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.
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.
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.
Self-similar dynamics of a relativistically hot gas
NASA Astrophysics Data System (ADS)
Lou, Yu-Qing; Cao, Yi
2008-02-01
In the presence of self-gravity, we investigate the self-similar dynamics of a relativistically hot gas with or without shocks in astrophysical processes of stellar core collapse, formation of compact objects, and supernova remnants with central voids. The model system is taken to be spherically symmetric and the conservation of specific entropy along streamlines is adopted for a relativistic hot gas whose energy-momentum relation is expressed approximately by with ɛ and being the energy and momentum of a particle and c being the speed of light. In terms of equation of state, this leads to a polytropic index γ = 4/3. The conventional polytropic gas of P = κργ, where P is the thermal pressure, ρ is the mass density, γ is the polytropic index and κ is a global constant, is included in our theoretical model framework. Two qualitatively different solution classes arise according to the values of a simple power-law scaling index a, each of which is analysed separately and systematically. With explicit conditions, all sonic critical lines appear straight. We obtain new asymptotic solutions that exist only for γ = 4/3. Global and asymptotic solutions in various limits as well as eigensolutions across sonic critical lines are derived analytically and numerically with or without shocks. By specific entropy conservation along streamlines, we extend the analysis of Goldreich & Weber for a distribution of variable specific entropy with time t and radius r and discuss consequences in the context of a homologous core collapse prior to supernovae. As an alternative rebound shock model, we construct an Einstein-de Sitter explosion with shock connections with various outer flows including a static outer part of a singular polytropic sphere. Under the joint action of thermal pressure and self-gravity, we can also construct self-similar solutions with central spherical voids with sharp density variations along their edges.
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.
Self-similar aftershock rates.
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. PMID:27627324
Self-similar aftershock rates.
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.
Self-similar flows in spherical geometry
NASA Astrophysics Data System (ADS)
Gerin-Roze, Jean
2007-06-01
If we are looking at the implosion of a sphere starting with a strong shock, the study of self-similar flows is a classical problem. We will assume that: - The sphere contains a perfect gas with a polytropic coefficient γ=5/3. - The shock follows the equation: rc=A(-t)^α with t0
Study of polytropes with generalized polytropic equation of state
NASA Astrophysics Data System (ADS)
Azam, M.; Mardan, S. A.; Noureen, I.; Rehman, M. A.
2016-06-01
The aim of this paper is to discuss the theory of Newtonian and relativistic polytropes with a generalized polytropic equation of state. For this purpose, we formulated the general framework to discuss the physical properties of polytropes with an anisotropic inner fluid distribution under conformally flat condition in the presence of charge. We investigate the stability of these polytropes in the vicinity of a generalized polytropic equation through the Tolman mass. It is concluded that one of the derived models is physically acceptable.
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…
Charged cylindrical polytropes with generalized polytropic equation of state
NASA Astrophysics Data System (ADS)
Azam, M.; Mardan, S. A.; Noureen, I.; Rehman, M. A.
2016-09-01
We study the general formalism of polytropes in the relativistic regime with generalized polytropic equations of state in the vicinity of cylindrical symmetry. We take a charged anisotropic fluid distribution of matter with a conformally flat condition for the development of a general framework of the polytropes. We discuss the stability of the model by the Whittaker formula and conclude that one of the models developed is physically viable.
NASA Astrophysics Data System (ADS)
Pesnell, W. Dean
2016-03-01
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.
General polytropic Larson-Penston-type collapses
NASA Astrophysics Data System (ADS)
Lou, Yu-Qing; Shi, Chun-Hui
2014-12-01
We investigate self-similar hydrodynamics of a general polytropic (GP) gas with spherical symmetry under self-gravity and extend the conventional polytropic (CP) relation n = 2 - γ for the self-similar index n and the polytropic index γ to a general relation n = 2(q + γ - 2)/(3q - 2), where q is a real parameter by specific entropy conservation along streamlines. We derive GP Larson-Penston (LP)-type solutions for q > 2/3 and γ > 4/3; Larson-Penston-Hunter (LPH)-type solutions are also constructed in a GP gas by a time-reversal operation on a GP-LP-type solution and by connecting to a GP free-fall-type solution across t = 0. These GP-LPH solutions describe dynamic processes that a GP gas globule, static and dense initially, undergoes a runaway collapse under self-gravity, forms a central mass singularity, and keeps accreting during a free-fall stage. We apply such GP-LPH-type solutions with variable envelope mass infall rates (EMIRs) for the dynamic evolution of globules and dense cores in star-forming molecular clouds. In particular, a GP-LPH-type solution can sustain an EMIR as low as 10-8 ˜ 10-6 M⊙ yr-1 or even lower - much lower than that of Shu's isothermal model for a cloud core in Class 0 and Class I phases. Such GP-LPH-type solutions with EMIRs as low as 10-9 ˜ 10-8 M⊙ yr-1 offer a sensible viable mechanism of forming brown dwarfs during the accretion stage in a collapsed GP globules with 1.495 ≤ γ ≤ 1.50 and 0.99 ≤ n ≤ 1.0. The GP-LPH solutions with 0.94 < n < 0.99 and 1.47 < γ < 1.495 can even give extremely low EMIRs of 10-12 ˜ 10-9 M⊙ yr-1 to form gaseous planet-type objects in mini gas globules.
Estimating the self-similar exponent of broad-sense self-similar processes
NASA Astrophysics Data System (ADS)
Zheng, Jing; Zhang, Guijun; Tong, Changqing
2016-02-01
In this paper, a new algorithm about the self-similar exponent of self-similar processes is introduced which is used to explore long memory in financial time series. This method can work for more general broad-sense self-similar processes. We prove that this algorithm performs much better than the classical methods.
A self-similar magnetohydrodynamic model for ball lightnings
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.
Self-similarity in Laplacian growth
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.
The baryonic self similarity of dark matter
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.
Universal self-similarity of propagating populations.
Eliazar, Iddo; Klafter, Joseph
2010-07-01
This paper explores the universal self-similarity of propagating populations. The following general propagation model is considered: particles are randomly emitted from the origin of a d-dimensional Euclidean space and propagate randomly and independently of each other in space; all particles share a statistically common--yet arbitrary--motion pattern; each particle has its own random propagation parameters--emission epoch, motion frequency, and motion amplitude. The universally self-similar statistics of the particles' displacements and first passage times (FPTs) are analyzed: statistics which are invariant with respect to the details of the displacement and FPT measurements and with respect to the particles' underlying motion pattern. Analysis concludes that the universally self-similar statistics are governed by Poisson processes with power-law intensities and by the Fréchet and Weibull extreme-value laws.
Universal self-similarity of propagating populations
NASA Astrophysics Data System (ADS)
Eliazar, Iddo; Klafter, Joseph
2010-07-01
This paper explores the universal self-similarity of propagating populations. The following general propagation model is considered: particles are randomly emitted from the origin of a d -dimensional Euclidean space and propagate randomly and independently of each other in space; all particles share a statistically common—yet arbitrary—motion pattern; each particle has its own random propagation parameters—emission epoch, motion frequency, and motion amplitude. The universally self-similar statistics of the particles’ displacements and first passage times (FPTs) are analyzed: statistics which are invariant with respect to the details of the displacement and FPT measurements and with respect to the particles’ underlying motion pattern. Analysis concludes that the universally self-similar statistics are governed by Poisson processes with power-law intensities and by the Fréchet and Weibull extreme-value laws.
Percolation in Self-Similar Networks
NASA Astrophysics Data System (ADS)
Serrano, M. Ángeles; Krioukov, Dmitri; Boguñá, Marián
2011-01-01
We provide a simple proof that graphs in a general class of self-similar networks have zero percolation threshold. The considered self-similar networks include random scale-free graphs with given expected node degrees and zero clustering, scale-free graphs with finite clustering and metric structure, growing scale-free networks, and many real networks. The proof and the derivation of the giant component size do not require the assumption that networks are treelike. Our results rely only on the observation that self-similar networks possess a hierarchy of nested subgraphs whose average degree grows with their depth in the hierarchy. We conjecture that this property is pivotal for percolation in networks.
Self-similar parabolic plasmonic beams.
Davoyan, Arthur R; Turitsyn, Sergei K; Kivshar, Yuri S
2013-02-15
We demonstrate that an interplay between diffraction and defocusing nonlinearity can support stable self-similar plasmonic waves with a parabolic profile. Simplicity of a parabolic shape combined with the corresponding parabolic spatial phase distribution creates opportunities for controllable manipulation of plasmons through a combined action of diffraction and nonlinearity.
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.
Self-similarity of complex networks.
Song, Chaoming; Havlin, Shlomo; Makse, Hernán A
2005-01-27
Complex networks have been studied extensively owing to their relevance to many real systems such as the world-wide web, the Internet, energy landscapes and biological and social networks. A large number of real networks are referred to as 'scale-free' because they show a power-law distribution of the number of links per node. However, it is widely believed that complex networks are not invariant or self-similar under a length-scale transformation. This conclusion originates from the 'small-world' property of these networks, which implies that the number of nodes increases exponentially with the 'diameter' of the network, rather than the power-law relation expected for a self-similar structure. Here we analyse a variety of real complex networks and find that, on the contrary, they consist of self-repeating patterns on all length scales. This result is achieved by the application of a renormalization procedure that coarse-grains the system into boxes containing nodes within a given 'size'. We identify a power-law relation between the number of boxes needed to cover the network and the size of the box, defining a finite self-similar exponent. These fundamental properties help to explain the scale-free nature of complex networks and suggest a common self-organization dynamics.
Self similar nonlocal electron heat flow
NASA Astrophysics Data System (ADS)
Matte, Jean-Pierre
2007-11-01
The well known self similar heat diffusion solutions of Zel'dovich and Raizer [1], for a heat wave advancing from a boundary at a fixed temperature or a fixed heat flux do not keep the ratio R of the scale length to the mean free path constant. Instead, R increases and the solution becomes increasingly valid because Spitzer-Harm [2] heat flow is increasingly applicable. A self similar solution exists which keeps R constant, if one assumes that the boundary heat flux increases in time. Similarly, for the problem of a uniform density plasma heated by a finite width laser beam, a self similar solution keeping R constant can be obtained by assuming that the beam intensity and width increase in time. Such solutions will be studied with the electron kinetic code FPI [3], and compared to simulations with more usual laser characteristics. [1] Ya. B. Zel'dovich and Yu. P. Raizer, ``Physics of Shock Waves '', Academic Press, New York, 1967. [2] L. Spitzer and R. Harm, Phys. Rev. 89, 977 (1953). [3] J.-P. Matte et al., Phys. Rev. Lett. 53, 1461 (1984) ; ibid 49, 1936 (1982).
CO2 volume fluxes outgassing from champagne glasses: the impact of champagne ageing.
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. PMID:20103140
CO2 volume fluxes outgassing from champagne glasses: the impact of champagne ageing.
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.
Statistical self-similarity of hotspot seamount volumes modeled as self-similar criticality
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.
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.
Self-similar Ultrarelativistic Jetted Blast Wave
NASA Astrophysics Data System (ADS)
Keshet, Uri; Kogan, Dani
2015-12-01
Following a suggestion that a directed relativistic explosion may have a universal intermediate asymptotic, we derive a self-similar solution for an ultrarelativistic jetted blast wave. The solution involves three distinct regions: an approximately paraboloid head where the Lorentz factor γ exceeds ∼ 1/2 of its maximal, nose value; a geometrically self-similar, expanding envelope slightly narrower than a paraboloid; and an axial core in which the (cylindrically, henceforth) radial flow {{u}} converges inward toward the axis. Most (∼80%) of the energy lies well beyond the leading, head region. Here, a radial cross section shows a maximal γ (separating the core and the envelope), a sign reversal in {{u}}, and a minimal γ, at respectively ∼1/6, ∼1/4, and ∼3/4 of the shock radius. The solution is apparently unique, and approximately agrees with previous simulations, of different initial conditions, that resolved the head. This suggests that unlike a spherical relativistic blast wave, our solution is an attractor, and may thus describe directed blast waves such as in the external shock phase of a γ-ray burst.
Cracking of general relativistic anisotropic polytropes
NASA Astrophysics Data System (ADS)
Herrera, L.; Fuenmayor, E.; León, P.
2016-01-01
We discuss the effect that small fluctuations of the local anisotropy of pressure and of the energy density may have on the occurrence of cracking in spherical compact objects, satisfying a polytropic equation of state. Two different kinds of polytropes are considered. For both, it is shown that departures from equilibrium may lead to the appearance of cracking, for a wide range of values of the parameters defining the polytrope. Prospective applications of the obtained results to some astrophysical scenarios are pointed out.
Self similar evolution of evaporative supernova remnants
NASA Astrophysics Data System (ADS)
Chieze, J. P.; Lazareff, B.
1981-02-01
The expansion of a supernova remnant into an inhomogeneous medium of evaporating clouds can be idealized as a self-similar problem. The equations are set up and solved in the two limiting cases of negligible and dominant large scale conductivity, in the presence of an ad hoc external intercloud density equal to the product of Gamma, a parameter dependent on the evaporation parameter and the energy deposited by the supernova, with the -5/3 power of the radial distance, with Gamma equals 0 as a limiting case. While the detailed structure depends on Gamma, the global properties such as the expansion law and the total mass are to a large extent independent of this parameter, and agree with previous approximate results of McKee and Ostriker (1977). The limitations of the formal solutions are briefly discussed.
On the losses of dissolved CO(2) during champagne serving.
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).
Conformally flat polytropes for anisotropic matter
NASA Astrophysics Data System (ADS)
Herrera, L.; Di Prisco, A.; Barreto, W.; Ospino, J.
2014-12-01
We analyze in detail conformally flat spherically symmetric fluid distributions, satisfying a polytropic equation of state. Among the two possible families of relativistic polytropes, only one contains models which satisfy all the required physical conditions. The ensuing configurations are necessarily anisotropic and show interesting physical properties. Prospective applications of the presented models to the study of super-Chandrasekhar white dwarfs, are discussed.
A Polytropic Model of the Solar Interior
NASA Astrophysics Data System (ADS)
Calvo-Mozo, B.; Buitrago Casas, J. C.; Martinez Oliveros, J. C.
2015-12-01
In this work we considered different processes in the solar interior that can be described using polytropes. This assumption implies a radially variable continuous polytropic exponent, that is, our model is a multi-polytropic model of the Sun. We derived the equations for this type of multi-polytropic structure and solved them using numerical integration methods. Both, the exponent and proportionality factor in the polytropic model equation of state were taken as input functions, for each spherical layer in the solar interior. Using the spatial distribution of the density and pressure terms from a solar standard model (SSM) we obtained the variable with depth polytropic exponents. We found that the radial distribution of these exponents show four different zones. These can be interpreted as a first region where the energy transport is controlled by radiation. The second region is defined by a sudden change in the polytropic index, which can be associated to the tachocline, followed by a region with a nearly constant polytropic index which suits well a convective zone. Finally, the exponent decreases radially at the photosphere.
[The wine from Champagne during the Empire].
Demouy, Patrick
2014-01-01
After the revolutionary upheavals (dispersal of the big properties of privileged persons and abolition of many rights) and a fold on the local market, the vine growing in Champagne found a new balance due to good grape harvests between 1804 and 1814 and due to the territorial expansion. Without supplanting the red wines, the sparkling white wines conquered a new foreign clientele. After the fall of the Eagle the traders rushed to the new markets offered by peace.
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.
Spherical polytropic balls cannot mimic black holes
NASA Astrophysics Data System (ADS)
Saida, Hiromi; Fujisawa, Atsuhito; Yoo, Chul-Moon; Nambu, Yasusada
2016-04-01
The so-called black hole shadow is a dark region which is expected to appear in a fine image of optical observation of black holes. It is essentially an absorption cross section of the black hole, and the boundary of shadow is determined by unstable circular orbits of photons (UCOP). If there exists a compact object possessing UCOP but no black hole horizon, it can provide us with the same shadow image as black holes, and detection of a shadow image cannot be direct evidence of black hole existence. This paper examines whether or not such compact objects can exist under some suitable conditions. We investigate thoroughly the static spherical polytropic ball of perfect fluid with single polytrope index, and then investigate a representative example of a piecewise polytropic ball. Our result is that the spherical polytropic ball which we have investigated cannot possess UCOP, if the speed of sound at the center is subluminal (slower than light). This means that, if the polytrope treated in this paper is a good model of stellar matter in compact objects, the detection of a shadow image can be regarded as good evidence of black hole existence. As a by-product, we have found the upper bound of the mass-to-radius ratio of a polytropic ball with single index, M_{ast }/R_{ast } < 0.281, under the condition of subluminal sound speed.
Advection by polytropic compressible turbulence
NASA Astrophysics Data System (ADS)
Ladeinde, F.; O'Brien, E. E.; Cai, X.; Liu, W.
1995-11-01
Direct numerical simulation (DNS) is used to examine scalar correlation in low Mach number, polytropic, homogeneous, two-dimensional turbulence (Ms≤0.7) for which the initial conditions, Reynolds, and Mach numbers have been chosen to produce three types of flow suggested by theory: (a) nearly incompressible flow dominated by vorticity, (b) nearly pure acoustic turbulence dominated by compression, and (c) nearly statistical equipartition of vorticity and compressions. Turbulent flows typical of each of these cases have been generated and a passive scalar field imbedded in them. The results show that a finite-difference based computer program is capable of producing results that are in reasonable agreement with pseudospectral calculations. Scalar correlations have been calculated from the DNS results and the relative magnitudes of terms in low-order scalar moment equations determined. It is shown that the scalar equation terms with explicit compressibility are negligible on a long time-averaged basis. A physical-space EDQNM model has been adapted to provide another estimate of scalar correlation evolution in these same two-dimensional, compressible cases. The use of the solenoidal component of turbulence energy, rather than total turbulence energy, in the EDQNM model gives results closer to those from DNS in all cases.
NASA Astrophysics Data System (ADS)
Litvinova, I. Yu.; Nadyozhin, D. K.
1990-01-01
Consideration is given to the self-similar solution to the hydrodynamic equations for the case when the outermost stellar layers are expanding after the emergence of a shock wave at the stellar surface. The conditions for validity of the self-similar solution are specified and calculations are performed for adiabatic indices gamma between 4/3 and 5/3 and for peripheral polytropic indices n between 1 and 15. It is shown that the self-similar solution describes the first three minutes of the SN 1987A outburst, when a soft X-ray pulse was generated. The increase in velocity of the outermost layer of SN 1987A during the expansion of matter in a vacuum after the emergence of a shock wave is estimated.
Self-similarity in incompressible Navier-Stokes equations.
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. PMID:26723165
Thermodynamic behavior and stability of Polytropic gas
NASA Astrophysics Data System (ADS)
Moradpour, H.; Abri, A.; Ebadi, H.
2016-10-01
We focus on the thermodynamic behavior of Polytropic gas as a candidate for dark energy (DE). We use the general arguments of thermodynamics to investigate its properties and behavior. We find that a Polytropic gas can exhibit the DE-like behavior. It also may be used to simulate a fluid with zero pressure at the small volume and high temperature limits. Briefly, our study shows that this gas may be used to describe the universe expansion history from the matter dominated era to the current accelerating era. By applying some initial conditions to the system, we can establish a relation between the Polytropic gas parameters and the initial conditions. Relationships with related works have also been addressed.
Quasinormal modes of the polytropic hydrodynamic vortex
NASA Astrophysics Data System (ADS)
Oliveira, Leandro A.; Cardoso, Vitor; Crispino, Luís C. B.
2015-07-01
Analogue systems are a powerful instrument to investigate and understand in a controlled setting many general-relativistic effects. Here, we focus on superradiant-triggered instabilities and quasinormal modes. We consider a compressible hydrodynamic vortex characterized by a polytropic equation of state, the polytropic hydrodynamic vortex, a purely circulating system with an ergoregion but no event horizon. We compute the quasinormal modes of this system numerically with different methods, finding excellent agreement between them. When the fluid velocity is larger than the speed of sound, an ergoregion appears in the effective spacetime, triggering an "ergoregion instability." We study the details of the instability for the polytropic vortex, and in particular find analytic expressions for the marginally stable configuration.
Annular self-similar solutions in ideal magnetogasdynamics
NASA Astrophysics Data System (ADS)
Lock, R. M.; Mestel, A. J.
2008-08-01
We consider the possibility of self-similar solutions describing the implosion of hollow cylindrical annuli driven by an azimuthal magnetic field, in essence a self-similar imploding liner z-pinch. We construct such solutions for gasdynamics, for ideal ‘β=0’ plasma and for ideal magnetogasdynamics (MGD). In the latter two cases some quantities are singular at the annular boundaries. Numerical solutions of the full ideal MGD initial value problem indicate that the self-similar solutions are not attractive for arbitrary initial conditions, possibly as a result of flux-freezing.
On the solution topologies of polytropic winds
NASA Technical Reports Server (NTRS)
Bailyn, C.; Rosner, R.; Tsinganos, K.
1985-01-01
Steady polytropic wind flows are studied by examining their solution topologies. The problem of whether the degeneracy of the continuous and standing shocked solutions in the isothermal case persist in the more general case of a polytropic expanding atmosphere is addressed. The effects of departures from spherical symmetry and nonthermal momentum addition are considered within the context of the new class of magnetospheric models proposed by Low and Tsinganos (1985). The flow near the boundary of a polar coronal hole is considered for the specific case of a magnetosphere in which this boundary asymptotically approaches the equator at large heliocentric distances.
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.
Self-similar solitary waves in Bessel optical lattices
Xu Siliu; Liang Jianchu; Yi Lin
2010-01-15
An analytical solitary wave solution to the generalized nonlinear Schroedinger equation (NLSE) with varying coefficients in Bessel optical lattices is obtained based on the self-similar method. Our results indicate that a new family of Bessel (BSL) self-similar spatial solitons can be formed in the Kerr nonlinear media in the confined cylindrical symmetric geometry in sizes. These soliton profiles are rather stable, independent of propagation distance.
Self-similar compression flows in spherical geometry: numerical calculations and implementations
NASA Astrophysics Data System (ADS)
Gerin-Roze, Jean
2009-06-01
During the previous APS-SCCM meeting(2007) we exhibited a set of theoretical solutions for the implosion of a sphere initiated by a strong shock. We assumed that: 1. The sphere contains a perfect gas with a polytropic coefficient γ=5/3. 2. The shock follows the equation: rs/r0=(-t/tfoc)^α where α is a positive constant and where --tfoc
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
Evaporation of droplets in a Champagne wine aerosol
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
General polytropic magnetohydrodynamic cylinder under self-gravity
NASA Astrophysics Data System (ADS)
Lou, Yu-Qing; Xing, Heng-Rui
2016-02-01
Based on general polytropic (GP) magnetohydrodynamics (MHD), we offer a self-similar dynamic formalism for a magnetized, infinitely long, axially uniform cylinder of axisymmetry under self-gravity with radial and axial flows and with helical magnetic field. We identify two major classes of solution domains and obtain a few valuable MHD integrals in general. We focus on one class that has the freedom of prescribing a GP dynamic equation of state including the isothermal limit and derive analytic asymptotic solutions for illustration. In particular, we re-visit the isothermal MHD problem of Tilley & Pudritz (TP) and find that TP's main conclusion regarding the MHD solution behaviour for a strong ring magnetic field of constant toroidal flux-to-mass ratio Γϕ to be incorrect. As this is important for conceptual scenarios, MHD cylinder models, testing numerical codes and potential observational diagnostics of magnetized filaments in various astrophysical contexts, we show comprehensive theoretical analysis and reasons as well as extensive numerical results to clarify pertinent points in this Letter. In short, for any given Γϕ value be it small or large, the asymptotic radial scaling of the reduced mass density α(x) at sufficiently large x should always be ˜x-4 instead of ˜x-2 contrary to the major claim of TP.
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.
Self-Similar Evolution of Cosmic-Ray Modified Shocks
NASA Astrophysics Data System (ADS)
Kang, H.; Ryu, D.
2010-09-01
Diffusive shock acceleration (DSA) is widely accepted as the primary mechanism through which cosmic rays (CRs) are produced in a variety of astrophysical environments. We used kinetic simulations of DSA to study the time-dependent evolution of the energy spectrum of CRs accelerated by plane, quasi-parallel shocks. We found that the precursor and subshock transition approach the time-asymptotic state, and then evolve in an approximately self-similar fashion, depending only on the similarity variable, x/(us t). During this self-similar stage, the CR spectrum at the subshock maintains a characteristic form as it evolves: the sum of two power-laws with the slopes determined by the subshock and total compression ratios with an exponential cutoff at the highest accelerated momentum. This analytic form may represent an approximate solution to the DSA problem for astrophysical shocks during the self-similar evolutionary stage.
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.
A class of self-similar hydrodynamics test problems
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.
Self-similarity and optical kinks in resonant nonlinear media
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.
Casimir energies of self-similar plate configurations
NASA Astrophysics Data System (ADS)
Shajesh, K. V.; Brevik, Iver; Cavero-Peláez, Inés; Parashar, Prachi
2016-09-01
We construct various self-similar configurations using parallel δ -function plates and show that it is possible to evaluate the Casimir interaction energy of these configurations using the idea of self-similarity alone. We restrict our analysis to interactions mediated by a scalar field, but the extension to the electromagnetic field is immediate. Our work unveils an easy and powerful method that can be easily employed to calculate the Casimir energies of a class of self-similar configurations. As a highlight, in an example, we determine the Casimir interaction energy of a stack of parallel plates constructed by positioning δ -function plates at the points constituting the Cantor set, a prototype of a fractal. This, to our knowledge, is the first time that the Casimir energy of a fractal configuration has been reported. Remarkably, the Casimir energy of some of the configurations we consider turn out to be positive, and a few even have zero Casimir energy. For the case of positive Casimir energy that is monotonically decreasing as the stacking parameter increases, the interpretation is that the pressure of vacuum tends to inflate the infinite stack of plates. We further support our results, derived using the idea of self-similarity alone, by rederiving them using the Green's function formalism. These expositions gives us insight into the connections between the regularization methods used in quantum field theories and regularized sums of divergent series in number theory.
Complexity measures and self-similarity on spreading depression waves
NASA Astrophysics Data System (ADS)
Piqueira, José Roberto C.; de Lima, Vera Maura Fernandes; Batistela, Cristiane M.
2014-05-01
Self-similarity has been considered to be present in most of the spatial pattern formation phenomena occurring in natural contexts. In the case of the spreading depression (SD), there are conjectures about the presence of self-similarity in the circular wave formations. Shiner-Davison-Landsberg (SDL) complexity measure framework has been used in several contexts, in order to understand and classify systems and behaviors that are supposed to be complex. Here, by using SDL measure over data collected on SD experiments, self-similarity conjecture is tested. The data came from chicken retina spreading depression experience by measuring two concomitant signals: the extra-cellular potential and the intrinsic optical signal, that were collected in two different spatial scales. The SDL complexity was calculated for the data and two main results appeared: all the studied substances present similar SDL dynamical behavior and, considering the same substance, optical signals present different SDL values for different spatial scales. Consequently, it is not possible to conclude that SD phenomenon presents self-similarity.
Self-similarity in the inertial region of wall turbulence
NASA Astrophysics Data System (ADS)
Klewicki, J.; Philip, J.; Marusic, I.; Chauhan, K.; Morrill-Winter, C.
2014-12-01
The inverse of the von Kármán constant κ is the leading coefficient in the equation describing the logarithmic mean velocity profile in wall bounded turbulent flows. Klewicki [J. Fluid Mech. 718, 596 (2013), 10.1017/jfm.2012.626] connects the asymptotic value of κ with an emerging condition of dynamic self-similarity on an interior inertial domain that contains a geometrically self-similar hierarchy of scaling layers. A number of properties associated with the asymptotic value of κ are revealed. This is accomplished using a framework that retains connection to invariance properties admitted by the mean statement of dynamics. The development leads toward, but terminates short of, analytically determining a value for κ . It is shown that if adjacent layers on the hierarchy (or their adjacent positions) adhere to the same self-similarity that is analytically shown to exist between any given layer and its position, then κ ≡Φ-2=0.381 966 ... , where Φ =(1 +√{5 })/2 is the golden ratio. A number of measures, derived specifically from an analysis of the mean momentum equation, are subsequently used to empirically explore the veracity and implications of κ =Φ-2 . Consistent with the differential transformations underlying an invariant form admitted by the governing mean equation, it is demonstrated that the value of κ arises from two geometric features associated with the inertial turbulent motions responsible for momentum transport. One nominally pertains to the shape of the relevant motions as quantified by their area coverage in any given wall-parallel plane, and the other pertains to the changing size of these motions in the wall-normal direction. In accord with self-similar mean dynamics, these two features remain invariant across the inertial domain. Data from direct numerical simulations and higher Reynolds number experiments are presented and discussed relative to the self-similar geometric structure indicated by the analysis, and in particular the
Self-similar radiation from numerical Rosenau-Hyman compactons
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.
Self-similar Isochoric Implosions for Fast Ignition
NASA Astrophysics Data System (ADS)
Clark, Daniel
2005-10-01
Fast Ignition (FI) exploits the ignition of a dense, uniform fuel assembly by an external energy source to achieve high gain. However, in conventional ICF implosions, the fuel assembles as a dense shell surrounding a low density, high-pressure hotspot. Such configurations are far from optimal for FI. Here, it is shown that a self-similar spherical implosion of the type studied by Guderley [Luftfahrtforschung 19, 302 (1942).] and later Meyer-ter-Vehn & Schalk [Z. Naturforsch. 37a, 955 (1982).] may be employed to implode dense, uniform fuel assemblies with minimal energy wastage in forming a hotspot. The connection to "realistic" (i.e., non-self-similar) implosion schemes using laser or X-ray drive is also investigated.
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.
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.
Self-similar solitary wave family in Bessel lattice
Cai Zebin; Liang Jianchu; Xia Xiongping; Jin Haiqin; Yi Lin; Jiang Yue
2011-05-15
We focus on the formation and propagation of self-similar solitary wave family in Kerr nonlinear media with external Bessel lattice. A novel analytical solitary wave solution to (3+1)-dimensional Gross-Pitaevskii equation with varying coefficients and an external potential is obtained. The components of solitary wave family are differentiated by three quantum parameters. The properties and the stability of the solitary wave family are discussed in detail.
Naked singularities in self-similar spherical gravitational collapse
Ori, A.; Piran, T.
