Variational methods for finding periodic orbits in the incompressible Navier–Stokes equations

Unstable periodic orbits are believed to underpin the dynamics of turbulence, but by their nature are hard to find computationally. We present a family of methods to converge such unstable periodic orbits for the incompressible Navier–Stokes equations, based on variations of an integral objective functional, and using traditional gradient-based optimisation strategies. Different approaches for handling the incompressibility condition are considered. The variational methods are applied to the specific case of periodic, two-dimensional Kolmogorov flow and compared against existing Newton iteration-based shooting methods. While computationally slow, our methods converge from very inaccurate initial guesses.<br/

Variational methods for finding periodic orbits in the incompressible Navier–Stokes equations

Unstable periodic orbits are believed to underpin the dynamics of turbulence, but by their nature are hard to find computationally. We present a family of methods to converge such unstable periodic orbits for the incompressible Navier–Stokes equations, based on variations of an integral objective functional, and using traditional gradient-based optimisation strategies. Different approaches for handling the incompressibility condition are considered. The variational methods are applied to the specific case of periodic, two-dimensional Kolmogorov flow and compared against existing Newton iteration-based shooting methods. While computationally slow, our methods converge from very inaccurate initial guesses.<br/

How does flow in a pipe become turbulent?

The transition to turbulence in pipe flow does not follow the scenario familiar from Rayleigh-Benard or Taylor-Couette flow since the laminar profile is stable against infinitesimal perturbations for all Reynolds numbers. Moreover, even when the flow speed is high enough and the perturbation sufficiently strong such that turbulent flow is established, it can return to the laminar state without any indication of the imminent decay. In this parameter range, the lifetimes of perturbations show a sensitive dependence on initial conditions and an exponential distribution. The turbulence seems to be supported by three-dimensional travelling waves which appear transiently in the flow field. The boundary between laminar and turbulent dynamics is formed by the stable manifold of an invariant chaotic state. We will also discuss the relation between observations in short, periodically continued domains, and the dynamics in fully extended puffs.Comment: for the proceedings of statphys 2

Hosts of Type II Quasars: an HST Study

Type II quasars are luminous Active Galactic Nuclei whose centers are obscured by large amounts of gas and dust. In this contribution we present 3-band HST images of nine type II quasars with redshifts 0.25<z<0.4 selected from the Sloan Digital Sky Survey based on their emission line properties. The intrinsic luminosities of these quasars are thought to be in the range -24>M_B>-26, but optical obscuration implies that host galaxies can be studied unencumbered by bright nuclei. Each object has been imaged in three filters (`red', `green' and `blue') placed between the strong emission lines. The spectacular, high quality images reveal a wealth of details about the structure of the host galaxies and their environments. Most galaxies in the sample are ellipticals, but strong deviations from de Vaucouleurs profiles are found, especially in the blue band. We argue that most of these deviations are due to the light from the nucleus scattered off interstellar material in the host galaxy. This scattered component can make a significant contribution to the broad-band flux and complicates the analysis of the colors of the stellar populations in the host galaxy. This extended component can be difficult to notice in unobscured luminous quasars and may bias the results of host galaxy studies.Comment: 6 pages including 2 color figures; proceedings of the 'QSO host galaxies: evolution and environment' conference, Leiden, August 200

Time-Varying Dark Energy Constraints From the Latest SN Ia, BAO and SGL

Based on the latest SNe Ia data provided by Hicken et al. (2009) with using MLCS17 light curve fitter, together with the Baryon Acoustic Oscillation(BAO) and strong gravitational lenses(SGL), we investigate the constraints on the dark energy equation-of-state parameter $w$ in the flat universe, especially for the time-varying case $w(z)=w_0+w_zz/(1+z)$. The constraints from SNe data alone are found to be: (a) $(\Omega_M, w)=(0.358, -1.09)$ as the best-fit results; (b) $(w_0, w_z)=(-0.73^{+0.23}_{-0.97}, 0.84^{+1.66}_{-10.34})$ for the two parameters in the time-varying case after marginalizing the parameter $\Omega_M$; (c) the likelihood of parameter $w_z$ has a high non-Gaussian distribution; (d) an extra restriction on $\Omega_M$ is necessary to improve the constraint of the SNe Ia data on the parameters ($w_0$, $w_z$). A joint analysis of SNe Ia data and BAO is made to break the degeneracy between $w$ and $\Omega_M$, and leads to the interesting maximum likelihoods $w_0 = -0.94$ and $w_z = 0$. When marginalizing the parameter $\Omega_M$, the fitting results are found to be $(w_0, w_z)=(-0.95^{+0.45}_{-0.18}, 0.41^{+0.79}_{-0.96})$. After adding the splitting angle statistic of SGL data, a consistent constraint is obtained $(\Omega_M, w)=(0.298, -0.907)$ and the constraints on time-varying dark energy are further improved to be $(w_0, w_z) = (-0.92^{+0.14}_{-0.10}, 0.35^{+0.47}_{-0.54})$, which indicates that the phantom type models are disfavored.Comment: 24 pages, 9 figures, to be published in JCA

