Expansive homeomorphisms of the plane

This article tackles the problem of the classification of expansive homeomorphisms of the plane. Necessary and sufficient conditions for a homeomorphism to be conjugate to a linear hyperbolic automorphism will be presented. The techniques involve topological and metric aspects of the plane. The use of a Lyapunov metric function which defines the same topology as the one induced by the usual metric but that, in general, is not equivalent to it is an example of such techniques. The discovery of a hypothesis about the behavior of Lyapunov functions at infinity allows us to generalize some results that are valid in the compact context. Additional local properties allow us to obtain another classification theorem.Comment: 29 pages, 22 figure

Stretching of polymers in a random three-dimensional flow

Behavior of a dilute polymer solution in a random three-dimensional flow with an average shear is studied experimentally. Polymer contribution to the shear stress is found to be more than two orders of magnitude higher than in a laminar shear flow. The results indicate that the polymer molecules get strongly stretched by the random motion of the fluid.Comment: 4 pages, 3 figure

Elastic turbulence in curvilinear flows of polymer solutions

Following our first report (A. Groisman and V. Steinberg, \sl Nature $\bf 405$, 53 (2000)) we present an extended account of experimental observations of elasticity induced turbulence in three different systems: a swirling flow between two plates, a Couette-Taylor (CT) flow between two cylinders, and a flow in a curvilinear channel (Dean flow). All three set-ups had high ratio of width of the region available for flow to radius of curvature of the streamlines. The experiments were carried out with dilute solutions of high molecular weight polyacrylamide in concentrated sugar syrups. High polymer relaxation time and solution viscosity ensured prevalence of non-linear elastic effects over inertial non-linearity, and development of purely elastic instabilities at low Reynolds number (Re) in all three flows. Above the elastic instability threshold, flows in all three systems exhibit features of developed turbulence. Those include: (i)randomly fluctuating fluid motion excited in a broad range of spatial and temporal scales; (ii) significant increase in the rates of momentum and mass transfer (compared to those expected for a steady flow with a smooth velocity profile). Phenomenology, driving mechanisms, and parameter dependence of the elastic turbulence are compared with those of the conventional high Re hydrodynamic turbulence in Newtonian fluids.Comment: 23 pages, 26 figure

On the quantum, classical and total amount of correlations in a quantum state

We give an operational definition of the quantum, classical and total amount of correlations in a bipartite quantum state. We argue that these quantities can be defined via the amount of work (noise) that is required to erase (destroy) the correlations: for the total correlation, we have to erase completely, for the quantum correlation one has to erase until a separable state is obtained, and the classical correlation is the maximal correlation left after erasing the quantum correlations. In particular, we show that the total amount of correlations is equal to the quantum mutual information, thus providing it with a direct operational interpretation for the first time. As a byproduct, we obtain a direct, operational and elementary proof of strong subadditivity of quantum entropy.Comment: 12 pages ReVTeX4, 2 eps figures. v2 has some arguments clarified and references update

Backward Evolving Quantum States

The basic concept of the two-state vector formalism, which is the time symmetric approach to quantum mechanics, is the backward evolving quantum state. However, due to the time asymmetry of the memory's arrow of time, the possible ways to manipulate a backward evolving quantum state differ from those for a standard, forward evolving quantum state. The similarities and the differences between forward and backward evolving quantum states regarding the no-cloning theorem, nonlocal measurements, and teleportation are discussed. The results are relevant not only in the framework of the two-state vector formalism, but also in the framework of retrodictive quantum theory.Comment: Contribution to the J.Phys. A special issue in honor of GianCarlo Ghirard

Solitary coherent structures in viscoelastic shear flow: computation and mechanism

Starting from stationary bifurcations in Couette-Dean flow, we compute nontrivial stationary solutions in inertialess viscoelastic circular Couette flow. These solutions are strongly localized vortex pairs, exist at arbitrarily large wavelengths, and show hysteresis in the Weissenberg number, similar to experimentally observed ``diwhirl'' patterns. Based on the computed velocity and stress fields, we elucidate a heuristic, fully nonlinear mechanism for these flows. We propose that these localized, fully nonlinear structures comprise fundamental building blocks for complex spatiotemporal dynamics in the flow of elastic liquids.Comment: 5 pages text and 4 figures. Submitted to Physical Review Letter

Scaling properties of a low-actuation pressure microfluidic valve

Using basic physical arguments, we present a design and method for the fabrication of microfluidic valves using multilayer soft lithography. These on-off valves have extremely low actuation pressures and can be used to fabricate active functions, such as pumps and mixers in integrated microfluidic chips. We characterized the performance of the valves by measuring both the actuation pressure and flow resistance over a wide range of design parameters, and compared them to both finite element simulations and alternative valve geometries

Imprinting the memory into paste and its visualization as crack patterns in drying process

In the drying process of paste, we can imprint into the paste the order how it should be broken in the future. That is, if we vibrate the paste before it is dried, it remembers the direction of the initial external vibration, and the morphology of resultant crack patterns is determined solely by the memory of the direction. The morphological phase diagram of crack patterns and the rheological measurement of the paste show that this memory effect is induced by the plasticity of paste.Comment: 4 pages, 3 figures, submitted to JPS

Faraday waves on a viscoelastic liquid

We investigate Faraday waves on a viscoelastic liquid. Onset measurements and a nonlinear phase diagram for the selected patterns are presented. By virtue of the elasticity of the material a surface resonance synchronous to the external drive competes with the usual subharmonic Faraday instability. Close to the bicriticality the nonlinear wave interaction gives rise to a variety of novel surface states: Localised patches of hexagons, hexagonal superlattices, coexistence of hexagons and lines. Theoretical stability calculations and qualitative resonance arguments support the experimental observations.Comment: 4 pages, 4figure

Magnetic field correlations in a random flow with strong steady shear

We analyze magnetic kinematic dynamo in a conducting fluid where the stationary shear flow is accompanied by relatively weak random velocity fluctuations. The diffusionless and diffusion regimes are described. The growth rates of the magnetic field moments are related to the statistical characteristics of the flow describing divergence of the Lagrangian trajectories. The magnetic field correlation functions are examined, we establish their growth rates and scaling behavior. General assertions are illustrated by explicit solution of the model where the velocity field is short-correlated in time