Effects of non-denumerable fixed points in finite dynamical systems

The motion of a spinning football brings forth the possible existence of a whole class of finite dynamical systems where there may be non-denumerably infinite number of fixed points. They defy the very traditional meaning of the fixed point that a point on the fixed point in the phase space should remain there forever, for, a fixed point can evolve as well! Under such considerations one can argue that a free-kicked football should be non-chaotic.Comment: This paper is a replaced version to modify the not-so-true claim, made unknowingly in the earlier version, of being first to propose the peculiar dynamical systems as described in the paper. With respect to the original workers, we present here our original finding

Numerical simulations of compressible Rayleigh-Taylor turbulence in stratified fluids

We present results from numerical simulations of Rayleigh-Taylor turbulence, performed using a recently proposed lattice Boltzmann method able to describe consistently a thermal compressible flow subject to an external forcing. The method allowed us to study the system both in the nearly-Boussinesq and strongly compressible regimes. Moreover, we show that when the stratification is important, the presence of the adiabatic gradient causes the arrest of the mixing process.Comment: 15 pages, 11 figures. Proceedings of II Conference on Turbulent Mixing and Beyond (TMB-2009

On visualizing continuous turbulence scales

Turbulent flows are multi‐scale with vortices spanning a wide range of scales continuously. Due to such complexities, turbulence scales are particularly difficult to analyse and visualize. In this work, we present a novel and efficient optimization‐based method for continuous‐scale turbulence structure visualization with scale decomposition directly in the Kolmogorov energy spectrum. To achieve this, we first derive a new analytical objective function based on integration approximation. Using this new formulation, we can significantly improve the efficiency of the underlying optimization process and obtain the desired filter in the Kolmogorov energy spectrum for scale decomposition. More importantly, such a decomposition allows a ‘continuous‐scale visualization’ that enables us to efficiently explore the decomposed turbulence scales and further analyse the turbulence structures in a continuous manner. With our approach, we can present scale visualizations of direct numerical simulation data sets continuously over the scale domain for both isotropic and boundary layer turbulent flows. Compared with previous works on multi‐scale turbulence analysis and visualization, our method is highly flexible and efficient in generating scale decomposition and visualization results. The application of the proposed technique to both isotropic and boundary layer turbulence data sets verifies the capability of our technique to produce desirable scale visualization results

Starcounts Redivivus. IV. Density Laws Through Photometric Parallaxes

In an effort to more precisely define the spatial distribution of Galactic field stars, we present an analysis of the photometric parallaxes of 70,000 stars covering nearly 15 square degrees in seven Kapteyn Selected Areas. We address the affects of Malmquist Bias, subgiant/giant contamination, metallicity and binary stars upon the derived density laws. The affect of binary stars is the most significant. We find that while the disk-like populations of the Milky Way are easily constrained in a simultaneous analysis of all seven fields, no good simultaneous solution for the halo is found. We have applied halo density laws taken from other studies and find that the Besancon flattened power law halo model (c/a=0.6, r^-2.75) produces the best fit to our data. With this halo, the thick disk has a scale height of 750 pc with an 8.5% normalization to the old disk. The old disk scale height is 280-300 pc. Corrected for a binary fraction of 50%, these scale heights are 940 pc and 350-375 pc, respectively. Even with this model, there are systematic discrepancies between the observed and predicted density distributions. Our model produces density overpredictions in the inner Galaxy and density underpredictions in the outer Galaxy. A possible solution is modeling the stellar halo as a two-component system in which the halo has a flattened inner distribution and a roughly spherical, but substructured outer distribution. Further reconciliation could be provided by a flared thick disk, a structure consistent with a merger origin for that population. (Abridged)Comment: 66 pages, accepted to Astrophysical journal, some figures compresse

