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Sample records for self-similar polytropic champagne

  1. Self-similar Champagne Flows in H II Regions

    NASA Astrophysics Data System (ADS)

    Shu, Frank H.; Lizano, Susana; Galli, Daniele; Cantó, Jorge; Laughlin, Gregory

    2002-12-01

    We consider the idealized expansion of an initially self-gravitating, static, singular, isothermal cloud core. For t>=0, the gas is ionized and heated to a higher uniform temperature by the formation of a luminous but massless star in its center. The approximation that the mass and gravity of the central star are negligible for the subsequent motion of the H II region holds for distances r much greater than ~100 AU and for the massive cloud cores that give rise to high-mass stars. If the initial ionization and heating are approximated to occur instantaneously at t=0, then the subsequent flow (for r>>100 AU) caused by the resulting imbalance between self-gravity and thermal pressure is self-similar. Because of the steep density profile (ρ~r-2), pressure gradients produce a shock front that travels into the cloud, accelerating the gas to supersonic velocities in what has been called the ``champagne phase.'' The expansion of the inner region at t>0 is connected to the outer envelope of the now ionized cloud core through this shock, whose strength depends on the temperature of the H II gas. In particular, we find a modified Larson-Penston (L-P) type of solution as part of the linear sequence of self-similar champagne outflows. The modification involves the proper insertion of a shock and produces the right behavior at infinity (v-->0) for an outflow of finite duration, reconciling the long-standing conflict on the correct (inflow or outflow) interpretation for the original L-P solution. For realistic heating due to a massive young central star that ionizes and heats the gas to ~104 K, we show that even the self-gravity of the ionized gas of the massive molecular cloud core can be neglected. We then study the self-similar solutions of the expansion of H II regions embedded in molecular clouds characterized by more general power-law density distributions: ρ~r-n with 3/2

  2. Self-similar dynamics of a magnetized polytropic gas

    NASA Astrophysics Data System (ADS)

    Wang, Wei-Gang; Lou, Yu-Qing

    2007-10-01

    In broad astrophysical contexts of large-scale gravitational collapses and outflows and as a basis for various further astrophysical applications, we formulate and investigate a theoretical problem of self-similar magnetohydrodynamics (MHD) for a non-rotating polytropic gas of quasi-spherical symmetry permeated by a completely random magnetic field. Within this framework, we derive two coupled nonlinear MHD ordinary differential equations (ODEs), examine properties of the magnetosonic critical curve, obtain various asymptotic and global semi-complete similarity MHD solutions, and qualify the applicability of our results. Unique to a magnetized gas cloud, a novel asymptotic MHD solution for a collapsing core is established. Physically, the similarity MHD inflow towards the central dense core proceeds in characteristic manners before the gas material eventually encounters a strong radiating MHD shock upon impact onto the central compact object. Sufficiently far away from the central core region enshrouded by such an MHD shock, we derive regular asymptotic behaviours. We study asymptotic solution behaviours in the vicinity of the magnetosonic critical curve and determine smooth MHD eigensolutions across this curve. Numerically, we construct global semi-complete similarity MHD solutions that cross the magnetosonic critical curve zero, one, and two times. For comparison, counterpart solutions in the case of an isothermal unmagnetized and magnetized gas flows are demonstrated in the present MHD framework at nearly isothermal and weakly magnetized conditions. For a polytropic index γ=1.25 or a strong magnetic field, different solution behaviours emerge. With a strong magnetic field, there exist semi-complete similarity solutions crossing the magnetosonic critical curve only once, and the MHD counterpart of expansion-wave collapse solution disappears. Also in the polytropic case of γ=1.25, we no longer observe the trend in the speed-density phase diagram of finding

  3. Self-Similar Solutions for Relativistic Shocks Emerging from Stars with Polytropic Envelopes

    NASA Astrophysics Data System (ADS)

    Pan, Margaret; Sari, Re'em

    2006-05-01

    We consider a strong ultrarelativistic shock moving through a star whose envelope has a polytrope-like density profile. When the shock is close to the star's outer boundary, its behavior follows the self-similar solution given by Sari for implosions in planar geometry. Here we outline this solution and find the asymptotic solution as the shock reaches the star's edge. We then show that the motion after the shock breaks out of the star is described by a self-similar solution remarkably like the solution for the motion inside the star. In particular, the characteristic Lorentz factor, pressure, and density vary with time according to the same power laws both before and after the shock breaks out of the star. After emergence from the star, however, the self-similar solution's characteristic position corresponds to a point behind the leading edge of the flow rather than at the shock front, and the relevant range of values for the similarity variable changes. Our numerical integrations agree well with the analytic results both before and after the shock reaches the star's edge.

  4. Relativistic self-similar dynamic gravitational collapses of a quasi-spherical general polytropic magnetofluid

    NASA Astrophysics Data System (ADS)

    Lou, Yu-Qing; Xia, Yu-Kai

    2017-05-01

    We study magnetohydrodynamic (MHD) self-similar collapses and void evolution, with or without shocks, of a general polytropic quasi-spherical magnetofluid permeated by random transverse magnetic fields under the Paczynski-Wiita gravity that captures essential general relativistic effects of a Schwarzschild black hole (BH) with a growing mass. Based on the derived set of non-linear MHD ordinary differential equations, we obtain various asymptotic MHD solutions, the geometric and analytical properties of the magnetosonic critical curve (MSCC) and MHD shock jump conditions. Novel asymptotic MHD solution behaviours near the rim of central expanding voids are derived analytically. By exploring numerical global MHD solutions, we identify allowable boundary conditions at large radii that accommodate a smooth solution and show that a reasonable amount of magnetization significantly increases the mass accretion rate in the expansion-wave-collapse solution scenario. We also construct the counterparts of envelope-expansion-core-collapse solutions that cross the MSCC twice, which are found to be closely paired with a sequence of global smooth solutions satisfying a novel type of central MHD behaviours. MHD shocks with static outer and various inner flow profiles are also examined. Astrophysical applications include dynamic core collapses of magnetized massive stars and compact objects as well as formation of supermassive, hypermassive, dark matter and mixed matter BHs in the Universe, including the early Universe. Such gigantic BHs can be detected in X-ray/gamma-ray sources, quasars, ultraluminous infrared galaxies or extremely luminous infrared galaxies and dark matter overwhelmingly dominated elliptical galaxies as well as massive dark matter halos, etc. Gravitational waves and electromagnetic wave emissions in broad band (including e.g., gamma-ray bursts and fast radio bursts) can result from this type of dynamic collapses of forming BHs involving magnetized media.

  5. Self-similar evolution of interplanetary magnetic clouds and Ulysses measurements of the polytropic index inside the cloud

    NASA Technical Reports Server (NTRS)

    Osherovich, Vladimir A.; Fainberg, J.; Stone, R. G.; MacDowall, R. J.; Berdichevsky, D.

    1997-01-01

    A self similar model for the expanding flux rope is developed for a magnetohydrodynamic model of interplanetary magnetic clouds. It is suggested that the dependence of the maximum magnetic field on the distance from the sun and the polytropic index gamma has the form B = r exp (-1/gamma), and that the ratio of the electron temperature to the proton temperature increases with distance from the sun. It is deduced that ion acoustic waves should be observed in the cloud. Both predictions were confirmed by Ulysses observations of a 1993 magnetic cloud. Measurements of gamma inside the cloud demonstrate sensitivity to the internal topology of the magnetic field in the cloud.

  6. Six secrets of champagne

    NASA Astrophysics Data System (ADS)

    Liger-Belair, Gérard

    2015-12-01

    Popping open a bottle of champagne is one of life's great delights, but how much do you really know about the science behind this greatest of wines? Gérard Liger-Belair reveals his six favourite champagne secrets.

  7. Champagne Heat Pump

    NASA Technical Reports Server (NTRS)

    Jones, Jack A.

    2004-01-01

    The term champagne heat pump denotes a developmental heat pump that exploits a cycle of absorption and desorption of carbon dioxide in an alcohol or other organic liquid. Whereas most heat pumps in common use in the United States are energized by mechanical compression, the champagne heat pump is energized by heating. The concept of heat pumps based on other absorption cycles energized by heat has been understood for years, but some of these heat pumps are outlawed in many areas because of the potential hazards posed by leakage of working fluids. For example, in the case of the water/ammonia cycle, there are potential hazards of toxicity and flammability. The organic-liquid/carbon dioxide absorption/desorption cycle of the champagne heat pump is similar to the water/ammonia cycle, but carbon dioxide is nontoxic and environmentally benign, and one can choose an alcohol or other organic liquid that is also relatively nontoxic and environmentally benign. Two candidate nonalcohol organic liquids are isobutyl acetate and amyl acetate. Although alcohols and many other organic liquids are flammable, they present little or no flammability hazard in the champagne heat pump because only the nonflammable carbon dioxide component of the refrigerant mixture is circulated to the evaporator and condenser heat exchangers, which are the only components of the heat pump in direct contact with air in habitable spaces.

  8. Champagne Patterns and Lake Nyos

    ERIC Educational Resources Information Center

    Science Teacher, 2005

    2005-01-01

    Carbon dioxide bubbles in a glass of champagne rise to the surface in fine threads, which are made of bubble groupings that change over time. Researchers from French and Brazilian universities have produced a new model that accounts for the patterns in strings of bubbles in champagne and other effervescent fluids. The research appears in Physical…

  9. Champagne Patterns and Lake Nyos

    ERIC Educational Resources Information Center

    Science Teacher, 2005

    2005-01-01

    Carbon dioxide bubbles in a glass of champagne rise to the surface in fine threads, which are made of bubble groupings that change over time. Researchers from French and Brazilian universities have produced a new model that accounts for the patterns in strings of bubbles in champagne and other effervescent fluids. The research appears in Physical…

  10. Self-similar aftershock rates

    NASA Astrophysics Data System (ADS)

    Davidsen, Jörn; Baiesi, Marco

    2016-08-01

    In many important systems exhibiting crackling noise—an intermittent avalanchelike relaxation response with power-law and, thus, self-similar distributed event sizes—the "laws" for the rate of activity after large events are not consistent with the overall self-similar behavior expected on theoretical grounds. This is particularly true for the case of seismicity, and a satisfying solution to this paradox has remained outstanding. Here, we propose a generalized description of the aftershock rates which is both self-similar and consistent with all other known self-similar features. Comparing our theoretical predictions with high-resolution earthquake data from Southern California we find excellent agreement, providing particularly clear evidence for a unified description of aftershocks and foreshocks. This may offer an improved framework for time-dependent seismic hazard assessment and earthquake forecasting.

  11. Self-similar aftershock rates.

    PubMed

    Davidsen, Jörn; Baiesi, Marco

    2016-08-01

    In many important systems exhibiting crackling noise-an intermittent avalanchelike relaxation response with power-law and, thus, self-similar distributed event sizes-the "laws" for the rate of activity after large events are not consistent with the overall self-similar behavior expected on theoretical grounds. This is particularly true for the case of seismicity, and a satisfying solution to this paradox has remained outstanding. Here, we propose a generalized description of the aftershock rates which is both self-similar and consistent with all other known self-similar features. Comparing our theoretical predictions with high-resolution earthquake data from Southern California we find excellent agreement, providing particularly clear evidence for a unified description of aftershocks and foreshocks. This may offer an improved framework for time-dependent seismic hazard assessment and earthquake forecasting.

  12. Flying Through Polytropes

    NASA Technical Reports Server (NTRS)

    Pesnell, W. Dean

    2016-01-01

    Dropping objects into a tunnel bored through Earth has been used to visualize simple harmonic motion for many years, and even imagined for use as rapid transport systems. Unlike previous studies that assumed a constant density Earth, here we calculate the fall-through time of polytropes, models of Earth's interior where the pressure varies as a power of the density. This means the fall-through time can be calculated as the central condensation varies from one to large within the family of polytropes. Having a family of models, rather than a single model, helps to explore the properties of planets and stars. Comparing the family of phase space solutions shows that the fall-through time and velocity approach the limit of radial free-fall onto a point mass as the central condensation increases. More condensed models give higher maximum velocities but do not have the right global properties for Earth. The angular distance one can travel along the surface is calculated as a brachistochrone (path of least time) tunnel that is a function of the depth to which the tunnel is bored. We also show that completely degenerate objects, simple models of white dwarf stars supported by completely degenerate electrons, have sizes similar to Earth but their much higher masses mean a much larger gravitational strength and a shorter fall-through time. Numerical integrations of the equations describing polytropes and completely degenerate objects are used to generate the initial models. Analytic solutions and numerical integration of the equations of motion are used to calculate the fall-through time for each model, and numerical integrations with analytic approximations at the boundaries are used to calculate the brachistochrones in the polytropes. Scaling relationships are provided to help use these results in other planets and stars.

  13. Two Quantum Polytropic Cycles

    NASA Astrophysics Data System (ADS)

    Arias-Hernández, L. A.; Morales-Serrano, A. F.

    2002-11-01

    In this work we follow the Bender et al paper [1] to study the quantum analogues of the Stirling and Ericsson polytropic cycles. In the context of the classical thermodynamics, the Stirling and Ericsson cycles correspond to reversible heat engines with two isothermal processes joined by two polytropic branches which occur in a device called regenerator. If this device is an ideal one, the efficiency of these cycles is the Carnot efficiency. Here, we introduce the quantum analogues of the Stirling and Ericsson cycles, the first one based on a double square potential well with a finite potential barrier, since in this system the tunnel effect could be the analogue to the regeneration classical process, therefore the isochoric quantum branches would really correspond to an internal energy storage, and the last one with an unknown system where the isobaric quantum processes don't induce changes in its quantum state. With these systems the quantum engines have cycles consisting of polytropic and isothermal quantum processes analogues to the corresponding classical processes. We show that in both cases the quantum cycles have an efficiency given by ηCQM = 1 - EC/EH, which is the same expression for the quantum analogue of the Carnot cycle studied by Bender.

  14. Self-similarity in nature

    NASA Astrophysics Data System (ADS)

    Timashev, S. F.

    2000-02-01

    A general phenomenological approach to the analysis of experimental temporal, spatial and energetic series for extracting truly physical non-model parameters ("passport data") is presented, which may be used to characterize and distinguish the evolution as well as the spatial and energetic structure of any open nonlinear dissipative system. This methodology is based on a postulate concerning the crucial information contained in the sequences of non-regularities of the measured dynamic variable (temporal, spatial, energetic). In accordance with this approach, multi-parametric formulas for dynamic variable power spectra as well as for structural functions of different orders are identical for every spatial-temporal-energetic level of the system under consideration. In effect, this entails the introduction of a new kind of self-similarity in Nature. An algorithm has been developed for obtaining as many "passport data" as are necessary for the characterization of a dynamic system. Applications of this approach in the analysis of various experimental series (temporal, spatial, energetic) demonstrate its potential for defining adequate phenomenological parameters of different dynamic processes and structures.

  15. Gravitational collapse of conventional polytropic cylinder

    NASA Astrophysics Data System (ADS)

    Lou, Yu-Qing; Hu, Xu-Yao

    2017-07-01

    In reference to general polytropic and conventional polytropic hydrodynamic cylinders of infinite length with axial uniformity and axisymmetry under self-gravity, the dynamic evolution of central collapsing mass string in free-fall dynamic accretion phase is re-examined in details. We compare the central mass accretion rate and the envelope mass infall rate at small radii. Among others, we correct mistakes and typos of Kawachi & Hanawa (KH hereafter) and in particular prove that their key asymptotic free-fall solution involving polytropic index γ in the two power exponents is erroneous by analytical analyses and numerical tests. The correct free-fall asymptotic solutions at sufficiently small \\hat{r} (the dimensionless independent self-similar variable) scale as {˜ } -|ln \\hat{r}|^{1/2} in contrast to KH's ˜ -|ln \\hat{r}|^{(2-γ )/2} for the reduced bulk radial flow velocity and as {˜ } \\hat{r}^{-1}|ln \\hat{r}|^{-1/2} in contrast to KH's {˜ } \\hat{r}^{-1} |ln \\hat{r}|^{-(2-γ )/2} for the reduced mass density. We offer consistent scenarios for numerical simulation code testing and theoretical study on dynamic filamentary structure formation and evolution as well as pertinent stability properties. Due to unavoidable Jeans instabilities along the cylinder, such collapsing massive filaments or strings can further break up into clumps and segments of various lengths as well as clumps embedded within segments and evolve into chains of gravitationally collapsed objects (such as gaseous planets, brown dwarfs, protostars, white dwarfs, neutron stars, black holes in a wide mass range, globular clusters, dwarf spheroidals, galaxies, galaxy clusters and even larger mass reservoirs etc.) in various astrophysical and cosmological contexts as articulated by Lou & Hu recently. As an example, we present a model scheme for comparing with observations of molecular filaments for forming protostars, brown dwarfs and gaseous planets and so forth.

  16. New classes of polytropic models

    NASA Astrophysics Data System (ADS)

    Ngubelanga, S. A.; Maharaj, S. D.

    2017-03-01

    The gravitational behaviour of a dense compact object is studied in isotropic coordinates. We obtain new classes of static, spherically symmetric classes of solutions to the Einstein-Maxwell field equations by assuming an anisotropic pressures and a barotropic equation of state which is polytropic. Four new classes of exact solutions are found with different polytropic indices. We can regain masses of several observed astronomical objects. A physical analysis indicates that the models are well behaved.

  17. A self-similar magnetohydrodynamic model for ball lightnings

    NASA Astrophysics Data System (ADS)

    Tsui, K. H.

    2006-07-01

    Ball lightning is modeled by magnetohydrodynamic (MHD) equations in two-dimensional spherical geometry with azimuthal symmetry. Dynamic evolutions in the radial direction are described by the self-similar evolution function y(t ). The plasma pressure, mass density, and magnetic fields are solved in terms of the radial label η. This model gives spherical MHD plasmoids with axisymmetric force-free magnetic field, and spherically symmetric plasma pressure and mass density, which self-consistently determine the polytropic index γ. The spatially oscillating nature of the radial and meridional field structures indicate embedded regions of closed field lines. These regions are named secondary plasmoids, whereas the overall self-similar spherical structure is named the primary plasmoid. According to this model, the time evolution function allows the primary plasmoid expand outward in two modes. The corresponding ejection of the embedded secondary plasmoids results in ball lightning offering an answer as how they come into being. The first is an accelerated expanding mode. This mode appears to fit plasmoids ejected from thundercloud tops with acceleration to ionosphere seen in high altitude atmospheric observations of sprites and blue jets. It also appears to account for midair high-speed ball lightning overtaking airplanes, and ground level high-speed energetic ball lightning. The second is a decelerated expanding mode, and it appears to be compatible to slowly moving ball lightning seen near ground level. The inverse of this second mode corresponds to an accelerated inward collapse, which could bring ball lightning to an end sometimes with a cracking sound.

  18. A self-similar magnetohydrodynamic model for ball lightnings

    SciTech Connect

    Tsui, K. H.

    2006-07-15

    Ball lightning is modeled by magnetohydrodynamic (MHD) equations in two-dimensional spherical geometry with azimuthal symmetry. Dynamic evolutions in the radial direction are described by the self-similar evolution function y(t). The plasma pressure, mass density, and magnetic fields are solved in terms of the radial label {eta}. This model gives spherical MHD plasmoids with axisymmetric force-free magnetic field, and spherically symmetric plasma pressure and mass density, which self-consistently determine the polytropic index {gamma}. The spatially oscillating nature of the radial and meridional field structures indicate embedded regions of closed field lines. These regions are named secondary plasmoids, whereas the overall self-similar spherical structure is named the primary plasmoid. According to this model, the time evolution function allows the primary plasmoid expand outward in two modes. The corresponding ejection of the embedded secondary plasmoids results in ball lightning offering an answer as how they come into being. The first is an accelerated expanding mode. This mode appears to fit plasmoids ejected from thundercloud tops with acceleration to ionosphere seen in high altitude atmospheric observations of sprites and blue jets. It also appears to account for midair high-speed ball lightning overtaking airplanes, and ground level high-speed energetic ball lightning. The second is a decelerated expanding mode, and it appears to be compatible to slowly moving ball lightning seen near ground level. The inverse of this second mode corresponds to an accelerated inward collapse, which could bring ball lightning to an end sometimes with a cracking sound.

  19. Self-similarity in active colloid motion

    NASA Astrophysics Data System (ADS)

    Constant, Colin; Sukhov, Sergey; Dogariu, Aristide

    The self-similarity of displacements among randomly evolving systems has been used to describe the foraging patterns of animals and predict the growth of financial systems. At micron scales, the motion of colloidal particles can be analyzed by sampling their spatial displacement in time. For self-similar systems in equilibrium, the mean squared displacement increases linearly in time. However, external forces can take the system out of equilibrium, creating active colloidal systems, and making this evolution more complex. A moment scaling spectrum of the distribution of particle displacements quantifies the degree of self-similarity in the colloid motion. We will demonstrate that, by varying the temporal and spatial characteristics of the external forces, one can control the degree of self-similarity in active colloid motion.

  20. Self-similarity in Laplacian growth

    SciTech Connect

    Mineev-weinstein, Mark; Zabrodin, Anton; Abanov, Artem

    2008-01-01

    We consider Laplacian Growth of self-similar domains in different geometries. Self-similarity determines the analytic structure of the Schwarz function of the moving boundary. The knowledge of this analytic structure allows us to derive the integral equation for the conformal map. It is shown that solutions to the integral equation obey also a second-order differential equation which is the 1D Schroedinger equation with the sinh{sup -2}-potential. The solutions, which are expressed through the Gauss hypergeometric function, characterize the geometry of self-similar patterns in a wedge. We also find the potential for the Coulomb gas representation of the self-similar Laplacian growth in a wedge and calculate the corresponding free energy.

  1. On cracking of charged anisotropic polytropes

    NASA Astrophysics Data System (ADS)

    Azam, M.; Mardan, S. A.

    2017-01-01

    Recently in [1], the role of electromagnetic field on the cracking of spherical polytropes has been investigated without perturbing charge parameter explicitly. In this study, we have examined the occurrence of cracking of anisotropic spherical polytropes through perturbing parameters like anisotropic pressure, energy density and charge. We consider two different types of polytropes in this study. We discuss the occurrence of cracking in two different ways (i) by perturbing polytropic constant, anisotropy and charge parameter (ii) by perturbing polytropic index, anisotropy and charge parameter for each case. We conclude that cracking appears for a wide range of parameters in both cases. Also, our results are reduced to [2] in the absence of charge.

  2. The baryonic self similarity of dark matter

    SciTech Connect

    Alard, C.

    2014-06-20

    The cosmological simulations indicates that dark matter halos have specific self-similar properties. However, the halo similarity is affected by the baryonic feedback. By using momentum-driven winds as a model to represent the baryon feedback, an equilibrium condition is derived which directly implies the emergence of a new type of similarity. The new self-similar solution has constant acceleration at a reference radius for both dark matter and baryons. This model receives strong support from the observations of galaxies. The new self-similar properties imply that the total acceleration at larger distances is scale-free, the transition between the dark matter and baryons dominated regime occurs at a constant acceleration, and the maximum amplitude of the velocity curve at larger distances is proportional to M {sup 1/4}. These results demonstrate that this self-similar model is consistent with the basics of modified Newtonian dynamics (MOND) phenomenology. In agreement with the observations, the coincidence between the self-similar model and MOND breaks at the scale of clusters of galaxies. Some numerical experiments show that the behavior of the density near the origin is closely approximated by a Einasto profile.

  3. CO2 volume fluxes outgassing from champagne glasses: the impact of champagne ageing.

    PubMed

    Liger-Belair, Gérard; Villaume, Sandra; Cilindre, Clara; Jeandet, Philippe

    2010-02-15

    It was demonstrated that CO(2) volume fluxes outgassing from a flute poured with a young champagne (elaborated in 2007) are much higher than those outgassing from the same flute poured with an older champagne (elaborated in the early 1990s). The difference in dissolved-CO(2) concentrations between the two types of champagne samples was found to be a crucial parameter responsible for differences in CO(2) volume fluxes outgassing from one champagne to another. Nevertheless, it was shown that, for a given identical dissolved-CO(2) concentration in both champagne types, the CO(2) volume flux outgassing from the flute poured with the old champagne is, in average, significantly lower than that outgassing from the flute poured with the young one. Therefore, CO(2) seems to "escape" more easily from the young champagne than from the older one. The diffusion coefficient of CO(2) in both champagne types was pointed as a key parameter to thoroughly determine in the future, in order to unravel our experimental observation. Copyright 2009 Elsevier B.V. All rights reserved.

  4. Self-similar evolution of magnetized plasmas. I - Quasi-static solution

    NASA Technical Reports Server (NTRS)

    Yang, Wei-Hong

    1992-01-01

    The concept of linear expansion suggested by Wei-Hong (1989 and 1990), describes the self-similar evolution of a magnetic structure. Linear expansion can be represented by a single function which connects the evolving physical parameters of the plasma with their initial values in explicit forms. A general self-similar dynamic equation, therefore, is derived. As the first step toward more general consideration, the quasi-static solution is investigated in this paper. It is shown that a gamma = 4/3 polytrope may evolve through consecutive equilibria if its magnetic field expands self-similarly. The change of the energy everywhere inside the plasma equals the work done by the internal plasma pressure and magnetic field for the expansion. For the special case of an expanding force-free magnetic field, the self-similar expansion is a clean expansion. No free magnetic energy is left anywhere inside the magnetic structure. The approximation in quasi-state modeling of a pressure confined magnetized plasmoid is analyzed.

  5. Self-similar scalar field collapse

    NASA Astrophysics Data System (ADS)

    Banerjee, Narayan; Chakrabarti, Soumya

    2017-01-01

    A spherically symmetric collapsing scalar field model is discussed with a dissipative fluid which includes a heat flux. This vastly general matter distribution is analyzed at the expense of a high degree of symmetry in the space-time, that of conformal flatness and self-similarity. Indeed collapsing models terminating into a curvature singularity can be obtained. The formation of black holes or the occurrence of naked singularities depends on the initial collapsing profiles.

  6. Self-Similar Compressible Free Vortices

    NASA Technical Reports Server (NTRS)

    vonEllenrieder, Karl

    1998-01-01

    Lie group methods are used to find both exact and numerical similarity solutions for compressible perturbations to all incompressible, two-dimensional, axisymmetric vortex reference flow. The reference flow vorticity satisfies an eigenvalue problem for which the solutions are a set of two-dimensional, self-similar, incompressible vortices. These solutions are augmented by deriving a conserved quantity for each eigenvalue, and identifying a Lie group which leaves the reference flow equations invariant. The partial differential equations governing the compressible perturbations to these reference flows are also invariant under the action of the same group. The similarity variables found with this group are used to determine the decay rates of the velocities and thermodynamic variables in the self-similar flows, and to reduce the governing partial differential equations to a set of ordinary differential equations. The ODE's are solved analytically and numerically for a Taylor vortex reference flow, and numerically for an Oseen vortex reference flow. The solutions are used to examine the dependencies of the temperature, density, entropy, dissipation and radial velocity on the Prandtl number. Also, experimental data on compressible free vortex flow are compared to the analytical results, the evolution of vortices from initial states which are not self-similar is discussed, and the energy transfer in a slightly-compressible vortex is considered.

  7. Statistical self-similarity of hotspot seamount volumes modeled as self-similar criticality

    USGS Publications Warehouse

    Tebbens, S.F.; Burroughs, S.M.; Barton, C.C.; Naar, D.F.

    2001-01-01

    The processes responsible for hotspot seamount formation are complex, yet the cumulative frequency-volume distribution of hotspot seamounts in the Easter Island/Salas y Gomez Chain (ESC) is found to be well-described by an upper-truncated power law. We develop a model for hotspot seamount formation where uniform energy input produces events initiated on a self-similar distribution of critical cells. We call this model Self-Similar Criticality (SSC). By allowing the spatial distribution of magma migration to be self-similar, the SSC model recreates the observed ESC seamount volume distribution. The SSC model may have broad applicability to other natural systems.

  8. SUPERPOSITION OF POLYTROPES IN THE INNER HELIOSHEATH

    SciTech Connect

    Livadiotis, G.

    2016-03-15

    This paper presents a possible generalization of the equation of state and Bernoulli's integral when a superposition of polytropic processes applies in space and astrophysical plasmas. The theory of polytropic thermodynamic processes for a fixed polytropic index is extended for a superposition of polytropic indices. In general, the superposition may be described by any distribution of polytropic indices, but emphasis is placed on a Gaussian distribution. The polytropic density–temperature relation has been used in numerous analyses of space plasma data. This linear relation on a log–log scale is now generalized to a concave-downward parabola that is able to describe the observations better. The model of the Gaussian superposition of polytropes is successfully applied in the proton plasma of the inner heliosheath. The estimated mean polytropic index is near zero, indicating the dominance of isobaric thermodynamic processes in the sheath, similar to other previously published analyses. By computing Bernoulli's integral and applying its conservation along the equator of the inner heliosheath, the magnetic field in the inner heliosheath is estimated, B ∼ 2.29 ± 0.16 μG. The constructed normalized histogram of the values of the magnetic field is similar to that derived from a different method that uses the concept of large-scale quantization, bringing incredible insights to this novel theory.

  9. On the losses of dissolved CO(2) during champagne serving.

    PubMed

    Liger-Belair, Gérard; Bourget, Marielle; Villaume, Sandra; Jeandet, Philippe; Pron, Hervé; Polidori, Guillaume

    2010-08-11

    Pouring champagne into a glass is far from being consequenceless with regard to its dissolved CO(2) concentration. Measurements of losses of dissolved CO(2) during champagne serving were done from a bottled Champagne wine initially holding 11.4 +/- 0.1 g L(-1) of dissolved CO(2). Measurements were done at three champagne temperatures (i.e., 4, 12, and 18 degrees C) and for two different ways of serving (i.e., a champagne-like and a beer-like way of serving). The beer-like way of serving champagne was found to impact its concentration of dissolved CO(2) significantly less. Moreover, the higher the champagne temperature is, the higher its loss of dissolved CO(2) during the pouring process, which finally constitutes the first analytical proof that low temperatures prolong the drink's chill and helps it to retain its effervescence during the pouring process. The diffusion coefficient of CO(2) molecules in champagne and champagne viscosity (both strongly temperature-dependent) are suspected to be the two main parameters responsible for such differences. Besides, a recently developed dynamic-tracking technique using IR thermography was also used in order to visualize the cloud of gaseous CO(2) which flows down from champagne during the pouring process, thus visually confirming the strong influence of champagne temperature on its loss of dissolved CO(2).

  10. Horton Law in Self-Similar Trees

    NASA Astrophysics Data System (ADS)

    Kovchegov, Yevgeniy; Zaliapin, Ilya

    2016-04-01

    Self-similarity of random trees is related to the operation of pruning. Pruning ℛ cuts the leaves and their parental edges and removes the resulting chains of degree-two nodes from a finite tree. A Horton-Strahler order of a vertex v and its parental edge is defined as the minimal number of prunings necessary to eliminate the subtree rooted at v. A branch is a group of neighboring vertices and edges of the same order. The Horton numbers 𝒩k[K] and 𝒩ij[K] are defined as the expected number of branches of order k, and the expected number of order-i branches that merged order-j branches, j > i, respectively, in a finite tree of order K. The Tokunaga coefficients are defined as Tij[K] = 𝒩ij[K]/𝒩j[K]. The pruning decreases the orders of tree vertices by unity. A rooted full binary tree is said to be mean-self-similar if its Tokunaga coefficients are invariant with respect to pruning: Tk := Ti,i+k[K]. We show that for self-similar trees, the condition limsupk→∞Tk1/k < ∞ is necessary and sufficient for the existence of the strong Horton law: 𝒩k[K]/𝒩1[K] → R1-k, as K →∞ for some R > 0 and every k ≥ 1. This work is a step toward providing rigorous foundations for the Horton law that, being omnipresent in natural branching systems, has escaped so far a formal explanation.

  11. Bayesian estimation of self-similarity exponent

    NASA Astrophysics Data System (ADS)

    Makarava, Natallia; Benmehdi, Sabah; Holschneider, Matthias

    2011-08-01

    In this study we propose a Bayesian approach to the estimation of the Hurst exponent in terms of linear mixed models. Even for unevenly sampled signals and signals with gaps, our method is applicable. We test our method by using artificial fractional Brownian motion of different length and compare it with the detrended fluctuation analysis technique. The estimation of the Hurst exponent of a Rosenblatt process is shown as an example of an H-self-similar process with non-Gaussian dimensional distribution. Additionally, we perform an analysis with real data, the Dow-Jones Industrial Average closing values, and analyze its temporal variation of the Hurst exponent.

  12. Spherically Symmetric Cold Collapse: The Exact Solutions and a Comparison with Self-similar Solutions

    NASA Astrophysics Data System (ADS)

    Coughlin, Eric R.

    2017-01-01

    We present the exact solutions for the collapse of a spherically symmetric cold (i.e., pressureless) cloud under its own self-gravity, valid for arbitrary initial density profiles and not restricted to the realm of self-similarity. These solutions exhibit a number of remarkable features, including the self-consistent formation of and subsequent accretion onto a central point mass. A number of specific examples are provided, and we show that Penston’s solution of pressureless self-similar collapse is recovered for polytropic density profiles; importantly, however, we demonstrate that the time over which this solution holds is fleetingly short, implying that much of the collapse proceeds non-self-similarly. We show that our solutions can naturally incorporate turbulent pressure support, and we investigate the evolution of overdensities—potentially generated by such turbulence—as the collapse proceeds. Finally, we analyze the evolution of the angular velocity and magnetic fields in the limit that their dynamical influence is small, and we recover exact solutions for these quantities. Our results may provide important constraints on numerical models that attempt to elucidate the details of protostellar collapse when the initial conditions are far less idealized.

  13. Self-similar Relativisitic Disks revisted

    NASA Astrophysics Data System (ADS)

    Cai, M. J.; Shu, F. H.

    2001-05-01

    We revisit the rotating self-similar disk first studied by Lynden-Bell and Pineault and extend it to include pressure. A two-parameter family of solutions is constructed numerically. These disks are parameterized by the constant linear rotation velocity v, and the isothermal sound speed γ 1/2. For sufficiently high velocities, an ergo region develops in the form of the exterior of a cone. For each value of γ , there is a maximum velocity vc above which there is no equilibrium solutions. For this solution the frame dragging is infinite and the ergo cone closes on the rotation axis. The null geodesic equations are also integrated numerically. Due to the infinite extend and mass of the system, all photon trajectories are focused towards the disk. The behavior of equatorial photons orbits is qualitatively the same as that of cold disks.

  14. Self-similar dynamics of bacterial chemotaxis

    NASA Astrophysics Data System (ADS)

    Ngamsaad, Waipot; Khompurngson, Kannika

    2012-12-01

    Colonies of bacteria grown on thin agar plate exhibit fractal patterns as a result of adaptation to their environments. The bacterial colony pattern formation is regulated crucially by chemotaxis, the movement of cells along a chemical concentration gradient. Here, the dynamics of pattern formation in a bacterial colony is investigated theoretically through a continuum model that considers chemotaxis. In the case of the gradient sensed by the bacterium is nearly uniform, the bacterial colony patterns are self-similar, which means they look the same at every scale. The scaling law of the bacterial colony growth has been revealed explicitly. Chemotaxis biases the movement of the bacterial population in colony to trend toward the chemical attractant. Moreover, the bacterial colonies evolve for a long time as the traveling wave with a sharp front.

  15. General polytropic dynamic cylinder under self-gravity

    NASA Astrophysics Data System (ADS)

    Lou, Yu-Qing

    2015-12-01

    We explore self-similar hydrodynamics of general polytropic (GP) and isothermal cylinders of infinite length with axial uniformity and axisymmetry under self-gravity. Specific entropy conservation along streamlines serves as the dynamic equation of state. Together with possible axial flows, we construct classes of analytic and semi-analytic non-linear dynamic solutions for either cylindrical expansion or contraction radially by solving cylindrical Lane-Emden equations. By extensive numerical explorations and fitting trials in reference to asymptotes derived for large index n, we infer several convenient empirical formulae for characteristic solution properties of cylindrical Lane-Emden equations in terms of n values. A new type of asymptotic solutions for small x is also derived in the Appendix. These analyses offer hints for self-similar dynamic evolution of molecular filaments for forming protostars, brown dwarfs and gaseous planets and of large-scale gaseous arms or starburst rings in (barred) spiral galaxies for forming young massive stars. Such dynamic solutions are necessary starting background for further three-dimensional (in)stability analysis of various modes. They may be used to initialize numerical simulations and serve as important benchmarks for testing numerical codes. Such GP formalism can be further generalized to include magnetic field for a GP magnetohydrodynamic analysis.

  16. Global picture of self-similar and non-self-similar decay in Burgers turbulence.

    PubMed

    Noullez, Alain; Gurbatov, Sergey N; Aurell, Erik; Simdyankin, Sergey I

    2005-05-01

    This paper continues earlier investigations of the decay of Burgers turbulence in one dimension from Gaussian random initial conditions of the power-law spectral type E0(k) approximately |k|(n). Depending on the power n , different characteristic regions are distinguished. The main focus of this paper is to delineate the regions in wave number k and time t in which self-similarity can (and cannot) be observed, taking into account small-k and large-k cutoffs. The evolution of the spectrum can be inferred using physical arguments describing the competition between the initial spectrum and the new frequencies generated by the dynamics. For large wave numbers, we always have a k(-2) region, associated with the shocks. When n is less than 1, the large-scale part of the spectrum is preserved in time and the global evolution is self-similar, so that scaling arguments perfectly predict the behavior in time of the energy and integral scale. If n is larger than 2, the spectrum tends for long times to a universal scaling form independent of the initial conditions, with universal behavior k(2) at small wave numbers. In the interval 2self-similar, independent of n and with universal behavior k(2) at small wave number. When 1

  17. Fast approximation of self-similar network traffic

    SciTech Connect

    Paxson, V.

    1995-01-01

    Recent network traffic studies argue that network arrival processes are much more faithfully modeled using statistically self-similar processes instead of traditional Poisson processes [LTWW94a, PF94]. One difficulty in dealing with self-similar models is how to efficiently synthesize traces (sample paths) corresponding to self-similar traffic. We present a fast Fourier transform method for synthesizing approximate self-similar sample paths and assess its performance and validity. We find that the method is as fast or faster than existing methods and appears to generate a closer approximation to true self-similar sample paths than the other known fast method (Random Midpoint Displacement). We then discuss issues in using such synthesized sample paths for simulating network traffic, and how an approximation used by our method can dramatically speed up evaluation of Whittle`s estimator for H, the Hurst parameter giving the strength of long-range dependence present in a self-similar time series.

  18. Lipschitz equivalence of self-similar sets with touching structures

    NASA Astrophysics Data System (ADS)

    Ruan, Huo-Jun; Wang, Yang; Xi, Li-Feng

    2014-06-01

    Lipschitz equivalence of self-similar sets is an important area in the study of fractal geometry. It is known that two dust-like self-similar sets with the same contraction ratios are always Lipschitz equivalent. However, when self-similar sets have touching structures the problem of Lipschitz equivalence becomes much more challenging and intriguing at the same time. So far, all the known results only cover self-similar sets in {R} with no more than three branches. In this study we establish results for the Lipschitz equivalence of self-similar sets with touching structures in {R} with arbitrarily many branches. Key to our study is the introduction of a geometric condition for self-similar sets called substitutable.

  19. Magnetic flux concentrations in a polytropic atmosphere

    NASA Astrophysics Data System (ADS)

    Losada, I. R.; Brandenburg, A.; Kleeorin, N.; Rogachevskii, I.

    2014-04-01

    Context. Strongly stratified hydromagnetic turbulence has recently been identified as a candidate for explaining the spontaneous formation of magnetic flux concentrations by the negative effective magnetic pressure instability (NEMPI). Much of this work has been done for isothermal layers, in which the density scale height is constant throughout. Aims: We now want to know whether earlier conclusions regarding the size of magnetic structures and their growth rates carry over to the case of polytropic layers, in which the scale height decreases sharply as one approaches the surface. Methods: To allow for a continuous transition from isothermal to polytropic layers, we employ a generalization of the exponential function known as the q-exponential. This implies that the top of the polytropic layer shifts with changing polytropic index such that the scale height is always the same at some reference height. We used both mean-field simulations (MFS) and direct numerical simulations (DNS) of forced stratified turbulence to determine the resulting flux concentrations in polytropic layers. Cases of both horizontal and vertical applied magnetic fields were considered. Results: Magnetic structures begin to form at a depth where the magnetic field strength is a small fraction of the local equipartition field strength with respect to the turbulent kinetic energy. Unlike the isothermal case where stronger fields can give rise to magnetic flux concentrations at larger depths, in the polytropic case the growth rate of NEMPI decreases for structures deeper down. Moreover, the structures that form higher up have a smaller horizontal scale of about four times their local depth. For vertical fields, magnetic structures of super-equipartition strengths are formed, because such fields survive downward advection that causes NEMPI with horizontal magnetic fields to reach premature nonlinear saturation by what is called the "potato-sack" effect. The horizontal cross-section of such

  20. Evaporation of droplets in a Champagne wine aerosol.

    PubMed

    Ghabache, Elisabeth; Liger-Belair, Gérard; Antkowiak, Arnaud; Séon, Thomas

    2016-04-29

    In a single glass of champagne about a million bubbles nucleate on the wall and rise towards the surface. When these bubbles reach the surface and rupture, they project a multitude of tiny droplets in the form of a particular aerosol holding a concentrate of wine aromas. Based on the model experiment of a single bubble bursting in idealized champagnes, the key features of the champagne aerosol are identified. In particular, we show that film drops, critical in sea spray for example, are here nonexistent. We then demonstrate that compared to a still wine, champagne fizz drastically enhances the transfer of liquid into the atmosphere. There, conditions on bubble radius and wine viscosity that optimize aerosol evaporation are provided. These results pave the way towards the fine tuning of flavor release during sparkling wine tasting, a major issue for the sparkling wine industry.

  1. Evaporation of droplets in a Champagne wine aerosol

    NASA Astrophysics Data System (ADS)

    Ghabache, Elisabeth; Liger-Belair, Gérard; Antkowiak, Arnaud; Séon, Thomas

    2016-04-01

    In a single glass of champagne about a million bubbles nucleate on the wall and rise towards the surface. When these bubbles reach the surface and rupture, they project a multitude of tiny droplets in the form of a particular aerosol holding a concentrate of wine aromas. Based on the model experiment of a single bubble bursting in idealized champagnes, the key features of the champagne aerosol are identified. In particular, we show that film drops, critical in sea spray for example, are here nonexistent. We then demonstrate that compared to a still wine, champagne fizz drastically enhances the transfer of liquid into the atmosphere. There, conditions on bubble radius and wine viscosity that optimize aerosol evaporation are provided. These results pave the way towards the fine tuning of flavor release during sparkling wine tasting, a major issue for the sparkling wine industry.

  2. Evaporation of droplets in a Champagne wine aerosol

    PubMed Central

    Ghabache, Elisabeth; Liger-Belair, Gérard; Antkowiak, Arnaud; Séon, Thomas

    2016-01-01

    In a single glass of champagne about a million bubbles nucleate on the wall and rise towards the surface. When these bubbles reach the surface and rupture, they project a multitude of tiny droplets in the form of a particular aerosol holding a concentrate of wine aromas. Based on the model experiment of a single bubble bursting in idealized champagnes, the key features of the champagne aerosol are identified. In particular, we show that film drops, critical in sea spray for example, are here nonexistent. We then demonstrate that compared to a still wine, champagne fizz drastically enhances the transfer of liquid into the atmosphere. There, conditions on bubble radius and wine viscosity that optimize aerosol evaporation are provided. These results pave the way towards the fine tuning of flavor release during sparkling wine tasting, a major issue for the sparkling wine industry. PMID:27125240

  3. The physics behind the fizz in champagne and sparkling wines

    NASA Astrophysics Data System (ADS)

    Liger-Belair, G.

    2012-02-01

    Bubbles in a glass of champagne may seem like the acme of frivolity to most of people, but in fact they may rather be considered as a fantastic playground for any physicist. Actually, the so-called effervescence process, which enlivens champagne and sparkling wines tasting, is the result of the fine interplay between CO2 dissolved gas molecules, tiny air pockets trapped within microscopic particles during the pouring process, and some both glass and liquid properties. Results obtained concerning the various steps where the CO2 molecule plays a role (from its ingestion in the liquid phase during the fermentation process to its progressive release in the headspace above the tasting glass as bubbles collapse) are gathered and synthesized to propose a self-consistent and global overview of how gaseous and dissolved CO2 impact champagne and sparkling wine science. Physicochemical processes behind the nucleation, rise, and burst of gaseous CO2 bubbles found in glasses poured with champagne and sparkling wines are depicted. Those phenomena observed in close-up through high-speed photography are often visually appealing. I hope that your enjoyment of champagne will be enhanced after reading this fully illustrated review dedicated to the science hidden right under your nose each time you enjoy a glass of champagne.

  4. Self-similar motion of a Nambu-Goto string

    NASA Astrophysics Data System (ADS)

    Igata, Takahisa; Houri, Tsuyoshi; Harada, Tomohiro

    2016-09-01

    We study the self-similar motion of a string in a self-similar spacetime by introducing the concept of a self-similar string, which is defined as the world sheet to which a homothetic vector field is tangent. It is shown that in Nambu-Goto theory, the equations of motion for a self-similar string reduce to those for a particle. Moreover, under certain conditions such as the hypersurface orthogonality of the homothetic vector field, the equations of motion for a self-similar string simplify to the geodesic equations on a (pseudo)Riemannian space. As a concrete example, we investigate a self-similar Nambu-Goto string in a spatially flat Friedmann-Lemaître-Robertson-Walker expanding universe with self-similarity and obtain solutions of open and closed strings, which have various nontrivial configurations depending on the rate of the cosmic expansion. For instance, we obtain a circular solution that evolves linearly in the cosmic time while keeping its configuration by the balance between the effects of the cosmic expansion and string tension. We also show the instability for linear radial perturbation of the circular solutions.

  5. Self-similarity in incompressible Navier-Stokes equations.

    PubMed

    Ercan, Ali; Kavvas, M Levent

    2015-12-01

    The self-similarity conditions of the 3-dimensional (3D) incompressible Navier-Stokes equations are obtained by utilizing one-parameter Lie group of point scaling transformations. It is found that the scaling exponents of length dimensions in i = 1, 2, 3 coordinates in 3-dimensions are not arbitrary but equal for the self-similarity of 3D incompressible Navier-Stokes equations. It is also shown that the self-similarity in this particular flow process can be achieved in different time and space scales when the viscosity of the fluid is also scaled in addition to other flow variables. In other words, the self-similarity of Navier-Stokes equations is achievable under different fluid environments in the same or different gravity conditions. Self-similarity criteria due to initial and boundary conditions are also presented. Utilizing the proposed self-similarity conditions of the 3D hydrodynamic flow process, the value of a flow variable at a specified time and space can be scaled to a corresponding value in a self-similar domain at the corresponding time and space.

  6. Effective geometries in self-gravitating polytropes

    SciTech Connect

    Bini, D.; Cherubini, C.; Filippi, S.

    2008-09-15

    Perturbations of a perfect barotropic and irrotational Newtonian self-gravitating fluid are studied using a generalization of the so-called 'effective geometry' formalism. The case of polytropic spherical stars, as described by the Lane-Emden equation, is studied in detail in the known cases of existing explicit solutions. The present formulation gives a natural scenario in which the acoustic analogy has relevance for both stellar and galactic dynamics.

  7. Double-polytropic closure in the magentosheath

    NASA Technical Reports Server (NTRS)

    Hau, L.-N.; Phan, T.-D.; Sonnerup, B. U. O.; Paschmann, G.

    1993-01-01

    The magnetosheath plasma is usually neither isotropic nor adiabatic. This paper contains an attempt to decribe its thermodynamic properties in terms of two polytropic laws, p(sub perpendicular)/rho B(exp gamma(sub perpendicular)-1) = C(sub perpendicular) and p(sub parallel)B(exp gamma(sub parallel)-1)/rho(exp gamma(sub parallel)) = C(sub parallel), such that for gamma(sub perpendicular) = 2, gamma(sub parallel) = 3 the usual Chew-Goldberger-Low double-adiabatic expressions are recovered and for gamma(sub perpendicular) = 1, gamma(sub parallel) = 1 double-isothermal conditions are obtained. Using data from the AMPTE/IRM spacecraft, we show that the subsolar magnetosheath plasma may be better described by the double-polytropic laws than by the mirror instability threshold, in particular in the low beta region near the magnetopause. The inferred polytropic exponents vary from event to event but are typically in the ranges of gamma(sub perpendicular) = 0.94 +/- 0.10 and gamma(sub parallel) = 1.14 +/- 0.13 for the 29 cases we have examined.

  8. Fibonacci chain polynomials: Identities from self-similarity

    NASA Technical Reports Server (NTRS)

    Lang, Wolfdieter

    1995-01-01

    Fibonacci chains are special diatomic, harmonic chains with uniform nearest neighbor interaction and two kinds of atoms (mass-ratio r) arranged according to the self-similar binary Fibonacci sequence ABAABABA..., which is obtained by repeated substitution of A yields AB and B yields A. The implications of the self-similarity of this sequence for the associated orthogonal polynomial systems which govern these Fibonacci chains with fixed mass-ratio r are studied.

  9. The shape of a rapidly rotating polytrope with index unity

    NASA Astrophysics Data System (ADS)

    Knopik, Jerzy; Mach, Patryk; Odrzywołek, Andrzej

    2017-01-01

    We show that the solutions obtained in the paper `An exact solution for arbitrarily rotating gaseous polytropes with index unity' by Kong, Zhang, and Schubert represent only approximate solutions of the free-boundary Euler-Poisson system of equations describing uniformly rotating, self-gravitating polytropes with index unity. We discuss the quality of such solutions as approximations to the rigidly rotating equilibrium polytropic configurations.

  10. Slightly two- or three-dimensional self-similar solutions

    NASA Astrophysics Data System (ADS)

    Sari, Re'em; Bode, Nate; Yalinewich, Almog; MacFadyen, Andrew

    2012-08-01

    Self-similarity allows for analytic or semi-analytic solutions to many hydrodynamics problems. Most of these solutions are one-dimensional. Using linear perturbation theory, expanded around such a one-dimensional solution, we find self-similar hydrodynamic solutions that are two- or three-dimensional. Since the deviation from a one-dimensional solution is small, we call these slightly two-dimensional and slightly three-dimensional self-similar solutions, respectively. As an example, we treat strong spherical explosions of the second type. A strong explosion propagates into an ideal gas with negligible temperature and density profile of the form ρ(r, θ, ϕ) = r-ω[1 + σF(θ, ϕ)], where ω > 3 and σ ≪ 1. Analytical solutions are obtained by expanding the arbitrary function F(θ, ϕ) in spherical harmonics. We compare our results with two-dimensional numerical simulations, and find good agreement.

  11. Recent advances in the science of champagne bubbles.

    PubMed

    Liger-Belair, Gérard; Polidori, Guillaume; Jeandet, Philippe

    2008-11-01

    The so-called effervescence process, which enlivens champagne and sparkling wines tasting, is the result of the fine interplay between CO(2)-dissolved gas molecules, tiny air pockets trapped within microscopic particles during the pouring process, and some liquid properties. This critical review summarizes recent advances obtained during the past decade concerning the physicochemical processes behind the nucleation, rise, and burst of bubbles found in glasses poured with champagne and sparkling wines. Those phenomena observed in close-up through high-speed photography are often visually appealing. Let's hope that your enjoyment of champagne will be enhanced after reading this fully illustrated review dedicated to the deep beauties of nature often hidden behind many everyday phenomena (51 references).

  12. Visual perception of effervescence in champagne and other sparkling beverages.

    PubMed

    Liger-Belair, Gérard

    2010-01-01

    The so-called effervescence process, which enlivens champagne, sparkling wines, beers, and carbonated beverages in general, is the result of the fine interplay between CO₂-dissolved gas molecules, tiny air pockets trapped within microscopic particles during the pouring process, and some liquid properties. This chapter summarizes recent advances obtained during the last decade concerning the physicochemical processes behind the nucleation, rise, and burst of bubbles found in glasses poured with sparkling beverages. Those phenomena observed in close-up through high-speed photography are often visually appealing. Moreover, the kinetics of gas discharging from freshly poured glasses was monitored with time, whether champagne is served into a flute or into a coupe. The role of temperature was also examined. We hope that your enjoyment of champagne will be enhanced after reading this fully illustrated review dedicated to the deep beauties of nature often hidden behind many everyday phenomena. Copyright © 2010 Elsevier Inc. All rights reserved.

  13. A class of self-similar hydrodynamics test problems

    SciTech Connect

    Ramsey, Scott D; Brown, Lowell S; Nelson, Eric M; Alme, Marv L

    2010-12-08

    We consider self-similar solutions to the gas dynamics equations. One such solution - a spherical geometry Gaussian density profile - has been analyzed in the existing literature, and a connection between it, a linear velocity profile, and a uniform specific internal energy profile has been identified. In this work, we assume the linear velocity profile to construct an entire class of self-similar sol utions in both cylindrical and spherical geometry, of which the Gaussian form is one possible member. After completing the derivation, we present some results in the context of a test problem for compressible flow codes.

  14. Self-similarity and optical kinks in resonant nonlinear media

    SciTech Connect

    Ponomarenko, Sergey A.; Haghgoo, Soodeh

    2010-11-15

    We show that self-similar optical waves with a kink structure exist in a wide class of resonant nonlinear media, adequately treated in the two-level approximation. The self-similar structure of the present kinks is reflected in the time evolution of the field profile, atomic dipole moment, and one-atom inversion. We develop an analytical theory of such kinks. We show that the discovered kinks are accelerating nonlinear waves, asymptotically attaining their shape and the speed of light. We also numerically explore the formation and eventual disintegration of our kinks due to energy relaxation processes. Thus, the present kinks can be viewed as intermediate asymptotics of the system.

  15. PHOG analysis of self-similarity in aesthetic images

    NASA Astrophysics Data System (ADS)

    Amirshahi, Seyed Ali; Koch, Michael; Denzler, Joachim; Redies, Christoph

    2012-03-01

    In recent years, there have been efforts in defining the statistical properties of aesthetic photographs and artworks using computer vision techniques. However, it is still an open question how to distinguish aesthetic from non-aesthetic images with a high recognition rate. This is possibly because aesthetic perception is influenced also by a large number of cultural variables. Nevertheless, the search for statistical properties of aesthetic images has not been futile. For example, we have shown that the radially averaged power spectrum of monochrome artworks of Western and Eastern provenance falls off according to a power law with increasing spatial frequency (1/f2 characteristics). This finding implies that this particular subset of artworks possesses a Fourier power spectrum that is self-similar across different scales of spatial resolution. Other types of aesthetic images, such as cartoons, comics and mangas also display this type of self-similarity, as do photographs of complex natural scenes. Since the human visual system is adapted to encode images of natural scenes in a particular efficient way, we have argued that artists imitate these statistics in their artworks. In support of this notion, we presented results that artists portrait human faces with the self-similar Fourier statistics of complex natural scenes although real-world photographs of faces are not self-similar. In view of these previous findings, we investigated other statistical measures of self-similarity to characterize aesthetic and non-aesthetic images. In the present work, we propose a novel measure of self-similarity that is based on the Pyramid Histogram of Oriented Gradients (PHOG). For every image, we first calculate PHOG up to pyramid level 3. The similarity between the histograms of each section at a particular level is then calculated to the parent section at the previous level (or to the histogram at the ground level). The proposed approach is tested on datasets of aesthetic and

  16. Scaling and self-similarity in two-dimensional hydrodynamics.

    PubMed

    Ercan, Ali; Kavvas, M Levent

    2015-07-01

    The conditions under which depth-averaged two-dimensional (2D) hydrodynamic equations system as an initial-boundary value problem (IBVP) becomes self-similar are investigated by utilizing one-parameter Lie group of point scaling transformations. Self-similarity conditions due to the 2D k-ε turbulence model are also investigated. The self-similarity conditions for the depth-averaged 2D hydrodynamics are found for the flow variables including the time, the longitudinal length, the transverse length, the water depth, the flow velocities in x- and y-directions, the bed shear stresses in x- and y-directions, the bed shear velocity, the Manning's roughness coefficient, the kinematic viscosity of the fluid, the eddy viscosity, the turbulent kinetic energy, the turbulent dissipation, and the production and the source terms in the k-ε model. By the numerical simulations, it is shown that the IBVP of depth-averaged 2D hydrodynamic flow process in a prototype domain can be self-similar with that of a scaled domain. In fact, by changing the scaling parameter and the scaling exponents of the length dimensions, one can obtain several different scaled domains. The proposed scaling relations obtained by the Lie group scaling approach may provide additional spatial, temporal, and economical flexibility in setting up physical hydraulic models in which two-dimensional flow components are important.

  17. Self-similarity of Boussinesq Miscible Thermals: an Experimental Study

    NASA Astrophysics Data System (ADS)

    Zhao, Bing; Lai, Adrian; Law, Adrian; Adams, Eric

    2012-11-01

    The gross characteristics of fully-developed round miscible thermals have been well studied and reported to be self-similar (e.g. Scorer, 1957). However, there have been very few studies (Bond & Johari, 2005; Hart, 2008) concerning the internal structures of the thermal. Many important questions related to the interior fluid dynamics inside the thermal, including the self-similarity of the internal velocity and scalar distributions, remain outstanding. In the present study, detailed PIV and PLIF measurements were conducted in the axisymmetric plane (i.e. side view) of a negatively buoyant Boussinesq thermal to reveal the detailed internal structures, with CCD cameras that synchronized with a unique release mechanism that minimized the initial variations. Synchronized simultaneous flow visualization (with spotlights and a video camera) were also made to monitor the developmental shape of the thermal through a bottom view. The simultaneous information enabled an objective assessment of the experimental quality. The results showed that the maximum radius of the miscible thermal grows linearly with travel distance, which agrees with previous studies using dimensional analysis with self-similarity. The radius of the vortex ring is found to be expanding linearly, but surprising at a smaller growth rate that the overall thermal size. This raises a critical question whether the self-similarity with thermals truly exists or not. The results will be presented at the meeting.

  18. Effect of traffic self-similarity on network performance

    NASA Astrophysics Data System (ADS)

    Park, Kihong; Kim, Gitae; Crovella, Mark E.

    1997-10-01

    Recent measurements of network traffic have shown that self- similarity is an ubiquitous phenomenon present in both local area and wide area traffic traces. In previous work, we have shown a simple, robust application layer causal mechanism of traffic self-similarity, namely, the transfer of files in a network system where the file size distributions are heavy- tailed. In this paper, we study the effect of scale- invariant burstiness on network performance when the functionality of the transport layer and the interaction of traffic sources sharing bounded network resources is incorporated. First, we show that transport layer mechanisms are important factors in translating the application layer causality into link traffic self-similarity. Network performance as captured by throughput, packet loss rate, and packet retransmission rate degrades gradually with increased heavy-tailedness while queueing delay, response time, and fairness deteriorate more drastically. The degree to which heavy-tailedness affects self-similarity is determined by how well congestion control is able to shape a source traffic into an on-average constant output stream while conserving information. Second, we show that increasing network resources such as link bandwidth and buffer capacity results in a superlinear improvement in performance. When large file transfers occur with nonnegligible probability, the incremental improvement in throughput achieved for large buffer sizes is accompanied by long queueing delays vis-a- vis the case when the file size distribution is not heavy- tailed. Buffer utilization continues to remain at a high level implying that further improvement in throughput is only achieved at the expense of a disproportionate increase in queueing delay. A similar trade-off relationship exists between queueing delay and packet loss rate, the curvature of the performance curve being highly sensitive to the degree of self-similarity. Third, we investigate the effect of congestion

  19. Hierarchical Self-Similarity in Group and Crowd Behaviors

    NASA Astrophysics Data System (ADS)

    Ivancevic, Vladimir G.; Reid, Darryn J.

    2015-11-01

    In this Chapter, a nonlinear, complex, Hamiltonian description of socio-cognio-physical dynamics at the oscopic, classical, inter-personal crowd level and microscopic, quantum, intra-personal agent level, is presented, uniquely, in the form of the open Liouville equation. At the microscopic level, this can be considered to be a nonlinear extension of the linear correlation and factor dynamics. This implies the arrow of time in both microscopic and oscopic processes and shows the existence of the formal crowd-agent space-time self-similarity. This in itself shows the existence of a unique control law, which acts on different scales of agent functioning. This self-similar socio-cognio-physical control law enables us to use the crowd dynamics simulator (previously developed at Defence Science & Technology Organisation, Australia), for recursive simulation of individual agents' representation spaces on a cluster of computers.

  20. Self-similar solutions for a nonlinear radiation diffusion equation

    SciTech Connect

    Garnier, Josselin; Malinie, Guy; Saillard, Yves; Cherfils-Clerouin, Catherine

    2006-09-15

    This paper considers the hydrodynamic equations with nonlinear conduction when the internal energy and the opacity have power-law dependences in the density and in the temperature. This system models the situation in which a dense solid is brought into contact with a thermal bath. It supports self-similar solutions that depend on the surface temperature. The self-similar solution can exhibit a shock wave followed by an ablation front if the surface temperature does not increase too fast in time, but it can exhibit a heat front followed by an isothermal shock otherwise. These flows are carefully studied in order to clarify the role of the initial solid density in the energy absorption and the ablation process. Comparisons with numerical simulations show excellent agreement.

  1. Dynamics and processing in finite self-similar networks

    PubMed Central

    DeDeo, Simon; Krakauer, David C.

    2012-01-01

    A common feature of biological networks is the geometrical property of self-similarity. Molecular regulatory networks through to circulatory systems, nervous systems, social systems and ecological trophic networks show self-similar connectivity at multiple scales. We analyse the relationship between topology and signalling in contrasting classes of such topologies. We find that networks differ in their ability to contain or propagate signals between arbitrary nodes in a network depending on whether they possess branching or loop-like features. Networks also differ in how they respond to noise, such that one allows for greater integration at high noise, and this performance is reversed at low noise. Surprisingly, small-world topologies, with diameters logarithmic in system size, have slower dynamical time scales, and may be less integrated (more modular) than networks with longer path lengths. All of these phenomena are essentially mesoscopic, vanishing in the infinite limit but producing strong effects at sizes and time scales relevant to biology. PMID:22378750

  2. Dynamics and processing in finite self-similar networks.

    PubMed

    DeDeo, Simon; Krakauer, David C

    2012-09-07

    A common feature of biological networks is the geometrical property of self-similarity. Molecular regulatory networks through to circulatory systems, nervous systems, social systems and ecological trophic networks show self-similar connectivity at multiple scales. We analyse the relationship between topology and signalling in contrasting classes of such topologies. We find that networks differ in their ability to contain or propagate signals between arbitrary nodes in a network depending on whether they possess branching or loop-like features. Networks also differ in how they respond to noise, such that one allows for greater integration at high noise, and this performance is reversed at low noise. Surprisingly, small-world topologies, with diameters logarithmic in system size, have slower dynamical time scales, and may be less integrated (more modular) than networks with longer path lengths. All of these phenomena are essentially mesoscopic, vanishing in the infinite limit but producing strong effects at sizes and time scales relevant to biology.

  3. Sensitivity of self-similar ZND waves in condensed media

    NASA Astrophysics Data System (ADS)

    Logan, J. David; Woerner, Edwin L.

    A class of one-dimensional, time-dependent, self-similar motions of a reacting fluid where the chemical reaction is initiatied by a strong shock is studied. The chemical source term is assumed to be a simple power law, which can be characteristic of the combustion of condensed materials. The calculations are made in a Lagrangian coordinate system with time measured from the arrival of the shock. The sensitivity of the system with respect to a modeling number k, which is the ratio of chemical to hydrodynamic energy, is examined. For values of k beyond a critical value, the reactive flow is characterized by a singular line beyond which the solution cannot be continued. For these values of k, the self-similar solution is pathological in that the singular line is reached before the reaction ends. For large k, a perturbation solution is obtained.

  4. After notes on self-similarity exponent for fractal structures

    NASA Astrophysics Data System (ADS)

    Fernández-Martínez, Manuel; Caravaca Garratón, Manuel

    2017-06-01

    Previous works have highlighted the suitability of the concept of fractal structure, which derives from asymmetric topology, to propound generalized definitions of fractal dimension. The aim of the present article is to collect some results and approaches allowing to connect the self-similarity index and the fractal dimension of a broad spectrum of random processes. To tackle with, we shall use the concept of induced fractal structure on the image set of a sample curve. The main result in this paper states that given a sample function of a random process endowed with the induced fractal structure on its image, it holds that the self-similarity index of that function equals the inverse of its fractal dimension.

  5. Self-similar radiation from numerical Rosenau-Hyman compactons

    SciTech Connect

    Rus, Francisco Villatoro, Francisco R.

    2007-11-10

    The numerical simulation of compactons, solitary waves with compact support, is characterized by the presence of spurious phenomena, as numerically induced radiation, which is illustrated here using four numerical methods applied to the Rosenau-Hyman K(p, p) equation. Both forward and backward radiations are emitted from the compacton presenting a self-similar shape which has been illustrated graphically by the proper scaling. A grid refinement study shows that the amplitude of the radiations decreases as the grid size does, confirming its numerical origin. The front velocity and the amplitude of both radiations have been studied as a function of both the compacton and the numerical parameters. The amplitude of the radiations decreases exponentially in time, being characterized by a nearly constant scaling exponent. An ansatz for both the backward and forward radiations corresponding to a self-similar function characterized by the scaling exponent is suggested by the present numerical results.

  6. Self-similar breakup of near-inviscid liquids

    NASA Astrophysics Data System (ADS)

    Castrejon-Pita, Alfonso A.; Castrejon-Pita, J. Rafael; Lister, John R.; Hinch, E. John; Hutchings, Ian M.

    2012-11-01

    Experimental results are presented for the final stages of drop pinch-off and ligament breakup for different initial conditions. Water and ethanol were used as working fluids. High-speed imaging and image analysis were utilized in order to determine the contraction rate of the thinning neck and the shape of the liquid thread just before the breakup. Our results show that the geometry of the breakup of near-inviscid fluids is self-similar in the domain of simple dripping. We also demonstrate that, independently of the initial conditions, the necking of these liquids scales with τ 2 / 3, asymptotically giving a unique breakup angle of 18 . 0 +/- 0 .4° . Both observations are in complete agreement with previous theoretical predictions. The angle converges towards self similarity like τ 1 / 2, also as predicted. Project supported by the EPSRC-UK (EP/G029458/1 and EP/H018913/1) and Cambridge-KACST.

  7. Microscopic origin of self-similarity in granular blast waves

    NASA Astrophysics Data System (ADS)

    Barbier, M.; Villamaina, D.; Trizac, E.

    2016-08-01

    The self-similar expansion of a blast wave, well-studied in air, has peculiar counterparts in dense and dissipative media such as granular gases. Recent results have shown that, while the traditional Taylor-von Neumann-Sedov (TvNS) derivation is not applicable to such granular blasts, they can nevertheless be well understood via a combination of microscopic and hydrodynamic insights. In this article, we provide a detailed analysis of these methods associating molecular dynamics simulations and continuum equations, which successfully predict hydrodynamic profiles, scaling properties, and the instability of the self-similar solution. We also present new results for the energy conserving case, including the particle-level analysis of the classic TvNS solution and its breakdown at higher densities.

  8. Ordered Self-Similar Patterns in Anisotropic Stochastic Growth.

    PubMed

    Yao, Zhenwei; Olvera de la Cruz, Monica

    2016-07-07

    We propose an anisotropic stochastic growth model to rationalize the anisotropic self-assembly of supramolecules to form elongated two-dimensional ribbon structures in a recent experiment. The model exhibits distinct growth scenarios that are critically controlled by the ratio of the transverse and the longitudinal growth rate. In the regime of suppressed transverse growth, the model generates the experimentally observed elongated structures through layer-by-layer growing. We further observe the convergence of rough clusters toward smooth regular elliptic patterns by averaging over a number of independent growth processes. Remarkably, these resulting elliptic clusters are self-similar in each instantaneous moment in the growth process. Statistical analysis suggests that the realization of such ordered patterns does not rely on the delicate coordination of different parts in the cluster growth. The self-similarity phenomenon derived from this idealized model may have wider implications, notably in the designed clustering of various elementary building blocks with anisotropic interactions.