1987-11-09
We present general-relativistic solutions of self-similar spherical collapse of an adiabatic perfect fluid. We show that if the equation of state is soft enough (GAMMA-1<<1), a naked singularity forms. The singularity resembles the shell-focusing naked singularities that arise in dust collapse. This solution increases significantly the range of matter fields that should be ruled out in order that the cosmic-censorship hypothesis will hold.
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} .
Self-similar solutions for converging shocks and collapsing cavities
Lazarus, R.B.
1981-04-01
A complete analysis is attempted of the self-similar solutions for the converging shock and collapsing cavity problems, in spherical and cylindrical geometry, for a perfect gas with arbitrary adiabatic exponent ..gamma.. > 1. Emphasis is given to the rich variety of previously neglected nonanalytic solutions, and to a numerically and what can be derived algebraically. New solutions are described which contain additional converging shocks, arriving at the origin concurrently with the initial shock or free surface. Some of these new solutions are entirely analytic, except at the shocks themselves, and some are not; in some cases, only one secondary shock is possible, in other cases an arbitrary number. The physical significance of previously rejected partial solutions is discussed. The stability of solutions is discussed in a narrow (one-dimensional) sense. Finally, a study is urged of the asymptotic approach (or nonapproach) to self-similarity of direct numerical integrations of the original partial differential equations; it is argued that the evidence for approach to a unique self-similar solution is not convincing.
Self-Similarity and Observed Properties in Blazars
NASA Astrophysics Data System (ADS)
Georganopoulos, Markos; Marscher, Alan P.
We propose a unification scheme for BL Lac objects (BLs) based on the angle Theta that describes the orientation of the relativistic jet and on the kinetic luminosity Lambdakin of the jet. We assume that Lambdakin scales with the size of the jet {r} in a self-similar fashion (Lambdakin propto r^2), as supported by observational data. The jets are self-similar in geometry and have the same pressure and median magnetic field at the inlet, independent of size. The self-similarity is broken for the highest energy electrons, which radiate mainly at high frequencies, since for large sources they suffer more severe radiative energy losses over a given fraction of the jet length. The negative apparent evolution of X-ray selected BLs is explained as a result of positive evolution of the jet kinetic luminosity Lambdakin. We review observational arguments in favor of the existence of scaled-down accretion disks and broad emission-line regions in BLs. The proposed unification scheme can explain the lack of observed broad emission lines in X-ray selected BLs, as well as the existence of those lines preferentially in luminous radio-selected BLs. Finally, we review observational arguments that suggest the extension of this unification scheme to all blazars.
Visual perception of effervescence in champagne and other sparkling beverages.
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. PMID:21092901
Warm-Polytropic Inflationary Universe Model
NASA Astrophysics Data System (ADS)
Setare, M. R.; Houndjo, M. J. S.; Kamali, V.
2013-07-01
In this paper, we study warm inflationary universe models in the context of a polytropic gas. We derive the characteristics of this model in slow-roll approximation and develop our model in two cases: (1) for a constant dissipative parameter Γ; (2) Γ as a function of scalar field ϕ. In these cases, we will obtain exact solution for the scalar field and Hubble parameter. We will also obtain explicit expressions for the tensor-scalar ratio R, scalar spectrum index ns and its running αs in slow-roll approximation.
Tokunaga self-similarity for symmetric homogeneous Markov chains
NASA Astrophysics Data System (ADS)
Kovchegov, Y.; Zaliapin, I.
2010-12-01
Hierarchical branching organization is ubiquitous in nature. It is readily seen in river basins, drainage networks, bronchial passages, botanical trees, and snowflakes, to mention but a few. Empirical evidence suggests that one can describe many natural hierarchies by so-called Tokunaga self-similar trees (SSTs) [Shreve, 1969; Tokunaga, 1978; Ossadnik, 1992; Peckham, 1995; Newman et al., 1997; Pelletier and Turcotte, 2000]; Tokunaga SST have been proven to describe the Galton-Watson critical branching [Burd et al., 2000] and a general particle coagulation process [Gabrielov et al., 1999]. Tokunaga SSTs form a special two-parametric class of SSTs that preserves its statistical properties under the operation of pruning, i.e., cutting the leaves. It has been conjectured (Webb and Zaliapin, 2009; Zaliapin et al. 2009) that Tokunaga self-similarity is a characteristic property of the inverse aggregation (coagulation) process. This study provides further evidence in support of this hypothesis by focusing on trees that describe the topological structure of level sets of a time series, so-called level-set trees (LST). We prove that the LST for a symmetric homogeneous Markov chain (HMC) is a Tokunaga SST with the same parameters as the famous Shreve tree and critical Galton-Watson tree. We show, furthermore, that the Tokunaga property holds for any transformation F[X(G(t))] of a symmetric HMC X(t), where F and G are monotone increasing functions, and as a result - for the regular Brownian motion. At the same time, the Tokunaga property does not hold in general in asymmetric HMCs, a Brownian motion with a drift, ARMA, and some other conventional models. We discuss the relation of our results to the Tokunaga self-similarity of the nearest-neighbor trees for random point sets. References: 1. Gabrielov, A., W.I. Newman, D.L. Turcotte (1999) An exactly soluble hierarchical clustering model: inverse cascades, self-similarity, and scaling. Phys. Rev. E, 1999, 60, 5293-5300. 2
Self-similar perturbations of a Friedmann universe
NASA Technical Reports Server (NTRS)
Carr, Bernard J.; Yahil, Amos
1990-01-01
The present analysis of spherically symmetric self-similar solutions to the Einstein equations gives attention to those solutions that are asymptotically k = 0 Friedmann at large z values, and possess finite but perturbed density at the origin. Such solutions represent nonlinear density fluctuations which grow at the same rate as the universe's particle horizon. The overdense solutions span only a narrow range of parameters, and resemble static isothermal gas spheres just within the sonic point; the underdense solutions may have arbitrarily low density at the origin while exhibiting a unique relationship between amplitude and scale. Their relevance to large-scale void formation is considered.
Self-similar roughening of drying wet paper.
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.
Single-file diffusion on self-similar substrates
NASA Astrophysics Data System (ADS)
Suárez, G. P.; Mártin, H. O.; Iguain, J. L.
2014-07-01
We study the single file diffusion problem on a one-dimensional lattice with a self-similar distribution of hopping rates. We find that the time dependence of the mean-square displacement of both a tagged particle and the center of mass of the system present anomalous power laws modulated by logarithmic periodic oscillations. The anomalous exponent of a tagged particle is one half of the exponent of the center of mass, and always smaller than 1/4. Using heuristic arguments, the exponents and the periods of oscillation are analytically obtained and confirmed by Monte Carlo simulations.
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.
VISCOUS ACCRETION OF A POLYTROPIC SELF-GRAVITATING DISK IN THE PRESENCE OF WIND
Abbassi, Shahram; Nourbakhsh, Erfan; Shadmehri, Mohsen E-mail: e.nourbakhsh@mail.sbu.ac.ir
2013-03-10
Self-similar and semi-analytical solutions are found for the height-averaged equations governing the dynamical behavior of a polytropic, self-gravitating disk under the effects of winds around the nascent object. In order to describe the time evolution of the system, we adopt a radius-dependent mass loss rate, then highlight its importance on both the traditional {alpha} and innovative {beta} models of viscosity prescription. In agreement with some other studies, our solutions represent that the Toomre parameter is less than one in most regions on the {beta}-disk, which indicates that in such disks gravitational instabilities can occur at various distances from the central accretor. So, the {beta}-disk model might provide a good explanation of how the planetary systems form. The purpose of the present work is twofold: examining the structure of a disk with wind in comparison to a no-wind solution and seeing whether the adopted viscosity prescription significantly affects the dynamical behavior of the disk-wind system. We also considered the temperature distribution in our disk by a polytropic condition. The solutions imply that, under our boundary conditions, the radial velocity is larger for {alpha}-disks and increases as wind becomes stronger in both viscosity models. Also, we noticed that the disk thickness increases by amplifying the wind or adopting larger values for the polytropic exponent {gamma}. It also may globally decrease if one prescribes a {beta}-model for the viscosity. Moreover, in both viscosity models, the surface density and mass accretion rate diminish as the wind gets stronger or {gamma} increases.
Self-similar hot accretion flow onto a neutron star
NASA Astrophysics Data System (ADS)
Medvedev, Mikhail V.
2001-10-01
We present analytical and numerical solutions which describe a hot, viscous, two-temperature accretion flow onto a neutron star or any other compact star with a surface. We assume Coulomb coupling between the protons and electrons, and free-free cooling from the electrons. Outside a thin boundary layer, where the accretion flow meets the star, we show that there is an extended settling region which is well-described by two self-similar solutions: (1) a two-temperature solution which is valid in an inner zone r<=102.5 (r is in Schwarzchild units), and (2) a one-temperature solution at larger radii. In both zones, ρ~r-2, Ω~r-3/2, v~r0, Tp~r-1 in the two-temperature zone, Te~r-1/2. The luminosity of the settling zone arises from the rotational energy of the star as the star is braked by viscosity; hence the luminosity is independent of Ṁ. The settling solution is convectively and viscously stable and is unlikely to have strong winds or outflows. The flow is thermally unstable, but the instability may be stabilized by thermal conduction. The settling solution described here is not advection-dominated, and is thus different from the self-similar ADAF found around black holes. When the spin of the star is small enough, however, the present solution transforms smoothly to a (settling) ADAF. .
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.
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.
Self-similarity of solitary pulses on falling liquid films
NASA Astrophysics Data System (ADS)
Denner, Fabian; Charogiannis, Alexandros; Pradas, Marc; Markides, Christos N.; van Wachem, Berend G. M.; Kalliadasis, Serafim
2015-11-01
A gravity-driven liquid film is unstable to long-wave perturbations above a critical Reynolds number. At low frequencies these perturbations evolve into fast solitary pulses. These strongly non-linear structures have a dominant elevation with a long tail and steep front, typically with capillary ripples preceding the main wave hump. We present the results of a comprehensive numerical study of solitary pulses on gravity-driven inertia-dominated water films flowing down an inclined substrate for a range of inclination angles (45-90 degrees), Reynolds numbers (Re =20-120) and Kapitza numbers (Ka =2765-3887). Our results reveal a self-similarity of solitary pulses on falling films and provide an in-depth understanding of the driving physical mechanisms of such pulses. We formulate a consistent characterisation of the shape and non-linear dispersion of solitary pulses, founded on a newly proposed scaling derived from the Nusselt flat film solution. We present and discuss our findings and resulting correlations with respect to the self-similarity of the shape and non-linear dispersion of solitary pulses as well as the influence of gravity and surface tension on solitary pulses in general. We acknowledge financial support from the Engineering and Physical Sciences Research Council (EPSRC) through Grant No. EP/K008595/1 and Grant No. EP/M021556/1.
Self-similar evolution of the nonlinear magnetic buoyancy instability
NASA Technical Reports Server (NTRS)
Shibata, K.; Tajima, T.; Matsumoto, R.
1990-01-01
A new type of self-similar solution of ideal magnetohydrodynamics (MHD) in the nonlinear stage of the undular model (k parallel to B) of the magnetic buoyancy instability (the ballooning instability in fusion plasma physics or the Parker instability in astrophysics) is found through MHD simulation and theory. The linear theory developed agrees well with the simulation in the early (linear) stage. The nonlinear stages of the instability in the simulation show the self-similar evolution. One of the solutions obtained from the nonlinear analysis has the characteristics of nonlinear instability in Lagrangian coordinates; the fluid velocity and the Alfven speed on each magnetic loop increase exponentially with time, because the loop is evacuated by the field-aligned motion of matter resulting from gravitational acceleration. In the later stage of the nonlinear evolution, the solution property changes from exponential to power-law time dependence. The latter corresponds to a force-free expansion solution. The later saturation of the velocity increment is also discussed.
Global solution curves for self-similar equations
NASA Astrophysics Data System (ADS)
Korman, Philip
2014-10-01
We consider positive solutions of a semilinear Dirichlet problem Δu+λf(u)=0, for |x|<1, u=0, when |x|=1 on a unit ball in Rn. For four classes of self-similar equations it is possible to parameterize the entire (global) solution curve through the solution of a single initial value problem. This allows us to derive results on the multiplicity of solutions, and on their Morse indices. In particular, we easily recover the classical results of D.D. Joseph and T.S. Lundgren [6] on the Gelfand problem. Surprisingly, the situation turns out to be different for the generalized Gelfand problem, where infinitely many turns are possible for any space dimension n≥3. We also derive detailed results for the equation modeling electrostatic micro-electromechanical systems (MEMS), in particular we easily recover the main result of Z. Guo and J. Wei [4], and we show that the Morse index of the solutions increases by one at each turn. We also consider the self-similar Henon's equation.
Self-similarity of biopolymer backbones in the ribosome
NASA Astrophysics Data System (ADS)
Lee, Chang-Yong
2008-08-01
Self-similar properties of the biopolymer backbones in the ribosome are investigated in terms of the fractal dimension. We especially estimate the chain fractal and capacity dimensions of the ribosomal RNAs and proteins, which are constituents of the ribosome. The fractal dimensions of both biopolymers are compared with that of the self-avoiding walk, which is a typical model of a polymer without interaction between monomers. We demonstrate that the fractality found in the ribosomal RNAs is pertinent to explain their structural characteristics: local helix formation and long-range tertiary interaction forming three-dimensional structures. The fractal dimension of the ribosomal protein supports the existence of the long and extended domain, which is hardly seen in the globular protein. The self-similarity also upholds the fact that the ribosomal proteins function primarily to stabilize the structure of the ribosome by both the long-extended domain of the protein penetrating into the inside of the RNA, and the globular domain interacting with the RNA on the exterior of it. These results partially, if not whole, unravel the structural characteristics of the biopolymers in the ribosome.
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'
Self-similarity of proton spin and z-scaling
NASA Astrophysics Data System (ADS)
Tokarev, M.; Zborovský, I.
2016-02-01
The concept of z-scaling previously developed for analysis of inclusive reactions in proton-proton collisions is applied for description of processes with polarized particles. Hypothesis of self-similarity of the proton spin structure is discussed. The possibility of extracting information on spin-dependent fractal dimensions of hadrons and fragmentation process from the cross sections and asymmetries is justified. The double longitudinal spin asymmetry ALL of jet and π0-meson production and the coefficient of polarization transfer DLL measured in proton-proton collisions at √s = 200 GeV at RHIC are analyzed in the framework of z-scaling. The spin-dependent fractal dimension of proton is estimated.
Nested self-similar wrinkling patterns in skins
NASA Astrophysics Data System (ADS)
Efimenko, Kirill; Rackaitis, Mindaugas; Vaziri, Ashkan
2005-03-01
We describe a simple method for generating topographically corrugated elastomeric surfaces comprising multidimensional cascades of wrinkles. These wrinkled surfaces are generated by uniaxially stretching silicon elastomer films, exposing their surfaces to prolonged ultraviolet/ozone treatment and releasing the initial strain imposed on the specimens. We show that such elastomeric artificial skins wrinkle in a hierarchical pattern consisting of self-similar buckles extending over five orders of magnitude in length scale, ranging from a few nanometers to a few millimeters. We provide a mechanism for the formation of this hierarchical wrinkling pattern, and quantify our experimental findings with both comparative computations and a simple scaling theory. Understanding the wrinkle-forming mechanism allows us to harness the substrates for applications. In particular, we show how to utilize the multigeneration-wrinkled substrate for separating particles based on their size, while simultaneously forming linear chains of equisized particles.
Nested self-similar wrinkling patterns in skins
NASA Astrophysics Data System (ADS)
Efimenko, Kirill; Rackaitis, Mindaugas; Manias, Evangelos; Vaziri, Ashkan; Mahadevan, L.; Genzer, Jan
2005-04-01
Stiff thin films on soft substrates are both ancient and commonplace in nature; for instance, animal skin comprises a stiff epidermis attached to a soft dermis. Although more recent and rare, artificial skins are increasingly used in a broad range of applications, including flexible electronics, tunable diffraction gratings, force spectroscopy in cells, modern metrology methods, and other devices. Here we show that model elastomeric artificial skins wrinkle in a hierarchical pattern consisting of self-similar buckles extending over five orders of magnitude in length scale, ranging from a few nanometres to a few millimetres. We provide a mechanism for the formation of this hierarchical wrinkling pattern, and quantify our experimental findings with both computations and a simple scaling theory. This allows us to harness the substrates for applications. In particular, we show how to use the multigeneration-wrinkled substrate for separating particles based on their size, while simultaneously forming linear chains of monodisperse particles.
A self-similar model for extragalactic radio sources
NASA Astrophysics Data System (ADS)
Kaiser, Christian R.; Alexander, Paul
1997-03-01
An analytical model for extragalactic radio sources with pressure-confined jets is presented. We show that the properties of the bow shock and of the gas surrounding these objects force the sources to grow in a self-similar way provided the density in the external atmosphere falls less steeply than 1/d^2. Results from observations and numerical simulations are used to develop a self-consistent model for the large-scale structure of FRII objects. The jets in these sources are shown to be stable against turbulence for the observed properties of FRIIs and the divide between FRI and FRII objects in jet power is reproduced. The overall dynamics of a source are derived as a function of time and depend on the external density, the jet power and the scaleheight of the external atmosphere. Derived dynamical ages are consistent with observed spectral ages.
Self-Similarity in Game-Locked Aggregation
NASA Astrophysics Data System (ADS)
Wang, Chao; Xiong, Wan-Ting; Wang, You-Gui
2012-12-01
A collective game is studied via agent-based modeling approach, where a group of adaptive learning players seek for their best positions on a vertical line. The movements of players are driven by benefits obtained from interactions. The game falls into an evolutionary stable state, at which aggregations of players on the line emerge. The pattern of these aggregates exhibits self-similarity at different scales with a fractal dimension of 0.58. The underlying mechanism of this aggregation is unique in that aggregates are resulted from mutual lock-in of players. This game-locked aggregation, in contrast with the diffusion limited aggregation, is applicable to a broader scope of aggregation processes.
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.
Self-similar expansion of a warm dense plasma
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.
Self-similar and diffusive expansion of nonextensive plasmas
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.
Self-similar Hot Accretion Flow onto a Neutron Star
NASA Astrophysics Data System (ADS)
Medvedev, Mikhail V.; Narayan, Ramesh
2001-06-01
We consider hot, two-temperature, viscous accretion onto a rotating, unmagnetized neutron star. We assume Coulomb coupling between the protons and electrons, as well as free-free cooling from the electrons. We show that the accretion flow has an extended settling region that can be described by means of two analytical self-similar solutions: a two-temperature solution that is valid in an inner zone, r<~102.5, where r is the radius in Schwarzschild units; and a one-temperature solution that is valid in an outer zone, r>~102.5. In both zones the density varies as ρ~r-2 and the angular velocity as Ω~r-3/2. We solve the flow equations numerically and confirm that the analytical solutions are accurate. Except for the radial velocity, all gas properties in the self-similar settling zone, such as density, angular velocity, temperature, luminosity, and angular momentum flux, are independent of the mass accretion rate; these quantities do depend sensitively on the spin of the neutron star. The angular momentum flux is outward under most conditions; therefore, the central star is nearly always spun down. The luminosity of the settling zone arises from the rotational energy that is released as the star is braked by viscosity, and the contribution from gravity is small; hence, the radiative efficiency, η=Lacc/Mc2, is arbitrarily large at low M. For reasonable values of the gas adiabatic index γ, the Bernoulli parameter is negative; therefore, in the absence of dynamically important magnetic fields, a strong outflow or wind is not expected. The flow is also convectively stable but may be thermally unstable. The described solution is not advection dominated; however, when the spin of the star is small enough, the flow transforms smoothly to an advection-dominated branch of solution.
Mosaic, Self-Similarity Logic, and Biological Attraction principles
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
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.
A nonlinear eigenvalue problem for self-similar spherical force-free magnetic fields
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
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.
Self-similar energetics in large clusters of galaxies.
Miniati, Francesco; Beresnyak, Andrey
2015-07-01
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.
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.
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.
Critical ignition in rapidly expanding self-similar flows
NASA Astrophysics Data System (ADS)
Radulescu, Matei I.; Maxwell, Brian M.
2010-06-01
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 thermochemical 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. The critical ignition criteria, which are valid in the asymptotic limit n(γ -1)(Ea/RT)=O(1), were 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 startup, and for reactions in steady hypersonic flows around projectiles.
Self-similar spherical collapse with tidal torque
Zukin, Phillip; Bertschinger, Edmund
2010-11-15
N-body simulations have revealed a wealth of information about dark matter halos; however, their results are largely empirical. Using analytic means, we attempt to shed light on simulation results by generalizing the self-similar secondary infall model to include tidal torque. In this first of two papers, we describe our halo formation model and compare our results to empirical mass profiles inspired by N-body simulations. Each halo is determined by four parameters. One parameter sets the mass scale and the other three define how particles within a mass shell are torqued throughout evolution. We choose torque parameters motivated by tidal torque theory and N-body simulations and analytically calculate the structure of the halo in different radial regimes. We find that angular momentum plays an important role in determining the density profile at small radii. For cosmological initial conditions, the density profile on small scales is set by the time rate of change of the angular momentum of particles as well as the halo mass. On intermediate scales, however, {rho}{proportional_to}r{sup -2}, while {rho}{proportional_to}r{sup -3} close to the virial radius.
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.
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.
Time-dependent Magnetohydrodynamic Self-similar Extragalactic Jets
NASA Astrophysics Data System (ADS)
Tsui, K. H.; Serbeto, A.
2007-04-01
Extragalactic jets are visualized as dynamic eruptive events modeled by time-dependent magnetohydrodynamic (MHD) equations. The jet structure comes from the temporally self-similar solutions in two-dimensional axisymmetric spherical geometry. The two-dimensional magnetic field is solved in the finite plasma pressure regime, or finite-β regime, and it is described by an equation where plasma pressure plays the role of an eigenvalue. This allows a structure of magnetic lobes in space, among which the polar axis lobe is strongly peaked in intensity and collimated in angular spread compared to the others. For this reason, the polar lobe overwhelms the other lobes, and a jet structure naturally arises in the polar direction. Furthermore, within each magnetic lobe in space, there are small secondary regions with closed two-dimensional field lines embedded along this primary lobe. In these embedded magnetic toroids, plasma pressure and mass density are accordingly much higher. These are termed secondary plasmoids. The magnetic field lines in these secondary plasmoids circle in alternating sequence such that adjacent plasmoids have opposite field lines. In particular, along the polar primary lobe, such periodic plasmoid structure happens to be compatible with radio observations in which islands of high radio intensities are mapped.
Self-similar energetics in large clusters of galaxies.
Miniati, Francesco; Beresnyak, Andrey
2015-07-01
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. PMID:26135447
Self-similar energetics in large clusters of galaxies
NASA Astrophysics Data System (ADS)
Miniati, Francesco; Beresnyak, Andrey
2015-07-01
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.
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, $1/2\\le n\\le5$.
Self-similar collapse and accretion of radiative gas
NASA Astrophysics Data System (ADS)
Boily, C. M.; Lynden-Bell, D.
1995-09-01
The hydrodynamics of spherically symmetric radiative gas is discussed. Self-similar solutions are obtained for situations where the total emissivity epsilon of the gas has a power-law dependence on the density and temperature, epsilon~rho^alphaT^4+beta, in an optically thin medium. A perfect gas equation of state is used throughout. The flows have uniform density and contract uniformly initially. The region of uniform density becomes ever smaller with time, and gives way to power-law radial profiles. For each pair alpha and beta, there may exist three types of flows. Flows of the first type are far from dynamical equilibrium, and have gas converging steadily to the origin. These solutions develop strong velocity fields and supersonic motion. These are found for alpha, beta such that 1/2
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.
Analysis of self-similar problems of imploding shock waves by the method of characteristics
NASA Astrophysics Data System (ADS)
Nakamura, Y.
1983-05-01
The asymptotic self-similar form of cylindrically or spherically imploding shock waves is extracted by numerically solving non-self-similar problems. The shock wave is generated by a contracting piston with finite initial velocity. For the initial shock motion, a perturbation method is used to determine the starting condition for the numerical calculation. Propagation of the shock wave and flow field properties are obtained and the transition of the non-self-similar motion of the shock wave into the self-similar one is presented. Good agreement between self-similar exponents determined from the variation of the shock strength and those calculated by Guderley is obtained.
Riccati parameterized self-similar waves in tapered graded-index waveguides
NASA Astrophysics Data System (ADS)
Goyal, Amit; Gupta, Rama; Loomba, Shally; Kumar, C. N.
2012-10-01
We present a large family of self-similar waves by tailoring the tapering function, through Riccati parameter, in a tapered graded-index nonlinear waveguide amplifier. We show the existence of bright similaritons, self-similar Akhmediev breathers and self-similar rogue waves for generalized nonlinear Schrödinger equation with constant dispersion and nonlinearity, and a distributed gain. We illustrate the procedure to amplify the intensity of self-similar waves using isospectral Hamiltonian approach. This approach provides a handle to find analytically a wide class of tapering function and thus enabling one to control the self-similar wave structure and dynamical behavior.
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. PMID:24907802
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.
CO2 diffusion in champagne wines: a molecular dynamics study.
Perret, Alexandre; Bonhommeau, David A; Liger-Belair, Gérard; Cours, Thibaud; Alijah, Alexander
2014-02-20
Although diffusion is considered as the main physical process responsible for the nucleation and growth of carbon dioxide bubbles in sparkling beverages, the role of each type of molecule in the diffusion process remains unclear. In the present study, we have used the TIP5P and SPC/E water models to perform force field molecular dynamics simulations of CO2 molecules in water and in a water/ethanol mixture respecting Champagne wine proportions. CO2 diffusion coefficients were computed by applying the generalized Fick's law for the determination of multicomponent diffusion coefficients, a law that simplifies to the standard Fick's law in the case of champagnes. The CO2 diffusion coefficients obtained in pure water and water/ethanol mixtures composed of TIP5P water molecules were always found to exceed the coefficients obtained in mixtures composed of SPC/E water molecules, a trend that was attributed to a larger propensity of SPC/E water molecules to form hydrogen bonds. Despite the fact that the SPC/E model is more accurate than the TIP5P model to compute water self-diffusion and CO2 diffusion in pure water, the diffusion coefficients of CO2 molecules in the water/ethanol mixture are in much better agreement with the experimental values of 1.4 - 1.5 × 10(-9) m(2)/s obtained for Champagne wines when the TIP5P model is employed. This difference was deemed to rely on the larger propensity of SPC/E water molecules to maintain the hydrogen-bonded network between water molecules and form new hydrogen bonds with ethanol, although statistical issues cannot be completely excluded. The remarkable agreement between the theoretical CO2 diffusion coefficients obtained within the TIP5P water/ethanol mixture and the experimental data specific to Champagne wines makes us infer that the diffusion coefficient in these emblematic hydroalcoholic sparkling beverages is expected to remain roughly constant whathever their proportions in sugars, glycerol, or peptides.
Champagne experiences various rhythmical bubbling regimes in a flute.
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.
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. PMID:14561124
On the Stability of Self-Similar Solutions to Nonlinear Wave Equations
NASA Astrophysics Data System (ADS)
Costin, Ovidiu; Donninger, Roland; Glogić, Irfan; Huang, Min
2016-04-01
We consider an explicit self-similar solution to an energy-supercritical Yang-Mills equation and prove its mode stability. Based on earlier work by one of the authors, we obtain a fully rigorous proof of the nonlinear stability of the self-similar blowup profile. This is a large-data result for a supercritical wave equation. Our method is broadly applicable and provides a general approach to stability problems related to self-similar solutions of nonlinear wave equations.
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.
QUIPS: Time-dependent properties of quasi-invariant self-gravitating polytropes
Munier, A.; Feix, M.R.
1983-04-01
Quasi-invariance, a method based on group tranformations, is used to obtain time-dependent solutions for the expansion and/or contraction of a self-gravitating sphere of perfect gas with polytopic index n. Quasi-invariance transforms the equations of hydrodynamics into ''dual equations'' exhibiting extra terms such as a friction, a mass source or sink term, and a centripetal/centrifugal force. The search for stationary solutions in this ''dual space'' leads to a new class of time-dependent solutions, the QUIP (for Quasi-invariant polytrope), which generalizes Emden's static model and introduces a characteristic frequency a related to Jean's frequency. The second order differential equation describing the solution is integrated numerically. A critical point is seen always to exist for nnot =3. Solutions corresponding in the ''dual space'' to a time-dependent generalization of Eddington's standard model (n = 3) are discussed. These solutions conserve both the total mass and the energy. A transition between closed and open structures is seen to take place at a particular frequency a/sub c/. For n = 3, no critical point arises in the ''dual space'' due to the self-similar motion of the fluid. A new time-dependent mass-radius relation and a generalized Betti-Ritter relation are obtained. Conclusions about the existence of a minimum Q-factor are presented.
Champagne bottle neck sign in a patient with Moyamoya syndrome.
Shimogawa, Takafumi; Morioka, Takato; Sayama, Tetsuro; Hamamura, Takeshi; Yasuda, Chiharu; Arakawa, Shuji
2014-09-16
The champagne bottle neck (CBN) sign refers to a reduction in the diameter of the proximal portion of the internal carotid artery that resembles a CBN, and is a characteristic feature of Moyamoya disease. A 43-year-old woman with an infarction of the posterior limb of the left internal capsule was diagnosed with Moyamoya syndrome associated with Graves' disease. The CBN sign was observed bilaterally. Cerebral revascularization surgery was performed, including left-sided superficial temporal artery to middle cerebral artery anastomosis. During four years of follow-up, she maintained a euthyroid state and did not have any further cerebral ischemic events. The CBN signs remained unchanged on both sides during this time. This is the first report of the CBN sign in a patient with Moyamoya syndrome associated with Graves' disease. PMID:25232554
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).
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).
Champagne bottle neck sign in a patient with Moyamoya syndrome.
Shimogawa, Takafumi; Morioka, Takato; Sayama, Tetsuro; Hamamura, Takeshi; Yasuda, Chiharu; Arakawa, Shuji
2014-09-16
The champagne bottle neck (CBN) sign refers to a reduction in the diameter of the proximal portion of the internal carotid artery that resembles a CBN, and is a characteristic feature of Moyamoya disease. A 43-year-old woman with an infarction of the posterior limb of the left internal capsule was diagnosed with Moyamoya syndrome associated with Graves' disease. The CBN sign was observed bilaterally. Cerebral revascularization surgery was performed, including left-sided superficial temporal artery to middle cerebral artery anastomosis. During four years of follow-up, she maintained a euthyroid state and did not have any further cerebral ischemic events. The CBN signs remained unchanged on both sides during this time. This is the first report of the CBN sign in a patient with Moyamoya syndrome associated with Graves' disease.
