Precision Measurements of Stretching and Compression in Fluid Mixing

The mixing of an impurity into a flowing fluid is an important process in many areas of science, including geophysical processes, chemical reactors, and microfluidic devices. In some cases, for example periodic flows, the concepts of nonlinear dynamics provide a deep theoretical basis for understanding mixing. Unfortunately, the building blocks of this theory, i.e. the fixed points and invariant manifolds of the associated Poincare map, have remained inaccessible to direct experimental study, thus limiting the insight that could be obtained. Using precision measurements of tracer particle trajectories in a two-dimensional fluid flow producing chaotic mixing, we directly measure the time-dependent stretching and compression fields. These quantities, previously available only numerically, attain local maxima along lines coinciding with the stable and unstable manifolds, thus revealing the dynamical structures that control mixing. Contours or level sets of a passive impurity field are found to be aligned parallel to the lines of large compression (unstable manifolds) at each instant. This connection appears to persist as the onset of turbulence is approached.Comment: 5 pages, 5 figure

Parabolic resonances and instabilities in near-integrable two degrees of freedom Hamiltonian flows

When an integrable two-degrees-of-freedom Hamiltonian system possessing a circle of parabolic fixed points is perturbed, a parabolic resonance occurs. It is proved that its occurrence is generic for one parameter families (co-dimension one phenomenon) of near-integrable, t.d.o. systems. Numerical experiments indicate that the motion near a parabolic resonance exhibits new type of chaotic behavior which includes instabilities in some directions and long trapping times in others. Moreover, in a degenerate case, near a {\it flat parabolic resonance}, large scale instabilities appear. A model arising from an atmospherical study is shown to exhibit flat parabolic resonance. This supplies a simple mechanism for the transport of particles with {\it small} (i.e. atmospherically relevant) initial velocities from the vicinity of the equator to high latitudes. A modification of the model which allows the development of atmospherical jets unfolds the degeneracy, yet traces of the flat instabilities are clearly observed

Friction Drag on a Particle Moving in a Nematic Liquid Crystal

The flow of a liquid crystal around a particle does not only depend on its shape and the viscosity coefficients but also on the direction of the molecules. We studied the resulting drag force on a sphere moving in a nematic liquid crystal (MBBA) in a low Reynold's number approach for a fixed director field (low Ericksen number regime) using the computational artificial compressibility method. Taking the necessary disclination loop around the sphere into account, the value of the drag force anisotropy (F_\perp/F_\parallel=1.50) for an exactly computed field is in good agreement with experiments (~1.5) done by conductivity diffusion measurements. We also present data for weak anchoring of the molecules on the particle surface and of trial fields, which show to be sufficiently good for most applications. Furthermore, the behaviour of the friction close to the transition point nematic isotropic and for a rod-like and a disc-like liquid crystal will be given.Comment: 23 pages RevTeX, including 3 PS figures, 1 PS table and 1 PS-LaTeX figure; Accepted for publication in Phys. Rev.

Flow and magnetic structures in a kinematic ABC-dynamo

Dynamo theory describes the magnetic field induced by the rotating, convecting and electrically conducting fluid in a celestial body. The classical ABC-flow model represents fast dynamo action, required to sustain such a magnetic field. In this letter, Lagrangian coherent structures (LCSs) in the ABC-flow are detected through Finite-time Lyapunov exponents (FTLE). The flow skeleton is identified by extracting intersections between repelling and attracting LCSs. For the case A = B = C = 1, the skeleton structures are made up from lines connecting two different types of stagnation points in the ABC-flow. The corresponding kinematic ABC-dynamo problem is solved using a spectral method, and the distribution of cigar-like magnetic structures visualized. Inherent links are found to exist between LCSs in the ABC-flow and induced magnetic structures, which provides insight into the mechanism behind the ABC-dynamo

Blocking-state influence on shot noise and conductance in quantum dots

Quantum dots (QDs) investigated through electron transport measurements often exhibit varying, state-dependent tunnel couplings to the leads. Under specific conditions, weakly coupled states can result in a strong suppression of the electrical current and they are correspondingly called blocking states. Using the combination of conductance and shot noise measurements, we investigate blocking states in carbon nanotube (CNT) QDs. We report negative differential conductance and super-Poissonian noise. The enhanced noise is the signature of electron bunching, which originates from random switches between the strongly and weakly conducting states of the QD. Negative differential conductance appears here when the blocking state is an excited state. In this case, at the threshold voltage where the blocking state becomes populated, the current is reduced. Using a master equation approach, we provide numerical simulations reproducing both the conductance and the shot noise pattern observed in our measurements.Comment: 10 pages, 7 figure