  9. Self-Similar Subsets of Symmetric Cantor Sets

    NASA Astrophysics Data System (ADS)

    Zeng, Ying

    This paper concerns the affine embeddings of general symmetric Cantor sets. Under certain condition, we show that if a self-similar set F can be affinely embedded into a symmetric Cantor set E, then their contractions are rationally commensurable. Our result supports Conjecture 1.2 in [D. J. Feng, W. Huang and H. Rao, Affine embeddings and intersections of Cantor sets, J. Math. Pures Appl. 102 (2014) 1062-1079].

  10. Self-similar evolution of nonlinear magnetic bouyancy instability

    NASA Astrophysics Data System (ADS)

    Shibata, K.; Tajima, T.; Matsumoto, R.

    1988-06-01

    A new type of self-similar solution of ideal magnetohydrodynamics in the nonlinear stage of undular mode (k /parallel/ B) of magnetic buoyancy instability (Parker instability or ballooning instability) is found through MHD simulation and theory. The solution has the characteristics of nonlinear instability in Lagrangian coordinates; the fluid velocity and the Alfven speed on each magnetic loop increases exponentially with time, because the loop is evacuated by the field aligned motion of matter due to gravitational acceleration.

  11. Road shape recognition based on scene self-similarity

    NASA Astrophysics Data System (ADS)

    Postnikov, Vassili V.; Krohina, Darya A.; Prun, Victor E.

    2015-02-01

    A method of determining of the road shape and direction is proposed. The road can potentially have curved shape as well as be seen unclearly due to weather effects or relief features. The proposed method uses video taken from frontal camera that is rigidly placed in car as an input data. The method is based on self-similarity of typical road image, i.e. the smaller image inside the road is close to downscaled initial image.

  12. Self-similar Turing patterns: An anomalous diffusion consequence.

    PubMed

    Hernández, D; Herrera-Hernández, E C; Núñez-López, M; Hernández-Coronado, H

    2017-02-01

    In this work, we show that under specific anomalous diffusion conditions, chemical systems can produce well-ordered self-similar concentration patterns through diffusion-driven instability. We also find spiral patterns and patterns with mixtures of rotational symmetries. The type of anomalous diffusion discussed in this work, either subdiffusion or superdiffusion, is a consequence of the medium heterogeneity, and it is modeled through a space-dependent diffusion coefficient with a power-law functional form.

  13. Self-similar Turing patterns: An anomalous diffusion consequence

    NASA Astrophysics Data System (ADS)

    Hernández, D.; Herrera-Hernández, E. C.; Núñez-López, M.; Hernández-Coronado, H.

    2017-02-01

    In this work, we show that under specific anomalous diffusion conditions, chemical systems can produce well-ordered self-similar concentration patterns through diffusion-driven instability. We also find spiral patterns and patterns with mixtures of rotational symmetries. The type of anomalous diffusion discussed in this work, either subdiffusion or superdiffusion, is a consequence of the medium heterogeneity, and it is modeled through a space-dependent diffusion coefficient with a power-law functional form.

  14. A self-similar flash point for highly wound magnetostatics.

    NASA Astrophysics Data System (ADS)

    Lynden-Bell, D.

    A general theorem on force-free fields is proved and applied to highly wound field configurations. In axial-symmetry such configurations expand along a cone of semi-angle 60° as the system is wound up. The self-similar field structure is determined. After 1/√3 turns the system reaches flashpoint with a discharge around this cone releasing toroidal flux loops to infinity.

  15. The self-similarity theory of high pressure torsion.

    PubMed

    Beygelzimer, Yan; Kulagin, Roman; Toth, Laszlo S; Ivanisenko, Yulia

    2016-01-01

    By analyzing the problem of high pressure torsion (HPT) in the rigid plastic formulation, we show that the power hardening law of plastically deformed materials leads to self-similarity of HPT, admitting a simple mathematical description of the process. The analysis shows that the main parameters of HPT are proportional to β (q) , with β being the angle of the anvil rotation. The meaning of the parameter q is: q = 0 for velocity and strain rate, q = 1 for shear strain and von Mises strain, q = n for stress, pressure and torque (n is the exponent of a power hardening law). We conclude that if the hardening law is a power law in a rotation interval β, self-similar regimes can emerge in HPT if the friction with the lateral wall of the die is not too high. In these intervals a simple mathematical description can be applied based on self-similarity. Outside these ranges, the plasticity problem still has to be solved for each value of β. The results obtained have important practical implications for the proper design and analysis of HPT experiments.

  16. Description of interest regions with oriented local self-similarity

    NASA Astrophysics Data System (ADS)

    Liu, Jingneng; Zeng, Guihua

    2012-05-01

    Two novel approaches for extracting distinctive invariant features from interest regions are presented in this paper, i.e., Oriented Local Self-Similarities (OLSS,C) and Simplified and Oriented Local Self-Similarities (SOLSS,C) based on Cartesian location grid and gradient orientation for binning, which are the modified versions of the well-known Local Self-Similarities (LSS,LP) feature based on Log-Polar location grid. They combine the powers of well-known approaches, i.e., the SIFT and the LSS (LP), and are achieved by adopting the SIFT algorithm and using the novel LSS and the proposed simplified LSS feature instead of original gradient feature used in SIFT. Furthermore, a new binning strategy for creating feature histogram is proposed where the gradient orientation for binning is calculated from a larger patch in the diagonal direction. The performance of these oriented OLSS (C) and SOLSS (C) descriptors to image matching is studied through extensive experiments on the INRIA Oxford Affine dataset. Empirical results indicate that the proposed OLSS (C) and SOLSS (C) descriptors yield more stable and robust results, significantly outperform the original LSS (LP) descriptor, and also achieve better performance to the SIFT in these experimental evaluations with various geometric and photometric transformations.

  17. Drop impact on solid surface: Short time self-similarity

    NASA Astrophysics Data System (ADS)

    Philippi, Julien; Lagrée, Pierre-Yves; Antkowiak, Arnaud

    2014-11-01

    Drop impact on a solid surface is a problem with many industrial or environmental applications. Many studies focused on the last stages of this phenomenon as spreading or splashing. In this study we are interested in the early stages of drop impact on solid surface. Inspired by Wagner theory developed by water entry community we shown the self-similar structure of the velocity field and the pressure field. The latter is shown to exhibit a maximum not near the impact point, but rather at the contact line. The motion of the contact line is furthermore shown to exhibit a transition from ``tank treading'' motion to pure sweeping when the lamella appears. We performed numerical simulations with the open-cource code Gerris which are in good agreement with theoretical predictions. Interestingly the inviscid self-similar impact pressure and velocities depend on the self-similar variable r /√{ t} . This allows to construct a seamless uniform analytical solution encompassing both impact and viscous effects. We predict quantitatively observables of interest, such as the evolution of total and maximum viscous shear stresses and net total force. We finally demonstrate that the structure of the flow resembles a stagnation point flow unexpectedly involving r /√{ t} .

  18. The self-similarity theory of high pressure torsion

    PubMed Central

    Beygelzimer, Yan; Toth, Laszlo S; Ivanisenko, Yulia

    2016-01-01

    Summary By analyzing the problem of high pressure torsion (HPT) in the rigid plastic formulation, we show that the power hardening law of plastically deformed materials leads to self-similarity of HPT, admitting a simple mathematical description of the process. The analysis shows that the main parameters of HPT are proportional to βq, with β being the angle of the anvil rotation. The meaning of the parameter q is: q = 0 for velocity and strain rate, q = 1 for shear strain and von Mises strain, q = n for stress, pressure and torque (n is the exponent of a power hardening law). We conclude that if the hardening law is a power law in a rotation interval β, self-similar regimes can emerge in HPT if the friction with the lateral wall of the die is not too high. In these intervals a simple mathematical description can be applied based on self-similarity. Outside these ranges, the plasticity problem still has to be solved for each value of β. The results obtained have important practical implications for the proper design and analysis of HPT experiments. PMID:27826500

  19. Rapidly rotating polytropes in general relativity

    NASA Technical Reports Server (NTRS)

    Cook, Gregory B.; Shapiro, Stuart L.; Teukolsky, Saul A.

    1994-01-01

    We construct an extensive set of equilibrium sequences of rotating polytropes in general relativity. We determine a number of important physical parameters of such stars, including maximum mass and maximum spin rate. The stability of the configurations against quasi-radial perturbations is diagnosed. Two classes of evolutionary sequences of fixed rest mass and entropy are explored: normal sequences which behave very much like Newtonian evolutionary sequences, and supramassive sequences which exist solely because of relativistic effects. Dissipation leading to loss of angular momentum causes a star to evolve in a quasi-stationary fashion along an evolutionary sequence. Supramassive sequences evolve towards eventual catastrophic collapse to a black hole. Prior to collapse, the star must spin up as it loses angular momentum, an effect which may provide an observational precursor to gravitational collapse to a black hole.

  20. Rapidly rotating polytropes in general relativity

    NASA Technical Reports Server (NTRS)

    Cook, Gregory B.; Shapiro, Stuart L.; Teukolsky, Saul A.

    1994-01-01

    We construct an extensive set of equilibrium sequences of rotating polytropes in general relativity. We determine a number of important physical parameters of such stars, including maximum mass and maximum spin rate. The stability of the configurations against quasi-radial perturbations is diagnosed. Two classes of evolutionary sequences of fixed rest mass and entropy are explored: normal sequences which behave very much like Newtonian evolutionary sequences, and supramassive sequences which exist solely because of relativistic effects. Dissipation leading to loss of angular momentum causes a star to evolve in a quasi-stationary fashion along an evolutionary sequence. Supramassive sequences evolve towards eventual catastrophic collapse to a black hole. Prior to collapse, the star must spin up as it loses angular momentum, an effect which may provide an observational precursor to gravitational collapse to a black hole.

  1. Polytropic spheres containing regions of trapped null geodesics

    NASA Astrophysics Data System (ADS)

    Novotný, Jan; Hladík, Jan; Stuchlík, Zdeněk

    2017-02-01

    We demonstrate that in the framework of standard general relativity, polytropic spheres with properly fixed polytropic index n and relativistic parameter σ , giving a ratio of the central pressure pc to the central energy density ρc , can contain a region of trapped null geodesics. Such trapping polytropes can exist for n >2.138 , and they are generally much more extended and massive than the observed neutron stars. We show that in the n - σ parameter space, the region of allowed trapping increases with the polytropic index for intervals of physical interest, 2.138 0.677 from the allowed region. In order to relate the trapping phenomenon to astrophysically relevant situations, we restrict the validity of the polytropic configurations to their extension rextr corresponding to the gravitational mass M ˜2 M⊙ of the most massive observed neutron stars. Then, for the central density ρc˜1 015 g cm-3 , the trapped regions are outside rextr for all values of 2.138 polytropes. The region of trapped null geodesics is located close to the polytrope center and could have a relevant influence on the cooling of such polytropes or binding of gravitational waves in their interior.

  2. Rotating polytropic configurations in the bimetric theory of gravitation

    SciTech Connect

    Chubaryan, E.V.; Sarkisyan, A.V.; Grigoryan, O.A.

    1981-03-01

    The field equations of bimetric gravitation theory are solved for the case of an axisymmetric mass distribution. Numerical solutions are obtained in the first approximation with respect to angular velocity for configurations whose matter conforms to a polytropic equation of state. Integral parameters and the internal structure are calculated for configurations with a polytropic index n = 1, 1.5, 2, 2.5, 3 and for selected values of the relativistic parameter ..cap alpha...

  3. Self-similar evolution of nonlinear magnetic bouyancy instability

    SciTech Connect

    Shibata, K.; Tajima, T.; Matsumoto, R.

    1988-06-01

    A new type of self-similar solution of ideal magnetohydrodynamics in the nonlinear stage of undular mode (k /parallel/ B) of magnetic buoyancy instability (Parker instability or ballooning instability) is found through MHD simulation and theory. The solution has the characteristics of nonlinear instability in Lagrangian coordinates; the fluid velocity and the Alfven speed on each magnetic loop increases exponentially with time, because the loop is evacuated by the field aligned motion of matter due to gravitational acceleration. 10 refs., 3 figs., 1 tab.

  4. Optimal simulated annealing schedules for self similar systems

    NASA Astrophysics Data System (ADS)

    Ergenzinger, K.; Hoffmann, K. H.; Salamon, P.

    1995-06-01

    The successful application of the stochastic optimization method known as simulated annealing can depend very much on the appropriate annealing schedule. While determining optimal schedules for arbitrary complex optimization problems is beyond the current scope, we here determine optimal schedules for a special class of systems with known properties. The state spaces of these special systems have the structure of self similar trees. Using methods of optimal control theory, we are able to predict the optimal schedule analytically for two distinct optimization criteria. These predictions are shown to be in good agreement with numerical results.

  5. Self-similar roughening of drying wet paper.

    PubMed

    Balankin, Alexander S; Morales, Daniel; Susarrey, Orlando; Samayoa, Didier; Trinidad, José Martinez; Marquez, Jesús; García, Rafael

    2006-06-01

    We studied the kinetic roughening dynamics of drying wet paper. The configurations of dry paper sheets are found to be self-similar, rater than self-affine. Accordingly, the paper roughening dynamics corresponds to the new class of anomalous kinetic roughening [J. J. Ramasco, J. M. López, and M. A. Rodríguez, Phys. Rev. Lett. 84, 2199 (2000)], characterized by the equal local and global roughness exponents zeta = alpha = 1 and the dynamic exponent z = 1.0+/-0.2, whereas the spectral roughness exponent alpha(s) > 1 is determined by the long-range correlations characterized by the fractal dimension of D crumpled sheet.

  6. Self-similar infall models for cold dark matter haloes

    NASA Astrophysics Data System (ADS)

    Le Delliou, Morgan Patrick

    2002-04-01

    How can we understand the mechanisms for relaxation and the constitution of the density profile in CDM halo formation? Can the old Self-Similar Infall Model (SSIM) be made to contain all the elements essential for this understanding? In this work, we have explored and improved the SSIM, showing it can at once explain large N-body simulations and indirect observations of real haloes alike. With the use of a carefully-crafted simple shell code, we have followed the accretion of secondary infalls in different settings, ranging from a model for mergers to a distribution of angular momentum for the shells, through the modeling of a central black hole. We did not assume self-similar accretion from initial conditions but allowed for it to develop and used coordinates that make it evident. We found self-similar accretion to appear very prominently in CDM halo formation as an intermediate stable (quasi-equilibrium) stage of Large Scale Structure formation. Dark Matter haloes density profiles are shown to be primarily influenced by non-radial motion. The merger paradigm reveals itself through the SSIM to be a secondary but non-trivial factor in those density profiles: it drives the halo profile towards a unique attractor, but the main factor for universality is still the self-similarity. The innermost density cusp flattening observed in some dwarf and Low Surface Brightness galaxies finds a natural and simple explanation in the SSIM embedding a central black hole. Relaxation in cold collisionless collapse is clarified by the SSIM. It is a continuous process involving only the newly-accreted particles for just a few dynamical times. All memory of initial energy is not lost so relaxation is only moderately violent. A sharp cut off, or population inversion, originates in initial conditions and is maintained through relaxation. It characterises moderately violent relaxation in the system's Distribution Function. Finally, the SSIM has shown this relaxation to arise from phase

  7. Nonlinear Self-Similar Beams of Electromagnetic Waves in Vacuum

    NASA Astrophysics Data System (ADS)

    Vlasov, S. N.

    2015-12-01

    We study nonlinear beams of electromagnetic waves in vacuum. Within the lowest approximation, their structure is determined by the cubic self-focusing nonlinearity, which manifests itself with the maximum intensity in the presence of counterpropagating waves. It is shown that the fields in the beams have no singularities if their power is less than the critical power of the self-focusing. The dependences of the eigenfrequencies of the modes of the quasioptical resonator on the beam power are found. The structure of the fields of these modes corresponds to self-similar wave beams.

  8. ASYMPTOTIC SELF-SIMILAR SOLUTIONS WITH A CHARACTERISTIC TIMESCALE

    SciTech Connect

    Waxman, Eli; Shvarts, Dov

    2010-10-01

    For a wide variety of initial and boundary conditions, adiabatic one-dimensional flows of an ideal gas approach self-similar behavior when the characteristic length scale over which the flow takes place, R, diverges or tends to zero. It is commonly assumed that self-similarity is approached since in the R {yields} {infinity}(0) limit the flow becomes independent of any characteristic length or timescales. In this case, the flow fields f(r, t) must be of the form f(r,t)=t{sup {alpha}}{sub f}F(r/R) with R {proportional_to} ({+-}t){sup {alpha}}. We show that requiring the asymptotic flow to be independent only of characteristic length scales implies a more general form of self-similar solutions, f(r,t)=R{sup {delta}}{sub f}F(r/R) with R-dot {proportional_to}R{sup {delta}}, which includes the exponential ({delta} = 1) solutions, R {proportional_to} e {sup t/{tau}}. We demonstrate that the latter, less restrictive, requirement is the physically relevant one by showing that the asymptotic behavior of accelerating blast waves, driven by the release of energy at the center of a cold gas sphere of initial density {rho} {proportional_to} r {sup -{omega}}, changes its character at large {omega}: the flow is described by 0 {<=} {delta} < 1, R {proportional_to} t {sup 1/(1-{delta})}, solutions for {omega} < {omega}{sub c}, by {delta}>1 solutions with R {proportional_to} (-t){sup 1/({delta}-1)} diverging at finite time (t = 0) for {omega}>{omega}{sub c}, and by exponential solutions for {omega} = {omega}{sub c} ({omega}{sub c} depends on the adiabatic index of the gas, {omega}{sub c} {approx} 8 for 4/3 < {gamma} < 5/3). The properties of the new solutions obtained here for {omega} {>=} {omega}{sub c} are analyzed, and self-similar solutions describing the t>0 behavior for {omega}>{omega}{sub c} are also derived.

  9. The Intrinsic Beauty of Polytropic Spheres in Reduced Variables

    NASA Astrophysics Data System (ADS)

    Caimmi, Roberto

    The concept of reduced variables is revisited with regard to van der Waals' theory and an application is made to polytropic spheres, where the reduced radial coordinate is ${\\rm red}(r)=r/R=\\xi/\\Xi$, $R$ radius, and the reduced density is ${\\rm red}(\\rho)=\\rho/\\lambda=\\theta^n$, $\\lambda$ central density. Reduced density profiles are plotted for several polytropic indexes within the range, $0\\le n\\le5$, disclosing two noticeable features. First, any point of coordinates, $({\\rm red}(r),{\\rm red}(\\rho))$, $0\\le{\\rm red}(r)\\le1$, $0\\le{\\rm red}(\\rho)\\le1$, belongs to a reduced density profile of the kind considered. Second, sufficiently steep i.e. large $n$ reduced density profiles exhibit an oblique inflection point, where the threshold is found to be located at $n=n_{\\rm th}=0.888715$. Reduced pressure profiles, ${\\rm red}(P)=P/\\varpi=\\theta^{n+1}$, $\\varpi$ central pressure, Lane-Emden fucntions, $\\theta=(\\rho/\\lambda)^{1/n}$, and polytropic curves, ${\\rm red}(P)={\\rm red}(P)({\\rm red}(\\rho))$, are also plotted. The method can be extended to nonspherical polytropes with regard to a selected direction, ${\\rm red}(r)(\\mu)=r(\\mu)/R(\\mu)=\\xi(\\mu)/\\Xi(\\mu)$. The results can be extended to polytropic spheres made of collisionless particles, for polytropic index within a more restricted range, $1/2\\le n\\le5$.

  10. Self-similarity criteria in anisotropic flows with viscosity stratification

    NASA Astrophysics Data System (ADS)

    Danaila, L.; Voivenel, L.; Varea, E.

    2017-02-01

    Variable-viscosity flows exhibit a faster trend towards a fully developed turbulent state since fluctuations are produced at a larger amount. A legitimate expectation is that self-similarity to be tenable earlier than in classical, single-viscosity flows. The question which begs to be answered is: which are the self-similarity criteria for variable-viscosity, density-matched, flows? The similarity assumption, i.e., all scales evolve in a similar fashion in space/time, is applied to the transport equation for one- and two-point statistics of anisotropic, variable-viscosity flows. It is shown that the similarity assumption is valid for regions of the flow where viscosity (mean values and the fluctuations root-mean-square) is uniform. In regions where viscosity gradients are important, such as the sheared region and jet boundaries, similarity is not tenable. Our claims are applicable to any decaying flow, isotropic or anisotropic. Support is provided by experimental data obtained in the near field region of a jet issuing into a more viscous environment. The viscosity ratio is 3.5.

  11. On self-similar rupture of thin-film equations

    NASA Astrophysics Data System (ADS)

    Dallaston, Michael; Tseluiko, Dmitri; Zheng, Zhong; Fontelos, Marco; Kalliadasis, Serafim

    2016-11-01

    Many interfacial fluid dynamical settings consist of a thin film in the presence of two physical mechanisms, one stabilizing, typically surface tension, and the other one destabilizing. Examples include the Marangoni instability of a film heated from below, Rayleigh-Taylor instability of a film on a cylinder, and film dewetting due to intermolecular forces. Lubrication-type models of these phenomena lead to very similar equations for the evolution of the film thickness, differing only in the exponent of the coefficient function of the destabilizing term. However, the behavior of solutions can vary, depending on the value of this exponent. Here we report the results of analysis based on self-similarity, elements from dynamical systems theory and fully time-dependent computations. We find that branches of self-similar rupture solutions merge at critical values of the exponent, and, surprisingly, there are no stable solutions beyond the first value at which merging occurs. In this regime, time-dependent computations indicate the existence of a cascade of instabilities of increasingly short wavelengths. This work was supported by the EPSRC under Grant No. EP/K008595/1. The work of DT was partly supported by the EPSRC under Grant No. EP/K041134/1.

  12. Global self-similar protostellar disk/wind models

    NASA Astrophysics Data System (ADS)

    Teitler, Seth A.

    The magnetocentrifugal disk wind mechanism is the leading candidate for producing the large-scale, bipolar jets commonly seen in protostellar systems. I present a detailed formulation of a global, radially self-similar model for a fully general, non-ideal disk that launches a magnetocentrifugal disk wind. This formulation generalizes the conductivity tensor formalism previously used in radially localized disk models to a global disk model. The model involves matching a solution of the equations of non-ideal MHD describing matter in the disk to a solution of the equations of ideal MHD describing a "cold" wind. The disk solution is required to pass smoothly through the sonic point, the wind solution is required to pass smoothly through the Alfven point, and the two solutions must match at the disk/wind interface. This model includes for the first time a self-consistent treatment of the evolution of magnetic flux threading the disk, which can change on the disk accretion timescale. These constraints fix the distribution of the magnetic field threading the disk, the midplane accretion speed, and the midplane migration speed of flux surfaces. Specializing to the case of a disk in the ambipolar diffusivity regime, I present a representative solution using the neutral matter-field coupling constant. I conclude with a brief discussion of the importance of self-similar disk/wind models in studying global processes in protostellar systems.

  13. Kink stability of isothermal spherical self-similar flow revisited

    NASA Astrophysics Data System (ADS)

    Wang, Anzhong; Wu, Yumei

    2006-11-01

    The problem of kink stability of isothermal spherical self-similar flow in newtonian gravity is revisited. Using distribution theory we first develop a general formula of perturbations, linear or non-linear, which consists of three sets of differential equations, one in each side of the sonic line and the other along it. By solving the equations along the sonic line we find explicitly the spectrum, k, of the perturbations, whereby we obtain the stability criterion for the self-similar solutions. When the solutions are smoothly across the sonic line, our results reduce to those of Ori and Piran. To show such obtained perturbations can be matched to the ones in the regions outside the sonic line, we study the linear perturbations in the external region of the sonic line (the ones in the internal region are identically zero), by taking the solutions obtained along the line as the boundary conditions. After properly imposing other boundary conditions at spatial infinity, we are able to show that linear perturbations, satisfying all the boundary conditions, exist and do not impose any additional conditions on k. As a result, the complete treatment of perturbations in the whole spacetime does not alter the spectrum obtained by considering the perturbations only along the sonic line.

  14. Self-similarity and scaling theory of complex networks

    NASA Astrophysics Data System (ADS)

    Song, Chaoming

    Scale-free networks have been studied extensively due to their relevance to many real systems as diverse as the World Wide Web (WWW), the Internet, biological and social networks. We present a novel approach to the analysis of scale-free networks, revealing that their structure is self-similar. This result is achieved by the application of a renormalization procedure which coarse-grains the system into boxes containing nodes within a given "size". Concurrently, we identify a power-law relation between the number of boxes needed to cover the network and the size of the box defining a self-similar exponent, which classifies fractal and non-fractal networks. By using the concept of renormalization as a mechanism for the growth of fractal and non-fractal modular networks, we show that the key principle that gives rise to the fractal architecture of networks is a strong effective "repulsion" between the most connected nodes (hubs) on all length scales, rendering them very dispersed. We show that a robust network comprised of functional modules, such as a cellular network, necessitates a fractal topology, suggestive of a evolutionary drive for their existence. These fundamental properties help to understand the emergence of the scale-free property in complex networks.

  15. A self-similar hierarchy of the Korean stock market

    NASA Astrophysics Data System (ADS)

    Lim, Gyuchang; Min, Seungsik; Yoo, Kun-Woo

    2013-01-01

    A scaling analysis is performed on market values of stocks listed on Korean stock exchanges such as the KOSPI and the KOSDAQ. Different from previous studies on price fluctuations, market capitalizations are dealt with in this work. First, we show that the sum of the two stock exchanges shows a clear rank-size distribution, i.e., the Zipf's law, just as each separate one does. Second, by abstracting Zipf's law as a γ-sequence, we define a self-similar hierarchy consisting of many levels, with the numbers of firms at each level forming a geometric sequence. We also use two exponential functions to describe the hierarchy and derive a scaling law from them. Lastly, we propose a self-similar hierarchical process and perform an empirical analysis on our data set. Based on our findings, we argue that all money invested in the stock market is distributed in a hierarchical way and that a slight difference exists between the two exchanges.

  16. Self-similar relativistic blast waves with energy injection

    NASA Astrophysics Data System (ADS)

    van Eerten, Hendrik

    2014-08-01

    A sufficiently powerful astrophysical source with power-law luminosity in time will give rise to a self-similar relativistic blast wave with a reverse shock travelling into the ejecta and a forward shock moving into the surrounding medium. Once energy injection ceases and the last energy is delivered to the shock front, the blast wave will transit into another self-similar stage depending only on the total amount of energy injected. I describe the effect of limited duration energy injection into environments with density depending on radius as a power law, emphasizing optical/X-ray Gamma-ray Burst afterglows as applications. The blast wave during injection is treated analytically, the transition following last energy injection with one-dimensional simulations. Flux equations for synchrotron emission from the forward and reverse shock regions are provided. The reverse shock emission can easily dominate, especially with different magnetizations for both regions. Reverse shock emission is shown to support both the reported X-ray and optical correlations between afterglow plateau duration and end time flux, independently of the luminosity power-law slope. The model is demonstrated by application to bursts 120521A and 090515, and can accommodate their steep post-plateau light-curve slopes.

  17. Incoherent exciton trapping in self-similar aperiodic lattices

    SciTech Connect

    Dominguez-Adame, F.; Macia, E. ); Sanchez, A. Escuela Politecnica Superior, Universidad Carlos III de Madrid, C./Butarque 15, E-28911 Leganes, Madrid )

    1995-01-01

    Incoherent exciton dynamics in one-dimensional perfect lattices with traps at sites arranged according to aperiodic deterministic sequences is studied. We focus our attention on Thue-Morse and Fibonacci systems as canonical examples of self-similar aperiodic systems. Solving numerically the corresponding master equation we evaluate the survival probability and the mean-square displacement of an exciton initially created at a single site. Results are compared to systems of the same size with the same concentration of traps randomly as well as periodically distributed over the whole lattice. Excitons progressively extend over the lattice on increasing time and, in this sense, they act as a probe of the particular arrangements of traps in each system considered. The analysis of the characteristic features of their time decay indicates that exciton dynamics in self-similar aperiodic arrangements of traps is quite close to that observed in periodic ones, but differs significantly from that corresponding to random lattices. We also report on characteristic features of exciton motion suggesting that Fibonacci and Thue-Morse orderings might be clearly observed by appropriate experimental measurements. In the conclusions we comment on the implications of our work on the way towards a unified theory of the ordering of matter.

  18. Vere-Jones' self-similar branching model.

    PubMed

    Saichev, A; Sornette, D

    2005-11-01

    Motivated by its potential application to earthquake statistics as well as for its intrinsic interest in the theory of branching processes, we study the exactly self-similar branching process introduced recently by Vere-Jones. This model extends the ETAS class of conditional self-excited branching point-processes of triggered seismicity by removing the problematic need for a minimum (as well as maximum) earthquake size. To make the theory convergent without the need for the usual ultraviolet and infrared cutoffs, the distribution of magnitudes m' of daughters of first-generation of a mother of magnitude m has two branches m < m' with exponent beta - d and m' > m with exponent beta + d, where beta and d are two positive parameters. We investigate the condition and nature of the subcritical, critical, and supercritical regime in this and in an extended version interpolating smoothly between several models. We predict that the distribution of magnitudes of events triggered by a mother of magnitude m over all generations has also two branches m' < m with exponent and with exponent beta - h, with h=d squareroot of (1-s), where s is the fraction of triggered events. This corresponds to a renormalization of the exponent d into h by the hierarchy of successive generations of triggered events. For a significant part of the parameter space, the distribution of magnitudes over a full catalog summed over an average steady flow of spontaneous sources (immigrants) reproduces the distribution of the spontaneous sources with a single branch and is blind to the exponents beta, d of the distribution of triggered events. Since the distribution of earthquake magnitudes is usually obtained with catalogs including many sequences, we conclude that the two branches of the distribution of aftershocks are not directly observable and the model is compatible with real seismic catalogs. In summary, the exactly self-similar Vere-Jones model provides an attractive new approach to model triggered

  19. Vere-Jones' self-similar branching model

    NASA Astrophysics Data System (ADS)

    Saichev, A.; Sornette, D.

    2005-11-01

    Motivated by its potential application to earthquake statistics as well as for its intrinsic interest in the theory of branching processes, we study the exactly self-similar branching process introduced recently by Vere-Jones. This model extends the ETAS class of conditional self-excited branching point-processes of triggered seismicity by removing the problematic need for a minimum (as well as maximum) earthquake size. To make the theory convergent without the need for the usual ultraviolet and infrared cutoffs, the distribution of magnitudes m' of daughters of first-generation of a mother of magnitude m has two branches m'm with exponent β+d , where β and d are two positive parameters. We investigate the condition and nature of the subcritical, critical, and supercritical regime in this and in an extended version interpolating smoothly between several models. We predict that the distribution of magnitudes of events triggered by a mother of magnitude m over all generations has also two branches m'm with exponent β+h , with h=d1-s , where s is the fraction of triggered events. This corresponds to a renormalization of the exponent d into h by the hierarchy of successive generations of triggered events. For a significant part of the parameter space, the distribution of magnitudes over a full catalog summed over an average steady flow of spontaneous sources (immigrants) reproduces the distribution of the spontaneous sources with a single branch and is blind to the exponents β,d of the distribution of triggered events. Since the distribution of earthquake magnitudes is usually obtained with catalogs including many sequences, we conclude that the two branches of the distribution of aftershocks are not directly observable and the model is compatible with real seismic catalogs. In summary, the exactly self-similar Vere-Jones model provides an attractive new approach to model triggered seismicity, which

  20. Vere-Jones' self-similar branching model

    SciTech Connect

    Saichev, A.; Sornette, D.

    2005-11-01

    Motivated by its potential application to earthquake statistics as well as for its intrinsic interest in the theory of branching processes, we study the exactly self-similar branching process introduced recently by Vere-Jones. This model extends the ETAS class of conditional self-excited branching point-processes of triggered seismicity by removing the problematic need for a minimum (as well as maximum) earthquake size. To make the theory convergent without the need for the usual ultraviolet and infrared cutoffs, the distribution of magnitudes m{sup '} of daughters of first-generation of a mother of magnitude m has two branches m{sup '}m with exponent {beta}+d, where {beta} and d are two positive parameters. We investigate the condition and nature of the subcritical, critical, and supercritical regime in this and in an extended version interpolating smoothly between several models. We predict that the distribution of magnitudes of events triggered by a mother of magnitude m over all generations has also two branches m{sup '}m with exponent {beta}+h, with h=d{radical}(1-s), where s is the fraction of triggered events. This corresponds to a renormalization of the exponent d into h by the hierarchy of successive generations of triggered events. For a significant part of the parameter space, the distribution of magnitudes over a full catalog summed over an average steady flow of spontaneous sources (immigrants) reproduces the distribution of the spontaneous sources with a single branch and is blind to the exponents {beta},d of the distribution of triggered events. Since the distribution of earthquake magnitudes is usually obtained with catalogs including many sequences, we conclude that the two branches of the distribution of aftershocks are not directly observable and the model is compatible with real seismic catalogs. In summary, the exactly self-similar Vere-Jones model provides an

  1. Self-similarity and scaling in forest communities

    PubMed Central

    Simini, Filippo; Anfodillo, Tommaso; Carrer, Marco; Banavar, Jayanth R.; Maritan, Amos

    2010-01-01

    Ecological communities exhibit pervasive patterns and interrelationships between size, abundance, and the availability of resources. We use scaling ideas to develop a unified, model-independent framework for understanding the distribution of tree sizes, their energy use, and spatial distribution in tropical forests. We demonstrate that the scaling of the tree crown at the individual level drives the forest structure when resources are fully used. Our predictions match perfectly with the scaling behavior of an exactly solvable self-similar model of a forest and are in good accord with empirical data. The range, over which pure power law behavior is observed, depends on the available amount of resources. The scaling framework can be used for assessing the effects of natural and anthropogenic disturbances on ecosystem structure and functionality. PMID:20375286

  2. Obtaining self-similar scalings in focusing flows

    NASA Astrophysics Data System (ADS)

    Dijksman, Joshua; Mukhopadhyay, Shomeek; Gaebler, Cameron; Witelski, Thomas; Behringer, Robert

    The surface structure of converging thin fluid films displays self-similar behavior, as was shown in the work by Diez et al [Q. Appl. Math 210, 155, 1990]. Extracting the related similarity scaling exponents from either numerical or experimental data is non-trivial. Here we provide two such methods. We apply them to experimental and numerical data on converging fluid films driven by both surface tension and gravitational forcing. In the limit of pure gravitational driving, we recover Diez' semi-analytic result, but our methods also allow us to explore the entire regime of mixed capillary and gravitational driving, up to entirely surface tension driven flows. We find scaling forms of smoothly varying exponents up to surprisingly small Bond numbers. Our experimental results are in reasonable agreement with our numerical simulations, which confirm theoretically obtained relations between the scaling exponents.

  3. Obtaining self-similar scalings in focusing flows

    NASA Astrophysics Data System (ADS)

    Dijksman, Joshua A.; Mukhopadhyay, Shomeek; Gaebler, Cameron; Witelski, Thomas P.; Behringer, Robert P.

    2015-10-01

    The surface structure of converging thin fluid films displays self-similar behavior, as was shown in the work by Diez et al. [Q. Appl. Math. 210, 155 (1990)]. Extracting the related similarity scaling exponents from either numerical or experimental data is nontrivial. Here we provide two such methods. We apply them to experimental and numerical data on converging fluid films driven by both surface tension and gravitational forcing. In the limit of pure gravitational driving, we recover Diez' semianalytic result, but our methods also allow us to explore the entire regime of mixed capillary and gravitational driving, up to entirely surface-tension-driven flows. We find scaling forms of smoothly varying exponents up to surprisingly small Bond numbers. Our experimental results are in reasonable agreement with our numerical simulations, which confirm theoretically obtained relations between the scaling exponents.

  4. Vacuum self similar anisotropic cosmologies in F( R)-gravity

    NASA Astrophysics Data System (ADS)

    Apostolopoulos, Pantelis S.

    2017-04-01

    The implications from the existence of a proper Homothetic Vector Field on the dynamics of vacuum anisotropic models in F( R) gravitational theory are studied. The fact that every Spatially Homogeneous vacuum model is equivalent, formally, with a "flux"-free anisotropic fluid model in standard gravity and the induced power-law form of the functional F( R) due to self-similarity enable us to close the system of equations. We found some new exact anisotropic solutions that arise as fixed points in the associated dynamical system. The non-existence of Kasner-like (Bianchi type I) solutions in proper F( R)-gravity (i.e. R≠ 0) strengthens the belief that curvature corrections will prevent the shear influence into the past thus permitting an isotropic singularity. We also discuss certain issues regarding the lack of vacuum models of type III, IV, VIIh in comparison with the corresponding results in standard gravity.

  5. Self-similar expansion of a warm dense plasma

    SciTech Connect

    Djebli, Mourad; Moslem, Waleed M.

    2013-07-15

    The properties of an expanding plasma composed of degenerate electron fluid and non-degenerate ions are studied. For our purposes, we use fluid equations for ions together with the electron momentum equation that include quantum forces (e.g., the quantum statistical pressure, forces due to the electron-exchange and electron correlations effects) and the quasi-neutrality condition. The governing equation is written in a tractable form by using a self-similar transformation. Numerical results for typical beryllium plasma parameters revealed that, during the expansion, the ion acoustic speed decreases for both isothermal and adiabatic ion pressure. When compared with classical hydrodynamic plasma expansion model, the electrons and ions are found to initially escape faster in vacuum creating thus an intense electric field that accelerates most of the particles into the vacuum ahead of the plasma expansion. The relevancy of the present model to beryllium plasma produced by a femto-second laser is highlighted.

  6. Self-similar blast waves incorporating deflagrations of variable speed

    NASA Technical Reports Server (NTRS)

    Guirguis, R. H.; Kamel, M. M.; Oppenheim, A. K.

    1983-01-01

    The present investigation is concerned with the development of a systematic approach to the problem of self-similar blast waves incorporating nonsteady flames. The regime covered by the presented solutions is bounded on one side by an adiabatic strong explosion and, on the other, by deflagration propagating at an infinite acceleration. Results for a representative set of accelerations are displayed, taking into account the full range of propagation speeds from zero to velocities corresponding to the Chapman-Jouguet deflagration. It is found that the distribution of stored energy in the undisturbed medium determines the acceleration of the deflagration-shock wave system. The obtained results reveal the existence of a simple relation between the location of the deflagration and its Mach number.

  7. Apparent multifractality of self-similar Lévy processes

    NASA Astrophysics Data System (ADS)

    Zamparo, Marco

    2017-07-01

    Scaling properties of time series are usually studied in terms of the scaling laws of empirical moments, which are the time average estimates of moments of the dynamic variable. Nonlinearities in the scaling function of empirical moments are generally regarded as a sign of multifractality in the data. We show that, except for the Brownian motion, this method fails to disclose the correct monofractal nature of self-similar Lévy processes. We prove that for this class of processes it produces apparent multifractality characterised by a piecewise-linear scaling function with two different regimes, which match at the stability index of the considered process. This result is motivated by previous numerical evidence. It is obtained by introducing an appropriate stochastic normalisation which is able to cure empirical moments, without hiding their dependence on time, when moments they aim at estimating do not exist.

  8. Digital image analysis of self-similar cell profiles.

    PubMed

    Nonnenmacher, T F; Baumann, G; Barth, A; Losa, G A

    1994-10-01

    Many biological objects appear to have self-similar structures which can be characterized by their fractal dimension D. However, applications of the concept of fractal geometry are rather scarce in cell and tissue biology. Here we adapt and analyse critically 3 methods of digital image analysis to measure D of cellular profiles. As prototype examples we investigate in detail 2 samples of cells: (i) human T-lymphocytes from normal donors, and (ii) hairy leukemic cells. It is shown that D correlates to the structural complexity of the individual cell contour. The calculated D values for cells out of the same cell line scatter around a mean value D = 1.15 for T-lymphocytes (S.D. = 0.03) and D = 1.34 for hairy leukemic cells (S.D. = 0.04). Consequently, we interprete D as a statistical measure for the sample's fractal dimension.

  9. Self-similar blast waves incorporating deflagrations of variable speed

    NASA Technical Reports Server (NTRS)

    Guirguis, R. H.; Kamel, M. M.; Oppenheim, A. K.

    1983-01-01

    The present investigation is concerned with the development of a systematic approach to the problem of self-similar blast waves incorporating nonsteady flames. The regime covered by the presented solutions is bounded on one side by an adiabatic strong explosion and, on the other, by deflagration propagating at an infinite acceleration. Results for a representative set of accelerations are displayed, taking into account the full range of propagation speeds from zero to velocities corresponding to the Chapman-Jouguet deflagration. It is found that the distribution of stored energy in the undisturbed medium determines the acceleration of the deflagration-shock wave system. The obtained results reveal the existence of a simple relation between the location of the deflagration and its Mach number.

  10. Self-similarity Detection via Multi-scale Image Analysis

    NASA Astrophysics Data System (ADS)

    Kamejima, Kohji

    A dynamic scheme is presented for generating multi-scale images associated with self-similar patterns. By blurring with a small scale parameter, brightness distributions are extended to geometrically singular fractal patterns. Through weighted averaging with respect to scale factors, a multi-scale image is generated as a representation of the conditional probability for capturing unknown attractors. The local structure of the multi-scale image is analyzed to demonstrate the structural consistency of the capturing probability with respect to the imaging process associated with the attractor. By extracting stochastic features based on the capturing probability, a computational scheme is introduced for matching observed attractors with a preassigned dictionary of patterns. Proposed method was verified by simulation studies.

  11. Infrared image super-resolution via transformed self-similarity

    NASA Astrophysics Data System (ADS)

    Qi, Wei; Han, Jing; Zhang, Yi; Bai, Lian-fa

    2017-03-01

    Single image super-resolution is of great importance in computer vision. Various methods (e.g. learning methods) have been successfully developed in recent years. Despite the demonstrated success in the natural images, less research focuses on the infrared images. In this paper, we present a transformed self-similarity based super-resolution method without any learning priors, restore high-resolution infrared images from low-resolution ones. We exploit appearance similarity, dense error, and region covariances, and use the detected cues to guide the patch search process. We also add scale cue to consider local scale variations. We then present a compositional framework to simultaneously accommodate the four different cues. Experimental results demonstrate that our method performs better than previous methods, restores pleasant results, and high evaluate scores further show the effectiveness and robustness of our method for the infrared images.

  12. Estimation for time-changed self-similar stochastic processes

    NASA Astrophysics Data System (ADS)

    Arroum, W.; Jones, O. D.

    2005-12-01

    We consider processes of the form X(t) = X ~(θ(t)) where X ~ is a self-similar process with stationary increments and θ is a deterministic subordinator with a periodic activity function a = θ'> 0. Such processes have been proposed as models for high-frequency financial data, such as currency exchange rates, where there are known to be daily and weekly periodic fluctuations in the volatility, captured here by the periodic activity function. We review an existing estimator for the activity function then propose three new methods for estimating it and present some experimental studies of their performance. We finish with an application to some foreign exchange and FTSE100 futures data.

  13. Self-similarity of higher-order moving averages

    NASA Astrophysics Data System (ADS)

    Arianos, Sergio; Carbone, Anna; Türk, Christian

    2011-10-01

    In this work, higher-order moving average polynomials are defined by straightforward generalization of the standard moving average. The self-similarity of the polynomials is analyzed for fractional Brownian series and quantified in terms of the Hurst exponent H by using the detrending moving average method. We prove that the exponent H of the fractional Brownian series and of the detrending moving average variance asymptotically agree for the first-order polynomial. Such asymptotic values are compared with the results obtained by the simulations. The higher-order polynomials correspond to trend estimates at shorter time scales as the degree of the polynomial increases. Importantly, the increase of polynomial degree does not require to change the moving average window. Thus trends at different time scales can be obtained on data sets with the same size. These polynomials could be interesting for those applications relying on trend estimates over different time horizons (financial markets) or on filtering at different frequencies (image analysis).

  14. Characterizing self-similarity in bacteria DNA sequences

    NASA Astrophysics Data System (ADS)

    Lu, Xin; Sun, Zhirong; Chen, Huimin; Li, Yanda

    1998-09-01

    In this paper some parametric methods are introduced to characterize the self-similarity of DNA sequences. Compared with Fourier analysis, these methods perform statistically more stably and yield more reliable results. Using these methods, eight whole genomes of bacteria provided by NCBI are analyzed. Long-range correlation properties in the nucleotide density distribution along these DNA sequences are explored. Estimation results show that the long-range correlation structure prevails through the entire molecule of DNA. Higher order statistics through coarse graining reveal that rather than multifractal, there are only monofractal phenomena presented in the sequences. Hence, the nucleotide density distribution can be modeled asymptotically as fractional Gaussian noise. This result points to a new direction for analyzing and understanding the intrinsic structures of DNA sequences.

  15. Self-similar and diffusive expansion of nonextensive plasmas

    SciTech Connect

    Akbari-Moghanjoughi, M.

    2015-03-15

    Exact analytical self-similar solution is presented for free collisionless expansion of a two-component plasma of inertial ions and nonextensive electrons into vacuum, using the generalized nonextensive velocity distribution for electrons. Furthermore, a hydrodynamic model of plasma expansion in the presence of the ambipolar diffusion caused by collisions among the plasma species, such as electrons and ions, is developed and a Fokker-Planck-like generalized diffusion equation for steady-state expansion of a nonextensive electron-ion plasma is derived. For the case of generalized statistics and in the absence of particle diffusion, the density, velocity, electric potential, and field of expansion profiles are exactly obtained and studied in terms of the self-similar parameter. It is found that superthermal electrons lead to an accelerated expansion of plasma compared to that of Maxwellian electrons. It is also revealed that the nonextensivity parameter plays a fundamental role on the density, velocity, electric potential, and field configuration of the expansion. Therefore, one is able to distinguish three different regimes q < 1, q = 1, and q > 1 for expansion corresponding to sub-nonextensive, extensive, and super-nonextensive statistical profiles for electrons, respectively. Current research can provide useful information and suggests techniques for investigation of the involved statistical mechanism on the role of the energetic electron fluid in the expansion of plasma in strong pulsed laser-matter interaction experiments. It is also shown that the particle diffusion expansion mechanism becomes more dominant for relatively large values of the nonextensivity parameter, q.

  16. Global Self-similar Protostellar Disk/Wind Models

    NASA Astrophysics Data System (ADS)

    Teitler, Seth

    2011-05-01

    The magnetocentrifugal disk wind mechanism is the leading candidate for producing the large-scale, bipolar jets commonly seen in protostellar systems. I present a detailed formulation of a global, radially self-similar model for a non-ideal disk that launches a magnetocentrifugal wind. This formulation generalizes the conductivity tensor formalism previously used in radially localized disk models. The model involves matching a solution of the equations of non-ideal magnetohydrodynamics (MHD) describing matter in the disk to a solution of the equations of ideal MHD describing a "cold" wind. The disk solution must pass smoothly through the sonic point, the wind solution must pass smoothly through the Alfvén point, and the two solutions must match at the disk/wind interface. This model includes for the first time a self-consistent treatment of the evolution of magnetic flux threading the disk, which can change on the disk accretion timescale. The formulation presented here also allows a realistic conductivity profile for the disk to be used in a global disk/wind model for the first time. The physical constraints on the model solutions fix the distribution of the magnetic field threading the disk, the midplane accretion speed, and the midplane migration speed of flux surfaces. I present a representative solution that corresponds to a disk in the ambipolar conductivity regime with a nominal neutral-matter-magnetic-field coupling parameter that is constant along field lines, matched to a wind solution. I conclude with a brief discussion of the importance of self-similar disk/wind models in studying global processes such as dust evolution in protostellar systems. Presented as a dissertation to the Department of Astronomy and Astrophysics, The University of Chicago, in partial fulfillment of the requirements for the PhD degree.

  17. Mosaic, Self-Similarity Logic, and Biological Attraction principles

    PubMed Central

    Baluška, František; Barlow, Peter W; Guidolin, Diego

    2009-01-01

    From a structural standpoint, living organisms are organized like a nest of Russian matryoshka dolls, in which structures are buried within one another. From a temporal point of view, this type of organization is the result of a history comprised of a set of time backcloths which have accompanied the passage of living matter from its origins up to the present day. The aim of the present paper is to indicate a possible course of this ‘passage through time, and suggest how today’s complexity has been reached by living organisms. This investigation will employ three conceptual tools, namely the Mosaic, Self-Similarity Logic, and the Biological Attraction principles. Self-Similarity Logic indicates the self-consistency by which elements of a living system interact, irrespective of the spatiotemporal level under consideration. The term Mosaic indicates how, from the same set of elements assembled according to different patterns, it is possible to arrive at completely different constructions: hence, each system becomes endowed with different emergent properties. The Biological Attraction principle states that there is an inherent drive for association and merging of compatible elements at all levels of biological complexity. By analogy with the gravitation law in physics, biological attraction is based on the evidence that each living organism creates an attractive field around itself. This field acts as a sphere of influence that actively attracts similar fields of other biological systems, thereby modifying salient features of the interacting organisms. Three specific organizational levels of living matter, namely the molecular, cellular, and supracellular levels, have been considered in order to analyse and illustrate the interpretative as well as the predictive roles of each of these three explanatory principles. PMID:20195461

  18. A nonlinear eigenvalue problem for self-similar spherical force-free magnetic fields

    SciTech Connect

    Lerche, I.; Low, B. C.

    2014-10-15

    An axisymmetric force-free magnetic field B(r, θ) in spherical coordinates is defined by a function r sin θB{sub φ}=Q(A) relating its azimuthal component to its poloidal flux-function A. The power law r sin θB{sub φ}=aA|A|{sup 1/n}, n a positive constant, admits separable fields with A=(A{sub n}(θ))/(r{sup n}) , posing a nonlinear boundary-value problem for the constant parameter a as an eigenvalue and A{sub n}(θ) as its eigenfunction [B. C. Low and Y. Q Lou, Astrophys. J. 352, 343 (1990)]. A complete analysis is presented of the eigenvalue spectrum for a given n, providing a unified understanding of the eigenfunctions and the physical relationship between the field's degree of multi-polarity and rate of radial decay via the parameter n. These force-free fields, self-similar on spheres of constant r, have basic astrophysical applications. As explicit solutions they have, over the years, served as standard benchmarks for testing 3D numerical codes developed to compute general force-free fields in the solar corona. The study presented includes a set of illustrative multipolar field solutions to address the magnetohydrodynamics (MHD) issues underlying the observation that the solar corona has a statistical preference for negative and positive magnetic helicities in its northern and southern hemispheres, respectively; a hemispherical effect, unchanging as the Sun's global field reverses polarity in successive eleven-year cycles. Generalizing these force-free fields to the separable form B=(H(θ,φ))/(r{sup n+2}) promises field solutions of even richer topological varieties but allowing for φ-dependence greatly complicates the governing equations that have remained intractable. The axisymmetric results obtained are discussed in relation to this generalization and the Parker Magnetostatic Theorem. The axisymmetric solutions are mathematically related to a family of 3D time-dependent ideal MHD solutions for a polytropic fluid of index γ = 4/3 as

  19. General relativistic polytropes with a repulsive cosmological constant

    NASA Astrophysics Data System (ADS)

    Stuchlík, Zdeněk; Hledík, Stanislav; Novotný, Jan

    2016-11-01

    Spherically symmetric equilibrium configurations of perfect fluid obeying a polytropic equation of state are studied in spacetimes with a repulsive cosmological constant. The configurations are specified in terms of three parameters—the polytropic index n , the ratio of central pressure and central energy density of matter σ , and the ratio of energy density of vacuum and central density of matter λ . The static equilibrium configurations are determined by two coupled first-order nonlinear differential equations that are solved by numerical methods with the exception of polytropes with n =0 corresponding to the configurations with a uniform distribution of energy density, when the solution is given in terms of elementary functions. The geometry of the polytropes is conveniently represented by embedding diagrams of both the ordinary space geometry and the optical reference geometry reflecting some dynamical properties of the geodesic motion. The polytropes are represented by radial profiles of energy density, pressure, mass, and metric coefficients. For all tested values of n >0 , the static equilibrium configurations with fixed parameters n , σ , are allowed only up to a critical value of the cosmological parameter λc=λc(n ,σ ). In the case of n >3 , the critical value λc tends to zero for special values of σ . The gravitational potential energy and the binding energy of the polytropes are determined and studied by numerical methods. We discuss in detail the polytropes with an extension comparable to those of the dark matter halos related to galaxies, i.e., with extension ℓ>100 kpc and mass M >1 012 M⊙ . For such largely extended polytropes, the cosmological parameter relating the vacuum energy to the central density has to be larger than λ =ρvac/ρc˜10-9. We demonstrate that the extension of the static general relativistic polytropic configurations cannot exceed the so-called static radius related to their external spacetime, supporting the idea

  20. Hierarchical, Self-Similar Structure in Native Squid Pen

    NASA Astrophysics Data System (ADS)

    Yang, Fei-Chi; Peters, Robert; Dies, Hannah; Rheinstadter, Maikel

    2014-03-01

    Proteins, chitin and keratin form the elementary building blocks of many biomaterials. How these molecules assemble into larger, macroscopic structures with very different properties is the fundamental question we are trying to answer. Squid pen is a transparent backbone inside the squid, which supports the mantle of the squid. The pens show a hierarchical, self-similar structure under the microscope and the AFM with fibers from 500 μm to 0.2 μm in diameter. The chitin molecules form nano-crystallites of monoclinic lattice symmetry surrounded by a protein layer, resulting in β-chitin nano-fibrils. Signals corresponding to the α-coil protein phase and β-chitin were observed in X-ray experiments in-situ. The molecular structure is highly anisotropic with 90% of the α-coils and β-chitin crystallites oriented along the fiber-axis indicating a strong correlation between the structures on millimeters down to the molecular scale. This research was funded by NSERC, NRC, CFI, and the Ontario Ministry of Economic Development and Innovation.

  1. Subshifts of finite type and self-similar sets

    NASA Astrophysics Data System (ADS)

    Jiang, Kan; Dajani, Karma

    2017-02-01

    Let K\\subset {R} be a self-similar set generated by some iterated function system. In this paper we prove, under some assumptions, that K can be identified with a subshift of finite type. With this identification, we can calculate the Hausdorff dimension of K as well as the set of elements in K with unique codings using the machinery of Mauldin and Williams (1988 Trans. Am. Math. Soc. 309 811-29). We give three different applications of our main result. Firstly, we calculate the Hausdorff dimension of the set of points of K with multiple codings. Secondly, in the setting of β-expansions, when the set of all the unique codings is not a subshift of finite type, we can calculate in some cases the Hausdorff dimension of the univoque set. Motivated by this application, we prove that the set of all the unique codings is a subshift of finite type if and only if it is a sofic shift. This equivalent condition was not mentioned by de Vries and Komornik (2009 Adv. Math. 221 390-427, theorem 1.8). Thirdly, for the doubling map with asymmetrical holes, we give a sufficient condition such that the survivor set can be identified with a subshift of finite type. The third application partially answers a problem posed by Alcaraz Barrera (2014 PhD Thesis University of Manchester).

  2. Dyslexic and skilled reading dynamics are self-similar.

    PubMed

    Holden, John G; Greijn, Lieke T; van Rooij, Marieke M J W; Wijnants, Maarten L; Bosman, Anna M T

    2014-10-01

    The shape of a word pronunciation time distribution supplies information about the dynamic interactions that support reading performance. Speeded word-naming pronunciation and response time distributions were collected from 20 sixth grade Dutch students with dyslexia and 23 age-matched controls. The participants' pronunciation times were modeled and contrasted with a lognormal inverse power-law mixture distribution. Identical contrasts were also conducted on the same participants' response time distributions derived from flanker, color-naming, and arithmetic tasks. Results indicated that children with dyslexia yield slower, broader, and more variable pronunciation time distributions than their age-matched counterparts. This difference approximated a self-similar rescaling between the two group's aggregate pronunciation time distributions. Moreover, children with dyslexia produced similar, but less prominent trends toward slower and more variable performance across the three non-reading tasks. The outcomes support a proportional continuum rather than a localized deficit account of dyslexia. The mixture distribution's success at describing the participants' pronunciation and response time distributions suggests that differences in proportional contingencies among low-level neurophysiological, perceptual, and cognitive processes likely play a prominent role in the etiology of dyslexia.

  3. Self-similar Theory of Wind-driven Sea

    NASA Astrophysics Data System (ADS)

    Zakharov, V. E.

    2015-12-01

    More than two dozens field experiments performed in the ocean and on the lakes show that the fetch-limited growth of dimensionless energy and dimensionless peak frequency is described by powerlike functions of the dimensionless fetch. Moreover, the exponents of these two functions are connected with a proper accuracy by the standard "magic relation", 10q-2p=1. Recent massive numerical experiments as far as experiments in wave tanks also confirm this magic relation. All these experimental facts can be interpreted in a framework of the following simple theory. The wind-driven sea is described by the "conservative" Hasselmann kinetic equation. The source terms, wind input and white-capping dissipation, play a secondary role in comparison with the nonlinear term Snl that is responsible for the four-wave resonant interaction. This equation has four-parameter family of self-similar solutions. The magic relation holds for all numbers of this family. This fact gives strong hope that development of self-consistent analytic theory of wind-driven sea is quite realizable task.

  4. Extended void merging tree algorithm for self-similar models

    NASA Astrophysics Data System (ADS)

    Russell, Esra

    2014-02-01

    In hierarchical evolution, voids exhibit two different behaviours related with their surroundings and environments, they can merge or collapse. These two different types of void processes can be described by the two-barrier excursion set formalism based on Brownian random walks. In this study, the analytical approximate description of the growing void merging algorithm is extended by taking into account the contributions of voids that are embedded into overdense region(s) which are destined to vanish due to gravitational collapse. Following this, to construct a realistic void merging model that consists of both collapse and merging processes, the two-barrier excursion set formalism of the void population is used. Assuming spherical voids in the Einstein-de Sitter Universe, the void merging algorithm which allows us to consider the two main processes of void hierarchy in one formalism is constructed. In addition to this, the merger rates, void survival probabilities, void size distributions in terms of the collapse barrier and finally, the void merging tree algorithm in the self-similar models are defined and derived.

  5. Sorted self-similarity for multi-modal image registration.

    PubMed

    Kasiri, Keyvan; Fieguth, Paul; Clausi, David A

    2016-08-01

    In medical image analysis, registration of multimodal images has been challenging due to the complex intensity relationship between images. Classical multi-modal registration approaches evaluate the degree of the alignment by measuring the statistical dependency of the intensity values between images to be aligned. Employing statistical similarity measures, such as mutual information, is not promising in those cases with complex and spatially dependent intensity relations. A new similarity measure is proposed based on the assessing the similarity of pixels within an image, based on the idea that similar structures in an image are more probable to undergo similar intensity transformations. The most significant pixel similarity values are considered to transmit the most significant self-similarity information. The proposed method is employed in a framework to register different modalities of real brain scans and the performance of the method is compared to the conventional multi-modal registration approach. Quantitative evaluation of the method demonstrates the better registration accuracy in both rigid and non-rigid deformations.

  6. A parametric study of self-similar blast waves.

    NASA Technical Reports Server (NTRS)

    Oppenheim, A. K.; Kuhl, A. L.; Lundstrom, E. A.; Kamel, M. M.

    1972-01-01

    Comprehensive examination of self-similar blast waves with respect to two parameters, one describing the front velocity and the other the variation of the ambient density immediately ahead of the front. All possible front trajectories are taken into account, including limiting cases of the exponential and logarithmic form. The structure of the waves is analyzed by means of a phase plane defined in terms of two reduced coordinates. Loci of extrema of the integral curves in the phase plane are traced, and loci of singularities are determined on the basis of their intersections. Boundary conditons are introduced for the case where the medium into which the waves propagate is at rest. Representative solutions, pertaining to all the possible cases of blast waves bounded by shock fronts propagating into an atmosphere of uniform density, are obtained by evaluating the integral curves and determining the corresponding profiles of the gasdynamic parameters. Particular examples of integral curves for waves bounded by detonations are given, and all the degenerate solutions corresponding to cases where the integral curve is reduced to a point are delineated.

  7. Self-similar energetics in large clusters of galaxies.

    PubMed

    Miniati, Francesco; Beresnyak, Andrey

    2015-07-02

    Massive galaxy clusters are filled with a hot, turbulent and magnetized intra-cluster medium. Still forming under the action of gravitational instability, they grow in mass by accretion of supersonic flows. These flows partially dissipate into heat through a complex network of large-scale shocks, while residual transonic (near-sonic) flows create giant turbulent eddies and cascades. Turbulence heats the intra-cluster medium and also amplifies magnetic energy by way of dynamo action. However, the pattern regulating the transformation of gravitational energy into kinetic, thermal, turbulent and magnetic energies remains unknown. Here we report that the energy components of the intra-cluster medium are ordered according to a permanent hierarchy, in which the ratio of thermal to turbulent to magnetic energy densities remains virtually unaltered throughout the cluster's history, despite evolution of each individual component and the drive towards equipartition of the turbulent dynamo. This result revolves around the approximately constant efficiency of turbulence generation from the gravitational energy that is freed during mass accretion, revealed by our computational model of cosmological structure formation. The permanent character of this hierarchy reflects yet another type of self-similarity in cosmology, while its structure, consistent with current data, encodes information about the efficiency of turbulent heating and dynamo action.

  8. Critical ignition in rapidly expanding self-similar flows

    NASA Astrophysics Data System (ADS)

    Radulescu, Matei I.; McN. Maxwell, Brian

    2010-11-01

    The generic problem of ignition of a particle undergoing an expansion given by a power law rate of decay behind a decaying shock is addressed in the present study. It is demonstrated, using a one-step Arrhenius irreversible reaction, that a sufficiently strong expansion wave can quench the reaction. The critical conditions for extinction are obtained in closed form in terms of the time scale for the expansion process and the thermo-chemical properties of the gas, yielding a critical Damkohler number, i.e. the ratio of the expansion time scale to the homogeneous ignition time scale, given by (γ-1)Ea/RT-1/n, where n is the power law exponent of the self-similar expansion ρ˜t^-n. The critical ignition criteria, which is valid in the asymptotic limit n(γ-1)(Ea/RT)=O(1), was found in excellent agreement with numerical results. The applicability of the results obtained are discussed for ignition in rapidly expanding flows which occur behind decaying shock waves, as encountered in problems of detonation initiation by a Taylor-Sedov blast wave, and reacting jet start-up, and for reactions in steady hypersonic flows around projectiles.

  9. Interfacial thin films rupture and self-similarity

    NASA Astrophysics Data System (ADS)

    Ward, Margaret H.

    2011-06-01

    Two superposed thin layers of fluids are prone to interfacial instabilities due to London-van der Waals forces. Evolution equations for the film thicknesses are derived using lubrication theory. Using the intrinsic scales, for a single layer, results in a system with parametric dependence of four ratios of the two layers: surface tension, Hamaker constant, viscosity, and film thickness. In contrast to the single layer case, the bilayer system has two unstable eigenmodes: squeezing and bending. For some particular parameter regimes, the system exhibits the avoided crossing behavior, where the two eigenmodes are interchanged. Based on numerical analysis, the system evolves into four different rupture states: basal layer rupture, upper layer rupture, double layer rupture, and mixed layer rupture. The ratio of Hamaker constants and the relative film thickness of the two layers control the system dynamics. Remarkably, the line of avoided crossing demarks the transition region of mode mixing and energy transfer, affecting the scaling of the dynamical regime map consequentially. Asymptotic and numerical analyses are used to examine the self-similar ruptures and to extract the power law scalings for both the basal layer rupture and the upper layer rupture. The scaling laws for the basal layer rupture are the same as those of the single layer on top of a substrate. The scaling laws for the upper layer rupture are different: the lateral length scale decreases according to (tr-t)1/3 and the film thickness decreases according to (tr-t)1/6.

  10. Convergence to Self-Similar Regimes in Thin Polymer Films

    NASA Astrophysics Data System (ADS)

    Benzaquen, Michael; Salez, Thomas; Raphaël, Elie; Elie Raphaël Team; Kari Dalnoki-Veress Team

    2013-03-01

    The surface of a thin liquid film with nonconstant curvature is unstable, as the Laplace pressure drives a flow mediated by viscosity. Recent experiments and theory applied to stepped polymer films have shown excellent agreement and provide a technique for the study of polymer confinement, the glass transition, and slip at the fluid substrate interface to name a few. The thin film equation governs the evolution of the free surface profile in the lubrication approximation. Despite many efforts, this equation remains only partially solved. We present an analytical and numerical study of the thin film equation. Linearising this equation enables us to derive the Green's function of the problem and therefore obtain a complete set of solutions. We show that the solutions of the problem with equilibrium boundary conditions uniformly converge in time towards a first kind self-similar universal attractor. A numerical study enables us to extend our results to the nonlinear thin film equation. Laboratoire Physico-Chimie Théorique, UMR CNRS 7083 Gulliver. ESPCI, 10 rue Vauquelin, 75005, Paris, France.

  11. Integrable geodesic flows and super polytropic gas equations

    NASA Astrophysics Data System (ADS)

    Guha, Partha

    2003-06-01

    The polytropic gas equations are shown to be the geodesic flows with respect to an L2 metric on the semidirect product space Diff( S1)⊙ C∞( S1), where Diff( S1) is the group of orientation preserving diffeomorphisms of the circle. We also show that the N=1 supersymmetric polytropic gas equation constitute an integrable geodesic flow on the extended Neveu-Schwarz space. Recently other kinds of supersymmetrizations have been studied vigorously in connection with superstring theory and are called supersymmetric-B (SUSY-B) extension. In this paper we also show that the SUSY-B extension of the polytropic gas equation form a geodesic flow on the extension of the Neveu-Schwarz space.

  12. Modeling the Losses of Dissolved CO(2) from Laser-Etched Champagne Glasses.

    PubMed

    Liger-Belair, Gérard

    2016-04-21

    Under standard champagne tasting conditions, the complex interplay between the level of dissolved CO2 found in champagne, its temperature, the glass shape, and the bubbling rate definitely impacts champagne tasting by modifying the neuro-physicochemical mechanisms responsible for aroma release and flavor perception. On the basis of theoretical principles combining heterogeneous bubble nucleation, ascending bubble dynamics, and mass transfer equations, a global model is proposed, depending on various parameters of both the wine and the glass itself, which quantitatively provides the progressive losses of dissolved CO2 from laser-etched champagne glasses. The question of champagne temperature was closely examined, and its role on the modeled losses of dissolved CO2 was corroborated by a set of experimental data.

  13. Champagne experiences various rhythmical bubbling regimes in a flute.

    PubMed

    Liger-Belair, Gérard; Tufaile, Alberto; Jeandet, Philippe; Sartorelli, José-Carlos

    2006-09-20

    Bubble trains are seen rising gracefully from a few points on the glass wall (called nucleation sites) whenever champagne is poured into a glass. As time passes during the gas-discharging process, the careful observation of some given bubble columns reveals that the interbubble distance may change suddenly, thus revealing different rhythmical bubbling regimes. Here, it is reported that the transitions between the different bubbling regimes of some nucleation sites during gas discharging is a process which may be ruled by a strong interaction between tiny gas pockets trapped inside the nucleation site and/or also by an interaction between the tiny bubbles just blown from the nucleation site.

  14. A self-similar solution for thermal disc winds

    NASA Astrophysics Data System (ADS)

    Clarke, C. J.; Alexander, R. D.