Ultrafast fiber lasers based on self-similar pulse evolution: a review of current progress.
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.
Ultrafast fiber lasers based on self-similar pulse evolution: a review of current progress
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
NASA Astrophysics Data System (ADS)
Radev, Dimitar; Lokshina, Izabella
2010-11-01
The paper examines self-similar (or fractal) properties of real communication network traffic data over a wide range of time scales. These self-similar properties are very different from the properties of traditional models based on Poisson and Markov-modulated Poisson processes. Advanced fractal models of sequentional generators and fixed-length sequence generators, and efficient algorithms that are used to simulate self-similar behavior of IP network traffic data are developed and applied. Numerical examples are provided; and simulation results are obtained and analyzed.
Observations and analysis of self-similar branching topology in glacier networks
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.
Self-similar optical pulses in competing cubic-quintic nonlinear media with distributed coefficients
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.
Supersymmetric formulation of polytropic gas dynamics and its invariant solutions
Grundland, A. M.; Hariton, A. J.
2011-04-15
In this paper, a supersymmetric extension of the polytropic gas dynamics equations is constructed through the use of a superspace involving two independent fermionic variables and two bosonic superfields. A superalgebra of symmetries of the proposed extended model is determined and a systematic classification of the one-dimensional subalgebras of this superalgebra is performed. Through the use of the symmetry reduction method, a number of invariant solutions of the supersymmetric polytropic gas dynamics equations are found. Several types of solutions are obtained including algebraic-type solutions and propagation waves (simple and double waves). Many of the obtained solutions involve arbitrary functions of one or two bosonic or fermionic variables. In the case where the arbitrary functions involve only the independent fermionic variables, the solutions are expressed in terms of Taylor expansions.
Is scalar-tensor gravity consistent with polytropic stellar models?
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.
Solar wind polytropic index in the vicinity of stream interactions
NASA Astrophysics Data System (ADS)
Newbury, J. A.; Russell, C. T.; Lindsay, G. M.
In an ideal, 3-D, closed system that experiences compression and expansion, the temperature (T) and density (n) of a monatomic gas are related adiabatically through the polytropic law; i.e., T ∝ nα-1, where α is the polytropic index and equals 5/3. This relationship has been examined over a variety of scale sizes in the solar wind, and empirical measurements of α vary a great deal. As shown in this paper, blanket applications of the polytropic law to ambient solar wind can return misleading measurements of α, due to inhomogeneities in the solar wind originating at coronal source regions. However, on a smaller and more localized scale, adiabatic compression and expansion is observed. In this paper, we measure α by examining parcels of originally homogeneous material that have become compressed at stream interactions. A superposed epoch analysis of 73 isolated stream interactions observed by PVO illustrates this adiabatic behavior. Observations of individual stream interactions show clear intervals where α ˜ 5/3 and also a few cases where α ˜ 2, suggesting that the number of degrees of freedom may occasionally be restricted.
Stability analysis of self-similar behaviors in perfect fluid gravitational collapse
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}.
BRIEF COMMUNICATION: A self-similar solution for the implosion problem in a dusty gas
NASA Astrophysics Data System (ADS)
Hirschler, T.; Steiner, H.
2003-03-01
The present work considers the implosion problem in the self-similar limit. The obtained self-similar solution extends Guderley's classical solution [Luftfahrtforschung 19 (1942) 302] to a dust-loaded gas. It encompasses the whole temporal evolution of the flow beginning from the incoming shock ending up in the flow behind the reflected outgoing shock. The influence of the dust is illustrated by a comparison of the results obtained for different dust-loads with the dust-free case.
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
Near-polytropic stellar simulations with a radiative surface
NASA Astrophysics Data System (ADS)
Barekat, A.; Brandenburg, A.
2014-11-01
Context. Studies of solar and stellar convection often employ simple polytropic setups using the diffusion approximation instead of solving the proper radiative transfer equation. This allows one to control separately the polytropic index of the hydrostatic reference solution, the temperature contrast between top and bottom, and the Rayleigh and Péclet numbers. Aims: Here we extend such studies by including radiative transfer in the gray approximation using a Kramers-like opacity with freely adjustable coefficients. We study the properties of such models and compare them with results from the diffusion approximation. Methods: We use the Pencil code, which is a high-order finite difference code where radiation is treated using the method of long characteristics. The source function is given by the Planck function. The opacity is written as κ = κ0ρaTb, where a = 1 in most cases, b is varied from -3.5 to + 5, and κ0 is varied by four orders of magnitude. We adopt a perfect monatomic gas. We consider sets of one-dimensional models and perform a comparison with the diffusion approximation in one- and two-dimensional models. Results: Except for the case where b = 5, we find one-dimensional hydrostatic equilibria with a nearly polytropic stratification and a polytropic index close to n = (3 - b)/(1 + a), covering both convectively stable (n> 3/2) and unstable (n< 3/2) cases. For b = 3 and a = -1, the value of n is undefined a priori and the actual value of n depends then on the depth of the domain. For large values of κ0, the thermal adjustment time becomes long, the Péclet and Rayleigh numbers become large, and the temperature contrast increases and is thus no longer an independent input parameter, unless the Stefan-Boltzmann constant is considered adjustable. Conclusions: Proper radiative transfer with Kramers-like opacities provides a useful tool for studying stratified layers with a radiative surface in ways that are more physical than what is possible with
Caloric curves fitted by polytropic distributions in the HMF model
NASA Astrophysics Data System (ADS)
Campa, Alessandro; Chavanis, Pierre-Henri
2013-04-01
We perform direct numerical simulations of the Hamiltonian mean field (HMF) model starting from non-magnetized initial conditions with a velocity distribution that is (i) Gaussian; (ii) semi-elliptical, and (iii) waterbag. Below a critical energy E c , depending on the initial condition, this distribution is Vlasov dynamically unstable. The system undergoes a process of violent relaxation and quickly reaches a quasi-stationary state (QSS). We find that the distribution function of this QSS can be conveniently fitted by a polytrope with index (i) n = 2; (ii) n = 1; and (iii) n = 1/2. Using the values of these indices, we are able to determine the physical caloric curve T kin ( E) and explain the negative kinetic specific heat region C kin = dE/ d T kin < 0 observed in the numerical simulations. At low energies, we find that the system has a "core-halo" structure. The core corresponds to the pure polytrope discussed above but it is now surrounded by a halo of particles. In case (iii), we recover the "uniform" core-halo structure previously found by Pakter and Levin [Phys. Rev. Lett. 106, 200603 (2011)]. We also consider unsteady initial conditions with magnetization M 0 = 1 and isotropic waterbag velocity distribution and report the complex dynamics of the system creating phase space holes and dense filaments. We show that the kinetic caloric curve is approximately constant, corresponding to a polytrope with index n 0 ≃ 3.56 (we also mention the presence of an unexpected hump). Finally, we consider the collisional evolution of an initially Vlasov stable distribution, and show that the time-evolving distribution function f( θ,v,t) can be fitted by a sequence of polytropic distributions with a time-dependent index n( t) both in the non-magnetized and magnetized regimes. These numerical results show that polytropic distributions (also called Tsallis distributions) provide in many cases a good fit of the QSSs. They may even be the rule rather than the exception
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
More on the losses of dissolved CO(2) during champagne serving: toward a multiparameter modeling.
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.
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.
A novel flux-fluctuation law for network with self-similar traffic
NASA Astrophysics Data System (ADS)
Zhang, Yue; Huang, Ning; Xing, Liudong
2016-06-01
The actual network traffic can show self-similar and long-range dependent features, however, the revealed flux-fluctuation laws are only applicable to networks with short-range dependent traffic. In this paper, we propose an improved theoretical flux-fluctuation law of the self-similar traffic based on Pareto ON/OFF model. The proposed law shows that (i) the greater the self-similarity is, the stronger the influence of the internal factor is; (ii) the influence of the external factor is only determined by a single parameter characterizing the external network load. Numerical simulations illustrate the validity of the proposed flux-fluctuation law under diverse network scales and topologies with various self-similarity of traffic and time windows. We also demonstrate the effectiveness of the proposed law on the actual traffic data in the real GEANT network. As compared to the existing laws, the flux-fluctuation law proposed in this paper can better fit the actual variation of self-similar traffic and facilitate the detection of nodes with abnormal traffic.
Inevitable self-similar topology of binary trees and their diverse hierarchical density
NASA Astrophysics Data System (ADS)
Paik, K.; Kumar, P.
2007-11-01
Self-similar topology, which can be characterized as power law size distribution, has been found in diverse tree networks ranging from river networks to taxonomic trees. In this study, we find that the statistical self-similar topology is an inevitable consequence of any full binary tree organization. We show this by coding a binary tree as a unique bifurcation string. This coding scheme allows us to investigate trees over the realm from deterministic to entirely random trees. To obtain partial random trees, partial random perturbation is added to the deterministic trees by an operator similar to that used in genetic algorithms. Our analysis shows that the hierarchical density of binary trees is more diverse than has been described in earlier studies. We find that the connectivity structure of river networks is far from strict self-similar trees. On the other hand, organization of some social networks is close to deterministic supercritical trees.
Riccati parameterized self-similar waves in two-dimensional graded-index waveguide
NASA Astrophysics Data System (ADS)
Kumar De, Kanchan; Goyal, Amit; Raju, Thokala Soloman; Kumar, C. N.; Panigrahi, Prasanta K.
2015-04-01
An analytical method based on gauge-similarity transformation technique has been employed for mapping a (2+1)- dimensional variable coefficient coupled nonlinear Schrödinger equations (vc-CNLSE) with dispersion, nonlinearity and gain to standard NLSE. Under certain functional relations we construct a large family of self-similar waves in the form of bright similaritons, Akhmediev breathers and rogue waves. We report the effect of dispersion on the intensity of the solitary waves. Further, we illustrate the procedure to amplify the intensity of self-similar waves using isospectral Hamiltonian approach. This approach provides an efficient mechanism to generate analytically a wide class of tapering profiles and widths by exploiting the Riccati parameter. Equivalently, it enables one to control efficiently the self-similar wave structures and hence their evolution.
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.
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.
Newtonian polytropes for anisotropic matter: General framework and applications
NASA Astrophysics Data System (ADS)
Herrera, L.; Barreto, W.
2013-04-01
We set up the general formalism to model polytropic Newtonian stars with anisotropic pressure. We obtain the corresponding Lane-Emden equation. A heuristic model based on an ansatz to obtain anisotropic matter solutions from known solutions for isotropic matter is adopted to illustrate the effects of the pressure anisotropy on the structure of the star. In particular, we calculate the Chandrasekhar mass for a white dwarf. It is clearly displayed how the Chandrasekhar mass limit changes depending on the anisotropy. Prospective astrophysical applications of the proposed approach are discussed.
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.
Self-similar propagation of high-power parabolic pulses in optical fiber amplifiers.
Kruglov, V I; Peacock, A C; Dudley, J M; Harvey, J D
2000-12-15
Self-similarity techniques are used to study pulse propagation in a normal-dispersion optical fiber amplifier with an arbitrary longitudinal gain profile. Analysis of the nonlinear Schrödinger equation that describes such an amplifier leads to an exact solution in the high-power limit that corresponds to a linearly chirped parabolic pulse. The self-similar scaling of the propagating pulse in the amplifier is found to be determined by the functional form of the gain profile, and the solution is confirmed by numerical simulations. The implications for achieving chirp-free pulses after compression of the amplifier output are discussed.
Self-similar propagation and amplification of parabolic pulses in optical fibers.
Fermann, M E; Kruglov, V I; Thomsen, B C; Dudley, J M; Harvey, J D
2000-06-26
Ultrashort pulse propagation in high gain optical fiber amplifiers with normal dispersion is studied by self-similarity analysis of the nonlinear Schrödinger equation with gain. An exact asymptotic solution is found, corresponding to a linearly chirped parabolic pulse which propagates self-similarly subject to simple scaling rules. The solution has been confirmed by numerical simulations and experiments studying propagation in a Yb-doped fiber amplifier. Additional experiments show that the pulses remain parabolic after propagation through standard single mode fiber with normal dispersion.
The self-similar character of the microscopic thermal fluctuation inside an argon-copper nanofluid.
Jia, T; Gao, D
2016-08-01
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. PMID:27440418
Approach to universal self-similar attractor for the levelling of thin liquid films.
Benzaquen, Michael; Fowler, Paul; Jubin, Laetitia; Salez, Thomas; Dalnoki-Veress, Kari; Raphaël, Elie
2014-11-21
We compare the capillary levelling of a random surface perturbation on a thin polystyrene film with a theoretical study on the two-dimensional capillary-driven thin film equation. Using atomic force microscopy, we follow the time evolution of samples prepared with different initial perturbations of the free surface. In particular, we show that the surface profiles present long term self-similarity, and furthermore, that they converge to a universal self-similar attractor that only depends on the volume of the perturbation, consistent with the theory. Finally, we look at the convergence time for the different samples and find very good agreement with the analytical predictions.
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.
Riccati generalization of self-similar solutions of nonautonomous Gross-Pitaevskii equation
NASA Astrophysics Data System (ADS)
Panigrahi, P. K.; Gupta, Rama; Goyal, Amit; Kumar, C. N.
2013-07-01
We present a systematic analytical approach to construct a family of self-similar waves, related through a free parameter, in quasi one-dimension Gross-Pitaevskii equation with time-varying parameters. This approach enables us to control the dynamics of dark and bright similaritons, and first- and second- order self-similar rogue waves in Bose-Einstein condensate through the modulation of time dependent trapping potential. The analysis is done for the sech2- type time-varying quadratic trapping potential for two different choices of linear potential.
Approach to universal self-similar attractor for the levelling of thin liquid films.
Benzaquen, Michael; Fowler, Paul; Jubin, Laetitia; Salez, Thomas; Dalnoki-Veress, Kari; Raphaël, Elie
2014-11-21
We compare the capillary levelling of a random surface perturbation on a thin polystyrene film with a theoretical study on the two-dimensional capillary-driven thin film equation. Using atomic force microscopy, we follow the time evolution of samples prepared with different initial perturbations of the free surface. In particular, we show that the surface profiles present long term self-similarity, and furthermore, that they converge to a universal self-similar attractor that only depends on the volume of the perturbation, consistent with the theory. Finally, we look at the convergence time for the different samples and find very good agreement with the analytical predictions. PMID:25180467
Implementation of polytropic method to study initial structures of gas giant protoplanets
NASA Astrophysics Data System (ADS)
Paul, Gour Chandra; Barman, Mrinal Chandra; Mohit, Abdul Al
2014-12-01
In this paper we have determined the initial structures of gas giant protoplanets, formed via disk instability, having a mass range of 0.3-10 Jupiter masses by the simple polytropic method. The polytropic protoplanets or polytropes have been assumed to be spheres of solar composition, each of which is in a steady state of quasi-static equilibrium, where the only source of energy is the gravitational contraction of the gas. The results of our calculations for the polytropes with polytropic indices n = 1 and n = 1.5 are found to be closer to reality and are in good agreement with the findings obtained by other investigations with more rigorous treatment of the problem.
Naked singularities in non-self-similar gravitational collapse of radiation shells
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.
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.
Space-filling curves of self-similar sets (I): iterated function systems with order structures
NASA Astrophysics Data System (ADS)
Rao, Hui; Zhang, Shu-Qin
2016-07-01
This paper is the first part of a series which provides a systematic treatment of the space-filling curves of self-similar sets. In the present paper, we introduce a notion of linear graph-directed IFS (linear GIFS in short). We show that to construct a space-filling curve of a self-similar set, it amounts to exploring its linear GIFS structures. Compared to the previous methods, such as the L-system or recurrent set method, the linear GIFS approach is simpler, more rigorous and leads to further studies on this topic. We also propose a new algorithm for the beautiful visualization of space-filling curves. In a series of papers Dai et al (2015 arXiv:1511.05411 [math.GN]), Rao and Zhang (2015) and Rao and Zhang (2015), we investigate for a given self-similar set how to get ‘substitution rules’ for constructing space-filling curves, which was obscure in the literature. We solve the problem for self-similar sets of finite type, which covers most of the known results on constructions of space-filling curves.
Influence of heterogeneity on second-kind self-similar solutions for viscous gravity currents
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.
Influence of heterogeneity on second-kind self-similar solutions for viscous gravity currents
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
Non-one-dimensional self-similar solutions with plane waves in gas dynamics
NASA Astrophysics Data System (ADS)
Poslavskii, S. A.; Shikin, I. S.
1986-02-01
A set of new exact self-similar solutions describing the non-one-dimensional adiabatic motions of an ideal gas with plane waves is presented. The solutions include homogeneous gas expansion in planes perpendicular to the direction of the principal motion. It is shown that for such solutions, the system of gasdynamic equations is reduced to a system of ordinary differental equations.
Self-Similar 2d Euler Solutions with Mixed-Sign Vorticity
NASA Astrophysics Data System (ADS)
Elling, Volker
2016-11-01
We construct a class of self-similar 2d incompressible Euler solutions that have initial vorticity of mixed sign. The boundaries between regions of positive and negative vorticity form algebraic spirals, similar to the Kaden spiral and as opposed to Prandtl's logarithmic vortex spirals. Also unlike the Prandtl case, spirals are not initially present.
Leonardo's rule, self-similarity, and wind-induced stresses in trees.
Eloy, Christophe
2011-12-16
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.
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.
Carbon dioxide and ethanol release from champagne glasses, under standard tasting conditions.
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. PMID:23034119
Carbon dioxide and ethanol release from champagne glasses, under standard tasting conditions.
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.
Microbial life in Champagne Pool, a geothermal spring in Waiotapu, New Zealand.
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.
Dynamics Of A Laser-Induced Plume Self-Similar Expansion
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.
Violation of self-similarity in the expansion of a one-dimensional Bose gas
Pedri, P.; Santos, L.; Oehberg, P.; Stringari, S.
2003-10-01
The expansion of a one-dimensional Bose gas after releasing its initial harmonic confinement is investigated employing the Lieb-Liniger equation of state within the local-density approximation. We show that during the expansion the density profile of the gas does not follow a self-similar solution, as one would expect from a simple scaling ansatz. We carry out a variational calculation, which recovers the numerical results for the expansion, the equilibrium properties of the density profile, and the frequency of the lowest compressional mode. The variational approach allows for the analysis of the expansion in all interaction regimes between the mean-field and the Tonks-Girardeau limits, and in particular shows the range of parameters for which the expansion violates self-similarity.
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.
Electromagnetic radiation due to naked singularity formation in self-similar gravitational collapse
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.
Self-similar Expansion of Solar Coronal Mass Ejections: Implications for Lorentz Self-force Driving
NASA Astrophysics Data System (ADS)
Subramanian, Prasad; Arunbabu, K. P.; Vourlidas, Angelos; Mauriya, Adwiteey
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.
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.
Retinal Image Enhancement Using Robust Inverse Diffusion Equation and Self-Similarity Filtering
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
Retinal Image Enhancement Using Robust Inverse Diffusion Equation and Self-Similarity Filtering.
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.
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.
Self-Affinity, Self-Similarity and Disturbance of Soil Seed Banks by Tillage.
Dias, Luís S
2013-07-05
Soil seed banks were sampled in undisturbed soil and after soil had been disturbed by tillage (tine, harrow or plough). Seeds were sorted by size and shape, and counted. Size-number distributions were fitted by power law equations that allowed the identification of self-similarity and self-affinity. Self-affinity and thus non-random size-number distribution prevailed in undisturbed soil. Self-similarity and thus randomness of size-number distribution prevailed after tillage regardless of the intensity of disturbance imposed by cultivation. The values of fractal dimensions before and after tillage were low, suggesting that short-term, short-range factors govern size-number distribution of soil seed banks.
Tests of peak flow scaling in simulated self-similar river networks
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.
Retinal Image Enhancement Using Robust Inverse Diffusion Equation and Self-Similarity Filtering.
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. PMID:27388503
Self-similar expansion of solar coronal mass ejections: Implications for Lorentz self-force driving
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.
Self-similar propagation of Hermite-Gauss water-wave pulses.
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. PMID:26871174
More on the losses of dissolved CO(2) during champagne serving: toward a multiparameter modeling.
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. PMID:23110303
Shear instabilities in a fully compressible polytropic atmosphere
NASA Astrophysics Data System (ADS)
Witzke, V.; Silvers, L. J.; Favier, B.
2015-05-01
Shear flows have a significant impact on the dynamics in an assortment of different astrophysical objects, including accretion discs and stellar interiors. Investigating shear flow instabilities in a polytropic atmosphere provides a fundamental understanding of the motion in stellar interiors where turbulent motions, mixing processes, and magnetic field generation take place. Here, a linear stability analysis for a fully compressible fluid in a two-dimensional Cartesian geometry is carried out. Our study focuses on determining the critical Richardson number for different Mach numbers and the destabilising effects of high thermal diffusion. We find that there is a deviation in the predicted stability threshold for moderate Mach number flows, along with a significant effect on the growth rate of the linear instability for small Péclet numbers. We show that in addition to a Kelvin-Helmholtz instability, a Holmboe instability can appear, and we discuss the implication of this in stellar interiors.
Equation-free dynamic renormalization: Self-similarity in multidimensional particle system dynamics
Zou Yu; Kevrekidis, Ioannis; Ghanem, Roger
2005-10-01
We present an equation-free dynamic renormalization approach to the computational study of coarse-grained, self-similar dynamic behavior in multidimensional particle systems. The approach is aimed at problems for which evolution equations for coarse-scale observables (e.g., particle density) are not explicitly available. Our illustrative example involves Brownian particles in a 2D Couette flow; marginal and conditional inverse cumulative distribution functions (ICDFs) constitute the macroscopic observables of the evolving particle distributions.
Self-similar solution of the problem of a turbulent flow in a round submerged jet
NASA Astrophysics Data System (ADS)
Shmidt, A. V.
2015-05-01
A mathematical model of the flow in a round submerged turbulent jet is considered. The model includes differential transport equations for the normal components of the Reynolds stress tensor and Rodi's algebraic approximations for shear stresses. A theoretical-group analysis of the examined model is performed, and a reduced self-similar system of ordinary differential equations is derived and solved numerically. It is shown that the calculated results agree with available experimental data.
MAGNETIC HELICITY OF SELF-SIMILAR AXISYMMETRIC FORCE-FREE FIELDS
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.
Extracting features of Gaussian self-similar stochastic processes via the Bandt-Pompe approach.
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.
Self-similar erbium-doped fiber laser with large normal dispersion.
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.
Extracting features of Gaussian self-similar stochastic processes via the Bandt-Pompe approach
NASA Astrophysics Data System (ADS)
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.
Counting spanning trees in self-similar networks by evaluating determinants
NASA Astrophysics Data System (ADS)
Lin, Yuan; Wu, Bin; Zhang, Zhongzhi; Chen, Guanrong
2011-11-01
Spanning trees are relevant to various aspects of networks. Generally, the number of spanning trees in a network can be obtained by computing a related determinant of the Laplacian matrix of the network. However, for a large generic network, evaluating the relevant determinant is computationally intractable. In this paper, we develop a fairly generic technique for computing determinants corresponding to self-similar networks, thereby providing a method to determine the numbers of spanning trees in networks exhibiting self-similarity. We describe the computation process with a family of networks, called (x, y)-flowers, which display rich behavior as observed in a large variety of real systems. The enumeration of spanning trees is based on the relationship between the determinants of submatrices of the Laplacian matrix corresponding to the (x, y)-flowers at different generations and is devoid of the direct laborious computation of determinants. Using the proposed method, we derive analytically the exact number of spanning trees in the (x, y)-flowers, on the basis of which we also obtain the entropies of the spanning trees in these networks. Moreover, to illustrate the universality of our technique, we apply it to some other self-similar networks with distinct degree distributions, and obtain explicit solutions to the numbers of spanning trees and their entropies. Finally, we compare our results for networks with the same average degree but different structural properties, such as degree distribution and fractal dimension, and uncover the effect of these topological features on the number of spanning trees.
Self-Similar Evolution of Cosmic-Ray Modified Shocks: The Cosmic-Ray Spectrum
NASA Astrophysics Data System (ADS)
Kang, Hyesung; Ryu, Dongsu; Jones, T. W.
2009-04-01
We use kinetic simulations of diffusive shock acceleration (DSA) to study the time-dependent evolution of plane, quasi-parallel, cosmic-ray (CR) modified shocks. Thermal leakage injection of low-energy CRs and finite Alfvén wave propagation and dissipation are included. Bohm diffusion as well as the diffusion with the power-law momentum dependence are modeled. As long as the acceleration timescale to relativistic energies is much shorter than the dynamical evolution timescale of the shocks, the precursor and subshock transition approach the time-asymptotic state, which depends on the shock sonic and Alfvénic Mach numbers and the CR injection efficiency. For the diffusion models we employ, the shock precursor structure evolves in an approximately self-similar fashion, depending only on the similarity variable, x/(ust). During this self-similar stage, the CR distribution at the subshock maintains a characteristic form as it evolves: the sum of two power laws with the slopes determined by the subshock and total compression ratios with an exponential cutoff at the highest accelerated momentum, p max(t). Based on the results of the DSA simulations spanning a range of Mach numbers, we suggest functional forms for the shock structure parameters, from which the aforementioned form of CR spectrum can be constructed. These analytic forms may represent approximate solutions to the DSA problem for astrophysical shocks during the self-similar evolutionary stage as well as during the steady state stage if p max is fixed.
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.
Self-similarity of human protein interaction networks: a novel strategy of distinguishing proteins
Fadhal, Emad; Gamieldien, Junaid; Mwambene, Eric C.
2015-01-01
The successful determination of reliable protein interaction networks (PINs) in several species in the post-genomic era has hitherto facilitated the quest to understanding systems and structural properties of such networks. It is envisaged that a clearer understanding of their intrinsic topological properties would elucidate evolutionary and biological topography of organisms. This, in turn, may inform the understanding of diseases' aetiology. By analysing sub-networks that are induced in various layers identified by zones defined as distance from central proteins, we show that zones of human PINs display self-similarity patterns. What is observed at a global level is repeated at lower levels of inducement. Furthermore, it is observed that these levels of strength point to refinement and specialisations in these layers. This may point to the fact that various levels of representations in the self-similarity phenomenon offer a way of measuring and distinguishing the importance of proteins in the network. To consolidate our findings, we have also considered a gene co-expression network and a class of gene regulatory networks in the same framework. In all cases, the phenomenon is significantly evident. In particular, the truly unbiased regulatory networks show finer level of articulation of self-similarity. PMID:25720740
Second-type self-similar solutions to the strong explosion problem
NASA Astrophysics Data System (ADS)
Waxman, Eli; Shvarts, Dov
1993-04-01
The flow resulting from a strong explosion at the center of an ideal gas sphere, whose density drops with the distance r from the origin as r-ω, is assumed to approach asymptotically the self-similar solutions by Sedov and Taylor. It is shown that the Sedov-Taylor (ST) solutions that exist only for ω≤5 and are probably the most familiar example for self-similar solutions of the first type fail to describe the asymptotic flow obtained for 3≤ω≤5. New second-type self-similar solutions that describe the asymptotic flow for 3≤ω≤5, as well as for ω≥5, are presented and analyzed. The shock waves described by these solutions are accelerating while the shock waves described by the ST solutions for ω≤3 are decelerating. The new solutions are related to a new singular point in Guderley's map. They exist only for ω values smaller than some ωc that depends upon the adiabatic index of the gas. The asymptotic flow obtained for ω≥ωc is discussed in a subsequent paper.
Self-similar dynamic converging shocks - I. An isothermal gas sphere with self-gravity
NASA Astrophysics Data System (ADS)
Lou, Yu-Qing; Shi, Chun-Hui
2014-07-01
We explore novel self-similar dynamic evolution of converging spherical shocks in a self-gravitating isothermal gas under conceivable astrophysical situations. The construction of such converging shocks involves a time-reversal operation on feasible flow profiles in self-similar expansion with a proper care for the increasing direction of the specific entropy. Pioneered by Guderley since 1942 but without self-gravity so far, self-similar converging shocks are important for implosion processes in aerodynamics, combustion, and inertial fusion. Self-gravity necessarily plays a key role for grossly spherical structures in very broad contexts of astrophysics and cosmology, such as planets, stars, molecular clouds (cores), compact objects, planetary nebulae, supernovae, gamma-ray bursts, supernova remnants, globular clusters, galactic bulges, elliptical galaxies, clusters of galaxies as well as relatively hollow cavity or bubble structures on diverse spatial and temporal scales. Large-scale dynamic flows associated with such quasi-spherical systems (including collapses, accretions, fall-backs, winds and outflows, explosions, etc.) in their initiation, formation, and evolution are likely encounter converging spherical shocks at times. Our formalism lays an important theoretical basis for pertinent astrophysical and cosmological applications of various converging shock solutions and for developing and calibrating numerical codes. As examples, we describe converging shock triggered star formation, supernova explosions, and void collapses.
The "self-similarity logic" applied to the development of the vascular system.
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. PMID:21215741
Self-Similar Theory of Thermal Conduction and Application to the Solar Wind.
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. PMID:26196982
Self-Similar Theory of Thermal Conduction and Application to the Solar Wind.
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.
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.
The density ratio dependence of self-similar Rayleigh-Taylor mixing.
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.
Accretion disk dynamics. α-viscosity in self-similar self-gravitating models
NASA Astrophysics Data System (ADS)
Kubsch, Marcus; Illenseer, Tobias F.; Duschl, Wolfgang J.
2016-04-01
Aims: We investigate the suitability of α-viscosity in self-similar models for self-gravitating disks with a focus on active galactic nuclei (AGN) disks. Methods: We use a self-similar approach to simplify the partial differential equations arising from the evolution equation, which are then solved using numerical standard procedures. Results: We find a self-similar solution for the dynamical evolution of self-gravitating α-disks and derive the significant quantities. In the Keplerian part of the disk our model is consistent with standard stationary α-disk theory, and self-consistent throughout the self-gravitating regime. Positive accretion rates throughout the disk demand a high degree of self-gravitation. Combined with the temporal decline of the accretion rate and its low amount, the model prohibits the growth of large central masses. Conclusions: α-viscosity cannot account for the evolution of the whole mass spectrum of super-massive black holes (SMBH) in AGN. However, considering the involved scales it seems suitable for modelling protoplanetary disks.
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.