Dynamics and Excitation of Radio Galaxy Emission-Line Regions - I. PKS 2356-61

Results are presented from a programme of detailed longslit spectroscopic observations of the extended emission-line region (EELR) associated with the powerful radio galaxy PKS 2356-61. The observations have been used to construct spectroscopic datacubes, which yield detailed information on the spatial variations of emission-line ratios across the EELR, together with its kinematic structure. We present an extensive comparison between the data and results obtained from the MAPPINGS II shock ionization code, and show that the physical properties of the line-emitting gas, including its ionization, excitation, dynamics and overall energy budget, are entirely consistent with a scenario involving auto-ionizing shocks as the dominant ionization mechanism. This has the advantage of accounting for the observed EELR properties by means of a single physical process, thereby requiring less free parameters than the alternative scheme involving photoionization by radiation from the active nucleus. Finally, possible mechanisms of shock formation are considered in the context of the dynamics and origin of the gas, specifically scenarios involving infall or accretion of gas during an interaction between the host radio galaxy and a companion galaxy.Comment: 35 pages, LaTeX, uses aas2pp4.sty file, includes 9 PostScript figures. Two additional colour plates are available from the authors upon request. Accepted for publication in the Astrophysical Journa

The USNO-B Catalog

USNO-B is an all-sky catalog that presents positions, proper motions, magnitudes in various optical passbands, and star/galaxy estimators for 1,042,618,261 objects derived from 3,643,201,733 separate observations. The data were obtained from scans of 7,435 Schmidt plates taken for the various sky surveys during the last 50 years. USNO-B1.0 is believed to provide all-sky coverage, completeness down to V = 21, 0.2 arcsecond astrometric accuracy at J2000, 0.3 magnitude photometric accuracy in up to five colors, and 85% accuracy for distinguishing stars from non-stellar objects. A brief discussion of various issues is given here, but the actual data are available from http://www.nofs.navy.mil and other sites.Comment: Accepted by Astronomical Journa

Blood flow and coherent vortices in the normal and aneurysmatic aortas: a fluid dynamical approach to intra-luminal thrombus formation

Abdominal aortic aneurysms (AAAs) are frequently characterized by the development of an intra-luminal thrombus (ILT), which is known to have multiple biochemical and biomechanical implications. Development of the ILT is not well understood, and shear–stress-triggered activation of platelets could be the first step in its evolution. Vortical structures (VSs) in the flow affect platelet dynamics, which motivated the present study of a possible correlation between VS and ILT formation in AAAs. VSs educed by the λ2-method using computational fluid dynamics simulations of the backward-facing step problem, normal aorta, fusiform AAA and saccular AAA were investigated. Patient-specific luminal geometries were reconstructed from computed tomography scans, and Newtonian and Carreau–Yasuda models were used to capture salient rheological features of blood flow. Particularly in complex flow domains, results depended on the constitutive model. VSs developed all along the normal aorta, showing that a clear correlation between VSs and high wall shear stress (WSS) existed, and that VSs started to break up during late systole. In contrast, in the fusiform AAA, large VSs developed at sites of tortuous geometry and high WSS, occupying the entire lumen, and lasting over the entire cardiac cycle. Downward motion of VSs in the AAA was in the range of a few centimetres per cardiac cycle, and with a VS burst at that location, the release (from VSs) of shear-stress-activated platelets and their deposition to the wall was within the lower part of the diseased artery, i.e. where the thickest ILT layer is typically observed. In the saccular AAA, only one VS was found near the healthy portion of the aorta, while in the aneurysmatic bulge, no VSs occurred. We present a fluid-dynamics-motivated mechanism for platelet activation, convection and deposition in AAAs that has the potential of improving our current understanding of the pathophysiology of fluid-driven ILT growth