    2016-08-01

    We derive a self-similar description for the 2D streamline topology and flow structure of an axisymmetric, thermally driven wind originating from a disc in which the density is a power-law function of radius. Our scale-free solution is strictly only valid in the absence of gravity or centrifugal support; comparison with 2D hydrodynamic simulations of winds from Keplerian discs however demonstrates that the scale-free solution is a good approximation also in the outer regions of such discs, and can provide a reasonable description even for launch radii well within the gravitational radius of the flow. Although other authors have considered the flow properties along streamlines whose geometry has been specified in advance, this is the first isothermal calculation in which the flow geometry and variation of flow variables along streamlines is determined self-consistently. It is found that the flow trajectory is very sensitive to the power-law index of radial density variation in the disc: the steeper the density gradient, the stronger is the curvature of streamlines close to the flow base that is required in order to maintain momentum balance perpendicular to the flow. Steeper disc density profiles are also associated with more rapid acceleration, and a faster fall-off of density, with height above the disc plane. The derivation of a set of simple governing equations for the flow structure of thermal winds from the outer regions of power-law discs offers the possibility of deriving flow observables without having to resort to hydrodynamical simulation.

  15. Flow property and self-similarity in steady hydraulic jumps

    NASA Astrophysics Data System (ADS)

    Lin, Chang; Hsieh, Shih-Chun; Lin, I.-Ju; Chang, Kuang-An; Raikar, Rajkumar V.

    2012-11-01

    The flow structure in a steady hydraulic jump in both the non-aerated and aerated regions was measured using the image-based particle image velocimetry and bubble image velocimetry techniques, respectively. Three highly aerated steady jumps with Froude numbers varying from 4.51 to 5.35 were tested, and a weak jump with a Froude number of 2.43 was generated for comparison. Mean velocities and turbulence statistics were obtained by ensemble averaging the repeated velocity measurements. Based on the mean velocities, the flow structure in the steady jumps was classified into four regions to distinguish their distinct flow behaviors; they are the potential core region, the boundary layer region, the mixing layer region, and the recirculation region. The flow structure in the weak jump features only three regions without the recirculation region. In addition, spatial variations of mean velocities, turbulence intensity, and Reynolds stresses were also presented. It was observed that the maximum horizontal bubble velocity and maximum horizontal water velocity occur at the same location in the overlapping regions of potential core and mixing layer. The ratio between the maximum horizontal bubble velocity and maximum horizontal water velocity is between 0.6 and 0.8, depending on the Froude number. Examining the mean horizontal bubble velocities in the mixing layer, a similarity profile was revealed with representative mixing layer thickness as the characteristic length scale and the difference between the maximum positive and maximum negative velocities as the characteristic velocity scale. It was also found that the mean horizontal water velocities in the near-wall region are self-similar and behave like a wall jet. Further analyzing autocorrelation functions and energy spectra of the water and bubble velocity fluctuations found that the energy spectra in the water region follow the -5/3 slope, whereas the spectra in the bubble region follow a -2/5 slope. In addition, the

  16. Unveiling CO2 heterogeneous freezing plumes during champagne cork popping.

    PubMed

    Liger-Belair, Gérard; Cordier, Daniel; Honvault, Jacques; Cilindre, Clara

    2017-09-14

    Cork popping from clear transparent bottles of champagne stored at different temperatures (namely, 6, 12, and 20 °C) was filmed through high-speed video imaging in the visible light spectrum. During the cork popping process, a plume mainly composed of gaseous CO2 with traces of water vapour freely expands out of the bottleneck through ambient air. Most interestingly, for the bottles stored at 20 °C, the characteristic grey-white cloud of fog classically observed above the bottlenecks of champagne stored at lower temperatures simply disappeared. It is replaced by a more evanescent plume, surprisingly blue, starting from the bottleneck. We suggest that heterogeneous freezing of CO2 occurs on ice water clusters homogeneously nucleated in the bottlenecks, depending on the saturation ratio experienced by gas-phase CO2 after adiabatic expansion (indeed highly bottle temperature dependent). Moreover, and as observed for the bottles stored at 20 °C, we show that the freezing of only a small portion of all the available CO2 is able to pump the energy released through adiabatic expansion, thus completely inhibiting the condensation of water vapour found in air packages adjacent to the gas volume gushing out of the bottleneck.

  17. Metabolic influence of Botrytis cinerea infection in champagne base wine.

    PubMed

    Hong, Young-Shick; Cilindre, Clara; Liger-Belair, Gerard; Jeandet, Philippe; Hertkorn, Norbert; Schmitt-Kopplin, Philippe

    2011-07-13

    Botrytis cinerea infection of grape berries leads to changes in the chemical composition of grape and the corresponding wine and, thus, affects wine quality. The metabolic effect of Botrytis infection in Champagne base wine was investigated through a (1)H NMR-based metabolomic approach. Isoleucine, leucine, threonine, valine, arginine, proline, glutamine, γ-aminobutyric acid (GABA), succinate, malate, citrate, tartarate, fructose, glucose, oligosaccharides, amino acid derivatives, 2,3-butanediol, acetate, glycerol, tyrosine, 2-phenylethanol, trigonelline, and phenylpropanoids in a grape must and wine were identified by (1)H NMR spectroscopy and contributed to metabolic differentiations between healthy and botrytized wines by using multivariate statistical analysis such as principal component analysis (PCA). Lowered levels of glycerol, 2,3-butanediol, succinate, tyrosine, valine derivative, and phenylpropanoids but higher levels of oligosaccharides in the botrytized wines were main discriminant metabolites, demonstrating that Botrytis infection of grape caused the fermentative retardation during alcoholic fermentation because the main metabolites responsible for the differentiation are fermentative products. Moreover, higher levels of several oligosaccharides in the botrytized wines also indicated the less fermentative behavior of yeast in the botrytized wines. This study highlights a metabolomic approach for better understanding of the comprehensive metabolic influences of Botrytis infection of grape berries in Champagne wines.

  18. Numerical Modeling of Tidal Effects in Polytropic Accretion Discs

    NASA Technical Reports Server (NTRS)

    Godon, P.

    1996-01-01

    A two-dimensional time-dependent hybrid Fourier-Chebyshev method of collocation is developed and used for the study of tidal effects in accretion discs, under the assumption of a polytropic equation of state and a standard alpha viscosity prescription.

  19. Stability of charged thin shell wormhole supported by polytropic gas

    NASA Astrophysics Data System (ADS)

    Eid, A.

    2017-05-01

    In the framework of Darmois-Israel formalism, the general equations describing the motion of thin shell wormhole with a general form of equation of state of a polytropic gas are derived. The mechanical stability analysis of thin shell wormhole with charge in Reissner-Nordstrom (RN) to linearized spherically symmetric perturbation about static equilibrium solution is carried out.

  20. A varying polytropic gas universe and phase space analysis

    NASA Astrophysics Data System (ADS)

    Khurshudyan, M.

    2016-05-01

    In this paper, we will consider a phenomenological model of a dark fluid that is able to explain an accelerated expansion of our low redshift universe and the phase transition to this accelerated expanding universe. Recent developments in modern cosmology towards understanding of the accelerated expansion of the large scale universe involve various scenarios and approaches. Among these approaches, one of well-known and accepted practice is modeling of the content of our universe via dark fluid. There are various models of dark energy fluid actively studied in recent literature and polytropic gas is among them. In this work, we will consider a varying polytropic gas which is a phenomenological modification of polytropic gas. Our model of varying polytropic dark fluid has been constructed to analogue to a varying Chaplygin gas actively discussed in the literature. We will consider interacting models, where dark matter is a pressureless fluid, to have a comprehensive picture. Phase space analysis is an elegant mathematical tool to earn general understanding of large scale universe and easily see an existence of a solution to cosmological coincidence problem. Imposing some constraints on parameters of the models, we found late time attractors for each case analytically. Cosmological consequences for the obtained late time attractors are discussed.

  1. Warm-Polytropic Cosmology with and Without Bulk Viscosity

    NASA Astrophysics Data System (ADS)

    Saadat, Hassan

    2014-12-01

    In this paper we consider warm-polytropic cosmology including bulk viscosity and study cosmological parameters. We can obtain effect of viscosity on the important cosmological parameters such as Hubble expansion, deceleration and scale factor parameters. We compare our results with observational data and fix our solution. We find that the bulk viscosity increases both energy density and Hubble expansion parameter.

  2. Linear and nonlinear dynamic instability of rotating polytropes

    NASA Astrophysics Data System (ADS)

    Williams, Harold A.; Tohline, Joel E.

    1987-04-01

    A three-dimensional hydrodynamic computer program is used to study the growth of nonaxisymmetric structures in rapidly rotating, self-gravitating polytropes. Models with polytropic index n = 0.8, 1.0, 1.3, 1.5, and 1.8 are studied. The initially axisymmetric equilibria are constructed by the Ostriker-Mark self-consistent-field method. The nonaxisymmetric pattern that develops out of low-amplitude random noise is a two-armed spiral with a well-defined pattern speed and growth rate which closely match properties of the toroidal mode predicted from the linear, second-order tensor-virial equation. A Fourier analysis of each polytrope's azimuthal density distribution shows that, even in the linear amplitude regime, higher-order angular patterns also develop exponentially in time. The higher-order patterns ultimately move in synchronization with the broad two-armed spiral, creating a narrow two-armed spiral. As the polytropic index is decreased, a more open and centrally more barlike pattern develops.

  3. Kinetics of CO(2) fluxes outgassing from champagne glasses in tasting conditions: the role of temperature.

    PubMed

    Liger-Belair, Gérard; Villaume, Sandra; Cilindre, Clara; Jeandet, Philippe

    2009-03-11

    Measurements of CO(2) fluxes outgassing from a flute poured with a standard Champagne wine initially holding about 11 g L(-1) of dissolved CO(2) were presented, in tasting conditions, all along the first 10 min following the pouring process. Experiments were performed at three sets of temperature, namely, 4 degrees C, 12 degrees C, and 20 degrees C, respectively. It was demonstrated that the lower the champagne temperature, the lower CO(2) volume fluxes outgassing from the flute. Therefore, the lower the champagne temperature, the lower its progressive loss of dissolved CO(2) concentration with time, which constitutes the first analytical proof that low champagne temperatures prolong the drink's chill and helps retains its effervescence. A correlation was also proposed between CO(2) volume fluxes outgassing from the flute poured with champagne and its continuously decreasing dissolved CO(2) concentration. Finally, the contribution of effervescence to the global kinetics of CO(2) release was discussed and modeled by the use of results developed over recent years. The temperature dependence of the champagne viscosity was found to play a major role in the kinetics of CO(2) outgassing from a flute. On the basis of this bubbling model, the theoretical influence of champagne temperature on CO(2) volume fluxes outgassing from a flute was discussed and found to be in quite good accordance with our experimental results.

  4. Locations of accretion shocks around galaxy clusters and the ICM properties: insights from self-similar spherical collapse with arbitrary mass accretion rates

    NASA Astrophysics Data System (ADS)

    Shi, Xun

    2016-09-01

    Accretion shocks around galaxy clusters mark the position where the infalling diffuse gas is significantly slowed down, heated up, and becomes a part of the intracluster medium (ICM). They play an important role in setting the ICM properties. Hydrodynamical simulations have found an intriguing result that the radial position of this accretion shock tracks closely the position of the `splashback radius' of the dark matter, despite the very different physical processes that gas and dark matter experience. Using the self-similar spherical collapse model for dark matter and gas, we find that an alignment between the two radii happens only for a gas with an adiabatic index of γ ≈ 5/3 and for clusters with moderate mass accretion rates. In addition, we find that some observed ICM properties, such as the entropy slope and the effective polytropic index lying around ˜1.1-1.2, are captured by the self-similar spherical collapse model, and are insensitive to the mass accretion history.

  5. Comparison of the transmission properties of self-similar, periodic, and random multilayers at normal incidence.

    PubMed

    Ponge, Marie-Fraise; Jacob, Xavier; Gibiat, Vincent

    2014-06-01

    The effect of self-similarity on acoustic and elastic wave propagation at normal incidence is investigated using Classical Cantor and Fibonacci multilayered structures. They are made of two sorts of orthotropic plies having differently oriented orthotropic axes with respect to the propagation direction. The properties of their transmission coefficient are presented using a unidirectional numerical model based on a transfer matrix formalism. It was found that stack self-similarity influences the acoustic transmission properties. Transmission coefficients of self-similar stacks present a self-similar shape and behavior. A self-similar process, applied to layer orientation allows multilayered stacks to be created. A thickness-equivalent model was developed to compare these structures with standard self-similar multilayers which are finally compared to periodic and random stacks. The transmission coefficient of a deterministic self-similar Fibonacci structure is similar to that of an averaged transmission coefficient of random stacks.

  6. Phenolic composition of champagnes from Chardonnay and Pinot Noir vintages.

    PubMed

    Chamkha, Mohamed; Cathala, Bernard; Cheynier, Véronique; Douillard, Roger

    2003-05-07

    Nineteen phenolic compounds including hydroxybenzoic acids, hydroxycinnamic acids, flavonoids, phenolic alcohols, and phenolic aldehydes have been identified and quantified in two monovarietal champagnes, Chardonnay and Pinot Noir, by using a reverse-phase high-performance liquid chromatography (HPLC) system coupled with diode array detection. The identification of four hydroxycinnamic tartaric esters (caftaric, coutaric, fertaric, and 2-S-glutathionylcaftaric acids), two flavanonols (astilbin and engeletin), and some other compounds was confirmed by HPLC coupled with mass spectrometry. Caftaric acid and tyrosol were the major phenols. Hydroxybenzoic acids and flavonoids were present at low concentrations. The phenolic compositions of 2000 and 2001 Chardonnay and Pinot Noir vary quantitatively according to the year and the variety, but the chemical natures of the molecules are the same. The total phenolic content determined by colorimetric measurement ranges from 176 to 195 mg/L of gallic acid equivalent and is similar to that described in white wines.

  7. Brushed Target on Rock 'Champagne' in Gusev Crater

    NASA Technical Reports Server (NTRS)

    2005-01-01

    NASA's Mars Exploration Rover Spirit took this microscopic image of a target called 'Bubbles' on a rock called 'Champagne' after using its rock abrasion tool to brush away a coating of dust. The circular brushed area is about 5 centimeters (2 inches) across. This rock is different from rocks out on the plains of Gusev Crater but is similar to other rocks in this area of the 'Columbia Hills' in that it has higher levels of phosphorus. Plagioclase, a mineral commonly found in igneous rocks, is also present in these rocks, according to analysis with the minature thermal emission spectrometer. By using the alpha particle X-ray spectrometer to collect data over multiple martian days, or sols, scientists are also beginning to get measurements of trace elements in these rocks. Spirit took the images that are combined into this mosaic on sol 354 (Dec. 30, 2004).

  8. Abraded Target on Rock 'Champagne' in Gusev Crater

    NASA Technical Reports Server (NTRS)

    2005-01-01

    NASA's Mars Exploration Rover Spirit took this microscopic image of a target called 'Bubbles' on a rock called 'Champagne' after using its rock abrasion tool to grind a hole through the rock's outer surface. The circular area where the rock's interior is exposed is about 5 centimeters (2 inches) across. This rock is different from rocks out on the plains of Gusev Crater but is similar to other rocks in this area of the 'Columbia Hills' in that it rich in phosphorus. Plagioclase, a mineral commonly found in igneous rocks, is also present in these rocks, according to analysis with Spirit's miniature thermal emission spectrometer. By using the rover's alpha particle X-ray spectrometer to collect data for multiple martian days, or sols, scientists are also beginning to get measurements of trace elements in the rocks. Spirit took the images that are combined into this mosaic on sol 358 (Jan. 3, 2005).

  9. Consistency of f(R) gravity models around solar polytropes

    NASA Astrophysics Data System (ADS)

    Henttunen, K.; Vilja, I.

    2014-04-01

    It is stated that a class of f(R) gravity models seem to obtain ΛCDM behavior for high redshifts and general relativistic behavior locally at high curvatures. In the present Letter, we numerically study polytropic configurations that resemble stars like young sun with Hu and Sawicki's f(R) gravity field equations and compare the spacetime at the boundary to the general relativistic counterpart. These polytropes are stationary spherically symmetric configurations and have regular metrics at the origin. Since Birkhoff's theorem does not apply for modified gravity, the solution outside may deviate from Schwarzschild-de Sitter spacetime. At the boundary, Post-Newtonian parametrization was used to determine how much the studied model deviates from the general relativistic ΛCDM model.

  10. Interpersonal attraction and personality: what is attractive--self similarity, ideal similarity, complementarity or attachment security?

    PubMed

    Klohnen, Eva C; Luo, Shanhong

    2003-10-01

    Little is known about whether personality characteristics influence initial attraction. Because adult attachment differences influence a broad range of relationship processes, the authors examined their role in 3 experimental attraction studies. The authors tested four major attraction hypotheses--self similarity, ideal-self similarity, complementarity, and attachment security--and examined both actual and perceptual factors. Replicated analyses across samples, designs, and manipulations showed that actual security and self similarity predicted attraction. With regard to perceptual factors, ideal similarity, self similarity, and security all were significant predictors. Whereas perceptual ideal and self similarity had incremental predictive power, perceptual security's effects were subsumed by perceptual ideal similarity. Perceptual self similarity fully mediated actual attachment similarity effects, whereas ideal similarity was only a partial mediator.

  11. From bubble bursting to droplet evaporation in the context of champagne aerosols

    NASA Astrophysics Data System (ADS)

    Seon, Thomas; Ghabache, Elisabeth; Antkowiak, Arnaud; Liger-Belair, Gerard

    2015-11-01

    As champagne or sparkling wine is poured into a glass, a myriad of ascending bubbles collapse and therefore radiate a multitude of tiny droplets above the free surface into the form of very characteristic and refreshing aerosols. Because these aerosols have been found to hold the organoleptic ``essence'' of champagne they are believed to play a crucial role in the flavor release in comparison with that from a flat wine for example. Based on the model experiment of a single bubble bursting in idealized champagnes, the velocity, radius and maximum height of the first jet drop following bubble collapse have been characterized, with varying bubble size and liquid properties in the context of champagne aerosols. Using the experimental results and simple theoretical models for drop and surface evaporation, we show that bubble bursting aerosols drastically enhance the transfer of liquid in the atmosphere with respect to a flat liquid surface. Contrary to popular opinion, we exhibit that small bubbles are negative in terms of aroma release, and we underline bubble radii enabling to optimize the droplet height and evaporation in the whole range of champagne properties. These results pave the road to the fine tuning of champagne aroma diffusion, a major issue of the sparkling wine industry.

  12. Composite Polytrope Models of Molecular Clouds. I. Theory

    NASA Astrophysics Data System (ADS)

    Curry, Charles L.; McKee, Christopher F.

    2000-01-01

    We construct spherical, hydrostatic models of dense molecular cores and Bok globules consisting of two distinct, spatially separate gas components: a central, isothermal region surrounded by a negative-index, polytropic envelope. The clouds are supported against their own self-gravity by a combination of thermal, mean magnetic, and turbulent wave pressure. The latter two are included by allowing for locally adiabatic, nonisentropic pressure components. Such models are meant to represent, in a schematic manner, the velocity and density structure of cores and globules, as inferred from molecular line and dust continuum observations. In addition, our picture reflects the theoretical expectation that MHD wave motions, which are important at scales >~0.1 pc in typical low-mass star-forming regions, are damped at smaller scales, giving rise to a finite-sized, thermally dominated core region. We show that if the pressure components are isentropic, then the pressure drop from the center to the edge of the composite polytropes we consider is limited to 197, the square of the value for the Bonnor-Ebert sphere. If the pressure components are nonisentropic, it is possible to have arbitrarily large pressure drops, in agreement with the recent work of McKee & Holliman. However, we find that even for nonisentropic pressure components, the ratio of the mean to surface pressure in the composite polytropes we consider is less than 4. We show by explicit construction that it is possible to have dense cores comparable to the Jeans mass embedded in stable clouds of much larger mass. In a subsequent paper, we show that composite polytropes on the verge of gravitational instability can reproduce the observed velocity and density structure of cores and globules under a variety of physical conditions.

  13. Is scalar-tensor gravity consistent with polytropic stellar models?

    SciTech Connect

    Henttunen, K.; Vilja, I. E-mail: vilja@utu.fi

    2015-05-01

    We study the scalar field potential V(φ) in the scalar-tensor gravity with self-consistent polytropic stellar configurations. Without choosing a particular potential, we numerically derive the potential inside various stellar objects. We restrict the potential to conform to general relativity or to f(R) gravity inside and require the solution to arrive at SdS vacuum at the surface. The studied objects are required to obtain observationally valid masses and radii corresponding to solar type stars, white dwarfs and neutron stars. We find that the resulting scalar-tensor potential V(φ) for the numerically derived polytrope that conforms to general relativity, in each object class, is highly dependent on the matter configuration as well as on the vacuum requirement at the boundary. As a result, every stellar configuration arrives at a potential V(φ) that is not consistent with the other stellar class potentials. Therefore, a general potential that conforms to all these polytropic stellar classes could not be found.

  14. Fractality and scale-free effect of a class of self-similar networks

    NASA Astrophysics Data System (ADS)

    Xi, Lifeng; Wang, Lihong; Wang, Songjing; Yu, Zhouyu; Wang, Qin

    2017-07-01

    In this paper, given an initial directed graph as a self-similar pattern and fix two nodes in the pattern, we can iterate the graph by replacing any directed edge with the initial graph of pattern and identifying the fixed nodes of pattern with the endpoints of directed edge. Using the iteration again and again, we obtain a family of growing self-similar networks. Modify these networks to be undirected ones, we obtain growing self-similar undirected networks. We obtain the fractality of our self-similar networks and find out the scale-free effect in terms of the matrix related to two fixed nodes in the initial graph.

  15. Self-similar evolutions of parabolic, Hermite-Gaussian, and hybrid optical pulses: Universality and diversity.

    PubMed

    Chen, Shihua; Yi, Lin; Guo, Dong-Sheng; Lu, Peixiang

    2005-07-01

    Three novel types of self-similar solutions, termed parabolic, Hermite-Gaussian, and hybrid pulses, of the generalized nonlinear Schrödinger equation with varying dispersion, nonlinearity, and gain or absorption are obtained. The properties of the self-similar evolutions in various nonlinear media are confirmed by numerical simulations. Despite the diversity of their formations, these self-similar pulses exhibit many universal features which can facilitate significantly the achievement of well-defined linearly chirped output pulses from an optical fiber, an amplifier, or an absorption medium, under certain parametric conditions. The other intrinsic characteristics of each type of self-similar pulses are also discussed.

  16. Polytropic dark matter flows illuminate dark energy and accelerated expansion

    NASA Astrophysics Data System (ADS)

    Kleidis, K.; Spyrou, N. K.

    2015-04-01

    Currently, a large amount of data implies that the matter constituents of the cosmological dark sector might be collisional. An attractive feature of such a possibility is that, it can reconcile dark matter (DM) and dark energy (DE) in terms of a single component, accommodated in the context of a polytropic-DM fluid. In fact, polytropic processes in a DM fluid have been most successfully used in modeling dark galactic haloes, thus significantly improving the velocity dispersion profiles of galaxies. Motivated by such results, we explore the time evolution and the dynamical characteristics of a spatially-flat cosmological model, in which, in principle, there is no DE at all. Instead, in this model, the DM itself possesses some sort of fluidlike properties, i.e., the fundamental units of the Universe matter-energy content are the volume elements of a DM fluid, performing polytropic flows. In this case, together with all the other physical characteristics, we also take the energy of this fluid's internal motions into account as a source of the universal gravitational field. This form of energy can compensate for the extra energy, needed to compromise spatial flatness, namely, to justify that, today, the total energy density parameter is exactly unity. The polytropic cosmological model, depends on only one free parameter, the corresponding (polytropic) exponent, Γ. We find this model particularly interesting, because for Γ ≤ 0.541, without the need for either any exotic DE or the cosmological constant, the conventional pressure becomes negative enough so that the Universe accelerates its expansion at cosmological redshifts below a transition value. In fact, several physical reasons, e.g., the cosmological requirement for cold DM (CDM) and a positive velocity-of-sound square, impose further constraints on the value of Γ, which is eventually settled down to the range -0.089 < Γ ≤ 0. This cosmological model does not suffer either from the age problem or from the

  17. Champagne Groove Lipectomy: A Safe Technique to Contour the Upper Abdomen in Abdominoplasty

    PubMed Central

    Brooks, Ron; Chowdhry, Saeed; Tutela, John Paul; Kelishadi, Sean; Yonick, David; Choo, Joshua; Wilhelmi, Bradon J.

    2017-01-01

    Objective: Combined liposuction and abdominoplasty, or lipoabdominoplasty, is particularly helpful in sculpting a more aesthetically pleasing abdominal contour, particularly in the supraumbilical midline groove. This groove, coined the “champagne groove” by one of our patients, is a frequently sought-after attribute by patients. However, liposuction adds time and cost to an already costly abdominoplasty. We sought to create this groove without the addition of liposuction, utilizing what we call a champagne groove lipectomy. This study reports on our champagne groove lipectomy technique and compares our complication rates with those reported in the literature for standard abdominoplasty techniques. Methods: This is a retrospective review of a single surgeon's experience at our institution over a 6-year period (2007-2012). A total of 74 patients undergoing consecutive abdominoplasty were studied, all female nonsmokers. Two groups were recognized: 64 of 74 patients underwent abdominoplasty, partial belt lipectomy, and champagne groove lipectomy, while 10 of 74 patients underwent fleur-de-lis abdominoplasty without champagne groove lipectomy. Results: Overall, 10 of 74 patients (13.5%) suffered some type of complication, which compares favorably with reported rates in the literature. The majority of complications were related to delayed wound healing or superficial wound dehiscence. Among those patients who underwent champagne groove lipectomy, complications occurred in 6 of 64 patients (9.3%), versus 4 of 10 (40%) patients undergoing fleur-de-lis abdominoplasty. Conclusions: Champagne groove lipectomy is a cost-effective alternative to lipoabdominoplasty for achieving an aesthetically pleasing upper midline abdominal contour, with complication rates comparing favorably with those reported in the literature. PMID:28293334

  18. The Polytropic Equation of State of Primordial Gas Clouds

    NASA Astrophysics Data System (ADS)

    Spaans, Marco; Silk, Joseph

    2005-06-01

    The polytropic equation of state (EOS) of primordial gas clouds with modest enrichment is computed, motivated by the recent observations of very Fe-deficient stars, [Fe/H]~10-3.5 to 10-5, such as HE 0107-5240 and CS 29498-043. These stars are overabundant, relative to Fe, in C and O. We assume that the observed abundances of species like C, O, Si, and Fe are representative of the gas from which the currently observed metal-deficient stars formed. Under this assumption, we find that this primordial metal abundance pattern has profound consequences for the thermal balance and chemical composition of the gas and hence for the EOS of the parental cloud. The polytropic EOS is soft for low, [O/H]<10-3, oxygen abundances but stiffens to a polytropic index γ larger than unity for [O/H]>10-2 because of the large opacity in the CO and H2O cooling lines. It is further found that a regulating role is played by the presence and temperature of the dust, even when the overall carbon abundance is only [C/H]~10-2. When the dust is warmer than the gas, a region with γ~1.2 results around a density of ~104 cm-3. When the dust is colder than the gas, a region with γ~0.8 is found for a density of ~106 cm-3. Implications for the primordial initial mass function (IMF) as well as the IMF in starburst galaxies, for which the metallicity is supersolar, are explored and related to processes that influence the temperature of the ambient dust.

  19. Perturbation analysis of a general polytropic homologously collapsing stellar core

    NASA Astrophysics Data System (ADS)

    Cao, Yi; Lou, Yu-Qing

    2009-12-01

    For dynamic background models of Goldreich & Weber and Lou & Cao, we examine three-dimensional perturbation properties of oscillations and instabilities in a general polytropic homologously collapsing stellar core of a relativistically hot medium with a polytropic index γ = 4/3. Perturbation behaviours, especially internal gravity g modes, depend on the variation of specific entropy in the collapsing core. Among possible perturbations, we identify acoustic p modes and surface f modes as well as internal gravity g+ and g- modes. As in stellar oscillations of a static star, we define g+ and g- modes by the sign of the Brunt-Väisälä buoyancy frequency squared for a collapsing stellar core. A new criterion for the onset of instabilities is established for a homologous stellar core collapse. We demonstrate that the global energy criterion of Chandrasekhar is insufficient to warrant the stability of general polytropic equilibria. We confirm the acoustic p-mode stability of Goldreich & Weber, even though their p-mode eigenvalues appear in systematic errors. Unstable modes include g- modes and sufficiently high-order g+ modes, corresponding to core instabilities. Such instabilities occur before the stellar core bounce, in contrast to instabilities in other models of supernova (SN) explosions. The breakdown of spherical symmetry happens earlier than expected in numerical simulations so far. The formation and motion of the central compact object are speculated to be much affected by such g-mode instabilities. By estimates of typical parameters, unstable low-order l = 1 g-modes may produce initial kicks of the central compact object. Other high-order and high-degree unstable g modes may shred the nascent neutron core into pieces without an eventual compact remnant (e.g. SN 1987A). Formation of binary pulsars and planets around neutron stars might originate from unstable l = 2 g-modes and high-order high-degree g modes, respectively.

  20. More on the losses of dissolved CO(2) during champagne serving: toward a multiparameter modeling.

    PubMed

    Liger-Belair, Gérard; Parmentier, Maryline; Cilindre, Clara

    2012-11-28

    Pouring champagne into a glass is far from being inconsequential with regard to the dissolved CO(2) concentration found in champagne. Three distinct bottle types, namely, a magnum bottle, a standard bottle, and a half bottle, were examined with regard to their loss of dissolved CO(2) during the service of successively poured flutes. Whatever the bottle size, a decreasing trend is clearly observed with regard to the concentration of dissolved CO(2) found within a flute (from the first to the last one of a whole service). Moreover, when it comes to champagne serving, the bottle size definitely does matter. The higher the bottle volume, the better its buffering capacity with regard to dissolved CO(2) found within champagne during the pouring process. Actually, for a given flute number in a pouring data series, the concentration of dissolved CO(2) found within the flute was found to decrease as the bottle size decreases. The impact of champagne temperature (at 4, 12, and 20 °C) on the losses of dissolved CO(2) found in successively poured flutes for a given standard 75 cL bottle was also examined. Cold temperatures were found to limit the decreasing trend of dissolved CO(2) found within the successively poured flutes (from the first to the last one of a whole service). Our experimental results were discussed on the basis of a multiparameter model that accounts for the major physical parameters that influence the loss of dissolved CO(2) during the service of a whole bottle type.

  1. Flow analysis from PIV in engraved champagne tasting glasses: flute versus coupe

    NASA Astrophysics Data System (ADS)

    Beaumont, Fabien; Liger-Belair, Gérard; Polidori, Guillaume

    2015-08-01

    Glass shape, and especially its open aperture, is suspected to play an important role as concerns the kinetics of CO2 and flavor release during champagne tasting. In recent years, much interest has been devoted to depict each and every parameter involved in the release of gaseous CO2 from glasses poured with champagne. One cannot understand the bubbling and aromatic exhalation events in champagne tasting, however, without studying the flow-mixing mechanisms inside the glass. Indeed, a key assumption is that a causal link may exist between flow structures created in the wine due to bubble motion and the process of CO2 release and flavor exhalation. In the present work, two quite emblematic types of champagne drinking vessels are studied. The particle image velocimetry technique has been used in order to reveal the velocity field of the liquid due to the ascending bubble-driven flow for both glasses poured with champagne. The contribution of glass shape on the flow patterns and CO2 release in both glasses are discussed by the use of experimental results. The results show that the continuous flow of ascending bubbles strongly modifies the mixing and convection conditions of the surrounding liquid medium whose behavior is strongly glass shape dependent.

  2. The Presence of the Self-Similarity in Architecture: Some Examples

    NASA Astrophysics Data System (ADS)

    Sala, Nicoletta

    Benoit Mandelbrot showed how Fractals can occur in many different places in both Mathematics and elsewhere in Nature. A fractal object is self - similar if it has undergone a transformation whereby the dimensions of the structure were all modified by the same scaling factor. The new shape may be smaller, larger, translated, and/or rotated, but its shape remains similar. "Similar" means that the relative proportions of the shapes' sides and internal angles remain the same. Our sense, having evolved in nature's self-similar cascade, appreciate self-similar in designed objects. It is possible to demonstrate which the fractal shapes have known to artists and architects for centuries. The aim of this paper is to present some examples of self-similarity in architectural and design projects. We will refer of the building's self-similarity in different cultures (e.g., Western and Oriental culture) and in different periods (e.g. in the Middle Ages until today). We have organized our study using two different approaches: the unconscious building's self-similarity (as a result of an aesthetics sense), and the conscious building's self- similarity (as a result of a specific and conscious act of design).

  3. Self-similar solutions for the dynamical condensation of a radiative gas layer

    NASA Astrophysics Data System (ADS)

    Iwasaki, Kazunari; Tsuribe, Toru

    2008-07-01

    A new self-similar solution describing the dynamical condensation of a radiative gas is investigated under a plane-parallel geometry. The dynamical condensation is caused by thermal instability. The solution is applicable to generic flow with a net cooling rate per unit volume and time ~ ρ2Tα, where ρ,T and α are the density, temperature and a free parameter, respectively. Given α, a family of self-similar solutions with one parameter η is found in which the central density and pressure evolve as follows: ρ(x = 0, t) ~ (tc - t)-η/(2-α) and P(x = 0, t) ~ (tc - t)(1-η)/(1-α), where tc is the epoch at which the central density becomes infinite. For η ~ 0 the solution describes the isochoric mode, whereas for η ~ 1 the solution describes the isobaric mode. The self-similar solutions exist in the range between the two limits; that is, for 0 < η < 1. No self-similar solution is found for α > 1. We compare the obtained self-similar solutions with the results of one-dimensional hydrodynamical simulations. In a converging flow, the results of the numerical simulations agree well with the self-similar solutions in the high-density limit. Our self-similar solutions are applicable to the formation of interstellar clouds (HI clouds and molecular clouds) by thermal instability.

  4. Ultrafast fiber lasers based on self-similar pulse evolution: a review of current progress

    PubMed Central

    Chong, Andy; Wright, Logan G; Wise, Frank W

    2016-01-01

    Self-similar fiber oscillators are a relatively new class of mode-locked lasers. In these lasers, the self-similar evolution of a chirped parabolic pulse in normally-dispersive passive, active, or dispersion-decreasing fiber (DDF) is critical. In active (gain) fiber and DDF, the novel role of local nonlinear attraction makes the oscillators fundamentally different from any mode-locked lasers considered previously. In order to reconcile the spectral and temporal expansion of a pulse in the self-similar segment with the self-consistency required by a laser cavity's periodic boundary condition, several techniques have been applied. The result is a diverse range of fiber oscillators which demonstrate the exciting new design possibilities based on the self-similar model. Here, we review recent progress on self-similar oscillators both in passive and active fiber, and extensions of self-similar evolution for surpassing the limits of rare-earth gain media. We discuss some key remaining research questions and important future directions. Self-similar oscillators are capable of exceptional performance among ultrashort pulsed fiber lasers, and may be of key interest in the development of future ultrashort pulsed fiber lasers for medical imaging applications, as well as for low-noise fiber-based frequency combs. Their uniqueness among mode-locked lasers motivates study into their properties and behaviors and raises questions about how to understand mode-locked lasers more generally. PMID:26496377

  5. Ultrafast fiber lasers based on self-similar pulse evolution: a review of current progress.

    PubMed

    Chong, Andy; Wright, Logan G; Wise, Frank W

    2015-11-01

    Self-similar fiber oscillators are a relatively new class of mode-locked lasers. In these lasers, the self-similar evolution of a chirped parabolic pulse in normally-dispersive passive, active, or dispersion-decreasing fiber (DDF) is critical. In active (gain) fiber and DDF, the novel role of local nonlinear attraction makes the oscillators fundamentally different from any mode-locked lasers considered previously. In order to reconcile the spectral and temporal expansion of a pulse in the self-similar segment with the self-consistency required by a laser cavity's periodic boundary condition, several techniques have been applied. The result is a diverse range of fiber oscillators which demonstrate the exciting new design possibilities based on the self-similar model. Here, we review recent progress on self-similar oscillators both in passive and active fiber, and extensions of self-similar evolution for surpassing the limits of rare-earth gain media. We discuss some key remaining research questions and important future directions. Self-similar oscillators are capable of exceptional performance among ultrashort pulsed fiber lasers, and may be of key interest in the development of future ultrashort pulsed fiber lasers for medical imaging applications, as well as for low-noise fiber-based frequency combs. Their uniqueness among mode-locked lasers motivates study into their properties and behaviors and raises questions about how to understand mode-locked lasers more generally.

  6. Polytropic index of central plasma sheet ions based on MHD Bernoulli integral

    NASA Astrophysics Data System (ADS)

    Pang, Xuexia; Cao, Jinbin; Liu, Wenlong; Ma, Yuduan; Lu, Haoyu; Yang, Junying; Li, Liuyuan; Liu, Xu; Wang, Jing; Wang, Tieyan; Yu, Jiang

    2015-06-01

    This paper uses the data of Cluster from 2001 to 2009 to study the polytropic processes of central plasma sheet (CPS) ions. We first adopt the approach of MHD Bernoulli integral (MBI) to identify homogeneous streamflow tubes (quasi-invariant MBI regions) and then calculate the polytropic index of ions for those streamflow tubes whose outward electromagnetic energy ratios δ < 0.05. The central plasma sheet is actually a complicated system, which comprises many streamflow tubes with different polytropic relations and the transition layers in between. The polytropic indexes of the CPS ions range from 0.1 to 1.8 and have a quasi-Gaussian distribution. The median polytropic index is 0.93 for AE < 200 nT and 0.91 for AE ≥ 200 nT. Thus, there is no obvious difference between the polytropic indexes of the quiet time and the substorm time CPS ions, which suggests that the thinning and thickening processes of plasma sheet during substorm times do not change obviously the polytropic relation of the CPS ions. The statistical analysis using different δ (δ < 0.05, 0.025, and 0.01) shows that the outward emission of electromagnetic energy is an effective cooling mechanism and can make the polytropic index to decrease and shift toward isobaric. It is inferred that the CPS ions as a whole much likely behave in a way between isobaric and isothermal.

  7. Observations and analysis of self-similar branching topology in glacier networks

    USGS Publications Warehouse

    Bahr, D.B.; Peckham, S.D.

    1996-01-01

    Glaciers, like rivers, have a branching structure which can be characterized by topological trees or networks. Probability distributions of various topological quantities in the networks are shown to satisfy the criterion for self-similarity, a symmetry structure which might be used to simplify future models of glacier dynamics. Two analytical methods of describing river networks, Shreve's random topology model and deterministic self-similar trees, are applied to the six glaciers of south central Alaska studied in this analysis. Self-similar trees capture the topological behavior observed for all of the glaciers, and most of the networks are also reasonably approximated by Shreve's theory. Copyright 1996 by the American Geophysical Union.

  8. Self-similar optical pulses in competing cubic-quintic nonlinear media with distributed coefficients

    SciTech Connect

    Zhang Jiefang; Tian Qing; Wang Yueyue; Dai Chaoqing; Wu Lei

    2010-02-15

    We present a systematic analysis of the self-similar propagation of optical pulses within the framework of the generalized cubic-quintic nonlinear Schroedinger equation with distributed coefficients. By appropriately choosing the relations between the distributed coefficients, we not only retrieve the exact self-similar solitonic solutions, but also find both the approximate self-similar Gaussian-Hermite solutions and compact solutions. Our analytical and numerical considerations reveal that proper choices of the distributed coefficients could make the unstable solitons stable and could restrict the nonlinear interaction between the neighboring solitons.

  9. Intermittency and extended self-similarity in the solar wind turbulence

    NASA Technical Reports Server (NTRS)

    Bruno, R.; Carbone, V.

    1995-01-01

    Using the satellite measurements of the velocity field in the interplanetary plasma. we present some analysis which show the presence of a self-similar intermittent state in the solar wind turbulence. We used the so called Extended Self-Similarity hypothesis, which is well visible in the solar wind turbulence, showing convincing evidences for the presence of universal anomalous scaling laws. Through the Extended Self-Similarity we are able to calculate the scaling exponents of the velocity structure functions with very small uncertainties, and we show that these scaling exponents are in very good agreement with the multifractal models describing intermittency in magnetohydrodynamic flows.

  10. Self-similarity of single-channel transmission for electron transport in nanowires.

    PubMed

    Gelin, M F; Li, Zhenyu; Kosov, D S

    2006-03-14

    We demonstrate that the single-channel transmission in the resonance tunneling regime exhibits self-similarity as a function of the nanowire length and the energy of incident electrons. The self-similarity is used to design the nonlinear transformation of the nanowire length and energy which, on the basis of known values of transmission for a certain region on the energy-length plane, yields transmissions for other regions on this plane. Test calculations with a one-dimensional tight-binding model illustrate the described transformations. Density function theory based transport calculations of Na atomic wires confirm the existence of the self-similarity in the transmission.

  11. Drift of particles in self-similar systems and its Liouvillian interpretation.

    PubMed

    Barra, Felipe; Gilbert, Thomas; Romo, Mauricio

    2006-02-01

    We study the dynamics of classical particles in different classes of spatially extended self-similar systems, consisting of (i) a self-similar Lorentz billiard channel, (ii) a self-similar graph, and (iii) a master equation. In all three systems, the particles typically drift at constant velocity and spread ballistically. These transport properties are analyzed in terms of the spectral properties of the operator evolving the probability densities. For systems (i) and (ii), we explain the drift from the properties of the Pollicott-Ruelle resonance spectrum and corresponding eigenvectors.

  12. A synchronized particle image velocimetry and infrared thermography technique applied to convective mass transfer in champagne glasses

    NASA Astrophysics Data System (ADS)

    Beaumont, Fabien; Liger-Belair, Gérard; Bailly, Yannick; Polidori, Guillaume

    2016-05-01

    In champagne glasses, it was recently suggested that ascending bubble-driven flow patterns should be involved in the release of gaseous carbon dioxide (CO2) and volatile organic compounds. A key assumption was that the higher the velocity of the upward bubble-driven flow patterns in the liquid phase, the higher the volume fluxes of gaseous CO2 desorbing from the supersaturated liquid phase. In the present work, simultaneous monitoring of bubble-driven flow patterns within champagne glasses and gaseous CO2 escaping above the champagne surface was performed, through particle image velocimetry and infrared thermography techniques. Two quite emblematic types of champagne drinking vessels were investigated, namely a long-stemmed flute and a wide coupe. The synchronized use of both techniques proved that the cloud of gaseous CO2 escaping above champagne glasses strongly depends on the mixing flow patterns found in the liquid phase below.

  13. New characterization aspects of carbonate accumulation horizons in Chalky Champagne (NE of the Paris Basin, France)

    NASA Astrophysics Data System (ADS)

    Linoir, Damien; Thomachot-Schneider, Céline; Gommeaux, Maxime; Fronteau, Gilles; Barbin, Vincent

    2016-05-01

    The soil profiles of the Champagne area (NE of Paris Basin, France) occasionally show carbonate accumulation horizons (CAHs). From the top to the bottom, these soil profiles include a rendic leptosol horizon, a Quaternary cryoturbated paleosol (QCP), and a chalky substratum. The CAHs are located in the top part of the QCP. This study is aimed at highlighting the specific characteristics of CAHs compared to other soil profile horizons using geophysics, geochemistry, micromorphology, and mercury injection porosimetry. It is the first essential step for understanding the impact of CAHs on water transfers into the Champagne soil profiles. Our analyses show that Champagne CAHs are not systematically characterized by a typical induration unlike generally put forward in the regional literature. They are more porous and heterogeneous than their parent material (QCP). Carbonate accumulation horizons are also characterized by singular colorimetric parameters that are linked to their geochemical specific content, even if they bear a signature of the initial QCP before the pedogenic modification.

  14. Differentiation of sparkling wines (cava and champagne) according to their mineral content.

    PubMed

    Jos, A; Moreno, I; González, A G; Repetto, G; Cameán, A M

    2004-05-28

    The metal content of a number of sparkling wines was determined by atomic spectrometry techniques. Al, Ba, Ca, Cu, Fe, K, Mg, Mn, Na, P, Sr and Zn by using inductively coupled plasma atomic emission spectrometry (ICP-AES); Cd, Ni and Pb by graphite furnace atomic absorption spectrometry (GFAAS) and As from hydride generation AAS (HGAAS). Two kinds of sparkling wines were studied with D.O. trademark: cava and champagne. 18 samples of "brut" cava and 17 samples of "brut" champagne of different brands were analyzed following the procedure described in the paper. By using the metal concentrations as chemical descriptors the two classes of samples (cava and champagne) are perfectly discriminated, when applying pattern supervised learning recognition techniques such as linear discriminant analysis (LDA) and soft independent modeling of class analogie (SIMCA). The number of false positives and negatives were zero, which indicates a remarkable authentication power of the descriptors used.

  15. Self-similar conductance patterns in graphene Cantor-like structures.

    PubMed

    García-Cervantes, H; Gaggero-Sager, L M; Díaz-Guerrero, D S; Sotolongo-Costa, O; Rodríguez-Vargas, I

    2017-04-04

    Graphene has proven to be an ideal system for exotic transport phenomena. In this work, we report another exotic characteristic of the electron transport in graphene. Namely, we show that the linear-regime conductance can present self-similar patterns with well-defined scaling rules, once the graphene sheet is subjected to Cantor-like nanostructuring. As far as we know the mentioned system is one of the few in which a self-similar structure produces self-similar patterns on a physical property. These patterns are analysed quantitatively, by obtaining the scaling rules that underlie them. It is worth noting that the transport properties are an average of the dispersion channels, which makes the existence of scale factors quite surprising. In addition, that self-similarity be manifested in the conductance opens an excellent opportunity to test this fundamental property experimentally.

  16. Stability analysis of self-similar behaviors in perfect fluid gravitational collapse

    SciTech Connect

    Mitsuda, Eiji; Tomimatsu, Akira

    2006-06-15

    Stability of self-similar solutions for gravitational collapse is an important problem to be investigated from the perspectives of their nature as an attractor, critical phenomena, and instability of a naked singularity. In this paper we study spherically symmetric non-self-similar perturbations of matter and metrics in spherically symmetric self-similar backgrounds. The collapsing matter is assumed to be a perfect fluid with the equation of state P={alpha}{rho}. We construct a single wave equation governing the perturbations, which makes their time evolution in arbitrary self-similar backgrounds analytically tractable. Further we propose an analytical application of this master wave equation to the stability problem by means of the normal mode analysis for the perturbations having the time dependence given by exp(i{omega}log vertical t vertical bar), and present some sufficient conditions for the absence of nonoscillatory unstable normal modes with purely imaginary {omega}.

  17. A general method for computing Tutte polynomials of self-similar graphs

    NASA Astrophysics Data System (ADS)

    Gong, Helin; Jin, Xian'an

    2017-10-01

    Self-similar graphs were widely studied in both combinatorics and statistical physics. Motivated by the construction of the well-known 3-dimensional Sierpiński gasket graphs, in this paper we introduce a family of recursively constructed self-similar graphs whose inner duals are of the self-similar property. By combining the dual property of the Tutte polynomial and the subgraph-decomposition trick, we show that the Tutte polynomial of this family of graphs can be computed in an iterative way and in particular the exact expression of the formula of the number of their spanning trees is derived. Furthermore, we show our method is a general one that is easily extended to compute Tutte polynomials for other families of self-similar graphs such as Farey graphs, 2-dimensional Sierpiński gasket graphs, Hanoi graphs, modified Koch graphs, Apollonian graphs, pseudofractal scale-free web, fractal scale-free network, etc.

  18. Self-similarity of the large-scale motions in turbulent pipe flow

    NASA Astrophysics Data System (ADS)

    Hellström, Leo; Marusic, Ivan; Smits, Alexander

    2016-11-01

    Townsend's attached eddy hypothesis assumes the existence of a set of energetic and geometrically self-similar eddies in the logarithmic layer in wall-bounded turbulent flows. These eddies can be completely scaled with the distance from their center to the wall. We performed stereo PIV measurements together with a proper orthogonal decomposition (POD) analysis, to address the self-similarity of the energetic motions, or eddies, in fully-developed turbulent pipe flow. The resulting modes/eddies, extracted at Reτ = 2460 , show a self-similar behavior for eddies with wall-normal length scales spanning a decade. This single length scale provides a complete description of the cross-sectional shape of the self-similar eddies. ONR Grant N00014-15-1-2402 and the Australian Research Council.

  19. On the Liouville Type Theorems for Self-Similar Solutions to the Navier-Stokes Equations

    NASA Astrophysics Data System (ADS)

    Chae, Dongho; Wolf, Jörg

    2017-07-01

    We prove Liouville type theorems for the self-similar solutions to the Navier-Stokes equations. One of our results generalizes the previous ones by Nečas-Ru˙žička-Šverák and Tsai. Using a Liouville type theorem, we also remove a scenario of asymptotically self-similar blow-up for the Navier-Stokes equations with the profile belonging to {L^{p, ∞} (R^3) with {p > 3/2}.

  20. On the mechanical behavior of bio-inspired materials with non-self-similar hierarchy.

    PubMed

    An, Bingbing; Zhao, Xinluo; Zhang, Dongsheng

    2014-06-01

    Biological materials exhibiting non-self-similar hierarchical structures possess desirable mechanical properties. Motivated by their penetration resistance and fracture toughness, the mechanical performance of model materials with non-self-similar hierarchical structures was explored and the distinct advantages were identified. A numerical model was developed, based on microscopic observation of enamel prisms. Computational simulations showed that the systems with non-self-similar hierarchy displayed lateral expansion when subjected to longitudinal tensile loading, which reflected negative Poisson׳s ratio and potential for greater volume strain energies when compared with conventional materials with positive Poisson׳s ratio. Employing the non-self-similar hierarchical design, the capability of resilience can be improved. Additionally, the non-self-similar hierarchical structure exhibited larger toughness, resulting from the large pull-out work of the reinforcements. The findings of this study not only elucidate the deformation mechanisms of biological materials with non-self-similar hierarchical structure, but also provide a new path for bio-inspired materials design.

  1. Horton and Tokunaga self-similarity in basic models of branching, aggregation, time series

    NASA Astrophysics Data System (ADS)

    Zaliapin, I.; Kovchegov, Y.

    2012-12-01

    Hierarchical branching structures are readily seen in river and drainage networks, lightening, botanical trees, vein structure of leaves, snowflakes, and bronchial passages, to mention but a few. Empirical evidence reveals a surprising similarity among natural hierarchies of diverse origin; many of them are closely approximated by so-called self-similar trees (SSTs). A two-parametric subclass of Tokunaga SSTs plays a special role in theory and applications, as it has been shown to emerge in unprecedented variety of modeled and natural phenomena. The Tokunaga SSTs with a broad range of parameters are seen in studies of river networks, aftershock sequences, vein structure of botanical leaves, numerical analyses of diffusion limited aggregation, two dimensional site percolation, and nearest-neighbor clustering in Euclidean spaces. The omnipresence of Tokunaga self-similarity hints at the existence of universal underlying mechanisms responsible for its appearance and prompts the question: What basic probability models may generate Tokunaga self-similar trees? This paper reviews the existing results on Tokunaga self-similarity of the critical binary Galton-Watson process, also known as Shreve's random topology model or equiprobable binary tree model. We then present new analytic results that establish Horton and Tokunaga self-similarity in (i) level-set tree representation of white noise, (ii) level-set tree representation of random walk and Brownian motion, and (iii) Kingman's coalescent process. We also formulate a conjecture, based on extensive numerical experiments, about Tokunaga self-similarity for the (iv) additive and (v) multiplicative coalescents as well as (vi) fractional Brownian motion. The listed processes are among the essential building blocks in natural and computer sciences modeling. Accordingly, the results of this study may provide at least a partial explanation for the presence of Horton and Tokunaga self-similarity in observed and modeled branching

  2. Testing statistical self-similarity in the topology of river networks

    USGS Publications Warehouse

    Troutman, Brent M.; Mantilla, Ricardo; Gupta, Vijay K.

    2010-01-01

    Recent work has demonstrated that the topological properties of real river networks deviate significantly from predictions of Shreve's random model. At the same time the property of mean self-similarity postulated by Tokunaga's model is well supported by data. Recently, a new class of network model called random self-similar networks (RSN) that combines self-similarity and randomness has been introduced to replicate important topological features observed in real river networks. We investigate if the hypothesis of statistical self-similarity in the RSN model is supported by data on a set of 30 basins located across the continental United States that encompass a wide range of hydroclimatic variability. We demonstrate that the generators of the RSN model obey a geometric distribution, and self-similarity holds in a statistical sense in 26 of these 30 basins. The parameters describing the distribution of interior and exterior generators are tested to be statistically different and the difference is shown to produce the well-known Hack's law. The inter-basin variability of RSN parameters is found to be statistically significant. We also test generator dependence on two climatic indices, mean annual precipitation and radiative index of dryness. Some indication of climatic influence on the generators is detected, but this influence is not statistically significant with the sample size available. Finally, two key applications of the RSN model to hydrology and geomorphology are briefly discussed.

  3. The self-similarly expanding Eshelby ellipsoidal inclusion: I. Field solution

    NASA Astrophysics Data System (ADS)

    Ni, Luqun; Markenscoff, Xanthippi

    2016-11-01

    The solution of a self-similarly (subsonically) dynamically expanding ellipsoidal inclusion with general spatially uniform transformation strain temporally constant is obtained by the use of the Radon transform and the satisfaction of the zero initial conditions and the radiation condition at infinity. It constitutes the self-similar evolution of the inclusion singularity (jump discontinuity at the inclusion boundary) starting from zero dimension. The field solutions for the displacement gradient and particle velocity are presented. Due to the fact that for a self-similarly expanding subsonic motion the hyperbolic system of the partial differential equations of motion becomes elliptic (as proved in Ni and Markenscoff, 2015), it is shown here explicitly that the solution for the displacement gradient in the interior domain of the expanding ellipsoid is constant, thus extending the Eshelby property to the self-similarly expanding ellipsoids as pointed out by Burridge and Willis (1969). Also, the particle velocity is shown to be zero in the interior domain (lacuna) as the waves emitted by the self-similarly expanding inclusion cancel each other due to the symmetries of geometry and motion.

  4. Scaling Relations and Self-Similarity of 3-Dimensional Reynolds-Averaged Navier-Stokes Equations.

    PubMed

    Ercan, Ali; Kavvas, M Levent

    2017-07-25

    Scaling conditions to achieve self-similar solutions of 3-Dimensional (3D) Reynolds-Averaged Navier-Stokes Equations, as an initial and boundary value problem, are obtained by utilizing Lie Group of Point Scaling Transformations. By means of an open-source Navier-Stokes solver and the derived self-similarity conditions, we demonstrated self-similarity within the time variation of flow dynamics for a rigid-lid cavity problem under both up-scaled and down-scaled domains. The strength of the proposed approach lies in its ability to consider the underlying flow dynamics through not only from the governing equations under consideration but also from the initial and boundary conditions, hence allowing to obtain perfect self-similarity in different time and space scales. The proposed methodology can be a valuable tool in obtaining self-similar flow dynamics under preferred level of detail, which can be represented by initial and boundary value problems under specific assumptions.

  5. Self-similar characteristics of the currency exchange rate in an economy in transition

    NASA Astrophysics Data System (ADS)

    Scarlat, E. I.; Stan, Cristina; Cristescu, C. P.

    2007-06-01

    In this paper, we present an analysis of the self-similar characteristics of the temporal series describing the daily exchange rate of the Romanian currency unit “Leu” (ROL) with respect to the US Dollar (USD). The relevance of this investigation consists in the exchange rate being a proper indicator for the dynamics of an economy in transition from a command-type structure towards an open market one. The time series is exhibiting self-similar cells of dimensions obeying a definite power law scaling rule that is related to different categories of economic agents. By using a crossing-type analysis based on the Hurst exponent and the frequency spectrum, five categories were detected. A simple model based on active filters with prevailing feedforward loops working close to the unstable regime, each one describing an economic agent under the stress of a hostile economic environment, is proposed for the dynamics of the fragmentation-defragmentation process. The model qualitatively reproduces the self-similarity characteristics of the currency exchange rate of an economy in transition, subjected to deep structural changes. We observe that the “in-phase evolution” of the economic agents causes the statistical self-similarity to resemble a theoretical self-similarity.

  6. Testing statistical self-similarity in the topology of river networks

    NASA Astrophysics Data System (ADS)

    Mantilla, Ricardo; Troutman, Brent M.; Gupta, Vijay K.

    2010-09-01

    Recent work has demonstrated that the topological properties of real river networks deviate significantly from predictions of Shreve's random model. At the same time the property of mean self-similarity postulated by Tokunaga's model is well supported by data. Recently, a new class of network model called random self-similar networks (RSN) that combines self-similarity and randomness has been introduced to replicate important topological features observed in real river networks. We investigate if the hypothesis of statistical self-similarity in the RSN model is supported by data on a set of 30 basins located across the continental United States that encompass a wide range of hydroclimatic variability. We demonstrate that the generators of the RSN model obey a geometric distribution, and self-similarity holds in a statistical sense in 26 of these 30 basins. The parameters describing the distribution of interior and exterior generators are tested to be statistically different and the difference is shown to produce the well-known Hack's law. The inter-basin variability of RSN parameters is found to be statistically significant. We also test generator dependence on two climatic indices, mean annual precipitation and radiative index of dryness. Some indication of climatic influence on the generators is detected, but this influence is not statistically significant with the sample size available. Finally, two key applications of the RSN model to hydrology and geomorphology are briefly discussed.

  7. Carbon dioxide and ethanol release from champagne glasses, under standard tasting conditions.

    PubMed

    Liger-Belair, Gérard; Beaumont, Fabien; Bourget, Marielle; Pron, Hervé; Parvitte, Bertrand; Zéninari, Virginie; Polidori, Guillaume; Cilindre, Clara

    2012-01-01

    A simple glass of champagne or sparkling wine may seem like the acme of frivolity to most people, but in fact, it may rather be considered as a fantastic playground for any fluid physicist or physicochemist. In this chapter, results obtained concerning various steps where the CO₂ molecule plays a role (from its ingestion in the liquid phase during the fermentation process to its progressive release in the headspace above the tasting glass) are gathered and synthesized to propose a self-consistent and global overview of how gaseous and dissolved CO₂ impact champagne and sparkling wine science. Some recent investigations, conducted through laser tomography techniques, on ascending bubbles and ascending-bubble-driven flow patterns found in champagne glasses are reported, which illustrate the fine interplay between ascending bubbles and the fluid around under standard tasting conditions. The simultaneous monitoring of gaseous CO₂ and ethanol in the headspace of both a flute and a coupe filled with champagne was reported, depending on whether or not the glass shows effervescence. Both gaseous CO₂ and ethanol were found to be enhanced by the presence of ascending bubbles, thus confirming the close link between ascending bubbles, ascending-bubble-driven flow patterns, and the release of gaseous CO₂ and volatile organic compounds. Copyright © 2012 Elsevier Inc. All rights reserved.

  8. Microbial life in Champagne Pool, a geothermal spring in Waiotapu, New Zealand.

    PubMed

    Hetzer, Adrian; Morgan, Hugh W; McDonald, Ian R; Daughney, Christopher J

    2007-07-01

    Surveys of Champagne Pool, one of New Zealand's largest terrestrial hot springs and rich in arsenic ions and compounds, have been restricted to geological and geochemical descriptions, and a few microbiological studies applying culture-independent methods. In the current investigation, a combination of culture and culture-independent approaches were chosen to determine microbial density and diversity in Champagne Pool. Recovered total DNA and adenosine 5'-triphosphate (ATP) content of spring water revealed relatively low values compared to other geothermal springs within New Zealand and are in good agreement with low cell numbers of 5.6 +/- 0.5 x 10(6) cells/ml obtained for Champagne Pool water samples by 4',6-diamidino-2-phenylindole (DAPI) staining. Denaturing Gradient Gel Electrophoresis (DGGE) and 16S rRNA (small-subunit ribosomal nucleic acid) gene clone library analyses of environmental DNA indicated the abundance of Sulfurihydrogenibium, Sulfolobus, and Thermofilum-like populations in Champagne Pool. From these results, media were selected to target the enrichment of hydrogen-oxidizing and sulfur-dependent microorganisms. Three isolates were successfully obtained having 16S rRNA gene sequences with similarities of approximately 98% to Thermoanaerobacter tengcongensis, 94% to Sulfurihydrogenibium azorense, and 99% to Thermococcus waiotapuensis, respectively.

  9. Coherent structures of a self-similar adverse pressure gradient turbulent boundary layer

    NASA Astrophysics Data System (ADS)

    Sekimoto, Atsushi; Kitsios, Vassili; Atkinson, Callum; Jiménez, Javier; Soria, Julio

    2016-11-01

    The turbulence statistics and structures are studied in direct numerical simulation (DNS) of a self-similar adverse pressure gradient turbulent boundary layer (APG-TBL). The self-similar APG-TBL at the verged of separation is achieved by a modification of the far-field boundary condition to produce the desired pressure gradient. The turbulence statistics in the self-similar region collapse by using the scaling of the external velocity and the displacement thickness. The coherent structures of the APG-TBL are investigated and compared to those of zero-pressure gradient case and homogeneous shear flow. The support of the ARC, NCI and Pawsey SCC funded by the Australian and Western Australian governments as well as the support of PRACE funded by the European Union are gratefully acknowledged.

  10. Horton and Tokunaga self-similarity for multiplicative coalescent: numerical approach

    NASA Astrophysics Data System (ADS)

    Tejedor, A.; Zaliapin, I.

    2012-12-01

    The Horton and Tokunaga branching laws provide a convenient and powerful framework for studying self-similarity in branching structures represented by random tree graphs. The Horton self-similarity, described by the Horton exponent R, is a weaker property that addresses the principal branching in a tree; it is a counterpart of the power-law size distribution for elements of a branching system. The stronger Tokunaga self-similarity, parameterized by a positive pair (a, c), addresses so-called side branching and implies that different hierarchical levels of a tree have the same statistical structure. The Horton and Tokunaga self-similarity have been empirically established in numerous observed and modeled systems and proven for the following paradigmatic models: (i) the critical binary Galton-Watson branching process with finite progeny, also known in hydrology as Shreve's random topology model, (ii) level-set tree representation of white noise and (iii) random walk, and (iv) Kingman's coalescent process. This work addresses the problem of testing the Tokunaga self-similarity hypothesis and statistical estimation of Horton and Tokunaga parameters in a single finite tree. We use critical binary Galton-Watson trees to illustrate and quantify finite-size effects that influence estimation as well as compare among estimation techniques based on regression and maximum likelihood approaches. Next, we apply the developed testing and estimation procedure to study the multiplicative coalescent process. The results of our numerical experiments suggest that the multiplicative coalescent is Tokunaga self-similar with parameters (a, c) = (1, 2), the same as that for the critical binary Galton-Watson process and level-set tree representation of a random walk.

  11. Structure and chemical composition of layers adsorbed at interfaces with champagne.

    PubMed

    Aguié-Béghin, V; Adriaensen, Y; Péron, N; Valade, M; Rouxhet, P; Douillard, R

    2009-11-11

    The structure and the chemical composition of the layer adsorbed at interfaces involving champagne have been investigated using native champagne, as well as ultrafiltrate (UFch) and ultraconcentrate (UCch) obtained by ultrafiltration with a 10(4) nominal molar mass cutoff. The layer adsorbed at the air/liquid interface was examined by surface tension and ellipsometry kinetic measurements. Brewster angle microscopy demonstrated that the layer formed on polystyrene by adsorption or drop evaporation was heterogeneous, with a domain structure presenting similarities with the layer adsorbed at the air/liquid interface. The surface chemical composition of polystyrene with the adlayer was determined by X-ray photoelectron spectroscopy (XPS). The contribution of champagne constituents varied according to the liquid (native, UFch, and UCch) and to the procedure of adlayer formation (evaporation, adsorption, and adsorption + rinsing). However, their chemical composition was not significantly influenced either by ultrafiltration or by the procedure of deposition on polystyrene. Modeling this composition in terms of classes of model compounds gave approximately 35% (w/w) of proteins and 65% (w/w) of polysaccharides. In the adlayer, the carboxyl groups or esters represent about 18% of carbon due to nonpolypeptidic compounds, indicating the presence of either uronic acids in the complex structure of pectic polysaccharides or of polyphenolic esters. This structural and chemical information and its relationship with the experimental procedures indicate that proteins alone cannot be used as a realistic model for the macromolecules forming the adsorption layer of champagne. Polysaccharides, the other major macromolecular components of champagne wine, are assembled with proteins at the interfaces, in agreement with the heterogeneous character of the adsorbed layer at interfaces.

  12. Missense Mutation in Exon 2 of SLC36A1 Responsible for Champagne Dilution in Horses

    PubMed Central

    Cook, Deborah; Brooks, Samantha; Bellone, Rebecca; Bailey, Ernest

    2008-01-01

    Champagne coat color in horses is controlled by a single, autosomal-dominant gene (CH). The phenotype produced by this gene is valued by many horse breeders, but can be difficult to distinguish from the effect produced by the Cream coat color dilution gene (CR). Three sires and their families segregating for CH were tested by genome scanning with microsatellite markers. The CH gene was mapped within a 6 cM region on horse chromosome 14 (LOD = 11.74 for θ = 0.00). Four candidate genes were identified within the region, namely SPARC [Secreted protein, acidic, cysteine-rich (osteonectin)], SLC36A1 (Solute Carrier 36 family A1), SLC36A2 (Solute Carrier 36 family A2), and SLC36A3 (Solute Carrier 36 family A3). SLC36A3 was not expressed in skin tissue and therefore not considered further. The other three genes were sequenced in homozygotes for CH and homozygotes for the absence of the dilution allele (ch). SLC36A1 had a nucleotide substitution in exon 2 for horses with the champagne phenotype, which resulted in a transition from a threonine amino acid to an arginine amino acid (T63R). The association of the single nucleotide polymorphism (SNP) with the champagne dilution phenotype was complete, as determined by the presence of the nucleotide variant among all 85 horses with the champagne dilution phenotype and its absence among all 97 horses without the champagne phenotype. This is the first description of a phenotype associated with the SLC36A1 gene. PMID:18802473

  13. The polytropic approximation and X-ray scaling relations: constraints on gas and dark matter profiles for galaxy groups and clusters

    NASA Astrophysics Data System (ADS)

    Capelo, Pedro R.; Coppi, Paolo S.; Natarajan, Priyamvada

    2012-05-01

    The X-ray properties of groups and clusters of galaxies obey scaling relations that provide insight into the physics of their formation and evolution. In this paper, we constrain gas and dark matter parameters of these systems, by comparing the observed relations to theoretical expectations, obtained assuming that the gas is in hydrostatic equilibrium with the dark matter and follows a polytropic relation. In this exercise, we vary four parameters: the gas polytropic index Γ, its temperature at large radii, the dark matter logarithmic slope at large radii ζ and its concentration. When comparing the model to the observed mass-temperature relation of local high-mass systems, we find our results to be independent of both the gas temperature at large radii and of the dark matter concentration. We thus obtain constraints on Γ, by fixing the dark matter profile, and on ζ, by fixing the gas profile. For a Navarro-Frenk-White dark matter profile, we find that Γ must lie between 6/5 and 13/10. This value is consistent with numerical simulations and observations of individual clusters. Taking 6/5 ≲Γ≲ 13/10 allows the dark matter profile to be slightly steeper than the Navarro-Frenk-White profile at large radii. Upon including local low-mass systems, we obtain constraints on the mass dependence of Γ and on the value of the gas temperature at large radii. Interestingly, by fixing Γ= 6/5 and ζ=-3, we reproduce the observed steepening/breaking of the mass-temperature relation at low masses if the temperature of the intercluster medium is between 106 and 107 K, consistent with numerical simulations and observations of the warm-hot intergalactic medium. When extrapolated to high redshift, the model with a constant Γ reproduces the expected self-similar behaviour. Given our formulation, we can also naturally account for the observed, non-self-similar relations provided by some high-redshift clusters, as they simply provide constraints on the evolution of Γ. In

  14. The self-similar character of the microscopic thermal fluctuation inside an argon-copper nanofluid.

    PubMed

    Jia, T; Gao, D

    2016-08-03

    The microscopic thermal behavior inside an argon-copper nanofluid is investigated based on equilibrium molecular dynamics simulation. A self-similar structure appears in the signal of the microscopic heat current in the nanofluid system at the equilibrium state. The fractal dimension is calculated to mathematically quantify the self-similar structure. It is found that the fractal dimension increases with the thermal conductivity of the nanofluid. The relationship between the fractal dimension of the microscopic heat current and the thermal conductivity of the nanofluid serves as a link between the microscopic and macroscopic properties of the nanofluid.

