Fractal clustering of inertial particles in random flows

It is shown that preferential concentrations of inertial (finite-size) particle suspensions in turbulent flows follow from the dissipative nature of their dynamics. In phase space, particle trajectories converge toward a dynamical fractal attractor. Below a critical Stokes number (non-dimensional viscous friction time), the projection on position space is a dynamical fractal cluster; above this number, particles are space filling. Numerical simulations and semi-heuristic theory illustrating such effects are presented for a simple model of inertial particle dynamics.Comment: 4 pages, 4 figures, Physics of Fluids, in pres

Thurston equivalence of topological polynomials

We answer Hubbard's question on determining the Thurston equivalence class of ``twisted rabbits'', i.e. images of the ``rabbit'' polynomial under n-th powers of the Dehn twists about its ears. The answer is expressed in terms of the 4-adic expansion of n. We also answer the equivalent question for the other two families of degree-2 topological polynomials with three post-critical points. In the process, we rephrase the questions in group-theoretical language, in terms of wreath recursions.Comment: 40 pages, lots of figure

Delay of Disorder by Diluted Polymers

We study the effect of diluted flexible polymers on a disordered capillary wave state. The waves are generated at an interface of a dyed water sugar solution and a low viscous silicon oil. This allows for a quantitative measurement of the spatio-temporal Fourier spectrum. The primary pattern after the first bifurcation from the flat interface are squares. With increasing driving strength we observe a melting of the square pattern. It is replaced by a weak turbulent cascade. The addition of a small amount of polymers to the water layer does not affect the critical acceleration but shifts the disorder transition to higher driving strenghs and the short wave length - high frequency fluctuations are suppressed

Fields Medals and Nevanlinna Prize Presented at ICM-94 in Zurich

The Notices solicited the following five articles describing the work of the Fields Medalists and Nevanlinna Prize winner

Surface oscillations in channeled snow flows

An experimental device has been built to measure velocity profiles and friction laws in channeled snow flows. The measurements show that the velocity depends linearly on the vertical position in the flow and that the friction coefficient is a first-order polynomial in velocity (u) and thickness (h) of the flow. In all flows, oscillations on the surface of the flow were observed throughout the channel and measured at the location of the probes. The experimental results are confronted with a shallow water approach. Using a Saint-Venant modeling, we show that the flow is effectively uniform in the streamwise direction at the measurement location. We show that the surface oscillations produced by the Archimedes's screw at the top of the channel persist throughout the whole length of the channel and are the source of the measured oscillations. This last result provides good validation of the description of such channeled snow flows by a Saint-Venant modeling

Pemodelan Dimensi Fraktal Multiskala untuk Mengenali Bentuk Daun

Penelitian ini membangun model untuk membedakan bentuk daun menggunakan dimensi fraktal multiskala. Identifikasi tumbuhan obat sangat penting mengingat keanekaragaman hayati di Indonesia dan peran pentingnya di Indonesia. Identifikasi tanaman dapat dilakukan menggunakan analisis bentuk dengan daun sebagai cirinya. Dimensi fraktal multiskala adalah salah satu metode analisis bentuk yang menganalisis bentuk melalui kompleksitasnya. Empat tipe bentuk daun dari spesies berbeda dimodelkan dalam penelitian ini. Analisis multiskala mampu memberikan informasi tambahan mengenai alur Perubahan luas bidang dilasi, namun tidak mencirikan bentuk daun yang diuji dalam penelitian ini

Complex bounds for multimodal maps: bounded combinatorics

We proved the so called complex bounds for multimodal, infinitely renormalizable analytic maps with bounded combinatorics: deep renormalizations have polynomial-like extensions with definite modulus. The complex bounds is the first step to extend the renormalization theory of unimodal maps to multimodal maps.Comment: 20 pages, 3 figure

Double exponential stability of quasi-periodic motion in Hamiltonian systems

We prove that generically, both in a topological and measure-theoretical sense, an invariant Lagrangian Diophantine torus of a Hamiltonian system is doubly exponentially stable in the sense that nearby solutions remain close to the torus for an interval of time which is doubly exponentially large with respect to the inverse of the distance to the torus. We also prove that for an arbitrary small perturbation of a generic integrable Hamiltonian system, there is a set of almost full positive Lebesgue measure of KAM tori which are doubly exponentially stable. Our results hold true for real-analytic but more generally for Gevrey smooth systems