NASA Astrophysics Data System (ADS)
Huo, Jiayu; Xu, Tiantian; Guo, Yubin; Wang, Ke; Gao, Bo
2016-05-01
Self-similar pulses are one of the domestic and international research hotspots in the field of nonlinear fiber optics because it can suppress optical wave breaking at high energies. The influence of pumping schemes on the characteristics of self-similar pulses in a passively mode-locked Yb-doped fiber laser is theoretically investigated. The temporal profile and optical spectrum of self-similar pulses in passively mode-locked fiber lasers of different pumping schemes are obtained in the simulation. This study focuses on analyzing the influence of gain bandwidth of gain fiber on the pulse duration, peak power, and single-pulse energy of self-similar pulses.
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
Exploiting the self-similarity in ERP images by nonlocal means for single-trial denoising.
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.
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.
Electromagnetically driven relativistic jets - A class of self-similar solutions
NASA Technical Reports Server (NTRS)
Li, Zhi-Yun; Chiueh, Tzihong; Begelman, Mitchell C.
1992-01-01
A class of self-similar solutions for relativistic winds driven by rotating magnetic fields is constructed. These winds are collimated to cylindrical jet flows of finite radii and may attain supermagnetosonic speeds with high Lorentz factors. Most of the flow acceleration results from the 'magnetic nozzle' effect and occurs beyond the fast magnetosonic point, which is typically located a few light cylinder radii from the rotation axis. Approximate equipartition between the electromagnetic and flow kinetic energies is generally achieved for these jets, in contrast to the radial wind case in which the flow is magnetically dominated at all radii.
Renormalization of the fragmentation equation: exact self-similar solutions and turbulent cascades.
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. PMID:23367898
Kagan, Grigory; Svyatskiy, D; Rinderknecht, H G; Rosenberg, M J; Zylstra, A B; Huang, C-K; McDevitt, C J
2015-09-01
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. 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. PMID:26382682
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.
Experimental determination of self-similarity constant for converging cylindrical shocks
NASA Astrophysics Data System (ADS)
Kjellander, Malte; Tillmark, Nils; Apazidis, Nicholas
2011-11-01
Guderley's self-similarity solution r = r0(1 - t/t0)α for strong converging cylindrical shocks is investigated experimentally for three different gases with adiabatic exponents γ = 1.13; 1.40; and 1.66 and various values of the initial Mach number. Corresponding values of the similarity exponent α which determines the strength of shock convergence are obtained for each gas thus giving the variation of α with γ. Schlieren imaging with multiple exposure technique is used to track the propagation of a single shock front during convergence. The present experimental results are compared with previous experimental, numerical, and theoretical investigations.
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.
Self-similar continuous cascades supported by random Cantor sets: Application to rainfall data.
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.
Self-similar magnetohydrodynamic model for direct current discharge fireball experiments
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)].
Self-similar spectral structures and edge-locking hierarchy in open-boundary spin chains
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.
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.
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
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.
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.
Exact self-similar Bianchi II solutions for some scalar-tensor theories
NASA Astrophysics Data System (ADS)
Belinchón, J. A.
2013-06-01
We study how may behave the gravitational and the cosmological "constants", ( G and Λ) in several scalar-tensor theories with Bianchi II symmetries. By working under the hypothesis of self-similarity we find exact solutions for three different theoretical models, which are: the Jordan-Brans-Dicke (JBD) with Λ( ϕ), the usual JBD model with potential U( ϕ) (that mimics the behavior of Λ( ϕ)) and the induced gravity (IG) model proposed by Sakharov and Zee. After a careful study of the obtained solutions we may conclude that the solutions are quite similar although the IG model shows some peculiarities.
Self-similar continuous cascades supported by random Cantor sets: Application to rainfall data.
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. PMID:27300908
Self-similar spatial structure of a streamer-free nanosecond discharge
NASA Astrophysics Data System (ADS)
Karelin, V. I.; Tren'kin, A. A.
2008-03-01
The microstructure of a current channel is experimentally found under the conditions when homogeneous air gaps are subjected to nanosecond voltage pulses in an electric field insufficient for streamer generation. As a possible mechanism of microstructure formation, instability of the ionization process at the avalanche stage leading to the formation of a self-similar spatial structure is considered. The fractal dimension of this structure is determined. In inhomogeneous gaps, the avalanche is shown to be unstable as well. The energy benefit of structuring is considered. It is demonstrated that the microstructure of streamer discharges in homogeneous gaps can also be treated in terms of the model suggested.
New methods for MRI denoising based on sparseness and self-similarity.
Manjón, José V; Coupé, Pierrick; Buades, Antonio; Louis Collins, D; Robles, Montserrat
2012-01-01
This paper proposes two new methods for the three-dimensional denoising of magnetic resonance images that exploit the sparseness and self-similarity properties of the images. The proposed methods are based on a three-dimensional moving-window discrete cosine transform hard thresholding and a three-dimensional rotationally invariant version of the well-known nonlocal means filter. The proposed approaches were compared with related state-of-the-art methods and produced very competitive results. Both methods run in less than a minute, making them usable in most clinical and research settings. PMID:21570894
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)].
Quantum singularity structure of a class of continuously self-similar spacetimes
NASA Astrophysics Data System (ADS)
Konkowski, Deborah; Helliwell, Thomas; Wiliams, Jon
2016-03-01
The dynamical, classical timelike singularity in a class of continuously self-similar, conformally-static, spherically-symmetric, power-law spacetimes is probed using massless scalar test fields. Ranges of metric parameters for which these classical singularities may be resolved quantum mechanically are determined; however, the wave operator is shown to be not essentially self-adjoint using Weyl's limit point-limit circle criterion. Thus, unfortunately, in this class of spacetimes the wave packet evolution still has the usual ambiguity associated with scattering off singularities. These spacetimes are not healed quantum mechanically.
Ma, Li; Zhou, Jack; Lau, Alan; Low, Samuel; deWit, Roland
2002-01-01
The indentation process of pressing a Rockwell diamond indenter into inelastic material has been studied to provide a means for the analysis, simulation and prediction of Rockwell hardness tests. The geometrical characteristics of the spheroconical-shaped Rockwell indenter are discussed and fit to a general function in a self-similar way. The complicated moving boundary problem in Rockwell hardness tests is simplified to an intermediate stationary one for a flat die indenter using principle of similarity and cumulative superposition approach. This method is applied to both strain hardening and strain rate dependent materials. The effects of different material properties and indenter geometries on the indentation depth are discussed. PMID:27446740
Self-similar fast-reaction limits for reaction-diffusion systems on unbounded domains
NASA Astrophysics Data System (ADS)
Crooks, E. C. M.; Hilhorst, D.
2016-08-01
We present a unified approach to characterising fast-reaction limits of systems of either two reaction-diffusion equations, or one reaction-diffusion equation and one ordinary differential equation, on unbounded domains, motivated by models of fast chemical reactions where either one or both reactant(s) is/are mobile. For appropriate initial data, solutions of four classes of problems each converge in the fast-reaction limit k → ∞ to a self-similar limit profile that has one of four forms, depending on how many components diffuse and whether the spatial domain is a half or whole line. For fixed k, long-time convergence to these same self-similar profiles is also established, thanks to a scaling argument of Kamin. Our results generalise earlier work of Hilhorst, van der Hout and Peletier to a much wider class of problems, and provide a quantitative description of the penetration of one substance into another in both the fast-reaction and long-time regimes.
Self similar solution of superradiant amplification of ultrashort laser pulses in plasma
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.
Scaling of flow distance in random self-similar channel networks
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.
Self-similar solutions of the one-dimensional Landau-Lifshitz-Gilbert equation
NASA Astrophysics Data System (ADS)
Gutiérrez, Susana; de Laire, André
2015-05-01
We consider the one-dimensional Landau-Lifshitz-Gilbert (LLG) equation, a model describing the dynamics for the spin in ferromagnetic materials. Our main aim is the analytical study of the bi-parametric family of self-similar solutions of this model. In the presence of damping, our construction provides a family of global solutions of the LLG equation which are associated with discontinuous initial data of infinite (total) energy, and which are smooth and have finite energy for all positive times. Special emphasis will be given to the behaviour of this family of solutions with respect to the Gilbert damping parameter. We would like to emphasize that our analysis also includes the study of self-similar solutions of the Schrödinger map and the heat flow for harmonic maps into the 2-sphere as special cases. In particular, the results presented here recover some of the previously known results in the setting of the 1D-Schrödinger map equation.
Evidence of Long Range Dependence and Self-similarity in Urban Traffic Systems
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.
Tapering photonic crystal fibers for generating self-similar ultrashort pulses at 1550 nm
NASA Astrophysics Data System (ADS)
Manimegalai, Annamalai; Senthilnathan, Krishnamoorthy; Nakkeeran, Kaliyaperumal; Babu, Padmanabhan Ramesh
2016-06-01
The generation of high-quality self-similar ultrashort pulses at 1550 nm by tapering the photonic crystal fibers (PCFs) is numerically demonstrated. We taper the PCF to achieve the exponentially decreasing dispersion and exponentially increasing nonlinearity profiles, which turn out to be the fundamental requirements for generating the chirped self-similar pulses. Further, we find that the chirped solitons could also be generated with the other three possible exponential variations. Thus, for the first time, we attempt tapering the PCFs for bringing in these exponentially varying dispersion and nonlinear profiles. We carry out the detailed pulse compression studies for various decay rates of the dispersion profiles as the decay rates of dispersion depend on the initial chirp and hence on compression factor, too. The unique feature of this pulse compressor lies in the fact that the required length of the tapered PCF is about 20 times less than that of the previously reported pulse compressor operating at 850 nm.
Self-similar space-time evolution of an initial density discontinuity
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.
Self-similarity of solitary waves on inertia-dominated falling liquid films.
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.
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.
Walkable Worlds give a Rich Self-Similar Structure to the Real Line
NASA Astrophysics Data System (ADS)
Rosinger, Elemér E.
2010-05-01
It is a rather universal tacit and unquestioned belief—and even more so among physicists—that there is one and only one real line, namely, given by the coodinatisation of Descartes through the usual field R of real numbers. Such a dramatically limiting and thus harmful belief comes, unknown to equally many, from the similarly tacit acceptance of the ancient Archimedean Axiom in Euclid's Geometry. The consequence of that belief is a similar belief in the uniqueness of the coordinatization of the plane by the usual field C of complex numbers, and therefore, of the various spaces, manifolds, etc., be they finite or infinite dimensional, constructed upon the real or complex numbers, including the Hilbert spaces used in Quantum Mechanics. A near total lack of awareness follows therefore about the rich self-similar structure of other possible coordinatisations of the real line, possibilities given by various linearly ordered scalar fields obtained through the ultrapower construction. Such fields contain as a rather small subset the usual field R of real numbers. The concept of walkable world, which has highly intuitive and pragmatic algebraic and geometric meaning, illustrates the mentioned rich self-similar structure.
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.
Characterization of self-similarity properties of turbulence in magnetized plasmas
Scipioni, A.; Rischette, P.; Bonhomme, G.; Devynck, P.
2008-11-15
The understanding of turbulence in magnetized plasmas and its role in the cross field transport is still greatly incomplete. Several previous works reported on evidences of long-time correlations compatible with an avalanche-type of radial transport. Persistence properties in time records have been deduced from high values of the Hurst exponent obtained with the rescaled range R/S analysis applied to experimental probe data acquired in the edge of tokamaks. In this paper the limitations of this R/S method, in particular when applied to signals having mixed statistics are investigated, and the great advantages of the wavelets decomposition as a tool to characterize the self-similarity properties of experimental signals are highlighted. Furthermore the analysis of modified simulated fractional Brownian motions (fBm) and fractional Gaussian noises (fGn) allows us to discuss the relationship between high values of the Hurst exponent and long range correlations. It is shown that for such simulated signals with mixed statistics persistence at large time scales can still reflect the self-similarity properties of the original fBm and do not imply the existence of long range correlations, which are destroyed. It is thus questionable to assert the existence of long range correlations for experimental signals with non-Gaussian and mixed statistics just from high values of the Hurst exponent.
Self-similar pinch-off mechanism and scaling of ferrofluid drops.
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. PMID:26764624
CAN AGN FEEDBACK BREAK THE SELF-SIMILARITY OF GALAXIES, GROUPS, AND CLUSTERS?
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.
Self-similarity of solitary waves on inertia-dominated falling liquid films
NASA Astrophysics Data System (ADS)
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.
Drag reduction through self-similar bending of a flexible body.
Alben, Silas; Shelley, Michael; Zhang, Jun
2002-12-01
The classical theory of high-speed flow predicts that a moving rigid object experiences a drag proportional to the square of its speed. However, this reasoning does not apply if the object in the flow is flexible, because its shape then becomes a function of its speed--for example, the rolling up of broad tree leaves in a stiff wind. The reconfiguration of bodies by fluid forces is common in nature, and can result in a substantial drag reduction that is beneficial for many organisms. Experimental studies of such flow-structure interactions generally lack a theoretical interpretation that unifies the body and flow mechanics. Here we use a flexible fibre immersed in a flowing soap film to measure the drag reduction that arises from bending of the fibre by the flow. Using a model that couples hydrodynamics to bending, we predict a reduced drag growth compared to the classical theory. The fibre undergoes a bending transition, producing shapes that are self-similar; for such configurations, the drag scales with the length of self-similarity, rather than the fibre profile width. These predictions are supported by our experimental data.
Dynamics and Stability of Self-similar Pinch-off via Surface Diffusion
NASA Astrophysics Data System (ADS)
Bernoff, Andrew J.; Bertozzi, Andrea L.; Witelski, Thomas P.
1998-11-01
The motion of an interface via surface diffusion is a well-known model in the study of thin solid filaments with application to such fields as integrated circuit technology. The interface moves with a normal velocity proportional to minus the surface Laplacian of its mean curvature. This flow conserves the volume enclosed inside the surface while minimizing its surface area. A cylindrical surface is unstable to long-wave perturbations, analogous to the Rayleigh instability in fluid dynamics. The initial instability leads to a conical pinch-off of the cylinder to form isolated spheres. We examine the structure of the pinch-off, showing it has self-similar structure, using asymptotic, numerical and analytical methods. In addition to a previously known solution(Wong et al. Scripta Mater.) 39(1):55, 1998, we find a countable set of similarity solutions, each with a different cone angle. We develop a stability theory in similarity variables that selects the original similarity solution as the only linearly stable one and consequently the only observable one. We confirm this theory via numerical simulations, using self-similar adaptive mesh refinement, of the pinch-off.
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.
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.
Scale Invariance and Self-Similarity of 1-Dimensional Non-equilibrium Suspended Sediment Transport
NASA Astrophysics Data System (ADS)
Carr, K. J.; Ercan, A.; Kavvas, M. L.
2014-12-01
The conditions under which the governing equation for non-equilibrium one-dimensional suspended sediment transport in unsteady flows is scale-invariant and self-similar are examined by applying the one-parameter Lie group of point scaling transformations. Self-similarity conditions imposed due to initial and boundary conditions are also examined. Furthermore, one-parameter Lie group point scaling transformations required to physically scale the transport process without scaling the sediment material properties are identified and investigated. Preserving sediment density and diameter is believed to eliminate some of the scale errors encountered in traditional scaling methods. Under these conditions, not only are sediment diameter and density unscaled, but so too are the critical and total shear, kinematic viscosity and particle Reynolds number. The similarity of suspended sediment transport is increased through more accurate representation of suspended sediment concentration and carrying capacity of flow. The proposed method meets the needs of modelers by; maintaining the benefits found from distortion such as reduced cost, space, and model run-time; removing the need to apply scaled sediment or surrogate sediment; avoiding some of the scale effects and resulting errors of traditional flow and sediment transport scaling.
Self-similarity of solitary waves on inertia-dominated falling liquid films.
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. PMID:27078461
Self-similarity of phase-space networks of frustrated spin models and lattice gas models
NASA Astrophysics Data System (ADS)
Peng, Yi; Wang, Feng; Han, Yilong
2013-03-01
We studied the self-similar properties of the phase-spaces of two frustrated spin models and two lattice gas models. The frustrated spin models included (1) the anti-ferromagnetic Ising model on a two-dimensional triangular lattice (1a) at the ground states and (1b) above the ground states and (2) the six-vertex model. The two lattice gas models were (3) the one-dimensional lattice gas model and (4) the two-dimensional lattice gas model. The phase spaces were mapped to networks so that the fractal analysis of complex networks could be applied, i.e. the box-covering method and the cluster-growth method. These phase spaces, in turn, establish new classes of networks with unique self-similar properties. Models 1a, 2, and 3 with long-range power-law correlations in real space exhibit fractal phase spaces, while models 1b and 4 with short-range exponential correlations in real space exhibit nonfractal phase spaces. This behavior agrees with one of untested assumptions in Tsallis nonextensive statistics. Hong Kong GRC grants 601208 and 601911
Self-similar log-periodic structures in western stock markets from 2000
M. Bartolozzi; S. Drozdz; D. B. Leinweber; J. Speth; A. W. Thomas
2005-09-01
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 lambda~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.
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.
Self-similar turbulent boundary layer with imposed pressure gradient. Four flow regimes
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.
Self-similarity in Hall plasma discharges: Applications to particle models
Taccogna, Francesco; Longo, Savino; Capitelli, Mario; Schneider, Ralf
2005-05-15
Electron transport is a key process in the physics of Hall thruster discharges. Therefore, a kinetic description of the heavy particles (Xe) as well as electrons is required. The ideal numerical model would be a particle model for all the species. Nowadays, such a model is unpractical because it would need too large an amount of computation time due to the very different time scales of electrons and heavy particles dynamics. For this purpose two scalings to speed-up the execution time of a two-dimensional fully kinetic Particle-in-Cell/Monte Carlo Collision simulation of the Hall thruster SPT-100 are proposed. These two different scaling schemes generate self-similar systems of the acceleration channel including the process of secondary electron emission from the dielectric walls. Instead of using the common approach of a smaller neutral and ion mass or a larger vacuum permittivity the channel dimensions are reduced keeping the main dimensionless physics parameters constant. This leads to scaling laws for the input (magnetic field, mass flow rate, current and voltage discharge, etc.) and output parameters obeying self-similarity. This scaling methodology makes the simulation faster and allows improved modeling of electron interactions and fundamental processes. This model has demonstrated its outstanding capability in improving the physics insight into the processes in SPT-100 under the scaling constraints for the geometrical reduction. The application to particle models of different plasma based devices is suggested for such systems where a linearization of the Boltzmann equation is possible.
Ultra-low-level measurements of 3H and 14C in wines and champagne
NASA Astrophysics Data System (ADS)
Scherer, U. W.; Jacobi, M.; Castillo, J.; Förstel, D. H.
Methods to measure low concentrations of tritium and radiocarbon in wine and champagne, respectively, have been tested by using liquid scintillation counting after chemical sample processing. It could be shown that tritium activity was too low to be measured by our standard low-level liquid scintillation counter, WALLAC Guardian 1414. Positive results could be achieved when using a WALLAC Quantulus. The methods will be established as standard methods to detect forgeries and to improve consumer safety.
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.
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
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
Self-similar accelerative propagation of expanding wrinkled flames and explosion triggering.
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. PMID:21405904
Observation of Self-Similar Behavior of the 3D, Nonlinear Rayleigh-Taylor Instability
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.
Even perturbations of the self-similar Vaidya space-time
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.
Log-periodic oscillations for diffusion on self-similar finitely ramified structures.
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.
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 atmore » the National Ignition Facility.« less
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.
Self-similar accelerative propagation of expanding wrinkled flames and explosion triggering.
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.
Geographical networks stochastically constructed by a self-similar tiling according to population
NASA Astrophysics Data System (ADS)
Hayashi, Yukio; Ono, Yasumasa
2010-07-01
In real communication and transportation networks, the geographical positions of nodes are very important for the efficiency and the tolerance of connectivity. Considering spatially inhomogeneous positions of nodes according to a population, we introduce a multiscale quartered (MSQ) network that is stochastically constructed by recursive subdivision of polygonal faces as a self-similar tiling. It has several advantages: the robustness of connectivity, the bounded short path lengths, and the shortest distance routing algorithm in a distributive manner. Furthermore, we show that the MSQ network is more efficient with shorter link lengths and more suitable with lower load for avoiding traffic congestion than other geographical networks which have various topologies ranging from river to scale-free networks. These results will be useful for providing an insight into the future design of ad hoc network infrastructures.
NASA Astrophysics Data System (ADS)
Robinson, A. P. L.; Schmitz, H.; Fox, T. E.; Pasley, J.; Symes, D. R.
2015-03-01
When strong shocks interact with transverse density gradients, it is well known that vorticity deposition occurs. When two non-planar blast waves interact, a strong shock will propagate through the internal structure of each blast wave where the shock encounters such density gradients. There is therefore the potential for the resulting vorticity to produce pronounced density structures long after the passage of these shocks. If the two blast waves have evolved to the self-similar (Sedov) phase this is not a likely prospect, but for blast waves at a relatively early stage of their evolution this remains possible. We show, using 2D numerical simulations, that the interactions of two 'marginally young' blast waves can lead to strong vorticity deposition which leads to the generation of a strong protrusion and vortex ring as mass is driven into the internal structure of the weaker blast wave.
Self-Similar evolution of Richtmyer-Meshkov instability under re-shock conditions
NASA Astrophysics Data System (ADS)
Malamud, Guy; Leinov, Eli; Formoza, Asi; Sadot, Oren; Levin, Arie; Ben-Dor, Gabi; Elbaz, Yonatan; Shvarts, Dov
2011-10-01
The Richtmyer-Meshkov (RM) instability is of critical importance in inertial confinement fusion (ICF) and astrophysics. In the present work a systematic study has been made of the growth of the turbulent mixing zone (TMZ) under re-shock conditions. In this study, shock-tube experiments were done by Leinov et al. changing the re-shock arrival time, by varying the shock-tube end wall distance, as well as the shock Mach number. Using 3D direct numerical simulations as well as 3D bubble-competition model, for various initial 3D conditions, it was found that the best agreement with the experimental results is achieved when the TMZ evolution is dominated by the self-similar behavior of the bubble size and amplitude distributions. The TMZ power law at the first and second shock was deducted from the experimental and numerical data and compared with the results of the bubble competition model.
Self-similar solution of the problem of consolidation and thawing of frozen soil
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.
Self-similar texture modeling using FARIMA processes with applications to satellite images.
Ilow, J; Leung, H
2001-01-01
A texture model for synthetic aperture radar (SAR) images is presented. Specifically, a sea surface in satellite images is modeled using the two-dimensional (2-D) fractionally integrated autoregressive-moving average (FARIMA) process with a non-Gaussian white driving sequence. The FARIMA process is an ARMA type model which is asymptotically self-similar. It captures the long-range as well as short-range spatial dependence structure of an image with a small number of parameters. To estimate these parameters, an efficient estimation procedure based on a spectral fit is presented. Real-life ocean surveillance radar images collected by the RADARSAT sensor are used to evaluate the practicality of this FARIMA approach. Using the radial power spectral density, the new model is shown to provide a more accurate description of the SAR images than the conventional moving-average (MA), autoregressive (AR), and fractionally differenced (FD) models. PMID:18249668
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.
Self-similar formation of an inverse cascade in vibrating elastic plates
NASA Astrophysics Data System (ADS)
Düring, Gustavo; Josserand, Christophe; Rica, Sergio
2015-05-01
The dynamics of random weakly nonlinear waves is studied in the framework of vibrating thin elastic plates. Although it has been previously predicted that no stationary inverse cascade of constant wave action flux could exist in the framework of wave turbulence for elastic plates, we present substantial evidence of the existence of a time-dependent inverse cascade, opening up the possibility of self-organization for a larger class of systems. This inverse cascade transports the spectral density of the amplitude of the waves from short up to large scales, increasing the distribution of long waves despite the short-wave fluctuations. This dynamics appears to be self-similar and possesses a power-law behavior in the short-wavelength limit which significantly differs from the exponent obtained via a Kolmogorov dimensional analysis argument. Finally, we show explicitly a tendency to build a long-wave coherent structure in finite time.
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.
Scale-invariant cellular automata and self-similar Petri nets
NASA Astrophysics Data System (ADS)
Schaller, M.; Svozil, K.
2009-05-01
Two novel computing models based on an infinite tessellation of space-time are introduced. They consist of recursively coupled primitive building blocks. The first model is a scale-invariant generalization of cellular automata, whereas the second one utilizes self-similar Petri nets. Both models are capable of hypercomputations and can, for instance, “solve” the halting problem for Turing machines. These two models are closely related, as they exhibit a step-by-step equivalence for finite computations. On the other hand, they differ greatly for computations that involve an infinite number of building blocks: the first one shows indeterministic behavior, whereas the second one halts. Both models are capable of challenging our understanding of computability, causality, and space-time.
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.
Self-similar micron-size and nanosize drops of liquid generated by surface acoustic waves.
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. PMID:23368125
Self-similar hot accretion flow onto a rotating neutron star: Structure and stability
NASA Astrophysics Data System (ADS)
Medvedev, Mikhail V.; Narayan, Ramesh
2001-10-01
We present analytical and numerical solutions which describe a hot, viscous, two-temperature accretion flow onto a rotating neutron star or any other rotating compact star with a surface. We assume Coulomb coupling between the protons and electrons, and free-free cooling from the electrons. Outside a thin boundary layer, where the accretion flow meets the star, we show that there is an extended settling region which is well-described by two self-similar solutions: (i) a two-temperature solution which is valid in an inner zone r<=102.5 (r is in Schwarzchild units), and (ii) a one-temperature solution at larger radii. In both zones, ρ~r-2, Ω~r-3/2, v~r0, Tp~r-1 in the two-temperature zone, Te~r-1/2. The luminosity of the settling zone arises from the rotational energy of the star as the star is braked by viscosity. Hence the luminosity and the flow parameters (density, temperature, angular velocity) are independent of M. The settling solution described here is not advection-dominated, and is thus different from the self-similar ADAF found around black holes. When the spin of the star is small enough, however, the present solution transforms smoothly to a (settling) ADAF. We carried out a stability analysis of the settling flow. The flow is convectively and viscously stable and is unlikely to have strong winds or outflows. Unlike another cooling-dominated system-the SLE disk,-the settling flow is thermally stable provided that thermal conduction is taken into account. This strong saturated-like thermoconduction does not change the structure of the flow. .
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.
SELF-SIMILAR DYNAMICAL RELAXATION OF DARK MATTER HALOS IN AN EXPANDING UNIVERSE
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.
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.
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.
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
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
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
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.
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
General relativistic polytropes for anisotropic matter: The general formalism and applications
NASA Astrophysics Data System (ADS)
Herrera, L.; Barreto, W.
2013-10-01
We set up in detail the general formalism to model polytropic general relativistic stars with anisotropic pressure. We shall consider two different possible polytropic equations, all of which yield the same Lane-Emden equation in the Newtonian limit. A heuristic model based on an ansatz to obtain anisotropic matter solutions from known solutions for isotropic matter is adopted to illustrate the effects of the pressure anisotropy on the structure of the star. In this context, the Tolman mass, which is a measure of the active gravitational mass, is invoked to explain some features of the models. Prospective extensions of the proposed approach are pointed out.
NASA Astrophysics Data System (ADS)
Zhang, Yunchao; Charles, Christine; Boswell, Rod
2016-09-01
Non-local electron energy probability functions (EEPFs) are shown to have an important effect on the thermodynamic behavior of plasmas in the context of solar wind and laboratory plasmas. A conservation relation is held for electron enthalpy and plasma potential during the electron transport. For an adiabatic system governed by non-local electron dynamics, the correlation between electron temperature and density can be approximated by a polytropic relation, with different indexes demonstrated using three cases of bi-Maxwellian EEPFs. This scenario differs from a local thermodynamic equilibrium having a single polytropic index of 5/3 for adiabaticity.
Viscoelastic properties of the nematode Caenorhabditis elegans, a self-similar, shear-thinning worm.
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. PMID:23460699
Multidimensional self-similar analytical solutions of two-phase flow in porous media
NASA Astrophysics Data System (ADS)
Fučík, Radek; Illangasekare, Tissa H.; Beneš, Michal
2016-04-01
In general, analytical solutions serve a useful purpose to obtain better insights and to verify numerical codes. For flow of two incompressible and immiscible phases in homogeneous porous media without gravity, one such method that neglects capillary pressure in the solution was first developed by Buckley and Leverett (1942). Subsequently, McWhorter and Sunada (1990) derived an exact solution for the one and two dimensional cases that factored in capillary effects. This solution used a similarity transform that allowed to reduce the governing equations into a single ordinary differential equation (ODE) that can be further integrated into an equivalent integral equation. We present a revision to McWhorter and Sunada solution by extending the self-similar solution into a general multidimensional space. Inspired by the derivation proposed by McWhorter and Sunada (1990), we integrate the resulting ODE in the third and higher dimensions into a new integral equation that can be subsequently solved iteratively by means of numerical integration. We developed implementations of the iterative schemes for one- and higher dimensional cases that can be accessed online on the authors' website.
Self-similar nonequilibrium dynamics of a many-body system with power-law interactions.
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. PMID:26764669
Self similar growth of a 1D granular fan under laminar flow near threshold
NASA Astrophysics Data System (ADS)
Guerit, Laure; Métivier, François; Devauchelle, Olivier; Lajeunesse, Eric; Barrier, Laurie
2014-05-01
Alluvial fans are major sedimentary bodies that make the transition between the reliefs and the sedimentary basins. They are found at the outlet of some drainages catchments, where rivers are free to diverge and avulse, and to depose part of their sedimentary load. Understanding their dynamics of formation and evolution is a great problem of sediment transport. Rivers and fan profiles are usually described as diffusive systems but this is only true if the shear stress exerted on the bed is high compared to the critical shear stress. This might be the case for sand bed rivers, but not for gravel bed rivers, for which it is known that the shear stress is only slightly higher than the critical one. This is why we need to develop a new model to describe the evolution of alluvial fans built by gravel bed rivers. To do this analytically, we work in 1D, with a laminar flow and one grain-size in order to be able to describe both the fluid and the sediment transport. In addition, the conditions of the experiments insured that the boundary shear stress is near the critical value for motion inception of the granular material. Using Taylor expansion, we show that for asymptotically long times, the fan growth is self-similar and can be decomposed into a triangular ``threshold" shape plus a small quadratic deviation. We performed experiments with glass beads and glycerol to test and successfully validate this theory.
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.
Fast Diffusion to Self-Similarity: Complete Spectrum, Long-Time Asymptotics, and Numerology
NASA Astrophysics Data System (ADS)
Denzler, Jochen; McCann, Robert J.
