Passive Scalars and Three-Dimensional Liouvillian Maps

Global aspects of the motion of passive scalars in time-dependent incompressible fluid flows are well described by volume-preserving (Liouvillian) three-dimensional maps. In this paper the possible invariant structures in Liouvillian maps and the two most interesting nearly-integrable cases are investigated. In addition, the fundamental role of invariant lines in organizing the dynamics of this type of system is exposed. Bifurcations involving the destruction of some invariant lines and tubes and the creation of new ones are described in detail.Comment: 18 pages, plain TeX, appears in Physica D, 76, 22-33, 1994. (Lack of figures in original submission corrected in this new upload.

Global Diffusion in a Realistic Three-Dimensional Time-Dependent Nonturbulent Fluid Flow

We introduce and study the first model of an experimentally realizable three-dimensional time-dependent nonturbulent fluid flow to display the phenomenon of global diffusion of passive-scalar particles at arbitrarily small values of the nonintegrable perturbation. This type of chaotic advection, termed {\it resonance-induced diffusion\/}, is generic for a large class of flows.Comment: 4 pages, uuencoded compressed postscript file, to appear in Phys. Rev. Lett. Also available on the WWW from http://formentor.uib.es/~julyan/, or on paper by reques

Localization in Strongly Chaotic Systems

We show that, in the semiclassical limit and whenever the elements of the Hamiltonian matrix are random enough, the eigenvectors of strongly chaotic time-independent systems in ordered bases can on average be exponentially localized across the energy shell and decay faster than exponentially outside the energy shell. Typically however, matrix elements are strongly correlated leading to deviations from such behavior.Comment: RevTeX, 5 pages + 3 postscript figures, submitted to Phys. Rev. Let

Band Distributions for Quantum Chaos on the Torus

Band distributions (BDs) are introduced describing quantization in a toral phase space. A BD is the uniform average of an eigenstate phase-space probability distribution over a band of toral boundary conditions. A general explicit expression for the Wigner BD is obtained. It is shown that the Wigner functions for {\em all} of the band eigenstates can be reproduced from the Wigner BD. Also, BDs are shown to be closer to classical distributions than eigenstate distributions. Generalized BDs, associated with sets of adjacent bands, are used to extend in a natural way the Chern-index characterization of the classical-quantum correspondence on the torus to arbitrary rational values of the scaled Planck constant.Comment: 12 REVTEX page

Transport of Passive scalars: Kam Surfaces and Diffusion in Three-Dimensional Liouvillian Maps

The global aspects of the motion of passive scalars in time-dependent incompressible fluid flows are well described by volume-preserving (Liouvillian) three-dimensional maps. In this paper the possible invariant structures Liouvillian maps and the two most interesting nearly integrable cases are investigated in detail.Facultad de Ciencias Exacta

On the universality class dependence of period doubling indices

The dependence on ν of the period doubling scaling indices for unimodal maps with a critical point of the form |x|ν is numerically investigated. A new symbolic dynamics based computation technique working in configuration space is introduced. The existence of an upper bound for δ(ν→∞) is numerically verified. An accurate estimate of 29.8 is given for this limit. Moreover, the global functional form of δ(ν) is shown to have an interesting symmetry.Facultad de Ciencias Exacta

Treadmilling analysis reveals new insights into dynamic FtsZ ring architecture

FtsZ, the primary protein of the bacterial Z ring guiding cell division, has been recently shown to engage in intriguing treadmilling dynamics along the circumference of the division plane. When coreconstituted in vitro with FtsA, one of its natural membrane anchors, on flat supported membranes, these proteins assemble into dynamic chiral vortices compatible with treadmilling of curved polar filaments. Replacing FtsA by a membrane-targeting sequence (mts) to FtsZ, we have discovered conditions for the formation of dynamic rings, showing that the phenomenon is intrinsic to FtsZ. Ring formation is only observed for a narrow range of protein concentrations at the bilayer, which is highly modulated by free Mg2+ and depends upon guanosine triphosphate (GTP) hydrolysis. Interestingly, the direction of rotation can be reversed by switching the mts from the C-terminus to the N-terminus of the protein, implying that the filament attachment must have a perpendicular component to both curvature and polarity. Remarkably, this chirality switch concurs with previously shown inward or outward membrane deformations by the respective FtsZ mutants. Our results lead us to suggest an intrinsic helicity of FtsZ filaments with more than one direction of curvature, supporting earlier hypotheses and experimental evidence