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

Observations of NGC 4151 During 1970 in the Optical and Infra-red

Observations of NGC 4151 at seven wavelengths from 0.3 to 3.4 microns made during the 1970 season are presented. Variations are found at all observed wavelengths but the optical and infra-red light curves are different: an optical maximum was reached in April but the galaxy continued brightening at 2.2 μ . until the end of June. The energy distributions of the point source and the background galaxy have been separated and that of the point source Closely resembles that of the quasar 3C273. The general form of the light curves can possibly be attributed to a dust model for the infra-red emission but this would be ruled out if suspected rapid infra-red variations are confirmed

Observations of NGC 4151 During 1970 in the Optical and Infra-red

Observations of NGC 4151 at seven wavelengths from 0.3 to 3.4 microns made during the 1970 season are presented. Variations are found at all observed wavelengths but the optical and infra-red light curves are different: an optical maximum was reached in April but the galaxy continued brightening at 2.2 μ . until the end of June. The energy distributions of the point source and the background galaxy have been separated and that of the point source Closely resembles that of the quasar 3C273. The general form of the light curves can possibly be attributed to a dust model for the infra-red emission but this would be ruled out if suspected rapid infra-red variations are confirmed

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

Convective and Conductive Selection Criteria of a Stable Dendritic Growth and Their Stitching

The paper deals with the analysis of stable thermo-solutal dendritic growth in the presence of intense convection. The n-fold symmetry of crystalline anisotropy as well as the two- and three-dimensional growth geometries are considered. The steady-state analytical solutions are found with allowance for the convective-type heat and mass exchange boundary conditions at the dendritic surface. A linear morphological stability analysis determining the marginal wavenumber is carried out. The new stability criterion is derived from the solvability theory and stability analysis. This selection criterion takes place in the regions of small undercooling. To describe a broader undercooling diapason, the obtained selection criterion, which describes the case of intense convection, is stitched together with the previously known selection criterion for the conductive-type boundary conditions. It is demonstrated that the stitched selection criterion well describes a broad diapason of experimental undercoolings. © 2020 John Wiley & Sons, Ltd.The present work comprises different parts of research studies including (i) the model formulation, stability and solvability analyses, derivation of the selection criterion in the case of intense convection, its sewing with the criterion for the conductive boundary conditions, (ii) numerical simulations, (iii) experiments, and their comparison. Different parts of the present work were supported by different grants and programs. With this in mind, the authors are grateful to the following foundations, programs, and grants. Theoretical part (i) was supported by the Russian Foundation for Basic Research (grant no. 19-32-51009). Numerical part (ii) was made possible due to the financial support of the Ministry of Science and Higher Education of the Russian Federation (Ural Mathematical Center, project no. 075-02-2020-1537/1). The experimental part (iii) was supported by the German Space Center Space Management under contract number 50WM1941

Simple Viscous Flows: from Boundary Layers to the Renormalization Group

The seemingly simple problem of determining the drag on a body moving through a very viscous fluid has, for over 150 years, been a source of theoretical confusion, mathematical paradoxes, and experimental artifacts, primarily arising from the complex boundary layer structure of the flow near the body and at infinity. We review the extensive experimental and theoretical literature on this problem, with special emphasis on the logical relationship between different approaches. The survey begins with the developments of matched asymptotic expansions, and concludes with a discussion of perturbative renormalization group techniques, adapted from quantum field theory to differential equations. The renormalization group calculations lead to a new prediction for the drag coefficient, one which can both reproduce and surpass the results of matched asymptotics

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

Gas dynamics in high-luminosity polarized He-3 targets using diffusion and convection

The dynamics of the movement of gas is discussed for two-chambered polarized He-3 target cells of the sort that have been used successfully for many electron scattering experiments. A detailed analysis is presented showing that diffusion is a limiting factor in target performance, particularly as these targets are run at increasingly high luminosities. Measurements are presented on a new prototype polarized He-3 target cell in which the movement of gas is due largely to convection instead of diffusion. NMR tagging techniques have been used to visualize the gas flow, showing velocities along a cylindrically-shaped target of between 5-80 cm/min. The new target design addresses one of the principle obstacles to running polarized He-3 targets at substantially higher luminosities while simultaneously providing new flexibility in target geometry.Comment: First revision: 14 pages, 9 figures, submitted to Phys. Rev. C. We have shortened our discussion of the limitations inherent in various historical He-3 targets, and we have added a discussion exploring the optimal performance that can be expected from a suitably modified target based on diffusion-based mixing. A reference (Jones et. al.) was added. The results we present have not change

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