2005-03-01
The complete spectrum is determined for the operator on the Sobolev space W1,2ρ(Rn) formed by closing the smooth functions of compact support with respect to the norm Here the Barenblatt profile ρ is the stationary attractor of the rescaled diffusion equation in the fast, supercritical regime m the same diffusion dynamics represent the steepest descent down an entropy E(u) on probability measures with respect to the Wasserstein distance d2. Formally, the operator H=HessρE is the Hessian of this entropy at its minimum ρ, so the spectral gap H≧α:=2-n(1-m) found below suggests the sharp rate of asymptotic convergence: from any centered initial data 0≦u(0,x) ∈ L1(Rn) with second moments. This bound improves various results in the literature, and suggests the conjecture that the self-similar solution u(t,x)=R(t)-nρ(x/R(t)) is always slowest to converge. The higher eigenfunctions which are polynomials with hypergeometric radial parts and the presence of continuous spectrum yield additional insight into the relations between symmetries of Rn and the flow. Thus the rate of convergence can be improved if we are willing to replace the distance to ρ with the distance to its nearest mass-preserving dilation (or still better, affine image). The strange numerology of the spectrum is explained in terms of the number of moments of ρ.
Local gain control and focal accommodation in the Self Similar Stack vision model.
Haig, N D
1993-01-01
The aim of this paper is to report an extension to the computationally efficient Self Similar Stack model (Burton et al. Biol., Cybernet. 53, 397-403, 1986) to include the effects of local gain control in the retina. The method employed to do this has been to fit a family of difference-of-Gaussian functions to the human contrast sensitivity function curves of van Nes and Bouman (J. Opt. Soc. Am. 57, 401-406, 1967). The centre frequencies of the DoGs within each family are octave-related, in a simplified manifestation of the DoG channels found by Wilson et al. (Vision Res. 23, 873-882, 1983). The sensitivity of each level, or channel, that formed the original Stack model is modulated individually according to the fitted values, as the local illumination varies within an image. The model was tested against psychometric data obtained by Haig and Burton (Appl. Optics 26, 492-500, 1987) during experiments on visual discrimination. The consistency of the results indicates the validity of the approximations and the robustness of the model, either for machine vision purposes or for predicting human visual performance. A simple algorithm, developed for use with a machine vision application of this model, provides a means by which a TV camera may be focused automatically. The success of this algorithm, using the newly computed channel sensitivities, suggests that human focal accommodation may be regulated by a similar form of mechanism. PMID:8494807
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.
Self-similar inverse cascade of magnetic helicity driven by the chiral anomaly
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
Self-similar inverse cascade of magnetic helicity driven by the chiral anomaly
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.
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.
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.
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.
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.
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.
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.
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.
Manifold angles, the concept of self-similarity, and angle-enhanced bifurcation diagrams
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. PMID:26732416
Tabulation of complex chemistry based on self-similar behavior of laminar premixed flames
Ribert, G.; Gicquel, O.; Darabiha, N.; Veynante, D.
2006-09-15
Detailed mechanisms describing complex phenomena of combustion chemistry, such as flame propagation or pollutant formation, involve hundreds of species and thousands of elementary reactions and cannot be handled in practical simulations of turbulent combustion. A widely used way to reduce chemistry is to build look-up tables where chemical parameters such as reaction rates and/or species mass fractions are determined from a reduced set of coordinates (ILDM, FPI, or FGM methods). Nevertheless, these tables may require large memory spaces and nonnegligible access times, especially when running on massively parallel computers. In this work, the self-similarity behavior of laminar premixed flames is first put into evidence and then theoretically sustained. This property provides a way to reduce the size of chemical databases, especially for computations on massively parallel machines, under the FPI (flame prolongation of ILDM) framework. The database is reduced to similarity profiles for the species reaction rates (or the species mass fractions), stored together with scaling rules. This new formulation is then implemented in the PREMIX code and numerical simulations of laminar premixed flames successfully compare with full chemistry computation, validating this promising approach. (author)
Lévy Flights and Self-Similar Exploratory Behaviour of Termite Workers: Beyond Model Fitting
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
Self-Similar Random Process and Chaotic Behavior In Serrated Flow of High Entropy Alloys
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
Analyzing Self-Similar and Fractal Properties of the C. elegans Neural Network
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
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.
Self-Similar Random Process and Chaotic Behavior In Serrated Flow of High Entropy Alloys.
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
Berntson, G. M.; Stoll, P.
1997-01-01
Fractal geometry is a potentially valuable tool for quantitatively characterizing complex structures. The fractal dimension (D) can be used as a simple, single index for summarizing properties of real and abstract structures in space and time. Applications in the fields of biology and ecology range from neurobiology to plant architecture, landscape structure, taxonomy and species diversity. However, methods to estimate the D have often been applied in an uncritical manner, violating assumptions about the nature of fractal structures. The most common error involves ignoring the fact that ideal, i.e. infinitely nested, fractal structures exhibit self-similarity over any range of scales. Unlike ideal fractals, real-world structures exhibit self-similarity only over a finite range of scales. Here we present a new technique for quantitatively determining the scales over which real-world structures show statistical self-similarity. The new technique uses a combination of curve-fitting and tests of curvilinearity of residuals to identify the largest range of contiguous scales that exhibit statistical self-similarity. Consequently, we estimate D only over the statistically identified region of self-similarity and introduce the finite scale- corrected dimension (FSCD). We demonstrate the use of this method in two steps. First, using mathematical fractal curves with known but variable spatial scales of self-similarity (achieved by varying the iteration level used for creating the curves), we demonstrate that our method can reliably quantify the spatial scales of self-similarity. This technique therefore allows accurate empirical quantification of theoretical Ds. Secondly, we apply the technique to digital images of the rhizome systems of goldenrod (Solidago altissima). The technique significantly reduced variations in estimated fractal dimensions arising from variations in the method of preparing digital images. Overall, the revised method has the potential to significantly
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.
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 É) (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 É and h. In this study, we expand this to a more general É-η-h relationship. We approach É-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.
Signal-noise separation based on self-similarity testing in 1D-timeseries data
NASA Astrophysics Data System (ADS)
Bourdin, Philippe A.
2015-08-01
The continuous improvement of the resolution delivered by modern instrumentation is a cost-intensive part of any new space- or ground-based observatory. Typically, scientists later reduce the resolution of the obtained raw-data, for example in the spatial, spectral, or temporal domain, in order to suppress the effects of noise in the measurements. In practice, only simple methods are used that just smear out the noise, instead of trying to remove it, so that the noise can nomore be seen. In high-precision 1D-timeseries data, this usually results in an unwanted quality-loss and corruption of power spectra at selected frequency ranges. Novel methods exist that are based on non-local averaging, which would conserve much of the initial resolution, but these methods are so far focusing on 2D or 3D data. We present here a method specialized for 1D-timeseries, e.g. as obtained by magnetic field measurements from the recently launched MMS satellites. To identify the noise, we use a self-similarity testing and non-local averaging method in order to separate different types of noise and signals, like the instrument noise, non-correlated fluctuations in the signal from heliospheric sources, and correlated fluctuations such as harmonic waves or shock fronts. In power spectra of test data, we are able to restore significant parts of a previously know signal from a noisy measurement. This method also works for high frequencies, where the background noise may have a larger contribution to the spectral power than the signal itself. We offer an easy-to-use software tools set, which enables scientists to use this novel technique on their own noisy data. This allows to use the maximum possible capacity of the instrumental hardware and helps to enhance the quality of the obtained scientific results.
Self-similar fragmentation regulated by magnetic fields in a region forming massive stars.
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.
Cote, Yoann; Senet, Patrick; Delarue, Patrice; Maisuradze, Gia G; Scheraga, Harold A
2010-11-16
Structural fluctuations of a protein are essential for the function of native proteins and for protein folding. To understand how the main chain in the native state of a protein fluctuates on different time scales, we examined the rotational correlation functions (RCFs), C(t), of the backbone N-H bonds and of the dihedral angles γ built on four consecutive C(α) atoms. Using molecular dynamics simulations of a model α/β protein (VA3) in its native state, we demonstrate that these RCFs decay as stretched exponentials, ln[C(t)] ≈ D(α)t(α) with a constant D(α) and an exponent α (0 < α < 0.35) varying with the free-energy profiles (FEPs) along the amino acid sequence. The probability distributions of the fluctuations of the main chain computed at short time scale (1 ps) were identical to those computed at large time scale (1 ns) if the time is rescaled by a factor depending on α < 1. This self-similar property and the nonexponential decays (α ≠ 1) of the RCFs are described by a rotational diffusion equation with a time-dependent diffusion coefficient D(t) = αD(α)t(α-1). The present findings agree with observations of subdiffusion (α < 1) of fluorescent probes within a protein molecule. The subdiffusion of (15)N-H bonds did not affect the value of the order parameter S(2) extracted from the NMR relaxation data by assuming normal diffusion (α = 1) of (15)N-H bonds on a nanosecond time scale. However, we found that the RCF does not converge to S(2) on the nanosecond time scale for residues with multiple-minima FEPs.
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.
NASA Astrophysics Data System (ADS)
He, Jun-Rong; Yi, Lin
2014-06-01
We study the propagations of optical self-similar solutions in a tapered graded-index nonlinear-fiber amplifier with an external source through asymmetric twin-core fiber amplifiers. Various types of exact self-similar solutions, including the W-shaped and U-shaped solutions, trigonometric function solutions, and periodic wave solutions are found. The results show that these different types of self-similar optical structures can be generated and effectively controlled by modulating the amplitude of the source. The influences of nonlinear tunneling effects on the propagation of optical pulses are investigated as well. The obtained results may have potential applications in a tapered graded-index nonlinear-fiber amplifier with an external source.
The cometary H II regions of DR 21: Bow shocks or champagne flows or both?
NASA Astrophysics Data System (ADS)
Immer, K.; Cyganowski, C.; Reid, M. J.; Menten, K. M.
2014-03-01
We present deep Very Large Array H66α radio recombination line (RRL) observations of the two cometary H II regions in DR 21. With these sensitive data, we test the "hybrid" bow shock/champagne flow model previously proposed for the DR 21 H II regions. The ionized gas down the tail of the southern H II region is redshifted by up to ~30 km s-1 with respect to the ambient molecular gas, as expected in the hybrid scenario. The RRL velocity structure, however, reveals the presence of two velocity components in both the northern and southern H II regions. This suggests that the ionized gas is flowing along cone-like shells, swept-up by stellar winds. The observed velocity structure of the well-resolved southern H II region is most consistent with a picture that combines a stellar wind with stellar motion (as in bow shock models) along a density gradient (as in champagne flow models). The direction of the implied density gradient is consistent with that suggested by maps of dust continuum and molecular line emission in the DR 21 region. The image cubes are only available as a FITS file at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/563/A39Table 2, Fig. 4, and Appendices A and B are available in electronic form at http://www.aanda.org
Zolotovskii, Igor' O; Okhotnikov, Oleg G; Sementsov, Dmitrii I; Sysolyatin, A A; Fotiadi, A A
2012-09-30
This paper examines the possibility of efficient amplification of self-similar frequency-modulated wave packets in longitudinally inhomogeneous active fibres. We analyse the dynamics of parabolic pulses with a constant frequency modulation rate and derive algorithms for optimising the group velocity dispersion profile in order to ensure self-similar propagation of such pulses. We demonstrate that the use of a cascade scheme can ensure efficient amplification of individual subpicosecond pulses of this type. (optical fibres, lasers and amplifiers. properties and applications)
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
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
NASA Astrophysics Data System (ADS)
Lee, Y.; Ma, K.; Yen, Y.
2013-12-01
The work of finite fault slip models have been done in several earthquake events. We compiled the finite fault slip models of 19 earthquakes in Taiwan within the magnitude range from Mw=4.56 to 7.69 which include different fault types. We analyzed the distribution of slip on the fault surface to get the scaling relation of slip values, and found the scaling relation can be shown as Rs=10^(a+n(Rd)) (where Rd is (d/dm) as the ratio of slip, d, to the average of the effective slip, dm, Rs is A/Ae as the ratio of the fault area, A, where slip d>R_d×d_m to the effective area, Ae. The effective area and slip were determined according to the normalization of the autocorrelation of slip in length and width. The fault slip was displayed a self-similar scaling, the scaling exponent values (n) are within n=0~-1.1 which can be relative with fractal dimension of fault slip system. The scaling exponents (n) also can be seen as a measure for the roughness degree of the slip distribution on the fault surface. For lower values of n, the gradient of the slip distribution increases, and the slip models become more heterogeneous. Based on the definition of asperity as Sa(d/dm>1.5), we also got a scaling relation between asperity and magnitude as Sa(d/dm>1.5)=1.27Mw-6.49. As found in several large earthquakes, we also observed that Sa is about 20% of Ae, where Sa is the area with the slip larger than 1.5 times of the mean slip. Very intriguing feature on the relationship of the average area ratio of the examined earthquakes (M~4.5-7.6) for Rs as function of Rd follows a fractal dimension of about 0.5, as logRs= 0.428Rd-0.078. This fractal dimension might bring some hints in understanding of earthquake rupture mechanics on fault fracturing. The correlation between the average area ratio of the examined earthquakes (M~4.5-7.6) for Rs to Rd. Rs is the ratio of the fault area where slip d>R_d×d_m to the effective area, and Rd is the ratio of slip to the average of the effective slip.
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.
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
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.
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
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. PMID:22347390
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.
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.
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
2015-01-01
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. PMID:25897020
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
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
2D Self-Similar Profile for Laser Beam Propagation in Medium with Saturating Multi-Photon Absorption
NASA Astrophysics Data System (ADS)
Trofimov, Vyacheslav A.; Lysak, Tatiana M.; Zakharova, Irina G.
2016-02-01
We study a self-similar mode of 2D laser beam propagation in media with multiphoton absorption (MA) taking into account a resonant nonlinearity and nonlinear absorption saturating. An analytical solution of the corresponding equations describing the problems under consideration is derived using an eigenvalue problem method generalization for soliton- like solution finding. The developed solution is used as incident beam profile and phase front for computer simulation of the 2D laser beam propagation. In particular, we demonstrate numerically that the laser beam propagation in a self-similar mode occurs within a certain distance, which depends on medium properties. Under certain relations between the nonlinear absorption and resonant nonlinearity, and cubic nonlinear response, we observe the super long distance of the beam propagation without any beam profile distributions.
NASA Astrophysics Data System (ADS)
Essone Mezeme, M.; Lasquellec, S.; Brosseau, C.
2011-08-01
We apply first-principles methodology to study the spatial localization of electric field enhancement at plasmonic resonance and magnetic field enhancement at gyroresonance in a self-similar chain of magnetoplasmonic core-shell nanostructures (MCSNs). Localized regions of high electric and magnetic fields in the vicinity of metal nanostructures can be created in a controlled manner by adjusting the physical parameters characterizing this system and the polarization of the external harmonic excitations. We demonstrate the high degree of control achieved on electric field confinement, of the order of 103, down to a feature size of λ/1000 in self-similar chains of MCSNs, where λ denotes the free space wavelength of the resonant excitation. We also compare our findings with recent investigations in related plasmonic nanostructures.
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.
High-power self-similar amplification seeded by a 1 GHz harmonically mode-locked Yb-fiber laser
NASA Astrophysics Data System (ADS)
Luo, Daping; Li, Wenxue; Liu, Yang; Wang, Chao; Zhu, Zhiwei; Zhang, Wenchao; Zeng, Heping
2016-08-01
We demonstrate 1 GHz, 75 W, 65 fs pulse generation through chirped-pulse and self-similar amplification of a second-harmonic mode-locked Yb fiber oscillator. To confirm the experimental results of a chirped-pulse pre-amplifier, a theoretically calculative model is designed to simulate gain narrowing in the amplification. Specifically, the Kelly sidebands generated by a seed laser experience similar evolution under both conditions. The grism-based self-similar amplifier together with a high-efficiency grating compressor contribute to high-power ultrashort pulses whose spectra are efficiently broadened to a maximum 10 dB bandwidth of 56 nm with a center wavelength of 1032.2 nm owing to self-phase modulation in a gain fiber.
Effect of self-similar traffic on the performance and buffer requirements of ATM ABR edge devices
Dastangoo, S.; Miller, G.J.; Chen, H.; Brandt, J.
1996-02-05
Previous studies demonstrated that Ethemet local area network traffic is statistically self-similar and that the commonly used Poisson models are not able to capture the fractal characteristics of Ethemet traffic. This contribution uses simulated self-similar traffic traces from the MITRE Corporation and Sandia`s simulation software to evaluate the ABR performance of an ATM backbone. The ATM backbone interconnects Ethemet LANs via edge devices such as routers and bridges. We evaluate the overall network performance in terms of throughput, response time, fairness, and buffer requirements. Because typical edge devices perform simple forwarding functions, their usual mechanism for signaling network congestion is packet dropping. Therefore, we believe that the proper provisioning of buffer resources in ATM edge devices is crucial to the overall network performance.
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.
Courtial, J; Padgett, M J
2000-12-18
A novel mechanism is proposed for the generation of self-similar structure over a limited range of length scales. Our mechanism, which we call the monitor-outside-a-monitor effect, comprises repeated magnification and addition of small-scale structure. We invoke this mechanism to explain recent observations of fractal structure in the eigenmodes of unstable optical resonators [G. P. Karman et al., Nature (London) 402, 138 (1999)]. PMID:11135986
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.
NASA Astrophysics Data System (ADS)
Lin, Min-Kai
2012-07-01
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.
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.
The ion polytropic coefficient in a collisionless sheath containing hot ions
NASA Astrophysics Data System (ADS)
Lin, Binbin; Xiang, Nong; Ou, Jing
2016-08-01
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.
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.
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.
Lancia, L; Giribono, A; Vassura, L; Chiaramello, M; Riconda, C; Weber, S; Castan, A; Chatelain, A; Frank, A; Gangolf, T; Quinn, M N; Fuchs, J; Marquès, J-R
2016-02-19
Plasma-based laser amplification is considered as a possible way to overcome the technological limits of present day laser systems and achieve exawatt laser pulses. Efficient amplification of a picosecond laser pulse by stimulated Brillouin scattering (SBS) of a pump pulse in a plasma requires to reach the self-similar regime of the strongly coupled (SC) SBS. In this Letter, we report on the first observation of the signatures of the transition from linear to self-similar regimes of SC-SBS, so far only predicted by theory and simulations. With a new fully head-on collision geometry, subpicosecond pulses are amplified by a factor of 5 with energy transfers of few tens of mJ. We observe pulse shortening, frequency spectrum broadening, and down-shifting for increasing gain, signatures of SC-SBS amplification entering the self-similar regime. This is also confirmed by the power law dependence of the gain on the amplification length: doubling the interaction length increases the gain by a factor 1.4. Pump backward Raman scattering (BRS) on SC-SBS amplification has been measured for the first time, showing a strong decrease of the BRS amplitude and frequency bandwidth when SBS seed amplification occurs. PMID:26943539
NASA Astrophysics Data System (ADS)
Funning, G.; Ferreira, A. M.; Weston, J. M.; Bloomfield, H.
2013-12-01
The question of how moment release in earthquakes scales to other earthquake source parameters, such as fault length and average slip, is a long-standing controversy (e.g. Scholz, 1982, 1994; Romanowicz, 1992). It is a problem that speaks to issues of earthquake source mechanics, specifically the self-similarity of earthquakes - is stress drop constant across all magnitudes? Theoretically, two end-member scaling models have been proposed - the so-called ';W-model', whereby seismic moment scales linearly with fault length, and the alternative ';L-model', where moment scales with the square of fault length. Existing data on earthquake rupture dimensions, typically from field observations or aftershock locations, do not conclusively favor one over the other. A W-model implies a constant stress drop for all earthquakes in the same tectonic setting, and therefore that earthquakes are self-similar. The L-model does not imply self-similarity, but is consistent with the idea that ';large earthquakes' (i.e. earthquakes that rupture the full thickness of the brittle upper crust) grow by increasing their rupture length, with average slip being proportional to fault length. To address this problem, we use a compilation of source parameter information from over 130 published studies of 101 individual earthquakes (Mw 4.7-9.0) studied using InSAR. There are several reasons to suggest that this information will be highly suitable for the study of earthquake scaling. The high spatial resolution and centimetric precision of InSAR data provide strong constraints on estimates of fault length and slip. In addition, in a previous study, we found good agreement between moment estimates from InSAR studies and the Global CMT catalog, derived from long-period seismic data (Weston et al., 2011). Considering events of all mechanisms together, we find a scaling relationship between moment (M0) and fault length (L), such that M0 ∝ L1.8. We find differences in this power law exponent with
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
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
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. PMID:27080902
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
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
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
Lee, Yik Ching; Clark, Alys R; Fuld, Matthew K; Haynes, Susan; Divekar, Abhay A; Hoffman, Eric A; Tawhai, Merryn H
2013-05-01
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
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.
Multi-time-scale congestion control mechanism based on the alpha-stable self-similar processes
NASA Astrophysics Data System (ADS)
Ge, Xiaohu; Zhu, Guangxi; Zhu, Yaoting; Shi, Chunyan
2004-04-01
A multi-time scale congestion control mechanism has been proposed in this paper, which utilizes the characteristic of self-similar in the network. Based on the theory of the alpha-stable processes, a prediction model is brought forward and a frame of multi-time scale is designed. The aim of all of those is try to avoid the congestion of network in statistically. Moreover, the frame of the new congestion control mechanism is described and the working procedure of the new congestion control mechanism is explained.
Qin Hong; Davidson, Ronald C.
2011-08-15
In a linear trap confining a one-component nonneutral plasma, the external focusing force is a linear function of the configuration coordinates and/or the velocity coordinates. Linear traps include the classical Paul trap and the Penning trap, as well as the newly proposed rotating-radio-frequency traps and the Mobius accelerator. This paper describes a class of self-similar nonlinear solutions of nonneutral plasma in general time-dependent linear focusing devices, with self-consistent electrostatic field. This class of nonlinear solutions includes many known solutions as special cases.
NASA Astrophysics Data System (ADS)
Qin, Hong; Davidson, Ronald C.
2011-08-01
In a linear trap confining a one-component nonneutral plasma, the external focusing force is a linear function of the configuration coordinates and/or the velocity coordinates. Linear traps include the classical Paul trap and the Penning trap, as well as the newly proposed rotating-radio-frequency traps and the Mobius accelerator. This paper describes a class of self-similar nonlinear solutions of nonneutral plasma in general time-dependent linear focusing devices, with self-consistent electrostatic field. This class of nonlinear solutions includes many known solutions as special cases.
Hong Qin and Ronald C. Davidson
2011-07-19
In a linear trap confining a one-component nonneutral plasma, the external focusing force is a linear function of the configuration coordinates and/or the velocity coordinates. Linear traps include the classical Paul trap and the Penning trap, as well as the newly proposed rotating-radio- frequency traps and the Mobius accelerator. This paper describes a class of self-similar nonlinear solutions of nonneutral plasma in general time-dependent linear focusing devices, with self-consistent electrostatic field. This class of nonlinear solutions includes many known solutions as special cases.
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
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.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
NASA Astrophysics Data System (ADS)
Lane, Taylor K.; McClarren, Ryan G.
2013-09-01
This work presents semi-analytic solutions to a radiation-hydrodynamics problem of a radiation source driving an initially cold medium. Our solutions are in the equilibrium diffusion limit, include material motion and allow for radiation-dominated situations where the radiation energy is comparable to (or greater than) the material internal energy density. As such, this work is a generalization of the classical Marshak wave problem that assumes no material motion and that the radiation energy is negligible. Including radiation energy density in the model serves to slow down the wave propagation. The solutions provide insight into the impact of radiation energy and material motion, as well as present a novel verification test for radiation transport packages. As a verification test, the solution exercises the radiation-matter coupling terms and their v/c treatment without needing a hydrodynamics solve. An example comparison between the self-similar solution and a numerical code is given. Tables of the self-similar solutions are also provided.
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.
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 ~10^{2}s (refs 1-4). Here, using molecular dynamics simulations, we show that, on timescales from 10^{–12} to 10^{–5}s, 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.
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.
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.
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
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.
Self-similar pulse evolution in a fiber laser with a comb-like dispersion-decreasing fiber.
Tang, Yuxing; Liu, Zhanwei; Fu, Walter; Wise, Frank W
2016-05-15
We demonstrate an erbium fiber laser with self-similar pulse evolution inside a comb-like dispersion-decreasing fiber. We show numerically and experimentally that the comb-like dispersion-decreasing fiber works as well as an ideal one, and offers major practical advantages. The existence of a nonlinear attractor is verified by the invariant pulse chirp over a wide range of net cavity dispersion in experiments. The laser generates 1.3 nJ pulses with parabolic shapes and linear chirps, which can be dechirped to 37 fs. Comb-like dispersion-decreasing fiber should enable the generation of high-energy few-cycle pulses directly from a fiber oscillator. PMID:27176985
MICRO-SIGMOIDS AS PROGENITORS OF CORONAL JETS: IS ERUPTIVE ACTIVITY SELF-SIMILARLY MULTI-SCALED?
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.
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
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.
Large mass self-similar solutions of the parabolic-parabolic Keller-Segel model of chemotaxis.
Biler, Piotr; Corrias, Lucilla; Dolbeault, Jean
2011-07-01
In two space dimensions, the parabolic-parabolic Keller-Segel system shares many properties with the parabolic-elliptic Keller-Segel system. In particular, solutions globally exist in both cases as long as their mass is less than a critical threshold M(c). However, this threshold is not as clear in the parabolic-parabolic case as it is in the parabolic-elliptic case, in which solutions with mass above M(c) always blow up. Here we study forward self-similar solutions of the parabolic-parabolic Keller-Segel system and prove that, in some cases, such solutions globally exist even if their total mass is above M(c), which is forbidden in the parabolic-elliptic case.
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.
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.
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.
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.
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.
Chays, André; Labrousse, Marc; Makeieff, Marc
2014-01-01
In France, universal newborn hearing screening has been mandatory since April23rd, 2012, but it began in the Champagne-Ardenne region on January 15th 2004. More than 99 % of 160 196 newborns have since been systematically screened in this region. Bilateral hearing impairment was thus identified in 116 infants when they were around 3.5 months old. Earlier diagnosis improves the outcome of deafness, which is only diagnosed around age 20 months without screening. The authors report their experience and the lessons learnt.
CO2 volume fluxes outgassing from champagne glasses in tasting conditions: flute versus coupe.
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.
NASA Astrophysics Data System (ADS)
Yang, X. I. A.; Meneveau, C.; Marusic, I.; Biferale, L.
2016-08-01
In wall-bounded turbulence, the moment generating functions (MGFs) of the streamwise velocity fluctuations
NASA Astrophysics Data System (ADS)
Testik, F. Y.; Ungarish, M.
2016-05-01
Self-similar propagation of gravity currents through vegetation-like obstruction arrays was elucidated. We conducted a theoretical analysis by using an approximate model for one-layer and two-layer situations. This model incorporates a balance between the driving buoyancy (i.e., pressure) force and the resisting obstruction-induced drag force that is proportional to |" separators=" u | λ (where |" separators=" u | —speed in the layer and λ —a constant). We focused our attention on solutions with λ ≥ 1. We considered both gravity currents in a deep ambient fluid (including both continuous-flux release currents and constant-volume currents) and lock-exchange currents and demonstrated that a variety of such flows are governed by physically acceptable similarity solutions. For gravity currents in a deep ambient fluid, our theoretical analysis revealed four distinct classes of similarity solutions. Class I solutions predict gravity currents with a triangular profile (i.e., linear current interface with a constant negative slope) and a front/nose position that is a linear function of time. The physical presence of such self-similar currents was reported in recent experimental observations for currents sustained by a continuous-flux release source. We showed that theoretical predictions of Class I solutions capture the behavior of these experimental currents well. Class II solutions predict gravity currents with a non-linear profile/interface and a constant height at the source. Though physically acceptable, we could not relate this class of solutions to presently known currents. Class III solutions correspond to constant-volume currents and predict a linear increase of velocity within the current toward the nose. We discussed this class of similarity solutions using previously reported experimental observations of such currents. Class IV solutions cover the rest of the parameter domain for all other continuous-flux release gravity currents (except those that
Development of a self-similar strike-slip duplex system in the Atacama Fault system, Chile
NASA Astrophysics Data System (ADS)
Jensen, E.; Cembrano, J.; Faulkner, D.; Veloso, E.; Arancibia, G.
2011-11-01
Fault development models are crucial to predict geometry and distribution of fractures at all scales. We present here structures related to the development of the Bolfín Fault in the Atacama Fault System (AFS), covering a range of scales of 7 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, has a trend ∼170° and length >45 km. It cuts mainly meta-diorites and exhibits a 100-200 m thick core of subvertical bands of altered fractured host rock and of foliated cataclasites. This foliation is made up of several trend-parallel cm-thick shear bands, composed of plagioclase fragments (>0.1 mm) surrounded by epidote. In the compressive quadrant around the 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 observed from meters to millimeters scale. The fractures in the strike-slip duplex pattern can be separated into two types. Main Faults: trend-parallel, longer and with larger offsets; and Secondary Fractures: sigmoid-shape fractures distributed in the regions between Main Faults, all oriented between 15° and 75° with respect to the Main Faults, measured counterclockwise (i.e. in P-diedra). On the basis of the distribution of the two types of recognized fractures, the relative sequence of propagation can be inferred. Main Faults, the more widely distributed, propagated earlier. The Secondary Fractures, in turn, distributed in thinner areas between the larger Main Faults, were propagated later as linking fractures. The duplex pattern is self-similar: Multiple-Core Faults with internal structure of multiple-duplex are itself in turn secondary faults within a larger km-scale duplex (Caleta Coloso Duplex). The duplex width (W) and the length (L) of the Main Faults forming the duplex show an almost linear relationship, for
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
Application of a Self-Similar Pressure Profile to Sunyaev-Zeldovich Effect Data from Galaxy Clusters
NASA Technical Reports Server (NTRS)
Mroczkowski, Tony; Bonamente, Max; Carlstrom, John E.; Culverhouse, Thomas L.; Greer, Christopher; Hawkins, David; Hennessy, Ryan; Joy, Marshall; Lamb, James W.; Leitch, Erik M.; Loh, Michael; Maughan, Ben; Marrone, Daniel P.; Miller, Amber; Muchovej, Stephen; Nagai, Daisuke; Pryke, Clem; Sharp, Matthew; Woody, David
2009-01-01
We investigate the utility of a new, self-similar pressure profile for fitting Sunyaev-Zel'dovich (SZ) effect observations of galaxy clusters. Current SZ imaging instruments-such as the Sunyaev-Zel'dovich Array (SZA)- are capable of probing clusters over a large range in a physical scale. A model is therefore required that can accurately describe a cluster's pressure profile over a broad range of radii from the core of the cluster out to a significant fraction of the virial radius. In the analysis presented here, we fit a radial pressure profile derived from simulations and detailed X-ray analysis of relaxed clusters to SZA observations of three clusters with exceptionally high-quality X-ray data: A1835, A1914, and CL J1226.9+3332. From the joint analysis of the SZ and X-ray data, we derive physical properties such as gas mass, total mass, gas fraction and the intrinsic, integrated Compton y-parameter. We find that parameters derived from the joint fit to the SZ and X-ray data agree well with a detailed, independent X-ray-only analysis of the same clusters. In particular, we find that, when combined with X-ray imaging data, this new pressure profile yields an independent electron radial temperature profile that is in good agreement with spectroscopic X-ray measurements.