  15. Failure of self-similarity for large (Mw > 81/4) earthquakes.

    USGS Publications Warehouse

    Hartzell, S.H.; Heaton, T.H.

    1988-01-01

    Compares teleseismic P-wave records for earthquakes in the magnitude range from 6.0-9.5 with synthetics for a self-similar, omega 2 source model and conclude that the energy radiated by very large earthquakes (Mw > 81/4) is not self-similar to that radiated from smaller earthquakes (Mw < 81/4). Furthermore, in the period band from 2 sec to several tens of seconds, it is concluded that large subduction earthquakes have an average spectral decay rate of omega -1.5. This spectral decay rate is consistent with a previously noted tendency of the omega 2 model to overestimate Ms for large earthquakes.-Authors

  16. Modeling the self-similarity in complex networks based on Coulomb's law

    NASA Astrophysics Data System (ADS)

    Zhang, Haixin; Wei, Daijun; Hu, Yong; Lan, Xin; Deng, Yong

    2016-06-01

    Recently, self-similarity of complex networks have attracted much attention. Fractal dimension of complex network is an open issue. Hub repulsion plays an important role in fractal topologies. This paper models the repulsion among the nodes in the complex networks in calculation of the fractal dimension of the networks. Coulomb's law is adopted to represent the repulse between two nodes of the network quantitatively. A new method to calculate the fractal dimension of complex networks is proposed. The Sierpinski triangle network and some real complex networks are investigated. The results are illustrated to show that the new model of self-similarity of complex networks is reasonable and efficient.

  17. An Introduction to the Theory of Self-Similar Stochastic Processes

    NASA Astrophysics Data System (ADS)

    Embrechts, Paul; Maejima, Makoto

    Self-similar processes such as fractional Brownian motion are stochastic processes that are invariant in distribution under suitable scaling of time and space. These processes can typically be used to model random phenomena with long-range dependence. Naturally, these processes are closely related to the notion of renormalization in statistical and high energy physics. They are also increasingly important in many other fields of application, as there are economics and finance. This paper starts with some basic aspects on self-similar processes and discusses several topics from the point of view of probability theory.

  18. Singularly continuous spectrum of a self-similar Laplacian on the half-line

    NASA Astrophysics Data System (ADS)

    Chen, Joe P.; Teplyaev, Alexander

    2016-05-01

    We investigate the spectrum of the self-similar Laplacian, which generates the so-called "pq random walk" on the integer half-line ℤ+. Using the method of spectral decimation, we prove that the spectral type of the Laplacian is singularly continuous whenever p ≠ /1 2 . This serves as a toy model for generating singularly continuous spectrum, which can be generalized to more complicated settings. We hope it will provide more insight into Fibonacci-type and other weakly self-similar models.

  19. Solar wind polytropic index estimates based on single spacecraft plasma and interplanetary magnetic field measurements

    NASA Astrophysics Data System (ADS)

    Kartalev, M.; Dryer, M.; Grigorov, K.; Stoimenova, E.

    2006-10-01

    We propose an approach for estimating the polytropic index in the solar wind. This is an artificially introduced parameter simplifying essentially the gasdynamic or magnetogasdynamic modeling of the interplanetary plasma. The problem in the straightforward utilization of the polytropic equation is to find sufficient homogeneous fragments of the solar wind flow, observed by single spacecraft only, where the application of this polytropic equation is correct. We propose an algorithm for following the plasma data time series to ensure the separation of data segments that belong, with high probability, to the same plasma flow flux tube. A linear regression model between logarithms of plasma density and temperature within such a segment provides an estimate for the polytropic index. Some preliminary applications of the algorithm to real data from spacecraft crossings of different solar wind structures are performed for the Bastille event of 14-16 July 2000.

  20. Ellipsoidal figures of equilibrium - Compressible models. [for self-gravitating Newtonian fluids in rotating polytropes

    NASA Technical Reports Server (NTRS)

    Lai, Dong; Rasio, Frederic A.; Shapiro, Stuart L.

    1993-01-01

    The results of Chandrasekhar (1969) are generalized to polytropes, using a formalism based on ellipsoidal energy variational principle to construct approximate stellar equilibrium solutions and study their stability. After reviewing the energy variational method and describing the approach, several equivalent stability conditions are established and secular vs. dynamical instabilities are discussed. Then, the equilibrium structure equations are derived for isolated, rotating polytropes, and axisymmetric configurations (compressible Maclaurin spheroids) are considered. Particular attention is given to triaxial configurations, either in a state of uniform rotation (generalizing the classical Jacobi ellipsoids) or with internal fluid motions of uniform vorticity (the compressible analogues of Riemann-S ellipsoids) and to the stability of these single star configurations. The compressible generalizations of the Roche and Roche-Riemann problems for a polytrope in orbit about a point-mass companion are solved, and the generalized Darwin problem for two identical polytropes in a binary is considered.

  1. Study of polytropic exponent based on high pressure switching expansion reduction

    NASA Astrophysics Data System (ADS)

    Wang, Xuanyin; Luo, Yuxi; Xu, Zhipeng

    2011-10-01

    Switching expansion reduction (SER) uses a switch valve to substitute the throttle valve to reduce pressure for high pressure pneumatics. The experiments indicate that the simulation model well predicts the actual characteristics. The heat transfers and polytropic exponents of the air in expansion tank and supply tanks of SER have been studied on the basis of the experiments and the simulation model. Through the mathematical reasoning in this paper, the polytropic exponent can be calculated by the air mass, heat, and work exchanges of the pneumatic container. For the air in a constant volume tank, when the heat-absorption is large enough to raise air temperature in discharging process, the polytropic exponent is less than 1; when the air is experiencing a discharging and heat-releasing process, the polytropic exponent exceeds the specific heat ratio (the value of 1.4).

  2. Equiangular Surfaces, Self-Similar Surfaces, and the Geometry of Seashells

    ERIC Educational Resources Information Center

    Boyadzhiev, Khristo N.

    2007-01-01

    Logarithmic spirals are among the most fascinating curves in the plane, being the only curves that are equiangular, and the only ones that are self-similar. In this article, we show that in three dimensions, these two properties are independent. Although there are surfaces that have both properties, there are some that are equiangular, but not…

  3. Leonardo's Rule, Self-Similarity, and Wind-Induced Stresses in Trees

    NASA Astrophysics Data System (ADS)

    Eloy, Christophe

    2011-12-01

    Examining botanical trees, Leonardo da Vinci noted that the total cross section of branches is conserved across branching nodes. In this Letter, it is proposed that this rule is a consequence of the tree skeleton having a self-similar structure and the branch diameters being adjusted to resist wind-induced loads.

  4. Influence of heterogeneity on second-kind self-similar solutions for gravity currents

    NASA Astrophysics Data System (ADS)

    Zheng, Zhong; Christov, Ivan; Stone, Howard; Complex Fluid Group Team

    2013-11-01

    We report experimental, theoretical and numerical results on the effects of horizontal heterogeneity on the propagation of viscous gravity currents. We use two geometries to highlight these effects: (a) a horizontal channel (or crack) whose gap thickness varies as a power-law function of the streamwise coordinate; (b) a heterogeneous porous medium whose permeability and porosity have power-law variations. We demonstrate that two types of self-similar behaviors emerge as a result of horizontal heterogeneity: (a) a first-kind self-similar solution is found using dimensional analysis (scaling) for viscous gravity currents that propagate away from the origin (point of zero permeability); (b) a second-kind self-similar solution is found using a phase-plane analysis for gravity currents that propagate toward the origin. These theoretical predictions, obtained using the ideas of self-similar intermediate asymptotics, are compared to experimental results and numerical solutions of the governing partial differential equations developed under the lubrication approximation. All three results are found to be in good agreement.

  5. A note on the self-similar solutions to the spontaneous fragmentation equation

    NASA Astrophysics Data System (ADS)

    Breschi, Giancarlo; Fontelos, Marco A.

    2017-05-01

    We provide a method to compute self-similar solutions for various fragmentation equations and use it to compute their asymptotic behaviours. Our procedure is applied to specific cases: (i) the case of mitosis, where fragmentation results into two identical fragments, (ii) fragmentation limited to the formation of sufficiently large fragments, and (iii) processes with fragmentation kernel presenting a power-like behaviour.

  6. Influence of heterogeneity on second-kind self-similar solutions for viscous gravity currents

    SciTech Connect

    Zheng, Zhong; Christov, Ivan  C.; Stone, Howard  A.

    2014-05-01

    We report experimental, theoretical and numerical results on the effects of horizontal heterogeneities on the propagation of viscous gravity currents. We use two geometries to highlight these effects: (a) a horizontal channel (or crack) whose gap thickness varies as a power-law function of the streamwise coordinate; (b) a heterogeneous porous medium whose permeability and porosity have power-law variations. We demonstrate that two types of self-similar behaviours emerge as a result of horizontal heterogeneity: (a) a first-kind self-similar solution is found using dimensional analysis (scaling) for viscous gravity currents that propagate away from the origin (a point of zero permeability); (b) a second-kind self-similar solution is found using a phase-plane analysis for viscous gravity currents that propagate toward the origin. These theoretical predictions, obtained using the ideas of self-similar intermediate asymptotics, are compared with experimental results and numerical solutions of the governing partial differential equation developed under the lubrication approximation. All three results are found to be in good agreement.

  7. Influence of heterogeneity on second-kind self-similar solutions for viscous gravity currents

    DOE PAGES

    Zheng, Zhong; Christov, Ivan  C.; Stone, Howard  A.

    2014-05-01

    We report experimental, theoretical and numerical results on the effects of horizontal heterogeneities on the propagation of viscous gravity currents. We use two geometries to highlight these effects: (a) a horizontal channel (or crack) whose gap thickness varies as a power-law function of the streamwise coordinate; (b) a heterogeneous porous medium whose permeability and porosity have power-law variations. We demonstrate that two types of self-similar behaviours emerge as a result of horizontal heterogeneity: (a) a first-kind self-similar solution is found using dimensional analysis (scaling) for viscous gravity currents that propagate away from the origin (a point of zero permeability); (b)more » a second-kind self-similar solution is found using a phase-plane analysis for viscous gravity currents that propagate toward the origin. These theoretical predictions, obtained using the ideas of self-similar intermediate asymptotics, are compared with experimental results and numerical solutions of the governing partial differential equation developed under the lubrication approximation. All three results are found to be in good agreement.« less

  8. Naked singularities in non-self-similar gravitational collapse of radiation shells

    SciTech Connect

    Joshi, P.S.; Dwivedi, I.H. )

    1992-03-15

    Non-self-similar gravitational collapse of imploding radiation is shown to give rise to a strong curvature naked singularity. The conditions are specified for the singularity to be globally naked and the strength of the same is examined along nonspacelike curves and along all the families of nonspacelike geodesics terminating at the singularity in the past.

  9. Self-similar cosmological solutions with dark energy. II. Black holes, naked singularities, and wormholes

    SciTech Connect

    Maeda, Hideki; Harada, Tomohiro; Carr, B. J.

    2008-01-15

    We use a combination of numerical and analytical methods, exploiting the equations derived in a preceding paper, to classify all spherically symmetric self-similar solutions which are asymptotically Friedmann at large distances and contain a perfect fluid with equation of state p=({gamma}-1){mu} with 0<{gamma}<2/3. The expansion of the Friedmann universe is accelerated in this case. We find a one-parameter family of self-similar solutions representing a black hole embedded in a Friedmann background. This suggests that, in contrast to the positive pressure case, black holes in a universe with dark energy can grow as fast as the Hubble horizon if they are not too large. There are also self-similar solutions which contain a central naked singularity with negative mass and solutions which represent a Friedmann universe connected to either another Friedmann universe or some other cosmological model. The latter are interpreted as self-similar cosmological white hole or wormhole solutions. The throats of these wormholes are defined as two-dimensional spheres with minimal area on a spacelike hypersurface and they are all nontraversable because of the absence of a past null infinity.

  10. DNS of self-similar adverse pressure gradient turbulent boundary layer

    NASA Astrophysics Data System (ADS)

    Soria, Julio; Kitsios, Vassili; Sekimoto, Atsushi; Atkinson, Callum; Jiménez, Javier

    2016-11-01

    A direct numerical simulation (DNS) of a self-similar adverse pressure gradient (APG) turbulent boundary layer (TBL) at the verge of separation has been set-up and carried out. The DNS APG TBL has a displacement thickness based Reynolds number that ranges up to 30,000. The conditions for self-similarity and appropriate scaling will be highlighted, with the first and second order velocity statistical profiles non-dimensionalised using this scaling. The details of the DNS and the required boundary conditions that are necessary to establish this self-similar APG-TBL will be presented. The statistical properties of the self-similar adverse pressure gradient (APG) turbulent boundary layer (TBL) DNS will presented, as will the profiles of the terms in the momentum equation, spanwise/wall-normal kinetic energy spectrum and two-point correlations, which will be compared to those of a zero pressure gradient turbulent boundary layer. NCI and Pawsey SCC funded by the Australian and Western Australian governments as well as the support of PRACE funded by the European Union are gratefully acknowledged.

  11. Large resistivity in numerical simulations of radially self-similar outflows

    NASA Astrophysics Data System (ADS)

    Čemeljić, Miljenko; Vlahakis, Nektarios; Tsinganos, Kanaris

    2011-08-01

    We investigate conditions in a radially self-similar outflow in the regime of large resistivity. Using the PLUTO code, we performed simulations with proper choice of boundary conditions, relaxed at the footpoints of critical surfaces in the flow. We investigate outflow propagation in a high-resistive disk corona, and compare it to the results with small or vanishing resistivity.

  12. Sponge Cake or Champagne? Bubbles, Magmatic Degassing and Volcanic Eruptions

    NASA Astrophysics Data System (ADS)

    Cashman, K.; Pioli, L.; Belien, I.; Wright, H.; Rust, A.

    2007-12-01

    Vesiculation is an unavoidable consequence of magma decompression; the extent to which bubbles travel with ascending magma or leave the system by separated or permeable flow will determine the nature of the ensuing eruption. Bubbles travel with the melt from which they exsolve if the rise time of bubbles through the melt (the 'drift velocity') is much less than the rise rate of the magma (sponge cake). This condition is most likely to be met in viscous melts (where bubble rise velocities are low) and in melts that experience rapid decompression (high ascent velocities). Under these conditions, bubble expansion within the melt continues until sufficient bubble expansion causes coalescence and the development of a permeable network. Typical pumice vesicularities of 70-80% and permeabilities of 10-12 m2 constrain this limit under conditions appropriate for subplinian to plinian eruptions (mass fluxes > 106 kg/s). Slower rise rates (and lower mass fluxes) that characterize effusive eruptions produce silicic lavas with a wider range of vesicularities. In general, permeability decreases with decreasing sample vesicularity as bubbles deform (as evidenced by anisotropy in permeability and electrical conductivity) and pore apertures diminish. Degassing efficiency (and resulting densification of magma within the conduit) under these conditions is determined by permeability and the time allowed for gas escape. Bubbles rise through the melt if the drift velocity exceeds the velocity of magma ascent (champagne). This condition is most easily met in volatile-rich, low viscosity (mafic) melts at low to moderate fluxes. At very low magma flux, magma eruption rate is determined by the extent to which magma is entrained and ejected by rising gases (strombolian eruptions); when bubbles are too small, or are rising too slowly, they may not break the surface at all, but instead may be concentrated in a near-surface layer (surface foam). As the magma flux increases, segregation of

  13. Relativistic self-similar equilibria and non-axisymmetric neutral modes

    NASA Astrophysics Data System (ADS)

    Cai, Michael Jun

    By semi-analytic means, we examined a class of scale-free solutions to the Einstein equations with perfect fluid matter source. These spacetimes are self-similar under the simultaneous transformation r → ar and t → a1-nt for any constant a. From first principles, the fluid is supported against gravity by rotation and isothermal pressure that are a priori independent of each other. We thus explored the two- dimensional solution space parameterized by the resealing index n and the sound speed γ1/2. As preparatory work toward a more realistic model, we first studied the razor-thin self-similar disks with a two-dimensional scalar pressure. We then relaxed the infinitesimal vertical thickness assumption and considered three-dimensional rotating self-similar solutions. The isopycnic surfaces (surfaces of constant density) are in general toroids, with a certain degree of flattening given by the level of rotation. When the linear rotation velocity is large compared to the sound speed, we recover the disk solution. However, since relativity limits the rotation velocity to be less than that of light, complete flattening is impossible for a sound speed that is not infinitesimal. The last part of this dissertation returns to razor thin- disks and considers the non-axisymmetric neutral modes. By restricting ourselves to self-similar polar perturbations with azimuthal dependence given by eimø , we performed a stability analysis of an axisym-metric disk. We discovered two sets of tracks where the characteristic frequency vanishes in an inertial frame. These solutions are formally infinite in mass and extent, and thus cannot represent realistic astrophysical systems. However, if the properties do not change qualitatively when the self-similar configurations are truncated, then these solutions may serve as initial data for dynamic collapse in the monolithic formation of black holes. (Abstract shortened by UMI.)

  14. N,S,O-Heterocycles in Aged Champagne Reserve Wines and Correlation with Free Amino Acid Concentrations.

    PubMed

    Le Menn, Nicolas; Marchand, Stephanie; de Revel, Gilles; Demarville, Dominique; Laborde, Delphine; Marchal, Richard

    2017-03-14

    Champagne regulations allow winegrowers to stock still wines to compensate for quality shifts in vintages, mainly due to climate variations. According to their technical requirements and house style, Champagne producers use these stored wines in their blends to enhance complexity. The presence of lees and aging at low pH (2.95-3.15), as in Champagne wines, lead to several modifications in wine composition. These conditions, combined with extended aging, result in the required environment for the Maillard chemical reaction, involving aromatic molecules, including sulfur, oxygen, and nitrogen heterocycles (such as thiazole, furan, and pyrazine derivatives), which may have a sensory impact on wine. Some aromatic heterocycles in 50 monovarietal wines aged from 1 to 27 years provided by Veuve Clicquot Ponsardin Champagne house were determined by the SPME-GC-MS method. The most interesting result highlighted a strong correlation between certain heterocycle concentrations and wine age. The second revealed a correlation between heterocyclic compound and free amino acid concentrations measured in the wines, suggesting that these compounds are potential aromatic precursors when wine is aged on lees and, thus, potential key compounds in the bouquet of aged Champagnes. The principal outcome of these assays was to reveal, for the first time, that aromatic heterocycle concentrations in Champagne base wines are correlated with wine age.

  15. Foaming properties of various Champagne wines depending on several parameters: grape variety, aging, protein and CO2 content.

    PubMed

    Cilindre, Clara; Liger-Belair, Gérard; Villaume, Sandra; Jeandet, Philippe; Marchal, Richard

    2010-02-15

    A comparison of the foaming parameters of various Champagne wines was undergone with two well distinct methods: (i) a classical gas-sparging method providing standardized but artificial effervescence conditions (the so-called Mosalux), and (ii) a computer assisted viewing equipment (CAVE), much closer to the real champagne tasting conditions. The latter one is the only apparatus which enables a thorough descriptive analysis of foam behavior, during the pouring process of a sparkling wine, and from the end of its pouring. Various Champagne wines elaborated from two grape varieties (Chardonnay and Pinot Meunier) and having experienced different aging-periods (15 months and 5 years) were analyzed and compared to a model sparkling wine, elaborated from a model base wine (devoid of grape colloids). The CO(2) and protein content was also investigated to discuss the foaming behavior of these wines. A significant loss of the CO(2) content during aging was observed and might be the reason for the worse foaming properties of the old champagnes, as determined with CAVE. It is worth noting that contradictory foaming parameters were obtained through the Mosalux method, which is indeed more intrusive than the CAVE, and finally far from the real champagne tasting conditions, since it requires filtration and champagne degassing prior experiment.

  16. Numerical Modeling of Tidal Effects in Polytropic Accretion Disks

    NASA Technical Reports Server (NTRS)

    Godon, Patrick

    1997-01-01

    A two-dimensional time-dependent hybrid Fourier-Chebyshev method of collocation is developed and used for the study of tidal effects in accretion disks, under the assumptions of a polytropic equation of state and a standard alpha viscosity prescription. Under the influence of the m = 1 azimuthal component of the tidal potential, viscous oscillations in the outer disk excite an m = 1 eccentric instability in the disk. While the m = 2 azimuthal component of the tidal potential excites a Papaloizou-Pringle instability in the inner disk (a saturated m = 2 azimuthal mode), with an elliptic pattern rotating at about a fraction (approx. = 1/3) of the local Keplerian velocity in the inner disk. The period of the elliptic mode corresponds well to the periods of the short-period oscillations observed in cataclysmic variables. In cold disks (r(Omega)/c(sub s) = M approx. = 40) we also find a critical value of the viscosity parameter (alpha approx. = 0.01), below which shock dissipation dominates and is balanced by the wave amplification due to the wave action conservation. In this case the double spiral shock propagates all the way to the inner boundary with a Mach number M(sub s) approx. = 1.3.

  17. Polytropic scaling of a flow Z-pinch

    NASA Astrophysics Data System (ADS)

    Hughes, M. C.; Shumlak, U.; Nelson, B. A.; Golingo, R. P.; Claveau, E. L.; Doty, S. A.; Forbes, E. G.; Kim, B.; Ross, M. P.; Weed, J. R.

    2015-11-01

    The ZaP Flow Z-Pinch project investigates the use of velocity shear to mitigate MHD instabilities. The ZaP-HD experiment produces 50 cm long pinches of varying radii. The power to the experiment is split between the plasma formation and acceleration process and the pinch assembly and compression process. Once the pinch is formed, low magnetic fluctuations indicate a quiescent, long-lived pinch. The split power supply allows more control of the pinch current than previous machine iterations, with a designed range from 50 to 150 kA. Radial force balance leads to the Bennett relation which indicates that as the pinch compresses due to increasing currents, the plasma pressure and/or linear density must change. Through ion spectroscopy and digital holographic interferometry coupled with magnetic measurements of the pinch current, the components of the Bennett relation can be fully measured. A scaling relation is then assumed to follow a polytrope as the pinch pressure, initially approximately 250 kPa, increases from an initially formed state to much higher values, approaching 100 MPa. A preliminary analysis of pinch scaling is shown corroborating with other diagnostics on the machine along with extrapolations to required currents for an HEDLP machine. This work is supported by grants from the U.S. Department of Energy and the U.S. National Nuclear Security Administration.

  18. Critical rotation of general-relativistic polytropic models revisited

    NASA Astrophysics Data System (ADS)

    Geroyannis, V.; Karageorgopoulos, V.

    2013-09-01

    We develop a perturbation method for computing the critical rotational parameter as a function of the equatorial radius of a rigidly rotating polytropic model in the "post-Newtonia approximation" (PNA). We treat our models as "initial value problems" (IVP) of ordinary differential equations in the complex plane. The computations are carried out by the code dcrkf54.f95 (Geroyannis and Valvi 2012 [P1]; modified Runge-Kutta-Fehlberg code of fourth and fifth order for solving initial value problems in the complex plane). Such a complex-plane treatment removes the syndromes appearing in this particular family of IVPs (see e.g. P1, Sec. 3) and allows continuation of the numerical integrations beyond the surface of the star. Thus all the required values of the Lane-Emden function(s) in the post-Newtonian approximation are calculated by interpolation (so avoiding any extrapolation). An interesting point is that, in our computations, we take into account the complete correction due to the gravitational term, and this issue is a remarkable difference compared to the classical PNA. We solve the generalized density as a function of the equatorial radius and find the critical rotational parameter. Our computations are extended to certain other physical characteristics (like mass, angular momentum, rotational kinetic energy, etc). We find that our method yields results comparable with those of other reliable methods. REFERENCE: V.S. Geroyannis and F.N. Valvi 2012, International Journal of Modern Physics C, 23, No 5, 1250038:1-15.

  19. On self-similar blast waves headed by the Chapman-Jouguet detonation.

    NASA Technical Reports Server (NTRS)

    Oppenheim, A. K.; Kuhl, A. L.; Kamel, M. M.

    1972-01-01

    Consideration of the whole class of self-similar solutions for blast waves bounded by Chapman-Jouguet detonations that propagate into a uniform, quiescent, zero counterpressure atmosphere of a perfect gas with constant specific heats. Since such conditions can be approached quite closely by some actual chemical systems at NTP, this raises the interesting possibility of the existence of Chapman-Jouguet detonations of variable velocity. The principal virtue of the results presented is, however, more of theoretical significance. They represent the limiting case for all the self-similar blast waves headed by gasdynamic discontinuities associated with a deposition of finite amounts of energy, and they exhibit some unique features owing to the singular nature of the Chapman-Jouguet condition.

  20. On the role of self-similarity in component-based software.

    SciTech Connect

    Elwasif, Wael; Armstrong, Robert C.; Bernholdt, David E.; Allan, Benjamin A.

    2005-03-01

    This is a speculative work meant to stimulate discussion about the role of subsumability in self-similar software structures for computational simulations. As in natural phenomena, self-similar features in framework structures allow the size and complexity of code to grow without bound and still maintain apparent coherence. As in crystal growth, the coherence may be maintained by the application of a repeated pattern, or patterns may, as in fluid mechanical turbulence, be scaled by size and nested. Examples of these kinds of patterns applied to component systems in particular will be given. Conclusions and questions for discussion will be drawn regarding the applicability of these ideas to component architectures, complexity, and scientific computing.

  1. Retinal Image Enhancement Using Robust Inverse Diffusion Equation and Self-Similarity Filtering.

    PubMed

    Wang, Lu; Liu, Guohua; Fu, Shujun; Xu, Lingzhong; Zhao, Kun; Zhang, Caiming

    2016-01-01

    As a common ocular complication for diabetic patients, diabetic retinopathy has become an important public health problem in the world. Early diagnosis and early treatment with the help of fundus imaging technology is an effective control method. In this paper, a robust inverse diffusion equation combining a self-similarity filtering is presented to detect and evaluate diabetic retinopathy using retinal image enhancement. A flux corrected transport technique is used to control diffusion flux adaptively, which eliminates overshoots inherent in the Laplacian operation. Feature preserving denoising by the self-similarity filtering ensures a robust enhancement of noisy and blurry retinal images. Experimental results demonstrate that this algorithm can enhance important details of retinal image data effectively, affording an opportunity for better medical interpretation and subsequent processing.

  2. Self-similar distribution function and the production of runaway electrons

    SciTech Connect

    Silin, V.P.; Uryupin, S.A.

    1992-09-01

    The theory of the suppression of anomalous plasma resistivity due to ion-cyclotron turbulence resulting from the formation of runaway electrons has long attracted the attention of researchers. The purpose of this communication was to describe how the approach to the asymptotic regime noted in Vekshtein, et al. occurs, and how the electron distribution is transformed as a result. It was shown that over a time much larger than that required for the temperature to double, a self-similar distribution is obtained for the bulk of the electrons. It was concluded that the self-similar distribution occurs for the bulk of the particles, followed by leakage at times much larger than the already anomalously large time t{sub 0}.

  3. Self-similar Shape Mode of Optical Pulse Propagation in Medium with non-stationary Absorption

    NASA Astrophysics Data System (ADS)

    Trofimov, Vycheslav A.; Lysak, Tatyana M.; Fedotov, Mihail V.; Prokopenko, Alexander S.

    2015-03-01

    We discuss laser pulse propagation with the self-similar shape in a medium with instantaneous nonlinear absorption. We consider two cases of the laser pulse propagation. First one corresponds to problem of laser-induced plasma generation in silica under action of TW laser pulse. The second one corresponds to femtosecond laser pulse propagation in medium with nanoparticles of noble metals. In both cases the mode of the self-similar shape of pulse is of interest. We discuss also a physical mechanism of non-linear acceleration or slowing-down for laser pulse propagation in a medium with nanoparticles. The last phenomena are important, in particular, for a problem of data processing of all optical method. We used analytical approach for considered problem as well as computer simulation.

  4. Approximate self-similar solutions to a nonlinear diffusion equation with time-fractional derivative

    NASA Astrophysics Data System (ADS)

    Płociniczak, Łukasz; Okrasińska, Hanna

    2013-10-01

    In this paper, we consider a fractional nonlinear problem for anomalous diffusion. The diffusion coefficient we use is of power type, and hence the investigated problem generalizes the porous-medium equation. A generalization is made by introducing a fractional time derivative. We look for self-similar solutions for which the fractional setting introduces other than classical space-time scaling. The resulting similarity equations are of nonlinear integro-differential type. We approximate these equations by an expansion of the integral operator and by looking for solutions in a power function form. Our method can be easily adapted to solve various problems in self-similar diffusion. The approximations obtained give very good results in numerical analysis. Their simplicity allows for easy use in applications, as our fitting with experimental data shows. Moreover, our derivation justifies theoretically some previously used empirical models for anomalous diffusion.

  5. Electromagnetic radiation due to naked singularity formation in self-similar gravitational collapse

    SciTech Connect

    Mitsuda, Eiji; Yoshino, Hirotaka; Tomimatsu, Akira

    2005-04-15

    Dynamical evolution of test fields in background geometry with a naked singularity is an important problem relevant to the Cauchy horizon instability and the observational signatures different from black hole formation. In this paper we study electromagnetic perturbations generated by a given current distribution in collapsing matter under a spherically symmetric self-similar background. Using the Green's function method, we construct the formula to evaluate the outgoing energy flux observed at the future null infinity. The contributions from 'quasinormal' modes of the self-similar system as well as 'high-frequency' waves are clarified. We find a characteristic power-law time evolution of the outgoing energy flux which appears just before naked singularity formation and give the criteria as to whether or not the outgoing energy flux diverges at the future Cauchy horizon.

  6. Self-similar expansion of solar coronal mass ejections: Implications for Lorentz self-force driving

    SciTech Connect

    Subramanian, Prasad; Arunbabu, K. P.; Mauriya, Adwiteey; Vourlidas, Angelos

    2014-08-01

    We examine the propagation of several coronal mass ejections (CMEs) with well-observed flux rope signatures in the field of view of the SECCHI coronagraphs on board the STEREO satellites using the graduated cylindrical shell fitting method of Thernisien et al. We find that the manner in which they propagate is approximately self-similar; i.e., the ratio (κ) of the flux rope minor radius to its major radius remains approximately constant with time. We use this observation of self-similarity to draw conclusions regarding the local pitch angle (γ) of the flux rope magnetic field and the misalignment angle (χ) between the current density J and the magnetic field B. Our results suggest that the magnetic field and current configurations inside flux ropes deviate substantially from a force-free state in typical coronagraph fields of view, validating the idea of CMEs being driven by Lorentz self-forces.

  7. A Stable Self-Similar Singularity of Evaporating Drops: Ellipsoidal Collapse to a Point

    NASA Astrophysics Data System (ADS)

    Fontelos, Marco A.; Hong, Seok Hyun; Hwang, Hyung Ju

    2015-08-01

    We study the problem of evaporating drops contracting to a point. Going back to Maxwell and Langmuir, the existence of a spherical solution for which evaporating drops collapse to a point in a self-similar manner is well established in the physical literature. The diameter of the drop follows the so-called D 2 law: the second power of the drop-diameter decays linearly in time. In this study we provide a complete mathematical proof of this classical law. We prove that evaporating drops which are initially small perturbations of a sphere collapse to a point and the shape of the drop converges to a self-similar ellipsoid whose center, orientation, and semi-axes are determined by the initial shape.

  8. On self-similar blast waves headed by the Chapman-Jouguet detonation.

    NASA Technical Reports Server (NTRS)

    Oppenheim, A. K.; Kuhl, A. L.; Kamel, M. M.

    1972-01-01

    Consideration of the whole class of self-similar solutions for blast waves bounded by Chapman-Jouguet detonations that propagate into a uniform, quiescent, zero counterpressure atmosphere of a perfect gas with constant specific heats. Since such conditions can be approached quite closely by some actual chemical systems at NTP, this raises the interesting possibility of the existence of Chapman-Jouguet detonations of variable velocity. The principal virtue of the results presented is, however, more of theoretical significance. They represent the limiting case for all the self-similar blast waves headed by gasdynamic discontinuities associated with a deposition of finite amounts of energy, and they exhibit some unique features owing to the singular nature of the Chapman-Jouguet condition.

  9. Tests of peak flow scaling in simulated self-similar river networks

    USGS Publications Warehouse

    Menabde, M.; Veitzer, S.; Gupta, V.; Sivapalan, M.

    2001-01-01

    The effect of linear flow routing incorporating attenuation and network topology on peak flow scaling exponent is investigated for an instantaneously applied uniform runoff on simulated deterministic and random self-similar channel networks. The flow routing is modelled by a linear mass conservation equation for a discrete set of channel links connected in parallel and series, and having the same topology as the channel network. A quasi-analytical solution for the unit hydrograph is obtained in terms of recursion relations. The analysis of this solution shows that the peak flow has an asymptotically scaling dependence on the drainage area for deterministic Mandelbrot-Vicsek (MV) and Peano networks, as well as for a subclass of random self-similar channel networks. However, the scaling exponent is shown to be different from that predicted by the scaling properties of the maxima of the width functions. ?? 2001 Elsevier Science Ltd. All rights reserved.

  10. Self-similar flow channel designs for parallel multiscale transport of multiple fluid species

    NASA Astrophysics Data System (ADS)

    Lee, Kenneth; Savas, Omer

    2011-11-01

    The need for multiscale fluid transport arises in a number of engineering applications involving fluid delivery or collection over a range of different lengthscales. A ``tree-shaped'' system of flow channels has been an efficient transport solution commonly practiced by biomimetics. There has been much work in optimizing these dendritic flow systems, primarily for cooling applications. However, most designs can be costly to manufacture and limited in scalability. Moreover, most systems are restricted to the transport of a single fluid species. This work explores the feasibility of self-similar flow channel designs to provide parallel multiscale transport of multiple fluid species. The self-similar characteristic of these designs simplifies manufacturing and allows for flexible scalability. Prototypes for the parallel transport of one and two independent fluid species are supported with analytical theory and experimental work. Designs for three and four species are presented as well. Supported by Joint Center for Artificial Photosynthesis (JCAP)

  11. Self-similar propagation of Hermite-Gauss water-wave pulses.

    PubMed

    Fu, Shenhe; Tsur, Yuval; Zhou, Jianying; Shemer, Lev; Arie, Ady

    2016-01-01

    We demonstrate both theoretically and experimentally propagation dynamics of surface gravity water-wave pulses, having Hermite-Gauss envelopes. We show that these waves propagate self-similarly along an 18-m wave tank, preserving their general Hermite-Gauss envelopes in both the linear and the nonlinear regimes. The measured surface elevation wave groups enable observing the envelope phase evolution of both nonchirped and linearly frequency chirped Hermite-Gauss pulses, hence allowing us to measure Gouy phase shifts of high-order Hermite-Gauss pulses for the first time. Finally, when increasing pulse amplitude, nonlinearity becomes essential and the second harmonic of Hermite-Gauss waves was observed. We further show that these generated second harmonic bound waves still exhibit self-similar Hermite-Gauss shapes along the tank.

  12. Dynamics Of A Laser-Induced Plume Self-Similar Expansion

    SciTech Connect

    Bennaceur-Doumaz, D.; Djebli, M.

    2008-09-23

    The dynamics of a laser ablation plume during the first stage of its expansion, just after the termination of the laser pulse is modeled. First, we suppose the laser fluence range low enough to consider a neutral vapor. The expansion of the evaporated material is described by one-component fluid and one-dimensional Euler equations. The vapor is assumed to follow an ideal gas flow. For high energetic ions, the charge separation can be neglected and the hydrodynamics equations can be solved using self-similar formulation. The obtained ordinary differential equations are solved numerically. Secondly, the effect of ionization is investigated when the evaporated gas temperature is sufficiently high. In this case, Saha equation is included in the formulation of the model. We find a self-similar solution for a finite value of the similarity variable which depends on the laser ablation parameters.

  13. Self-similar accretion in thin discs around near-extremal black holes

    NASA Astrophysics Data System (ADS)

    Compère, Geoffrey; Oliveri, Roberto

    2017-07-01

    Near-maximally spinning black holes display conformal symmetry in their near-horizon region, which is therefore the locus of critical phenomena. In this paper, we revisit the Novikov-Thorne accretion thin disc model and find a new self-similar radiation-dominated solution in the extremely high spin regime. Motivated by the self-consistency of the model, we require that matter flows at the sound speed at the innermost stable circular orbit (ISCO). We observe that, when the disc pressure is dominated by radiation at the ISCO, which occurs for the best-fitting Novikov-Thorne model of GRS 1915+105, the Shakura-Sunyaev viscosity parameter can be expressed in terms of the spin, mass accretion rate and radiative efficiency. We quantitatively describe how the exact thin disc solution approaches the self-similar solution in the vicinity of the ISCO and for increasing spins.

  14. Two-particle anomalous diffusion: probability density functions and self-similar stochastic processes.

    PubMed

    Pagnini, Gianni; Mura, Antonio; Mainardi, Francesco

    2013-05-13

    Two-particle dispersion is investigated in the context of anomalous diffusion. Two different modelling approaches related to time subordination are considered and unified in the framework of self-similar stochastic processes. By assuming a single-particle fractional Brownian motion and that the two-particle correlation function decreases in time with a power law, the particle relative separation density is computed for the cases with time sub-ordination directed by a unilateral M-Wright density and by an extremal Lévy stable density. Looking for advisable mathematical properties (for instance, the stationarity of the increments), the corresponding self-similar stochastic processes are represented in terms of fractional Brownian motions with stochastic variance, whose profile is modelled by using the M-Wright density or the Lévy stable density.

  15. Random vortex-street model for a self-similar plane turbulent jet.

    PubMed

    L'vov, Victor S; Pomyalov, Anna; Procaccia, Itamar; Govindarajan, Rama

    2008-08-29

    We ask what determines the (small) angle of turbulent jets. To answer this question we first construct a deterministic vortex-street model representing the large-scale structure in a self-similar plane turbulent jet. Without adjustable parameters the model reproduces the mean velocity profiles and the transverse positions of the large-scale structures, including their mean sweeping velocities, in a quantitative agreement with experiments. Nevertheless, the exact self-similar arrangement of the vortices (or any other deterministic model) necessarily leads to a collapse of the jet angle. The observed (small) angle results from a competition between vortex sweeping tending to strongly collapse the jet and randomness in the vortex structure, with the latter resulting in a weak spreading of the jet.

  16. Phase transitions for the multifractal analysis of self-similar measures

    NASA Astrophysics Data System (ADS)

    Testud, B.

    2006-05-01

    We are interested in the multifractal analysis of a class of self-similar measures with overlaps. This class, for which we obtain explicit formulae for the Lq-spectrum, τ(q), as well as the singularity spectrum f(α), is sufficiently large to point out new phenomena in the multifractal structure of self-similar measures. We show that, unlike in the classical quasi-Bernoulli case, the Lq-spectrum, τ(q), of the measures studied can have an arbitrarily large number of non-differentiability points (phase transitions). These singularities occur only for the negative values of q and yield to measures that do not satisfy the usual multifractal formalism. The weak quasi-Bernoulli property is the key point of most of the arguments.

  17. Self-similar formation of the Kolmogorov spectrum in the Leith model of turbulence

    NASA Astrophysics Data System (ADS)

    Nazarenko, S. V.; Grebenev, V. N.

    2017-01-01

    The last stage of evolution toward the stationary Kolmogorov spectrum of hydrodynamic turbulence is studied using the Leith model [1]. This evolution is shown to manifest itself as a reflection wave in the wavenumber space propagating from the largest toward the smallest wavenumbers, and is described by a self-similar solution of a new (third) kind. This stage follows the previously studied stage of an initial explosive propagation of the spectral front from the smallest to the largest wavenumbers reaching arbitrarily large wavenumbers in a finite time, and which was described by a self-similar solution of the second kind [2-4]. Nonstationary solutions corresponding to ‘warm cascades’ characterised by a thermalised spectrum at large wavenumbers are also obtained.

  18. Propagation of femtosecond pulse with self-similar shape in medium with nonlinear absorption

    NASA Astrophysics Data System (ADS)

    Trofimov, Vyacheslav A.; Zakharova, Irina G.

    2015-05-01

    We investigate the propagation of laser pulse with self-similar shape in homogeneous medium with various mechanisms of nonlinear absorption: multi-photon absorption or resonant nonlinearity under detuning the frequency, corresponding to energy transition, from the current frequency of wave packet, or nonlinear absorption with its saturation. Both types of sign for frequency detuning are considered. This results in appearance of a refractive index grating which induced a laser pulse self-action. We analyze also the influence of the laser pulse self-modulation due to cubic nonlinearity on existence of the laser pulse propagation mode with self-similar shape. We develop an analytical solution of the corresponding nonlinear eigenfunction problem for laser pulse propagation in medium with nonlinear absorption. This solution is confirmed by computer simulation of the eigenfunction problem for Schrödinger equation with considered nonlinearity. This mode of laser pulse propagation is very important for powerful TW laser pulse propagating in glass.

  19. Retinal Image Enhancement Using Robust Inverse Diffusion Equation and Self-Similarity Filtering

    PubMed Central

    Fu, Shujun; Xu, Lingzhong; Zhao, Kun; Zhang, Caiming

    2016-01-01

    As a common ocular complication for diabetic patients, diabetic retinopathy has become an important public health problem in the world. Early diagnosis and early treatment with the help of fundus imaging technology is an effective control method. In this paper, a robust inverse diffusion equation combining a self-similarity filtering is presented to detect and evaluate diabetic retinopathy using retinal image enhancement. A flux corrected transport technique is used to control diffusion flux adaptively, which eliminates overshoots inherent in the Laplacian operation. Feature preserving denoising by the self-similarity filtering ensures a robust enhancement of noisy and blurry retinal images. Experimental results demonstrate that this algorithm can enhance important details of retinal image data effectively, affording an opportunity for better medical interpretation and subsequent processing. PMID:27388503

  20. Scaling and interaction of self-similar modes in models of high Reynolds number wall turbulence

    NASA Astrophysics Data System (ADS)

    Sharma, A. S.; Moarref, R.; McKeon, B. J.

    2017-03-01

    Previous work has established the usefulness of the resolvent operator that maps the terms nonlinear in the turbulent fluctuations to the fluctuations themselves. Further work has described the self-similarity of the resolvent arising from that of the mean velocity profile. The orthogonal modes provided by the resolvent analysis describe the wall-normal coherence of the motions and inherit that self-similarity. In this contribution, we present the implications of this similarity for the nonlinear interaction between modes with different scales and wall-normal locations. By considering the nonlinear interactions between modes, it is shown that much of the turbulence scaling behaviour in the logarithmic region can be determined from a single arbitrarily chosen reference plane. Thus, the geometric scaling of the modes is impressed upon the nonlinear interaction between modes. Implications of these observations on the self-sustaining mechanisms of wall turbulence, modelling and simulation are outlined.

  1. Chirped self-similar optical pulses in tapered centrosymmetric nonlinear waveguides doped with resonant impurities

    NASA Astrophysics Data System (ADS)

    He, J. R.; Xu, S. L.; Xue, L.

    2017-06-01

    Exact chirped self-similar optical pulses propagating in tapered centrosymmetric nonlinear waveguides doped with resonant impurities are reported. The propagation behaviors of the pulses are studied by tailoring of the tapering function. Numerical simulations and stability analysis reveal that the tapering can be used to postpone the wave dispersion and the addition of a small cubic self-focusing term to the governing equation could stabilize the chirped bright pulses. An example of possible experimental protocol that may generate the pulses in realistic waveguides is given. The obtained chirped self-similar optical pulses are particularly useful in the design of amplifying or attenuating pulse compressors for chirped solitary waves in tapered centrosymmetric nonlinear waveguides doped with resonant impurities.

  2. ON A GENERALIZED SELF-SIMILARITY IN THE p-ADIC FIELD

    NASA Astrophysics Data System (ADS)

    Mukhamedov, Farrukh; Khakimov, Otabek

    2016-08-01

    In the present paper, we introduce a new set which defines a generalized self-similar set for contractive functions {fi}i=1N on the unit ball ℤp of p-adic numbers. This set is called unconventional limit set. We prove that the unconventional limit set is compact, perfect and uniformly disconnected. Moreover, we provide an example of two contractions for which the corresponding unconventional limiting set is quasi-symmetrically equivalent to the symbolic Cantor set.

  3. Self-similarity and quasi-idempotence in neural networks and related dynamical systems

    NASA Astrophysics Data System (ADS)

    Minati, Ludovico; Winkel, Julia; Bifone, Angelo; Oświecimka, Paweł; Jovicich, Jorge

    2017-04-01

    Self-similarity across length scales is pervasively observed in natural systems. Here, we investigate topological self-similarity in complex networks representing diverse forms of connectivity in the brain and some related dynamical systems, by considering the correlation between edges directly connecting any two nodes in a network and indirect connection between the same via all triangles spanning the rest of the network. We note that this aspect of self-similarity, which is distinct from hierarchically nested connectivity (coarse-grain similarity), is closely related to idempotence of the matrix representing the graph. We introduce two measures, ι ( 1 ) and ι ( ∞ ) , which represent the element-wise correlation coefficients between the initial matrix and the ones obtained after squaring it once or infinitely many times, and term the matrices which yield large values of these parameters "quasi-idempotent". These measures delineate qualitatively different forms of "shallow" and "deep" quasi-idempotence, which are influenced by nodal strength heterogeneity. A high degree of quasi-idempotence was observed for partially synchronized mean-field Kuramoto oscillators with noise, electronic chaotic oscillators, and cultures of dissociated neurons, wherein the expression of quasi-idempotence correlated strongly with network maturity. Quasi-idempotence was also detected for macro-scale brain networks representing axonal connectivity, synchronization of slow activity fluctuations during idleness, and co-activation across experimental tasks, and preliminary data indicated that quasi-idempotence of structural connectivity may decrease with ageing. This initial study highlights that the form of network self-similarity indexed by quasi-idempotence is detectable in diverse dynamical systems, and draws attention to it as a possible basis for measures representing network "collectivity" and pattern formation.

  4. Characterization of local self-similarity and criticality in the solar active regions

    NASA Astrophysics Data System (ADS)

    Rosa, R. R.; Vats, H. O.; Ramos, F. M.; Zanandrea, A.; Rodrigues Neto, C.; Fernandes, F. C. R.; Bolzan, M. J. A.; Rempel, E. L.; Brito, R. C.; Vijaykumar, N. L.; Sawant, H. S.

    From solar radio burst data we computed wavelet transforms and frequency distribution for investigation of self-similar temporal variability and power-laws, as the fundamental conditions for characterization of dynamical criticality (self or forced) in the solar active regions. The main result indicates that, as for the global activity, the local coronal magnetic field, in millisecond time scales, can be in a critical state where the dynamics of solar active regions works as avalanches of many small intermittent particle acceleration events.

  5. Self-similar erbium-doped fiber laser with large normal dispersion.

    PubMed

    Liu, Hui; Liu, Zhanwei; Lamb, Erin S; Wise, Frank

    2014-02-15

    We report a large normal dispersion erbium-doped fiber laser with self-similar pulse evolution in the gain fiber. The cavity is stabilized by the local nonlinear attractor in the gain fiber through the use of a narrow filter. Experimental results are accounted for by numerical simulations. This laser produces 3.5 nJ pulses, which can be dechirped to 70 fs with an external grating pair.

  6. Self-similar solutions and converging shocks at the stellar surfaces

    NASA Astrophysics Data System (ADS)

    Saxena, Monica; Jena, J.

    2017-09-01

    In this paper, Lie group of transformations method is used to investigate the self-similar solutions for the system of one-dimensional hydrodynamic equations describing the post-shock flow at the stellar surface. Necessary conditions for the existence of similarity solutions for strong shocks are obtained. The similarity exponent using Lie group of transformations and characteristic rule are obtained. Collapses of imploding cylindrical and spherical shocks are worked out in detail.

  7. The non-integer operation associated to random variation sets of the self-similar set

    NASA Astrophysics Data System (ADS)

    Ren, Fu-Yao; Liang, Jin-Rong

    2000-10-01

    When memory sets are random variation sets of the self-similar set and the total number of remaining states in each stage of the division of this set is normalized to unity, the corresponding flux and fractional integral are “robust” and stable under some conditions. This answers an open problem proposed by Alian Le Mehaute et al. in their book entitled Irreversibilitê Temporel et Geometrie Fractale.

  8. Self-similar erbium-doped fiber laser with large normal dispersion

    PubMed Central

    Liu, Hui; Liu, Zhanwei; Lamb, Erin S.; Wise, Frank

    2014-01-01

    We report a large normal dispersion erbium-doped fiber laser with self-similar pulse evolution in the gain fiber. The cavity is stabilized by the local nonlinear attractor in the gain fiber through the use of a narrow filter. Experimental results are accounted for by numerical simulations. This laser produces 3.5 nJ pulses, which can be dechirped to 70 fs with an external grating pair. PMID:24562267

  9. A note on the self-similar solutions to the spontaneous fragmentation equation.

    PubMed

    Breschi, Giancarlo; Fontelos, Marco A

    2017-05-01

    We provide a method to compute self-similar solutions for various fragmentation equations and use it to compute their asymptotic behaviours. Our procedure is applied to specific cases: (i) the case of mitosis, where fragmentation results into two identical fragments, (ii) fragmentation limited to the formation of sufficiently large fragments, and (iii) processes with fragmentation kernel presenting a power-like behaviour.

  10. Extracting features of Gaussian self-similar stochastic processes via the Bandt-Pompe approach.

    PubMed

    Rosso, O A; Zunino, L; Pérez, D G; Figliola, A; Larrondo, H A; Garavaglia, M; Martín, M T; Plastino, A

    2007-12-01

    By recourse to appropriate information theory quantifiers (normalized Shannon entropy and Martín-Plastino-Rosso intensive statistical complexity measure), we revisit the characterization of Gaussian self-similar stochastic processes from a Bandt-Pompe viewpoint. We show that the ensuing approach exhibits considerable advantages with respect to other treatments. In particular, clear quantifiers gaps are found in the transition between the continuous processes and their associated noises.

  11. Self-Similar Solutions up to Flashpoint in Highly Wound Magnetostatics

    NASA Astrophysics Data System (ADS)

    Lynden-Bell, D.; Boily, C.

    1994-03-01

    A general theorem on force-free fields is proved and applied to highly wound field configurations. In axial symmetry such configurations expand along a cone of semi-angle 60° as the system is wound up. The self-similar field structure is determined. After 1/√3 turns the system reaches flashpoint with a discharge around this cone releasing toroidal flux loops to infinity. All poloidal flux then visits infinity.

  12. Quantization of probability distributions under norm-based distortion measures II: Self-similar distributions

    NASA Astrophysics Data System (ADS)

    Delattre, Sylvain; Graf, Siegfried; Luschgy, Harald; Pages, Gilles

    2006-06-01

    For a probability measure P on and consider where the infimum is taken over all subsets [alpha] of with card([alpha])[less-than-or-equals, slant]n and V is a nondecreasing function. Under certain conditions on V, we derive the precise n-asymptotics of en for self-similar distributions P and we find the asymptotic performance of optimal quantizers using weighted empirical measures.

  13. MAGNETIC HELICITY OF SELF-SIMILAR AXISYMMETRIC FORCE-FREE FIELDS

    SciTech Connect

    Zhang Mei; Flyer, Natasha; Low, Boon Chye

    2012-08-10

    In this paper, we continue our theoretical studies addressing the possible consequences of magnetic helicity accumulation in the solar corona. Our previous studies suggest that coronal mass ejections (CMEs) are natural products of coronal evolution as a consequence of magnetic helicity accumulation and that the triggering of CMEs by surface processes such as flux emergence also have their origin in magnetic helicity accumulation. Here, we use the same mathematical approach to study the magnetic helicity of axisymmetric power-law force-free fields but focus on a family whose surface flux distributions are defined by self-similar force-free fields. The semi-analytical solutions of the axisymmetric self-similar force-free fields enable us to discuss the properties of force-free fields possessing a huge amount of accumulated magnetic helicity. Our study suggests that there may be an absolute upper bound on the total magnetic helicity of all bipolar axisymmetric force-free fields. With the increase of accumulated magnetic helicity, the force-free field approaches being fully opened up with Parker-spiral-like structures present around a current-sheet layer as evidence of magnetic helicity in the interplanetary space. It is also found that among the axisymmetric force-free fields having the same boundary flux distribution, the one that is self-similar is the one possessing the maximum amount of total magnetic helicity. This gives a possible physical reason why self-similar fields are often found in astrophysical bodies, where magnetic helicity accumulation is presumably also taking place.

  14. Relativistic Self-similar Equilibria and Non-axisymmetric Neutral Modes

    NASA Astrophysics Data System (ADS)

    Cai, Mike J.; Shu, F. H.

    2002-05-01

    We have constructed semi-analytic axisymmetric scale free solutions to Einstein field equations with perfect fluid matter source. These spacetimes are self-similar under the simultaneous transformation r'= ar and t'=a1-nt. We explored the two dimensional solution space parameterized by the rescaling index n and the isothermal sound speed γ 1/2. The isopycnic surfaces are in general toroids. As the equilibrium configuration rotates faster, an ergo region develops in the form of the exterior of a cone centered about the symmetry axis. The sequence of solution terminates when frame dragging becomes infinite and the ergo cone closes onto the axis. In the extreme flattening limit, we have also searched for non-axisymmetric neutral modes in a self-similar disk. Two separate sets of tracks are discovered in the solution space. One corresponds to the bifurcation points to non-axisymmetric equilibria, which is confined in the non-ergo solutions. The other track signals the onset of instability driven by gravitational radiation. These solutions are formally infinite in extent, and thus can not represent realistic astrophysical systems. However, if these properties do not alter qualitatively when the self-similar configurations are truncated, then these solutions may serve as initial data for dynamic collapse in super massive black hole formation.

  15. Self-similar cosmological solutions with dark energy. I. Formulation and asymptotic analysis

    NASA Astrophysics Data System (ADS)

    Harada, Tomohiro; Maeda, Hideki; Carr, B. J.

    2008-01-01

    Based on the asymptotic analysis of ordinary differential equations, we classify all spherically symmetric self-similar solutions to the Einstein equations which are asymptotically Friedmann at large distances and contain a perfect fluid with equation of state p=(γ-1)μ with 0<γ<2/3. This corresponds to a “dark energy” fluid and the Friedmann solution is accelerated in this case due to antigravity. This extends the previous analysis of spherically symmetric self-similar solutions for fluids with positive pressure (γ>1). However, in the latter case there is an additional parameter associated with the weak discontinuity at the sonic point and the solutions are only asymptotically “quasi-Friedmann,” in the sense that they exhibit an angle deficit at large distances. In the 0<γ<2/3 case, there is no sonic point and there exists a one-parameter family of solutions which are genuinely asymptotically Friedmann at large distances. We find eight classes of asymptotic behavior: Friedmann or quasi-Friedmann or quasistatic or constant-velocity at large distances, quasi-Friedmann or positive-mass singular or negative-mass singular at small distances, and quasi-Kantowski-Sachs at intermediate distances. The self-similar asymptotically quasistatic and quasi-Kantowski-Sachs solutions are analytically extendible and of great cosmological interest. We also investigate their conformal diagrams. The results of the present analysis are utilized in an accompanying paper to obtain and physically interpret numerical solutions.

  16. The "self-similarity logic" applied to the development of the vascular system.

    PubMed

    Guidolin, Diego; Crivellato, Enrico; Ribatti, Domenico

    2011-03-01

    From a structural standpoint, living systems exhibit a hierarchical pattern of organization in which structures are nested within one another. From a temporal point of view, this type of organization is the outcome of a 'history' resulting from a set of developmental steps. Recently, it has been suggested that some auto similarity prevails at each nested level or time step and a principle of "self-similarity logic" has been proposed to convey the concept of a multi-level organization in which very similar rules (logic) apply at each level. In this study, the hypothesis is put forward that such a principle is particularly apparent in many morphological and developmental aspects of the vascular system. In fact, not only the morphology of the vascular system exhibits a high degree of geometrical self-similarity, but its remodelling processes also seem to be characterized by the application of almost the same rules, from the macroscopic to the endothelial cell to the sub-cellular levels, potentially allowing a unitary description of features such as sprouting and intussusceptive angiogenesis, and phenotypic differences of endothelial cells. The influence of the "self-similarity logic" shaping the vascular system on the organogenesis has been also discussed.

  17. Neural processing of race during imitation: self-similarity versus social status

    PubMed Central

    Reynolds Losin, Elizabeth A.; Cross, Katy A.; Iacoboni, Marco; Dapretto, Mirella

    2017-01-01

    People preferentially imitate others who are similar to them or have high social status. Such imitative biases are thought to have evolved because they increase the efficiency of cultural acquisition. Here we focused on distinguishing between self-similarity and social status as two candidate mechanisms underlying neural responses to a person’s race during imitation. We used fMRI to measure neural responses when 20 African American (AA) and 20 European American (EA) young adults imitated AA, EA and Chinese American (CA) models and also passively observed their gestures and faces. We found that both AA and EA participants exhibited more activity in lateral fronto-parietal and visual regions when imitating AAs compared to EAs or CAs. These results suggest that racial self-similarity is not likely to modulate neural responses to race during imitation, in contrast with findings from previous neuroimaging studies of face perception and action observation. Furthermore, AA and EA participants associated AAs with lower social status than EAs or CAs, suggesting that the social status associated with different racial groups may instead modulate neural activity during imitation of individuals from those groups. Taken together, these findings suggest that neural responses to race during imitation are driven by socially-learned associations rather than self-similarity. This may reflect the adaptive role of imitation in social learning, where learning from higher-status models can be more beneficial. This study provides neural evidence consistent with evolutionary theories of cultural acquisition. PMID:23813738

  18. Self-Similarity of Wakes in Wave-Driven Canopy Flow

    NASA Astrophysics Data System (ADS)

    Zeller, Robert; Zarama, Francisco; Weitzman, Joel; Koseff, Jeffrey

    2014-11-01

    Wave-driven flow within a canopy is characterized by complex spatial heterogeneity caused by element wakes. Capturing this variability is difficult in numerical simulations and laboratory experiments because of computational cost and measurement access restrictions, respectively. In light of these issues, one way to account for horizontal variability is to assume that element wakes are self-similar. However, self-similarity depends on two conditions that are not necessarily satisfied in wave-driven canopy flows: 1) the wakes must be quasi-steady and 2) the wakes must be 2-D. In this study, phase-averaged particle image velocimetry measurements within a rigid canopy were used to evaluate the assumption of self-similarity. It was found to predict some flow statistics more accurately than others. In addition, the accuracy was found to be dependent on both the Keulegan-Carpenter number and the vertical location within the canopy. At low Keulegan-Carpenter number, the quasi-steady condition was violated because the wakes did not have time to develop. Near the top of the canopy, the 2-D assumption was violated because of the influence of the mixing layer.

  19. The density ratio dependence of self-similar Rayleigh-Taylor mixing.

    PubMed

    Youngs, David L

    2013-11-28

    Previous research on self-similar mixing caused by Rayleigh-Taylor (RT) instability is summarized and a recent series of high resolution large eddy simulations is described. Mesh sizes of approximately 2000 ×1000 × 1000 are used to investigate the properties of high Reynolds number self-similar RT mixing at a range of density ratios from 1.5 : 1 to 20 : 1. In some cases, mixing evolves from 'small random perturbations'. In other cases, random long wavelength perturbations (k(-3) spectrum) are added to give self-similar mixing at an enhanced rate, more typical of that observed in experiments. The properties of the turbulent mixing zone (volume fraction distributions, turbulence kinetic energy, molecular mixing parameter, etc.) are related to the RT growth rate parameter, α. Comparisons are made with experimental data on the internal structure and the asymmetry of the mixing zone (spike distance/bubble distance). The main purpose of this series of simulations is to provide data for calibration of engineering models (e.g. Reynolds-averaged Navier-Stokes models). It is argued that the influence of initial conditions is likely to be significant in most applications and the implications of this for engineering modelling are discussed.

  20. Self-Similar Theory of Thermal Conduction and Application to the Solar Wind.

    PubMed

    Horaites, K; Boldyrev, S; Krasheninnikov, S I; Salem, C; Bale, S D; Pulupa, M

    2015-06-19

    We propose a self-similar kinetic theory of thermal conductivity in a magnetized plasma, and discuss its application to the solar wind. We study a collisional kinetic equation in a spatially expanding magnetic flux tube, assuming that the magnetic field strength, the plasma density, and the plasma temperature decline as power laws of distance along the tube. We demonstrate that the electron kinetic equation has a family of scale-invariant solutions for a particular relation among the magnetic-, density-, and temperature-scaling exponents. These solutions describe the heat flux as a function of the temperature Knudsen number γ, which we require to be constant along the flux tube. We observe that self-similarity may be realized in the solar wind; for the Helios data 0.3-1  AU we find that the scaling exponents for density, temperature, and heat flux are close to those dictated by scale invariance. We find steady-state solutions of the self-similar kinetic equation numerically, and show that these solutions accurately reproduce the electron strahl population seen in the solar wind, as well as the measured heat flux.

  1. A Uniqueness Result for Self-Similar Profiles to Smoluchowski's Coagulation Equation Revisited

    NASA Astrophysics Data System (ADS)

    Niethammer, B.; Throm, S.; Velázquez, J. J. L.

    2016-07-01

    In this note we indicate how to correct the proof of a uniqueness result in [6] for self-similar solutions to Smoluchowski's coagulation equation for kernels K=K(x,y) that are homogeneous of degree zero and close to constant in the sense that begin{aligned} -\\varepsilon le K(x,y)-2 le \\varepsilon Big ( Big (x/yBig )^{α } + Big (y/xBig )^{α }Big ) for α in [0,1/2). Under the additional assumption, in comparison to [6], that K has an analytic extension to mathbb {C}{setminus } (-infty ,0] and that the precise asymptotic behaviour of K at the origin is prescribed, we prove that self-similar solutions with given mass are unique if \\varepsilon is sufficiently small. The complete details of the proof are available in [4]. In addition, we give here the proof of a uniqueness result for a related but simpler problem that appears in the description of self-similar solutions for x → infty.

  2. Flow patterns of bubble nucleation sites (called fliers) freely floating in champagne glasses.

    PubMed

    Liger-Belair, Gérard; Beaumont, Fabien; Jeandet, Philippe; Polidori, Guillaume

    2007-10-23

    Laser tomography techniques were used to capture the dynamics of bubbles released from particles (arbitrarily called fliers) freely floating in traditional flutes poured with champagne. By use of long exposure time photography, the trajectories of bubbles released by fliers were found to leave very elegant and characteristic "prints" as they crossed a section of champagne illuminated with a 1 mm thick laser sheet. This characteristic print was made with a succession of lighting filaments. Fine analysis of these prints left by fliers enabled us to deduce the bubbling frequency of each flier (which ranged from about 4 bubbles/s up to about 22 bubbles/s a few seconds after pouring), as well as its velocity through the liquid medium (which ranged from about 0.8 mm/s to about 7.6 mm/s). Finally, this flow visualization technique, very recently applied to the science of champagne and sparkling wines, also proved to be a useful technique to underscore fliers' bubbling instabilities along their rather erratic way through the liquid medium.

  3. Effervescence in champagne and sparkling wines: From bubble bursting to droplet evaporation

    NASA Astrophysics Data System (ADS)

    Séon, T.; Liger-Belair, G.

    2017-01-01

    When a bubble reaches an air-liquid interface, it ruptures, projecting a multitude of tiny droplets in the air. Across the oceans, an estimated 1018 to 1020 bubbles burst every second, and form the so called sea spray, a major player in earth's climate system. At a smaller scale, in a glass of champagne about a million bubbles nucleate on the wall, rise towards the surface and burst, giving birth to a particular aerosol that holds a concentrate of wine aromas. Based on the model experiment of a single bubble bursting in simple liquids, we depict each step of this effervescence, from bubble bursting to drop evaporation. In particular, we propose simple scaling laws for the jet velocity and the top drop size. We unravel experimentally the intricate roles of bubble shape, capillary waves, gravity, and liquid properties in the jet dynamics and the drop detachment. We demonstrate how damping action of viscosity produces faster and smaller droplets and more generally how liquid properties enable to control the bubble bursting aerosol characteristics. In this context, the particular case of Champagne wine aerosol is studied in details and the key features of this aerosol are identified. We demonstrate that compared to a still wine, champagne fizz drastically enhances the transfer of liquid into the atmosphere. Conditions on bubble radius and wine viscosity that optimize aerosol evaporation are provided. These results pave the way towards the fine tuning of aerosol characteristics and flavor release during sparkling wine tasting, a major issue of the sparkling wine industry.

  4. Effervescence in champagne and sparkling wines: From grape harvest to bubble rise

    NASA Astrophysics Data System (ADS)

    Liger-Belair, Gérard

    2017-01-01

    Bubbles in a glass of champagne may seem like the acme of frivolity to most of people, but in fact they may rather be considered as a fantastic playground for any fluid physicist. Under standard tasting conditions, about a million bubbles will nucleate and rise if you resist drinking from your flute. The so-called effervescence process, which enlivens champagne and sparkling wines tasting, is the result of the complex interplay between carbon dioxide (CO2) dissolved in the liquid phase, tiny air pockets trapped within microscopic particles during the pouring process, and some both glass and liquid properties. In this tutorial review, the journey of yeast-fermented CO2 is reviewed (from its progressive dissolution in the liquid phase during the fermentation process, to its progressive release in the headspace above glasses). The most recent advances about the physicochemical processes behind the nucleation, and rise of gaseous CO2 bubbles, under standard tasting conditions, have been gathered hereafter. Let's hope that your enjoyment of champagne will be enhanced after reading this tutorial review dedicated to the unsuspected physics hidden right under your nose each time you enjoy a glass of bubbly.

  5. Effect of champagne compared to still white wine on peripheral neurotransmitter concentrations.

    PubMed

    Boyer, Jean-Christophe; Bancel, Etiennette; Perray, Pascale Fabbro; Pouderoux, Philippe; Balmes, Jean-Louis; Bali, Jean-Pierre

    2004-09-01

    To evaluate how the peripheral release of neurotransmitters such as serotonin, dopamine, cholecystokinin, and beta-endorphin is involved in drinking behavior, blood concentrations of these neurotransmitters were followed in 40 healthy young volunteers during the first hour after ingestion of a moderate dose of some common alcoholic beverages (champagne, still white wine) as compared to water. Concerning serotonin levels, two groups of subjects are statistically distinct: one with low basal serotonin levels (< 620 nmol/L) which responded with an increase in serotonin (52% in 10 minutes), and a second group with higher basal serotonin levels (> 620 nmol/L) which responded with a decrease ( 190% in 60 minutes). Variations in serotonin concentrations appear to depend upon the alcoholic content of the beverage. A rapid increase in plasma dopamine concentrations after consumption of champagne seems to be due to the nonalcoholic content of the beverage. Cholecystokinin values were not significantly different between the three beverages: the observed increase can be explained by a moderate gastric distention. Beta-endorphin levels didn't change significantly after drinking. In conclusion, some significant blood variations of serotonin and dopamine appeared even after moderately dose of champagne or still white wine. These changes might be partially responsible for the different drinking behavior.

