Invariant Solution underlying Oblique Stripe Patterns in Plane Couette Flow

When subcritical shear flows transition to turbulence, laminar and turbulent flow often coexists in space, giving rise to turbulent-laminar patterns. Most prominent are regular stripe patterns with large-scale periodicity and oblique orientation. Oblique stripes are a robust phenomenon, observed in experiments and flow simulations, yet their origin remains unclear. We demonstrate the existence of an invariant equilibrium solution of the fully nonlinear 3D Navier-Stokes equations that resembles the oblique pattern of turbulent-laminar stripes in plane Couette flow. We uncover the origin of the stripe equilibrium and show how it emerges from the well-studied Nagata equilibrium via two successive symmetry-breaking bifurcations

MINOS Results, Progress and Future Prospects

The MINOS long baseline experiment has been collecting neutrino beam data since March 2005 and has accumulated 3 x 10^{20} protons-on-target (POT) to date. MINOS uses Fermilab's NuMI neutrino beam which is measured by two steel-scintillator tracking calorimeters, one at Fermilab and the other 735 km downstream, in northern Minnesota. By observing the oscillatory structure in the neutrino energy spectrum, MINOS can precisely measure the neutrino oscillation parameters in the atmospheric sector. From analysis of the first year of data, corresponding to 1.27 x 10^{20} POT, these parameters were determined to be |\Delta m^2_{32}|=2.74^{+0.44}_{-0.26} x 10^{-3} eV^2 and sin^2(2\theta_{23})>0.87 (68% C.L.). MINOS is able to measure the neutrino velocity by comparing the arrival times of the neutrino beam in its two detectors. Using a total of 473 Far Detector events, (v-c)/c = (5.1 +/- 2.9) x 10^{-5} (68% C.L.) was measured. In addition, we report recent progress in the analysis of neutral current events and give an outline of experimental goals for the future.Comment: 8 pages, 7 figures, prepared for the proceedings of the XLIInd Rencontres de Moriond, Electroweak Interactions and Unified Theories, La Thuile, March 200

Transition probabilities and measurement statistics of postselected ensembles

It is well-known that a quantum measurement can enhance the transition probability between two quantum states. Such a measurement operates after preparation of the initial state and before postselecting for the final state. Here we analyze this kind of scenario in detail and determine which probability distributions on a finite number of outcomes can occur for an intermediate measurement with postselection, for given values of the following two quantities: (i) the transition probability without measurement, (ii) the transition probability with measurement. This is done for both the cases of projective measurements and of generalized measurements. Among other constraints, this quantifies a trade-off between high randomness in a projective measurement and high measurement-modified transition probability. An intermediate projective measurement can enhance a transition probability such that the failure probability decreases by a factor of up to 2, but not by more.Comment: 23 pages, 5 figures, minor updat

Studying edge geometry in transiently turbulent shear flows

In linearly stable shear flows at moderate Re, turbulence spontaneously decays despite the existence of a codimension-one manifold, termed the edge of chaos, which separates decaying perturbations from those triggering turbulence. We statistically analyse the decay in plane Couette flow, quantify the breaking of self-sustaining feedback loops and demonstrate the existence of a whole continuum of possible decay paths. Drawing parallels with low-dimensional models and monitoring the location of the edge relative to decaying trajectories we provide evidence, that the edge of chaos separates state space not globally. It is instead wrapped around the turbulence generating structures and not an independent dynamical structure but part of the chaotic saddle. Thereby, decaying trajectories need not cross the edge, but circumnavigate it while unwrapping from the turbulent saddle.Comment: 11 pages, 6 figure