From nucleotides to DNA analysis by a SERS substrate of a self similar chain of silver nanospheres
NASA Astrophysics Data System (ADS)
Coluccio, M. L.; Gentile, F.; Das, G.; Perozziello, G.; Malara, N.; Alrasheed, S.; Candeloro, P.; Di Fabrizio, E.
2015-11-01
In this work we realized a device of silver nanostructures designed so that they have a great ability to sustain the surface-enhanced Raman scattering effect. The nanostructures were silver self-similar chains of three nanospheres, having constant ratios between their diameters and between their reciprocal distances. They were realized by electron beam lithography, to write the pattern, and by silver electroless deposition technique, to fill it with the metal. The obtained device showed the capability to increase the Raman signal coming from the gap between the two smallest nanospheres (whose size is around 10 nm) and so it allows the detection of biomolecules fallen into this hot spot. In particular, oligonucleotides with 6 DNA bases, deposited on these devices with a drop coating method, gave a Raman spectrum characterized by a clear fingerprint coming from the hot spot and, with the help of a fitting method, also oligonucleotides of 9 bases, which are less than 3 nm long, were resolved. In conclusion the silver nanolens results in a SERS device able to measure all the molecules, or part of them, held into the hot spot of the nanolenses, and thus it could be a future instrument with which to analyze DNA portions.
NASA Astrophysics Data System (ADS)
Krasnyuk, I. B.; Taranets, R. M.; Yurchenko, V. M.
2011-04-01
We examine the response to an external magnetic field by a multi-layer superconductor with an electrical resistance ρff(b)αbσ, where b is the dimensionless magnetic induction and σ is a parameter characterizing the ratio of the pinning activation energy to the energy of thermal fluctuations. When σ > 1 the sample is in the vortex glass phase, when 0 < σ < 1, it is in the vortex liquid phase, and a vortex glass to vortex liquid phase transition takes place at σ = 1. In the vortex glass phase, the magnetic field penetrates into the superconductor in the form of a self-similar wave. At all times it penetrates to a finite depth and its front moves at a finite velocity which depends on the parameters of the problem, such as the rate of pumping by the external magnetic field. In the vortex liquid phase the magnetic field penetrates to an infinite depth. Thus, the magnetic field penetrates to an infinite depth in the superconductor during a transition from the vortex glass phase into the vortex liquid phase.
NASA Astrophysics Data System (ADS)
Kuo, Shu-Tsung; Kao, Ming-Seng
2010-02-01
We propose a novel multilevel wavelength-division multiplexing optical network based on the concept of self-similarity to simplify network structure and operation. Our approach lies on a simple network topology as well as an efficient wavelength management scheme being uniformly applied to all network levels. The proposed network is a compound packet-switched and wavelength-routed network with packet switching performed on the bottom level and wavelength routing on all upper levels. This network retains the efficiency of packet-switched networks and the simplicity of wavelength-routed networks. Switching operations are concentrated at some special nodes in the multilevel network, significantly simplifying the node configuration and wavelength routing. Moreover, the idea of λ bands is applied to unify wavelength management on all network levels. Network analysis is performed to assess the feasibility of our approach. A queueing model using the quality of service enhanced optical burst switching protocol is employed to analyze the blocking performance of the proposed network. Also, the numerical results based on the queueing model are provided.
NASA Astrophysics Data System (ADS)
Habibi, F.; Pazhouhesh, R.; Shaghaghian, M.
2015-01-01
In this paper, we investigate the time evolution of an accreting magneto-fluid with finite conductivity. For the case of a thin disk, the fluid equations along with Maxwell's equations are derived in a simplified, one-dimensional model that neglects the latitudinal dependence of the flow. The finite electrical conductivity of the plasma is taken into account by Ohm's law; however, the shear viscous stress is neglected, as well as the self-gravity of the disk. In order to solve the integrated equations that govern the dynamical behaviour of the magneto-fluid, we have used a self-similar solution. We introduce two dimensionless variables, S_0 and ɛ_ρ, which represent the size of the electrical conductivity and the density behaviour with time, respectively. The effect of each of these on the structure of the disk is studied. While the pressure is obtained simply by solving an ordinary differential equation, the density, the magnetic field, the radial velocity, and the rotational velocity are presented analytically. The solutions show that the S_0 and ɛ_ρ parameters affect the radial thickness of the disk. Also, radial velocity and gas pressure are more sensitive to the electrical conductivity in the inner regions of disk. Moreover, the parameter ɛ_ρ has a more significant effect on the physical quantities for small radii.
Self-similar solutions of the non-linear diffusion equation and application to near-critical fluids
NASA Astrophysics Data System (ADS)
Fröhlich, T.; Bouquet, S.; Bonetti, M.; Garrabos, Y.; Beysens, D.
1995-02-01
We use analytic self-similar solutions of both the linear and non-linear diffusion equation to determine the behavior of a heat conducting system experiencing a time-dependent energy production. Supposing a power law evolution of the system parameters, we calculate the corresponding exponents to describe the temporal behavior of the system. In the non-linear case, we are able to introduce a variation of both the coefficient of diffusion and the amplitude of the heat source. The analytic solutions are checked numerically. These results can be considered, for example, as the basis for further developments on the non-linear behavior of supercritical fluids in a microgravity environment, e.g. the “Piston Effect” (M. Bonetti et al., Phys. Rev. E 49 (1994) 4779) or the “Jet Instability” (D. Beysens et al., Near-critical Fluids in Space, in: Lectures on Thermodynamics and Statistical Mechanics, M. Costas et al., eds. (World Scientific, Singapore, 1994) p. 88).
Smith, Duncan D; Sperry, John S; Enquist, Brian J; Savage, Van M; McCulloh, Katherine A; Bentley, Lisa P
2014-01-01
The West, Brown, Enquist (WBE) model derives symmetrically self-similar branching to predict metabolic scaling from hydraulic conductance, K, (a metabolism proxy) and tree mass (or volume, V). The original prediction was Kα V(0.75). We ask whether trees differ from WBE symmetry and if it matters for plant function and scaling. We measure tree branching and model how architecture influences K, V, mechanical stability, light interception and metabolic scaling. We quantified branching architecture by measuring the path fraction, Pf : mean/maximum trunk-to-twig pathlength. WBE symmetry produces the maximum, Pf = 1.0. We explored tree morphospace using a probability-based numerical model constrained only by biomechanical principles. Real tree Pf ranged from 0.930 (nearly symmetric) to 0.357 (very asymmetric). At each modeled tree size, a reduction in Pf led to: increased K; decreased V; increased mechanical stability; and decreased light absorption. When Pf was ontogenetically constant, strong asymmetry only slightly steepened metabolic scaling. The Pf ontogeny of real trees, however, was 'U' shaped, resulting in size-dependent metabolic scaling that exceeded 0.75 in small trees before falling below 0.65. Architectural diversity appears to matter considerably for whole-tree hydraulics, mechanics, photosynthesis and potentially metabolic scaling. Optimal architectures likely exist that maximize carbon gain per structural investment.
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.
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.
NASA Astrophysics Data System (ADS)
Dauenhauer, Eric C.; Majdalani, Joseph
2003-06-01
This article describes a self-similarity solution of the Navier-Stokes equations for a laminar, incompressible, and time-dependent flow that develops within a channel possessing permeable, moving walls. The case considered here pertains to a channel that exhibits either injection or suction across two opposing porous walls while undergoing uniform expansion or contraction. Instances of direct application include the modeling of pulsating diaphragms, sweat cooling or heating, isotope separation, filtration, paper manufacturing, irrigation, and the grain regression during solid propellant combustion. To start, the stream function and the vorticity equation are used in concert to yield a partial differential equation that lends itself to a similarity transformation. Following this similarity transformation, the original problem is reduced to solving a fourth-order differential equation in one similarity variable η that combines both space and time dimensions. Since two of the four auxiliary conditions are of the boundary value type, a numerical solution becomes dependent upon two initial guesses. In order to achieve convergence, the governing equation is first transformed into a function of three variables: The two guesses and η. At the outset, a suitable numerical algorithm is applied by solving the resulting set of twelve first-order ordinary differential equations with two unspecified start-up conditions. In seeking the two unknown initial guesses, the rapidly converging inverse Jacobian method is applied in an iterative fashion. Numerical results are later used to ascertain a deeper understanding of the flow character. The numerical scheme enables us to extend the solution range to physical settings not considered in previous studies. Moreover, the numerical approach broadens the scope to cover both suction and injection cases occurring with simultaneous wall motion.
NASA Astrophysics Data System (ADS)
Volpes, L.; Bothmer, V.
2015-10-01
We present an application of the stereoscopic self-similar-expansion model (SSSEM) to Solar Terrestrial Relations Observatory (STEREO)/ Sun-Earth Connection Coronal and Heliospheric Investigation (SECCHI) observations of the CME on 3 April 2010 and its associated shock. The aim is to verify whether CME-driven shock parameters can be inferred from the analysis of j-maps. For this purpose, we used the SSSEM to derive the CME and the shock kinematics. Arrival times and speeds, inferred assuming either propagation at constant speed or with uniform deceleration, agree well with Advanced Composition Explorer (ACE) measurements. The shock standoff distance [Δ], the density compression [ρd/ρu], and the Mach number [M] were calculated by combining the results obtained for the CME and shock kinematics with models for the shock location. Their values were extrapolated to L1 and compared to in-situ data. The in-situ standoff distance was obtained from ACE solar-wind measurements, and the Mach number and compression ratio were provided by the interplanetary shock database of the Harvard-Smithsonian Center for Astrophysics. They are ρd/ρu =2.84 and M = 2.2. The best fit to observations was obtained when the SSSEM half-width λ= 40°, and the CME and shock propagate with uniform deceleration. In this case we found Δ= 23 R_{⊙}, ρd/ρu =2.61, and M = 2.93. The study shows that CME-driven shock parameters can be estimated from the analysis of time-elongation plots and can be used to predict their in-situ values.
NASA Astrophysics Data System (ADS)
Basu, Shantanu
1997-08-01
We use a semianalytic model to examine the collapse of supercritical cores (i.e., cores with a mass-to-flux ratio exceeding a critical value). Recent numerical simulations of the formation and contraction of supercritical cores show that the inner solution tends toward self-similar evolution. We use this feature to develop analytic expressions for quantities such as the density, angular velocity, and magnetic field. All forces involved in the problem (gravitational, magnetic, thermal, and centrifugal) can be calculated analytically in the thin-disk geometry of the problem. The role of each force during the contraction is analyzed. We identify the key role of ambipolar diffusion in producing a departure from an exact similarity solution. The slow leakage of magnetic flux during the supercritical phase is enough to significantly accelerate an otherwise near-quasi-static contraction. This leads to dynamic collapse with supersonic infall speeds in the innermost region of the core by the time of protostar formation. We find a time-dependent semianalytic solution for the late supercritical phase, and asymptotic forms are obtained for important profiles at the moment that a central protostar is formed. We obtain estimates for the rotational velocity, infall velocity, and mass accretion rate at this moment. The mass accretion rate is significantly greater than the canonical C3/G (where C is the isothermal sound speed and G is the universal gravitational constant) at the moment of protostar formation, although we argue that it is time-dependent and will eventually decrease. Comparisons are made with the predictions of existing spherical similarity solutions.
Lidz, B.H.; Brock, J.C.; Nagle, D.B.
2008-01-01
A recently developed remote-sensing instrument acquires high-quality digital photographs in shallow-marine settings within water depths of 15 m. The technology, known as the Along-Track Reef-Imaging System, provides remarkably clear, georeferenced imagery that allows visual interpretation of benthic class (substrates, organisms) for mapping coral reef habitats, as intended. Unforeseen, however, are functions new to the initial technologic purpose: interpr??table evidence for real-time biogeologic processes and for perception of scaled-up skeletal self-similarity of scleractinian microstructure. Florida reef sea trials lacked the grid structure required to map contiguous habitat and submarine topography. Thus, only general observations could be made relative to times and sites of imagery. Degradation of corals was nearly universal; absence of reef fish was profound. However, ???1% of more than 23,600 sea-trial images examined provided visual evidence for local environs and processes. Clarity in many images was so exceptional that small tracks left by organisms traversing fine-grained carbonate sand were visible. Other images revealed a compelling sense, not yet fully understood, of the microscopic wall structure characteristic of scleractinian corals. Conclusions drawn from classifiable images are that demersal marine animals, where imaged, are oblivious to the equipment and that the technology has strong capabilities beyond mapping habitat. Imagery acquired along predetermined transects that cross a variety of geomorphic features within depth limits will ( 1) facilitate construction of accurate contour maps of habitat and bathymetry without need for ground-truthing, (2) contain a strong geologic component of interpreted real-time processes as they relate to imaged topography and regional geomorphology, and (3) allow cost-effective monitoring of regional- and local-scale changes in an ecosystem by use of existing-image global-positioning system coordinates to re
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.
Zhao, Jian; Li, Wenxue; Wang, Chao; Liu, Yang; Zeng, Heping
2014-12-29
We report on the generation of 80-W average power 38-fs laser pulse from a 2-m polarization-maintaining large-mode-area photonic crystal fiber amplifier with high pump absorption coefficient. The pre-chirping management was demonstrated to play a key role on the self-similar amplification. The achieved spectral bandwidth and compressed pulse duration were determined by the interplay between self-phase modulation and finite gain bandwidth. The power scaling in the self-similar fiber amplifier system was eventually limited by the onset of stimulated Raman scattering. PMID:25607187
NASA Astrophysics Data System (ADS)
Kierkels, A. H. M.; Velázquez, J. J. L.
2016-06-01
We construct a family of self-similar solutions with fat tails to a quadratic kinetic equation. This equation describes the long time behaviour of weak solutions with finite mass to the weak turbulence equation associated to the nonlinear Schrödinger equation. The solutions that we construct have finite mass, but infinite energy. In Kierkels and Velázquez (J Stat Phys 159:668-712, 2015) self-similar solutions with finite mass and energy were constructed. Here we prove upper and lower exponential bounds on the tails of these solutions.
Kushnir, Doron; Waxman, Eli
2010-11-01
Shock waves driven by the release of energy at the center of a cold ideal gas sphere of initial density {rho} {proportional_to} r {sup -}{omega} approach a self-similar behavior, with velocity R-dot {proportional_to}R{sup {delta}}, as R {yields} {infinity}. For {omega}>3 the solutions are second-type solutions, i.e., {delta} is determined by the requirement that the flow should include a sonic point. No solution satisfying this requirement exists, however, in the 3 {<=} {omega} {<=} {omega}{sub g}({gamma}) 'gap' ({omega}{sub g} = 3.26 for adiabatic index {gamma} = 5/3). We argue that in general second-type solutions should not be required to include a sonic point. Rather, it is sufficient to require the existence of a characteristic line r{sub c} (t), such that the energy in the region r{sub c} (t) < r < R approaches a constant as R {yields} {infinity}, and an asymptotic solution given by the self-similar solution at r{sub c} (t) < r < R and deviating from it at r < r{sub c} may be constructed. The two requirements coincide for {omega}>{omega}{sub g} and the latter identifies {delta} = 0 solutions as the asymptotic solutions for 3 {<=} {omega} {<=} {omega}{sub g} (as suggested by Gruzinov). In these solutions, r{sub c} is a C{sub 0} characteristic. Using numerical solutions of the hydrodynamic equations, it is difficult to check whether the flow indeed approaches a {delta} = 0 self-similar behavior as R {yields} {infinity}, due to the slow convergence to self-similarity for {omega} {approx} 3. We show that in this case the flow may be described by a modified self-similar solution, d ln R-dot/d ln R = {delta} with slowly varying {delta}(R), {eta} {identical_to} d{delta}/dln R << 1, and spatial profiles given by a sum of the self-similar solution corresponding to the instantaneous value of {delta} and a self-similar correction linear in {eta}. The modified self-similar solutions provide an excellent approximation to numerical solutions obtained for {omega} {approx} 3
NASA Astrophysics Data System (ADS)
Kushnir, Doron; Waxman, Eli
2010-11-01
Shock waves driven by the release of energy at the center of a cold ideal gas sphere of initial density ρ vprop r -ω approach a self-similar behavior, with velocity \\dot{R}∝ R^δ, as R → ∞. For ω>3 the solutions are second-type solutions, i.e., δ is determined by the requirement that the flow should include a sonic point. No solution satisfying this requirement exists, however, in the 3 <= ω <= ω g (γ) "gap" (ω g = 3.26 for adiabatic index γ = 5/3). We argue that in general second-type solutions should not be required to include a sonic point. Rather, it is sufficient to require the existence of a characteristic line rc (t), such that the energy in the region rc (t) < r < R approaches a constant as R → ∞, and an asymptotic solution given by the self-similar solution at rc (t) < r < R and deviating from it at r < rc may be constructed. The two requirements coincide for ω>ω g and the latter identifies δ = 0 solutions as the asymptotic solutions for 3 <= ω <= ω g (as suggested by Gruzinov). In these solutions, rc is a C 0 characteristic. Using numerical solutions of the hydrodynamic equations, it is difficult to check whether the flow indeed approaches a δ = 0 self-similar behavior as R → ∞, due to the slow convergence to self-similarity for ω ~ 3. We show that in this case the flow may be described by a modified self-similar solution, d ln \\dot{R}/d ln R=δ with slowly varying δ(R), η ≡ dδ/dln R Lt 1, and spatial profiles given by a sum of the self-similar solution corresponding to the instantaneous value of δ and a self-similar correction linear in η. The modified self-similar solutions provide an excellent approximation to numerical solutions obtained for ω ~ 3 at large R, with δ → 0 (and η ≠ 0) for 3 <= ω <= ω g .
NASA Astrophysics Data System (ADS)
Cheng, Q.
2010-12-01
We demonstrate that exploratory geochemical landscapes created from concentration values of trace elements in the earth surface media (rocks, tills, soils, stream sediments and water) in mineral district or environment impact district show non-linear properties such as singularity, self-similarity and self-organized criticality which can be mathematically described by density-area fractal and multifractal models. The regions can be delineated according to strength of singularity to be estimated and mapped with several methods from the geochemical landscape. In general, the landscape related to regional geo-processes such as sedimentation, metamorphism and igneous activities usually depict regular geochemical concentration or density with high-order differentiability whereas that in regions where has been impacted by localized and anomalous mineralization processes may show fractal density with strong singularity and poor differentiability. Target areas delineated by the singularity in various scales (entire map, sub-areas of maps and pixels) can be used as permissible areas for finding mineral deposits. Due to its independency on the scale the singularity has been demonstrated providing an powerful tool for extracting useful geochemical anomalies caused by mineralization or ore bodies in depth. This paper introduces several indexes of local singularity and multifractality that have been proposed for mapping spatial variability of geochemical fields and for delineating anomalous areas for prediction of undiscovered mineral deposits. The methods have been successfully applied to process the concentration values of multiple mineralization associated elements such as As, Fe, Zn and Pb etc in stream sediments in various mineral districts in China. Stream sediments are sampled at the spatial resolution of 1 sample per 2km x 2km grid. It shows that hydrothermal mineralization processes corresponding to iron, copper, gold, lead/zinc, tin and nickel etc. in the study areas
Besnard, E; Chenu, C; Robert, M
2001-01-01
The intensive use for over 100 years of copper sulfate (Bordeaux mixture) to fight against mildew in vineyard soils has led to an important, widespread accumulation of Cu (100 to 1500 mg Cu kg-1 soil). In Champagne vineyards, organic amendments are used currently to increase soil fertility and to limit soil erosion. Organic amendments may have a direct effect on the retention of Cu in the soil. To assess the influence of the organic management on the fate of Cu in calcareous Champagne vineyard soils, we studied Cu distribution (1) in the soil profile and (2) among primary soil particles, in vineyard parcels with different amendments. Amendments were oak-bark, vine-shoots and urban compost. The results were compared with the amount and the distribution of Cu in an unamended calcareous soil. Physical soil fractionations were carried out to separate soil primary particles according to their size and density. Cu has a heterogeneous distribution among soil particle fractions. Two fractions were mainly responsible for Cu retention in soils: the organic debris larger than 50 microns or coarse particulate organic matter (POM) issued from the organic amendments, and the clay-sized fraction < 2 microns. The POM contained up to 2000 mg Cu kg-1 fraction and the clay fraction contained up to 500 mg Cu kg-1 fraction. The clay-sized fraction was responsible for almost 40% of the total amount of Cu in the four parcels. POM was predominantly responsible for the differences in Cu contents between the unamended and the three amended parcels. Our results attested that methods of soil particle-size fractionation can be successfully used to assess the distribution of metal elements in soils.
Zhuang, Jin-Ying; Zhang, Sen; Xu, Jing; Hu, Die
2014-01-01
Attractiveness judgment in the context of mate preferences is thought to reflect an assessment of mate quality in relation to an absolute scale of genetic fitness and a relative scale of self-similarity. In this study, subjects judged the attractiveness and trustworthiness of faces in composite images that were manipulated to produce self-similar (self-resemblance) and dissimilar (other-resemblance) images. Males differentiated between self- and other-resemblance as well as among different degrees of self-resemblance in their attractiveness ratings; females did not. Specifically, in Experiment 1, using a morphing technique, we created previously unseen face images possessing different degrees (0%, 30%, 40%, or 50%) of incorporation of the subject's images (different degrees of self-resemblance) and found that males preferred images that were closer to average (0%) rather than more self-similar, whereas females showed no preference for any degree of self-similarity. In Experiment 2, we added a pro-social question about trustworthiness. We replicated the Experiment 1 attractiveness rating results and further found that males differentiated between self- and other-resemblance for the same degree of composites; women did not. Both males and females showed a similar preference for self-resemblances when judging trustworthiness. In conclusion, only males factored self-resemblance into their attractiveness ratings of opposite-sex individuals in a manner consistent with cues of reproductive fitness, although both sexes favored self-resemblance when judging trustworthiness.
Zhuang, Jin-Ying; Zhang, Sen; Xu, Jing; Hu, Die
2014-01-01
Attractiveness judgment in the context of mate preferences is thought to reflect an assessment of mate quality in relation to an absolute scale of genetic fitness and a relative scale of self-similarity. In this study, subjects judged the attractiveness and trustworthiness of faces in composite images that were manipulated to produce self-similar (self-resemblance) and dissimilar (other-resemblance) images. Males differentiated between self- and other-resemblance as well as among different degrees of self-resemblance in their attractiveness ratings; females did not. Specifically, in Experiment 1, using a morphing technique, we created previously unseen face images possessing different degrees (0%, 30%, 40%, or 50%) of incorporation of the subject's images (different degrees of self-resemblance) and found that males preferred images that were closer to average (0%) rather than more self-similar, whereas females showed no preference for any degree of self-similarity. In Experiment 2, we added a pro-social question about trustworthiness. We replicated the Experiment 1 attractiveness rating results and further found that males differentiated between self- and other-resemblance for the same degree of composites; women did not. Both males and females showed a similar preference for self-resemblances when judging trustworthiness. In conclusion, only males factored self-resemblance into their attractiveness ratings of opposite-sex individuals in a manner consistent with cues of reproductive fitness, although both sexes favored self-resemblance when judging trustworthiness. PMID:24594644
Zhuang, Jin-Ying; Zhang, Sen; Xu, Jing; Hu, Die
2014-01-01
Attractiveness judgment in the context of mate preferences is thought to reflect an assessment of mate quality in relation to an absolute scale of genetic fitness and a relative scale of self-similarity. In this study, subjects judged the attractiveness and trustworthiness of faces in composite images that were manipulated to produce self-similar (self-resemblance) and dissimilar (other-resemblance) images. Males differentiated between self- and other-resemblance as well as among different degrees of self-resemblance in their attractiveness ratings; females did not. Specifically, in Experiment 1, using a morphing technique, we created previously unseen face images possessing different degrees (0%, 30%, 40%, or 50%) of incorporation of the subject's images (different degrees of self-resemblance) and found that males preferred images that were closer to average (0%) rather than more self-similar, whereas females showed no preference for any degree of self-similarity. In Experiment 2, we added a pro-social question about trustworthiness. We replicated the Experiment 1 attractiveness rating results and further found that males differentiated between self- and other-resemblance for the same degree of composites; women did not. Both males and females showed a similar preference for self-resemblances when judging trustworthiness. In conclusion, only males factored self-resemblance into their attractiveness ratings of opposite-sex individuals in a manner consistent with cues of reproductive fitness, although both sexes favored self-resemblance when judging trustworthiness. PMID:24594644
NASA Astrophysics Data System (ADS)
Valiyev, Kh. F.; Kraiko, A. N.
2013-03-01
In some problems concerning cylindrically and spherically symmetric unsteady ideal (inviscid and nonheat-conducting) gas flows at the axis and center of symmetry (hereafter, at the center of symmetry), the gas density vanishes and the speed of sound becomes infinite starting at some time. This situation occurs in the problem of a shock wave reflecting from the center of symmetry. For an ideal gas with constant heat capacities and their ratio γ (adiabatic exponent), the solution of this problem near the reflection point is self-similar with a self-similarity exponent determined in the course of the solution construction. Assuming that γ on the reflected shock wave decreases, if this decrease exceeds a threshold value, the flow changes substantially. Assuming that the type of the solution remains unchanged for such γ, self-similarity is preserved if a piston starts expanding from the center of symmetry at the reflection time preceded by a finite-intensity reflected shock wave propagating at the speed of sound. To answer some questions arising in this formulation, specifically, to find the solution in the absence of the piston, the evolution of a close-to-self-similar solution calculated by the method of characteristics is traced. The required modification of the method of characteristics and the results obtained with it are described. The numerical results reveal a number of unexpected features. As a result, new self-similar solutions are constructed in which two (rather than one) shock waves reflect from the center of symmetry in the absence of the piston.
NASA Astrophysics Data System (ADS)
Klapp, J.; Cervantes-Cota, J.; Chauvet, P.
1990-11-01
RESUMEN. A nivel cosmol6gico pensamos que se ha estado prodticiendo radiaci6n gravitacional en cantidades considerables dentro de las galaxias. Si los eventos prodnctores de radiaci6n gravitatoria han venido ocurriendo desde Ia epoca de Ia formaci6n de las galaxias, cuando menos, sus efectos cosmol6gicos pueden ser tomados en cuenta con simplicidad y elegancia al representar la producci6n de radiaci6n y, por consiguiente, su interacci6n con materia ordinaria fenomenol6gicamente a trave's de una ecuaci6n de estado politr6pica, como lo hemos mostrado en otros trabajos. Presentamos en este articulo resultados nunericos de este modelo. ABSTRACT A common believe in cosmology is that gravitational radiation in considerable quantities is being produced within the galaxies. Ifgravitational radiation production has been running since the galaxy formation epoch, at least, its cosmological effects can be assesed with simplicity and elegance by representing the production of radiation and, therefore, its interaction with ordinary matter phenomenologically through a polytropic equation of state as shown already elsewhere. We present in this paper the numerical results of such a model. K words: COSMOLOGY - GRAVITATION
NASA Technical Reports Server (NTRS)
Lerche, I.
1978-01-01
One-dimensional self-similar isothermal flow behind a blast wave propagating in a medium whose density varies with distance is investigated for the cases of one-dimensional and two-dimensional flow. The isothermal flow model is adopted as an alternative to adiabatic models of self-similar flow, which neglect heat flux. The topology of the one-dimensional flow solutions, the singularities, and the influence of boundary conditions are discussed; the instability of the isothermal blast waves against nonself-similar perturbations is also considered. The number of critical points in the two-dimensional solutions is found to vary from the number in the one-dimensional problem.
NASA Astrophysics Data System (ADS)
Harko, T.; Mak, M. K.
2016-09-01
Obtaining exact solutions of the spherically symmetric general relativistic gravitational field equations describing the interior structure of an isotropic fluid sphere is a long standing problem in theoretical and mathematical physics. The usual approach to this problem consists mainly in the numerical investigation of the Tolman-Oppenheimer-Volkoff and of the mass continuity equations, which describes the hydrostatic stability of the dense stars. In the present paper we introduce an alternative approach for the study of the relativistic fluid sphere, based on the relativistic mass equation, obtained by eliminating the energy density in the Tolman-Oppenheimer-Volkoff equation. Despite its apparent complexity, the relativistic mass equation can be solved exactly by using a power series representation for the mass, and the Cauchy convolution for infinite power series. We obtain exact series solutions for general relativistic dense astrophysical objects described by the linear barotropic and the polytropic equations of state, respectively. For the polytropic case we obtain the exact power series solution corresponding to arbitrary values of the polytropic index n. The explicit form of the solution is presented for the polytropic index n=1, and for the indexes n=1/2 and n=1/5, respectively. The case of n=3 is also considered. In each case the exact power series solution is compared with the exact numerical solutions, which are reproduced by the power series solutions truncated to seven terms only. The power series representations of the geometric and physical properties of the linear barotropic and polytropic stars are also obtained.
NASA Astrophysics Data System (ADS)
Musakaev, N. G.; Khasanov, M. K.
2016-10-01
In this paper the research of carbon dioxide injection into a porous medium initially saturated with methane and its hydrate was performed. The mathematical model of heat and mass transfer in a porous media, accompanied by the formation of carbon dioxide hydrate, is presented. The self-similar solutions, for the axisymmetric problem definition, were built. These solutions describe the distribution of the fluid parameters in a reservoir.
NASA Astrophysics Data System (ADS)
Xue, Liutang
2016-11-01
Motivated by the numerical simulation and the study on several 1D models, we consider the locally self-similar singular solutions for the surface quasi-geostrophic equation with decaying or non-decaying blowup profiles. Based on a suitable local Lp-inequality in terms of the profile and the bootstrapping method, we show some exclusion results and derive the asymptotic behavior of the possible blowup profiles.