  6. Multipressure Polytropes as Models for the Structure and Stability of Molecular Clouds. I. Theory

    NASA Astrophysics Data System (ADS)

    McKee, Christopher F.; Holliman, John H., II

    1999-09-01

    We present a theoretical formalism for determining the structure of molecular clouds and the precollapse conditions in star-forming regions. The model consists of a pressure-bounded, self-gravitating sphere of an ideal gas that is supported by several distinct pressures. Since each pressure component is assumed to obey a polytropic law Pi(r)~ργpi, we refer to these models as ``multipressure polytropes.'' We treat the case without rotation. The time evolution of one of these polytropes depends additionally on the adiabatic index γi of each component, which is modified to account for the effects of any thermal coupling to the environment of the cloud. We derive structure equations as well as perturbation equations for performing a linear stability analysis. Special attention is given to representing properly the significant pressure components in molecular clouds: thermal motions, static magnetic fields, and turbulence. The fundamental approximation in our treatment is that the effects of turbulent motions in supporting a cloud against gravity can be approximated by a polytropic pressure component. In particular, we approximate the turbulent motions as a superposition of Alfvén waves. We generalize the standard treatment of the stability of polytropes to allow for the flow of entropy in response to a perturbation, as expected for the entropy associated with wave pressure. In contrast to the pressure components within stars, the pressure components within interstellar clouds are ``soft,'' with polytropic indices γpi<=4/3 and (except for Alfvén waves) adiabatic indices γi<=4/3. This paper focuses on the characteristics of adiabatic polytropes with a single pressure component that are near the brink of gravitational instability as a function of γpi and γi for γpi<=4/3. The properties of such polytropes are generally governed by the conditions at the surface. We obtain upper limits for the mass and size of polytropes in terms of the density and sound speed at

  7. Earthquake source scaling and self-similarity estimation from stacking P and S spectra

    NASA Astrophysics Data System (ADS)

    Prieto, GermáN. A.; Shearer, Peter M.; Vernon, Frank L.; Kilb, Debi

    2004-08-01

    We study the scaling relationships of source parameters and the self-similarity of earthquake spectra by analyzing a cluster of over 400 small earthquakes (ML = 0.5 to 3.4) recorded by the Anza seismic network in southern California. We compute P, S, and preevent noise spectra from each seismogram using a multitaper technique and approximate source and receiver terms by iteratively stacking the spectra. To estimate scaling relationships, we average the spectra in size bins based on their relative moment. We correct for attenuation by using the smallest moment bin as an empirical Green's function (EGF) for the stacked spectra in the larger moment bins. The shapes of the log spectra agree within their estimated uncertainties after shifting along the ω-3 line expected for self-similarity of the source spectra. We also estimate corner frequencies and radiated energy from the relative source spectra using a simple source model. The ratio between radiated seismic energy and seismic moment (proportional to apparent stress) is nearly constant with increasing moment over the magnitude range of our EGF-corrected data (ML = 1.8 to 3.4). Corner frequencies vary inversely as the cube root of moment, as expected from the observed self-similarity in the spectra. The ratio between P and S corner frequencies is observed to be 1.6 ± 0.2. We obtain values for absolute moment and energy by calibrating our results to local magnitudes for these earthquakes. This yields a S to P energy ratio of 9 ± 1.5 and a value of apparent stress of about 1 MPa.

  8. Scaling of Peak Flows with Constant Flow Velocity in Random Self-Similar Networks

    NASA Astrophysics Data System (ADS)

    Mantilla, R.; Gupta, V. K.; Troutman, B. M.

    2010-12-01

    We present a methodology to understand the role of the statistical self-similar topology of real river networks on flow hydrographs for rainfall-runoff events. Monte Carlo generated ensembles of 1000 Random Self-similar Networks (RSNs) with geometrically distributed interior and exterior generators are created. We show how these networks emulate the statistical self-similarity present in real networks by presenting results for 30 river networks in the continental USA. Hydrographs for every link in each of these networks are obtained by numerically solving the link-based mass and momentum conservation equation under the assumption of constant flow velocity. From these simulated hydrographs for an ensemble of RSNs, the scaling parameters for the peak of the width function (β) and the hydrograph peak flow (φ) are estimated. It was found that φ > β, which supports a similar finding first reported for the Walnut Gulch basin, Arizona, and that is qualitatively different from previous results on idealized river networks (e.g. Peano Network, Mandelbrot- Viscek Network). Scaling of peak flows for individual rainfall runoff events is a new area of research that offers a path to physically understand regional scaling of flood quantiles. It addresses an important open problem in river network hydrology through studying the statistics of ensembles of multiple events in RSNs. In addition, our methodology provides a reference framework to study scaling exponents and intercepts under more complex scenarios of flow dynamics and runoff generation processes using ensembles of RSNs. Preliminary examples of such scenarios will also be given.

  9. Self-similar solutions for the Hasselmann equation and experimental scaling of wind-wave spectra

    NASA Astrophysics Data System (ADS)

    Badulin, S. I.; Pushkarev, A. N.; Resio, D.; Zakharov, V. E.

    2003-04-01

    The solutions for the Hasselmann equation (kinetic equation for wind-driven waves) are studied numerically for the case of duration-limited growth and different conventional parameterizations of wave sources and sinks (Snyderet al. 1981; Plant 1982; Hsiao &Shemdin 1983; Komen, Hasselmann & Hasselmann 1984; Donelan, Pierson 1987). The strong self-similar behavior of the numerical solutions is found for all the parameterizations in a wide range of wind speeds and wave ages. Moreover, the resulting self-similar solutions are found to be surprisingly close to experimentally established approximations in magnitudes and shapes of frequency spectra. The comparison with JONSWAP modified spectra (Donelan et al. 1985) is detailed. It is found that this approximation being obtained for the case of fetch-limited growth fits quite well the corresponding spectra for the numerical duration limited solutions in a wide range of wave ages (C_p/U10 ≈ 0.4div 1.4 ). Theoretical overview of self-similar solutions for the kinetic equation is given in its relation to the experimentally observed dependencies of mean parameters (i.e. mean energy, frequency) of wind-driven waves both in cases of fetch-limited and duration limited growth. Universality features of the dependencies are treated as a result of dominating nonlinear transfer in wind-wave field. The research was conducted under the U.S. Army Corps of Engineers, RDT&E program, grant DACA 42-00-C0044, ONR grant N00014-98-1-0070 and NSF grant NDMS0072803, INTAS grant 01-234 and Russian Foundation for Basic Research 01-05-64603, 01-05-64464, 02-05-65140. This support is gratefully acknowledged.

  10. Exploiting the self-similarity in ERP images by nonlocal means for single-trial denoising.

    PubMed

    Strauss, Daniel J; Teuber, Tanja; Steidl, Gabriele; Corona-Strauss, Farah I

    2013-07-01

    Event related potentials (ERPs) represent a noninvasive and widely available means to analyze neural correlates of sensory and cognitive processing. Recent developments in neural and cognitive engineering proposed completely new application fields of this well-established measurement technique when using an advanced single-trial processing. We have recently shown that 2-D diffusion filtering methods from image processing can be used for the denoising of ERP single-trials in matrix representations, also called ERP images. In contrast to conventional 1-D transient ERP denoising techniques, the 2-D restoration of ERP images allows for an integration of regularities over multiple stimulations into the denoising process. Advanced anisotropic image restoration methods may require directional information for the ERP denoising process. This is especially true if there is a lack of a priori knowledge about possible traces in ERP images. However due to the use of event related experimental paradigms, ERP images are characterized by a high degree of self-similarity over the individual trials. In this paper, we propose the simple and easy to apply nonlocal means method for ERP image denoising in order to exploit this self-similarity rather than focusing on the edge-based extraction of directional information. Using measured and simulated ERP data, we compare our method to conventional approaches in ERP denoising. It is concluded that the self-similarity in ERP images can be exploited for single-trial ERP denoising by the proposed approach. This method might be promising for a variety of evoked and event-related potential applications, including nonstationary paradigms such as changing exogeneous stimulus characteristics or endogenous states during the experiment. As presented, the proposed approach is for the a posteriori denoising of single-trial sequences.

  11. Self similarity and sample length dependence of conductance in quasiperiodic lateral magnetic superlattices

    NASA Astrophysics Data System (ADS)

    Zeng, Z. Y.; Claro, F.

    2002-02-01

    We study the transport of electrons in a Fibonacci magnetic superlattice produced on a two-dimensional electron gas modulated by parallel magnetic-field stripes arranged in a Fibonacci sequence. Both the transmission coefficient and conductance exhibit self similarity and the six-circle property. The presence of extended states yields a finite conductivity at infinite length, that may be detected as an abrupt change in the conductance as the Fermi energy is varied, much as a metal-insulator transition. This is a unique feature of transport in this kind of structure, arising from its inherent two-dimensional nature.

  12. Universal Self-Similar Scaling of Spatial Wilson Loops Out of Equilibrium

    NASA Astrophysics Data System (ADS)

    Berges, J.; Mace, M.; Schlichting, S.

    2017-05-01

    We investigate strongly correlated non-Abelian plasmas out of equilibrium. Based on numerical simulations, we establish a self-similar scaling property for the time evolution of spatial Wilson loops that characterizes a universal state of matter far from equilibrium. Most remarkably, it exhibits a generalized area law which holds for a sufficiently large ratio of spatial area and fractional power of time. Performing calculations also for the perturbative regime at higher momenta, we are able to characterize the full nonthermal scaling properties of S U (2 ) and S U (3 ) symmetric plasmas from short to large distance scales in terms of two independent universal exponents and associated scaling functions.

  13. Measuring the self-similarity exponent in Lévy stable processes of financial time series

    NASA Astrophysics Data System (ADS)

    Fernández-Martínez, M.; Sánchez-Granero, M. A.; Trinidad Segovia, J. E.

    2013-11-01

    Geometric method-based procedures, which will be called GM algorithms herein, were introduced in [M.A. Sánchez Granero, J.E. Trinidad Segovia, J. García Pérez, Some comments on Hurst exponent and the long memory processes on capital markets, Phys. A 387 (2008) 5543-5551], to efficiently calculate the self-similarity exponent of a time series. In that paper, the authors showed empirically that these algorithms, based on a geometrical approach, are more accurate than the classical algorithms, especially with short length time series. The authors checked that GM algorithms are good when working with (fractional) Brownian motions. Moreover, in [J.E. Trinidad Segovia, M. Fernández-Martínez, M.A. Sánchez-Granero, A note on geometric method-based procedures to calculate the Hurst exponent, Phys. A 391 (2012) 2209-2214], a mathematical background for the validity of such procedures to estimate the self-similarity index of any random process with stationary and self-affine increments was provided. In particular, they proved theoretically that GM algorithms are also valid to explore long-memory in (fractional) Lévy stable motions. In this paper, we prove empirically by Monte Carlo simulation that GM algorithms are able to calculate accurately the self-similarity index in Lévy stable motions and find empirical evidence that they are more precise than the absolute value exponent (denoted by AVE onwards) and the multifractal detrended fluctuation analysis (MF-DFA) algorithms, especially with a short length time series. We also compare them with the generalized Hurst exponent (GHE) algorithm and conclude that both GM2 and GHE algorithms are the most accurate to study financial series. In addition to that, we provide empirical evidence, based on the accuracy of GM algorithms to estimate the self-similarity index in Lévy motions, that the evolution of the stocks of some international market indices, such as U.S. Small Cap and Nasdaq100, cannot be modelized by means of a

  14. Self-similar collapse in nebular disk and the Titius-Bode law.

    NASA Astrophysics Data System (ADS)

    Li, X. Q.; Zhang, H.; Li, Q. B.

    1995-12-01

    Nonlinear development and evolution of density disturbances in nebular disk are examined on the basis of our previous study(Li & Zhang 1994). It is shown that the perturbed density is unstable with respect to self-modulation, leading to the formation of the density field localization; in the nonlinear stage of the instability, development of the localized field will lead to collapse. For the case of self-similar collapse, perturbed density inially increases with time and then tends to form of steady rings with very large but limit amplitudes; and their distances r_n_ from the center form a geometric progression, which is similar to the Titius-Bode law.

  15. Self-similarly corrected Padé approximants for the indeterminate problem

    NASA Astrophysics Data System (ADS)

    Gluzman, S.; Yukalov, V. I.

    2016-09-01

    A method is suggested for treating the well-known deficiency in the use of Padé approximants that are well suited for approximating rational functions, but confront problems in approximating irrational functions. We develop the approach of self-similarly corrected Padé approximants, making it possible to essentially increase the class of functions treated by these approximants. The method works well even in those cases where the standard Padé approximants are not applicable, resulting in divergent sequences. Numerical convergence of our method is demonstrated by several physical examples.

  16. Stable Self-Similar Blow-Up Dynamics for Slightly {L^2}-Supercritical Generalized KDV Equations

    NASA Astrophysics Data System (ADS)

    Lan, Yang

    2016-07-01

    In this paper we consider the slightly {L^2}-supercritical gKdV equations {partial_t u+(u_{xx}+u|u|^{p-1})_x=0}, with the nonlinearity {5 < p < 5+\\varepsilon} and {0 < \\varepsilon≪ 1}. We will prove the existence and stability of a blow-up dynamics with self-similar blow-up rate in the energy space {H^1} and give a specific description of the formation of the singularity near the blow-up time.

  17. Self-similar structure and experimental signatures of suprathermal ion distribution in inertial confinement fusion implosions

    SciTech Connect

    Kagan, Grigory; Svyatskiy, D.; Rinderknecht, H. G.; Rosenberg, M. J.; Zylstra, A. B.; Huang, C. -K.; McDevitt, C. J.

    2015-09-03

    The distribution function of suprathermal ions is found to be self-similar under conditions relevant to inertial confinement fusion hot spots. By utilizing this feature, interference between the hydrodynamic instabilities and kinetic effects is for the first time assessed quantitatively to find that the instabilities substantially aggravate the fusion reactivity reduction. Thus, the ion tail depletion is also shown to lower the experimentally inferred ion temperature, a novel kinetic effect that may explain the discrepancy between the exploding pusher experiments and rad-hydro simulations and contribute to the observation that temperature inferred from DD reaction products is lower than from DT at the National Ignition Facility.

  18. Prediction of oil contamination distribution in aquifers using self similar solutions

    NASA Astrophysics Data System (ADS)

    Pistiner, Arieh

    2016-12-01

    Oil contaminant migration in an aquifer is analyzed by applying some power law relationships between the porous medium parameters and oil saturation. Such an application generates a self-similar model whose solutions are used to analyze the effect of the porous structure and the oil properties on the oil migration in the aquifer. By using hypothetical saturation data, the model was used to find the characteristic length and time scales of the aquifer, and then to predict the temporal saturation distribution of the oil contamination in the aquifer.

  19. Self-similar magnetohydrodynamic model for direct current discharge fireball experiments

    SciTech Connect

    Tsui, K. H.; Navia, C. E.; Robba, M. B.; Carneiro, L. T.; Emelin, S. E.

    2006-11-15

    Ball lightning models and corresponding laboratory efforts in generating fireballs are briefly summarized to give an overview of the current status. In particular, emphasis is given to direct current discharge experiments at atmospheric pressure such as capillary discharge with a plasma plume in front of the anode opening [Emelin et al., Tech. Phys. Letters 23, 758 (1997)] and water resistor discharge with fluttering fireball overhead [Egorov and Stepanov, Tech. Phys. 47, 1584 (2002)]. These fireballs are interpreted as laboratory demonstrations of the self-similar magnetohydrodynamic (MHD) model of ball lightning [Tsui, Phys. Plasmas 13, 072102 (2006)].

  20. Self-similar magnetohydrodynamic model for direct current discharge fireball experiments

    NASA Astrophysics Data System (ADS)

    Tsui, K. H.; Navia, C. E.; Robba, M. B.; Carneiro, L. T.; Emelin, S. E.

    2006-11-01

    Ball lightning models and corresponding laboratory efforts in generating fireballs are briefly summarized to give an overview of the current status. In particular, emphasis is given to direct current discharge experiments at atmospheric pressure such as capillary discharge with a plasma plume in front of the anode opening [Emelin et al., Tech. Phys. Letters 23, 758 (1997)] and water resistor discharge with fluttering fireball overhead [Egorov and Stepanov, Tech. Phys. 47, 1584 (2002)]. These fireballs are interpreted as laboratory demonstrations of the self-similar magnetohydrodynamic (MHD) model of ball lightning [Tsui, Phys. Plasmas 13, 072102 (2006)].

  1. Landmark matching based automatic retinal image registration with linear programming and self-similarities.

    PubMed

    Zheng, Yuanjie; Hunter, Allan A; Wu, Jue; Wang, Hongzhi; Gao, Jianbin; Maguire, Maureen G; Gee, James C

    2011-01-01

    In this paper, we address the problem of landmark matching based retinal image registration. Two major contributions render our registration algorithm distinguished from many previous methods. One is a novel landmark-matching formulation which enables not only a joint estimation of the correspondences and transformation model but also the optimization with linear programming. The other contribution lies in the introduction of a reinforced self-similarities descriptor in characterizing the local appearance of landmarks. Theoretical analysis and a series of preliminary experimental results show both the effectiveness of our optimization scheme and the high differentiating ability of our features.

  2. Thermal vacuum, cosmic microwave radiation, neutrino masses and fractal-like self-similar structure

    NASA Astrophysics Data System (ADS)

    Capolupo, Antonio; Lambiase, Gaetano; Vitiello, Giuseppe

    2017-08-01

    The behavior of thermal vacuum condensates of scalar and fermion fields is analyzed and it is shown that the condensate of Maxwell fields reproduces the characteristics of the cosmic microwave radiation. By studying fermion thermal states with the temperature of the cosmic neutrino background, we derive a value of the sum of the active neutrino masses which is compatible with its estimated lower bound. Moreover, we reveal the fractal self-similar structure of the thermal radiation and we relate it to the coherent structure of the thermal vacuum.

  3. Renormalization of the fragmentation equation: exact self-similar solutions and turbulent cascades.

    PubMed

    Saveliev, V L; Gorokhovski, M A

    2012-12-01

    Using an approach developed earlier for renormalization of the Boltzmann collision integral [Saveliev and Nanbu, Phys. Rev. E 65, 051205 (2002)], we derive an exact divergence form for the fragmentation operator. Then we reduce the fragmentation equation to the continuity equation in size space, with the flux given explicitly. This allows us to obtain self-similar solutions and to find the integral of motion for these solutions (we call it the bare flux). We show how these solutions can be applied as a description of cascade processes in three- and two-dimensional turbulence. We also suggested an empirical cascade model of impact fragmentation of brittle materials.

  4. A self-similar transformation for a dodecagonal quasiperiodic covering with T-clusters

    NASA Astrophysics Data System (ADS)

    Liao, Longguang; Zhang, Wenbin; Yu, Tongxu; Cao, Zexian

    2013-06-01

    A single cluster covering for the ship tiling of a dodecagonal quasiperiodic structure is obtained via a self-similar transformation, by which a turtle-like cluster, dubbed as a T-cluster, comprising seven squares, twenty regular triangles and two 30°-rhombuses, is changed into twenty scaled-down T-clusters, each centering at a vertex of the original one. Remarkably, there are three types of transformations according to the distinct configuration of the 20 scaled-down T-clusters. Detailed data for the transformations are specified. The results are expected to be helpful for the study of the physical and structural properties of dodecagonal quasicrystals.

  5. Self-similar continuous cascades supported by random Cantor sets: Application to rainfall data

    NASA Astrophysics Data System (ADS)

    Muzy, Jean-François; Baïle, Rachel

    2016-05-01

    We introduce a variant of continuous random cascade models that extends former constructions introduced by Barral-Mandelbrot and Bacry-Muzy in the sense that they can be supported by sets of arbitrary fractal dimension. The so-introduced sets are exactly self-similar stationary versions of random Cantor sets formerly introduced by Mandelbrot as "random cutouts." We discuss the main mathematical properties of our construction and compute its scaling properties. We then illustrate our purpose on several numerical examples and we consider a possible application to rainfall data. We notably show that our model allows us to reproduce remarkably the distribution of dry period durations.

  6. Gold Nanoparticle Self-Similar Chain Structure Organized by DNA Origami

    SciTech Connect

    Ding, Baoquan; Deng, Zhengtao; Yan, Hao; Cabrini, Stefano; Zuckermann, Ronald N.; Bokor, Jeffrey

    2010-03-17

    Here we demonstrate Au nanoparticle self-similar chain structure organized by triangle DNA origami with well-controlled orientation and <10 nm spacing. We show for the first time that a large DNA complex (origami) and multiple AuNP conjugates can be well-assembled and purified with reliable yields. The assembled structure could be used to generate high local-field enhancement. The same method can be used to precisely localize multiple components on a DNA template for potential applications in nanophotonic, nanomagnetic, and nanoelectronic devices.

  7. Effects of internal heat transfer on the structure of self-similar blast waves

    NASA Technical Reports Server (NTRS)

    Ghoniem, A. F.; Berger, S. A.; Oppenheim, A. K.; Kamel, M. M.

    1982-01-01

    An analysis of the problem of self-similar, nonadiabatic blast waves, where both conduction and radiation are allowed to take place, show the problem to be reducible to the integration of a system of six coupled nonlinear ordinary differential equations. Consideration of these equations shows that although radiation tends to produce uniform fields through temperature gradient attenuation, all the energy carried by radiation is deposited on the front and the bounding shock becomes increasingly overdriven. When conduction is taken into account, the distribution of gasdynamic parameters in blast waves in the case of Rosseland diffusion radiation is more uniform than in the case of the Planck emission radiation.

  8. Self-similar spectral structures and edge-locking hierarchy in open-boundary spin chains

    SciTech Connect

    Haque, Masudul

    2010-07-15

    For an anisotropic Heisenberg (XXZ) spin chain, we show that an open boundary induces a series of approximately self-similar features at different energy scales, high up in the eigenvalue spectrum. We present a nonequilibrium phenomenon related to this fractal structure, involving states in which a connected block near the edge is polarized oppositely to the rest of the chain. We show that such oppositely polarized blocks can be 'locked' to the edge of the spin chain and that there is a hierarchy of edge-locking effects at various orders of the anisotropy. The phenomenon enables dramatic control of quantum-state transmission and magnetization control.

  9. Locally self-similar phase diagram of the disordered Potts model on the hierarchical lattice.

    PubMed

    Anglès d'Auriac, J-Ch; Iglói, Ferenc

    2013-02-01

    We study the critical behavior of the random q-state Potts model in the large-q limit on the diamond hierarchical lattice with an effective dimensionality d(eff)>2. By varying the temperature and the strength of the frustration the system has a phase transition line between the paramagnetic and the ferromagnetic phases which is controlled by four different fixed points. According to our renormalization group study the phase boundary in the vicinity of the multicritical point is self-similar; it is well represented by a logarithmic spiral. We expect an infinite number of reentrances in the thermodynamic limit; consequently one cannot define standard thermodynamic phases in this region.

  10. Field induced aggregation in electrorheological suspension: kernel form and self similar solutions

    NASA Astrophysics Data System (ADS)

    Mimouni, Zineb; Limage, René

    2009-05-01

    Within the framework of the study of the fibrillation mechanism in an electrorheological (ER) suspension, this work presents a comparison between the self similar solutions when the kernel is K i, j ~ ( i -1 + j -1) and the behaviour of the chains growth. Till now, the field induced chains formation has only been studied by numerical or experimental methods. The work of Fournier and Laurençot (Communications in Mathematical Physics 256 2005) on the Smoluchowski’s equation allows us to present an analytical solution for the field induced pearl chains in a colloidal ER suspension.

  11. Self-similar community structure in a network of human interactions.

    PubMed

    Guimerà, R; Danon, L; Díaz-Guilera, A; Giralt, F; Arenas, A

    2003-12-01

    We propose a procedure for analyzing and characterizing complex networks. We apply this to the social network as constructed from email communications within a medium sized university with about 1700 employees. Email networks provide an accurate and nonintrusive description of the flow of information within human organizations. Our results reveal the self-organization of the network into a state where the distribution of community sizes is self-similar. This suggests that a universal mechanism, responsible for emergence of scaling in other self-organized complex systems, as, for instance, river networks, could also be the underlying driving force in the formation and evolution of social networks.

  12. The global polytropic model for the solar and jovian systems revisited

    NASA Astrophysics Data System (ADS)

    Geroyannis, V.; Valvi, F.; Dallas, T.

    2013-09-01

    The "global polytropic model" (Geroyannis) 1993 [P1]; Geroyannis and Valvi 1994 [P2]) is based on the assumption of hydrostatic equilibrium for the solar/jovian system, described by the Lane-Emden differential equation. A polytropic sphere of polytropic index n and radius R1 represents the central component S1 (Sun/Jupiter) of a polytropic configuration with further components the polytropic spherical shells S2, S3, ..., defined by the pairs of radii (R1,R2), (R2,R3), ..., respectively. R1, R2, R3, ..., are the roots of the real part Re(theta(R)) of the complex Lane-Emden function theta(R). Each polytropic shell is assumed to be an appropriate place for a planet/satellite to be "born" and "live". This scenario has been studied numerically for the case of the solar system (P1) and the jovian system (P2). In the present paper, the Lane-Emden differential equation is solved numerically in the complex plane by using the Fortran code dcrkf54.f95 (Geroyannis and Valvi 2012; modified Runge-Kutta- Fehlberg code of fourth and fifth order for solving initial value problems in the complex plane). We include in our numerical study some trans-Neptunian objects. We emphasize on computing distances and comparing with previous results. REFERENCES: V.S. Geroyannis 1993, Earth, Moon, and Planets, 61, 131-139. V.S. Geroyannis and F.N. Valvi 1994, Earth, Moon, and Planets, 64, 217-225. V.S. Geroyannis and F.N. Valvi 2012, International Journal of Modern Physics C, 23, No 5, 1250038:1-15.

  13. General polytropic self-gravitating cylinder free-fall and accreting mass string with a chain of collapsed objects

    NASA Astrophysics Data System (ADS)

    Lou, Yu-Qing; Hu, Xu-Yao

    2016-06-01

    We present a theoretical model framework for general polytropic (GP) hydrodynamic cylinder under self-gravity of infinite length with axial uniformity and axisymmetry. For self-similar dynamic solutions, we derive valuable integrals, analytic asymptotic solutions, sonic critical curves, shock conditions, and global numerical solutions with or without expansion shocks. Among others, we investigate various dynamic solutions featured with central free-fall asymptotic behaviours, corresponding to a collapsed mass string with a sustained dynamic accretion from a surrounding mass reservoir. Depending on the allowed ranges of a scaling index a < -1, such cylindrical dynamic mass accretion rate could be steady, increasing with time and decreasing with time. Physically, such a collapsed mass string or filament would break up into a sequence of sub-clumps and segments as induced by gravitational Jeans instabilities. Depending on the scales involved, such sub-clumps would evolve into collapsed objects or gravitationally bound systems. In diverse astrophysical and cosmological contexts, such a scenario can be adapted on various temporal, spatial and mass scales to form a chain of collapsed clumps and/or compact objects. Examples include the formation of chains of proto-stars, brown dwarfs and gaseous planets along molecular filaments; the formation of luminous massive stars along magnetized spiral arms and circum-nuclear starburst rings in barred spiral galaxies; the formation of chains of compact stellar objects such as white dwarfs, neutron stars, and black holes along a highly condensed mass string. On cosmological scales, one can perceive the formation of chains of galaxies, chains of galaxy clusters or even chains of supermassive and hypermassive black holes in the Universe including the early Universe. All these chains referred to above include possible binaries.

  14. The stability of differentially rotating self-gravitating gas clouds. II - Polytropic configurations

    NASA Astrophysics Data System (ADS)

    Schmitz, F.; Ebert, R.

    1987-07-01

    The stability of differentially rotating gas clouds with polytropic equations of state is investigated. The equilibrium states are self-consistent. The structure of the infinitely extended configurations is very simple. Perpendicular to the rotation axis, the density distribution and the differential rotational velocity are described by power laws. In the limit of vanishing rotation the authors obtain the familiar polytropic gas spheres. Only marginal axisymmetric perturbations are considered. The structure of the equilibrium states and the form of the perturbations are both calculated with the approximation method presented in paper I.

  15. Analytic study of the classical equilibrium of highly rotating spheroidal polytropes.

    NASA Astrophysics Data System (ADS)

    Sharma, J. P.; Yadava, R. B.

    1992-11-01

    The theory of polytropes is fundamental in investigations of stellar structure, star formation, galactic dynamics etc., but also in the rough estimation of some processes in real stars. Some aspects of the structural features of the classical (Newtonian) equilibrium of a highly rotating spheroidal polytrope n = 1 are considered. Approximate analytical solutions to the equilibrium equations suitable for use in very short computer programs or on calculators are given. Under certain transformations, the equilibrium equation was written into first order differential equations. Transformations connecting solutions in these planes were derived. It was found that the present approach is also more suitable for the study of both slowly and highly rotating configurations.

  16. Leonardo's branching rule in trees: How self-similar structures resist wind

    NASA Astrophysics Data System (ADS)

    Eloy, Christophe

    2011-11-01

    In his notebooks, Leonardo da Vinci observed that ``all the branches of a tree at every stage of its height when put together are equal in thickness to the trunk,'' which means that the total cross-sectional area of branches is conserved across branching nodes. The usual explanation for this rule involves vascular transport of sap, but this argument is questionable because the portion of wood devoted to transport varies across species and can be as low as 5%. It is proposed here that Leonardo's rule is a consequence of the tree skeleton having a self-similar structure and the branch diameters being adjusted to resist wind-induced loads. To address this problem, a continuous model is first considered by neglecting the geometrical details of branching and wind incident angles. The robustness of this analytical model is then assessed with numerical simulations on tree skeletons generated with a simple branching rule producing self-similar structures. This study was supported by the European Union through the fellowship PIOF-GA-2009-252542.

  17. Self-similar pinch-off mechanism and scaling of ferrofluid drops.

    PubMed

    Jiang, Xiao F; Li, Huai Z

    2015-12-01

    The pinch off of heterogeneous ferrofluid drops at a nozzle in air was experimentally investigated with a magnetic field (downward or upward) and without a magnetic field. Compared to homogeneous drops, the self-similarity and universal scaling law were verified through modifying the initial conditions, such as the nozzle diameter, flow rate, and magnitude and direction of the magnetic fields. Two pinch-off points were observed, and the two consecutive pinch-off dynamics were characterized through scaling laws. Here our scaling exponent remains within the scope of (0.70-0.80) for the primary whereas it remains within the scope of (0.60-0.70) for the secondary pinch off, respectively, comparable to the classic range from 2/3 to 1 for homogeneous drops. The gravity-compensating and gravity-superimposing magnetic fields display a negligible effect on the exponent but determine the sequence of double pinch offs. The universal character of the self-similar pinch off is extended to a heterogeneous fluid.

  18. Can AGN Feedback Break the Self-similarity of Galaxies, Groups, and Clusters?

    NASA Astrophysics Data System (ADS)

    Gaspari, M.; Brighenti, F.; Temi, P.; Ettori, S.

    2014-03-01

    It is commonly thought that active galactic nucleus (AGN) feedback can break the self-similar scaling relations of galaxies, groups, and clusters. Using high-resolution three-dimensional hydrodynamic simulations, we isolate the impact of AGN feedback on the L x-T x relation, testing the two archetypal and common regimes, self-regulated mechanical feedback and a quasar thermal blast. We find that AGN feedback has severe difficulty in breaking the relation in a consistent way. The similarity breaking is directly linked to the gas evacuation within R 500, while the central cooling times are inversely proportional to the core density. Breaking self-similarity thus implies breaking the cool core, morphing all systems to non-cool-core objects, which is in clear contradiction with the observed data populated by several cool-core systems. Self-regulated feedback, which quenches cooling flows and preserves cool cores, prevents dramatic evacuation and similarity breaking at any scale; the relation scatter is also limited. The impulsive thermal blast can break the core-included L x-T x at T 500 <~ 1 keV, but substantially empties and overheats the halo, generating a perennial non-cool-core group, as experienced by cosmological simulations. Even with partial evacuation, massive systems remain overheated. We show that the action of purely AGN feedback is to lower the luminosity and heat the gas, perpendicular to the fit.

  19. Self-Similar Log-Periodic Structures in Western STOCK Markets from 2000

    NASA Astrophysics Data System (ADS)

    Bartolozzi, M.; Drożdż, S.; Leinweber, D. B.; Speth, J.; Thomas, A. W.

    The presence of log-periodic structures before and after stock market crashes is considered to be an imprint of an intrinsic discrete scale invariance (DSI) in this complex system. The fractal framework of the theory leaves open the possibility of observing self-similar log-periodic structures at different time scales. In the present work, we analyze the daily closures of four of the most important indices worldwide since 2000: the DAX for Germany and the NASDAQ-100, the S&P 500 and the Dow Jones for the United States. The qualitative behavior of these different markets is similar during the temporal frame studied. Evidence is found for decelerating log-periodic oscillations of duration about two years and starting in September 2000. Moreover, a nested sub-structure starting in May 2002 is revealed, bringing more evidence to support the hypothesis of self-similar, log-periodic behavior. Ongoing log-periodic oscillations are also revealed. A Lomb analysis over the aforementioned periods indicates a preferential scaling factor λ~2. Higher order harmonics are also present. The spectral pattern of the data has been found to be similar to that of a Weierstrass-type function, used as a prototype of a log-periodic fractal function.

  20. Self-similar space-time evolution of an initial density discontinuity

    SciTech Connect

    Rekaa, V. L.; Pécseli, H. L.; Trulsen, J. K.

    2013-07-15

    The space-time evolution of an initial step-like plasma density variation is studied. We give particular attention to formulate the problem in a way that opens for the possibility of realizing the conditions experimentally. After a short transient time interval of the order of the electron plasma period, the solution is self-similar as illustrated by a video where the space-time evolution is reduced to be a function of the ratio x/t. Solutions of this form are usually found for problems without characteristic length and time scales, in our case the quasi-neutral limit. By introducing ion collisions with neutrals into the numerical analysis, we introduce a length scale, the collisional mean free path. We study the breakdown of the self-similarity of the solution as the mean free path is made shorter than the system length. Analytical results are presented for charge exchange collisions, demonstrating a short time collisionless evolution with an ensuing long time diffusive relaxation of the initial perturbation. For large times, we find a diffusion equation as the limiting analytical form for a charge-exchange collisional plasma, with a diffusion coefficient defined as the square of the ion sound speed divided by the (constant) ion collision frequency. The ion-neutral collision frequency acts as a parameter that allows a collisionless result to be obtained in one limit, while the solution of a diffusion equation is recovered in the opposite limit of large collision frequencies.

  1. Self-similarity of solitary waves on inertia-dominated falling liquid films.

    PubMed

    Denner, Fabian; Pradas, Marc; Charogiannis, Alexandros; Markides, Christos N; van Wachem, Berend G M; Kalliadasis, Serafim

    2016-03-01

    We propose consistent scaling of solitary waves on inertia-dominated falling liquid films, which accurately accounts for the driving physical mechanisms and leads to a self-similar characterization of solitary waves. Direct numerical simulations of the entire two-phase system are conducted using a state-of-the-art finite volume framework for interfacial flows in an open domain that was previously validated against experimental film-flow data with excellent agreement. We present a detailed analysis of the wave shape and the dispersion of solitary waves on 34 different water films with Reynolds numbers Re=20-120 and surface tension coefficients σ=0.0512-0.072 N m(-1) on substrates with inclination angles β=19°-90°. Following a detailed analysis of these cases we formulate a consistent characterization of the shape and dispersion of solitary waves, based on a newly proposed scaling derived from the Nusselt flat film solution, that unveils a self-similarity as well as the driving mechanism of solitary waves on gravity-driven liquid films. Our results demonstrate that the shape of solitary waves, i.e., height and asymmetry of the wave, is predominantly influenced by the balance of inertia and surface tension. Furthermore, we find that the dispersion of solitary waves on the inertia-dominated falling liquid films considered in this study is governed by nonlinear effects and only driven by inertia, with surface tension and gravity having a negligible influence.

  2. Self-similar patterns of nature: insect diversity at local to global scales

    PubMed Central

    Finlay, Bland J; Thomas, Jeremy A; McGavin, George C; Fenchel, Tom; Clarke, Ralph T

    2006-01-01

    The insects are probably the most hyperdiverse and economically important metazoans on the planet, but there is no consensus on the best way to model the dimensions of their diversity at multiple spatial scales, and the huge amount of information involved hinders data synthesis and the revelation of ‘patterns of nature’. Using a sample of more than 600k insect species in the size range 1–100 mm, we analysed insect body sizes and revealed self-similar patterns persisting across spatial scales from several hectares to the World. The same patterns were found in both Northern and Southern Hemispheres. The patterns include: parallel rank-abundance distributions; flatter species–area curves in smaller insects—indicating their wider geographical distribution; the recurrence of the same species-rich family in the same body-size class at all spatial scales—which generates self-similar size-frequency distributions (SFDs)—and the discovery that with decreasing mean body size, local species richness represents an increasing fraction of global species richness. We describe how these ‘rationalizing’ patterns can be translated into methods for monitoring and predicting species diversity and community structure at all spatial scales. PMID:16822755

  3. CAN AGN FEEDBACK BREAK THE SELF-SIMILARITY OF GALAXIES, GROUPS, AND CLUSTERS?

    SciTech Connect

    Gaspari, M.; Brighenti, F.; Temi, P.

    2014-03-01

    It is commonly thought that active galactic nucleus (AGN) feedback can break the self-similar scaling relations of galaxies, groups, and clusters. Using high-resolution three-dimensional hydrodynamic simulations, we isolate the impact of AGN feedback on the L {sub x}-T {sub x} relation, testing the two archetypal and common regimes, self-regulated mechanical feedback and a quasar thermal blast. We find that AGN feedback has severe difficulty in breaking the relation in a consistent way. The similarity breaking is directly linked to the gas evacuation within R {sub 500}, while the central cooling times are inversely proportional to the core density. Breaking self-similarity thus implies breaking the cool core, morphing all systems to non-cool-core objects, which is in clear contradiction with the observed data populated by several cool-core systems. Self-regulated feedback, which quenches cooling flows and preserves cool cores, prevents dramatic evacuation and similarity breaking at any scale; the relation scatter is also limited. The impulsive thermal blast can break the core-included L {sub x}-T {sub x} at T {sub 500} ≲ 1 keV, but substantially empties and overheats the halo, generating a perennial non-cool-core group, as experienced by cosmological simulations. Even with partial evacuation, massive systems remain overheated. We show that the action of purely AGN feedback is to lower the luminosity and heat the gas, perpendicular to the fit.

  4. Scaling of flow distance in random self-similar channel networks

    USGS Publications Warehouse

    Troutman, B.M.

    2005-01-01

    Natural river channel networks have been shown in empirical studies to exhibit power-law scaling behavior characteristic of self-similar and self-affine structures. Of particular interest is to describe how the distribution of distance to the outlet changes as a function of network size. In this paper, networks are modeled as random self-similar rooted tree graphs and scaling of distance to the root is studied using methods in stochastic branching theory. In particular, the asymptotic expectation of the width function (number of nodes as a function of distance to the outlet) is derived under conditions on the replacement generators. It is demonstrated further that the branching number describing rate of growth of node distance to the outlet is identical to the length ratio under a Horton-Strahler ordering scheme as order gets large, again under certain restrictions on the generators. These results are discussed in relation to drainage basin allometry and an application to an actual drainage network is presented. ?? World Scientific Publishing Company.

  5. Self-similar evolution of 2D aquatic dunes over an erodible bed

    NASA Astrophysics Data System (ADS)

    Doppler, Delphine; Lagrée, Pierre Yves; Gondret, Philippe; Rabaud, Marc

    2015-11-01

    Scale invariance of shape is a common feature of erosion patterns, such as barchan dunes, sand ripples under shoaling waves or scour holes. Due to their universal and fascinating crescentic shape, barchans dunes have received much attention and scaling laws have been deduced from field observations, satellite images and laboratory experiments. On the other hand, the dynamical long term evolution of ripples and dunes formed over an erodible bed has been far less studied while the temporal behavior of erosion patterns contains substantial information on the physical processes involved. Here, we present experimental results obtained in a linear, quasi-2D closed water channel. When a granular bed is submitted to a uniform shear flow, periodic sand ripples appear all along the channel. We found that the first ripple near the channel inlet exhibit unreported long-term scale-invariant growth. The self-similar dune shape and power-law growth exponent are extracted by image processing for several flow velocity. A simple linear model is built using mass conservation and a granular flux law, so that the bed form is described by a self-similar order 2 linear system. Experimental data fit nicely with the model results.

  6. Robustness of Estimators of Long-Range Dependence and Self-Similarity under non-Gaussianity

    NASA Astrophysics Data System (ADS)

    Franzke, C.; Watkins, N. W.; Graves, T.; Gramacy, R.; Hughes, C.

    2011-12-01

    Long-range dependence and non-Gaussianity are ubiquitous in many natural systems like ecosystems, biological systems and climate. However, it is not always appreciated that both phenomena may occur together in natural systems and that self-similarity in a system can be a superposition of both phenomena. These features, which are common in complex systems, impact the attribution of trends and the occurrence and clustering of extremes. The risk assessment of systems with these properties will lead to different outcomes (e.g. return periods) than the more common assumption of independence of extremes. Two paradigmatic models are discussed which can simultaneously account for long-range dependence and non-Gaussianity: Autoregressive Fractional Integrated Moving Average (ARFIMA) and Linear Fractional Stable Motion (LFSM). Statistical properties of estimators for long-range dependence and self-similarity are critically assessed. It is found that the most popular estimators can be biased in the presence of important features of many natural systems like trends and multiplicative noise. Also the long-range dependence and non-Gaussianity of two typical natural time series are discussed.

  7. Self-Similar Apical Sharpening of an Ideal Perfecting Conducting Fluid Subject to Maxwell Stresses

    NASA Astrophysics Data System (ADS)

    Zhou, Chengzhe; Troian, Sandra M.

    2016-11-01

    We examine the apical behavior of an ideal, perfectly conducting incompressible fluid surrounded by vacuum in circumstances where the capillary, Maxwell and inertial forces contribute to formation of a liquid cone. A previous model based on potential flow describes a family of self-similar solutions with conic cusps whose interior angles approach the Taylor cone angle. These solutions were obtained by matching powers of the leading order terms in the velocity and electric field potential to the asymptotic form dictated by a stationary cone shape. In re-examining this earlier work, we have found a more important, neglected leading order term in the velocity and field potentials, which satisfies the governing, interfacial and far-field conditions as well. This term allows for the development of additional self-similar, sharpening apical shapes, including time reversed solutions for conic tip recoil after fluid ejection. We outline the boundary-element technique for solving the exact similarity solutions, which have parametric dependence on the far-field conditions, and discuss consequences of our findings.

  8. Self-similar turbulent boundary layer with imposed pressure gradient. Four flow regimes

    SciTech Connect

    Vigdorovich, I. I.

    2014-11-15

    Self-similar flows of an incompressible fluid in a turbulent boundary layer, when the free-stream velocity is a power function (with the exponent m) of the longitudinal coordinate, have been studied. It has been shown that there are four different self-similar flow regimes corresponding to four individual similarity parameters one of which is the known Clauser parameter and the three other parameters have been established for the first time. At adverse pressure gradient, when the exponent m lies in a certain range depending on Reynolds number, the problem has two solutions with different values of the boundary-layer thickness and skin friction; consequently, hysteresis in a pre-separation flow is possible. Separation occurs not at the minimal value of m that corresponds to the strongest adverse pressure gradient, but at m = −0.216 −0.4 Re{sub p}{sup −1/3} + O(Re{sub p}{sup −2/3}), where Re{sub p} is the Reynolds number based on longitudinal pressure gradient. The theoretical results are in good agreement with experimental data.

  9. How self-similarity leads to streamlining of a flexible body

    NASA Astrophysics Data System (ADS)

    Alben, Silas; Shelley, Michael; Zhang, Jun

    2003-11-01

    The ability to reduce fluid drag is an important survival factor for organisms which inhabit high-speed flows. Flexibility plays a central role in drag reduction, particularly for plants, which are restricted to a somewhat ``passive'' interaction with a flow field. We have examined the role of flexibility in drag reduction experimentally using a flexible glass fiber immersed in a soap-film flow, and numerically through a simple free-streamline model which emphasizes the flow-body interaction. In this work we present an asymptotic argument which uncovers the governing phenomenon in the model: the formation of a ``tip region'' on the fiber, which gives rise to self-similarity. Our work shows that an assumed self-similar form explains the salient features of the numerical solutions: a drag which scales as flow speed to the 4/3 power, and a body shape and separation streamlines which assume a unified, parabolic form. We also present numerical results indicating that these features persist under modifications to the model suggested by the experiment: the presence of flow tunnel walls and a back pressure in the body wake. This provides support for the applicability of our results to general steady wake flows past flexible bodies.

  10. Shear flow over a self-similar expanding pulmonary alveolus during rhythmical breathing

    NASA Astrophysics Data System (ADS)

    Haber, S.; Butler, J. P.; Brenner, H.; Emanuel, I.; Tsuda, A.

    2000-02-01

    Alternating shear flow over a self-similar, rhythmically expanding hemispherical depression is investigated. It provides a fluid-mechanical model for an alveolated respiratory unit, by means of which the effect of lung rhythmical expansion on gas mixing as well as aerosol dispersion and deposition can be studied. The flow is assumed to be very slow and governed by the quasi-steady linear Stokes equations. Consequently, superposition of the following two cases provides an easy route toward characterizing the aforementioned flow field. The first case treats the flow field that is generated by a rhythmically expanding spherical cap (the alveolus). The cap is attached at its rim to a circular opening in an expanding unbounded plane bounding a semi-infinite fluid region. The rate of expansion of the cap and the plane are chosen such as to maintain the system's configurational self-similarity. The second case addresses the flow disturbance that is generated by an alternating shear flow encountering a rigid hemispherical cavity in a plane bounding a semi-infinite fluid domain.

  11. Self similar solution of superradiant amplification of ultrashort laser pulses in plasma

    SciTech Connect

    Moghadasin, H.; Niknam, A. R. Shokri, B.

    2015-05-15

    Based on the self-similar method, superradiant amplification of ultrashort laser pulses by the counterpropagating pump in a plasma is investigated. Here, we present a governing system of partial differential equations for the signal pulse and the motion of the electrons. These equations are transformed to ordinary differential equations by the self-similar method and numerically solved. It is found that the increase of the signal intensity is proportional to the square of the propagation distance and the signal frequency has a red shift. Also, depending on the pulse width, the signal breaks up into a train of short pulses or its duration decreases with the inverse square root of the distance. Moreover, we identified two distinct categories of the electrons by the phase space analysis. In the beginning, one of them is trapped in the ponderomotive potential well and oscillates while the other is untrapped. Over time, electrons of the second kind also join to the trapped electrons. In the potential well, the electrons are bunched to form an electron density grating which reflects the pump pulse into the signal pulse. It is shown that the backscattered intensity is enhanced with the increase of the electron bunching parameter which leads to the enhanced efficiency of superradiant amplification.

  12. Statistical self-similarity of width function maxima with implications to floods

    USGS Publications Warehouse

    Veitzer, S.A.; Gupta, V.K.

    2001-01-01

    Recently a new theory of random self-similar river networks, called the RSN model, was introduced to explain empirical observations regarding the scaling properties of distributions of various topologic and geometric variables in natural basins. The RSN model predicts that such variables exhibit statistical simple scaling, when indexed by Horton-Strahler order. The average side tributary structure of RSN networks also exhibits Tokunaga-type self-similarity which is widely observed in nature. We examine the scaling structure of distributions of the maximum of the width function for RSNs for nested, complete Strahler basins by performing ensemble simulations. The maximum of the width function exhibits distributional simple scaling, when indexed by Horton-Strahler order, for both RSNs and natural river networks extracted from digital elevation models (DEMs). We also test a powerlaw relationship between Horton ratios for the maximum of the width function and drainage areas. These results represent first steps in formulating a comprehensive physical statistical theory of floods at multiple space-time scales for RSNs as discrete hierarchical branching structures. ?? 2001 Published by Elsevier Science Ltd.

  13. Evidence of Long Range Dependence and Self-similarity in Urban Traffic Systems

    SciTech Connect

    Thakur, Gautam S; Helmy, Ahmed; Hui, Pan

    2015-01-01

    Transportation simulation technologies should accurately model traffic demand, distribution, and assignment parame- ters for urban environment simulation. These three param- eters significantly impact transportation engineering bench- mark process, are also critical in realizing realistic traffic modeling situations. In this paper, we model and charac- terize traffic density distribution of thousands of locations around the world. The traffic densities are generated from millions of images collected over several years and processed using computer vision techniques. The resulting traffic den- sity distribution time series are then analyzed. It is found using the goodness-of-fit test that the traffic density dis- tributions follows heavy-tail models such as Log-gamma, Log-logistic, and Weibull in over 90% of analyzed locations. Moreover, a heavy-tail gives rise to long-range dependence and self-similarity, which we studied by estimating the Hurst exponent (H). Our analysis based on seven different Hurst estimators strongly indicate that the traffic distribution pat- terns are stochastically self-similar (0.5 H 1.0). We believe this is an important finding that will influence the design and development of the next generation traffic simu- lation techniques and also aid in accurately modeling traffic engineering of urban systems. In addition, it shall provide a much needed input for the development of smart cities.

  14. Self-similar pinch-off mechanism and scaling of ferrofluid drops

    NASA Astrophysics Data System (ADS)

    Jiang, Xiao F.; Li, Huai Z.

    2015-12-01

    The pinch off of heterogeneous ferrofluid drops at a nozzle in air was experimentally investigated with a magnetic field (downward or upward) and without a magnetic field. Compared to homogeneous drops, the self-similarity and universal scaling law were verified through modifying the initial conditions, such as the nozzle diameter, flow rate, and magnitude and direction of the magnetic fields. Two pinch-off points were observed, and the two consecutive pinch-off dynamics were characterized through scaling laws. Here our scaling exponent remains within the scope of (0.70-0.80) for the primary whereas it remains within the scope of (0.60-0.70) for the secondary pinch off, respectively, comparable to the classic range from 2/3 to 1 for homogeneous drops. The gravity-compensating and gravity-superimposing magnetic fields display a negligible effect on the exponent but determine the sequence of double pinch offs. The universal character of the self-similar pinch off is extended to a heterogeneous fluid.

  15. Nucléation, ascension et éclatement d'une bulle de champagne

    NASA Astrophysics Data System (ADS)

    Liger-Belair, G.

    2006-03-01

    People have long been fascinated by bubbles and foams dynamics, and since the pioneering work of Leonardo da Vinci in the early 16th century, this subject has generated a huge bibliography. However, only quite recently, much interest was devoted to bubbles in Champagne wines and carbonated beverages. Since the time of the benedictine monk dom Pierre Perignon (1638-1715), champagne is the wine of celebration. This fame is largely linked to the elegance of its effervescence and foaming properties. In this book, the latest results about the chemical physics behind the bubbling properties of Champagne and sparkling wines are collected and fully illustrated. The first chapter is devoted to the history of champagne and to a presentation of the tools of the physical chemistry of interfaces needed for a whole comprehension of the book. Then, the three main steps of a fleeting champagne bubble's life are presented in chronological order, that is, the bubble nucleation on the glass wall (Chap.2), the bubble ascent and growth through the liquid matrix (Chap.3), and the bursting of bubbles at the liquid surface (Chap.4), which constitutes the most intriguing, functional, and visually appealing step. L'objectif général de ce travail consacré à l'étude des processus physicochimiques liés à l'effervescence des vins de Champagne était de décortiquer les différentes étapes de la vie d'une bulle de champagne en conditions réelles de consommation, dans une flûte. Nous résumons ci-après les principaux résultats obtenus pour chacune des étapes de la vie de la bulle, depuis sa naissance sur les parois d'une flûte, jusqu'à son éclatement en surface. Nucléation À l'aide d'une caméra rapide munie d'un objectif de microscope, nous avons pu mettre à mal une idée largement répandue. Ce ne sont pas les anfractuosités de la surface du verre ou de la flûte qui sont responsable de la nucléation hétérogène des bulles, mais des particules adsorbées sur les parois du

  16. Integration, Disintegration, and Self-Similarity: Characterizing the Scales of Shape Variation in Landmark Data.

    PubMed

    Bookstein, Fred L

    The biologist examining samples of multicellular organisms in anatomical detail must already have an intuitive concept of morphological integration. But quantifying that intuition has always been fraught with difficulties and paradoxes, especially for the anatomically labelled Cartesian coordinate data that drive today's toolkits of geometric morphometrics. Covariance analyses of interpoint distances, such as the Olson-Miller factor approach of the 1950's, cannot validly be extended to handle the spatial structure of complete morphometric descriptions; neither can analyses of shape coordinates that ignore the mean form. This paper introduces a formal parametric quantification of integration by analogy with how time series are approached in modern paleobiology. Over there, a finding of trend falls under one tail of a distribution for which stasis comprises the other tail. The null hypothesis separating these two classes of finding is the random walks, which are self-similar, meaning that they show no interpretable structure at any temporal scale. Trend and stasis are the two contrasting ways of deviating from this null. The present manuscript introduces an analogous maneuver for the spatial aspects of ontogenetic or phylogenetic organismal studies: a subspace within the space of shape covariance structures for which the standard isotropic (Procrustes) model lies at one extreme of a characteristic parameter and the strongest growth-gradient models at the other. In-between lies the suggested new construct, the spatially self-similar processes that can be generated within the standard morphometric toolkit by a startlingly simple algebraic manipulation of partial warp scores. In this view, integration and "disintegration" as in the Procrustes model are two modes of organismal variation according to which morphometric data can deviate from this common null, which, as in the temporal domain, is formally featureless, incapable of supporting any summary beyond a single

  17. Size distribution of dust grains: A problem of self-similarity

    NASA Technical Reports Server (NTRS)

    Henning, TH.; Dorschner, J.; Guertler, J.

    1989-01-01

    Distribution functions describing the results of natural processes frequently show the shape of power laws, e.g., mass functions of stars and molecular clouds, velocity spectrum of turbulence, size distributions of asteroids, micrometeorites and also interstellar dust grains. It is an open question whether this behavior is a result simply coming about by the chosen mathematical representation of the observational data or reflects a deep-seated principle of nature. The authors suppose the latter being the case. Using a dust model consisting of silicate and graphite grains Mathis et al. (1977) showed that the interstellar extinction curve can be represented by taking a grain radii distribution of power law type n(a) varies as a(exp -p) with 3.3 less than or equal to p less than or equal to 3.6 (example 1) as a basis. A different approach to understanding power laws like that in example 1 becomes possible by the theory of self-similar processes (scale invariance). The beta model of turbulence (Frisch et al., 1978) leads in an elementary way to the concept of the self-similarity dimension D, a special case of Mandelbrot's (1977) fractal dimension. In the frame of this beta model, it is supposed that on each stage of a cascade the system decays to N clumps and that only the portion beta N remains active further on. An important feature of this model is that the active eddies become less and less space-filling. In the following, the authors assume that grain-grain collisions are such a scale-invarient process and that the remaining grains are the inactive (frozen) clumps of the cascade. In this way, a size distribution n(a) da varies as a(exp -(D+1))da (example 2) results. It seems to be highly probable that the power law character of the size distribution of interstellar dust grains is the result of a self-similarity process. We can, however, not exclude that the process leading to the interstellar grain size distribution is not fragmentation at all. It could be, e

  18. Self-similar spiral flow structure in low Reynolds number isotropic and decaying turbulence

    NASA Astrophysics Data System (ADS)

    Vassilicos, J. C.; Brasseur, James G.

    1996-07-01

    It is rigorously proved for axisymmetric incompressible flows with bounded axial vorticity at infinity that if a spiral-helical streamline has a Kolmogorov capacity (box-counting dimension) DK>~1, then the velocity field must have a singularity at the axis of symmetry. Furthermore, certain types of singularity with DK=1 can be excluded. The Burgers and the Lundgren vortices are examples of strained vortices with different types of near-singular structure, and in both cases sections of streamlines have a well-defined DK>~1. However, the strain severely limits the region in space where DK is larger than 1. An algorithm is developed which detects streamlines with persistently strong curvature and calculates both the DK of the streamlines and the lower bound scale δmin of the range of self-similar scaling defined by DK. Error bounds on DK are also computed. The use of this algorithm partly relies on the fact that two to three turns of a spiral are enough to determine a spiral's DK. We detect well-defined self-similar scaling in the geometry of streamlines around vortex tubes in decaying isotropic direct numerical simulation turbulence with exceptionally fine small-scale resolution and Reλ around 20. The measured values of DK vary from DK=1 to DK~=1.60, and in general the self-similar range of length scales over which DK is well defined extends over one decade and ends at one of two well-defined inner scales, one just above and the other just below the Kolmogorov microscale η. We identify two different types of accumulation of length scales with DK>~1 on streamlines around the vortex tubes in the simulated turbulence: an accumulation of the streamline towards a central axis of the vortex tube in a spiral-helical fashion, and a helical and axial accumulation of the streamline towards a limit circle at the periphery of the vortex tube. In the latter case, the limit circle lies in a region along the axis of the vortex tube where there is a rapid drop in enstrophy. The

  19. Self-similar structure and experimental signatures of suprathermal ion distribution in inertial confinement fusion implosions

    DOE PAGES

    Kagan, Grigory; Svyatskiy, D.; Rinderknecht, H. G.; ...

    2015-09-03

    The distribution function of suprathermal ions is found to be self-similar under conditions relevant to inertial confinement fusion hot spots. By utilizing this feature, interference between the hydrodynamic instabilities and kinetic effects is for the first time assessed quantitatively to find that the instabilities substantially aggravate the fusion reactivity reduction. Thus, the ion tail depletion is also shown to lower the experimentally inferred ion temperature, a novel kinetic effect that may explain the discrepancy between the exploding pusher experiments and rad-hydro simulations and contribute to the observation that temperature inferred from DD reaction products is lower than from DT atmore » the National Ignition Facility.« less

  20. [Study on self-similarity of property combination mode of traditional Chinese medicines].

    PubMed

    Sun, Jing; Zhang, Bai-Xia; Yan, Su-Rong; Zhang, Yan-Ling; Wang, Yun; Qiao, Yan-Jiang

    2014-07-01

    The combination of medicinal properties refers to expression forms of elements with active properties combined according to a specific sequence. The mode of medicinal property combination refers to the compatible relationship multiple medicinal property combinations. In this paper, based on the mode, safflower, Taohong Siwu decoction, Xuefu Zhuyu decoction and Buyang Huanwu decoction were taken for example to study the characteristics of the compatibility among single herb, herbal pairs and prescriptions. The authors discovered the similarities and differences among them, interpreted the self-similarity in medicinal property combinations of traditional Chinese medicines, and analyzed the compatible relationship among multiple medicinal property combinations, so as to bring forth new ideas in discovering the correlation between the compatibility study mode of traditional Chinese medicines based medicinal property combinations and the efficient compatibility of medicinal property combination.

  1. Self-similar accelerative propagation of expanding wrinkled flames and explosion triggering.

    PubMed

    Akkerman, V'yacheslav; Law, Chung K; Bychkov, Vitaly

    2011-02-01

    The formulation of Taylor on the self-similar propagation of an expanding spherical piston with constant velocity was extended to an instability-wrinkled deflagration front undergoing acceleration with R(F)∝t(α), where R(F) is the instantaneous flame radius, t the time, and α a constant exponent. The formulation describes radial compression waves pushed by the front, trajectories of gas particles, and the explosion condition in the gas upstream of the front. The instant and position of explosion are determined for a given reaction mechanism. For a step-function induction time, analytic formulas for the explosion time and position are derived, showing their dependence on the reaction and flow parameters including thermal expansion, specific heat ratio, and acceleration of the front. ©2011 American Physical Society

  2. Cantor set spectra and self-similar critical modes in a 1D-quasicrystal

    NASA Astrophysics Data System (ADS)

    Desideri, J. P.; Legrand, O.; Macon, L.; Sornette, D.

    1989-09-01

    Specific properties of the propagation of surface acoustic waves on quasiperiodically corrugated solids are reviewed. This problem is shown to correspond to the critical regime of the Anderson localization transition, characterized by critical proper modes which are neither extended nor localized and which exhibit remarkable scaling features. The spectrum is also predicted to have a Cantor-like structure. The experimental system is made of a thousand grooves engraved according to a Fibonacci sequence. For the first time, the self-similar spatial structure of the critical proper modes is observed through an optical diffraction experiment. Signatures of the fractal spectrum are also reported. These results are explained in terms of the asymptotic approximation of the quasicrystal by periodic systems of increasing periods.

  3. Self-similarity of asymmetric sand-ripple profiles formed under nonlinear shoaling waves

    NASA Astrophysics Data System (ADS)

    Testik, F. Y.; Voropayev, S. I.; Balasubramanian, S.; Fernando, H. J. S.

    2006-10-01

    We report the results of laboratory experiments conducted to study equilibrium profiles of asymmetric sand ripples that form under nonlinear shoaling waves. Waves were generated in a large wave tank with a sandy slope that mimics the oceanic coastal zone. The measurements revealed that, to the first approximation, the equilibrium asymmetric sand ripples profiles can be considered as self-similar. In the experimental parameter range considered (wave asymmetry A =1.3-5; mobility parameter Ψ =8-70; shoaling coefficient S =1.03-1.6), the ripple profiles can be described by a simple similarity profile of "sawtooth" shape with "universal" onshore θ1 (≈34°) and offshore θ2 (≈18°) ripple slope angles. The results may be useful in parameterization of coastal bed roughness, in underwater acoustics and sediment transport applications.

  4. Even perturbations of the self-similar Vaidya space-time

    SciTech Connect

    Nolan, Brien C.; Waters, Thomas J.

    2005-05-15

    We study even parity metric and matter perturbations of all angular modes in self-similar Vaidya space-time. We focus on the case where the background contains a naked singularity. Initial conditions are imposed, describing a finite perturbation emerging from the portion of flat space-time preceding the matter-filled region of space-time. The most general perturbation satisfying the initial conditions is allowed to impinge upon the Cauchy horizon (CH), where the perturbation remains finite: There is no 'blue-sheet' instability. However, when the perturbation evolves through the CH and onto the second future similarity horizon of the naked singularity, divergence necessarily occurs: This surface is found to be unstable. The analysis is based on the study of individual modes following a Mellin transform of the perturbation. We present an argument that the full perturbation remains finite after resummation of the (possibly infinite number of) modes.

  5. Self-similar solution of the problem of consolidation and thawing of frozen soil

    SciTech Connect

    Klement'ev, A.F.; Klement'eva, E.A.

    1988-10-01

    This article presents a new mathematical model of the process of thawing of frozen soil taking consolidation into account. Two solutions were obtained: the self-similar solution for the unidimensional biphase problem and an approximate analytical solution for the simplified single-phase problem. A comparison with the results of physical modeling showed that the method is fairly effective in the case of warm permafrost. The mean error in predicting the position of the interface between the thawed and frozen zones for different soils over a period of one to ten years amounted to 20.9%. The use of the method of the All-Union Research Institute of Pipeline Construction yielded an error of 31.6% and the method of the All-Union Research Institute of the Gas Industry an error of 39.6% by comparison.

  6. Self-similar inverse cascade of magnetic helicity driven by the chiral anomaly

    NASA Astrophysics Data System (ADS)

    Hirono, Yuji; Kharzeev, Dmitri E.; Yin, Yi

    2015-12-01

    For systems with charged chiral fermions, the imbalance of chirality in the presence of magnetic field generates an electric current—this is the chiral magnetic effect (CME). We study the dynamical real-time evolution of electromagnetic fields coupled by the anomaly to the chiral charge density and the CME current by solving the Maxwell-Chern-Simons equations. We find that the CME induces the inverse cascade of magnetic helicity toward the large distances, and that at late times this cascade becomes self-similar, with universal exponents. We also find that in terms of gauge field topology the inverse cascade represents the transition from linked electric and magnetic fields (Hopfions) to the knotted configuration of magnetic field (Chandrasekhar-Kendall states). The magnetic reconnections are accompanied by the pulses of the CME current directed along the magnetic field lines. We devise an experimental signature of these phenomena in heavy ion collisions, and speculate about implications for condensed matter systems.

  7. Self-Similar Nanocavity Design with Ultrasmall Mode Volume for Single-Photon Nonlinearities

    NASA Astrophysics Data System (ADS)

    Choi, Hyeongrak; Heuck, Mikkel; Englund, Dirk

    2017-06-01

    We propose a photonic crystal nanocavity design with self-similar electromagnetic boundary conditions, achieving ultrasmall mode volume (Veff). The electric energy density of a cavity mode can be maximized in the air or dielectric region, depending on the choice of boundary conditions. We illustrate the design concept with a silicon-air one-dimensional photon crystal cavity that reaches an ultrasmall mode volume of Veff˜7.01 ×10-5λ3 at λ ˜1550 nm . We show that the extreme light concentration in our design can enable ultrastrong Kerr nonlinearities, even at the single-photon level. These features open new directions in cavity quantum electrodynamics, spectroscopy, and quantum nonlinear optics.

  8. Log-periodic oscillations for diffusion on self-similar finitely ramified structures.

    PubMed

    Padilla, L; Mártin, H O; Iguain, J L

    2010-07-01

    Under certain circumstances, the time behavior of a random walk is modulated by logarithmic-periodic oscillations. Using heuristic arguments, we give a simple explanation of the origin of this modulation for diffusion on a substrate with two properties: self-similarity and finite ramification order. On these media, the time dependence of the mean-square displacement shows log-periodic modulations around a leading power law, which can be understood on the basis of a hierarchical set of diffusion constants. Both the random walk exponent and the period of oscillations are analytically obtained for a pair of examples, one is fractal and the other is nonfractal, and confirmed by Monte Carlo simulations. The last example shows that the anomalous diffusion can arise from substrates without holes of all sizes.

  9. Large resistivity in numerical simulations of radially self-similar outflows

    NASA Astrophysics Data System (ADS)

    Čemeljić, M.; Vlahakis, N.; Tsinganos, K.

    2014-08-01

    We investigate the differences between an outflow in a highly resistive accretion disc corona, and the results with smaller or vanishing resistivity. For the first time, we determine conditions at the base of a two-dimensional radially self-similar outflow in the regime of very large resistivity. We performed simulations using the PLUTO magnetohydrodynamics (MHD) code, and found three modes of solutions. The first mode, with small resistivity, is similar to the ideal-MHD solutions. In the second mode, with larger resistivity, the geometry of the magnetic field changes, with a `bulge' above the superfast critical surface. At even larger resistivities, the third mode of solutions sets in, in which the magnetic field is no longer collimated, but is pressed towards the disc. This third mode is also the final one: it does not change with further increase of resistivity. These modes describe topological change in a magnetic field above the accretion disc because of the uniform, constant Ohmic resistivity.

  10. Convection of viscous fluids: Energetics, self-similarity, experiments, geophysical applications and analogies

    NASA Technical Reports Server (NTRS)

    Golitsyn, G. S.

    1977-01-01

    The main results were the formulas for the mean convection velocities, of a viscous fluid and for the mean temperature difference in the bulk of the convecting fluid. These were obtained: by scaling analysis of the Boussinesq equations, by analysis of the energetics of the process, and by using similarity and dimensional arguments. The last approach defines the criteria of similarity and allows the proposition of some self-similarity hypotheses. By several simple new ways, an expression for the efficiency coefficient gamma of the thermal convection was also obtained. An analogy is pointed out between non-turbulent convection of a viscous fluid and the structure of turbulence for scales less than Kolmogorov's internal viscous microscale of turbulence.

  11. Observation of Self-Similar Behavior of the 3D, Nonlinear Rayleigh-Taylor Instability

    SciTech Connect

    Sadot, O.; Smalyuk, V.A.; Delettrez, J.A.; Sangster, T.C.; Goncharov, V.N.; Meyerhofer, D.D.; Betti, R.; Shvarts, D.

    2005-12-31

    The Rayleigh-Taylor unstable growth of laser-seeded, 3D broadband perturbations was experimentally measured in the laser-accelerated, planar plastic foils. The first experimental observation showing the self-similar behavior of the bubble size and amplitude distributions under ablative conditions is presented. In the nonlinear regime, the modulation {sigma}{sub rms} grows as {alpha}{sub {sigma}}gt{sup 2}, where g is the foil acceleration, t is the time, and {alpha}{sub {sigma}} is constant. The number of bubbles evolves as N(t){proportional_to}({omega}t{radical}(g)+C){sup -4} and the average size evolves as <{lambda}>(t){proportional_to}{omega}{sup 2}gt{sup 2}, where C is a constant and {omega}=0.83{+-}0.1 is the measured scaled bubble-merging rate.