Wave Energy

Part of the immense solar energy input to the earth is converted by natural processes into energy associated with ocean waves. The geographical location of the United Kingdom renders it one of the world ' s most favoured countries with respect to the potential availability of wave energy. In principle. the waves reaching our coastal waters from the North Atlantic might satisfy a considerable fraction of our electricity demand provided that reasonably high overall conversion efficiencies can be achieved . Inventors have recognised the power of the sea for many decades. and there has been no lack of ideas on how it might be tapped . But none of the ideas was developed on a substantial scale. since ample and relatively cheap supplies of other resources were always available . In recent years. however. there has been a growing recognition that--on a world scale-the presently used forms of energy may become too expensive,. too scarce or otherwise unavailable to meet our energy needs by themselves . The Government's responsibility is to ensure that as wide a range as possible of energy supply options are available when they may be needed . Research and development can provide the necessary technical and econom i c data on which the ultimate choices can be made . Within this context. the Government announced in 197 6 the start of an R and D programme on wave energy for which the first phase was to be a feasibility study lasting for two years. The funding level has been increased twice since that time to maintain the momentum of the programme in the light of technical progress . The programme has had three main components: -exploratory deve lopment of several different engineering concepts of wave energy converter; -supporting research in relevant engineering and scientific areas : • the collection and analysis of wave data. • analysis of the structural response to wave-induced motions. • mooring. • energy conversion and transm issi on. • environmental aspects ; -working up preliminary reference designs of full scale stations for tech nical and economic appraisal. The purpose of this paper is to review the present state of knowledge of wave energy in the light of the achievements of the first two-year phase of the programme . Development of the converters Four potential designs of converter were adopted for initial study. since the sparse data available were insufficient to enable a single concept to be chosen with confidence. Proposals for alternative concepts are received on a continuing basis and are assessed against a number of criteria: two of them have so far been added to the programme in order to explore new principles Apart from the basic technical differences the six designs differ from each other in their degree of complexity and their state of development. as described in Chapter 3 . Work on two of the designs has been advanced from laboratory wave tanks to the testing of 1 / 1 0th scale models in natural open water at Loch Ness and in the Solent. For all the designs . a combination of theoretical studies. laboratory work and engineering appraisal has clarified the factors which will prove to be the most crucial in determining which of them could be chosen for more extensive development. The programme has progressed from establishing the scientific feasibility of wave energy converters to confirming the engineering feasibility of designing and building some of the designs . In very broad terms: -the early part of the programme placed considerable emphasis on optimising the efficiency of extraction of the wave energy and proving the scientific feasibility ; -the present stage is concerned with the technical viability and is identifying the main cost centres in the designs . which can then be tackled by further R and D; -the immediate future must also place emphasis not only on the problems of construction . operation and maintenance. and on ways in which unit costs may be reduced . but also on the ability to survive in the most severe wave conditions . Whilst the technical feasibility of some types of converter has been established, we are far from the stage of recommending that a full scale generating station should be built . Of the four original concepts. no single design has yet emerged which is outstandingly better than the other designs when all factors are taken into account . The designs have changed considerably in the course of the feasibility study. and a continuing process of evol ution can be expected as in the early stages of any technical development programme. The optimum design may emerge from further changes in one of the original concepts. from a synthesis of ideas or from an alternative concept . The wave energy is distributed over a wide frequency and energy bandwidth and no des ign has yet been optimised to operate at or near peak efficiency over the whole spectrum. However, one of the new concepts introduced into the programme recently may offer significant advantages in this respect. Supporting research The extent of the available data on waves in the sea areas of primary interest is inadequate as yet for the full assessment of the resource . A start has been made in collecting and analysing new data. which will take several years to reach a satisfactory level. The results so far confirm the general point that the locations around the United Kingdom with the most abundant wave energy lie to the west of the Outer Hebrides, where several hundred km of searoom are available with average annual power levels in the range 35-60 kW / m of wavefront. The majority of the designs un der consideration are free-floating and the converters would operate on or near the water surface-- one of the most hostile environments for engineering structures . The ult imate feasibility. technical and economic . of all designs of floating converter will depend upon extensive further work on mooring and anchoring . Whilst over-designed mooring systems based on present knowledge have allowed the open water trials to proceed with the objective of gaining experience . the existing knowledge is not adequate to design cost-effective mooring systems which will ensure survival at full scale under storm conditions . Considerable progress has been made in assessing and under3tanding suitable energy conversion and transmission systems for the various designs of converter , but much more remains to be done to arrive at the most cost-effective solutions . The general engineering difficulties are quite basic and are related to the properties of the natural wave spectrum : -the conversion system must be able to handle large short-term variations in the instantaneous power level ; -the peak power level in the sea (of the order of 10,OOO kW /m) can be many times greater than the average power level (a few tens of kW / m) ; -the primary output is not in a form which can be handled conventionally (it is . of course . variable with time in a complex way). Moreover. apart from the randomness. other general problems arise from the low energy density of the input and the relatively low speeds and frequency of movement induced by the waves . Engineering devices to transmit large amounts of energy under such conditions must themselves be large. heavy and expensive . The efficient generation of electricity requires machinery operating at relatively high and preferably constant speed . The transition from the one regime to the other appears to be more straightforward for systems involving air turbines than for those which do not: some designs of converter may prove to be intractable in this respect. Many possible forms of energy transmission to the mainland have been reviewed . as summarised in Chapter 6 . Whilst it has been recommended that several options should be kept open in the continuing studies it is likely that most attention will be given to electricity. The overall flow of energy from the waves to a final user connected to the electricity grid involves many separate steps . each of which can involve loss of some of the energy . This can have a considerable influence on the system economics and further work in this area will need to concentrate on both reducing the number of steps and increasing the efficiency (including the directional efficiency of t he converters themselves ) of those which must remain . Unless this can be achieved the usable resource will be only a small proportion of our needs : some pointers to substantial improvements are beginning to emerge. Environmental studies have not revealed any major detrimental effects of the converters provided they are well offshore. More information is needed on the behaviour of salmon and herring off the Outer Hebrides to confirm that the fisheries would not be affected significantly by the widespread installation of converters. Concluding remarks: The costing studies of the reference designs which have been evolved so far indicate that wave-produced electricity is likely to be expensive compared with either nuclear or fossil fuels unless some major breakthrough in the engineering can be achieved . However . this does not imply that the possibility of wave energy should be abandoned at this stage . It must be emphasised that the subject is still at a very ear ly state of development and many unknown factors remain to be resolved . Under these circumstances, wave energy is best regarded at present as a possible insurance technology- the consequences of failure of one of our existing major energy supplies are so severe that it is worth paying an insurance premium to explore fully the alternatives . Nevertheless. the evidence from the feasibility study so far does not allow a recommendation for a full-scale development programme to be made at this time . Much more can be achieved to explore and then to narrow the design choices by continuing work at about the 1 / 1 0th scale coupled with . on the one hand . limited trials of some critical components at larger scale and . on the other hand . f urther creative engineering on the drawing board and laboratory work in a new generation of wave tanks (of which the forerunner has been successfully commissioned at Edinburgh University). The programme has generated a broad basis of knowledge of all aspects of wave energy which did not exist before. so that we can now identify clearly the critical problems to be tackled by further work