Kim, Jeong-Gyu; Kim, Woong-Tae; Seo, Young Min; Hong, Seung Soo E-mail: wkim@astro.snu.ac.kr E-mail: sshong@astro.snu.ac.kr
2012-12-20
We investigate the gravitational instability (GI) of rotating, vertically stratified, pressure-confined, polytropic gas disks using a linear stability analysis as well as analytic approximations. The disks are initially in vertical hydrostatic equilibrium and bounded by a constant external pressure. We find that the GI of a pressure-confined disk is in general a mixed mode of the conventional Jeans and distortional instabilities, and is thus an unstable version of acoustic-surface-gravity waves. The Jeans mode dominates in weakly confined disks or disks with rigid boundaries. On the other hand, when the disk has free boundaries and is strongly pressure confined, the mixed GI is dominated by the distortional mode that is surface-gravity waves driven unstable under their own gravity and thus incompressible. We demonstrate that the Jeans mode is gravity-modified acoustic waves rather than inertial waves and that inertial waves are almost unaffected by self-gravity. We derive an analytic expression for the effective sound speed c{sub eff} of acoustic-surface-gravity waves. We also find expressions for the gravity reduction factors relative to a razor-thin counterpart that are appropriate for the Jeans and distortional modes. The usual razor-thin dispersion relation, after correcting for c{sub eff} and the reduction factors, closely matches the numerical results obtained by solving a full set of linearized equations. The effective sound speed generalizes the Toomre stability parameter of the Jeans mode to allow for the mixed GI of vertically stratified, pressure-confined disks.
Harrington, Rebecca M.; Kwiatek, Grzegorz; Moran, Seth C.
2015-01-01
We analyze a group of 6073 low-frequency earthquakes recorded during a week-long temporary deployment of broadband seismometers at distances of less than 3 km from the crater at Mount St. Helens in September of 2006. We estimate the seismic moment (M0) and spectral corner frequency (f0) using a spectral ratio approach for events with a high signal-to-noise (SNR) ratio that have a cross-correlation coefficient of 0.8 or greater with at least five other events. A cluster analysis of cross-correlation values indicates that the group of 421 events meeting the SNR and cross-correlation criteria forms eight event families that exhibit largely self-similar scaling. We estimate the M0 and f0 values of the 421 events and calculate their static stress drop and scaled energy (ER/M0) values. The estimated values suggest self-similar scaling within families, as well as between five of eight families (i.e., and constant). We speculate that differences in scaled energy values for the two families with variable scaling may result from a lack of resolution in the velocity model. The observation of self-similar scaling is the first of its kind for such a large group of low-frequency volcanic tectonic events occurring during a single active dome extrusion eruption.
NASA Astrophysics Data System (ADS)
Gerlich, Nikolas; Rostek, Stefan
2015-09-01
We derive a heuristic method to estimate the degree of self-similarity and serial correlation in financial time series. Especially, we propagate the use of a tailor-made selection of different estimation techniques that are used in various fields of time series analysis but until now have not consequently found their way into the finance literature. Following the idea of portfolio diversification, we show that considerable improvements with respect to robustness and unbiasedness can be achieved by using a basket of estimation methods. With this methodological toolbox at hand, we investigate real market data to show that noticeable deviations from the assumptions of constant self-similarity and absence of serial correlation occur during certain periods. On the one hand, this may shed a new light on seemingly ambiguous scientific findings concerning serial correlation of financial time series. On the other hand, a proven time-changing degree of self-similarity may help to explain high-volatility clusters of stock price indices.
Bouda, Martin; Caplan, Joshua S; Saiers, James E
2016-01-01
Fractal dimension (FD), estimated by box-counting, is a metric used to characterize plant anatomical complexity or space-filling characteristic for a variety of purposes. The vast majority of published studies fail to evaluate the assumption of statistical self-similarity, which underpins the validity of the procedure. The box-counting procedure is also subject to error arising from arbitrary grid placement, known as quantization error (QE), which is strictly positive and varies as a function of scale, making it problematic for the procedure's slope estimation step. Previous studies either ignore QE or employ inefficient brute-force grid translations to reduce it. The goals of this study were to characterize the effect of QE due to translation and rotation on FD estimates, to provide an efficient method of reducing QE, and to evaluate the assumption of statistical self-similarity of coarse root datasets typical of those used in recent trait studies. Coarse root systems of 36 shrubs were digitized in 3D and subjected to box-counts. A pattern search algorithm was used to minimize QE by optimizing grid placement and its efficiency was compared to the brute force method. The degree of statistical self-similarity was evaluated using linear regression residuals and local slope estimates. QE, due to both grid position and orientation, was a significant source of error in FD estimates, but pattern search provided an efficient means of minimizing it. Pattern search had higher initial computational cost but converged on lower error values more efficiently than the commonly employed brute force method. Our representations of coarse root system digitizations did not exhibit details over a sufficient range of scales to be considered statistically self-similar and informatively approximated as fractals, suggesting a lack of sufficient ramification of the coarse root systems for reiteration to be thought of as a dominant force in their development. FD estimates did not
Bouda, Martin; Caplan, Joshua S; Saiers, James E
2016-01-01
Fractal dimension (FD), estimated by box-counting, is a metric used to characterize plant anatomical complexity or space-filling characteristic for a variety of purposes. The vast majority of published studies fail to evaluate the assumption of statistical self-similarity, which underpins the validity of the procedure. The box-counting procedure is also subject to error arising from arbitrary grid placement, known as quantization error (QE), which is strictly positive and varies as a function of scale, making it problematic for the procedure's slope estimation step. Previous studies either ignore QE or employ inefficient brute-force grid translations to reduce it. The goals of this study were to characterize the effect of QE due to translation and rotation on FD estimates, to provide an efficient method of reducing QE, and to evaluate the assumption of statistical self-similarity of coarse root datasets typical of those used in recent trait studies. Coarse root systems of 36 shrubs were digitized in 3D and subjected to box-counts. A pattern search algorithm was used to minimize QE by optimizing grid placement and its efficiency was compared to the brute force method. The degree of statistical self-similarity was evaluated using linear regression residuals and local slope estimates. QE, due to both grid position and orientation, was a significant source of error in FD estimates, but pattern search provided an efficient means of minimizing it. Pattern search had higher initial computational cost but converged on lower error values more efficiently than the commonly employed brute force method. Our representations of coarse root system digitizations did not exhibit details over a sufficient range of scales to be considered statistically self-similar and informatively approximated as fractals, suggesting a lack of sufficient ramification of the coarse root systems for reiteration to be thought of as a dominant force in their development. FD estimates did not
Bouda, Martin; Caplan, Joshua S.; Saiers, James E.
2016-01-01
Fractal dimension (FD), estimated by box-counting, is a metric used to characterize plant anatomical complexity or space-filling characteristic for a variety of purposes. The vast majority of published studies fail to evaluate the assumption of statistical self-similarity, which underpins the validity of the procedure. The box-counting procedure is also subject to error arising from arbitrary grid placement, known as quantization error (QE), which is strictly positive and varies as a function of scale, making it problematic for the procedure's slope estimation step. Previous studies either ignore QE or employ inefficient brute-force grid translations to reduce it. The goals of this study were to characterize the effect of QE due to translation and rotation on FD estimates, to provide an efficient method of reducing QE, and to evaluate the assumption of statistical self-similarity of coarse root datasets typical of those used in recent trait studies. Coarse root systems of 36 shrubs were digitized in 3D and subjected to box-counts. A pattern search algorithm was used to minimize QE by optimizing grid placement and its efficiency was compared to the brute force method. The degree of statistical self-similarity was evaluated using linear regression residuals and local slope estimates. QE, due to both grid position and orientation, was a significant source of error in FD estimates, but pattern search provided an efficient means of minimizing it. Pattern search had higher initial computational cost but converged on lower error values more efficiently than the commonly employed brute force method. Our representations of coarse root system digitizations did not exhibit details over a sufficient range of scales to be considered statistically self-similar and informatively approximated as fractals, suggesting a lack of sufficient ramification of the coarse root systems for reiteration to be thought of as a dominant force in their development. FD estimates did not
Marin, M; Tailor, C S; Nouri, A; Kozak, S L; Kabat, D
1999-11-01
The differential susceptibilities of mouse strains to xenotropic and polytropic murine leukemia viruses (X-MLVs and P-MLVs, respectively) are poorly understood but may involve multiple mechanisms. Recent evidence has demonstrated that these viruses use a common cell surface receptor (the X-receptor) for infection of human cells. We describe the properties of X-receptor cDNAs with distinct sequences cloned from five laboratory and wild strains of mice and from hamsters and minks. Expression of these cDNAs in resistant cells conferred susceptibilities to the same viruses that naturally infect the animals from which the cDNAs were derived. Thus, a laboratory mouse (NIH Swiss) X-receptor conferred susceptibility to P-MLVs but not to X-MLVs, whereas those from humans, minks, and several wild mice (Mus dunni, SC-1 cells, and Mus spretus) mediated infections by both X-MLVs and P-MLVs. In contrast, X-receptors from the resistant mouse strain Mus castaneus and from hamsters were inactive as viral receptors. These results suggest that X-receptor polymorphisms are a primary cause of resistances of mice to members of the X-MLV/P-MLV family of retroviruses and are responsible for the xenotropism of X-MLVs in laboratory mice. By site-directed mutagenesis, we substituted sequences between the X-receptors of M. dunni and NIH Swiss mice. The NIH Swiss protein contains two key differences (K500E in presumptive extracellular loop 3 [ECL 3] and a T582 deletion in ECL 4) that are both required to block X-MLV infections. Accordingly, a single inverse mutation in the NIH Swiss protein conferred X-MLV susceptibility. Furthermore, expression of an X-MLV envelope glycoprotein in Chinese hamster ovary cells interfered efficiently with X-MLV and P-MLV infections mediated by X-receptors that contained K500 and/or T582 but had no effect on P-MLV infections mediated by X-receptors that lacked these amino acids. In contrast, moderate expression of a P-MLV (MCF247) envelope glycoprotein did not
Nitta, Shin-ya
2010-08-20
We applied the 'self-similar evolutionary model' of magnetic reconnection to simple pre-flare reconnection events driven by flux emergence as the first step in inspecting the realizability of the reconnection events predicted by this model. Previous works paid scant attention to the dependence of the magnetic Reynolds number (R*{sub em}) on reconnection events. We aim to clarify how the pre-flare phase of reconnection events in the high R*{sub em} range that is frequently encountered in astrophysical applications is observed. We clarify that (1) the time variation of the emission measure distribution strongly depends on R*{sub em}, (2) the expected light curve for sufficiently low R*{sub em} shows a long lifetime property while that for high R*{sub em} shows an impulsive property, and (3) in the case of recurrent small reconnection events on the same loop, the released magnetic energy scale is inversely correlated to the rear-end speed of the moving bright point along the loop. Note that other reconnection models cannot totally explain integration of these properties. If evidence of phenomena with these properties can be detected from, e.g., the Hinode observation, it strongly supports the validity of the self-similar reconnection model.
NASA Astrophysics Data System (ADS)
Jin, Y.; Gu, S.; Bennett, L. H.; Della Torre, E.; Provenzano, V.; Zhao, Q.
2012-04-01
A temperature scaling methodology to obtain a self-similar field dependence (∂M/∂T)H curve for metamagnetic material exhibiting first-order ferro-to-paramagnetic transitions is presented. The methodology extends Franco's transformation by (i) performing the scaling methodology on the (∂M/∂T)H curve instead of the ΔSM(T,H) curve and (ii) redefining the arbitrary temperature references, Tr1 and Tr2, used by Franco, by employing the physical constants TFM and TPM, which can be determined from the (∂2M/∂T2)H curves. (∂M/∂T)H of the metamagnetic material, Gd5Si2Ge2, exhibiting first-order ferro-to-paramagnetic transition is shown as an example. Applying the new modified Franco's transformation, Gd5Si2Ge2's (∂M/∂T)H curves collapse onto a self-similar curve with a low index of dispersion. The collapsed curve is asymmetrical with a negative skewness, which reflects the intrinsic transition differences in the mixed-state region.
NASA Astrophysics Data System (ADS)
van den Eeckhaut, M.; Marre, A.; Poesen, J.
2009-04-01
The vineyards of the Champagne region are planted on steep south-oriented cuesta fronts receiving a maximum of sun radiation. However, due to the location of the vineyards on steep hillslopes, the viticultural activity is threatened by slope failures. In this study we attempt to better understand the spatial variability of landslides by comparing two techniques for landslide susceptibility assessment in a 1120 km² study area in the Champagne Ardenne. The first landslide susceptibility map was derived from an heuristic model adopted from the Bureau de Recherches Géologiques et Minières, geomorphologists of Reims University and the Comité Interprofessionnel du Vin de Champagne. In this qualitative model expert knowledge of the Champagne region was used to assign weights to all slope classes and lithologies located in the area. The second landslide susceptibility map was developed in this study by the application of a statistical model, logistic regression, to a calibration dataset of ‘old' (Holocene) landslides. This map was successfully evaluated using ROC curves and κ values. Both models 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) evaluation with the location of mapped ‘old' (Holocene) landslides and through (2) temporal validation with spatial data of ‘recent' (between forty and ten years old) and ‘very recent' (less than ten years old) landslides showed that the statistical model produced in this study allowed better prediction of sites already affected by landslides. In total the statistically-derived susceptibility map succeeded in correctly classifying 83.2% of the ‘old' and 84.0% of the ‘recent' and ‘very recent' landslides. The heuristic model on the other hand classified only 50.6% of the ‘old' and 58.5% of the ‘recent' and ‘very recent' landslides correctly as unstable. Taking into account the
NASA Astrophysics Data System (ADS)
Huesca, Margarita; Merino-de-Miguel, Silvia; Eklundh, Lars; Litago, Javier; Cicuéndez, Victor; Rodríguez-Rastrero, Manuel; Ustin, Susan L.; Palacios-Orueta, Alicia
2015-12-01
Remote sensing (RS) time series are an excellent operative source for information about the land surface across several scales and different levels of landscape heterogeneity. Ustin and Gamon (2010) proposed the new concept of "optical types" (OT), meaning "optically distinguishable functional types", as a way to better understand remote sensing signals related to the actual functional behavior of species that share common physiognomic forms but differ in functionality. Whereas the OT approach seems to be promising and consistent with ecological theory as a way to monitor vegetation derived from RS, it received little implementation. This work presents a method for implementing the OT concept for efficient monitoring of ecosystems based on RS time series. We propose relying on an ecosystem's repetitive pattern in the temporal domain (self-similarity) to assess its dynamics. Based on this approach, our main hypothesis is that distinct dynamics are intrinsic to a specific OT. Self-similarity level in the temporal domain within a broadleaf forest class was quantitatively assessed using the auto-correlation function (ACF), from statistical time series analysis. A vector comparison classification method, spectral angle mapper, and principal component analysis were used to identify general patterns related to forest dynamics. Phenological metrics derived from MODIS NDVI time series using the TIMESAT software, together with information from the National Forest Map were used to explain the different dynamics found. Results showed significant and highly stable self-similarity patterns in OTs that corresponded to forests under non-moisture-limited environments with an adaptation strategy based on a strong phenological synchrony with climate seasonality. These forests are characterized by dense closed canopy deciduous forests associated with high productivity and low biodiversity in terms of dominant species. Forests in transitional areas were associated with patterns of less
NASA Technical Reports Server (NTRS)
Ghosh, S.; Matthaeus, W. H.
1992-01-01
Theory suggests that three distinct types of turbulence can occur in the low Mach number limit of polytropic flow: nearly incompressible flows dominated by vorticity, nearly pure acoustic turbulence dominated by compression, and flows characterized by near statistical equipartition of vorticity and compressions. Distinctions between these kinds of turbulence are investigated here by direct numerical simulation of two-dimensional compressible hydrodynamic turbulence. Dynamical scalings of density fluctuations, examination of the ratio of transverse to longitudinal velocity fluctuations, and spectral decomposition of the fluctuations are employed to distinguish the nature of these low Mach number solutions. A strong dependence on the initial data is observed, as well as a tendency for enhanced effects of compressibility at later times and at higher wave numbers, as suggested by theories of nearly incompressible flows.
Kong, Dali; Zhang, Keke; Schubert, Gerald; Anderson, John E-mail: K.Zhang@exeter.ac.uk
2013-02-15
We present a new three-dimensional numerical method for calculating the non-spherical shape and internal structure of a model of a rapidly rotating gaseous body with a polytropic index of unity. The calculation is based on a finite-element method and accounts for the full effects of rotation. After validating the numerical approach against the asymptotic solution of Chandrasekhar that is valid only for a slowly rotating gaseous body, we apply it to models of Jupiter and a rapidly rotating, highly flattened star ({alpha} Eridani). In the case of Jupiter, the two-dimensional distributions of density and pressure are determined via a hybrid inverse approach by adjusting an a priori unknown coefficient in the equation of state until the model shape matches the observed shape of Jupiter. After obtaining the two-dimensional distribution of density, we then compute the zonal gravity coefficients and the total mass from the non-spherical model that takes full account of rotation-induced shape change. Our non-spherical model with a polytropic index of unity is able to produce the known mass of Jupiter with about 4% accuracy and the zonal gravitational coefficient J {sub 2} of Jupiter with better than 2% accuracy, a reasonable result considering that there is only one parameter in the model. For {alpha} Eridani, we calculate its rotationally distorted shape and internal structure based on the observationally deduced rotation rate and size of the star by using a similar hybrid inverse approach. Our model of the star closely approximates the observed flattening.
NASA Astrophysics Data System (ADS)
Yan, Kun
2007-04-01
In this paper, by discussing the basic hypotheses about the continuous orbit and discrete orbit in two research directions of the background medium theory for celestial body motion, the concrete equation forms and their summary of the theoretic frame of celestial body motion are introduced. Future more, by discussing the general form of Binet's equation of celestial body motion orbit and it's solution of the advance of the perihelion of planets, the relations and differences between the continuous orbit theory and Newton's gravitation theory and Einstein's general relativity are given. And by discussing the fractional-dimension expanded equation for the celestial body motion orbits, the concrete equations and the prophesy data of discrete orbit or stable orbits of celestial bodies which included the planets in the Solar system, satellites in the Uranian system, satellites in the Earth system and satellites obtaining the Moon obtaining from discrete orbit theory are given too. Especially, as the preliminary exploration and inference to the gravitation curve of celestial bodies in broadly range, the concept for the ideal black hole with trend to infinite in mass density difficult to be formed by gravitation only is explored. By discussing the position hypothesis of fractional-dimension derivative about general function and the formula form the hypothesis of fractional-dimension derivative about power function, the concrete equation formulas of fractional-dimension derivative, differential and integral are described distinctly further, and the difference between the fractional-dimension derivative and the fractional-order derivative are given too. Subsequently, the concrete forms of measure calculation equations of self-similar fractal obtaining by based on the definition of form in fractional-dimension calculus about general fractal measure are discussed again, and the differences with Hausdorff measure method or the covering method at present are given. By applying
NASA Astrophysics Data System (ADS)
Xavier, Morvan; Christophe, Naisse; Issa Oumarou, Malam; Jean-François, Desprats; Anne, Combaud; Olivier, Cerdan
2015-04-01
In the literature, grass cover is often considered to be one of the best methods of limiting runoff in the vineyards; But results can vary, especially when the plot area is <2 m². However, in any study to our knowledge, the way grass cover is structured in the inter-row is taken into account to explain the variability of runoff and soil loss. The objective of this study, conducted in Champagne vineyards in France, was to quantify the influence of the cultivation practices in the inter-rows of vines and determine the influence of the density of the grass cover in the wheel tracks on the surface runoff and soil erosion in experimental plots of 0.25 m2 under simulated rainfall. Three types of ground cover were studied. In the bark-and-vine-prunings plots, the runoff coefficient ranged from 1.3 to 4.0% and soil losses were <1 g/m²/h. In the bare soil plot, the highest runoff coefficient of the study was found (80.0%) and soil losses reached 7.4 g/m²/h. In the grass cover plots, the runoff coefficient and amount of eroded soil were highly variable: the runoff coefficients ranged from 0.4 to 77.0%, and soil losses were between less than 1 and 13.4 g/m²/h. Soil type, soil moisture, slope and agricultural practices did not account for the variability. In fact, the density of grass cover in the wheel tracks explained a portion of this variability. The lack of grass in the centre of the inter-row allowed for a preferential flow and created an erosion line in the wheel tracks where the soil was compacted. This study showed that grass cover in a vineyard was not necessarily sufficient to reduce surface runoff and prevent soil erosion. To be effective, the grass cover must be dense enough in the wheel tracks of agricultural machinery to avoid runoff coefficients close to those achieved with bare soil.
NASA Technical Reports Server (NTRS)
Sittler, E. C., Jr.; Scudder, J. D.
1980-01-01
In this paper empirical evidence is presented that between 0.4 and 5 AU the thermal portion (but not all) of the solar wind electron population obeys a polytrope relation. It is also shown that this functional relationship is a member of a broader class of possible laws required of a steady state, fully ionized plasma whose proper frame electric field is dominated by the polarization electric field. The empirically determined, thermodynamically interesting value of the polytrope index (1.175) is virtually that predicted (1.16) by the theoretical considerations of Scudder and Olbert (1979). Strong, direct, empirical evidence for the nearly isothermal behavior of solar wind electrons as has been indirectly argued in the literature for some time is provided.
NASA Astrophysics Data System (ADS)
Martín, Miguel Angel; Muñoz, Francisco J.; Reyes, Miguel; Taguas, F. Javier
2014-09-01
A 2D computer simulation method of random packings is applied to sets of particles generated by a self-similar uniparametric model for particle size distributions (PSDs) in granular media. The parameter p which controls the model is the proportion of mass of particles corresponding to the left half of the normalized size interval [0,1]. First the influence on the total porosity of the parameter p is analyzed and interpreted. It is shown that such parameter, and the fractal exponent of the associated power scaling, are efficient packing parameters, but this last one is not in the way predicted in a former published work addressing an analogous research in artificial granular materials. The total porosity reaches the minimum value for p = 0.6. Limited information on the pore size distribution is obtained from the packing simulations and by means of morphological analysis methods. Results show that the range of pore sizes increases for decreasing values of p showing also different shape in the volume pore size distribution. Further research including simulations with a greater number of particles and image resolution are required to obtain finer results on the hierarchical structure of pore space.
NASA Astrophysics Data System (ADS)
Nath, G.
2012-01-01
A self-similar solution is obtained for one dimensional adiabatic flow behind a cylindrical shock wave propagating in a rotating dusty gas in presence of heat conduction and radiation heat flux with increasing energy. The dusty gas is assumed to be a mixture of non-ideal (or perfect) gas and small solid particles, in which solid particles are continuously distributed. It is assumed that the equilibrium flow-condition is maintained and variable energy input is continuously supplied by the piston (or inner expanding surface). The heat conduction is expressed in terms of Fourier's law and the radiation is considered to be of the diffusion type for an optically thick grey gas model. The thermal conductivity K and the absorption coefficient αR are assumed to vary with temperature only. In order to obtain the similarity solutions the initial density of the ambient medium is assumed to be constant and the angular velocity of the ambient medium is assumed to be decreasing as the distance from the axis increases. The effects of the variation of the heat transfer parameters and non-idealness of the gas in the mixture are investigated. The effects of an increase in (i) the mass concentration of solid particles in the mixture and (ii) the ratio of the density of solid particles to the initial density of the gas on the flow variables are also investigated.
Våge, Selina; Thingstad, T. Frede
2015-01-01
Trophic interactions are highly complex and modern sequencing techniques reveal enormous biodiversity across multiple scales in marine microbial communities. Within the chemically and physically relatively homogeneous pelagic environment, this calls for an explanation beyond spatial and temporal heterogeneity. Based on observations of simple parasite-host and predator-prey interactions occurring at different trophic levels and levels of phylogenetic resolution, we present a theoretical perspective on this enormous biodiversity, discussing in particular self-similar aspects of pelagic microbial food web organization. Fractal methods have been used to describe a variety of natural phenomena, with studies of habitat structures being an application in ecology. In contrast to mathematical fractals where pattern generating rules are readily known, however, identifying mechanisms that lead to natural fractals is not straight-forward. Here we put forward the hypothesis that trophic interactions between pelagic microbes may be organized in a fractal-like manner, with the emergent network resembling the structure of the Sierpinski triangle. We discuss a mechanism that could be underlying the formation of repeated patterns at different trophic levels and discuss how this may help understand characteristic biomass size-spectra that hint at scale-invariant properties of the pelagic environment. If the idea of simple underlying principles leading to a fractal-like organization of the pelagic food web could be formalized, this would extend an ecologists mindset on how biological complexity could be accounted for. It may furthermore benefit ecosystem modeling by facilitating adequate model resolution across multiple scales. PMID:26648929
Teo, B K; Zhang, H
1991-01-01
A systematic structural investigation of a new series of high-nuclearity Au-Ag clusters containing 25, 37, 38, and 46 metal atoms led to the description of these clusters as "clusters of clusters" based on vertex-sharing icosahedra as building blocks. Based on the observed structures, a growth sequence is proposed here for the formation of these secondary clusters (clusters of clusters) from a single 13-atom icosahedron to a 127-atom icosahedron of icosahedra via successive additions of vertex-sharing icosahedral units. This cluster-of-clusters growth mechanism parallels the atom-by-atom growth pathway for the primary clusters from a single atom to a 13-atom icosahedron. It is hypothesized that the formation of these clusters of clusters is a manifestation of the spontaneous self-organization and self-similarity processes often observed in nature. It is conceivable that the concept of cluster of clusters may be important in the intermediate stages of some cluster growth as exemplified by the polyicosahedral growth of Au-Ag supraclusters. Images PMID:11607191
NASA Astrophysics Data System (ADS)
Zhang, Keke; Kong, D.; Schubert, G.; Anderson, J.
2012-10-01
An accurate calculation of the rotationally distorted shape and internal structure of Jupiter is required to understand the high-precision gravitational field that will be measured by the Juno spacecraft now on its way to Jupiter. We present a three-dimensional non-spherical numerical calculation of the shape and internal structure of a model of Jupiter with a polytropic index of unity. The calculation is based on a finite element method and accounts for the full effects of rotation. After validating the numerical approach against the asymptotic solution of Chandrasekhar (1933) that is valid only for a slowly rotating gaseous planet, we apply it to a model of Jupiter whose rapid rotation causes a significant departure from spherical geometry. The two-dimensional distribution of the density and the pressure within Jupiter is then determined via a hybrid inverse approach by matching the a priori unknown coefficient in the equation of state to the observed shape of Jupiter. After obtaining the two-dimensional distribution of Jupiter's density, we then compute the zonal gravity coefficients and the total mass from the non-spherical Jupiter model that takes full account of rotation-induced shape changes. Our non-spherical model with a polytrope of unit index is able to produce the known mass and zonal gravitational coefficients of Jupiter. Chandrasekhar, S. 1933, The equilibrium of distorted polytropes, MNRAS 93, 390
Chopin, E I B; Marin, B; Mkoungafoko, R; Rigaux, A; Hopgood, M J; Delannoy, E; Cancès, B; Laurain, M
2008-12-01
Soil and Vitis vinifera L. (coarse and fine roots, leaves, berries) concentration and geochemical partitioning of Cu, Pb and Zn were determined in a contaminated calcareous Champagne plot to assess their mobility and transfer. Accumulation ratios in roots remained low (0.1-0.4 for Cu and Zn, <0.05 for Pb). Differences between elements resulted from vegetation uptake strategy and soil partitioning. Copper, significantly associated with the oxidisable fraction (27.8%), and Zn with the acid soluble fraction (33.3%), could be mobilised by rhizosphere acidification and oxidisation, unlike Pb, essentially contained in the reducible fraction (72.4%). Roots should not be considered as a whole since the more reactive fine roots showed higher accumulation ratios than coarse ones. More sensitive response of fine roots, lack of correlation between chemical extraction results and vegetation concentrations, and very limited translocation to aerial parts showed that fine root concentrations should be used when assessing bioavailability.
NASA Astrophysics Data System (ADS)
Imamura, James N.; Durisen, Richard H.; Pickett, Brian K.
2000-01-01
Dynamic nonaxisymmetric instabilities in rapidly rotating stars and protostars have a range of potential applications in astrophysics, including implications for binary formation during protostellar cloud collapse and for the possibility of aborted collapse to neutron star densities at late stages of stellar evolution (``fizzlers''). We have recently presented detailed linear analyses for polytropes of the most dynamically unstable global modes, the barlike modes. These produce bar distortions in the regions near the rotation axis but have trailing spiral arms toward the equator. In this paper, we use our linear eigenfunctions to predict the early nonlinear behavior of the dynamic instability and compare these ``quasi-linear'' predictions with several fully nonlinear hydrodynamics simulations. The comparisons demonstrate that the nonlinear saturation of the barlike instability is due to the self-interaction gravitational torques between the growing central bar and the spiral arms, where angular momentum is transferred outward from bar to arms. We also find a previously unsuspected resonance condition that accurately predicts the mass of the bar regions in our own simulations and in those published by other researchers. The quasi-linear theory makes other accurate predictions about consequences of instability, including properties of possible end-state bars and increases in central density, which can be large under some conditions. We discuss in some detail the application of our results to binary formation during protostellar collapse and to the formation of massive rotating black holes.
NASA Astrophysics Data System (ADS)
Chaverra, Eliana; Mach, Patryk; Sarbach, Olivier
2016-05-01
We analyze the properties of a polytropic fluid that is radially accreted into a Schwarzschild black hole. The case where the adiabatic index γ lies in the range of 1\\lt γ ≤slant 5/3 has been treated in previous work. In this article, we analyze the complementary range of 5/3\\lt γ ≤slant 2. To this purpose, the problem is cast into an appropriate Hamiltonian dynamical system, whose phase flow is analyzed. While, for 1\\lt γ ≤slant 5/3, the solutions are always characterized by the presence of a unique critical saddle point, we show that, when 5/3\\lt γ ≤slant 2, an additional critical point might appear, which is a center point. For the parametrization used in this paper, we prove that, whenever this additional critical point appears, there is a homoclinic orbit. Solutions corresponding to homoclinic orbits differ from standard transonic solutions with vanishing asymptotic velocities in two aspects: they are local (i.e., they cannot be continued to arbitrarily large radii); the dependence of the density or the value of the velocity on the radius is not monotonic.