A U-HPLC-ESI-MS/MS-based stable isotope dilution method for the detection and quantitation of methotrexate in plasma

INTRODUCTION: High-dose methotrexate (MTX) is used in the treatment of proliferative diseases such as acute lymphoblastic leukemia. Therapeutic drug monitoring of plasma MTX is important to monitor efficacy and adverse events. The authors aimed to develop a liquid chromatography, electrospray ionization, tandem mass spectrometry (LC-ESI-MS/MS)-based method to determine MTX in plasma for therapeutic drug monitoring and pharmacokinetic studies. METHODS: Samples were analyzed using a Waters Acquity UPLC and Quattro Premier XE. A Waters Acquity UPLC BEH C18 column (2.1 mm x 100 mm, 1.7 μm) was used running an isocratic mobile phase of 21% methanol and 10 mM ammonium bicarbonate. The electrospray was operated in the positive ionization mode monitoring the following mass transitions: m/z 455.2 > 308.2 for MTX and m/z 458.2 > 311.2 for MTXd3. The analysis combined straightforward sample preparation, consisting of dilution and protein precipitation, with a 3-minute run time. RESULTS: The method was linear up to 50 μM (r > 0.99), and the coefficient of variation was 1:10, was 5 nM. Method comparison with the Abbott TDx fluorescent polarization immunoassay (FPIA) showed excellent agreement, and a small but significant negative constant bias was detected (LC-MS/MS = 0.98 x FPIA - 7.3). CONLUSIONS: The authors developed a specific and sensitive stable isotope dilution LC-ESI-MS/MS method to monitor MTX concentrations in plasma within the clinically relevant range. The method can be easily applied in clinical laboratories because it combines straightforward sample pretreatment with LC-MS/MS. Copyrigh

Melting and Dimensionality of the Vortex Lattice in Underdoped YBa2Cu3O6.60

Muon spin rotation measurements of the magnetic field distribution in the vortex state of the oxygen deficient high-Tc superconductor YBa{2}Cu{3}O{6.60} reveal a vortex-lattice melting transition at much lower temperature than that in the fully oxygenated material. The transition is best described by a model in which adjacent layers of ``pancake'' vortices decouple in the liquid phase. Evidence is also found for a pinning-induced crossover from a solid 3D to quasi-2D vortex lattice, similar to that observed in the highly anisotropic superconductor Bi{2+x}Sr{2-x}CaCu{2}O{8+y}.Comment: 8 pages, 4 figures, 5 postscript file

Investigating the topology of interacting networks - Theory and application to coupled climate subnetworks

Network theory provides various tools for investigating the structural or functional topology of many complex systems found in nature, technology and society. Nevertheless, it has recently been realised that a considerable number of systems of interest should be treated, more appropriately, as interacting networks or networks of networks. Here we introduce a novel graph-theoretical framework for studying the interaction structure between subnetworks embedded within a complex network of networks. This framework allows us to quantify the structural role of single vertices or whole subnetworks with respect to the interaction of a pair of subnetworks on local, mesoscopic and global topological scales. Climate networks have recently been shown to be a powerful tool for the analysis of climatological data. Applying the general framework for studying interacting networks, we introduce coupled climate subnetworks to represent and investigate the topology of statistical relationships between the fields of distinct climatological variables. Using coupled climate subnetworks to investigate the terrestrial atmosphere's three-dimensional geopotential height field uncovers known as well as interesting novel features of the atmosphere's vertical stratification and general circulation. Specifically, the new measure "cross-betweenness" identifies regions which are particularly important for mediating vertical wind field interactions. The promising results obtained by following the coupled climate subnetwork approach present a first step towards an improved understanding of the Earth system and its complex interacting components from a network perspective

Comparison of some Reduced Representation Approximations

In the field of numerical approximation, specialists considering highly complex problems have recently proposed various ways to simplify their underlying problems. In this field, depending on the problem they were tackling and the community that are at work, different approaches have been developed with some success and have even gained some maturity, the applications can now be applied to information analysis or for numerical simulation of PDE's. At this point, a crossed analysis and effort for understanding the similarities and the differences between these approaches that found their starting points in different backgrounds is of interest. It is the purpose of this paper to contribute to this effort by comparing some constructive reduced representations of complex functions. We present here in full details the Adaptive Cross Approximation (ACA) and the Empirical Interpolation Method (EIM) together with other approaches that enter in the same category