510 research outputs found
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
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
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
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
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