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

The SuperCOSMOS all-sky galaxy catalogue

We describe the construction of an all-sky galaxy catalogue, using SuperCOSMOS scans of Schmidt photographic plates from the UKST and POSS2 surveys. The photographic photometry is calibrated using SDSS data, with results that are linear to 2% or better. All-sky photometric uniformity is achieved by matching plate overlaps and also by requiring homogeneity in optical-to-2MASS colours, yielding zero points that are uniform to 0.03 mag. or better. The typical AB depths achieved are B_J<21, R_F<19.5 and I_N<18.5, with little difference between hemispheres. In practice, the I_N plates are shallower than the B_J & R_F plates, so for most purposes we advocate the use of a catalogue selected in these two latter bands. At high Galactic latitudes, this catalogue is approximately 90% complete with 5% stellar contamination; we quantify how the quality degrades towards the Galactic plane. At low latitudes, there are many spurious galaxy candidates resulting from stellar blends: these approximately match the surface density of true galaxies at |b|=30 deg. Above this latitude, the catalogue limited in B_J & R_F contains in total about 20 million galaxy candidates, of which 75% are real. This contamination can be removed, and the sky coverage extended, by matching with additional datasets. This SuperCOSMOS catalogue has been matched with 2MASS and with WISE, yielding quasi-allsky samples of respectively 1.5 million and 18.5 million galaxies, to median redshifts of 0.08 and 0.20. This legacy dataset thus continues to offer a valuable resource for large-angle cosmological investigations.Comment: Submitted to MNRAS. Data available at http://ssa.roe.ac.uk/allSk