  12. Self-similar mesostructure evolution of the growing mollusc shell reminiscent of thermodynamically driven grain growth

    NASA Astrophysics Data System (ADS)

    Bayerlein, Bernd; Zaslansky, Paul; Dauphin, Yannicke; Rack, Alexander; Fratzl, Peter; Zlotnikov, Igor

    2014-12-01

    Significant progress has been made in understanding the interaction between mineral precursors and organic components leading to material formation and structuring in biomineralizing systems. The mesostructure of biological materials, such as the outer calcitic shell of molluscs, is characterized by many parameters and the question arises as to what extent they all are, or need to be, controlled biologically. Here, we analyse the three-dimensional structure of the calcite-based prismatic layer of Pinna nobilis, the giant Mediterranean fan mussel, using high-resolution synchrotron-based microtomography. We show that the evolution of the layer is statistically self-similar and, remarkably, its morphology and mesostructure can be fully predicted using classical materials science theories for normal grain growth. These findings are a fundamental step in understanding the constraints that dictate the shape of these biogenic minerals and shed light on how biological organisms make use of thermodynamics to generate complex morphologies.

  13. Plasma Membrane is Compartmentalized by a Self-Similar Cortical Actin Meshwork

    NASA Astrophysics Data System (ADS)

    Sadegh, Sanaz; Higgins, Jenny L.; Mannion, Patrick C.; Tamkun, Michael M.; Krapf, Diego

    2017-01-01

    A broad range of membrane proteins display anomalous diffusion on the cell surface. Different methods provide evidence for obstructed subdiffusion and diffusion on a fractal space, but the underlying structure inducing anomalous diffusion has never been visualized because of experimental challenges. We addressed this problem by imaging the cortical actin at high resolution while simultaneously tracking individual membrane proteins in live mammalian cells. Our data confirm that actin introduces barriers leading to compartmentalization of the plasma membrane and that membrane proteins are transiently confined within actin fences. Furthermore, superresolution imaging shows that the cortical actin is organized into a self-similar meshwork. These results present a hierarchical nanoscale picture of the plasma membrane.

  14. Methods of construction and study of Frankl system self-similar solutions in the hyperbolic case

    NASA Astrophysics Data System (ADS)

    Shemyakina, T.; Alekseenkκo, S.

    2016-11-01

    Self-similar solution of the Frankl system in the hyperbolic case was found. The Frankl system is a system of mixed type equations. Under certain conditions, it describes a model of the membrane theory of shells. The Frankl system describes a stationary irrotational motion of an ideal gas in the transition vicinity from subsonic to supersonic speeds. We find a sufficient condition on the initial data that guarantees existence of a global classical solution continued from a local solution. The proof of the nonlocal solvability of the problem in the original variables is based on the additional argument method. It allowed justify and construct a numerical solution. Numerical experiments were carried out for model examples of the Frankl system.

  15. Self-similar mesostructure evolution of the growing mollusc shell reminiscent of thermodynamically driven grain growth.

    PubMed

    Bayerlein, Bernd; Zaslansky, Paul; Dauphin, Yannicke; Rack, Alexander; Fratzl, Peter; Zlotnikov, Igor

    2014-12-01

    Significant progress has been made in understanding the interaction between mineral precursors and organic components leading to material formation and structuring in biomineralizing systems. The mesostructure of biological materials, such as the outer calcitic shell of molluscs, is characterized by many parameters and the question arises as to what extent they all are, or need to be, controlled biologically. Here, we analyse the three-dimensional structure of the calcite-based prismatic layer of Pinna nobilis, the giant Mediterranean fan mussel, using high-resolution synchrotron-based microtomography. We show that the evolution of the layer is statistically self-similar and, remarkably, its morphology and mesostructure can be fully predicted using classical materials science theories for normal grain growth. These findings are a fundamental step in understanding the constraints that dictate the shape of these biogenic minerals and shed light on how biological organisms make use of thermodynamics to generate complex morphologies.

  16. Self-similarity and non-Markovian behavior in traded stock volumes

    NASA Astrophysics Data System (ADS)

    Brown, Frank R.; Pravica, David; Bier, Martin

    2015-11-01

    The volume traded daily for 17 stocks is followed over a period of about half a century. We look at the volume of stocks traded in a certain time interval (day, week, month) and analyze how long that traded volume keeps monotonically increasing or decreasing. On all three times scales we find that the sequence of traded volumes behaves neither like a sequence of independent and identically distributed variables, nor like a Markov sequence. A compressed exponential survival function with the same parameters at all timescales is firmly established. A day with an increase (decrease) of traded volume is most likely followed by a day with a decrease (increase) of traded volume. We show how the apparent self-similarity results because the small day-to-day anticorrelation carries over when larger time intervals are considered. The observed small anticorrelation can be explained as a consequence of market forces and trader reactions.

  17. Observation of self-similar behavior of the 3D, nonlinear Rayleigh-Taylor instability.

    PubMed

    Sadot, O; Smalyuk, V A; Delettrez, J A; Meyerhofer, D D; Sangster, T C; Betti, R; Goncharov, V N; Shvarts, D

    2005-12-31

    The Rayleigh-Taylor unstable growth of laser-seeded, 3D broadband perturbations was experimentally measured in the laser-accelerated, planar plastic foils. The first experimental observation showing the self-similar behavior of the bubble size and amplitude distributions under ablative conditions is presented. In the nonlinear regime, the modulation sigma(rms) grows as alpha(sigma)gt(2), where g is the foil acceleration, t is the time, and alpha(sigma) is constant. The number of bubbles evolves as N(t) alpha(omegat sq.rt(9) + C)(-4) and the average size evolves as (t) alpha omega(2)gt(2), where C is a constant and omega = 0.83 +/- 0.1 is the measured scaled bubble-merging rate.

  18. Local self-similarity descriptor for point-of-interest reconstruction of real-world scenes

    NASA Astrophysics Data System (ADS)

    Gao, Xianglu; Wan, Weibing; Zhao, Qunfei; Zhang, Xianmin

    2015-08-01

    Scene reconstruction is utilized commonly in close-range photogrammetry, with diverse applications in fields such as industry, biology, and aerospace industries. Presented surfaces or wireframe three-dimensional (3D) model reconstruction applications are either too complex or too inflexible to accommodate various types of real-world scenes, however. This paper proposes an algorithm for acquiring point-of-interest (referred to throughout the study as POI) coordinates in 3D space, based on multi-view geometry and a local self-similarity descriptor. After reconstructing several POIs specified by a user, a concise and flexible target object measurement method, which obtains the distance between POIs, is described in detail. The proposed technique is able to measure targets with high accuracy even in the presence of obstacles and non-Lambertian surfaces. The method is so flexible that target objects can be measured with a handheld digital camera. Experimental results further demonstrate the effectiveness of the algorithm.

  19. The Phase Transitions of Self-similar Small-world Networks

    NASA Astrophysics Data System (ADS)

    Brunson, Trent; Boettcher, Stefan

    2010-03-01

    A novel set of self-similar networks called Hanoi networksfootnotetextS. Boettcher, B Goncalves, Europhysics Letters 84, 30002 (2008). (HN) have been developed to study the critical phenomena of small-world networks using the renormalization group (RG). Physically, HNs contain a more desirable geometry than random small-world networks. Their structure consists of a one-dimensional backbone with a hierarchy of long-range bonds, which allows the flexibility of studying planar and non-planar networks with either a regular or exponential degree distribution. The RG and Ising model simulation results for HNs reveal unique phase transitions and non-universal behavior, which can be attributed to their hierarchical structure.footnotetextSee also http://www.physics.emory.edu/faculty/boettcher/.

  20. Self-similar micron-size and nanosize drops of liquid generated by surface acoustic waves.

    PubMed

    Taller, Daniel; Go, David B; Chang, Hsueh-Chia

    2012-11-30

    A planar surface acoustic wave on a solid substrate and its radiated sound into a static liquid drop produce time-averaged, exponentially decaying acoustic and electric Maxwell pressures near the contact line. These localized contact-line pressures are shown to generate two sequences of hemispherical satellite droplets at the tens of microns and submicron scales, both obeying self-similar exponential scaling but with distinct exponents that correspond to viscous dissipation and field leakage length scales, respectively. The acoustic pressure becomes dominant when the film thickness exceeds (1/4π) of the surface acoustic wave wavelength and it affects the shape and stability of the mother drop. The Maxwell pressure of the nanodrops, which exceeds ten atmospheres, is sensitive to the contact angle.

  1. Self-similar pulse-shape mode for femtosecond pulse propagation in medium with resonant nonlinearity

    NASA Astrophysics Data System (ADS)

    Trofimov, Vyacheslav A.; Zakharova, Irina G.; Konar, Swapan

    2014-05-01

    We investigate the mode of laser pulse propagation in homogeneous medium with resonant nonlinearity, at which the shape of pulse is self-similar one along some distance of propagation. We take into account a laser pulse frequency detuning from resonant frequency. Both types of sign for frequency detuning are considered. This results in appearance of a refractive index grating which induced self-action of a laser pulse. I certain cases we develop analytical solution of corresponding nonlinear eigenfunction problem of laser pulse propagation in medium for multi-photon resonance. This solution is confirmed by computer simulation of an eigenfunction problem for Schrödinger equation with considered nonlinearity. Using computer simulation, one shows a validity of existence of such kind of laser pulse propagation in a medium with resonant nonlinear response.

  2. Self-similar pseudobands and localization of magnetoplasmons in finite multilayered Fibonacci superlattices

    SciTech Connect

    Liu, N. Department of Physics, Ji An Teachers Training College, Ji An Jiangxi 343009 ); Feng, W. , P.O. Box 8730, Beijing Pohl Institute of Solid State Physics, Tongji University, Shanghai 200092 ); Wu, X. , P.O. Box 8730, Beijing International Centre for Materials Physics, Academia Sinica, Shengyang Pohl Institute of Solid State Physics, Tongji University, Shanghai 200092 )

    1993-12-15

    The collective plasmon-polariton excitations in finite Fibonacci semiconductor superlattices, which are subjected to a static magnetic field applied parallel to the interfaces, are studied by using local-field theory with retardation. We find that for a given in-plane wave vector, the discrete modes are composed of pseudobands and show rich self-similar patterns. The dispersion relations of the modes are obviously modified by the application of the magnetic field, and the propagation of the surface waves shows remarkable nonreciprocal behavior in the field. A number of coupled guided modes are found when the retardation effects are taken into account. We plot the profiles of the amplitudes to investigate the localization properties of the polaritons. The results show that those modes isolated from the pseudobands are localized, the modes located in the pseudobands are extended, while those located at the edges of the bands are critical.

  3. Scaling of Peak Flows with Constant Flow Velocity in Random Self-Similar Networks

    NASA Astrophysics Data System (ADS)

    Mantilla, Ricardo; Gupta, Vijay K.; Troutman, Brent M.

    2010-05-01

    We present a methodology to understand the role of the statistical self-similar topology of real river networks on flow hydrographs for rainfall-runoff events. Monte Carlo generated ensembles of 1000 Random Self-similar Networks (RSNs) with geometrically distributed interior and exterior generators are created. These networks emulate the topology of real networks. Hydrographs for every link in each of these networks are obtained by numerically solving the link-based mass and momentum conservation equation under the assumption of constant flow velocity. From these simulated RSNs and hydrographs, the scaling parameters for the peak of the width function β and the hydrograph peak flow ? are estimated. It was found that ? > β, which supports a similar finding first reported for the Walnut Gulch basin, Arizona, and that is in qualitatively different from previous results on idealized river networks (e.g. Peano Network, Mandelbrot- Viscek Network). The use of numerical simulations is necessary as theoretical estimation of β and ? in RSNs is a complex mathematical open problem. However, other scaling features of the average width function can the average hydrograph are calculated analytically and compared with the estimation from the RSN-ensemble. Scaling of peak flows during individual rainfall runoff events is a new area of research that offers a path to understand regional scaling of flood quantiles, an important open problem in river network hydrology. For example, our results show an interesting connection between unit-hydrograph theory and flow dynamics. In addition, our methodology provides a reference framework to study scaling exponents under more complex scenarios of flow dynamics and runoff generation processes using ensembles of RSNs.

  4. Mosaic, self-similarity logic, and biological attraction principles: three explanatory instruments in biology.

    PubMed

    Agnati, Luigi F; Baluska, Frantisek; Barlow, Peter W; Guidolin, Diego

    2009-11-01

    From a structural standpoint, living organisms are organized like a nest of Russian matryoshka dolls, in which structures are buried within one another. From a temporal point of view, this type of organization is the result of a history comprised of a set of time backcloths which have accompanied the passage of living matter from its origins up to the present day. The aim of the present paper is to indicate a possible course of this 'passage through time, and suggest how today's complexity has been reached by living organisms. This investigation will employ three conceptual tools, namely the Mosaic, Self-Similarity Logic, and the Biological Attraction principles. Self-Similarity Logic indicates the self-consistency by which elements of a living system interact, irrespective of the spatiotemporal level under consideration. The term Mosaic indicates how, from the same set of elements assembled according to different patterns, it is possible to arrive at completely different constructions: hence, each system becomes endowed with different emergent properties. The Biological Attraction principle states that there is an inherent drive for association and merging of compatible elements at all levels of biological complexity. By analogy with the gravitation law in physics, biological attraction is based on the evidence that each living organism creates an attractive field around itself. This field acts as a sphere of influence that actively attracts similar fields of other biological systems, thereby modifying salient features of the interacting organisms. Three specific organizational levels of living matter, namely the molecular, cellular, and supracellular levels, have been considered in order to analyse and illustrate the interpretative as well as the predictive roles of each of these three explanatory principles.

  5. Self similar evolution of a vortex in a rotating stratified flow - Application to Meddies

    NASA Astrophysics Data System (ADS)

    Facchini, G.

    2015-12-01

    Meddies are large coherent anticyclones which form at Gibraltar Straits, where warm and salty water from the Mediterranean sea exits in the Atlantic Ocean. These vortical structures show a striking long lifetime of 2-3 years. The understanding of the fundamental mechanisms which allow Meddies to persist for such a long time, motivates our experimental, numerical and theoretical study. We look at the time evolution of an isolated vortex generated by injecting a small amount of fluid at the center of a rotating tank filled with salty water linearly stratified in density. In experiments, the fluid motion is investigated using PIV techniques, providing the velocity field in the plane orthogonal to the vorticity vector. Our two control parameters are the background Coriolis and buoyancy frequencies. We observe that vortices universally take an ellipsoidal shape defined by the geostrophic equilibrium, and slowly evolve in a quasi-steady self-similar way. They expand in the radial direction and slow down, but remain extremely coherent over several hundreds of background rotations. Fluid equations can be simplified in the limit of small Rossby and Ekman numbers. At the first order in time, we obtain a diffusion like equation for the pressure, the density anomaly and the azimuthal velocity in Our analytical solution describes well our experimental and numerical results.the vortex. The behavior of the vortex depends on the ratio between the background Coriolis and buoyancy frequencies. When these two frequencies are equal, an exact self-similar solution is found, predicting a simple power law for the time evolution of the Rossby number and, surprisingly, a diffusion of the azimuthal velocity profile in the radial direction only, even when the aspect ratio of the vortex is small (i.e. "pancake shape", like in real meddies). Our analytical solution is in good agreement with our experimental and numerical results.

  6. Co-location and Self-Similar Topologies of Urban Infrastructure Networks

    NASA Astrophysics Data System (ADS)

    Klinkhamer, Christopher; Zhan, Xianyuan; Ukkusuri, Satish; Elisabeth, Krueger; Paik, Kyungrock; Rao, Suresh

    2016-04-01

    The co-location of urban infrastructure is too obvious to be easily ignored. For reasons of practicality, reliability, and eminent domain, the spatial locations of many urban infrastructure networks, including drainage, sanitary sewers, and road networks, are well correlated. However, important questions dealing with correlations in the network topologies of differing infrastructure types remain unanswered. Here, we have extracted randomly distributed, nested subnets from the urban drainage, sanitary sewer, and road networks in two distinctly different cities: Amman, Jordan; and Indianapolis, USA. Network analyses were performed for each randomly chosen subnet (location and size), using a dual-mapping approach (Hierarchical Intersection Continuity Negotiation). Topological metrics for each infrastructure type were calculated and compared for all subnets in a given city. Despite large differences in the climate, governance, and populace of the two cities, and functional properties of the different infrastructure types, these infrastructure networks are shown to be highly spatially homogenous. Furthermore, strong correlations are found between topological metrics of differing types of surface and subsurface infrastructure networks. Also, the network topologies of each infrastructure type for both cities are shown to exhibit self-similar characteristics (i.e., power law node-degree distributions, [p(k) = ak-γ]. These findings can be used to assist city planners and engineers either expanding or retrofitting existing infrastructure, or in the case of developing countries, building new cities from the ground up. In addition, the self-similar nature of these infrastructure networks holds significant implications for the vulnerability of these critical infrastructure networks to external hazards and ways in which network resilience can be improved.

  7. SELF-SIMILAR DYNAMICAL RELAXATION OF DARK MATTER HALOS IN AN EXPANDING UNIVERSE

    SciTech Connect

    Lapi, A.; Cavaliere, A.

    2011-12-20

    We investigate the structure of cold dark matter halos using advanced models of spherical collapse and accretion in an expanding universe. These are based on solving time-dependent equations for the moments of the phase-space distribution function in the fluid approximation; our approach includes non-radial random motions and, most importantly, an advanced treatment of both dynamical relaxation effects that take place in the infalling matter: phase-mixing associated with shell crossing and collective collisions related to physical clumpiness. We find self-similar solutions for the spherically averaged profiles of mass density {rho}(r), pseudo phase-space density Q(r), and anisotropy parameter {beta}(r). These profiles agree with the outcomes of state-of-the-art N-body simulations in the radial range currently probed by the latter; at smaller radii, we provide specific predictions. In the perspective provided by our self-similar solutions, we link the halo structure to its two-stage growth history and propose the following picture. During the early fast collapse of the inner region dominated by a few merging clumps, efficient dynamical relaxation plays a key role in producing closely universal mass density and pseudo phase-space density profiles; in particular, these are found to depend only weakly on the detailed shape of the initial perturbation and the related collapse times. The subsequent inside-out growth of the outer regions feeds on the slow accretion of many small clumps and diffuse matter; thus the outskirts are only mildly affected by dynamical relaxation but are more sensitive to asymmetries and cosmological variance.

  8. Self-similarity, small-world, scale-free scaling, disassortativity, and robustness in hierarchical lattices

    NASA Astrophysics Data System (ADS)

    Zhang, Z.-Z.; Zhou, S.-G.; Zou, T.

    2007-04-01

    In this paper, firstly, we study analytically the topological features of a family of hierarchical lattices (HLs) from the view point of complex networks. We derive some basic properties of HLs controlled by a parameter q: scale-free degree distribution with exponent γ=2+ln 2/(ln q), null clustering coefficient, power-law behavior of grid coefficient, exponential growth of average path length (non-small-world), fractal scaling with dimension dB=ln (2q)/(ln 2), and disassortativity. Our results show that scale-free networks are not always small-world, and support the conjecture that self-similar scale-free networks are not assortative. Secondly, we define a deterministic family of graphs called small-world hierarchical lattices (SWHLs). Our construction preserves the structure of hierarchical lattices, including its degree distribution, fractal architecture, clustering coefficient, while the small-world phenomenon arises. Finally, the dynamical processes of intentional attacks and collective synchronization are studied and the comparisons between HLs and Barabási-Albert (BA) networks as well as SWHLs are shown. We find that the self-similar property of HLs and SWHLs significantly increases the robustness of such networks against targeted damage on hubs, as compared to the very vulnerable non fractal BA networks, and that HLs have poorer synchronizability than their counterparts SWHLs and BA networks. We show that degree distribution of scale-free networks does not suffice to characterize their synchronizability, and that networks with smaller average path length are not always easier to synchronize.

  9. Liquid Carbon Dioxide Venting at the Champagne Hydrothermal Site, NW Eifuku Volcano, Mariana Arc

    NASA Astrophysics Data System (ADS)

    Lupton, J.; Lilley, M.; Butterfield, D.; Evans, L.; Embley, R.; Olson, E.; Proskurowski, G.; Resing, J.; Roe, K.; Greene, R.; Lebon, G.

    2004-12-01

    In March/April 2004, submersible dives with the remotely-operated vehicle ROPOS discovered an unusual CO2-rich hydrothermal system near the summit of NW Eifuku, a submarine volcano located at 21.49° N, 144.04° E in the northern Mariana Arc. Although several sites of hydrothermal discharge were located on NW Eifuku, the most intense venting was found at 1600-m depth at the Champagne site, slightly west of the volcano summit. The Champagne site was found to be discharging two distinct fluids into the ocean: a) several small white chimneys were emitting milky 103° C gas-rich hydrothermal fluid with at least millimolar levels of H2S and b) cold (< 4° C) droplets coated with a milky skin were rising slowly from the sediment. These droplets were later determined to consist mainly of liquid CO2, with H2S as a probable secondary component. The droplets were sticky, and did not tend to coalesce into larger droplets, even though they adhered to the ROV like clumps of grapes. The film coating the droplets was assumed to be CO2 hydrate (or clathrate) which is known to form whenever liquid CO2 contacts water under these P,T conditions. Samples of the 103° C hydrothermal fluids were collected in special gas-tight titanium sampling bottles that were able to withstand the high internal pressures created by the dissolved gases. The Champagne hydrothermal fluids contained a surprising 2.3 moles/kg of CO2, an order of magnitude higher than any CO2 values previously reported for submarine hydrothermal fluids. The overall gas composition was 87% CO2, < 0.1% CH4, < 2 ppm H2, 0.012 mM/kg 4He, with the remaining 13% (322 mM/kg) assumed to be sulfur gases (H2S, SO2, etc.). (Additional analyses planned will confirm the speciation of this sulfur gas component). The helium had R/RA = 7.3, typical of subduction zone systems (R = 3He/4He and RA = Rair). Isotopic analysis of the CO2 yielded δ 13C = -1.75 ‰ , much heavier than the -6.0 ‰ typical for carbon in MOR vent fluids. The C/3He

  10. MASS ACCRETION AND ITS EFFECTS ON THE SELF-SIMILARITY OF GAS PROFILES IN THE OUTSKIRTS OF GALAXY CLUSTERS

    SciTech Connect

    Lau, Erwin T.; Nagai, Daisuke; Avestruz, Camille; Nelson, Kaylea; Vikhlinin, Alexey

    2015-06-10

    Galaxy clusters exhibit remarkable self-similar behavior which allows us to establish simple scaling relationships between observable quantities and cluster masses, making galaxy clusters useful cosmological probes. Recent X-ray observations suggested that self-similarity may be broken in the outskirts of galaxy clusters. In this work, we analyze a mass-limited sample of massive galaxy clusters from the Omega500 cosmological hydrodynamic simulation to investigate the self-similarity of the diffuse X-ray emitting intracluster medium (ICM) in the outskirts of galaxy clusters. We find that the self-similarity of the outer ICM profiles is better preserved if they are normalized with respect to the mean density of the universe, while the inner profiles are more self-similar when normalized using the critical density. However, the outer ICM profiles as well as the location of accretion shock around clusters are sensitive to their mass accretion rate, which causes the apparent breaking of self-similarity in cluster outskirts. We also find that the collisional gas does not follow the distribution of collisionless dark matter (DM) perfectly in the infall regions of galaxy clusters, leading to 10% departures in the gas-to-DM density ratio from the cosmic mean value. Our results have a number implications for interpreting observations of galaxy clusters in X-ray and through the Sunyaev–Zel’dovich effect, and their applications to cosmology.

  11. Randomness and Self-similarity in the Topology of River Networks and its Implications for predicting scaling in floods (Invited)

    NASA Astrophysics Data System (ADS)

    Gupta, V. K.; Mantilla, R.; Troutman, B. M.

    2010-12-01

    Properties of randomness (Random model) and mean self-similarity (Tokunaga model) in the topology of river networks have been investigated independently of each other for over forty years. It has been observed that the random model does not predict the observed topology of river networks but Tokunaga model does. However, it does not include randomness that is an important feature of river networks. A new class of river network models called random self-similar networks (RSN) that combines self-similarity and randomness has been introduced to understand important topological features observed in river networks. We will present new results from a set of 30 basins located across the continental United States and representing a wide range of hydroclimatic variability that support the hypothesis of statistical self-similarity postulated by the RSN model. The generators of the RSN model obey a geometric distribution, and self-similarity holds in a statistical sense in 26 of these 30 basins. We will describe how topological self-similarity in river networks provides a theoretical framework to understand observed scaling (power laws) in peak flows by solving mass and momentum conservation equations that describe river-flow generation and its transport in a river network for a rainfall-runoff event.

  12. Human-based percussion and self-similarity detection in electroacoustic music

    NASA Astrophysics Data System (ADS)

    Mills, John Anderson, III

    Electroacoustic music is music that uses electronic technology for the compositional manipulation of sound, and is a unique genre of music for many reasons. Analyzing electroacoustic music requires special measures, some of which are integrated into the design of a preliminary percussion analysis tool set for electroacoustic music. This tool set is designed to incorporate the human processing of music and sound. Models of the human auditory periphery are used as a front end to the analysis algorithms. The audio properties of percussivity and self-similarity are chosen as the focus because these properties are computable and informative. A collection of human judgments about percussion was undertaken to acquire clearly specified, sound-event dimensions that humans use as a percussive cue. A total of 29 participants was asked to make judgments about the percussivity of 360 pairs of synthesized snare-drum sounds. The grouped results indicate that of the dimensions tested rise time is the strongest cue for percussivity. String resonance also has a strong effect, but because of the complex nature of string resonance, it is not a fundamental dimension of a sound event. Gross spectral filtering also has an effect on the judgment of percussivity but the effect is weaker than for rise time and string resonance. Gross spectral filtering also has less effect when the stronger cue of rise time is modified simultaneously. A percussivity-profile algorithm (PPA) is designed to identify those instants in pieces of music that humans also would identify as percussive. The PPA is implemented using a time-domain, channel-based approach and psychoacoustic models. The input parameters are tuned to maximize performance at matching participants' choices in the percussion-judgment collection. After the PPA is tuned, the PPA then is used to analyze pieces of electroacoustic music. Real electroacoustic music introduces new challenges for the PPA, though those same challenges might affect

  13. Self-Similar Conformations and Dynamics of Non-Concatenated Entangled Ring Polymers

    NASA Astrophysics Data System (ADS)

    Ge, Ting

    A scaling model of self-similar conformations and dynamics of non-concatenated entangled ring polymers is developed. Topological constraints force these ring polymers into compact conformations with fractal dimension D =3 that we call fractal loopy globules (FLGs). This result is based on the conjecture that the overlap parameter of loops on all length scales is equal to the Kavassalis-Noolandi number 10-20. The dynamics of entangled rings is self-similar, and proceeds as loops of increasing sizes are rearranged progressively at their respective diffusion times. The topological constraints associated with smaller rearranged loops affect the dynamics of larger loops by increasing the effective friction coefficient, but have no influence on the tubes confining larger loops. Therefore, the tube diameter defined as the average spacing between relevant topological constraints increases with time, leading to ``tube dilation''. Analysis of the primitive paths in molecular dynamics (MD) simulations suggests complete tube dilation with the tube diameter on the order of the time-dependent characteristic loop size. A characteristic loop at time t is defined as a ring section that has diffused a distance of its size during time t. We derive dynamic scaling exponents in terms of fractal dimensions of an entangled ring and the underlying primitive path and a parameter characterizing the extent of tube dilation. The results reproduce the predictions of different dynamic models of a single non-concatenated entangled ring. We demonstrate that traditional generalization of single-ring models to multi-ring dynamics is not self-consistent and develop a FLG model with self-consistent multi-ring dynamics and complete tube dilation. Various dynamic scaling exponents predicted by the self-consistent FLG model are consistent with recent computer simulations and experiments. We also perform MD simulations of nanoparticle (NP) diffusion in melts of non-concatenated entangled ring polymers

  14. Evidence For Departure in Self-Similarity: A New Spectral Ratio Method Using Narrowband Coda Envelopes

    SciTech Connect

    Mayeda, K; Malagnini, L; Walter, W R

    2007-03-16

    This study is motivated by renewed interest within the seismic source community to resolve the long-standing question on energy scaling of earthquakes, specifically, 'Do earthquakes scale self-similarly or are large earthquakes dynamically different than small ones?' This question is important from a seismic hazard prediction point of view, as well as for understanding basic rupture dynamics for earthquakes. Estimating the total radiated energy (ER) from earthquakes requires significant broadband corrections for path and site effects. Moreover, source radiation pattern and directivity corrections can be equally significant and also must be accounted for. Regional studies have used a number of different methods, each with their own advantages and disadvantages. These methods include: integration of squared shear wave moment-rate spectra, direct integration of broadband velocity-squared waveforms, empirical Green's function deconvolution, and spectral ratio techniques. The later two approaches have gained popularity because adjacent or co-located events recorded at common stations have shared path and site effects, which therefore cancel. In spite of this, a number of such studies find very large amplitude variance across a network of stations. In this paper we test the extent to which narrowband coda envelopes can improve upon the traditional spectral ratio using direct phases, allowing a better comparison with theoretical models to investigate similarity. The motivation for using the coda is its stability relative to direct waves and its unique property of spatially homogenizing its energy. The local and regional coda is virtually insensitive to lateral crustal heterogeneity and source radiation pattern, and the use of the coda might allow for more stable amplitude ratios to better constrain source differences between event pairs. We first compared amplitude ratio performance between local and near-regional S and coda waves in the San Francisco Bay region for

  15. Scaling of peak flows with constant flow velocity in random self-similar networks

    USGS Publications Warehouse

    Troutman, Brent M.; Mantilla, Ricardo; Gupta, Vijay K.

    2011-01-01

    A methodology is presented to understand the role of the statistical self-similar topology of real river networks on scaling, or power law, in peak flows for rainfall-runoff events. We created Monte Carlo generated sets of ensembles of 1000 random self-similar networks (RSNs) with geometrically distributed interior and exterior generators having parameters pi and pe, respectively. The parameter values were chosen to replicate the observed topology of real river networks. We calculated flow hydrographs in each of these networks by numerically solving the link-based mass and momentum conservation equation under the assumption of constant flow velocity. From these simulated RSNs and hydrographs, the scaling exponents β and φ characterizing power laws with respect to drainage area, and corresponding to the width functions and flow hydrographs respectively, were estimated. We found that, in general, φ > β, which supports a similar finding first reported for simulations in the river network of the Walnut Gulch basin, Arizona. Theoretical estimation of β and φ in RSNs is a complex open problem. Therefore, using results for a simpler problem associated with the expected width function and expected hydrograph for an ensemble of RSNs, we give heuristic arguments for theoretical derivations of the scaling exponents β(E) and φ(E) that depend on the Horton ratios for stream lengths and areas. These ratios in turn have a known dependence on the parameters of the geometric distributions of RSN generators. Good agreement was found between the analytically conjectured values of β(E) and φ(E) and the values estimated by the simulated ensembles of RSNs and hydrographs. The independence of the scaling exponents φ(E) and φ with respect to the value of flow velocity and runoff intensity implies an interesting connection between unit hydrograph theory and flow dynamics. Our results provide a reference framework to study scaling exponents under more complex scenarios

  16. Chemical messages in 170-year-old champagne bottles from the Baltic Sea: Revealing tastes from the past.

    PubMed

    Jeandet, Philippe; Heinzmann, Silke S; Roullier-Gall, Chloé; Cilindre, Clara; Aron, Alissa; Deville, Marie Alice; Moritz, Franco; Karbowiak, Thomas; Demarville, Dominique; Brun, Cyril; Moreau, Fabienne; Michalke, Bernhard; Liger-Belair, Gérard; Witting, Michael; Lucio, Marianna; Steyer, Damien; Gougeon, Régis D; Schmitt-Kopplin, Philippe

    2015-05-12

    Archaeochemistry as the application of the most recent analytical techniques to ancient samples now provides an unprecedented understanding of human culture throughout history. In this paper, we report on a multiplatform analytical investigation of 170-y-old champagne bottles found in a shipwreck at the bottom of the Baltic Sea, which provides insight into winemaking practices used at the time. Organic spectroscopy-based nontargeted metabolomics and metallomics give access to the detailed composition of these wines, revealing, for instance, unexpected chemical characteristics in terms of small ion, sugar, and acid contents as well as markers of barrel aging and Maillard reaction products. The distinct aroma composition of these ancient champagne samples, first revealed during tasting sessions, was later confirmed using state-of-the-art aroma analysis techniques. After 170 y of deep sea aging in close-to-perfect conditions, these sleeping champagne bottles awoke to tell us a chapter of the story of winemaking and to reveal their extraordinary archaeometabolome and elemental diversity in the form of chemical signatures related to each individual step of champagne production.

  17. Monitoring gaseous CO2 and ethanol above champagne glasses: flute versus coupe, and the role of temperature.

    PubMed

    Liger-Belair, Gérard; Bourget, Marielle; Pron, Hervé; Polidori, Guillaume; Cilindre, Clara

    2012-01-01

    In champagne tasting, gaseous CO(2) and volatile organic compounds progressively invade the headspace above glasses, thus progressively modifying the chemical space perceived by the consumer. Simultaneous quantification of gaseous CO(2) and ethanol was monitored through micro-gas chromatography (μGC), all along the first 15 minutes following pouring, depending on whether a volume of 100 mL of champagne was served into a flute or into a coupe. The concentration of gaseous CO(2) was found to be significantly higher above the flute than above the coupe. Moreover, a recently developed gaseous CO(2) visualization technique based on infrared imaging was performed, thus confirming this tendency. The influence of champagne temperature was also tested. As could have been expected, lowering the temperature of champagne was found to decrease ethanol vapor concentrations in the headspace of a glass. Nevertheless, and quite surprisingly, this temperature decrease had no impact on the level of gaseous CO(2) found above the glass. Those results were discussed on the basis of a multiparameter model which describes fluxes of gaseous CO(2) escaping the liquid phase into the form of bubbles.

  18. Monitoring Gaseous CO2 and Ethanol above Champagne Glasses: Flute versus Coupe, and the Role of Temperature

    PubMed Central

    Liger-Belair, Gérard; Bourget, Marielle; Pron, Hervé; Polidori, Guillaume; Cilindre, Clara

    2012-01-01

    In champagne tasting, gaseous CO2 and volatile organic compounds progressively invade the headspace above glasses, thus progressively modifying the chemical space perceived by the consumer. Simultaneous quantification of gaseous CO2 and ethanol was monitored through micro-gas chromatography (μGC), all along the first 15 minutes following pouring, depending on whether a volume of 100 mL of champagne was served into a flute or into a coupe. The concentration of gaseous CO2 was found to be significantly higher above the flute than above the coupe. Moreover, a recently developed gaseous CO2 visualization technique based on infrared imaging was performed, thus confirming this tendency. The influence of champagne temperature was also tested. As could have been expected, lowering the temperature of champagne was found to decrease ethanol vapor concentrations in the headspace of a glass. Nevertheless, and quite surprisingly, this temperature decrease had no impact on the level of gaseous CO2 found above the glass. Those results were discussed on the basis of a multiparameter model which describes fluxes of gaseous CO2 escaping the liquid phase into the form of bubbles. PMID:22347390

  19. Self-similarity and scaling transitions during rupture of thin free films of Newtonian fluids

    NASA Astrophysics Data System (ADS)

    Thete, Sumeet; Anthony, Christopher; Doshi, Pankaj; Harris, Michael; Basaran, Osman

    2016-11-01

    Rupture of thin liquid sheets (free films) is central to diverse industrial and natural phenomena, e.g. foam stability. Rupture of Newtonian films is analyzed under the competing influences of inertial, viscous, van der Waals, and capillary forces by solving numerically a system of spatially one-dimensional evolution equations for film thickness and lateral velocity. As the dynamics close to the rupture singularity is self-similar, the dynamics is also analyzed by solving a set of ordinary differential equations in similarity space. For sheets with negligible inertia, the dominant balance of forces involves solely viscous and van der Waals forces. By contrast, for sheets of inviscid fluids, the dominant balance is between inertial, capillary, and van der Waals forces. For real fluids, the afore-mentioned viscous and inertial regimes are demonstrated to be transitory and hence can only describe the initial thinning of highly viscous and slightly viscous sheets. Moreover, regardless of the fluid's viscosity, it is shown that for sheets that initially thin in either of these two regimes, their dynamics transition to a final inertial-viscous regime in which all forces except capillary force remains important, in accordance with Vaynblat, Lister, and Witelski (2001).

  20. Manifold angles, the concept of self-similarity, and angle-enhanced bifurcation diagrams.

    PubMed

    Beims, Marcus W; Gallas, Jason A C

    2016-01-06

    Chaos and regularity are routinely discriminated by using Lyapunov exponents distilled from the norm of orthogonalized Lyapunov vectors, propagated during the temporal evolution of the dynamics. Such exponents are mean-field-like averages that, for each degree of freedom, squeeze the whole temporal evolution complexity into just a single number. However, Lyapunov vectors also contain a step-by-step record of what exactly happens with the angles between stable and unstable manifolds during the whole evolution, a big-data information permanently erased by repeated orthogonalizations. Here, we study changes of angles between invariant subspaces as observed during temporal evolution of Hénon's system. Such angles are calculated numerically and analytically and used to characterize self-similarity of a chaotic attractor. In addition, we show how standard tools of dynamical systems may be angle-enhanced by dressing them with informations not difficult to extract. Such angle-enhanced tools reveal unexpected and practical facts that are described in detail. For instance, we present a video showing an angle-enhanced bifurcation diagram that exposes from several perspectives the complex geometrical features underlying the attractors. We believe such findings to be generic for extended classes of systems.

  1. Universal self-similar dynamics of relativistic and nonrelativistic field theories near nonthermal fixed points

    NASA Astrophysics Data System (ADS)

    Piñeiro Orioli, Asier; Boguslavski, Kirill; Berges, Jürgen

    2015-07-01

    We investigate universal behavior of isolated many-body systems far from equilibrium, which is relevant for a wide range of applications from ultracold quantum gases to high-energy particle physics. The universality is based on the existence of nonthermal fixed points, which represent nonequilibrium attractor solutions with self-similar scaling behavior. The corresponding dynamic universality classes turn out to be remarkably large, encompassing both relativistic as well as nonrelativistic quantum and classical systems. For the examples of nonrelativistic (Gross-Pitaevskii) and relativistic scalar field theory with quartic self-interactions, we demonstrate that infrared scaling exponents as well as scaling functions agree. We perform two independent nonperturbative calculations, first by using classical-statistical lattice simulation techniques and second by applying a vertex-resummed kinetic theory. The latter extends kinetic descriptions to the nonperturbative regime of overoccupied modes. Our results open new perspectives to learn from experiments with cold atoms aspects about the dynamics during the early stages of our universe.

  2. Using Self-Similarity to Simulate Meniscus Evolution Around TMV Due to Surface Diffusion

    NASA Astrophysics Data System (ADS)

    Potter, Richard; Zhang, Yue; Fakhraai, Zahra

    It has been hypothesized that enhanced surface diffusion allows the formation of stable molecular glasses during physical vapor deposition. The improved properties of these glasses, such as increased density and kinetic stability can help improve material properties in pioneering fields of technology such as organic electronics and pharmaceutical drug delivery. While surface diffusion has been measured previously on the surfaces of organic glasses, direct measurements on the surface of vapor-deposited stable glasses has proven more challenging. This research focuses on a straightforward method for measuring the surface diffusion coefficients of molecular glasses through the use of tobacco mosaic virus (TMV) nanorods as probe particles. In conjunction, mathematical models based on the thin film equation were used to simulate fast meniscus formation around the nanorods on the glassy surface. The evolution of the meniscus is self-similar, which allows quick quantification of the diffusion coefficient, by solving the time evolution for a single experiment. Experimental data were compared and fit to these simulations to derive a quantity for the surface diffusion coefficient, Ds. Nsf-CAREER DMR-1350044.

  3. Analyzing Self-Similar and Fractal Properties of the C. elegans Neural Network

    PubMed Central

    Reese, Tyler M.; Brzoska, Antoni; Yott, Dylan T.; Kelleher, Daniel J.

    2012-01-01

    The brain is one of the most studied and highly complex systems in the biological world. While much research has concentrated on studying the brain directly, our focus is the structure of the brain itself: at its core an interconnected network of nodes (neurons). A better understanding of the structural connectivity of the brain should elucidate some of its functional properties. In this paper we analyze the connectome of the nematode Caenorhabditis elegans. Consisting of only 302 neurons, it is one of the better-understood neural networks. Using a Laplacian Matrix of the 279-neuron “giant component” of the network, we use an eigenvalue counting function to look for fractal-like self similarity. This matrix representation is also used to plot visualizations of the neural network in eigenfunction coordinates. Small-world properties of the system are examined, including average path length and clustering coefficient. We test for localization of eigenfunctions, using graph energy and spacial variance on these functions. To better understand results, all calculations are also performed on random networks, branching trees, and known fractals, as well as fractals which have been “rewired” to have small-world properties. We propose algorithms for generating Laplacian matrices of each of these graphs. PMID:23071485

  4. Self-similar random process and chaotic behavior in serrated flow of high entropy alloys

    SciTech Connect

    Chen, Shuying; Yu, Liping; Ren, Jingli; Xie, Xie; Li, Xueping; Xu, Ying; Zhao, Guangfeng; Li, Peizhen; Yang, Fuqian; Ren, Yang; Liaw, Peter K.

    2016-07-20

    Here, the statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, and there is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk.

  5. Self-Similar Random Process and Chaotic Behavior In Serrated Flow of High Entropy Alloys

    PubMed Central

    Chen, Shuying; Yu, Liping; Ren, Jingli; Xie, Xie; Li, Xueping; Xu, Ying; Zhao, Guangfeng; Li, Peizhen; Yang, Fuqian; Ren, Yang; Liaw, Peter K.

    2016-01-01

    The statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, and there is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk. PMID:27435922

  6. Self-duality and self-similarity of little string orbifolds

    NASA Astrophysics Data System (ADS)

    Hohenegger, Stefan; Iqbal, Amer; Rey, Soo-Jong

    2016-08-01

    We study a class of N =(1 ,0 ) little string theories obtained from orbifolds of M-brane configurations. These are realized in two different ways that are dual to each other: either as M parallel M5-branes probing a transverse AN -1 singularity or N M5-branes probing an AM -1 singularity. These backgrounds can further be dualized into toric, noncompact Calabi-Yau threefolds XN ,M which have double elliptic fibrations and thus give a natural geometric description of T-duality of the little string theories. The little string partition functions are captured by the topological string partition function of XN ,M . We analyze in detail the free energies ΣN ,M associated with the latter in a special region in the Kähler moduli space of XN ,M and discover a remarkable property: in the Nekrasov-Shatashvili limit, ΣN ,M is identical to N M times Σ1 ,1. This entails that the Bogomol'nyi-Prasad-Sommerfield (BPS) degeneracies for any (N ,M ) can uniquely be reconstructed from the (N ,M )=(1 ,1 ) configuration, a property we refer to as self-similarity. Moreover, as Σ1 ,1 is known to display a number of recursive structures, BPS degeneracies of little string configurations for arbitrary (N ,M ) as well acquire additional symmetries. These symmetries suggest that in this special region the two little string theories described above are self-dual under T-duality.

  7. Manifold angles, the concept of self-similarity, and angle-enhanced bifurcation diagrams

    NASA Astrophysics Data System (ADS)

    Beims, Marcus W.; Gallas, Jason A. C.

    2016-01-01

    Chaos and regularity are routinely discriminated by using Lyapunov exponents distilled from the norm of orthogonalized Lyapunov vectors, propagated during the temporal evolution of the dynamics. Such exponents are mean-field-like averages that, for each degree of freedom, squeeze the whole temporal evolution complexity into just a single number. However, Lyapunov vectors also contain a step-by-step record of what exactly happens with the angles between stable and unstable manifolds during the whole evolution, a big-data information permanently erased by repeated orthogonalizations. Here, we study changes of angles between invariant subspaces as observed during temporal evolution of Hénon’s system. Such angles are calculated numerically and analytically and used to characterize self-similarity of a chaotic attractor. In addition, we show how standard tools of dynamical systems may be angle-enhanced by dressing them with informations not difficult to extract. Such angle-enhanced tools reveal unexpected and practical facts that are described in detail. For instance, we present a video showing an angle-enhanced bifurcation diagram that exposes from several perspectives the complex geometrical features underlying the attractors. We believe such findings to be generic for extended classes of systems.

  8. Self-similar characteristics of single nucleotide polymorphisms in the rice genome

    NASA Astrophysics Data System (ADS)

    Lee, Chang-Yong

    2016-11-01

    With single nucleotide polymorphism (SNP) data from the 3,000 rice genome project, we investigate the mutational characteristics of the rice genome from the perspective of statistical physics. From the frequency distributions of the space between adjacent SNPs, we present evidence that SNPs are not spaced randomly, but clustered across the genome. The clustering property is related to a long-range correlation in SNP locations, suggesting that a mutation occurring in a locus may affect other mutations far away along the sequence in a chromosome. In addition, the reliability of the existence of the long-range correlation is supported by the agreement between the results of two independent analysis methods. The highly-skewed and long-tailed distribution of SNP spaces is further characterized by a multi-fractal, showing that SNP spaces possess a rich structure of a statistical self-similarity. These results can be used for an optimal design of a microarray assay and a primer, as well as for genotyping quality control.

  9. Self-similarity analysis of eubacteria genome based on weighted graph.

    PubMed

    Qi, Zhao-Hui; Li, Ling; Zhang, Zhi-Meng; Qi, Xiao-Qin

    2011-07-07

    We introduce a weighted graph model to investigate the self-similarity characteristics of eubacteria genomes. The regular treating in similarity comparison about genome is to discover the evolution distance among different genomes. Few people focus their attention on the overall statistical characteristics of each gene compared with other genes in the same genome. In our model, each genome is attributed to a weighted graph, whose topology describes the similarity relationship among genes in the same genome. Based on the related weighted graph theory, we extract some quantified statistical variables from the topology, and give the distribution of some variables derived from the largest social structure in the topology. The 23 eubacteria recently studied by Sorimachi and Okayasu are markedly classified into two different groups by their double logarithmic point-plots describing the similarity relationship among genes of the largest social structure in genome. The results show that the proposed model may provide us with some new sights to understand the structures and evolution patterns determined from the complete genomes.

  10. Self-similar slip instability on interfaces with rate- and state-dependent friction

    NASA Astrophysics Data System (ADS)

    Viesca, Robert C.

    2016-08-01

    We examine the development of a frictional instability, with diverging sliding rate, at the interface of elastic bodies in contact. Evolution of friction is determined by a slip rate and state dependence. Following Viesca (2016 Phys. Rev. E 93, 060202(R). (doi:10.1103/PhysRevE.93.060202)), we show through an appropriate change of variable, the existence of blow-up solutions that are fixed points of a dynamical system. The solutions show self-similarity of the simple variety: separable dependence of time and space. For an interface with uniform frictional properties, there is a single-problem parameter. We examine the linear stability of these fixed points, as this problem parameter is varied. Specifically, we consider two archetypical elastic settings of the slip surface, in which interactions between points on the surface are either local or non-local. We show that, independent of the nature of elastic interactions, the fixed-points lose stability in the same matter as the parameter is increased towards a limit value: an apparently infinite sequence of Hopf bifurcations. However, for any value of the parameter, the nonlinear development of the instability is attraction, if not asymptotic convergence, towards these fixed points, owing to the existence of stable eigenmodes. For comparison, we perform numerical solutions of the original evolution equations and find precise agreement with the results of the analysis.

  11. Dark energy in six nearby galaxy flows: Synthetic phase diagrams and self-similarity

    NASA Astrophysics Data System (ADS)

    Chernin, A. D.; Teerikorpi, P.; Dolgachev, V. P.; Kanter, A. A.; Domozhilova, L. M.; Valtonen, M. J.; Byrd, G. G.

    2012-09-01

    Outward flows of galaxies are observed around groups of galaxies on spatial scales of about 1 Mpc, and around galaxy clusters on scales of 10 Mpc. Using recent data from the Hubble Space Telescope (HST), we have constructed two synthetic velocity-distance phase diagrams: one for four flows on galaxy-group scales and the other for two flows on cluster scales. It has been shown that, in both cases, the antigravity produced by the cosmic dark-energy background is stronger than the gravity produced by the matter in the outflow volume. The antigravity accelerates the flows and introduces a phase attractor that is common to all scales, corresponding to a linear velocity-distance relation (the local Hubble law). As a result, the bundle of outflow trajectories mostly follow the trajectory of the attractor. A comparison of the two diagrams reveals the universal self-similar nature of the outflows: their gross phase structure in dimensionless variables is essentially independent of their physical spatial scales, which differ by approximately a factor of 10 in the two diagrams.

  12. Non-uniqueness of solutions in asymptotically self-similar shock reflections

    NASA Astrophysics Data System (ADS)

    Lau-Chapdelaine, Sebastien Sm.; Radulescu, Matei I.

    2013-11-01

    The present study numerically addresses the self-similarity of an unsteady shock reflection on an inclined wedge. The wedge-tip conditions are modified, allowing for a finite radius of curvature, and the following shock reflection configuration is observed at large distances from the tip. It is found that the type of shock reflection observed far from the corner, namely regular or Mach reflection, depends intimately on the wedge tip geometry, as the flow ``remembers'' how it was started. Substantial differences from a sharp-tipped wedge (without curvature) were found. For example, a shock with incident Mach number M = 6 . 6 and an isentropic exponent γ = 1 . 2 reflecting over wedge with a sharp tip will result in a Mach reflection when a wedge angle of 44° is used, while a 45° wedge will result in a regular reflection. This transition angle increases to between 57° and 58° when a wedge with a concave, curved tip is introduced. A vanishing length scale is introduced with the curved tip in a way which is similar to those of viscous and relaxation effects. While the length scale only dominates the solution at early times, this study shows that its effects play a dominant role in determining the asymptotic pseudo-steady shock reflection configuration.

  13. Self-similar decay of high Reynolds number Taylor-Couette turbulence

    NASA Astrophysics Data System (ADS)

    Verschoof, Ruben A.; Huisman, Sander G.; van der Veen, Roeland C. A.; Sun, Chao; Lohse, Detlef

    2016-10-01

    We study the decay of high-Reynolds-number Taylor-Couette turbulence, i.e., the turbulent flow between two coaxial rotating cylinders. To do so, the rotation of the inner cylinder (Re i=2 ×106 , the outer cylinder is at rest) is stopped within 12 s, thus fully removing the energy input to the system. Using a combination of laser Doppler anemometry and particle image velocimetry measurements, six decay decades of the kinetic energy could be captured. First, in the absence of cylinder rotation, the flow-velocity during the decay does not develop any height dependence in contrast to the well-known Taylor vortex state. Second, the radial profile of the azimuthal velocity is found to be self-similar. Nonetheless, the decay of this wall-bounded inhomogeneous turbulent flow does not follow a strict power law as for decaying turbulent homogeneous isotropic flows, but it is faster, due to the strong viscous drag applied by the bounding walls. We theoretically describe the decay in a quantitative way by taking the effects of additional friction at the walls into account.

  14. Self-similar distributions of fluid velocity and stress heterogeneity in a dissolving porous limestone

    NASA Astrophysics Data System (ADS)

    Linga, Gaute; Mathiesen, Joachim; Renard, François

    2017-03-01

    In a porous rock, the spatial distribution of the pore space induces a strong heterogeneity in fluid flow rates and in the stress distribution in the rock mass. If the rock microstructure evolves through time, for example, by dissolution, fluid flow and stress will evolve accordingly. Here we consider a core sample of porous limestone that has undergone several steps of dissolution. Based on 3-D X-ray tomography scans, we calculate numerically the coupled system of fluid flow in the pore space and stress in the solid. We determine how the flow field affects the stress distribution both at the pore wall surface and in the bulk of the solid matrix. We show that during dissolution, the heterogeneous stress evolves in a self-similar manner as the porosity is increased. Conversely, the fluid velocity shows a stretched exponential distribution. The scalings of these common master distributions offer a unified description of the porosity evolution, pore flow, and the heterogeneity in stress for a rock with evolving microstructure. Moreover, the probability density functions of stress invariants (mechanical pressure or von Mises stress) display heavy tails toward large stresses. If these results can be extended to other kinds of rocks, they provide an additional explanation of the sensitivity to failure of porous rocks under slight changes of stress.

  15. Self-similar evolution of stress distributions in a porous limestone under dissolution

    NASA Astrophysics Data System (ADS)

    Linga, Gaute; Mathiesen, Joachim; Renard, Francois

    2017-04-01

    The heterogeneous spatial distribution of pore space within a porous rock leads to a strong heterogeneity in fluid flow rates and in the stress distribution in the rock mass. In this work, we consider a limestone sample that has undergone several steps of dissolution, which at each step has been scanned by 3D X-ray tomography. We calculate numerically at each step the coupled system of steady-state fluid flow in the pore space and elasticity in the solid. We quantify by using probability density functions (PDFs) the effect of the fluid flow field upon the stress distribution both at the pore wall surface and in the solid rock matrix. We find that, during dissolution, the distributions of stress evolve in a self-similar manner as the porosity is increased. Moreover, the PDFs display heavy tails towards large stresses. The common master curves offer a unified description of the stress for a rock with evolving microstructure, and if the results can be generalized to other porous media, they may provide an additional explanation of the sensitivity to failure of porous rocks under small changes of stress.

  16. Self-similar inverse cascade of magnetic helicity driven by the chiral anomaly

    SciTech Connect

    Hirono, Yuji; Kharzeev, Dmitri E.; Yin, Yi

    2015-12-28

    For systems with charged chiral fermions, the imbalance of chirality in the presence of magnetic field generates an electric current—this is the chiral magnetic effect (CME). We study the dynamical real-time evolution of electromagnetic fields coupled by the anomaly to the chiral charge density and the CME current by solving the Maxwell-Chern-Simons equations. We find that the CME induces the inverse cascade of magnetic helicity toward the large distances, and that at late times this cascade becomes self-similar, with universal exponents. We also find that in terms of gauge field topology the inverse cascade represents the transition from linked electric and magnetic fields (Hopfions) to the knotted configuration of magnetic field (Chandrasekhar-Kendall states). The magnetic reconnections are accompanied by the pulses of the CME current directed along the magnetic field lines. In conclusion, we devise an experimental signature of these phenomena in heavy ion collisions, and speculate about implications for condensed matter systems.

  17. 3D simulations of wet foam coarsening evidence a self similar growth regime.

    PubMed

    Thomas, Gilberto L; Belmonte, Julio M; Graner, François; Glazier, James A; de Almeida, Rita M C

    2015-05-20

    In wet liquid foams, slow diffusion of gas through bubble walls changes bubble pressure, volume and wall curvature. Large bubbles grow at the expenses of smaller ones. The smaller the bubble, the faster it shrinks. As the number of bubbles in a given volume decreases in time, the average bubble size increases: i.e. the foam coarsens. During coarsening, bubbles also move relative to each other, changing bubble topology and shape, while liquid moves within the regions separating the bubbles. Analyzing the combined effects of these mechanisms requires examining a volume with enough bubbles to provide appropriate statistics throughout coarsening. Using a Cellular Potts model, we simulate these mechanisms during the evolution of three-dimensional foams with wetnesses of ϕ = 0.00, 0.05 and 0.20. We represent the liquid phase as an ensemble of many small fluid particles, which allows us to monitor liquid flow in the region between bubbles. The simulations begin with 2 × 10(5) bubbles for ϕ = 0.00 and 1.25 × 10(5) bubbles for ϕ = 0.05 and 0.20, allowing us to track the distribution functions for bubble size, topology and growth rate over two and a half decades of volume change. All simulations eventually reach a self-similar growth regime, with the distribution functions time independent and the number of bubbles decreasing with time as a power law whose exponent depends on the wetness.

  18. Self similarity of two point correlations in wall bounded turbulent flows

    NASA Technical Reports Server (NTRS)

    Hunt, J. C. R.; Moin, P.; Moser, R. D.; Spalart, P. R.

    1987-01-01

    The structure of turbulence at a height y from a wall is affected by the local mean shear at y, by the direct effect of the wall on the eddies, and by the action of other eddies close to or far from the wall. Some researchers believe that a single one of these mechanisms is dominant, while others believe that these effects have to be considered together. It is important to understand the relative importance of these effects in order to develop closure models, for example for the dissipation or for the Reynolds stress equation, and to understand the eddy structure of cross correlation functions and other measures. The specific objective was to examine the two point correlation, R sub vv, of the normal velocity component v near the wall in a turbulent channel flow and in a turbulent boundary layer. The preliminary results show that even in the inhomogeneous turbulent boundary layer, the two-point correlation function may have self similar forms. The results also show that the effects of shear and of blocking are equally important in the form of correlation functions for spacing normal to the wall. But for spanwise spacing, it was found that the eddy structure is quire different in these near flows. So any theory for turbulent structure must take both these effects into account.

  19. Self-similar distribution of oil spills in European coastal waters

    NASA Astrophysics Data System (ADS)

    Redondo, Jose M; Platonov, Alexei K

    2009-01-01

    Marine pollution has been highlighted thanks to the advances in detection techniques as well as increasing coverage of catastrophes (e.g. the oil tankers Amoco Cadiz, Exxon Valdez, Erika, and Prestige) and of smaller oil spills from ships. The new satellite based sensors SAR and ASAR and new methods of oil spill detection and analysis coupled with self-similar statistical techniques allow surveys of environmental pollution monitoring large areas of the ocean. We present a statistical analysis of more than 700 SAR images obtained during 1996-2000, also comparing the detected small pollution events with the historical databases of great marine accidents during 1966-2004 in European coastal waters. We show that the statistical distribution of the number of oil spills as a function of their size corresponds to Zipf's law, and that the common small spills are comparable to the large accidents due to the high frequency of the smaller pollution events. Marine pollution from tankers and ships, which has been detected as oil spills between 0.01 and 100 km2, follows the marine transit routes. Multi-fractal methods are used to distinguish between natural slicks and spills, in order to estimate the oil spill index in European coastal waters, and in particular, the north-western Mediterranean Sea, which, due to the influence of local winds, shows optimal conditions for oil spill detection.

  20. Lévy Flights and Self-Similar Exploratory Behaviour of Termite Workers: Beyond Model Fitting

    PubMed Central

    Miramontes, Octavio; DeSouza, Og; Paiva, Leticia Ribeiro; Marins, Alessandra; Orozco, Sirio

    2014-01-01

    Animal movements have been related to optimal foraging strategies where self-similar trajectories are central. Most of the experimental studies done so far have focused mainly on fitting statistical models to data in order to test for movement patterns described by power-laws. Here we show by analyzing over half a million movement displacements that isolated termite workers actually exhibit a range of very interesting dynamical properties –including Lévy flights– in their exploratory behaviour. Going beyond the current trend of statistical model fitting alone, our study analyses anomalous diffusion and structure functions to estimate values of the scaling exponents describing displacement statistics. We evince the fractal nature of the movement patterns and show how the scaling exponents describing termite space exploration intriguingly comply with mathematical relations found in the physics of transport phenomena. By doing this, we rescue a rich variety of physical and biological phenomenology that can be potentially important and meaningful for the study of complex animal behavior and, in particular, for the study of how patterns of exploratory behaviour of individual social insects may impact not only their feeding demands but also nestmate encounter patterns and, hence, their dynamics at the social scale. PMID:25353958

  1. Lévy flights and self-similar exploratory behaviour of termite workers: beyond model fitting.

    PubMed

    Miramontes, Octavio; DeSouza, Og; Paiva, Leticia Ribeiro; Marins, Alessandra; Orozco, Sirio

    2014-01-01

    Animal movements have been related to optimal foraging strategies where self-similar trajectories are central. Most of the experimental studies done so far have focused mainly on fitting statistical models to data in order to test for movement patterns described by power-laws. Here we show by analyzing over half a million movement displacements that isolated termite workers actually exhibit a range of very interesting dynamical properties--including Lévy flights--in their exploratory behaviour. Going beyond the current trend of statistical model fitting alone, our study analyses anomalous diffusion and structure functions to estimate values of the scaling exponents describing displacement statistics. We evince the fractal nature of the movement patterns and show how the scaling exponents describing termite space exploration intriguingly comply with mathematical relations found in the physics of transport phenomena. By doing this, we rescue a rich variety of physical and biological phenomenology that can be potentially important and meaningful for the study of complex animal behavior and, in particular, for the study of how patterns of exploratory behaviour of individual social insects may impact not only their feeding demands but also nestmate encounter patterns and, hence, their dynamics at the social scale.

  2. Båth's law and the self-similarity of earthquakes

    NASA Astrophysics Data System (ADS)

    Console, Rodolfo; Lombardi, Anna Maria; Murru, Maura; Rhoades, David

    2003-02-01

    We revisit the issue of the so-called Båth's law concerning the difference D1 between the magnitude of the main shock and the second largest shock in the same sequence. A mathematical formulation of the problem is developed with the only assumption being that all the events belong to the same self-similar set of earthquakes following the Gutenberg-Richter magnitude distribution. This model shows a substantial dependence of D1 on the magnitude thresholds chosen for the main shocks and the aftershocks and in this way partly explains the large D1 values reported in the past. Analysis of the New Zealand and Preliminary Determination of Epicenters (PDE) catalogs of shallow earthquakes demonstrates a rough agreement between the average D1 values predicted by the theoretical model and those observed. Limiting our attention to the average D1 values, Båth's law does not seem to strongly contradict the Gutenberg-Richter law. Nevertheless, a detailed analysis of the D1 distribution shows that the Gutenberg-Richter hypothesis with a constant b-value does not fully explain the experimental observations. The theoretical distribution has a larger proportion of low D1 values and a smaller proportion of high D1 values than the experimental observations. Thus, Båth's law and the Gutenberg-Richter law cannot be completely reconciled, although based on this analysis the mismatch is not as great as has sometimes been supposed.

  3. First and second type self-similar solutions of implosions and explosions containing ultrarelativistic shocks

    NASA Astrophysics Data System (ADS)

    Sari, Re'em

    2006-02-01

    We derive self-similar solutions for ultrarelativistic shock waves propagating into cold material of power law density profile in radius ρ~r-k. We treat both implosions and explosions in three geometries: planar, cylindrical, and spherical. For spherical explosions these are the first type solutions of Blandford and McKee for k<4 they are the second type solutions found by Best and Sari for k>5-3/4. In addition we find new, hollow (with evacuated interior), first type solutions that may be applicable for 4

  4. Self-Similar Random Process and Chaotic Behavior In Serrated Flow of High Entropy Alloys.

    PubMed

    Chen, Shuying; Yu, Liping; Ren, Jingli; Xie, Xie; Li, Xueping; Xu, Ying; Zhao, Guangfeng; Li, Peizhen; Yang, Fuqian; Ren, Yang; Liaw, Peter K

    2016-07-20

    The statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, and there is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk.

  5. Self-Similar Random Process and Chaotic Behavior In Serrated Flow of High Entropy Alloys

    NASA Astrophysics Data System (ADS)

    Chen, Shuying; Yu, Liping; Ren, Jingli; Xie, Xie; Li, Xueping; Xu, Ying; Zhao, Guangfeng; Li, Peizhen; Yang, Fuqian; Ren, Yang; Liaw, Peter K.

    2016-07-01

    The statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, and there is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk.

  6. Emergence of the self-similar property in gene expression dynamics

    NASA Astrophysics Data System (ADS)

    Ochiai, T.; Nacher, J. C.; Akutsu, T.

    2007-08-01

    Many theoretical models have recently been proposed to understand the structure of cellular systems composed of various types of elements (e.g., proteins, metabolites and genes) and their interactions. However, the cell is a highly dynamic system with thousands of functional elements fluctuating across temporal states. Therefore, structural analysis alone is not sufficient to reproduce the cell's observed behavior. In this article, we analyze the gene expression dynamics (i.e., how the amount of mRNA molecules in cell fluctuate in time) by using a new constructive approach, which reveals a symmetry embedded in gene expression fluctuations and characterizes the dynamical equation of gene expression (i.e., a specific stochastic differential equation). First, by using experimental data of human and yeast gene expression time series, we found a symmetry in short-time transition probability from time t to time t+1. We call it self-similarity symmetry (i.e., the gene expression short-time fluctuations contain a repeating pattern of smaller and smaller parts that are like the whole, but different in size). Secondly, we reconstruct the global behavior of the observed distribution of gene expression (i.e., scaling-law) and the local behavior of the power-law tail of this distribution. This approach may represent a step forward toward an integrated image of the basic elements of the whole cell.

  7. Distinctive Order Based Self-Similarity descriptor for multi-sensor remote sensing image matching

    NASA Astrophysics Data System (ADS)

    Sedaghat, Amin; Ebadi, Hamid

    2015-10-01

    Robust, well-distributed and accurate feature matching in multi-sensor remote sensing image is a difficult task duo to significant geometric and illumination differences. In this paper, a robust and effective image matching approach is presented for multi-sensor remote sensing images. The proposed approach consists of three main steps. In the first step, UR-SIFT (Uniform robust scale invariant feature transform) algorithm is applied for uniform and dense local feature extraction. In the second step, a novel descriptor namely Distinctive Order Based Self Similarity descriptor, DOBSS descriptor, is computed for each extracted feature. Finally, a cross matching process followed by a consistency check in the projective transformation model is performed for feature correspondence and mismatch elimination. The proposed method was successfully applied for matching various multi-sensor satellite images as: ETM+, SPOT 4, SPOT 5, ASTER, IRS, SPOT 6, QuickBird, GeoEye and Worldview sensors, and the results demonstrate its robustness and capability compared to common image matching techniques such as SIFT, PIIFD, GLOH, LIOP and LSS.

  8. Self-similarity and universality of void density profiles in simulation and SDSS data

    NASA Astrophysics Data System (ADS)

    Nadathur, S.; Hotchkiss, S.; Diego, J. M.; Iliev, I. T.; Gottlöber, S.; Watson, W. A.; Yepes, G.

    2015-06-01

    The stacked density profile of cosmic voids in the galaxy distribution provides an important tool for the use of voids for precision cosmology. We study the density profiles of voids identified using the ZOBOV watershed transform algorithm in realistic mock luminous red galaxy (LRG) catalogues from the Jubilee simulation, as well as in void catalogues constructed from the SDSS LRG and Main Galaxy samples. We compare different methods for reconstructing density profiles scaled by the void radius and show that the most commonly used method based on counts in shells and simple averaging is statistically flawed as it underestimates the density in void interiors. We provide two alternative methods that do not suffer from this effect; one based on Voronoi tessellations is also easily able to account from artefacts due to finite survey boundaries and so is more suitable when comparing simulation data to observation. Using this method, we show that the most robust voids in simulation are exactly self-similar, meaning that their average rescaled profile does not depend on the void size. Within the range of our simulation, we also find no redshift dependence of the mean profile. Comparison of the profiles obtained from simulated and real voids shows an excellent match. The mean profiles of real voids also show a universal behaviour over a wide range of galaxy luminosities, number densities and redshifts. This points to a fundamental property of the voids found by the watershed algorithm, which can be exploited in future studies of voids.