Aperiodic dynamical decoupling sequences in presence of pulse errors

Dynamical decoupling (DD) is a promising tool for preserving the quantum states of qubits. However, small imperfections in the control pulses can seriously affect the fidelity of decoupling, and qualitatively change the evolution of the controlled system at long times. Using both analytical and numerical tools, we theoretically investigate the effect of the pulse errors accumulation for two aperiodic DD sequences, the Uhrig's DD UDD) protocol [G. S. Uhrig, Phys. Rev. Lett. {\bf 98}, 100504 (2007)], and the Quadratic DD (QDD) protocol [J. R. West, B. H. Fong and D. A. Lidar, Phys. Rev. Lett {\bf 104}, 130501 (2010)]. We consider the implementation of these sequences using the electron spins of phosphorus donors in silicon, where DD sequences are applied to suppress dephasing of the donor spins. The dependence of the decoupling fidelity on different initial states of the spins is the focus of our study. We investigate in detail the initial drop in the DD fidelity, and its long-term saturation. We also demonstrate that by applying the control pulses along different directions, the performance of QDD protocols can be noticeably improved, and explain the reason of such an improvement. Our results can be useful for future implementations of the aperiodic decoupling protocols, and for better understanding of the impact of errors on quantum control of spins.Comment: updated reference

Post-traumatic stress disorder in parturients delivering by caesarean section and the implication of anaesthesia: a prospective cohort study.

Post-traumatic stress disorder (PTSD) occurs in 1-7% of women following childbirth. While having a caesarean section (C-section) is known to be a significant risk factor for postpartum PTSD, it is currently unknown whether coexisting anaesthesia-related factors are also associated to the disorder. The aim of this study was to assess anaesthesia-linked factors in the development of acute postpartum PTSD. We performed a prospective cohort study on women having a C-section in a tertiary hospital in Switzerland. Patients were followed up six weeks postpartum. Patient and procedure characteristics, past morbidity or traumatic events, psychosocial status and stressful perinatal events were measured. Outcome was divided into two categories: full PTSD disease and PTSD profile. This was based on the number of DSM-IV criteria of the Diagnostic and Statistical Manual of Mental Disorders 4th edition (DSM-IV) present. The PTSD Checklist Scale and the Clinician Administered PTSD Scale were used for measurement. Of the 280 patients included, 217 (77.5%) answered the questionnaires and 175 (62.5%) answered to an additional phone interview. Twenty (9.2%) had a PTSD profile and six (2.7%) a PTSD. When a full predictive model of risk factors for PTSD profile was built using logistic regression, maternal prepartum and intrapartum complications, anaesthetic complications and dissociative experiences during C-section were found to be the significant predictors for PTSD profile. This is the first study to show in parturients having a C-section that an anaesthesia complication is an independent risk factor for postpartum PTSD and PTSD profile development, in addition to known perinatal and maternal risk factors

Gribov Problem for Gauge Theories: a Pedagogical Introduction

The functional-integral quantization of non-Abelian gauge theories is affected by the Gribov problem at non-perturbative level: the requirement of preserving the supplementary conditions under gauge transformations leads to a non-linear differential equation, and the various solutions of such a non-linear equation represent different gauge configurations known as Gribov copies. Their occurrence (lack of global cross-sections from the point of view of differential geometry) is called Gribov ambiguity, and is here presented within the framework of a global approach to quantum field theory. We first give a simple (standard) example for the SU(2) group and spherically symmetric potentials, then we discuss this phenomenon in general relativity, and recent developments, including lattice calculations.Comment: 24 pages, Revtex 4. In the revised version, a statement has been amended on page 11, and References 14, 16 and 27 have been improve

Non-abelian plane waves and stochastic regimes for (2+1)-dimensional gauge field models with Chern-Simons term

An exact time-dependent solution of field equations for the 3-d gauge field model with a Chern-Simons (CS) topological mass is found. Limiting cases of constant solution and solution with vanishing topological mass are considered. After Lorentz boost, the found solution describes a massive nonlinear non-abelian plane wave. For the more complicate case of gauge fields with CS mass interacting with a Higgs field, the stochastic character of motion is demonstrated.Comment: LaTeX 2.09, 13 pages, 11 eps figure