres are generally accurate but somewhat complicated and time consuming. Therefore, they are not easily usable for atmospheric studies that need intensive computations. We propose here a simple and fast model, based on Mie scattering and a set of empirical rules, that determines the scattering and absorption cross sections as well as the intensity phase function of isotropic fractal aggregates of identical spheres. This model is 10–50 times faster than the mean field model it is based on, and is easily derivable from a regular Mie code. The parameters of the present model are optimized for values of the real refractive index between 1.2 and 2.2, for imaginary refractive index less than 1 and for the product of real refractive index and spherical size parameter less than 10. This range was chosen as representative of typical particles in planetary atmospheres, for example, Titans aerosols.

Fractals: Localization of dipole excitations and giant optical polarizabilities

Highly localized optical modes laser-excited on silver colloid fractal clusters were observed using photon scanning tunnelling microscopy (PSTM). The spatial distribution of the modes excited shows the frequency and polarization selectivity suggested by numerical simulations. The localization of the optical excitations on fractals results in very high local fields leading to the huge enhancement of resonant Rayleigh, Raman and, especially, nonlinear light scattering. The experimental results verify the main concepts of the developed resonant optical theory of fractals.

Cluster-cluster aggregation with dipolar interactions

The hierarchical cluster-cluster aggregation model is extended in the presence of dipolar interactions between the magnetic dipoles attached to each individual particle. It is found that the fractal dimension of the resulting clusters decreases when the intensity of the momenta increases, as observed in recent experiments.

Enhanced Raman scattering from self-affine thin films.

Surface-enhanced Raman scattering (SERS) from a self-affine surface is shown to be very large. A theory is developed expressing this SERS in terms of the eigenmodes of a self-affine surface; the theory successfully explains the observed SERS from cold-deposited thin films that are known to have a self-affine structure. Spatial distributions of local fields at the fundamental and Stokes frequencies are strongly inhomogeneous and contain hot zones (high-field areas) localized in nanometer-sized regions that can be spatially separated for the two waves.

Universal features of the order-parameter fluctuations: reversible and irreversible aggregation

We discuss the universal scaling laws of order-parameter fluctuations in any system in which a second-order critical behavior can be identified. These scaling laws can be derived rigorously for equilibrium systems when combined with a finite-size scaling analysis. The relation between the order parameter, the criticality, and the scaling law of fluctuations has been established, and the connection between the scaling function and the critical exponents has been found. We give examples in out-of-equilibrium aggregation models such as the Smoluchowski kinetic equations, or at-equilibrium Ising and percolation models.

Resonant excitations and nonlinear optics of fractals

A scale-invariant theory of nonlinear light scattering by fractal clusters is developed. Due to the presence of very high and strongly fluctuated local fields the scattering is hugely enhanced. The enhancement factor for coherent anti-Stokes Raman scattering (CARS) and optical phase conjugation (OPC) is found. Scaling properties of nonlinear light scattering by collective excitations of fractals are obtained. The corresponding exponent describing a dependence of the scattering enhancement factor on spectral variable is 2d0 + 6, where d0 is the optical spectral dimension. Computer simulations dealing with cluster-cluster aggregates are presented. The numerical results fully confirm the theoretical predictions of the magnitude of the enhanced nonlinear scattering and its scaling behavior as well. The results obtained are in agreement with experimental data on four-wave light scattering by silver fractal clusters.

Restructuring of colloidal aggregates in shear flow Coupling interparticle contact models with Stokesian dynamics

A method to couple interparticle contact models with Stokesian dynamics (SD) is introduced to simulate colloidal aggregates under flow conditions. The contact model mimics both the elastic and plastic behavior of the cohesive connections between particles within clusters. Owing to this, clusters can maintain their structures under low stress while restructuring or even breakage may occur under sufficiently high stress conditions. SD is an efficient method to deal with the long-ranged and many-body nature of hydrodynamic interactions for low Reynolds number flows. By using such a coupled model, the restructuring of colloidal aggregates under shear flows with stepwise increasing shear rates was studied. Irreversible compaction occurs due to the increase of hydrodynamic stress on clusters. Results show that the greater part of the fractal clusters are compacted to rod-shaped packed structures, while the others show isotropic compaction.Graphical abstract