  9. Self-similar slip instability on interfaces with rate- and state-dependent friction

    PubMed Central

    2016-01-01

    We examine the development of a frictional instability, with diverging sliding rate, at the interface of elastic bodies in contact. Evolution of friction is determined by a slip rate and state dependence. Following Viesca (2016 Phys. Rev. E 93, 060202(R). (doi:10.1103/PhysRevE.93.060202)), we show through an appropriate change of variable, the existence of blow-up solutions that are fixed points of a dynamical system. The solutions show self-similarity of the simple variety: separable dependence of time and space. For an interface with uniform frictional properties, there is a single-problem parameter. We examine the linear stability of these fixed points, as this problem parameter is varied. Specifically, we consider two archetypical elastic settings of the slip surface, in which interactions between points on the surface are either local or non-local. We show that, independent of the nature of elastic interactions, the fixed-points lose stability in the same matter as the parameter is increased towards a limit value: an apparently infinite sequence of Hopf bifurcations. However, for any value of the parameter, the nonlinear development of the instability is attraction, if not asymptotic convergence, towards these fixed points, owing to the existence of stable eigenmodes. For comparison, we perform numerical solutions of the original evolution equations and find precise agreement with the results of the analysis. PMID:27616923

  10. Self-similar processes and flicker noise from a fluctuating nanopore in a lipid membrane

    NASA Astrophysics Data System (ADS)

    Kotulska, Malgorzata; Koronkiewicz, Stanislawa; Kalinowski, Slawomir

    2004-03-01

    Stochastic properties of a fluctuating nanopore generated and sustained by an electric field in a lipid bilayer membrane are studied. It is shown that the process of voltage fluctuations, in the current clamp experiment, is a stochastic fractal with long memory, which is the main reason for its nonstationarity. The aging process contributes to the nonstationarity if molecular interactions in the membrane are weak. An attempt to classify the process reveals a non-Gaussian distribution with long tails, which contradicts the hypothesis of fractional Brownian motion, showing that stable motion may be possible. The self-similarity index, estimated by three different methods, depends on current value and membrane sensitivity to electric field in a well defined and explicable manner. The stochastic analysis provided for calculated conductance of nanopore revealed the process close to 1/f noise, the result observed only for the pores not exceeding 1 nm in diameter, induced in membranes with strong molecular interactions. Our results show that such a pore is the simplest biological system needed for flicker noise to occur, and the complexity of highly regulated protein channel is not a necessary factor. A case of noise 1/f2, observed for a pore with impeded dynamics, suggests a process without memory in such a situation. A physical interpretation is presented for some of the results.

  11. Viscoelastic properties of the nematode Caenorhabditis elegans, a self-similar, shear-thinning worm.

    PubMed

    Backholm, Matilda; Ryu, William S; Dalnoki-Veress, Kari

    2013-03-19

    Undulatory motion is common to many creatures across many scales, from sperm to snakes. These organisms must push off against their external environment, such as a viscous medium, grains of sand, or a high-friction surface; additionally they must work to bend their own body. A full understanding of undulatory motion, and locomotion in general, requires the characterization of the material properties of the animal itself. The material properties of the model organism Caenorhabditis elegans were studied with a micromechanical experiment used to carry out a three-point bending measurement of the worm. Worms at various developmental stages (including dauer) were measured and different positions along the worm were probed. From these experiments we calculated the viscoelastic properties of the worm, including the effective spring constant and damping coefficient of bending. C. elegans moves by propagating sinusoidal waves along its body. Whereas previous viscoelastic approaches to describe the undulatory motion have used a Kelvin-Voigt model, where the elastic and viscous components are connected in parallel, our measurements show that the Maxwell model, where the elastic and viscous components are in series, is more appropriate. The viscous component of the worm was shown to be consistent with a non-Newtonian, shear-thinning fluid. We find that as the worm matures it is well described as a self-similar elastic object with a shear-thinning damping term and a stiffness that becomes smaller as one approaches the tail.

  12. Viscoelastic properties of the nematode Caenorhabditis elegans, a self-similar, shear-thinning worm

    PubMed Central

    Backholm, Matilda; Ryu, William S.; Dalnoki-Veress, Kari

    2013-01-01

    Undulatory motion is common to many creatures across many scales, from sperm to snakes. These organisms must push off against their external environment, such as a viscous medium, grains of sand, or a high-friction surface; additionally they must work to bend their own body. A full understanding of undulatory motion, and locomotion in general, requires the characterization of the material properties of the animal itself. The material properties of the model organism Caenorhabditis elegans were studied with a micromechanical experiment used to carry out a three-point bending measurement of the worm. Worms at various developmental stages (including dauer) were measured and different positions along the worm were probed. From these experiments we calculated the viscoelastic properties of the worm, including the effective spring constant and damping coefficient of bending. C. elegans moves by propagating sinusoidal waves along its body. Whereas previous viscoelastic approaches to describe the undulatory motion have used a Kelvin–Voigt model, where the elastic and viscous components are connected in parallel, our measurements show that the Maxwell model, where the elastic and viscous components are in series, is more appropriate. The viscous component of the worm was shown to be consistent with a non-Newtonian, shear-thinning fluid. We find that as the worm matures it is well described as a self-similar elastic object with a shear-thinning damping term and a stiffness that becomes smaller as one approaches the tail. PMID:23460699

  13. A nonlinear self-similar solution to barotropic flow over rapidly varying topography

    NASA Astrophysics Data System (ADS)

    Ibanez, Ruy; Kuehl, Joseph

    2016-11-01

    Beginning from the Shallow Water Equations (SWE), a nonlinear self-similar analytic solution is derived for barotropic flow over rapidly varying topography. We study conditions relevant to the ocean slope where the flow is dominated by Earth's rotation and topography. Attention is paid to the northern Gulf of Mexico slope with application to pollutant dispersion and the Norwegian Coastal Current which sheds eddies into the Lofoten Basin that are believe to influence deep water formation. The solution is found to extend the topographic β-plume solution (Kuehl 2014, GRL) in two ways: 1) The solution is valid for intensifying jets. 2) The influence of nonlinear advection is included. The SWE are scaled to the case of a topographically controlled jet, then solved by introducing a similarity variable η = Cxy . The nonlinear solution, valid for topographies h =h0 - αxy3 , takes the form of the Lambert W Function for velocity. The linear solution, valid for topographies h =h0 - αxyγ , takes the form of the Error Function for transport. Kuehl's results considered the case - 1 <= γ < 1 which admits expanding jets, while the new result consider the case γ < - 1 which admits intensifying jets.

  14. Optimal design of self-similar serpentine interconnects embedded in stretchable electronics

    NASA Astrophysics Data System (ADS)

    Dong, Wentao; Zhu, Chen; Ye, Dong; Huang, YongAn

    2017-06-01

    The order-2 self-similar serpentine interconnects (SSIs) that joint rigid, functional devices can ensure mechanical integrity and stretchability in electronic systems under large deformations. However, the conventional design and analysis aim merely at the freestanding order-2 SSIs. The paper studies the design law and the stretchability of order-2 SSI that are bonded onto the polydimethylsiloxane (PDMS) substrate in stretchable electronics through analytical modeling, finite element method (FEM), and experiments. The scale law formula is built to predict the stretchability of the order-2 SSI with geometry parameters based on FEM simulation results. The out-of-plane and in-plane bending strains during lateral postbuckling processes are proportional to the thickness and width of the order-2 SSI, respectively. The stretchability of order-2 SSI decreases with the increasing ratio β of order-2 space L 2 to order-1 space L 1, and it would be approximate to the stretchability of order-1 serpentine interconnect when β > 32. The optimized order-2 SSI is demonstrated in stretchable electronics application with high stretchability.

  15. Self-similar nonequilibrium dynamics of a many-body system with power-law interactions

    NASA Astrophysics Data System (ADS)

    Gutiérrez, Ricardo; Garrahan, Juan P.; Lesanovsky, Igor

    2015-12-01

    The influence of power-law interactions on the dynamics of many-body systems far from equilibrium is much less explored than their effect on static and thermodynamic properties. To gain insight into this problem we introduce and analyze here an out-of-equilibrium deposition process in which the deposition rate of a given particle depends as a power law on the distance to previously deposited particles. This model draws its relevance from recent experimental progress in the domain of cold atomic gases, which are studied in a setting where atoms that are excited to high-lying Rydberg states interact through power-law potentials that translate into power-law excitation rates. The out-of-equilibrium dynamics of this system turns out to be surprisingly rich. It features a self-similar evolution which leads to a characteristic power-law time dependence of observables such as the particle concentration, and results in a scale invariance of the structure factor. Our findings show that in dissipative Rydberg gases out of equilibrium the characteristic distance among excitations—often referred to as the blockade radius—is not a static but rather a dynamic quantity.

  16. Modeling of locally self-similar processes using multifractional Brownian motion of Riemann-Liouville type.

    PubMed

    Muniandy, S V; Lim, S C

    2001-04-01

    Fractional Brownian motion (FBM) is widely used in the modeling of phenomena with power spectral density of power-law type. However, FBM has its limitation since it can only describe phenomena with monofractal structure or a uniform degree of irregularity characterized by the constant Holder exponent. For more realistic modeling, it is necessary to take into consideration the local variation of irregularity, with the Holder exponent allowed to vary with time (or space). One way to achieve such a generalization is to extend the standard FBM to multifractional Brownian motion (MBM) indexed by a Holder exponent that is a function of time. This paper proposes an alternative generalization to MBM based on the FBM defined by the Riemann-Liouville type of fractional integral. The local properties of the Riemann-Liouville MBM (RLMBM) are studied and they are found to be similar to that of the standard MBM. A numerical scheme to simulate the locally self-similar sample paths of the RLMBM for various types of time-varying Holder exponents is given. The local scaling exponents are estimated based on the local growth of the variance and the wavelet scalogram methods. Finally, an example of the possible applications of RLMBM in the modeling of multifractal time series is illustrated.

  17. Self-similar nonequilibrium dynamics of a many-body system with power-law interactions.

    PubMed

    Gutiérrez, Ricardo; Garrahan, Juan P; Lesanovsky, Igor

    2015-12-01

    The influence of power-law interactions on the dynamics of many-body systems far from equilibrium is much less explored than their effect on static and thermodynamic properties. To gain insight into this problem we introduce and analyze here an out-of-equilibrium deposition process in which the deposition rate of a given particle depends as a power law on the distance to previously deposited particles. This model draws its relevance from recent experimental progress in the domain of cold atomic gases, which are studied in a setting where atoms that are excited to high-lying Rydberg states interact through power-law potentials that translate into power-law excitation rates. The out-of-equilibrium dynamics of this system turns out to be surprisingly rich. It features a self-similar evolution which leads to a characteristic power-law time dependence of observables such as the particle concentration, and results in a scale invariance of the structure factor. Our findings show that in dissipative Rydberg gases out of equilibrium the characteristic distance among excitations-often referred to as the blockade radius-is not a static but rather a dynamic quantity.

  18. Self-similar inverse cascade of magnetic helicity driven by the chiral anomaly

    DOE PAGES

    Hirono, Yuji; Kharzeev, Dmitri E.; Yin, Yi

    2015-12-28

    For systems with charged chiral fermions, the imbalance of chirality in the presence of magnetic field generates an electric current—this is the chiral magnetic effect (CME). We study the dynamical real-time evolution of electromagnetic fields coupled by the anomaly to the chiral charge density and the CME current by solving the Maxwell-Chern-Simons equations. We find that the CME induces the inverse cascade of magnetic helicity toward the large distances, and that at late times this cascade becomes self-similar, with universal exponents. We also find that in terms of gauge field topology the inverse cascade represents the transition from linked electricmore » and magnetic fields (Hopfions) to the knotted configuration of magnetic field (Chandrasekhar-Kendall states). The magnetic reconnections are accompanied by the pulses of the CME current directed along the magnetic field lines. In conclusion, we devise an experimental signature of these phenomena in heavy ion collisions, and speculate about implications for condensed matter systems.« less

  19. Self-similar growth of an alluvial fan fed with bimodal sediment

    NASA Astrophysics Data System (ADS)

    Delorme, Pauline; Voller, Vaughan; Paola, Chris; Devauchelle, Olivier; Lajeunesse, Eric; Barrier, Laurie; Métivier, François

    2016-04-01

    At the outlet of mountain ranges, rivers flow onto flatter lowlands. The associated change of slope causes sediment deposition. As the river is free to move laterally, it builds conical sedimentary structures called alluvial fans. Their location at the interface between erosional and depositional areas makes them valuable sedimentary archives. To decipher these sedimentary records, we need to understand the dynamics of their growth. We carried out a series of experiments to investigate the growth of alluvial fans fed with mixed sediments. The density difference between silica and coal sediments mimics a bimodal grain-size distribution in nature. The sediment and water discharges are constant during an experiment. During the run, we track the evolution of the surface pattern by digital imaging. At the end of each run, we acquire the fan topography using a scanning laser. Finally, we cut a radial cross section to visualize the sedimentary deposit. We observe there is a distinct slope break at the transition that dominates the overall curvature of the fan surface. Based on mass conservation and observations, we propose that this alluvial fan grows in a self-similar way, thus causing the transition between silica and coal deposits to be a straight line. The shape of the experimental transition accords with this prediction.

  20. Self-similar random process and chaotic behavior in serrated flow of high entropy alloys

    DOE PAGES

    Chen, Shuying; Yu, Liping; Ren, Jingli; ...

    2016-07-20

    Here, the statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, and theremore » is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk.« less

  1. Spiral-driven accretion in protoplanetary discs. II. Self-similar solutions

    NASA Astrophysics Data System (ADS)

    Hennebelle, Patrick; Lesur, Geoffroy; Fromang, Sébastien

    2016-05-01

    Context. Accretion discs are ubiquitous in the Universe, and it is crucial to understand how angular momentum and mass are radially transported in these objects. Aims: Here, we study the role played by non-linear spiral patterns within hydrodynamical and non-self-gravitating accretion discs assuming that external disturbances such as infall onto the disc may trigger them. Methods: To do so, we computed self-similar solutions that describe discs in which a spiral wave propagates. These solutions present shocks and critical sonic points that were analyzed. Results: We calculated the wave structure for all allowed temperatures and for several spiral shocks. In particular, we inferred the angle of the spiral pattern, the stress it exerts on the disc, and the associated flux of mass and angular momentum as a function of temperature. We quantified the rate of angular momentum transport by means of the dimensionless α parameter. For the thickest disc we considered (corresponding to h/r values of about one-third), we found values of α as high as 0.1 that scaled with the temperature T such that α ∝ T3 / 2 ∝ (h/r)3. The spiral angle scales with the temperature as arctan(r/h). Conclusions: These solutions suggests that perturbations occurring at disc outer boundaries, such as perturbations due to infall motions, can propagate deep inside the disc and therefore should not be ignored, even when considering small radii.

  2. Self-similar evolution of self-gravitating viscous accretion discs

    NASA Astrophysics Data System (ADS)

    Illenseer, Tobias F.; Duschl, Wolfgang J.

    2015-06-01

    A new one-dimensional, dynamical model is proposed for geometrically thin, self-gravitating viscous accretion discs. The vertically integrated equations are simplified using the slow accretion limit and the monopole approximation with a time-dependent central point mass to account for self-gravity and accretion. It is shown that the system of partial differential equations can be reduced to a single non-linear advection diffusion equation which describes the time evolution of angular velocity. In order to solve the equation, three different turbulent viscosity prescriptions are considered. It is shown that for these parametrizations the differential equation allows for similarity transformations depending only on a single non-dimensional parameter. A detailed analysis of the similarity solutions reveals that this parameter is the initial power-law exponent of the angular velocity distribution at large radii. The radial dependence of the self-similar solutions is in most cases given by broken power laws. At small radii, the rotation law always becomes Keplerian with respect to the current central point mass. In the outer regions, the power-law exponent of the rotation law deviates from the Keplerian value and approaches asymptotically the value determined by the initial condition. It is shown that accretion discs with flatter rotation laws at large radii yield higher accretion rates. The methods are applied to self-gravitating accretion discs in active galactic nuclei. Fully self-gravitating discs are found to evolve faster than nearly Keplerian discs. The implications on supermassive black hole formation and Quasar evolution are discussed.

  3. Fractal atomic surfaces of self-similar quasiperiodic tilings of the plane

    NASA Astrophysics Data System (ADS)

    Godrèche, C.; Luck, J. M.; Janner, A.; Janssen, T.

    1993-09-01

    We consider in parallel three self-similar quasiperiodic tilings of the plane with eight-fold symmetry, made of two prototiles, the square and the 45-degree rhomb. They possess the same inflation rules up to a reordering of the tiles. We study the consequences of this reordering on the nature of the atomic surfaces, or acceptance domains, and on the Fourier spectra of the tilings. For two of the tilings the atomic surface has a fractal boundary. For one of them it is not a connected set. We argue that the situation described in this paper is generic. Nous considérons en parallèle trois pavages quasipériodiques auto-similaires du plan, de symétrie de rotation d'ordre huit, et constitués des deux mêmes tuiles : le carré et le losange à 45 degrés. Les trois pavages sont décrits par les mêmes règles d'inflation, à une permutation des tuiles près. Nous étudions l'influence de cette permutation sur les surfaces atomiques, ou domaines d'acceptance, et sur les spectres de Fourier des pavages. Le bord de la surface atomique de deux des pavages est fractal ; pour l'un d'entre eux ce bord n'est pas connexe. Les propriétés décrites sur cette famille d'exemples sont vraisemblablement génériques.

  4. Self-similar fragmentation regulated by magnetic fields in a region forming massive stars.

    PubMed

    Li, Hua-bai; Yuen, Ka Ho; Otto, Frank; Leung, Po Kin; Sridharan, T K; Zhang, Qizhou; Liu, Hauyu; Tang, Ya-Wen; Qiu, Keping

    2015-04-23

    Most molecular clouds are filamentary or elongated. For those forming low-mass stars (<8 solar masses), the competition between self-gravity and turbulent pressure along the dynamically dominant intercloud magnetic field (10 to 100 parsecs) shapes the clouds to be elongated either perpendicularly or parallel to the fields. A recent study also suggested that on the scales of 0.1 to 0.01 parsecs, such fields are dynamically important within cloud cores forming massive stars (>8 solar masses). But whether the core field morphologies are inherited from the intercloud medium or governed by cloud turbulence is unknown, as is the effect of magnetic fields on cloud fragmentation at scales of 10 to 0.1 parsecs. Here we report magnetic-field maps inferred from polarimetric observations of NGC 6334, a region forming massive stars, on the 100 to 0.01 parsec scale. NGC 6334 hosts young star-forming sites where fields are not severely affected by stellar feedback, and their directions do not change much over the entire scale range. This means that the fields are dynamically important. The ordered fields lead to a self-similar gas fragmentation: at all scales, there exist elongated gas structures nearly perpendicular to the fields. Many gas elongations have density peaks near the ends, which symmetrically pinch the fields. The field strength is proportional to the 0.4th power of the density, which is an indication of anisotropic gas contractions along the field. We conclude that magnetic fields have a crucial role in the fragmentation of NGC 6334.

  5. Reducing false alarms in the ICU by quantifying self-similarity of multimodal biosignals.

    PubMed

    Antink, Christoph Hoog; Leonhardt, Steffen; Walter, Marian

    2016-08-01

    False arrhythmia alarms pose a major threat to the quality of care in today's ICU. Thus, the PhysioNet/Computing in Cardiology Challenge 2015 aimed at reducing false alarms by exploiting multimodal cardiac signals recorded by a patient monitor. False alarms for asystole, extreme bradycardia, extreme tachycardia, ventricular flutter/fibrillation as well as ventricular tachycardia were to be reduced using two electrocardiogram channels, up to two cardiac signals of mechanical origin as well as a respiratory signal. In this paper, an approach combining multimodal rhythmicity estimation and machine learning is presented. Using standard short-time autocorrelation and robust beat-to-beat interval estimation, the signal's self-similarity is analyzed. In particular, beat intervals as well as quality measures are derived which are further quantified using basic mathematical operations (min, mean, max, etc). Moreover, methods from the realm of image processing, 2D Fourier transformation combined with principal component analysis, are employed for dimensionality reduction. Several machine learning approaches are evaluated including linear discriminant analysis and random forest. Using an alarm-independent reduction strategy, an overall false alarm reduction with a score of 65.52 in terms of the real-time scoring system of the challenge is achieved on a hidden dataset. Employing an alarm-specific strategy, an overall real-time score of 78.20 at a true positive rate of 95% and a true negative rate of 78% is achieved. While the results for some categories still need improvement, false alarms for extreme tachycardia are suppressed with 100% sensitivity and specificity.

  6. Inter-relationship between scaling exponents for describing self-similar river networks

    NASA Astrophysics Data System (ADS)

    Yang, Soohyun; Paik, Kyungrock

    2015-04-01

    Natural river networks show well-known self-similar characteristics. Such characteristics are represented by various power-law relationships, e.g., between upstream length and drainage area (exponent h) (Hack, 1957), and in the exceedance probability distribution of upstream area (exponent ɛ) (Rodriguez-Iturbe et al., 1992). It is empirically revealed that these power-law exponents are within narrow ranges. Power-law is also found in the relationship between drainage density (the total stream length divided by the total basin area) and specified source area (the minimum drainage area to form a stream head) (exponent η) (Moussa and Bocquillon, 1996). Considering that above three scaling relationships all refer to fundamental measures of 'length' and 'area' of a given drainage basin, it is natural to hypothesize plausible inter-relationship between these three scaling exponents. Indeed, Rigon et al. (1996) demonstrated the relationship between ɛ and h. In this study, we expand this to a more general ɛ-η-h relationship. We approach ɛ-η relationship in an analytical manner while η-h relationship is demonstrated for six study basins in Korea. Detailed analysis and implications will be presented. References Hack, J. T. (1957). Studies of longitudinal river profiles in Virginia and Maryland. US, Geological Survey Professional Paper, 294. Moussa, R., & Bocquillon, C. (1996). Fractal analyses of tree-like channel networks from digital elevation model data. Journal of Hydrology, 187(1), 157-172. Rigon, R., Rodriguez-Iturbe, I., Maritan, A., Giacometti. A., Tarboton, D. G., & Rinaldo, A. (1996). On Hack's Law. Water Resources Research, 32(11), 3367-3374. Rodríguez-Iturbe, I., Ijjasz-Vasquez, E. J., Bras, R. L., & Tarboton, D. G. (1992). Power law distributions of discharge mass and energy in river basins. Water Resources Research, 28(4), 1089-1093.

  7. Self-similar force-free wind from an accretion disc

    NASA Astrophysics Data System (ADS)

    Narayan, Ramesh; McKinney, Jonathan C.; Farmer, Alison J.

    2007-02-01

    We consider a self-similar force-free wind flowing out of an infinitely thin disc located in the equatorial plane. On the disc plane, we assume that the magnetic stream function P scales as P ~ Rν, where R is the cylindrical radius. We also assume that the azimuthal velocity in the disc is constant: vφ = Mc, where M < 1 is a constant. For each choice of the parameters ν and M, we find an infinite number of solutions that are physically well-behaved and have fluid velocity <= c throughout the domain of interest. Among these solutions, we show via physical arguments and time-dependent numerical simulations that the minimum-torque solution, i.e. the solution with the smallest amount of toroidal field, is the one picked by a real system. For ν >= 1, the Lorentz factor of the outflow increases along a field line as γ ~ M(z/Rfp)(2-ν)/2 ~ R/RA, where Rfp is the radius of the foot-point of the field line on the disc and RA = Rfp/M is the cylindrical radius at which the field line crosses the Alfvén surface or the light cylinder. For ν < 1, the Lorentz factor follows the same scaling for z/Rfp < M-1/(1-ν), but at larger distances it grows more slowly: γ ~ (z/Rfp)ν/2. For either regime of ν, the dependence of γ on M shows that the rotation of the disc plays a strong role in jet acceleration. On the other hand, the poloidal shape of a field line is given by z/Rfp ~ (R/Rfp)2/(2-ν) and is independent of M. Thus rotation has neither a collimating nor a decollimating effect on field lines, suggesting that relativistic astrophysical jets are not collimated by the rotational winding up of the magnetic field.

  8. A lognormal distribution of the lengths of terminal twigs on self-similar branches of elm trees.

    PubMed

    Koyama, Kohei; Yamamoto, Ken; Ushio, Masayuki

    2017-01-11

    Lognormal distributions and self-similarity are characteristics associated with a wide range of biological systems. The sequential breakage model has established a link between lognormal distributions and self-similarity and has been used to explain species abundance distributions. To date, however, there has been no similar evidence in studies of multicellular organismal forms. We tested the hypotheses that the distribution of the lengths of terminal stems of Japanese elm trees (Ulmus davidiana), the end products of a self-similar branching process, approaches a lognormal distribution. We measured the length of the stem segments of three elm branches and obtained the following results: (i) each occurrence of branching caused variations or errors in the lengths of the child stems relative to their parent stems; (ii) the branches showed statistical self-similarity; the observed error distributions were similar at all scales within each branch and (iii) the multiplicative effect of these errors generated variations of the lengths of terminal twigs that were well approximated by a lognormal distribution, although some statistically significant deviations from strict lognormality were observed for one branch. Our results provide the first empirical evidence that statistical self-similarity of an organismal form generates a lognormal distribution of organ sizes.

  9. Self-similarity of a Rayleigh-Taylor mixing layer at low Atwood number with a multimode initial perturbation

    NASA Astrophysics Data System (ADS)

    Morgan, Brandon; Olson, Britton; White, Justin; McFarland, Jacob

    2016-11-01

    High-fidelity large eddy simulation (LES) of a low-Atwood number (A = 0.05) Rayleigh-Taylor mixing layer is performed using the tenth-order compact difference code Miranda. An initial multimode perturbation spectrum is specified in Fourier space as a function of mesh resolution such that a database of results is obtained in which each successive level of increased grid resolution corresponds approximately to one additional doubling of the mixing layer width, or generation. The database is then analyzed to determine approximate requirements for self-similarity, and a new metric is proposed to quantify how far a given simulation is from the limit of self-similarity. It is determined that the present database reaches a high degree of self-similarity after approximately 4.5 generations. Finally, self-similar turbulence profiles from the LES database are compared with one-dimensional simulations using the k- L- a and BHR-2 Reynolds-averaged Navier-Stokes (RANS) models. The k- L- a model, which is calibrated to reproduce a quadratic turbulence kinetic energy profile for a self-similar mixing layer, is found to be in better agreement with the LES than BHR-2 results. This work was preformed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344.

  10. Performance analysis of ATM ABR service under self-similar traffic in the presence of background VBR traffic

    SciTech Connect

    Benke, G. |; Brandt, J.; Chen, H.; Dastangoo, S.; Miller, G.J.

    1996-05-01

    Recent empirical studies of traffic measurements of packet switched networks have demonstrated that actual network traffic is self-similar, or long range dependent, in nature. That is, the measured traffic is bursty over a wide range of time intervals. Furthermore, the emergence of high-speed network backbones demands the study of accurate models of aggregated traffic to assess network performance. This paper provides a method for generation of self-similar traffic, which can be used to drive network simulation models. The authors present the results of a simulation study of a two-node ATM network configuration that supports the ATM Forum`s Available Bit Rate (ABR) service. In this study, the authors compare the state of the queue at the source router at the edge of the ATM network under both Poisson and self-similar traffic loading. These findings indicate an order of magnitude increase in queue length for self-similar traffic loading as compared to Poisson loading. Moreover, when background VBR traffic is present, self-similar ABR traffic causes more congestion at the ATM switches than does Poisson traffic.

  11. Determination of electron polytropic indices in the environment of Comet P/Halley

    NASA Astrophysics Data System (ADS)

    Mazelle, C.; Belmont, G.

    1993-01-01

    We present a general experimental method to investigate the relations between the density variations and the pressure variations for one particle population of a hot collisionless plasma. A complete description is provided of the data analysis technique for an experimental case, from Giotto electron and magnetic field data measured in the environment of Comet P/Halley, used to verify the theory. The correlations between the electron characteristics, density and pressures, and the magnetic field strength are investigated. In this case, the method shows that the relation between the electron density and pressures can be satisfactorily represented by two polytropic laws. The values inferred for the polytropic indices strongly differ from those usually found in the literature but are nevertheless fully quantitatively explained from the theoretical analytical calculations.

  12. Stability of thin shell wormholes in Born-Infeld theory supported by polytropic phantom energy

    NASA Astrophysics Data System (ADS)

    Eid, Ali

    2017-02-01

    In the framework of the Darmois-Israel formalism, the dynamical equations of motion of spherically-symmetric thin-shell wormholes supported by a polytropic phantom energy in Einstein- Born-Infeld theory are constructed. A stability analysis of the spherically-symmetric thin-shell wormhole by using the standard potential method is carried out. The existence of stable, static solutions depends on the values of some parameters.

  13. Effective geometry of the n=1 uniformly rotating self-gravitating polytrope

    SciTech Connect

    Bini, D.; Cherubini, C.; Filippi, S.; Geralico, A.

    2010-08-15

    The ''effective geometry'' formalism is used to study the perturbations of a perfect barotropic Newtonian self-gravitating rotating and compressible fluid coupled with gravitational backreaction. The case of a uniformly rotating polytrope with index n=1 is investigated, due to its analytical tractability. Special attention is devoted to the geometrical properties of the underlying background acoustic metric, focusing, in particular, on null geodesics as well as on the analog light cone structure.

  14. Polytropic transonic galactic outflows in a dark matter halo with a central black hole

    NASA Astrophysics Data System (ADS)

    Igarashi, Asuka; Mori, Masao; Nitta, Shin-ya

    2017-09-01

    Polytropic transonic solutions of spherically symmetric and steady galactic winds in the gravitational potential of a dark matter halo (DMH) with a supermassive black hole (SMBH) are studied. The solutions are classified in terms of their topological features, and the gravitational potential of the SMBH adds a new branch to the transonic solutions generated by the gravity of the DMH. The topological types of the transonic solutions depend on the mass distribution, the amount of supplied energy, the polytropic index γ and the slope α of the DMH mass distribution. When α becomes larger than a critical value αc, the transonic solution types change dramatically. Further, our model predicts that it is possible for a slowly accelerating outflow to exist, even in quiescent galaxies with small γ. This slowly accelerating outflow differs from those considered in many of the previous studies focusing on supersonic outflows in active star-forming galaxies. In addition, our model indicates that outflows in active star-forming galaxies have only one transonic point in the inner region (∼0.01 kpc). The locus of this transonic point does not strongly depend on γ. We apply the polytropic model incorporating mass flux supplied by stellar components to the Sombrero galaxy, and conclude that it can reproduce the observed gas density and the temperature distribution well. This result differs significantly from the isothermal model, which requires an unrealistically large mass flux. Thus, we conclude that the polytropic model is more realistic than the isothermal model, and that the Sombrero galaxy can have a slowly accelerating outflow.

  15. Proteomic approach to identify champagne wine proteins as modified by Botrytis cinerea infection.

    PubMed

    Cilindre, Clara; Jégou, Sandrine; Hovasse, Agnès; Schaeffer, Christine; Castro, Antonio J; Clément, Christophe; Van Dorsselaer, Alain; Jeandet, Philippe; Marchal, Richard

    2008-03-01

    The presence of the fungal pathogen, Botrytis cinerea, in the vineyard causes reductions in both quality and quantity of grapes and wine. Because proteins are involved in the foam stabilization of sparkling wines, we have undertaken, for the first time, a thorough proteomic analysis of two champagne base wines prepared with either healthy or botrytized Chardonnay grapes, using two-dimensional electrophoresis (2DE) coupled with immunodetection and tandem mass spectrometry. Most of the identified proteins were from grape origin: invertase and pathogenesis-related (PR) proteins. The disappearance of numerous grape proteins was observed in the botrytized wine, suggesting that they were probably degraded or even repressed or the result of a differential expression of grape proteins upon fungal infection. On the other hand, two pectinolytic enzymes secreted by B. cinerea were found in the botrytized wine.

  16. The ion polytropic coefficient in a collisionless sheath containing hot ions

    SciTech Connect

    Lin, Binbin; Xiang, Nong Ou, Jing

    2016-08-15

    The fluid approach has been widely used to study plasma sheath dynamics. For a sheath containing hot ions whose temperature is greater than the electron's, how to truncate the fluid hierarchy chain equations while retaining to the fullest extent of the kinetic effects is always a difficult problem. In this paper, a one-dimensional, collisionless sheath containing hot ions is studied via particle-in-cell simulations. By analyzing the ion energy equation and taking the kinetic effects into account, we have shown that the ion polytropic coefficient in the vicinity of the sheath edge is approximately constant so that the state equation with the modified polytropic coefficient can be used to close the hierarchy chain of the ion fluid equations. The value of the polytropic coefficient strongly depends on the hot ion temperature and its concentration in the plasma. The semi-analytical model is given to interpret the simulation results. As an application, the kinetic effects on the ion saturation current density in the probe theory are discussed.

  17. ROSSBY WAVE INSTABILITY IN LOCALLY ISOTHERMAL AND POLYTROPIC DISKS: THREE-DIMENSIONAL LINEAR CALCULATIONS

    SciTech Connect

    Lin, Min-Kai

    2012-07-20

    Numerical calculations of the linear Rossby wave instability (RWI) in global three-dimensional (3D) disks are presented. The linearized fluid equations are solved for vertically stratified, radially structured disks with either a locally isothermal or polytropic equation of state, by decomposing the vertical dependence of the perturbed hydrodynamic quantities into Hermite and Gegenbauer polynomials, respectively. It is confirmed that the RWI operates in 3D. For perturbations with vertical dependence assumed above, there is little difference in growth rates between 3D and two-dimensional (2D) calculations. Comparison between 2D and 3D solutions of this type suggests the RWI is predominantly a 2D instability and that 3D effects, such as vertical motion, can be interpreted as a perturbative consequence of the dominant 2D flow. The vertical flow around corotation, where vortex formation is expected, is examined. In locally isothermal disks, the expected vortex center remains in approximate vertical hydrostatic equilibrium. For polytropic disks, the vortex center has positive vertical velocity, whose magnitude increases with decreasing polytropic index n.

  18. Small amplitude waves and linear firehose and mirror instabilities in rotating polytropic quantum plasma

    NASA Astrophysics Data System (ADS)

    Bhakta, S.; Prajapati, R. P.; Dolai, B.

    2017-08-01

    The small amplitude quantum magnetohydrodynamic (QMHD) waves and linear firehose and mirror instabilities in uniformly rotating dense quantum plasma have been investigated using generalized polytropic pressure laws. The QMHD model and Chew-Goldberger-Low (CGL) set of equations are used to formulate the basic equations of the problem. The general dispersion relation is derived using normal mode analysis which is discussed in parallel, transverse, and oblique wave propagations. The fast, slow, and intermediate QMHD wave modes and linear firehose and mirror instabilities are analyzed for isotropic MHD and CGL quantum fluid plasmas. The firehose instability remains unaffected while the mirror instability is modified by polytropic exponents and quantum diffraction parameter. The graphical illustrations show that quantum corrections have a stabilizing influence on the mirror instability. The presence of uniform rotation stabilizes while quantum corrections destabilize the growth rate of the system. It is also observed that the growth rate stabilizes much faster in parallel wave propagation in comparison to the transverse mode of propagation. The quantum corrections and polytropic exponents also modify the pseudo-MHD and reverse-MHD modes in dense quantum plasma. The phase speed (Friedrichs) diagrams of slow, fast, and intermediate wave modes are illustrated for isotropic MHD and double adiabatic MHD or CGL quantum plasmas, where the significant role of magnetic field and quantum diffraction parameters on the phase speed is observed.

  19. Self-similar wave produced by local perturbation of the Kelvin-Helmholtz shear-layer instability.

    PubMed

    Hoepffner, Jérôme; Blumenthal, Ralf; Zaleski, Stéphane

    2011-03-11

    We show that the Kelvin-Helmholtz instability excited by a localized perturbation yields a self-similar wave. The instability of the mixing layer was first conceived by Helmholtz as the inevitable growth of any localized irregularity into a spiral, but the search and uncovering of the resulting self-similar evolution was hindered by the technical success of Kelvin's wavelike perturbation theory. The identification of a self-similar solution is useful since its specific structure is witness of a subtle nonlinear equilibrium among the forces involved. By simulating numerically the Navier-Stokes equations, we analyze the properties of the wave: growth rate, propagation speed and the dependency of its shape upon the density ratio of the two phases of the mixing layer.

  20. Self-similar intermediate asymptotics for nonlinear degenerate parabolic free-boundary problems that occur in image processing.

    PubMed

    Barenblatt, G I

    2001-11-06

    In the boundary layers around the edges of images, basic nonlinear parabolic equations for image intensity used in image processing assume a special degenerate asymptotic form. An asymptotic self-similar solution to this degenerate equation is obtained in an explicit form. The solution reveals a substantially nonlinear effect-the formation of sharp steps at the edges of the images, leading to edge enhancement. Positions of the steps and the time shift parameter cannot be determined by direct construction of a self-similar solution; they depend on the initial condition of the pre-self-similar solution. The free-boundary problem is formulated describing the image intensity evolution in the boundary layer.

  1. Three-equation model for the self-similar growth of Rayleigh-Taylor and Richtmyer-Meskov instabilities

    NASA Astrophysics Data System (ADS)

    Morgan, Brandon E.; Wickett, Michael E.

    2015-04-01

    In the present work, the two-equation k -L model [G. Dimonte and R. Tipton, Phys. Fluids 18, 085101 (2006), 10.1063/1.2219768] is extended by the addition of a third equation for the mass-flux velocity. A set of model constants is derived to satisfy an ansatz of self-similarity in the low Atwood number limit. The model is then applied to the simulation of canonical Rayleigh-Taylor and Richtmyer-Meshkov test problems in one dimension and is demonstrated to reproduce analytical self-similar growth and to recover growth rates used to constrain the model.

  2. Unsupervised Eye Pupil Localization through Differential Geometry and Local Self-Similarity Matching

    PubMed Central

    Leo, Marco; Cazzato, Dario; De Marco, Tommaso; Distante, Cosimo

    2014-01-01

    's shape that is obtained through a differential analysis of image intensities and the subsequent combination with the local variability of the appearance represented by self-similarity coefficients. The experimental evidence of the effectiveness of the method was demonstrated on challenging databases containing facial images. Moreover, its capabilities to accurately detect the centers of the eyes were also favourably compared with those of the leading state-of-the-art methods. PMID:25122452

  3. Development of self-similar duplex systems. Atacama Fault System, Chile

    NASA Astrophysics Data System (ADS)

    Jensen, E.; Cembrano, J. M.; Veloso, E. E.

    2009-12-01

    Fault development models are very important to predict geometry and distribution of fractures at all scales. However, models based on structures from microns to km are relatively scarce due to the lack of well-exposed structures. We present structures related to the development of the Bolfín fault in the Atacama Fault System (AFS), covering a scale range of 9 orders of magnitude. The AFS is a 1000 km-long trench-parallel fault system located in the Andean Forearc. The Bolfín fault is a first-order fault of the Caleta Coloso Duplex; it has a trend ~170° and a length >45 km (Fig 1A). It cuts meta-diorites and exhibits a 100-200m wide core of subvertical bands of altered fractured host rock and of foliated cataclasites. Foliation is made of trend-parallel cm-wide shear bands composed of plagioclase fragments (>0,1mm) surrounded by epidote. Around the bands there are many micro fractures oriented within the P-diedra. In the compressive quadrant around a tip point of Bolfín fault, the lower strain faults exhibit an unusual internal structure consisting of fractures arranged in a multi-duplex pattern. This pattern can be seen from metric- (Parulo fault, fig 1C) to mm-scale (Palmera fault fig 1B). Fractures in the pattern can be separated in 2 types: Main Faults: Trend-parallel, longer and with larger offsets. Secondary Fractures: sigmoid-shape fractures distributed in the regions between main faults, all oriented between 15° and 75° with respect to the main faults, meassured in the shear-sense (i.e. in P-diedra). On the basis of the distribution of the 2 types of fractures, the generation sequence can be inferred. The main faults are more widely distributed, and were propagated earlier. The secondary fractures are distributed in smaller areas between larger displacement main faults, and propagated later as linking fractures. The duplex pattern is thus self-similar: faults with multiple-duplex internal structure (Parulo and Palmera fault)are in turn secondary faults

  4. Growth of river delta networks: Thresholds, periodicity, aging and self similarity (Invited)

    NASA Astrophysics Data System (ADS)

    Jerolmack, D. J.; Reitz, M. D.

    2010-12-01

    channel locations. A lobe is abandoned (avulsion) when every point on the shoreline has built out to the threshold slope. These dynamics result in self-similar (quasi-)radial growth of fan lobes, which can be described using a simple geometric model. Together, this work provides a complete description of the statistical spatio-temporal dynamics of fan growth. Experimental fan behavior agrees well with natural systems, even though laboratory fans exclude stochastically-varying boundary conditions and fluid turbulence effects. Thus, temporal and spatial patterns of depositional channel systems appear to be a robust result of mass conservation and transport thresholds.

  5. Self-similarity and scaling transitions during rupture of thin free films of Newtonian fluids

    NASA Astrophysics Data System (ADS)

    Thete, Sumeet Suresh; Anthony, Christopher; Doshi, Pankaj; Harris, Michael T.; Basaran, Osman A.

    2016-09-01

    Rupture of thin liquid films is crucial in many industrial applications and nature such as foam stability in oil-gas separation units, coating flows, polymer processing, and tear films in the eye. In some of these situations, a liquid film may have two free surfaces (referred to here as a free film or a sheet) as opposed to a film deposited on a solid substrate that has one free surface. The rupture of such a free film or a sheet of a Newtonian fluid is analyzed under the competing influences of inertia, viscous stress, van der Waals pressure, and capillary pressure by solving a system of spatially one-dimensional evolution equations for film thickness and lateral velocity. The dynamics close to the space-time singularity where the film ruptures is asymptotically self-similar and, therefore, the problem is also analyzed by reducing the transient partial differential evolution equations to a corresponding set of ordinary differential equations in similarity space. For sheets with negligible inertia, it is shown that the dominant balance of forces involves solely viscous and van der Waals forces, with capillary force remaining negligible throughout the thinning process in a viscous regime. On the other hand, for a sheet of an inviscid fluid for which the effect of viscosity is negligible, it is shown that the dominant balance of forces is between inertial, capillary, and van der Waals forces as the film evolves towards rupture in an inertial regime. Real fluids, however, have finite viscosity. Hence, for real fluids, it is further shown that the viscous and the inertial regimes are only transitory and can only describe the initial thinning dynamics of highly viscous and slightly viscous sheets, respectively. Moreover, regardless of the fluid's viscosity, it is shown that for sheets that initially thin in either of these two regimes, their dynamics transition to a late stage or final inertial-viscous regime in which inertial, viscous, and van der Waals forces balance

  6. Self-protection and self-similarity of the stably-stratified geophysical turbulence

    NASA Astrophysics Data System (ADS)

    Zilitinkevich, Sergej; Kleeorin, Nathan; Rogachevskii, Igor

    2014-05-01

    Following Richardson (1920), the effect of stratification on the shear-generated geophysical turbulence is determined by the gradient Richardson number Ri = (N/S)2, where Nis the Brunt-Vaisala frequency, S = dU/dz is vertical shear of the mean wind/current velocity U, and z is vertical coordinate. The concept of Richardson-number similarity postulates that dimensionless characteristics of turbulence are universal functions of Ri. Monin and Obukhov (1954) have proposed for the atmospheric surface layer a widely recognised Monin-Obukhov similarity theory (MOST). This theory postulates that dimensionless characteristics of turbulence are fully determined by the ratio z/L, where L = -u*3/Fb is the Obukhov length scale, u* is friction velocity and Fb is vertical turbulent flux of buoyancy. Nieuwstadt (1984) has employed local,z-dependent values of Fb and u* instead of the surface values, and demonstrated applicability of such version of MOST to the almost entire stably stratified planetary boundary layer. MOST is consistent with the Ri-similarity: in the surface layer Ri is a monotonously increasing function of z/L and vice versa (e.g., Sorbjan, 2010). In the strongly unstable stratification, MOST and Ri-similarity fail because of the self-organisation of convective turbulence (Elperin et al., 2006; Zilitinkevich et al., 2006). In this paper we employ the EFB turbulence closure theory (Zilitinkevich et al, 2013) together with available experimental, LES and DNS data to explain the most puzzling feature of the stably stratified geophysical turbulence, namely, its self-protection in very stable stratification, due to the counter-gradient heat-transfer mechanism missed in the traditional theory. We also explain the self-similarity of turbulence, due to the Kolmogorov's nature of dissipation for the turbulent kinetic energy (TKE), turbulent potential energy (TPE) and turbulent fluxes of heat and momentum. In non-steady regimes, traditional similarity criteria, such as z

  7. Unsupervised eye pupil localization through differential geometry and local self-similarity matching.

    PubMed

    Leo, Marco; Cazzato, Dario; De Marco, Tommaso; Distante, Cosimo

    2014-01-01

    's shape that is obtained through a differential analysis of image intensities and the subsequent combination with the local variability of the appearance represented by self-similarity coefficients. The experimental evidence of the effectiveness of the method was demonstrated on challenging databases containing facial images. Moreover, its capabilities to accurately detect the centers of the eyes were also favourably compared with those of the leading state-of-the-art methods.

  8. Self-similar hierarchical energetics in the ICM of massive galaxy clusters

    NASA Astrophysics Data System (ADS)

    Miniati, Francesco; Beresnyak, Andrey

    type of self-similarity in cosmology. Their specific values, while consistent with current data, indicate that thermal energy dominates the ICM energetics and the turbulent dynamo is always far from saturation, unlike the condition in other familiar astrophysical fluids (stars, interstellar medium of galaxies, compact objects, etc.). In addition, they have important physical meaning as their specific values encodes information about the efficiency of turbulent heating (the fraction of ICM thermal energy produced by turbulent dissipation) and the efficiency of dynamo action in the ICM (CE ).

  9. Characterization by optical measurements of the effects of some stages of champagne technology on the adsorption layer formed at the gas/wine interface.

    PubMed

    Saleh, K Abou; Aguié-Béghin, V; Foulon, L; Valade, M; Douillard, R

    2007-06-19

    This study analyzes the effects of some important factors of champagne technology on the ellipticity and Brewster angle microscopy (BAM) of the air/champagne interface in view of using the optical properties of the adsorption layer of base wine to forecast the stability of the champagne bubble collar. Using standard, ultrafiltered, and ultraconcentrated wines it was observed that champagne can lose amphiphilic macromolecules which adsorb on the inner glass wall of the bottle during storage, particles such as dead yeasts can adhere to the adsorption layer, a weak increase of the ethanol content during bottle fermentation can reduce significantly the ellipticity of the adsorption layer, and CO2 has no significant effect on the properties of that layer. Surprisingly, no visible differences of the adsorption layer were noticed between the experimental champagnes of the 2004 vintage of three vine varieties (Chardonnay, Pinot noir, and Pinot meunier). From analysis of all samples it is proposed that the mean value and standard deviation of the ellipticity measured during 30 min after pouring the wine in a Petri dish are physical quantities which satisfactorily characterize the adsorption layer of champagne. When needed, further characterization of the adsorption layer may be obtained by a detailed analysis of the kinetics of ellipticity during the same period and inspection of the BAM images of the interface.

  10. La physique des bulles de champagne Une première approche des processus physico-chimiques liés à l'effervescence des vins de Champagne

    NASA Astrophysics Data System (ADS)

    Liger-Belair, G.

    2002-07-01

    People have long been fascinated by bubbles and foams dynamics, and since the pioneering work of Leonardo da Vinci in the early 16th century, this subject has generated a huge bibliography. However, only very recently, much interest was devoted to bubbles in Champagne wines. Small bubbles rising through the liquid, as well as a bubble ring (the so-called collar) at the periphery of a flute poured with champagne are the hallmark of this traditionally festive wine, and even there is no scientific evidence yet to connect the quality of a champagne with its effervescence, people nevertheless often make a connection between them. Therefore, since the last few years, a better understanding of the numerous parameters involved in the bubbling process has become an important stake in the champagne research area. Otherwise, in addition to these strictly enological reasons, we also feel that the area of bubble dynamics could benefit from the simple but close observation of a glass poured with champagne. In this study, our first results concerning the close observation of the three main steps of a champagne bubble's life are presented, that is, the bubble nucleation on tiny particles stuck on the glass wall (Chap. 2), the bubble ascent through the liquid (Chap. 3), and the bursting of bubbles at the free surface, which constitutes the most intriguing and visually appealing step (Chap. 4). Our results were obtained in real consuming conditions, that is, in a classical crystal flute poured with a standard commercial champagne wine. Champagne bubble nucleation proved to be a fantastic everyday example to illustrate the non-classical heterogeneous bubble nucleation process in a weakly supersaturated liquid. Contrary to a generally accepted idea, nucleation sites are not located on irregularities of the glass itself. Most of nucleation sites are located on tiny hollow and roughly cylindrical exogenous fibres coming from the surrounding air or remaining from the wiping process

  11. Some features of α disc and advective-dominated accretion disc. Self-similar solutions and their comparison - II

    NASA Astrophysics Data System (ADS)

    Filipov, Lachezar; Yankova, Krasimira; Andreeva, Daniela

    Using the models from part I, we have derived the basic parameters, describing the discs. We have obtained the self-similar solutions of the evolution for both types - ADAD and α discs. The results are expressed quantitatively to demonstrate our conclusion.

  12. The Tutte polynomial of an infinite family of outerplanar, small-world and self-similar graphs

    NASA Astrophysics Data System (ADS)

    Liao, Yunhua; Fang, Aixiang; Hou, Yaoping

    2013-10-01

    In this paper we recursively describe the Tutte polynomial of an infinite family of outerplanar, small-world and self-similar graphs. In particular, we study the Abelian Sandpile Model on these graphs and obtain the generating function of the recurrent configurations. Further, we give some exact analytical expression for the Tutte polynomial at several special points

  13. Self-similarity of temperature profiles in distant galaxy clusters: the quest for a universal law

    NASA Astrophysics Data System (ADS)

    Baldi, A.; Ettori, S.; Molendi, S.; Gastaldello, F.

    2012-09-01

    Context. We present the XMM-Newton temperature profiles of 12 bright (LX > 4 × 1044 erg s-1) clusters of galaxies at 0.4 < z < 0.9, having an average temperature in the range 5 ≲ kT ≲ 11 keV. Aims: The main goal of this paper is to study for the first time the temperature profiles of a sample of high-redshift clusters, to investigate their properties, and to define a universal law to describe the temperature radial profiles in galaxy clusters as a function of both cosmic time and their state of relaxation. Methods: We performed a spatially resolved spectral analysis, using Cash statistics, to measure the temperature in the intracluster medium at different radii. Results: We extracted temperature profiles for the clusters in our sample, finding that all profiles are declining toward larger radii. The normalized temperature profiles (normalized by the mean temperature T500) are found to be generally self-similar. The sample was subdivided into five cool-core (CC) and seven non cool-core (NCC) clusters by introducing a pseudo-entropy ratio σ = (TIN/TOUT) × (EMIN/EMOUT)-1/3 and defining the objects with σ < 0.6 as CC clusters and those with σ ≥ 0.6 as NCC clusters. The profiles of CC and NCC clusters differ mainly in the central regions, with the latter exhibiting a slightly flatter central profile. A significant dependence of the temperature profiles on the pseudo-entropy ratio σ is detected by fitting a function of r and σ, showing an indication that the outer part of the profiles becomes steeper for higher values of σ (i.e. transitioning toward the NCC clusters). No significant evidence of redshift evolution could be found within the redshift range sampled by our clusters (0.4 < z < 0.9). A comparison of our high-z sample with intermediate clusters at 0.1 < z < 0.3 showed how the CC and NCC cluster temperature profiles have experienced some sort of evolution. This can happen because higher z clusters are at a less advanced stage of their formation and

  14. Microbial contributions to coupled arsenic and sulfur cycling in the acid-sulfide hot spring Champagne Pool, New Zealand.

    PubMed

    Hug, Katrin; Maher, William A; Stott, Matthew B; Krikowa, Frank; Foster, Simon; Moreau, John W

    2014-01-01

    Acid-sulfide hot springs are analogs of early Earth geothermal systems where microbial metal(loid) resistance likely first evolved. Arsenic is a metalloid enriched in the acid-sulfide hot spring Champagne Pool (Waiotapu, New Zealand). Arsenic speciation in Champagne Pool follows reaction paths not yet fully understood with respect to biotic contributions and coupling to biogeochemical sulfur cycling. Here we present quantitative arsenic speciation from Champagne Pool, finding arsenite dominant in the pool, rim and outflow channel (55-75% total arsenic), and dithio- and trithioarsenates ubiquitously present as 18-25% total arsenic. In the outflow channel, dimethylmonothioarsenate comprised ≤9% total arsenic, while on the outflow terrace thioarsenates were present at 55% total arsenic. We also quantified sulfide, thiosulfate, sulfate and elemental sulfur, finding sulfide and sulfate as major species in the pool and outflow terrace, respectively. Elemental sulfur concentration reached a maximum at the terrace. Phylogenetic analysis of 16S rRNA genes from metagenomic sequencing revealed the dominance of Sulfurihydrogenibium at all sites and an increased archaeal population at the rim and outflow channel. Several phylotypes were found closely related to known sulfur- and sulfide-oxidizers, as well as sulfur- and sulfate-reducers. Bioinformatic analysis revealed genes underpinning sulfur redox transformations, consistent with sulfur speciation data, and illustrating a microbial role in sulfur-dependent transformation of arsenite to thioarsenate. Metagenomic analysis also revealed genes encoding for arsenate reductase at all sites, reflecting the ubiquity of thioarsenate and a need for microbial arsenate resistance despite anoxic conditions. Absence of the arsenite oxidase gene, aio, at all sites suggests prioritization of arsenite detoxification over coupling to energy conservation. Finally, detection of methyl arsenic in the outflow channel, in conjunction with

  15. Microbial contributions to coupled arsenic and sulfur cycling in the acid-sulfide hot spring Champagne Pool, New Zealand

    PubMed Central

    Hug, Katrin; Maher, William A.; Stott, Matthew B.; Krikowa, Frank; Foster, Simon; Moreau, John W.

    2014-01-01

    Acid-sulfide hot springs are analogs of early Earth geothermal systems where microbial metal(loid) resistance likely first evolved. Arsenic is a metalloid enriched in the acid-sulfide hot spring Champagne Pool (Waiotapu, New Zealand). Arsenic speciation in Champagne Pool follows reaction paths not yet fully understood with respect to biotic contributions and coupling to biogeochemical sulfur cycling. Here we present quantitative arsenic speciation from Champagne Pool, finding arsenite dominant in the pool, rim and outflow channel (55–75% total arsenic), and dithio- and trithioarsenates ubiquitously present as 18–25% total arsenic. In the outflow channel, dimethylmonothioarsenate comprised ≤9% total arsenic, while on the outflow terrace thioarsenates were present at 55% total arsenic. We also quantified sulfide, thiosulfate, sulfate and elemental sulfur, finding sulfide and sulfate as major species in the pool and outflow terrace, respectively. Elemental sulfur concentration reached a maximum at the terrace. Phylogenetic analysis of 16S rRNA genes from metagenomic sequencing revealed the dominance of Sulfurihydrogenibium at all sites and an increased archaeal population at the rim and outflow channel. Several phylotypes were found closely related to known sulfur- and sulfide-oxidizers, as well as sulfur- and sulfate-reducers. Bioinformatic analysis revealed genes underpinning sulfur redox transformations, consistent with sulfur speciation data, and illustrating a microbial role in sulfur-dependent transformation of arsenite to thioarsenate. Metagenomic analysis also revealed genes encoding for arsenate reductase at all sites, reflecting the ubiquity of thioarsenate and a need for microbial arsenate resistance despite anoxic conditions. Absence of the arsenite oxidase gene, aio, at all sites suggests prioritization of arsenite detoxification over coupling to energy conservation. Finally, detection of methyl arsenic in the outflow channel, in conjunction with

  16. An empirical determination of the polytropic index for the free-streaming solar wind using Helios 1 data

    NASA Technical Reports Server (NTRS)

    Totten, T. L.; Freeman, J. W.; Arya, S.

    1995-01-01

    Observations of solar wind proton temperatures indicate that the solar wind is heated as it moves outward toward the orbit of Earth. This heating, which may be the results of electron heat conduction and perhaps MHD waves, has proven difficult to quantify and hence is often neglected in MHD models of the solar wind. An alternate approach to finding explicit heating terms for the MHD energy equation is to use a polytropic approximation. This paper discusses the properties of the polytropic approximation and its application to the solar wind plasma. By using data from the Helios 1 spacecraft, an empirical value for the polytropic index of the free-streaming solar wind is determined. Various corrections to the data are made to account for velocity, nonuniformity in radial sampling, and stream interaction regions. The polytropic index, as derived from proton data, is found to indepedent of speed state, within statistical error, and has an average value of 1.46. If magnetic pressure is included, the polytropic index has an average value of 1.58.

  17. Comparison of two landslide susceptibility assessments in the Champagne-Ardenne region (France)

    NASA Astrophysics Data System (ADS)

    Den Eeckhaut, M. Van; Marre, A.; Poesen, J.

    2010-02-01

    The vineyards of the Montagne de Reims are mostly planted on steep south-oriented cuesta fronts receiving a maximum of sun radiation. Due to the location of the vineyards on steep hillslopes, the viticultural activity is threatened by slope failures. This study attempts to better understand the spatial patterns of landslide susceptibility in the Champagne-Ardenne region by comparing a heuristic (qualitative) and a statistical (quantitative) model in a 1120 km² study area. The heuristic landslide susceptibility model was adopted from the Bureau de Recherches Géologiques et Minières, the GEGEAA - Reims University and the Comité Interprofessionnel du Vin de Champagne. In this model, expert knowledge of the region was used to assign weights to all slope classes and lithologies present in the area, but the final susceptibility map was never evaluated with the location of mapped landslides. For the statistical landslide susceptibility assessment, logistic regression was applied to a dataset of 291 'old' (Holocene) landslides. The robustness of the logistic regression model was evaluated and ROC curves were used for model calibration and validation. With regard to the variables assumed to be important environmental factors controlling landslides, the two models are in agreement. They both indicate that present and future landslides are mainly controlled by slope gradient and lithology. However, the comparison of the two landslide susceptibility maps through (1) an evaluation with the location of mapped 'old' landslides and through (2) a temporal validation with spatial data of 'recent' (1960-1999; n = 48) and 'very recent' (2000-2008; n = 46) landslides showed a better prediction capacity for the statistical model produced in this study compared to the heuristic model. In total, the statistically-derived landslide susceptibility map succeeded in correctly classifying 81.0% of the 'old' and 91.6% of the 'recent' and 'very recent' landslides. On the susceptibility map

  18. Champagne Pool (New Zealand) Thermophiles Yield Insights into the Evolution of Microbial Arsenic Resistance

    NASA Astrophysics Data System (ADS)

    Hug, K.; Krikowa, F.; Morgan, X.; Maher, W. A.; Stott, M. B.; Moreau, J. W.

    2011-12-01

    Arsenic is a highly toxic metalloid typically enriched in geothermal waters due to aqueous weathering of arsenic-bearing minerals. Investigation of enzymatic pathways by which thermophilic microorganisms cope with toxic arsenic levels may yield insights into the evolution of arsenic resistance mechanisms on the early Earth. At Wai-O-Tapu in the Taupo Volcanic Zone on the North Island of New Zealand, hot springs with temperatures of 30-90°C and elemental sulfur concentrations (expressed as equivalent sulfate) from 340 to 850 mg/l establish a range of environmental conditions. Total arsenic concentrations varied from 0.083 mg/l to 56 mg/l. Arsenic speciation analysis elucidated various biogeochemical arsenic transformations occurring within different springs. For example, in the Alum Cliff spring oxidizing conditions (Eh = 225 mV) were expected to stabilize dissolved arsenate (AsO43-). However, HPLC-ICPMS analyses yielded dissolved arsenate and arsenite (AsO33-) concentrations of 0.25 mg/l versus 43.3 mg/l, respectively, and point towards microbial arsenate reduction as the likely mechanism for arsenic redox transformation. 16S rRNA gene cloning of Alum Cliff DNA showed a predominantly archaeal population with the dominant clone "AC1_A1" most closely related (99% sequence similarity, NCBI BLAST°) to the uncultured Sulfolobus clone "ChP_97P" found in Champagne Pool (Childs et al., 2008). The closest isolated relative to AC1_A1 is Sulfolobus tokodaii str. TW with a sequence similarity of 94%. Arsenic speciation measurements from the Alum Cliff spring suggest that clone AC1_A1 features the arsenate reduction resistance mechanism, and we hypothesize therefore that an arsC (homolog or analog) provides this functionality. The organic arsenic species monomethylarsonic acid (MMA) and dimethylarsinic acid (DMA), detected via HPLC-ICPMS at concentrations ranging from 1 μg/l to 12 μg/l in various springs, may also implicate microbial methyl-group transfers as an active

  19. Closure of the hierarchy of fluid equations by means of the polytropic-coefficient function (PCF)

    SciTech Connect

    Kuhn, S.; Kamran, M.; Jelic, N.; Kos, L.; Tskhakaya, D. jr; Tskhakaya, D. D. sr

    2010-12-14

    The continuity and momentum equations of a fluid plasma component may be viewed as four scalar evolution equations for the four scalar fluid variables n(x-vector,t)(density) and u(x-vector,t)(fluid velocity), which are zeroth- and first order velocity moments of the velocity distribution function (VDF). However, the momentum equation in addition contains the gradient of the pressure p(x-vector,t), which is a second-order velocity moment for which another equation, the 'closure equation', is needed. In the present work, closure by means of the polytropic-coefficient function (PCF) is discussed which, by analogy with the well-known polytropic coefficient (also called the 'polytropic index' or 'polytropic exponent') in macroscopic thermodynamic systems, is formally defined by {gamma}(x-vector,t) = (nDp/Dt)(pDn/Dt) = (n/p)(Dp/Dn), with D/Dt = {partial_derivative}/{partial_derivative}t+u-vector{center_dot}{partial_derivative}/{partial_derivative}x-vector, which amounts to the closure equation if {gamma}(x-vector,t) is known. In fluid problems, however, the PCF is usually unknown and hence must be assumed or guessed, but in kinetic problems it can be calculated exactly. These general concepts are first developed and then applied specifically to the basic Tonks-Langmuir (TL) model [L. Tonks and I. Langmuir, Phys. Rev. 34, 876, 1929]. It is shown for the first time that results obtained from the fluid equations closed with the correct PCF coincide with the corresponding results calculated on the basis of the exact kinetic solution [K.-U. Riemann, Phys. Plasmas 13, 063508 (2006)], but differ visibly from those obtained from the approximate fluid equations closed with the zero-pressure approximation [Riemann et al., Plasma Phys. Control. Fusion 47, 1949 (2005)]. Also, it is again confirmed that the correct PCF may be a strongly varying function of position, so that the simple constant values of {gamma} usually assumed [K.-U. Riemann, XXVIII International Conference on

  20. Analytic solutions for single and multiple cylinders of gravitating polytropes in magnetostatic equilibrium

    NASA Technical Reports Server (NTRS)

    Lerche, I.; Low, B. C.

    1980-01-01

    Exact analytic solutions for the static equilibrium of a gravitating plasma polytrope in the presence of magnetic fields are presented. The means of generating various equilibrium configurations to illustrate directly the complex physical relationships between pressure, magnetic fields, and gravity in self-gravitating systems is demonstrated. One of the solutions is used to model interstellar clouds suspended by magnetic fields against the galactic gravity such as may be formed by the Parker (1966) instability. It is concluded that the pinching effect of closed loops of magnetic fields in the clouds may be a dominant agent in further collapsing the clouds following their formation.

  1. Stellar acoustics. I - Adiabatic pulse propagation and modal resonance in polytropic models of bump Cepheids

    NASA Astrophysics Data System (ADS)

    Whitney, C. A.

    1983-11-01

    An understanding of the Hertzsprung progression among bump Cepheids is sought in a dualistic viewpoint which combines the idea of propagating pulse echoes with that of modal resonance. Attention is focused on the spherically symmetric pulses that can be regenerated once per cycle if their round trip propagation time equals the period of the overall pulsation. The acoustic properties of polytropic models reveal that the conditions for such reinforcement are likely to be met in models for which the periods of the fundamental and the second overtone pulsation are in the ratio 2:1. Systematic departures from precise resonance may be responsible for the Hertzsprung progression.

  2. Continuous wavelet transform analysis for self-similarity properties of turbulence in magnetized DC glow discharge plasma

    NASA Astrophysics Data System (ADS)

    Sarma, Bornali; Chauhan, Sourabh S.; Wharton, A. M.; Iyengar, A. N. Sekar; Iyengar

    2013-10-01

    Characterization of self-similarity properties of turbulence in magnetized plasma is being carried out in DC glow discharge plasma. The time series floating potential fluctuation experimental data are acquired from the plasma by Langmuir probe. Continuous wavelet transform (CWT) analysis considering db4 mother wavelet has been applied to the experimental data and self-similarity properties are detected by evaluating the Hurst exponent from the wavelet variance plotting. From the CWT spectrum, effort is made to extract a highly correlated frequency by locating the brightest spot. Accordingly, those signals are treated for finding out correlation dimension and the Liapunov exponent so that the exact frequency responsible for the chaotic behavior could be found out.

  3. Further Remarks on the Luo-Hou's Ansatz for a Self-similar Solution to the 3D Euler Equations

    NASA Astrophysics Data System (ADS)

    Sperone, Gianmarco

    2017-01-01

    It is shown that the self-similar ansatz proposed by T. Hou and G. Luo to describe a singular solution of the 3D axisymmetric Euler equations leads, without assuming any asymptotic condition on the self-similar profiles, to an overdetermined system of partial differential equations that produces two families of solutions: a class of trivial solutions in which the vorticity field is identically zero, and a family of solutions that blow-up immediately, where the vorticity field is governed by a stationary regime. In any case, the analytical properties of these solutions are not consistent with the numerical observations reported by T. Hou and G. Luo. Therefore, this result is a refinement of the previous work published by D. Chae and T.-P. Tsai on this matter, where the authors found the trivial class of solutions under a certain decay condition of the blow-up profiles.

  4. Steady-state composition of a two-component gas bubble growing in a liquid solution: self-similar approach.

    PubMed

    Gor, G Yu; Kuchma, A E

    2009-12-21

    The paper presents an analytical description of the growth of a two-component bubble in a binary liquid-gas solution. We obtain asymptotic self-similar time dependence of the bubble radius and analytical expressions for the nonsteady profiles of dissolved gases around the bubble. We show that the necessary condition for the self-similar regime of bubble growth is the constant, steady-state composition of the bubble. The equation for the steady-state composition is obtained. We reveal the dependence of the steady-state composition on the solubility laws of the bubble components. Besides, the universal, independent from the solubility laws, expressions for the steady-state composition are obtained for the case of strong supersaturations, which are typical for the homogeneous nucleation of a bubble.

  5. Spin waves in a two-sublattice antiferromagnet. A self-similar solution of the Landau-Lifshitz equation

    NASA Astrophysics Data System (ADS)

    Gorobets, Y. I.; Gorobets, Y.; Kulish, V. V.

    2017-01-01

    In the paper, spin waves in a uniaxial two-sublattice antiferromagnet are investigated. A new class of self-similar solutions of the Landau-Lifshitz equation is obtained and, therefore, a new type of spin waves is described. Examples of solutions of the found class are presented. New type of solution admits both linear and non-linear spin waves, including solitons. Space transformations used in the solution are mathematically analogous to the relativistic transformations.

  6. Another self-similar blast wave: Early time asymptote with shock heated electrons and high thermal conductivity

    NASA Technical Reports Server (NTRS)

    Cox, D. P.; Edgar, R. J.

    1982-01-01

    Accurate approximations are presented for the self-similar structures of nonradiating blast waves with adiabatic ions, isothermal electrons, and equation ion and electron temperatures at the shock. The cases considered evolve in cavities with power law ambient densities (including the uniform density case) and have negligible external pressure. The results provide the early time asymptote for systems with shock heating of electrons and strong thermal conduction. In addition, they provide analytical results against which two fluid numerical hydrodynamic codes can be checked.

  7. Defect guidance in kagome-clad fibers: the role of photonic band gaps and self-similarity of the lattice

    NASA Astrophysics Data System (ADS)

    Perez, H.; Zheltikov, A. M.

    2017-01-01

    We examine the influence of the structural self-similarity of the kagome lattice on the defect modes and waveguiding properties of hollow-core kagome-cladding fibers. We show that the guidance of such fibers is influenced by photonic band gaps (PBGs) which appear for a subset of the kagome lattice. Using these insights, we provide design considerations to further decrease loss in kagome-clad fibers.

  8. Area volume properties of fluid interfaces in turbulence: scale-local self-similarity and cumulative scale dependence

    NASA Astrophysics Data System (ADS)

    Catrakis, Haris J.; Aguirre, Roberto C.; Ruiz-Plancarte, Jesus

    2002-07-01

    Area volume properties of fluid interfaces are investigated to quantify the scale-local and cumulative structure. An area volume density g3([lambda]) and ratio [Omega]3([lambda]) are introduced to examine the interfacial behaviour as a function of scale [lambda] or across a range of scales, respectively. These measures are demonstrated on mixed-fluid interfaces from whole-field [similar]10003 three-dimensional space time concentration measurements in turbulent jets above the mixing transition, at Re [similar] 20000 and Sc [similar] 2000, recorded by laser-induced-fluorescence and digital-imaging techniques, with Taylor's hypothesis applied. The cumulative structure is scale dependent in [Omega]3([lambda]), with a dimension D3([lambda]) that increases with increasing scale. In contrast, the scale-local structure exhibits self-similarity in g3([lambda]) with an exponent [alpha]g [approximate]1.3 for these interfaces. The scale dependence in the cumulative structure arises from the large scales, while the self-similarity corresponds to the small-scale area volume contributions. The small scales exhibit the largest area volume density and provide the dominant contributions to the total area volume ratio, which corresponds to [similar]10 times the area of a purely large-scale interface for the present flow conditions. The self-similarity in the scale-local structure at small scales provides the key ingredient to extrapolate the area volume behaviour to higher Reynolds numbers.

  9. Direct numerical simulation of a self-similar adverse pressure gradient turbulent boundary layer at the verge of separation

    NASA Astrophysics Data System (ADS)

    Kitsios, V.; Sekimoto, A.; Atkinson, C.; Sillero, J. A.; Borrell, G.; Gungor, A. G.; Jiménez, J.; Soria, J.

    2017-10-01

    The statistical properties are presented for the direct numerical simulation (DNS) of a self-similar adverse pressure gradient (APG) turbulent boundary layer (TBL) at the verge of separation. The APG TBL has a momentum thickness based Reynolds number range from $Re_{\\delta_2}=570$ to $13800$, with a self-similar region from $Re_{\\delta_2} = 10000$ to $12300$. Within this domain the average non-dimensional pressure gradient parameter $\\beta=39$, where for a unit density $\\beta=\\delta_1 P_e^\\prime / \\tau_w$, with $\\delta_1$ the displacement thickness, $\\tau_w$ the mean shear stress at the wall, and $P_e^\\prime$ the farfield pressure gradient. This flow is compared to previous zero pressure gradient (ZPG) and mild APG TBL ($\\beta=1$) results of similar Reynolds number. All flows are generated via the DNS of a TBL on a flat surface with farfield boundary conditions tailored to apply the desired pressure gradient. The conditions for self-similarity, and the appropriate length and velocity scales are derived. The mean and Reynolds stress profiles are shown to collapse when non-dimensionalised on the basis of these length and velocity scales. As the pressure gradient increases the flow has properties less like a ZPG TBL and more akin to a free shear layer.

  10. Implication of the polarization force on the self-similar expansion of a dusty plasma into vacuum

    NASA Astrophysics Data System (ADS)

    Bentabet, Karima; Tribeche, Mouloud

    2017-01-01

    The effects of the polarization force on the self-similar expansion into vacuum of an unmagnetized, collisionless dusty plasma are addressed. It is found that the polarization force may drastically influence the general trends of the self-similar expansion. It is noticed that when the polarization force dominates over the electrical one, the self-similar expansion of the dusty plasma cannot set in because the net force experienced by the dust grains is not a restoring force. Dust wave breaking and inherent dust bunching then occur preventing therefore the expansion of the dust grains. For any value of the polarization parameter R ranging from zero to a critical value Rcr , the sound-speed increases as the dust number density increases. As R increases, the values of the plasma sound-speed are shifted towards higher values before decreasing beyond the critical value Rcr . As R increases from zero to Rc, the plasma expansion becomes faster compared to those of the other cases, and larger velocities are communicated to the dust grains. This is attributed to the fact that as R increases from 0 to Rcr , the electrostatic potential and thus the electric field are sustained over a larger distance allowing therefore the dust particles to expand over a much farther distance.

  11. A Numerical Study of Self-Similarity in a Turbulent Plane Wake Using Large-Eddy Simulation

    NASA Technical Reports Server (NTRS)

    Ghosal, Sandip; Rogers, Michael M.

    1996-01-01

    Turbulent wakes are known to develop self-similarly sufficiently far downstream from obstacles that generate them. It has long been assumed that the spreading rate of the wake in the self-similar regime is independent of the details of the body generating the wake, being dependent only on the total drag (or momentum deficit). This assumption seems to be in contradiction with some recent experiments. In this study we attempt to complement these experimental investigations through a numerical study of a time-developing wake. A numerical study has the advantage of eliminating many of the uncontrolled factors present in experiments and allowing precise control of initial conditions. Large-eddy simulations employing the recently developed dynamic localization model are used to extend previous results from direct numerical simulations. The large-eddy simulation results are compared to the direct numerical simulation database, wherever such comparisons are feasible, as a check of the method. Like the experiments, the large-eddy simulations suggest that non-unique self-similar states, characterized by different spreading rates and turbulent statistics, are possible and that they can be maintained for significant time periods. The study also demonstrates the predictive capability of the dynamic localization subgrid model.

  12. A Numerical Study of Self-Similarity in a Turbulent Plane Wake Using Large-Eddy Simulation

    NASA Technical Reports Server (NTRS)

    Ghosal, Sandip; Rogers, Michael M.

    1996-01-01

    Turbulent wakes are known to develop self-similarly sufficiently far downstream from obstacles that generate them. It has long been assumed that the spreading rate of the wake in the self-similar regime is independent of the details of the body generating the wake, being dependent only on the total drag (or momentum deficit). This assumption seems to be in contradiction with some recent experiments. In this study we attempt to complement these experimental investigations through a numerical study of a time-developing wake. A numerical study has the advantage of eliminating many of the uncontrolled factors present in experiments and allowing precise control of initial conditions. Large-eddy simulations employing the recently developed dynamic localization model are used to extend previous results from direct numerical simulations. The large-eddy simulation results are compared to the direct numerical simulation database, wherever such comparisons are feasible, as a check of the method. Like the experiments, the large-eddy simulations suggest that non-unique self-similar states, characterized by different spreading rates and turbulent statistics, are possible and that they can be maintained for significant time periods. The study also demonstrates the predictive capability of the dynamic localization subgrid model.

  13. Deviations from self-similarity in barchan form and flux: The case of the Salton Sea dunes, California

    NASA Astrophysics Data System (ADS)

    Pelletier, Jon D.

    2013-12-01

    are the type of aeolian dune associated with a relatively uniform wind direction, incomplete sand coverage of the substrate, and low vegetation cover. Here I present an analysis of the morphology and migration rates of 40 dunes in the Salton Sea dune field using historical aerial orthophotographs, airborne laser swath mapping, terrestrial laser scanning, and measurements of the aerodynamic roughness length derived from wind velocity profiles. The data demonstrate that the Salton Sea dunes deviate from self-similarity such that smaller dunes have a lower ratio of slip face height to crest height and a lower slope, on average, compared with larger dunes and that smaller dunes migrate more slowly than would be predicted based on an inverse relationship between migration rate and dune height. The lack of self-similarity in barchans has been attributed to the dependence of speed-up ratios on dune size and the presence of a finite saturation length in the physics of aeolian transport. Here I argue that deviations from self-similarity at this study site are more likely due to the systematic decrease in aerodynamic roughness length with increasing elevation on stoss slopes. The data set I developed should prove useful to the aeolian geomorphic community for the further testing of models for barchan evolution.

  14. Self-similar analysis of fluid flow, heat, and mass transfer at orthogonal nanofluid impingement onto a flat surface

    NASA Astrophysics Data System (ADS)

    Avramenko, A. A.; Shevchuk, I. V.; Abdallah, S.; Blinov, D. G.; Tyrinov, A. I.

    2017-05-01

    Momentum, heat, and mass transfer in the vicinity of a stagnation point at uniform impingement of a nanofluid onto a flat plate were investigated. The novelty of the work consists in obtaining self-similar forms for the Hiemenz flow of a nanofluid and the self-similar representation of the velocity, thermal, and diffusion boundary layer equations derived on the basis of symmetry analysis using discrete symmetries. Momentum, energy, and concentration equations in the self-similar form were solved numerically. In frames of this analysis, functional dependence of the physical properties of nanofluids (viscosity, thermal conductivity, and diffusion coefficient) on concentration and temperature profiles was included as a part of the mathematical model, whose form enables including different models for the thermophysical properties of the nanofluid. Also novel are numerical results that revealed the influence of the nanoparticle concentration on the velocity, temperature, and concentration profiles, as well as on the normalized Nusselt numbers and surface friction coefficients illustrated in the form of analytical relations and graphically. The focus was put not only on modeling of heating of a colder wall by a hotter nanofluid but also on cooling of a hotter wall by a colder nanofluid. For the latter case, theoretical results were validated against experimental data available in the literature. Effects of various dimensionless parameters on the Nusselt number and surface friction coefficient were elucidated.

  15. Champagne flutes and brandy snifters: modelling protostellar outflow-cloud chemical interfaces

    NASA Astrophysics Data System (ADS)

    Rollins, R. P.; Rawlings, J. M. C.; Williams, D. A.; Redman, M. P.

    2014-10-01

    A rich variety of molecular species has now been observed towards hot cores in star-forming regions and in the interstellar medium. An increasing body of evidence from millimetre interferometers suggests that many of these form at the interfaces between protostellar outflows and their natal molecular clouds. However, current models have remained unable to explain the origin of the observational bias towards wide-angled `brandy snifter' shaped outflows over narrower `champagne flute' shapes in carbon monoxide imaging. Furthermore, these wide-angled systems exhibit unusually high abundances of the molecular ion HCO+. We present results from a chemodynamic model of such regions where a rich chemistry arises naturally as a result of turbulent mixing between cold, dense molecular gas and the hot, ionized outflow material. The injecta drives a rich and rapid ion-neutral chemistry in qualitative and quantitative agreement with the observations. The observational bias towards wide-angled outflows is explained naturally by the geometry-dependent ion injection rate causing rapid dissociation of CO in the younger systems.

  16. Statistically advanced, self-similar, radial probability density functions of atmospheric and under-expanded hydrogen jets

    NASA Astrophysics Data System (ADS)

    Ruggles, Adam J.

    2015-11-01

    This paper presents improved statistical insight regarding the self-similar scalar mixing process of atmospheric hydrogen jets and the downstream region of under-expanded hydrogen jets. Quantitative planar laser Rayleigh scattering imaging is used to probe both jets. The self-similarity of statistical moments up to the sixth order (beyond the literature established second order) is documented in both cases. This is achieved using a novel self-similar normalization method that facilitated a degree of statistical convergence that is typically limited to continuous, point-based measurements. This demonstrates that image-based measurements of a limited number of samples can be used for self-similar scalar mixing studies. Both jets exhibit the same radial trends of these moments demonstrating that advanced atmospheric self-similarity can be applied in the analysis of under-expanded jets. Self-similar histograms away from the centerline are shown to be the combination of two distributions. The first is attributed to turbulent mixing. The second, a symmetric Poisson-type distribution centered on zero mass fraction, progressively becomes the dominant and eventually sole distribution at the edge of the jet. This distribution is attributed to shot noise-affected pure air measurements, rather than a diffusive superlayer at the jet boundary. This conclusion is reached after a rigorous measurement uncertainty analysis and inspection of pure air data collected with each hydrogen data set. A threshold based upon the measurement noise analysis is used to separate the turbulent and pure air data, and thusly estimate intermittency. Beta-distributions (four parameters) are used to accurately represent the turbulent distribution moments. This combination of measured intermittency and four-parameter beta-distributions constitutes a new, simple approach to model scalar mixing. Comparisons between global moments from the data and moments calculated using the proposed model show excellent

  17. Innate immunity in the pathogenesis of polytropic retrovirus infection in the central nervous system.

    PubMed

    Peterson, Karin E; Du, Min

    2009-01-01

    Neuroinflammation, including astrogliosis, microgliosis, and the production of proinflammatory cytokines and chemokines is a common response in the central nervous system (CNS) to virus infection, including retrovirus infection. However, the contribution of this innate immune response in disease pathogenesis remains unresolved. Analysis of the neuroinflammatory response to polytropic retrovirus infection in the mouse has provided insight into the potential contribution of the innate immune response to retrovirus-induced neurologic disease. In this model, retroviral pathogenesis correlates with the induction of neuroinflammatory responses including the activation of astrocytes and microglia, as well as the production of proinflammatory cytokines and chemokines. Studies of the neurovirulent determinants of the polytropic envelope protein as well as studies with knockout mice suggest that retroviral pathogenesis in the brain is multifaceted and that cytokine and chemokine production may be only one mechanism of disease pathogenesis. Analysis of the activation of the innate immune response to retrovirus infection in the CNS indicates that toll-like receptor 7 (TLR7) is a contributing factor to retrovirus-induced neuroinflammation, but that other factors can compensate for the lack of TLR7 in inducing both neuroinflammation and neurologic disease.

  18. GRMHD Simulations of Binary Neutron Star Mergers with Piecewise Polytropic Equations of State

    NASA Astrophysics Data System (ADS)

    Giacomazzo, Bruno

    2015-04-01

    We present new results of fully general relativistic magnetohydrodynamic (GRMHD) simulations of binary neutron star (BNS) mergers performed with the Whisky code. Our new simulations consider both equal and unequal-mass systems and describe the NS matter via piecewise polytropic equations of state (EOSs). BNS mergers are powerful sources of gravitational waves (GWs) that can be detected by ground based detectors, such as advanced Virgo and LIGO, and they are also thought to be behind the central engine powering short gamma-ray bursts. In our simulations we therefore focus both on the GW emission and on the dynamics of matter and magnetic fields, both in the case a black hole is promptly formed and in the case of the formation of a long-lived magnetized NS. Since the EOS has an important role in both GW emission and matter dynamics, our simulations employ piecewise polytropic EOSs composed by seven pieces, four for the low-density regions (including the crust) and three for the core, in order to more accurately match physically motivated EOSs. Thermal effects are also included in order to more properly describe the post-merger dynamics.

  19. Application of the BPES to Lane-Emden equations governing polytropic and isothermal gas spheres

    NASA Astrophysics Data System (ADS)

    Boubaker, K.; Van Gorder, Robert A.

    2012-08-01

    We apply the Boubaker Polynomials Expansion Scheme (BPES) in order to obtain analytical-numerical solutions to two separate Lane-Emden problems: the Lane-Emden initial value problem of the first kind (describing the gravitational potential of a self-gravitating spherically symmetric polytropic gas), the Lane-Emden initial value problem of the second kind (describing isothermal gas spheres embedded in a pressurized medium at the maximum possible mass allowing for hydrostatic equilibrium). Both types of problems are simultaneously singular and nonlinear, and hence can be challenging to solve either numerically or analytically. We find that the BPES allows us to compute numerical solutions to both types of problems, and an error analysis demonstrates the accuracy of the method. In all cases, we demonstrate that relative error can be controlled to less than 1%. Furthermore, we compare our results to those of Hunter (2001). [Hunter, C., 2001. Series solutions for polytropes and the isothermal sphere. Monthly Notices of the Royal Astronomical Society, 328 839-847] and Mirza (2009). Approximate analytical solutions of the Lane-Emden equation for a self-gravitating isothermal gas sphere. Monthly Notices of the Royal Astronomical Society, 395 2288-2291. in order to demonstrate the accuracy of our method.

  20. Decay of passive scalars under the action of single scale smooth velocity fields in bounded two-dimensional domains: from non-self-similar probability distribution functions to self-similar eigenmodes.

    PubMed

    Sukhatme, Jai; Pierrehumbert, Raymond T

    2002-11-01

    We examine the decay of passive scalars with small, but nonzero, diffusivity in bounded two-dimensional (2D) domains. The velocity fields responsible for advection are smooth (i.e., they have bounded gradients) and of a single large scale. Moreover, the scale of the velocity field is taken to be similar to the size of the entire domain. The importance of the initial scale of variation of the scalar field with respect to that of the velocity field is strongly emphasized. If these scales are comparable and the velocity field is time periodic, we see the formation of a periodic scalar eigenmode. The eigenmode is numerically realized by means of a deterministic 2D map on a lattice. Analytical justification for the eigenmode is available from theorems in the dynamo literature. Weakening the notion of an eigenmode to mean statistical stationarity, we provide numerical evidence that the eigenmode solution also holds for aperiodic flows (represented by random maps). Turning to the evolution of an initially small scale scalar field, we demonstrate the transition from an evolving (i.e., non-self-similar) probability distribution function (pdf) to a stationary (self-similar) pdf as the scale of variation of the scalar field progresses from being small to being comparable to that of the velocity field (and of the domain). Furthermore, the non-self-similar regime itself consists of two stages. Both stages are examined and the coupling between diffusion and the distribution of the finite time Lyapunov exponents is shown to be responsible for the pdf evolution.

  1. MDCT-based quantification of porcine pulmonary arterial morphometry and self-similarity of arterial branching geometry

    PubMed Central

    Lee, Yik Ching; Clark, Alys R.; Fuld, Matthew K.; Haynes, Susan; Divekar, Abhay A.; Hoffman, Eric A.

    2013-01-01

    The pig is frequently used as an experimental model for studies of the pulmonary circulation, yet the branching and dimensional geometry of the porcine pulmonary vasculature remains poorly defined. The purposes of this study are to improve the geometric definition of the porcine pulmonary arteries and to determine whether the arterial tree exhibits self-similarity in its branching geometry. Five animals were imaged using thin slice spiral computed tomography in the prone posture during airway inflation pressure at 25 cmH2O. The luminal diameter and distance from the inlet of the left and right pulmonary arteries were measured along the left and right main arterial pathway in each lung of each animal. A further six minor pathways were measured in a single animal. The similarity in the rate of reduction of diameter with distance of all minor pathways and the two main pathways, along with similarity in the number of branches arising along the pathways, supports self-similarity in the arterial tree. The rate of reduction in diameter with distance from the inlet was not significantly different among the five animals (P > 0.48) when normalized for main pulmonary artery diameter and total main artery pathlength, which supports intersubject similarity. Other metrics to quantify the tree geometry are strikingly similar to those from airways of other quadrupeds, with the exception of a significantly larger length to diameter ratio, which is more appropriate for the vascular tree. A simplifying self-similar model for the porcine pulmonary arteries is proposed to capture the important geometric features of the arterial tree. PMID:23449941

  2. Horton laws for Hydraulic-Geometric variables and their scaling exponents in self-similar river networks

    NASA Astrophysics Data System (ADS)

    Gupta, V. K.; Mesa, O. J.

    2014-04-01

    An analytical theory is presented to predict Horton laws for five Hydraulic-Geometric (H-G) variables (stream discharge Q, width W, depth D, velocity U, slope S, and friction n'). The theory builds on the concept of dimensional analysis, and identifies six independent dimensionless River-Basin numbers. We consider self-similar Tokunaga networks and derive a mass conservation equation in the limit of large network order in terms of Horton bifurcation and discharge ratios. It is applied to obtain self-similar solutions of type-1 (SS-1), and predict Horton laws for width, depth and velocity as asymptotic relationships. Exponents of width and the Reynold's number are predicted. Assuming that SS-1 is valid for slope, depth and velocity, corresponding Horton laws and the H-G exponents are derived. The exponent values agree with that for the Optimal Channel Network (OCN) model, but do not agree with values from three field experiments. The deviations are substantial, suggesting that H-G in network does not obey optimality or SS-1. It fails because slope, a dimensionless River-Basin number, goes to 0 as network order increases, but, it cannot be eliminated from the asymptotic limit. Therefore, a generalization of SS-1, based in self-similar solutions of Type-2 (SS-2) is considered. It introduces two anomalous scaling exponents as free parameters, which enables us to show the existence of Horton laws for channel depth, velocity, slope and Manning's friction. The Manning's friction exponent, y, is predicted and tested against observed exponents from three field studies. We briefly sketch how the two anomalous scaling exponents could be estimated from the transport of suspended sediment load and the bed load. Statistical variability in the Horton laws for the H-G variables is also discussed. Both are important open problems for future research.

  3. Observation of self-similarity in the magnetic fields generated by the ablative nonlinear Rayleigh-Taylor instability.

    PubMed

    Gao, L; Nilson, P M; Igumenschev, I V; Fiksel, G; Yan, R; Davies, J R; Martinez, D; Smalyuk, V; Haines, M G; Blackman, E G; Froula, D H; Betti, R; Meyerhofer, D D

    2013-05-03

    Magnetic fields generated by the nonlinear Rayleigh-Taylor growth of laser-seeded three-dimensional broadband perturbations were measured in laser-accelerated planar targets using ultrafast proton radiography. The experimental data show self-similar behavior in the growing cellular magnetic field structures. These observations are consistent with a bubble competition and merger model that predicts the time evolution of the number and size of the bubbles, linking the cellular magnetic field structures with the Rayleigh-Taylor bubble and spike growth.

  4. Self-similar signature of the active solar corona within the inertial range of solar-wind turbulence.

    PubMed

    Kiyani, K; Chapman, S C; Hnat, B; Nicol, R M

    2007-05-25

    We quantify the scaling of magnetic energy density in the inertial range of solar-wind turbulence seen in situ at 1 AU with respect to solar activity. At solar maximum, when the coronal magnetic field is dynamic and topologically complex, we find self-similar scaling in the solar wind, whereas at solar minimum, when the coronal fields are more ordered, we find multifractality. This quantifies the solar-wind signature that is of direct coronal origin and distinguishes it from that of local MHD turbulence, with quantitative implications for coronal heating of the solar wind.

  5. A Comparison between Physics-based and Polytropic MHD Models for Stellar Coronae and Stellar Winds of Solar Analogs

    NASA Astrophysics Data System (ADS)

    Cohen, O.

    2017-02-01

    The development of the Zeeman–Doppler Imaging (ZDI) technique has provided synoptic observations of surface magnetic fields of low-mass stars. This led the stellar astrophysics community to adopt modeling techniques that have been used in solar physics using solar magnetograms. However, many of these techniques have been neglected by the solar community due to their failure to reproduce solar observations. Nevertheless, some of these techniques are still used to simulate the coronae and winds of solar analogs. Here we present a comparative study between two MHD models for the solar corona and solar wind. The first type of model is a polytropic wind model, and the second is the physics-based AWSOM model. We show that while the AWSOM model consistently reproduces many solar observations, the polytropic model fails to reproduce many of them, and in the cases where it does, its solutions are unphysical. Our recommendation is that polytropic models, which are used to estimate mass-loss rates and other parameters of solar analogs, must first be calibrated with solar observations. Alternatively, these models can be calibrated with models that capture more detailed physics of the solar corona (such as the AWSOM model) and that can reproduce solar observations in a consistent manner. Without such a calibration, the results of the polytropic models cannot be validated, but they can be wrongly used by others.

  6. Fungal adaptation to contemporary fungicide applications: the case of Botrytis cinerea populations from Champagne vineyards (France).

    PubMed

    Walker, A-S; Ravigne, V; Rieux, A; Ali, S; Carpentier, F; Fournier, E

    2017-04-01

    In addition to being one of the most acute problems impeding chemical control of fungal diseases, the evolution of fungicide resistance is an emblematic case of local adaptation to spatially heterogeneous and temporally variable selection pressures. Here we dissected the adaptation of Botrytis cinerea (the causal agent of grey mould) populations on grapes to several fungicides. We carried out a 2-year survey (four collection dates) on three treated/untreated pairs of plots from vineyards in Champagne (France) and monitored the frequency of four resistant phenotypes that are unambiguously associated with four distinct genotypes. For two loci under selection by currently used fungicides (MDR1 and MDR2), the frequencies of resistant mutations at vintage were greater in treated plots compared to untreated plots, showing that the effect of selection is detectable even at the plot scale. This effect was not detectable for two other loci under selection by previously used fungicides (BenR1 and ImiR1). We also found that treatment with currently used fungicides reduced B. cinerea effective population size, leading to a significant decrease in genic diversity and allelic richness in treated vs. untreated plots. We further highlight that even under ample drift and migration, fungal populations can present an efficient response to selection. Finally, for the four studied loci, the costs of fungicide resistance were estimated by modelling the decrease in the frequency of resistant mutations in the absence of treatment. We discuss the importance of these estimates for defining strategies for limiting or counteracting the local adaptation of pests to fungicides.

  7. CO2 volume fluxes outgassing from champagne glasses in tasting conditions: flute versus coupe.

    PubMed

    Liger-Belair, Gérard; Villaume, Sandra; Cilindre, Clara; Polidori, Guillaume; Jeandet, Philippe

    2009-06-10

    Measurements of CO(2) fluxes outgassing from glasses containing a standard Champagne wine initially holding about 11.5 g L(-1) of dissolved CO(2) were presented, in tasting conditions, during the first 10 min following the pouring process. Experiments were performed at room temperature, with a flute and a coupe, respectively. The progressive loss of dissolved CO(2) concentration with time was found to be significantly higher in the coupe than in the flute, which finally constitutes the first analytical proof that the flute prolongs the drink's chill and helps it to retain its effervescence in contrast with the coupe. Moreover, CO(2) volume fluxes outgassing from the coupe were found to be much higher in the coupe than in the flute in the early moments following pouring, whereas this tendency reverses from about 3 min after pouring. Correlations were proposed between CO(2) volume fluxes outgassing from the flute and the coupe and their continuously decreasing dissolved CO(2) concentration. The contribution of effervescence to the global kinetics of CO(2) release was discussed and modeled by use of results developed over recent years. Due to a much shallower liquid level in the coupe, bubbles collapsing at the free surface of the coupe were found to be significantly smaller than those collapsing at the free surface of the flute, and CO(2) volume fluxes released by collapsing bubbles only were found to be approximately 60% smaller in the coupe than in the flute. Finally, the contributions of gas discharge by invisible diffusion through the free surface areas of the flute and coupe were also approached and compared for each type of drinking vessel.

  8. The physics and chemistry behind the bubbling properties of champagne and sparkling wines: a state-of-the-art review.

    PubMed

    Liger-Belair, Gérard

    2005-04-20

    In this review, the latest results about the chemical physics behind the bubbling properties of Champagne and sparkling wines are collected and fully illustrated. The chemistry of carbon dioxide molecules dissolved into the liquid matrix (section 2) is presented, as are the three main steps of a fleeting bubble's life, that is, the bubble nucleation on tiny particles stuck on the glass wall (section 3), the bubble ascent and growth through the liquid matrix (section 4), and the bursting of bubbles at the liquid surface (section 5), which constitutes the most intriguing, functional, and visually appealing step.

  9. Self-gravitating rotating anisotropic pressure plasma in presence of Hall current and electrical resistivity using generalized polytrope laws

    SciTech Connect

    Prajapati, R. P.; Chhajlani, R. K.; Soni, G. D.

    2008-06-15

    The effects of uniform rotation, finite electrical resistivity, electron inertia, and Hall current on the self-gravitational instability of anisotropic pressure plasma with generalized polytrope laws have been studied. A general dispersion relation is obtained with the help of the relevant linearized perturbed magnetohydrodynamic (MHD) equations incorporating the relevant contributions of various effects of the problem using the method of normal mode analysis. The general dispersion relation is further reduced for the special cases of rotation; i.e., parallel and perpendicular to the direction of the magnetic field. The longitudinal and transverse modes of propagation are discussed separately for investigation of condition of instability. The effects of rotation, Hall current, finite electron inertia, and polytropic indices are discussed on the gravitational, ''firehose,'' and ''mirror'' instabilities. The numerical calculations have been performed to obtain the dependence of the growth rate of the gravitational unstable mode on the various physical parameters involved. The finite electrical resistivity, rotation, and Hall current have a stabilizing influence on the growth rate of the unstable mode of wave propagation. The finite electrical resistivity removes the effect of magnetic field and polytropic index from the condition of instability in the transverse mode of propagation for both the cases of rotation. It is also found that the Jeans criterion of gravitational instability depends upon rotation, electron inertia, and polytropic indices. In the case of transverse mode of propagation with the axis of rotation parallel to the magnetic field, it is observed that the region of instability and the value of the critical Jeans wavenumber are larger for the Chew-Goldberger-Low set of equations in comparison with the MHD set of equations. The stability of the system is discussed by applying Routh-Hurwitz criterion. The inclusion of rotation or Hall current or both

  10. Self-similar finite-time singularity formation in degenerate parabolic equations arising in thin-film flows

    NASA Astrophysics Data System (ADS)

    Dallaston, M. C.; Tseluiko, D.; Zheng, Z.; Fontelos, M. A.; Kalliadasis, S.

    2017-07-01

    A thin liquid film coating a planar horizontal substrate may be unstable to perturbations in the film thickness due to unfavourable intermolecular interactions between the liquid and the substrate, which may lead to finite-time rupture. The self-similar nature of the rupture has been studied before by utilising the standard lubrication approximation along with the Derjaguin (or disjoining) pressure formalism used to account for the intermolecular interactions, and a particular form of the disjoining pressure with exponent n  =  3 has been used, namely, \\Pi(h)\\propto -1/h3 , where h is the film thickness. In the present study, we use a numerical continuation method to compute discrete solutions to self-similar rupture for a general disjoining pressure exponent n (not necessarily equal to 3), which has not been previously performed. We focus on axisymmetric point-rupture solutions and show for the first time that pairs of solution branches merge as n decreases, starting at nc ≈ 1.485 . We verify that this observation also holds true for plane-symmetric line-rupture solutions for which the critical value turns out to be slightly larger than for the axisymmetric case, n_cplane≈ 1.499 . Computation of the full time-dependent problem also demonstrates the loss of stable similarity solutions and the subsequent onset of cascading, increasingly small structures.

  11. Enhanced Structural and Electrochemical Stability of Self-Similar Rice-Shaped SnO2 Nanoparticles.

    PubMed

    Pan, Du; Wan, Ning; Ren, Yong; Zhang, Weifeng; Lu, Xia; Wang, Yuesheng; Hu, Yong-Sheng; Bai, Ying

    2017-03-22

    A facile one-pot hydrothermal strategy is applied to prepare Co and F codoped SnO2 (Co-F/SnO2) nanoparticles, which exhibit a unique rice-shaped self-similar structure. Compared with the pristine and Co-doped counterparts (SnO2 and Co/SnO2), the Co-F/SnO2 electrode demonstrates higher capacity, better cyclability, and rate capability as anode material for lithium ion batteries (LIBs). A high charge capacity of 800 mAh g(-1) can be successfully delivered after 50 cycles at 0.1 C, and a high reversible capacity of 700 mAh g(-1) could be retained after 100 cycles at 5 C. The excellent lithium storage performances of the Co-F/SnO2 nanoparticles could be attributed to the synergetic effects of the doped Co and F, as well as the unique hierarchical self-similar structure with moderate oxygen defect and inactive pillars, which not only facilitates the fast diffusion of Li ions, but also stabilizes the structure during the electrochemical cycling.

  12. Analysis of Self Similar Scaling in Kinetic and Magnetic Energy Density as a Function of Distance From Sun

    NASA Astrophysics Data System (ADS)

    Banerjee, A.; Coplan, M. A.

    2009-12-01

    We analyze solar wind and interplanetary magnetic field data to study scaling properties of kinetic and magnetic energy density as a function of solar cycle and distance from the sun. In his original theory on turbulence, Kolmogorov predicted that in the inertial range the fluctuations in velocity differences should be self-similar. Analysis of solar wind data showed this not to be the case. On the other hand B. Hnat et.al.(Geophys. Res. Lett., 29 (10), 1446, 2002) and J.J Podesta (J. Geophys. Res., 111, A09105, 2006) showed that fluctuations in kinetic and magnetic energy density are approximately self-similar. We extend this analysis using data from the SWE and MFI experiments on the WIND spacecraft (at 1AU) during solar minimum (2006) and solar maximum (2001) and VHM/FGM experiment on the Ulysses spacecraft (1AU to 5AU). We calculate the cumulative distribution function (CDF) of the time delayed differences in kinetic and magnetic energy density and present a method through which the scaling exponent can be reliably calculated from the CDFs, instead of using structure functions which are very sensitive to large fluctuations. We compare the scaling exponents derived from the CDFs to the ones calculated from structure functions and study the rescaling properties of CDFs.

  13. Robustness of Estimators of Long-range Dependence and Self-Similarity for Non-Gaussian Datasets.

    NASA Astrophysics Data System (ADS)

    Watkins, N. W.; Franzke, C. L. E.; Graves, T.; Gramacy, R. B.; Hughes, C.

    2012-04-01

    Evidence for long-range dependence and non-Gaussianity is ubiquitous in many natural systems like ecosystems, biological systems and climate. However, it is not always appreciated that both phenomena frequently occur together in natural systems, and that self-similarity of a system can result from the superposition of both phenomena. These features, which are common in complex systems, impact the attribution of trends and the occurrence and clustering of extremes. The risk assessment of systems posessing these properties will lead to different outcomes (e.g. return periods) than the more common assumption of independence of extremes. We discuss two paradigmatic models which can simultaneously account for long-range dependence and non-Gaussianity: Autoregressive Fractional Integrated Moving Average (ARFIMA) and Linear Fractional Stable Motion (LFSM). The statistical properties of estimators for long-range dependence and self-similarity are critically assessed as applied to these models. It is seen that the most popular estimators are not robust. In particular, they can be biased in the presence of important features of many natural systems like annual cycles, trends and multiplicative noise. [Related paper in press, Phil. Trans. Roy. Soc. A; preprint at arXiv:1101.5018

  14. The Simple Map for a Single-null Divertor Tokamak: How to Look for Self-Similarity in Chaos

    NASA Astrophysics Data System (ADS)

    Nguyen, Christina; Ali, Halima; Punjabi, Alkesh

    2000-10-01

    The movement of magnetic field lines inside a single-null divertor tokamak can be described by the Simple Map^1. The Simple Map in the Poincaré Surface of Section is given by the equations: X_1=X_0-KY_0(1-Y_0) and Y_1=Y_0+KX_1. In these equations, K remains constant at 0.60. However, the values for X0 and Y0 are changed. These values are changed so that we can zoom into chaos. Chaos lies between the region (0,0.997) and (0,1). In chaos, there lies order. As we zoom into chaos, we again find chaos and order that looks like the original good surfaces and chaos. This phenomenon is called self-similarity. Self-similarity can occur for an infinite number of times if one magnifies into the chaotic region. For this work, we write a program in a computer language called Fortran 77 and Gnuplot. This work is supported by US DOE OFES. Ms. Christina Nguyen is a HU CFRT Summer Fusion High School Workshop Scholar from Andrew Hill High School in California. She is supported by NASA SHARP Plus Program. 1. Punjabi A, Verma A and Boozer A, Phys Rev Lett 69 3322 (1992) and J Plasma Phys 52 91 (1994)

  15. The dynamics of single protein molecules is non-equilibrium and self-similar over thirteen decades in time

    SciTech Connect

    Hu, Xiaohu; Hong, Liang; Smith, Micholas Dean; Neusius, Thomas; Cheng, Xiaolin; Smith, Jeremy C.

    2015-11-23

    Here, internal motions of proteins are essential to their function. The time dependence of protein structural fluctuations is highly complex, manifesting subdiffusive, non-exponential behavior with effective relaxation times existing over many decades in time, from ps up to ~102s (refs 1-4). Here, using molecular dynamics simulations, we show that, on timescales from 10–12 to 10–5s, motions in single proteins are self-similar, non-equilibrium and exhibit ageing. The characteristic relaxation time for a distance fluctuation, such as inter-domain motion, is observation-time-dependent, increasing in a simple, power-law fashion, arising from the fractal nature of the topology and geometry of the energy landscape explored. Diffusion over the energy landscape follows a non-ergodic continuous time random walk. Comparison with single-molecule experiments suggests that the non-equilibrium self-similar dynamical behavior persists up to timescales approaching the in vivo lifespan of individual protein molecules.

  16. The dynamics of single protein molecules is non-equilibrium and self-similar over thirteen decades in time

    DOE PAGES

    Hu, Xiaohu; Hong, Liang; Smith, Micholas Dean; ...

    2015-11-23

    Here, internal motions of proteins are essential to their function. The time dependence of protein structural fluctuations is highly complex, manifesting subdiffusive, non-exponential behavior with effective relaxation times existing over many decades in time, from ps up to ~102s (refs 1-4). Here, using molecular dynamics simulations, we show that, on timescales from 10–12 to 10–5s, motions in single proteins are self-similar, non-equilibrium and exhibit ageing. The characteristic relaxation time for a distance fluctuation, such as inter-domain motion, is observation-time-dependent, increasing in a simple, power-law fashion, arising from the fractal nature of the topology and geometry of the energy landscape explored.more » Diffusion over the energy landscape follows a non-ergodic continuous time random walk. Comparison with single-molecule experiments suggests that the non-equilibrium self-similar dynamical behavior persists up to timescales approaching the in vivo lifespan of individual protein molecules.« less

  17. A further study on Palatini f(R)-theories for polytropic stars

    SciTech Connect

    Mana, Annalisa; Fatibene, Lorenzo; Ferraris, Marco E-mail: lorenzo.fatibene@unito.it

    2015-10-01

    After briefly reviewing the results about polytropic stars in Palatini f(R)-theories, we first show how these results rely on the assumption of a regular function f(R). In particular, singular models allow to extend the parameter interval in which no singularity is formed. Furthermore, we show how the conformal metric can be matched smoothly in the cases where the original metric generates a singularity. In fact, the singularity comes from a singular conformal factor which is continuous though not differentiable at the stellar surface. This suggests that the correct metric to be considered as physical is the conformal metric.This is relevant because, even when matching the original metric is possible, the use of the conformal metric generates different stellar models.

  18. Frequencies of Nonaxisymmetric F-Modes in Rapidly Rotating Polytropes in Full General Relativity

    NASA Astrophysics Data System (ADS)

    Zink, Burkhard; Stergioulas, Nikolaos; Korobkin, Oleg; Schnetter, Erik; Diener, Peter; Tiglio, Manuel

    The computation of frequencies of nonaxisymmetric f-modes in rapidly rotating stars in full general relativity is a long-standing problem that has not been solved, to date, without resorting to some approximation, such as the slow-rotation approximation or the Cowling approximation. We present the first computation of such frequencies in full general relativity and rapid rotation, without any such approximation. We achieve this by using long-term simulations of oscillating polytropic models with a nonlinear numerical code, where spacetime is evolved in the harmonic formulation. We compare our results to previous results for zero-frequency (neutral modes) that were obtained with a perturbative method, and comment on the relevance of our work to the gravitational-radiation-driven (CFS) secular instability of nonaxisymmetric f-modes.

  19. The density structure and star formation rate of non-isothermal polytropic turbulence

    NASA Astrophysics Data System (ADS)

    Federrath, Christoph; Banerjee, Supratik

    2015-04-01

    The interstellar medium of galaxies is governed by supersonic turbulence, which likely controls the star formation rate (SFR) and the initial mass function (IMF). Interstellar turbulence is non-universal, with a wide range of Mach numbers, magnetic fields strengths and driving mechanisms. Although some of these parameters were explored, most previous works assumed that the gas is isothermal. However, we know that cold molecular clouds form out of the warm atomic medium, with the gas passing through chemical and thermodynamic phases that are not isothermal. Here we determine the role of temperature variations by modelling non-isothermal turbulence with a polytropic equation of state (EOS), where pressure and temperature are functions of gas density, P˜ ρ ^Γ, T ˜ ρΓ - 1. We use grid resolutions of 20483 cells and compare polytropic exponents Γ = 0.7 (soft EOS), Γ = 1 (isothermal EOS) and Γ = 5/3 (stiff EOS). We find a complex network of non-isothermal filaments with more small-scale fragmentation occurring for Γ < 1, while Γ > 1 smoothes out density contrasts. The density probability distribution function (PDF) is significantly affected by temperature variations, with a power-law tail developing at low densities for Γ > 1. In contrast, the PDF becomes closer to a lognormal distribution for Γ ≲ 1. We derive and test a new density variance-Mach number relation that takes Γ into account. This new relation is relevant for theoretical models of the SFR and IMF, because it determines the dense gas mass fraction of a cloud, from which stars form. We derive the SFR as a function of Γ and find that it decreases by a factor of ˜5 from Γ = 0.7 to 5/3.

  20. Tidal deformability and I-Love-Q relations for gravastars with polytropic thin shells

    NASA Astrophysics Data System (ADS)

    Uchikata, Nami; Yoshida, Shijun; Pani, Paolo

    2016-09-01

    The moment of inertia, the spin-induced quadrupole moment, and the tidal Love number of neutron-star and quark-star models are related through some relations which depend only mildly on the stellar equation of state. These "I-Love-Q" relations have important implications for astrophysics and gravitational-wave astronomy. An interesting problem is whether similar relations hold for other compact objects and how they approach the black hole limit. To answer these questions, here we investigate the deformation properties of a large class of thin-shell gravastars, which are exotic compact objects that do not possess an event horizon nor a spacetime singularity. Working in a small-spin and small-tidal field expansion, we calculate the moment of inertia, the quadrupole moment, and the (quadrupolar electric) tidal Love number of gravastars with a polytropic thin shell. The I-Love-Q relations of a thin-shell gravastar are drastically different from those of an ordinary neutron star. The Love number and quadrupole moment for less compact models have the opposite sign relative to those of ordinary neutron stars, and the I-Love-Q relations continuously approach the black hole limit. We consider a variety of polytropic equations of state for the matter shell and find no universality in the I-Love-Q relations. However, we cannot deny the possibility that, similarly to the neutron-star case, an approximate universality might emerge for a limited class of equations of state. Finally, we discuss how a measurement of the tidal deformability from the gravitational-wave detection of a compact-binary inspiral can be used to constrain exotic compact objects like gravastars.

  1. Chemosensory characterization of Chardonnay and Pinot Noir base wines of Champagne. Two very different varieties for a common product.

    PubMed

    Herrero, Paula; Sáenz-Navajas, Pilar; Culleré, Laura; Ferreira, Vicente; Chatin, Amelie; Chaperon, Vincent; Litoux-Desrues, François; Escudero, Ana

    2016-09-15

    Five different methodologies were applied for the quantitative analysis of 86 volatile molecules in 32 Chardonnay and 30 Pinot Noir Champagne white base wines. Sensory characterization was carried out by descriptive analysis. Pinot Noir wines had more constitutive compounds while Chardonnay wines had more discriminant compounds. Only four compounds predominated in Chardonnay wines: 4-vinylphenol, guaiacol, sotolon and 4-methyl-4-mercapto-2-pentanone. Correlation studies and PLSR models were calculated with sensory and chemical variables. For Pinot Noir wines, they were not as revealing as for Chardonnay base wines. Sulfur-related compounds were suggested to be involved in tropical fruit, dried fruit and citric sensory notes. This family of compounds seemed to be responsible for discriminant sensory terms in Champagne base wines. Fermentative compounds (aromatic buffer) were found at significantly higher levels in Pinot Noir wines, which would explain the fact that these wines were more difficult to describe in comparison with Chardonnay base wines. Copyright © 2016 Elsevier Ltd. All rights reserved.

  2. Self-similar clustering distribution of structural features on Ascraeus Mons (Mars): implications for magma chamber depth

    NASA Astrophysics Data System (ADS)

    Pozzobon, R.; Mazzarini, F.; Massironi, M.; Cremonese, G.

    2012-04-01

    The occurrence and spatial distribution of monogenic eruptive structures within volcanic areas are linked to fracture systems and associated stress fields. Moreover, they testify the presence of deep crustal or subcrustal magma reservoirs directly connected to the surface by a percolating fracture network. The correlation between vent distribution and fracture network properties (the so called backbone) can thus be studied in terms of self-similar (fractal) clustering. Self-similarity in vent distribution is described by a power law distribution with fractal exponent D and defined over a range of lengths (l) comprised between a lower limit (lower cutoff, Lco) and an upper limit (upper cutoff, Uco). The upper cutoff (Uco) for fractal clustering was compared with the respective crustal thickness obtained by existing independent geophysical data in the East African Rift System (Mazzarini and Isola, 2010). The computed Ucos for this sector well match the crustal thickness in these volcanic fields. More in detail this computational model verified the strong linear relationship existing between the upper cutoff of the power law distribution and the magma source depth. This method was thus applied to Ascraeus Mons on Mars, which displays basaltic magmatism and hundreds of collapse pits and vents around its flanks, giving a robust statistic to the calculations. Basing on a structural mapping performed on HRSC (High Resolution Stereo Camera onboard the ESA Mars Express mission) at 12 m/px and CTX (Context Camera, Mars Reconnaissance Orbiter mission) at 6 m/px mosaics, more than 2300 collapse pits and vents were analysed. Data analyses displayed a clustering in the structures distribution, showing two distinct populations. The obtained Uco values revealed the presence and the likely depth of both a deep big magma chamber and a small shallower chamber placed below the main caldera. Moreover, the resulting magma source depths are completely consistent and comparable with those

  3. Multidimensional Riemann problem with self-similar internal structure. Part II - Application to hyperbolic conservation laws on unstructured meshes

    NASA Astrophysics Data System (ADS)

    Balsara, Dinshaw S.; Dumbser, Michael

    2015-04-01

    Multidimensional Riemann solvers that have internal sub-structure in the strongly-interacting state have been formulated recently (D.S. Balsara (2012, 2014) [5,16]). Any multidimensional Riemann solver operates at the grid vertices and takes as its input all the states from its surrounding elements. It yields as its output an approximation of the strongly interacting state, as well as the numerical fluxes. The multidimensional Riemann problem produces a self-similar strongly-interacting state which is the result of several one-dimensional Riemann problems interacting with each other. To compute this strongly interacting state and its higher order moments we propose the use of a Galerkin-type formulation to compute the strongly interacting state and its higher order moments in terms of similarity variables. The use of substructure in the Riemann problem reduces numerical dissipation and, therefore, allows a better preservation of flow structures, like contact and shear waves. In this second part of a series of papers we describe how this technique is extended to unstructured triangular meshes. All necessary details for a practical computer code implementation are discussed. In particular, we explicitly present all the issues related to computational geometry. Because these Riemann solvers are Multidimensional and have Self-similar strongly-Interacting states that are obtained by Consistency with the conservation law, we call them MuSIC Riemann solvers. (A video introduction to multidimensional Riemann solvers is available on http://www.elsevier.com/xml/linking-roles/text/html". The MuSIC framework is sufficiently general to handle general nonlinear systems of hyperbolic conservation laws in multiple space dimensions. It can also accommodate all self-similar one-dimensional Riemann solvers and subsequently produces a multidimensional version of the same. In this paper we focus on unstructured triangular meshes. As examples of different systems of conservation laws we

  4. Structural preferential attachment: Stochastic process for the growth of scale-free, modular, and self-similar systems

    NASA Astrophysics Data System (ADS)

    Hébert-Dufresne, Laurent; Allard, Antoine; Marceau, Vincent; Noël, Pierre-André; Dubé, Louis J.

    2012-02-01

    Many complex systems have been shown to share universal properties of organization, such as scale independence, modularity, and self-similarity. We borrow tools from statistical physics in order to study structural preferential attachment (SPA), a recently proposed growth principle for the emergence of the aforementioned properties. We study the corresponding stochastic process in terms of its time evolution, its asymptotic behavior, and the scaling properties of its statistical steady state. Moreover, approximations are introduced to facilitate the modeling of real systems, mainly complex networks, using SPA. Finally, we investigate a particular behavior observed in the stochastic process, the peloton dynamics, and show how it predicts some features of real growing systems using prose samples as an example.

  5. MICRO-SIGMOIDS AS PROGENITORS OF CORONAL JETS: IS ERUPTIVE ACTIVITY SELF-SIMILARLY MULTI-SCALED?

    SciTech Connect

    Raouafi, N.-E.; Rust, D. M.; Bernasconi, P. N.; Georgoulis, M. K.

    2010-08-01

    Observations from the X-ray telescope (XRT) on Hinode are used to study the nature of X-ray-bright points, sources of coronal jets. Several jet events in the coronal holes are found to erupt from small-scale, S-shaped bright regions. This finding suggests that coronal micro-sigmoids may well be progenitors of coronal jets. Moreover, the presence of these structures may explain numerous observed characteristics of jets such as helical structures, apparent transverse motions, and shapes. Analogous to large-scale sigmoids giving rise to coronal mass ejections (CMEs), a promising future task would perhaps be to investigate whether solar eruptive activity, from coronal jets to CMEs, is self-similar in terms of properties and instability mechanisms.

  6. Scaling relations for a needle-like electron beam plasma from the self-similar behavior in beam propagation

    NASA Astrophysics Data System (ADS)

    Bai, Xiaoyan; Chen, Chen; Li, Hong; Liu, Wandong; Chen, Wei

    2017-10-01

    Scaling relations of the main parameters of a needle-like electron beam plasma (EBP) to the initial beam energy, beam current, and discharge pressures are presented. The relations characterize the main features of the plasma in three parameter space and can provide great convenience in plasma design with electron beams. First, starting from the self-similar behavior of electron beam propagation, energy and charge depositions in beam propagation were expressed analytically as functions of the three parameters. Second, according to the complete coupled theoretical model of an EBP and appropriate assumptions, independent equations controlling the density and space charges were derived. Analytical expressions for the density and charges versus functions of energy and charge depositions were obtained. Finally, with the combination of the expressions derived in the above two steps, scaling relations of the density and potential to the three parameters were constructed. Meanwhile, numerical simulations were used to test part of the scaling relations.

  7. Testing the Self-Similarity Exponent to Feature Extraction in Motor Imagery Based Brain Computer Interface Systems

    NASA Astrophysics Data System (ADS)

    Rodríguez-Bermúdez, Germán; Sánchez-Granero, Miguel Ángel; García-Laencina, Pedro J.; Fernández-Martínez, Manuel; Serna, José; Roca-Dorda, Joaquín

    2015-12-01

    A Brain Computer Interface (BCI) system is a tool not requiring any muscle action to transmit information. Acquisition, preprocessing, feature extraction (FE), and classification of electroencephalograph (EEG) signals constitute the main steps of a motor imagery BCI. Among them, FE becomes crucial for BCI, since the underlying EEG knowledge must be properly extracted into a feature vector. Linear approaches have been widely applied to FE in BCI, whereas nonlinear tools are not so common in literature. Thus, the main goal of this paper is to check whether some Hurst exponent and fractal dimension based estimators become valid indicators to FE in motor imagery BCI. The final results obtained were not optimal as expected, which may be due to the fact that the nature of the analyzed EEG signals in these motor imagery tasks were not self-similar enough.

  8. Gauge invariant perturbations of self-similar Lemaitre-Tolman-Bondi spacetime: Even parity modes with l{>=}2

    SciTech Connect

    Waters, Thomas J.; Nolan, Brien C.

    2009-04-15

    In this paper we consider gauge invariant linear perturbations of the metric and matter tensors describing the self-similar Lemaitre-Tolman-Bondi (timelike dust) spacetime containing a naked singularity. We decompose the angular part of the perturbation in terms of spherical harmonics and perform a Mellin transform to reduce the perturbation equations to a set of ordinary differential equations with singular points. We fix initial data so the perturbation is finite on the axis and the past null cone of the singularity, and follow the perturbation modes up to the Cauchy horizon. There we argue that certain scalars formed from the modes of the perturbation remain finite, indicating linear stability of the Cauchy horizon.

  9. Horton laws for hydraulic-geometric variables and their scaling exponents in self-similar Tokunaga river networks

    NASA Astrophysics Data System (ADS)

    Gupta, V. K.; Mesa, O. J.

    2014-09-01

    An analytical theory is developed that obtains Horton laws for six hydraulic-geometric (H-G) variables (stream discharge Q, width W, depth D, velocity U, slope S, and friction n') in self-similar Tokunaga networks in the limit of a large network order. The theory uses several disjoint theoretical concepts like Horton laws of stream numbers and areas as asymptotic relations in Tokunaga networks, dimensional analysis, the Buckingham Pi theorem, asymptotic self-similarity of the first kind, or SS-1, and asymptotic self-similarity of the second kind, or SS-2. A self-contained review of these concepts, with examples, is given as "methods". The H-G data sets in channel networks from three published studies and one unpublished study are summarized to test theoretical predictions. The theory builds on six independent dimensionless river-basin numbers. A mass conservation equation in terms of Horton bifurcation and discharge ratios in Tokunaga networks is derived. Assuming that the H-G variables are homogeneous and self-similar functions of stream discharge, it is shown that the functions are of a power law form. SS-1 is applied to predict the Horton laws for width, depth and velocity as asymptotic relationships. Exponents of width and the Reynolds number are predicted and tested against three field data sets. One basin shows deviations from theoretical predictions. Tentatively assuming that SS-1 is valid for slope, depth and velocity, corresponding Horton laws and the H-G exponents are derived. Our predictions of the exponents are the same as those previously predicted for the optimal channel network (OCN) model. In direct contrast to our work, the OCN model does not consider Horton laws for the H-G variables, and uses optimality assumptions. The predicted exponents deviate substantially from the values obtained from three field studies, which suggests that H-G in networks does not obey SS-1. It fails because slope, a dimensionless river-basin number, goes to 0 as network

  10. Semirational and symbiotic self-similar rogue waves in a (2+1)-dimensional graded-index waveguide

    NASA Astrophysics Data System (ADS)

    De, Kanchan Kumar; Soloman Raju, Thokala; Kumar, C. N.; Panigrahi, Prasanta K.

    2016-07-01

    We have investigated the (?)-dimensional variable coefficient-coupled nonlinear Schrödinger equation (vc-CNLSE) in a graded-index waveguide. Similarity transformations are used to convert the vc-CNLSE into constant coefficient CNLSE. Under certain functional constraints we could extract semirational, multi-parametric solution of the associated Manakov system. This family of solutions include known Peregrine soliton, mixture of either bright soliton and rogue wave or dark soliton and rogue wave or breather and rogue wave. Under a distinct set of self-phase modulation and cross-phase modulation coefficients we could establish symbiotic existence of different soliton pairs as solutions. These soliton pairs may constitute of one bright and a dark soliton, two bright solitons or two dark solitons. Finally, when two wave components are directly proportional, we find bright and dark similaritons, self-similar breathers, and rogue waves as different solutions.

  11. Probing multi-scale self-similarity of tissue structures using light scattering spectroscopy: prospects in pre-cancer detection

    NASA Astrophysics Data System (ADS)

    Chatterjee, Subhasri; Das, Nandan K.; Kumar, Satish; Mohapatra, Sonali; Pradhan, Asima; Panigrahi, Prasanta K.; Ghosh, Nirmalya

    2013-02-01

    Multi-resolution analysis on the spatial refractive index inhomogeneities in the connective tissue regions of human cervix reveals clear signature of multifractality. We have thus developed an inverse analysis strategy for extraction and quantification of the multifractality of spatial refractive index fluctuations from the recorded light scattering signal. The method is based on Fourier domain pre-processing of light scattering data using Born approximation, and its subsequent analysis through Multifractal Detrended Fluctuation Analysis model. The method has been validated on several mono- and multi-fractal scattering objects whose self-similar properties are user controlled and known a-priori. Following successful validation, this approach has initially been explored for differentiating between different grades of precancerous human cervical tissues.

  12. MAGIICAT III. Interpreting Self-similarity of the Circumgalactic Medium with Virial Mass Using Mg II Absorption

    NASA Astrophysics Data System (ADS)

    Churchill, Christopher W.; Trujillo-Gomez, Sebastian; Nielsen, Nikole M.; Kacprzak, Glenn G.

    2013-12-01

    In Churchill et al., we used halo abundance matching applied to 182 galaxies in the Mg II Absorber-Galaxy Catalog (MAGIICAT) and showed that the mean Mg II λ2796 equivalent width follows a tight inverse-square power law, Wr (2796)vprop(D/R vir)-2, with projected location relative to the galaxy virial radius and that the Mg II absorption covering fraction is effectively invariant with galaxy virial mass, M h, over the range 10.7 <= log M h/M ⊙ <= 13.9. In this work, we explore multivariate relationships between Wr (2796), virial mass, impact parameter, virial radius, and the theoretical cooling radius that further elucidate self-similarity in the cool/warm (T = 104-104.5 K) circumgalactic medium (CGM) with virial mass. We show that virial mass determines the extent and strength of the Mg II absorbing gas such that the mean Wr (2796) increases with virial mass at fixed distance while decreasing with galactocentric distance for fixed virial mass. The majority of the absorbing gas resides within D ~= 0.3 R vir, independent of both virial mass and minimum absorption threshold; inside this region, and perhaps also in the region 0.3 < D/R vir <= 1, the mean Wr (2796) is independent of virial mass. Contrary to absorber-galaxy cross-correlation studies, we show there is no anti-correlation between Wr (2796) and virial mass. We discuss how simulations and theory constrained by observations support self-similarity of the cool/warm CGM via the physics governing star formation, gas-phase metal enrichment, recycling efficiency of galactic scale winds, filament and merger accretion, and overdensity of local environment as a function of virial mass.

  13. A two-dimensional Riemann solver with self-similar sub-structure - Alternative formulation based on least squares projection

    NASA Astrophysics Data System (ADS)

    Balsara, Dinshaw S.; Vides, Jeaniffer; Gurski, Katharine; Nkonga, Boniface; Dumbser, Michael; Garain, Sudip; Audit, Edouard

    2016-01-01

    Just as the quality of a one-dimensional approximate Riemann solver is improved by the inclusion of internal sub-structure, the quality of a multidimensional Riemann solver is also similarly improved. Such multidimensional Riemann problems arise when multiple states come together at the vertex of a mesh. The interaction of the resulting one-dimensional Riemann problems gives rise to a strongly-interacting state. We wish to endow this strongly-interacting state with physically-motivated sub-structure. The self-similar formulation of Balsara [16] proves especially useful for this purpose. While that work is based on a Galerkin projection, in this paper we present an analogous self-similar formulation that is based on a different interpretation. In the present formulation, we interpret the shock jumps at the boundary of the strongly-interacting state quite literally. The enforcement of the shock jump conditions is done with a least squares projection (Vides, Nkonga and Audit [67]). With that interpretation, we again show that the multidimensional Riemann solver can be endowed with sub-structure. However, we find that the most efficient implementation arises when we use a flux vector splitting and a least squares projection. An alternative formulation that is based on the full characteristic matrices is also presented. The multidimensional Riemann solvers that are demonstrated here use one-dimensional HLLC Riemann solvers as building blocks. Several stringent test problems drawn from hydrodynamics and MHD are presented to show that the method works. Results from structured and unstructured meshes demonstrate the versatility of our method. The reader is also invited to watch a video introduction to multidimensional Riemann solvers on http://www.nd.edu/ dbalsara/Numerical-PDE-Course.

  14. Self-similar Hierarchical Wrinkles as a Potential Multifunctional Smart Window with Simultaneously Tunable Transparency, Structural Color, and Droplet Transport.

    PubMed

    Lin, Gaojian; Chandrasekaran, Prashant; Lv, Cunjing; Zhang, Qiuting; Tang, Yichao; Han, Lin; Yin, Jie

    2017-08-09

    Smart window has immense potential for energy savings in architectural and vehicular applications, while most studies focus on the tunability of a single property of optical transmittance. Here we explore harnessing dynamically tunable hierarchical wrinkles for design of a potential multifunctional smart window with combined structural color and water droplet transport control. The self-similar hierarchical wrinkles with both nanoscale and microscale features are generated on a prestrained poly(dimethylsiloxane) elastomer through sequential strain release and multistep oxygen plasma treatment. We show that the hierarchically wrinkled elastomer displays both opaqueness and iridescent structural color. We find that restretching/releasing the elastomer leads to the reversible and repeatable switch from opaqueness to transparency, arising from the flattening of large wrinkles (micrometer scale), while a nonvanishing structural color occurs due to the nondisappearing small wrinkles (nanoscale). The unique features of combined reversible large wrinkles and irreversible small wrinkles during hierarchical wrinkling are well reproduced by corresponding finite element simulation. The criteria for generating self-similar hierarchical wrinkles is revealed through a simplified theoretical model and validated by experiments. In addition to its tunable optical property, we further show its ability in control of water droplet transport on demand through mechanical stretching and release. We find that an initially pinned water droplet on the tilted hierarchically wrinkled surface starts to slide when the surface is stretched, and becomes pinned again upon strain release. Such a process is reversible and repeatable. The hierarchically wrinkled surface could find broad potential applications not only in multifunctional smart windows with additional features of aesthetics and water collection, but in microfluidics, design of slippery surfaces, and directional water transportation.

  15. Using self-similarity compensation for improving inter-layer prediction in scalable 3D holoscopic video coding

    NASA Astrophysics Data System (ADS)

    Conti, Caroline; Nunes, Paulo; Ducla Soares, Luís.

    2013-09-01

    Holoscopic imaging, also known as integral imaging, has been recently attracting the attention of the research community, as a promising glassless 3D technology due to its ability to create a more realistic depth illusion than the current stereoscopic or multiview solutions. However, in order to gradually introduce this technology into the consumer market and to efficiently deliver 3D holoscopic content to end-users, backward compatibility with legacy displays is essential. Consequently, to enable 3D holoscopic content to be delivered and presented on legacy displays, a display scalable 3D holoscopic coding approach is required. Hence, this paper presents a display scalable architecture for 3D holoscopic video coding with a three-layer approach, where each layer represents a different level of display scalability: Layer 0 - a single 2D view; Layer 1 - 3D stereo or multiview; and Layer 2 - the full 3D holoscopic content. In this context, a prediction method is proposed, which combines inter-layer prediction, aiming to exploit the existing redundancy between the multiview and the 3D holoscopic layers, with self-similarity compensated prediction (previously proposed by the authors for non-scalable 3D holoscopic video coding), aiming to exploit the spatial redundancy inherent to the 3D holoscopic enhancement layer. Experimental results show that the proposed combined prediction can improve significantly the rate-distortion performance of scalable 3D holoscopic video coding with respect to the authors' previously proposed solutions, where only inter-layer or only self-similarity prediction is used.

  16. Unraveling the evolving nature of gaseous and dissolved carbon dioxide in champagne wines: a state-of-the-art review, from the bottle to the tasting glass.

    PubMed

    Liger-Belair, Gérard; Polidori, Guillaume; Zéninari, Virginie

    2012-06-30

    In champagne and sparkling wine tasting, the concentration of dissolved CO(2) is indeed an analytical parameter of high importance since it directly impacts the four following sensory properties: (i) the frequency of bubble formation in the glass, (ii) the growth rate of rising bubbles, (iii) the mouth feel, and (iv) the nose of champagne, i.e., its so-called bouquet. In this state-of-the-art review, the evolving nature of the dissolved and gaseous CO(2) found in champagne wines is evidenced, from the bottle to the glass, through various analytical techniques. Results obtained concerning various steps where the CO(2) molecule plays a role (from its ingestion in the liquid phase during the fermentation process to its progressive release in the headspace above the tasting glass) are gathered and synthesized to propose a self-consistent and global overview of how gaseous and dissolved CO(2) impact champagne and sparkling wine science. Copyright © 2011 Elsevier B.V. All rights reserved.

  17. An empirical polytrope law for solar wind thermal electrons between 0.45 and 4.76 AU: Voyager 2 and Mariner 10

    NASA Technical Reports Server (NTRS)

    Sittler, E. C., Jr.; Scudder, J. D.

    1979-01-01

    Empirical evidence is presented that solar wind thermal electrons obey a polytrope law with polytrope index gamma = 1.175 plus or minus 0.03. The Voyager 2 and Mariner 10 data used as evidence are compared and discussed. The theoretical predictions that solar wind thermal electrons in the asymptotic solar wind should obey a polytrope law with polytrope index gamma = 1.16 plus or minus. The widespread impressions in the literature that solar wind electrons behave more like an isothermal than adiabatic gas, and the arguments that Coulomb collisions are the dominant stochastic process shaping observed electron distribution functions in the solar wind are reexamined, reviewed and evaluated. The assignment of the interplanetary potential as equal to approximately seven times the temperature of the thermal electrons is discussed.

  18. Gravitational instability of polytropic spheres containing region of trapped null geodesics: a possible explanation of central supermassive black holes in galactic halos

    NASA Astrophysics Data System (ADS)

    Stuchlík, Zdeněk; Schee, Jan; Toshmatov, Bobir; Hladík, Jan; Novotný, Jan

    2017-06-01

    We study behaviour of gravitational waves in the recently introduced general relativistic polytropic spheres containing a region of trapped null geodesics extended around radius of the stable null circular geodesic that can exist for the polytropic index N > 2.138 and the relativistic parameter, giving ratio of the central pressure pc to the central energy density ρc, higher than σ = 0.677. In the trapping zones of such polytropes, the effective potential of the axial gravitational wave perturbations resembles those related to the ultracompact uniform density objects, giving thus similar long-lived axial gravitational modes. These long-lived linear perturbations are related to the stable circular null geodesic and due to additional non-linear phenomena could lead to conversion of the trapping zone to a black hole. We give in the eikonal limit examples of the long-lived gravitational modes, their oscillatory frequencies and slow damping rates, for the trapping zones of the polytropes with N in (2.138,4). However, in the trapping polytropes the long-lived damped modes exist only for very large values of the multipole number l > 50, while for smaller values of l the numerical calculations indicate existence of fast growing unstable axial gravitational modes. We demonstrate that for polytropes with N >= 3.78, the trapping region is by many orders smaller than extension of the polytrope, and the mass contained in the trapping zone is about 10-3 of the total mass of the polytrope. Therefore, the gravitational instability of such trapping zones could serve as a model explaining creation of central supermassive black holes in galactic halos or galaxy clusters.

  19. Investigation of the Polytropic Relationship Between Density and Temperature Within Interplanetary Coronal Mass Ejections Using Numerical Simulations

    NASA Technical Reports Server (NTRS)

    Riley, Pete; Gosling, J. T.; Pizzo, V. J.

    2001-01-01

    Single-point spacecraft measurements within coronal mass ejections (CMEs) often exhibit a negative correlation between electron density and temperature. At least two opposing interpretations have been suggested for this relationship. If, on one hand, these single spacecraft observations provide direct measures of the polytropic properties of the plasma, then they imply that the polytropic index for the electrons gamma(sub e) is often < 1. Moreover, since the electrons carry the bulk of the pressure (via their significantly higher temperature), this further implies that the dynamics of CME evolution are dominated by an effective polytropic index gamma(sub e)ff < 1. On the other hand, gamma < 1 implies that as the ejecta propagate away from the Sun and expand, they also heat up; a result clearly at odds with in situ observations. In contrast to these CME intervals, many studies have shown that the quiescent solar wind exhibits a positive correlation between electron density and temperature, suggesting that gamma(sub e) > 1. In this study we simulate the evolution of a variety of CME-like disturbances in the solar wind using a one-dimensional, single-fluid model, to address the interpretation of the relationship between electron density and temperature within CMEs at fixed locations in space. Although we strictly impose a polytropic relationship (with gamma = constant) throughout our simulations, we demonstrate that a variety of correlations can exist between density and temperature at fixed points. Furthermore, we demonstrate that the presence of only local uncorrelated random fluctuations in density and temperature can produce a negative correlation. Consequently, we conclude that these single-point observations of negative correlations between electron density and temperature cannot be used to infer the value of gamma(sub e). Instead, we suggest that entropy variations, together with the plasma's tendency to achieve pressure balance with its surroundings, are

  20. Research Of Polytropic Exponent Changing For Influence Evaluation Of Actual Mixture Composition On Hydrocarbons Concentration Decreasing On Deep Throttling Operation

    NASA Astrophysics Data System (ADS)

    Smolenskaya, N. M.; Smolenskii, V. V.; Bobrovskij, I.

    2017-01-01

    The purpose of this article is to present study of polytropic exponent as rating of thermodynamic process in internal combustion motor operating to deep throttling in a subcase of idle running. It is necessary to consider the influence of hydrocarbon part in exhaust gases in a process of development a new internal combustion engines especially on deep throttling operation: on combustion procedure, on irregularity of exhaust gases composition.