NASA Astrophysics Data System (ADS)
Connaughton, Colm; Rajesh, R.; Zaboronski, Oleg
2006-10-01
We present a detailed study of the statistical properties of a system of diffusing aggregating particles in the presence of a steady source of monomers. We emphasize the case of low spatial dimensions where strong diffusive fluctuations invalidate the mean-field description provided by standard Smoluchowski kinetic theory. The presence of a source of monomers allows the system to reach a statistically stationary state at large times. This state is characterized by a constant flux of mass directed from small to large masses. It therefore admits a phenomenological description based on the assumption of self-similarity and constant mass flux analogous to the Kolmogorov’s 1941 theory of turbulence. Unlike turbulence, the aggregation problem is analytically tractable using powerful methods of statistical field theory. We explain in detail how these methods should be adapted to study the far-from-equilibrium, flux-dominated states characteristic of turbulent systems. We consider multipoint correlation functions of the mass density. By an exact evaluation of the scaling exponents for the one and two-point correlation functions, we show that the assumption of self-similiarity breaks down at large masses for spatial dimensions, d≤2. We calculate non-rigorously the exponents of the higher order correlation functions as an ɛ-expansion where ɛ=2-d. We show that the mass distribution exhibits non-trivial multiscaling. An analogy can be drawn with the case of hydrodynamic turbulence. The physical origin of this multiscaling is traced to the presence of strong correlations between particles participating in large mass aggregation events. These correlations stem from the recurrence of diffusion processes in d≤2. The analytic methods developed here will have more general applicability beyond the study of this specific problem.
Kalocsai, A.G.
1992-12-31
An asymptotic analysis is presented for two distinct and independent problems: (I) Wave propagation in dispersive optical media with quadratic nonlinearity (II) Hypersonic flows with three dimensional self-similarity. In the optics problem, we at first study single and multiple input propagating waves at frequencies away from dielectric resonances. Here we compare the Slowly Varying Envelope Approximation to the Method of Multiple Scales and show that the Method of Multiple Scales is a superior technique that can be applied self consistently to any perturbation order which in turn predicts new physical effects. For the single slowly modulated input wave problem, under appropriate conditions, we shown that at the O({epsilon}{sup 2}) perturbation, we obtain the cubic nonlinear Schrodinger equation. This means that for the single input wave propagating in a quadratic nonlinear medium, self-modulation effects and soliton behavior may be observed depending on the boundary conditions. For the single input wave near a classical dielectric resonance, we find that the wave number becomes amplitude dependent. The method of multiple scales is replaced by Whitham`s averaged Lagrangian. We derive the associated modulated envelope equations. We investigate an effective medium regime and the full nonlinear problem. The hypersonic flow problem requires the use of asymptotic matching that arises from the geometry from the problem. Here the pressure field and lift to drag C{sup 3/2}{sub L}/C{sub D} is evaluated for a wide delta wing with small power law curvature. Use is made of Hypersonic Small Disturbance Theory and three dimensional power law similarity. It is shown that an improvement for C{sup 3/2}{sub L}/C{sub D} occurs for wings with power law curvatures greater than one, when compared to flat delta wings. This improvement in performance agrees qualitatively with other types of concave wings.
Koch, Patrick M.; Ho, Paul T. P.; Tang, Ya-Wen
2012-03-01
Dust polarization observational results are analyzed for the high-mass star formation region W51 from the largest parent cloud ({approx}2 pc, James Clerk Maxwell Telescope) to the large-scale envelope ({approx}0.5 pc, BIMA array) down to the collapsing core e2 ({approx}60 mpc, Submillimeter Array). Magnetic field and dust emission gradient orientations reveal a correlation which becomes increasingly more tight with higher resolution. The previously developed polarization-intensity-gradient method is applied in order to quantify the magnetic field significance. This technique provides a way to estimate the local magnetic field force compared to gravity without the need of any mass or field strength measurements, solely making use of measured angles which reflect the geometrical imprint of the various forces. All three data sets clearly show regions with distinct features in the field-to-gravity force ratio. Azimuthally averaged radial profiles of this force ratio reveal a transition from a field dominance at larger distances to a gravity dominance closer to the emission peaks. Normalizing these profiles to a characteristic core scale points toward self-similarity. Furthermore, the polarization-intensity-gradient method is linked to the mass-to-flux ratio, providing a new approach to estimate the latter one without mass and field strength inputs. A transition from a magnetically supercritical to a subcritical state as a function of distance from the emission peak is found for the e2 core. Finally, based on the measured radius-dependent field-to-gravity force ratio we derive a modified star formation efficiency with a diluted gravity force. Compared to a standard (free-fall) efficiency, the observed field is capable of reducing the efficiency down to 10% or less.
NASA Astrophysics Data System (ADS)
Wang, Sijia; Liu, Bowen; Song, Youjian; Hu, Minglie
2016-04-01
We report on a simple passive scheme to reduce the intensity noise of high-power nonlinear fiber amplifiers by use of the spectral-breathing parabolic evolution of the pulse amplification with an optimized negative initial chirp. In this way, the influences of amplified spontaneous emission (ASE) on the amplifier intensity noise can be efficiently suppressed, owing to the lower overall pulse chirp, shorter spectral broadening distance, as well as the asymptotic attractive nature of self-similar pulse amplification. Systematic characterizations of the relative intensity noise (RIN) of a free-running nonlinear Yb-doped fiber amplifier are performed over a series of initial pulse parameters. Experiments show that the measured amplifier RIN increases respect to the decreased input pulse energy, due to the increased amount of ASE noise. For pulse amplification with a proper negative initial chirp, the increase of RIN is found to be smaller than with a positive initial chirp, confirming the ASE noise tolerance of the proposed spectral-breathing parabolic amplification scheme. At the maximum output average power of 27W (25-dB amplification gain), the incorporation of an optimum negative initial chirp (-0.84 chirp parameter) leads to a considerable amplifier root-mean-square (rms) RIN reduction of ~20.5% (integrated from 10 Hz to 10 MHz Fourier frequency). The minimum amplifier rms RIN of 0.025% (integrated from 1 kHz to 5 MHz Fourier frequency) is obtained along with the transform-limited compressed pulse duration of 55fs. To our knowledge, the demonstrated intensity noise performance is the lowest RIN level measured from highpower free-running femtosecond fiber amplifiers.
NASA Astrophysics Data System (ADS)
Carvalho, Joel C.; O'Dea, Christopher P.
2002-08-01
We have carried out two-dimensional axisymmetric numerical simulations of light, supersonic jets propagating into constant density atmospheres over a broad range of parameter space. We examine the evolution of the global properties of the sources as a function of source size, for a range of Mach numbers, density contrast, and jet power. We also compare our results with the expectations of current analytical self-similar models. The derived global parameters are not sensitive to small changes in input parameters. The material content of the relativistic jet does affect its propagation and the overall structure and energetics (see Paper II) of the source. The jet in case 1 (pressure dominated by relativistic electrons) propagates faster, the cocoon has a smaller aspect ratio and maintains higher pressure, and the bow shock expands at higher lateral velocity than case 2 jets (pressure dominated by relativistic electrons and protons). However, these differences generally become less important as the jet Lorentz factor increases. We have confirmed the suggestion of Wilson & Falle that the location of the first shock in the jet depends linearly on the jet radius and Mach number. We show that the result is largely independent of density contrast and that over a wide range in Mach number the relation can be used to make a crude estimate of the jet Mach number. We find that the pressure in the cocoon and the bow-shocked region varies both along and across the source axis. The degree to which the cocoon comes into pressure balance with the ambient medium depends on the jet Mach number, with intermediate-M jets having cocoons that are in pressure balance with the ambient medium over much of the length of the source, while high- or low-M jets have cocoons that are overpressured or underpressured, respectively. The bow shock lateral expansion decelerates quickly behind the jet head, but the velocity remains at least somewhat supersonic. On the other hand, the cocoon lateral
Rulli, Karen; Lobelle-Rich, Patricia A.; Trubetskoy, Alla; Lenz, Jack; Levy, Laura S.
2001-01-01
A time course analysis was performed to identify the sites of formation and timing of appearance of polytropic recombinant viruses following infection of NIH/Swiss mice with the murine retrovirus SL3-3 murine leukemia virus (SL3) or with a weakly pathogenic mutant termed SL3ΔMyb5. The results indicated that (i) polytropic recombinant viruses occur initially in the thymus of SL3-infected animals, (ii) the timing of appearance of polytropic recombinants in bone marrow is not consistent with their participation in the previously reported formation of transplantable tumor-forming cells at 3 to 4 week postinoculation, and (iii) the efficient generation of recombinant virus is correlated with efficient tumor induction. PMID:11119621
Rulli, K; Lobelle-Rich, P A; Trubetskoy, A; Lenz, J; Levy, L S
2001-01-01
A time course analysis was performed to identify the sites of formation and timing of appearance of polytropic recombinant viruses following infection of NIH/Swiss mice with the murine retrovirus SL3-3 murine leukemia virus (SL3) or with a weakly pathogenic mutant termed SL3DeltaMyb5. The results indicated that (i) polytropic recombinant viruses occur initially in the thymus of SL3-infected animals, (ii) the timing of appearance of polytropic recombinants in bone marrow is not consistent with their participation in the previously reported formation of transplantable tumor-forming cells at 3 to 4 week postinoculation, and (iii) the efficient generation of recombinant virus is correlated with efficient tumor induction.
Durisen, R.H.; Gingold, R.A.; Tohline, J.E.; Boss, A.P.
1986-06-01
The effectiveness of three different hydrodynamics models is evaluated for the analysis of the effects of fission instabilities in rapidly rotating, equilibrium flows. The instabilities arise in nonaxisymmetric Kelvin modes as rotational energy in the flow increases, which may occur in the formation of close binary stars and planets when the fluid proto-object contracts quasi-isostatically. Two finite-difference, donor-cell methods and a smoothed particle hydrodynamics (SPH) code are examined, using a polytropic index of 3/2 and ratios of total rotational kinetic energy to gravitational energy of 0.33 and 0.38. The models show that dynamic bar instabilities with the 3/2 polytropic index do not yield detached binaries and multiple systems. Ejected mass and angular momentum form two trailing spiral arms that become a disk or ring around the central remnant. The SPH code yields the same data as the finite difference codes but with less computational effort and without acceptable fluid constraints in low density regions. Methods for improving both types of codes are discussed. 68 references.
NASA Astrophysics Data System (ADS)
Stollsteiner, P.; Bessiere, H.; Nicolas, J.; Allier, D.; Berthet, O.
2015-04-01
This article is based on a BRGM study on piezometric indicators, threshold values of discharge and groundwater levels for the assessment of potentially-exploitable water resources of chalky watersheds. A method for estimating low water levels based on groundwater levels is presented from three examples representing chalk aquifers with different cycles: annual, combined and interannual. The first is located in Picardy and the two others in the Champagne-Ardennes region. Piezometers with annual cycles, used in these examples, are supposed to be representative of the aquifer hydro-dynamics. Except for multi-annual systems, the analysis between discharge measurements at a hydrometric station and groundwater levels measured at a piezometer representative of the main aquifer, leads to relatively precise and satisfactory relationships within a chalky context. These relationships may be useful for monitoring, validation, extension or reconstruction of the low water flow data. On the one hand, they allow definition of the piezometric levels corresponding to the different alert thresholds of river discharges. On the other hand, they clarify the proportions of low surface water flow from runoff or drainage of the aquifer. Finally, these correlations give an assessment of the minimum flow for the coming weeks. However, these correlations cannot be used to optimize the value of the exploitable water resource because it seems to be difficult to integrate the value of the effective rainfall that could occur during the draining period. Moreover, in the case of multi-annual systems, the solution is to attempt a comprehensive system modelling and, if it is satisfactory, using the simulated values to get rid of parasites or running the model for forecasting purposes.
NASA Astrophysics Data System (ADS)
Tirani, M. D.; Maleki, M.; Kajani, M. T.
2014-11-01
A numerical method for solving the Lane-Emden equations of the polytropic index α when 4.75 ≤ α ≤ 5 is introduced. The method is based upon nonclassical Gauss-Radau collocation points and Freud type weights. Nonclassical orthogonal polynomials, nonclassical Radau points and weighted interpolation are introduced and are utilized in the interval [0,1]. A smooth, strictly monotonic transformation is used to map the infinite domain x ∈ [0,∞) onto a half-open interval t ∈ [0,1). The resulting problem on the finite interval is then transcribed to a system of nonlinear algebraic equations using collocation. The method is easy to implement and yields very accurate results.
NASA Technical Reports Server (NTRS)
Gosling, J. T.; Riley, P.; Skoug, R. M.
2001-01-01
We strongly disagree with the essence of the Osherovich (hereafter Osherovich) comment on one of our papers. The following paragraphs provide the basis of our disagreement and elaborate on why we believe that none of the concluding statements in his Comment are true. Our most important point is that one can apply the model developed by Osherovich and colleagues to real data obtained at a single point in space to determine the polytropic index within magnetic clouds if and only if the highly idealized assumptions of that model conform to physical reality. There is good reason to believe that those assumptions do not provide an accurate physical description of real magnetic clouds in the spherically expanding solar wind.
Alter, Harvey J.; Mikovits, Judy A.; Switzer, William M.; Ruscetti, Francis W.; Lo, Shyh-Ching; Klimas, Nancy; Komaroff, Anthony L.; Montoya, Jose G.; Bateman, Lucinda; Levine, Susan; Peterson, Daniel; Levin, Bruce; Hanson, Maureen R.; Genfi, Afia; Bhat, Meera; Zheng, HaoQiang; Wang, Richard; Li, Bingjie; Hung, Guo-Chiuan; Lee, Li Ling; Sameroff, Stephen; Heneine, Walid; Coffin, John; Hornig, Mady; Lipkin, W. Ian
2012-01-01
ABSTRACT The disabling disorder known as chronic fatigue syndrome or myalgic encephalomyelitis (CFS/ME) has been linked in two independent studies to infection with xenotropic murine leukemia virus-related virus (XMRV) and polytropic murine leukemia virus (pMLV). Although the associations were not confirmed in subsequent studies by other investigators, patients continue to question the consensus of the scientific community in rejecting the validity of the association. Here we report blinded analysis of peripheral blood from a rigorously characterized, geographically diverse population of 147 patients with CFS/ME and 146 healthy subjects by the investigators describing the original association. This analysis reveals no evidence of either XMRV or pMLV infection. PMID:22991430
NASA Astrophysics Data System (ADS)
2011-01-01
Particle Physics: ATLAS unveils mural at CERN Prize: Corti Trust invites essay entries Astrophysics: CERN holds cosmic-ray conference Researchers in Residence: Lord Winston returns to school Music: ATLAS scientists record physics music Conference: Champagne flows at Reims event Competition: Students triumph at physics olympiad Teaching: Physics proves popular in Japanese schools Forthcoming Events
Satterfield, Brent C; Garcia, Rebecca A; Jia, Hongwei; Tang, Shaohua; Zheng, Haoqiang; Switzer, William M
2011-02-22
In 2009, a newly discovered human retrovirus, xenotropic murine leukemia virus (MuLV)-related virus (XMRV), was reported by Lombardi et al. in 67% of persons from the US with chronic fatigue syndrome (CFS) by PCR detection of gag sequences. Although six subsequent studies have been negative for XMRV, CFS was defined more broadly using only the CDC or Oxford criteria and samples from the US were limited in geographic diversity, both potentially reducing the chances of identifying XMRV positive CFS cases. A seventh study recently found polytropic MuLV sequences, but not XMRV, in a high proportion of persons with CFS. Here we tested blood specimens from 45 CFS cases and 42 persons without CFS from over 20 states in the United States for both XMRV and MuLV. The CFS patients all had a minimum of 6 months of post-exertional malaise and a high degree of disability, the same key symptoms described in the Lombardi et al. study. Using highly sensitive and generic DNA and RNA PCR tests, and a new Western blot assay employing purified whole XMRV as antigen, we found no evidence of XMRV or MuLV in all 45 CFS cases and in the 42 persons without CFS. Our findings, together with previous negative reports, do not suggest an association of XMRV or MuLV in the majority of CFS cases.
2011-01-01
In 2009, a newly discovered human retrovirus, xenotropic murine leukemia virus (MuLV)-related virus (XMRV), was reported by Lombardi et al. in 67% of persons from the US with chronic fatigue syndrome (CFS) by PCR detection of gag sequences. Although six subsequent studies have been negative for XMRV, CFS was defined more broadly using only the CDC or Oxford criteria and samples from the US were limited in geographic diversity, both potentially reducing the chances of identifying XMRV positive CFS cases. A seventh study recently found polytropic MuLV sequences, but not XMRV, in a high proportion of persons with CFS. Here we tested blood specimens from 45 CFS cases and 42 persons without CFS from over 20 states in the United States for both XMRV and MuLV. The CFS patients all had a minimum of 6 months of post-exertional malaise and a high degree of disability, the same key symptoms described in the Lombardi et al. study. Using highly sensitive and generic DNA and RNA PCR tests, and a new Western blot assay employing purified whole XMRV as antigen, we found no evidence of XMRV or MuLV in all 45 CFS cases and in the 42 persons without CFS. Our findings, together with previous negative reports, do not suggest an association of XMRV or MuLV in the majority of CFS cases. PMID:21342521
Analysis of self-similar solutions of multidimensional conservation laws
Keyfitz, Barbara
2014-02-15
This project focused on analysis of multidimensional conservation laws, specifically on extensions to the study of self-siminar solutions, a project initiated by the PI. In addition, progress was made on an approach to studying conservation laws of very low regularity; in this research, the context was a novel problem in chromatography. Two graduate students in mathematics were supported during the grant period, and have almost completed their thesis research.
Self-similar equilibration of strongly interacting systems from holography
NASA Astrophysics Data System (ADS)
Bakas, Ioannis; Skenderis, Kostas; Withers, Benjamin
2016-05-01
We study the equilibration of a class of far-from-equilibrium strongly interacting systems using gauge-gravity duality. The systems we analyze are 2 +1 dimensional and have a four-dimensional gravitational dual. A prototype example of a system we analyze is the equilibration of a two-dimensional fluid which is translational invariant in one direction and is attached to two different heat baths with different temperatures at infinity in the other direction. We realize such setup in gauge-gravity duality by joining two semi-infinite asymptotically anti-de Sitter (AdS) black branes of different temperatures, which subsequently evolve towards equilibrium by emitting gravitational radiation towards the boundary of AdS. At sufficiently late times the solution converges to a similarity solution, which is only sensitive to the left and right equilibrium states and not to the details of the initial conditions. This attractor solution not only incorporates the growing region of equilibrated plasma but also the outwardly propagating transition regions, and can be constructed by solving a single ordinary differential equation.
Self-similarity and self-inversion of quasicrystals
NASA Astrophysics Data System (ADS)
Madison, A. E.
2014-08-01
The discovery of quasicrystals played a revolutionary role in the condensed matter science and forced to renounce the dogma of the classical crystallography that the regular filling of the space by identical blocks is reduced solely to the Fedorov space groups. It is shown that aperiodic crystals, apart from the similarity, exhibit the self-inversion property. In a broadened sense, the self-inversion implies the possible composition of the inversion with translations, rotations, and homothety, whereas pure reflection by itself in a circle can be absent as an independent symmetry element. It is demonstrated that the symmetry of aperiodic tilings is described by Schottky groups (which belong to a particular type of Kleinian groups generated by the linear fractional Möbius transformations); in the theory of aperiodic crystals, the Schottky groups play the same role that the Fedorov groups play in the theory of crystal lattices. The local matching rules for the Penrose fractal tiling are derived, the problem of choice of the fundamental region of the group of motions of a quasicrystal is discussed, and the relation between the symmetry of aperiodic tilings and the symmetry of constructive fractals is analyzed.
Dyslexic and Skilled Reading Dynamics Are Self-Similar
ERIC Educational Resources Information Center
Holden, John G.; Greijn, Lieke T.; van Rooij, Marieke M. J. W.; Wijnants, Maarten L.; Bosman, Anna M. T.
2014-01-01
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…
MRI superresolution using self-similarity and image priors.
Manjón, José V; Coupé, Pierrick; Buades, Antonio; Collins, D Louis; Robles, Montserrat
2010-01-01
In Magnetic Resonance Imaging typical clinical settings, both low- and high-resolution images of different types are routinarily acquired. In some cases, the acquired low-resolution images have to be upsampled to match with other high-resolution images for posterior analysis or postprocessing such as registration or multimodal segmentation. However, classical interpolation techniques are not able to recover the high-frequency information lost during the acquisition process. In the present paper, a new superresolution method is proposed to reconstruct high-resolution images from the low-resolution ones using information from coplanar high resolution images acquired of the same subject. Furthermore, the reconstruction process is constrained to be physically plausible with the MR acquisition model that allows a meaningful interpretation of the results. Experiments on synthetic and real data are supplied to show the effectiveness of the proposed approach. A comparison with classical state-of-the-art interpolation techniques is presented to demonstrate the improved performance of the proposed methodology. PMID:21197094
MRI Superresolution Using Self-Similarity and Image Priors
Manjón, José V.; Coupé, Pierrick; Buades, Antonio; Collins, D. Louis; Robles, Montserrat
2010-01-01
In Magnetic Resonance Imaging typical clinical settings, both low- and high-resolution images of different types are routinarily acquired. In some cases, the acquired low-resolution images have to be upsampled to match with other high-resolution images for posterior analysis or postprocessing such as registration or multimodal segmentation. However, classical interpolation techniques are not able to recover the high-frequency information lost during the acquisition process. In the present paper, a new superresolution method is proposed to reconstruct high-resolution images from the low-resolution ones using information from coplanar high resolution images acquired of the same subject. Furthermore, the reconstruction process is constrained to be physically plausible with the MR acquisition model that allows a meaningful interpretation of the results. Experiments on synthetic and real data are supplied to show the effectiveness of the proposed approach. A comparison with classical state-of-the-art interpolation techniques is presented to demonstrate the improved performance of the proposed methodology. PMID:21197094
Analysis of Self-Similar Solutions of Multidimensional Conservation Laws
Tesdall, Allen M.
2012-08-31
This project brought large-scale, advanced methods for numerical solution of PDE to bear on the two-dimensional Riemann problem, and obtained numerical solution of problem. This numerical solution allowed us to describe key features of the solution. Analysis was combined with numerical solution to explain these numerical results. High-resolution, large-scale numerical computations show for the first time that a shock forms strictly in the supersonic region. Numerical solutions appear to show the disappearance of a diffracting shock at a sonic line.
A self-similarity based unification of BL Lacertae objects.
NASA Astrophysics Data System (ADS)
Georganopoulos, M.; Marscher, A. P.
1997-12-01
BL Lacertae (BL Lac) objects have been traditionally classified as radio selected BL Lacs (RBLs) or X-ray selected BL Lacs (XBLs) according to the discovery method. The recent discovery of a BL Lac population with observational properties intermediate between those of RBLs and XBLs, strongly suggest that this bimodal classification is misleading, and essentially reflects the two different discovery methods. We propose a unification scheme for BL Lac objects based on the following scenario: the kinetic luminosity of the jet Lambda_ {kin} scales with the size of the jet r, following the relation Lambda_ {kin} ~ r(2) . Additionally, the intensive physical variables that describe the relativistic jet in the BL Lac objects have a small intrinsic range of values. The combination of these two assumptions suggests a unification scheme, where the observed properties of a BL Lac depend mainly on the kinetic luminosity of the jet and the angle between the line of sight and the jet axis. We apply this scheme using the accelerating inner jet model, comparing the predictions of this unification with observational data from complete BL Lac samples. Finally, we briefly address the question of extending this unified scheme to include the family of flat spectrum radio quasars.
Building a Champagne Network on a Beer Budget
ERIC Educational Resources Information Center
Dolan, Jon; Pederson, Curt
2004-01-01
Oregon State University's demand for bandwidth to support scientific collaboration and research continues to grow exponentially, while state funding declines due to hard economic times. The challenge faced by these authors was to find creative yet fiscally responsible ways to meet OSU's bandwidth demands. Looking at their options for high-capacity…
Kazantsev, D.; Van Eyndhoven, G.; Lionheart, W. R. B.; Withers, P. J.; Dobson, K. J.; McDonald, S. A.; Atwood, R.; Lee, P. D.
2015-01-01
There are many cases where one needs to limit the X-ray dose, or the number of projections, or both, for high frame rate (fast) imaging. Normally, it improves temporal resolution but reduces the spatial resolution of the reconstructed data. Fortunately, the redundancy of information in the temporal domain can be employed to improve spatial resolution. In this paper, we propose a novel regularizer for iterative reconstruction of time-lapse computed tomography. The non-local penalty term is driven by the available prior information and employs all available temporal data to improve the spatial resolution of each individual time frame. A high-resolution prior image from the same or a different imaging modality is used to enhance edges which remain stationary throughout the acquisition time while dynamic features tend to be regularized spatially. Effective computational performance together with robust improvement in spatial and temporal resolution makes the proposed method a competitive tool to state-of-the-art techniques. PMID:25939621
Evidence for non-self-similarity of microearthquakes recorded at a Taiwan borehole seismometer array
NASA Astrophysics Data System (ADS)
Lin, Yen-Yu; Ma, Kuo-Fong; Kanamori, Hiroo; Song, Teh-Ru Alex; Lapusta, Nadia; Tsai, Victor C.
2016-08-01
We investigate the relationship between seismic moment M0 and source duration tw of microearthquakes by using high-quality seismic data recorded with a vertical borehole array installed in central Taiwan. We apply a waveform cross-correlation method to the three-component records and identify several event clusters with high waveform similarity, with event magnitudes ranging from 0.3 to 2.0. Three clusters—Clusters A, B and C—contain 11, 8 and 6 events with similar waveforms, respectively. To determine how M0 scales with tw, we remove path effects by using a path-averaged Q. The results indicate a nearly constant tw for events within each cluster, regardless of M0, with mean values of tw being 0.058, 0.056 and 0.034 s for Clusters A, B and C, respectively. Constant tw, independent of M0, violates the commonly used scaling relation
Self-similar rogue waves and nonlinear tunneling effects in inhomogeneous nonlinear fiber optics
NASA Astrophysics Data System (ADS)
Wang, Lei; Zhu, Yu-Jie; Jiang, Dong-Yang
2016-04-01
Analytical first- and second-order rogue wave solutions of the inhomogeneous modified nonlinear Schrödinger equation are presented by using similarity transformation. Then, by the proper choices of the inhomogeneous coefficients and free parameters, the controllable behaviors of the optical rogue waves are graphically discussed in the nonlinear fiber optics context. It is found that the width of the rogue wave can be tuned by adjusting the parameter ? and the locations of the rogue waves are linearly controlled by the parameter ?. The intensities of the rogue waves are influenced by the inhomogeneous linear gain/loss coefficient ? and parameter ?. The dispersion management function ? has effects on the periods and trajectories of the rogue waves and can induce maintenance (or annihilation) along ? direction. Interestingly, the composite rogue waves are revealed, the location of which is manipulated through changing the dispersion management function ?. Additionally, the nonlinear tunneling of those rogue waves is investigated as they propagate through a dispersion barrier (or well) and nonlinear barrier (or well).
ERIC Educational Resources Information Center
Monroe, Charles; Newman, John
2005-01-01
This simple example demonstrates the physical significance of similarity solutions and the utility of dimensional and asymptotic analysis of partial differential equations. A procedure to determine the existence of similarity solutions is proposed and subsequently applied to transient constant-flux heat transfer. Short-time expressions follow from…
An anomalous non-self-similar infiltration and fractional diffusion equation
NASA Astrophysics Data System (ADS)
Gerasimov, D. N.; Kondratieva, V. A.; Sinkevich, O. A.
2010-08-01
Problems of anomalous infiltration in porous media are considered. As follows from the analysis of experimental data, modification of the infiltration equation is necessary. A fractional diffusion equation with variable order of the time-derivative operator for describing the liquid infiltration in porous media is proposed. The physical meaning of this fractional equation is explained. This equation provides good agreement with existing experimental data for both the subdiffusion and the superdiffusion. The treatment of experimental data for the absorption of water in a fired-clay brick and for water infiltration in cement mortar using this fractional equation of diffusion is presented. Various formulae, which can be useful for applications, have been developed.
Large-scale analysis of unconfined self-similar Rayleigh-Taylor turbulence
NASA Astrophysics Data System (ADS)
Soulard, Olivier; Griffond, Jérôme; Gréa, Benoît-Joseph
2015-09-01
The large-scale properties of unconfined Rayleigh-Taylor turbulence are investigated using an eddy-damped quasi-normal markovianized approximation. Within this framework, turbulent spectra are shown to undergo at late times and at large scales, an evolution dominated by non-linear backscattering processes. As a result, the analysis predicts that large scale initial conditions are eventually forgotten: there is no large scale invariant and no equivalent of a principle of permanence of large eddies. Additional properties of Rayleigh-Taylor large scales are also discussed. In particular, their scaling and anisotropy are examined, with an emphasis put on the combined influence of buoyancy production and non-linearities. The different assumptions and predictions of this work are verified by performing an implicit large eddy simulation of a Rayleigh-Taylor configuration.
Evidence for non-self-similarity of microearthquakes recorded at a Taiwan borehole seismometer array
NASA Astrophysics Data System (ADS)
Lin, Yen-Yu; Ma, Kuo-Fong; Kanamori, Hiroo; Song, Teh-Ru Alex; Lapusta, Nadia; Tsai, Victor C.
2016-08-01
We investigate the relationship between seismic moment M0 and source duration tw of microearthquakes by using high-quality seismic data recorded with a vertical borehole array installed in central Taiwan. We apply a waveform cross-correlation method to the three-component records and identify several event clusters with high waveform similarity, with event magnitudes ranging from 0.3 to 2.0. Three clusters-Clusters A, B and C-contain 11, 8 and 6 events with similar waveforms, respectively. To determine how M0 scales with tw, we remove path effects by using a path-averaged Q. The results indicate a nearly constant tw for events within each cluster, regardless of M0, with mean values of tw being 0.058, 0.056 and 0.034 s for Clusters A, B and C, respectively. Constant tw, independent of M0, violates the commonly used scaling relation {t_w} ∝ M_0^{1/3}. This constant duration may arise either because all events in a cluster are hosted on the same isolated seismogenic patch, or because the events are driven by external factors of constant duration, such as fluid injections into the fault zone. It may also be related to the earthquake nucleation size.
How children perceive fractals: hierarchical self-similarity and cognitive development.
Martins, Maurício Dias; Laaha, Sabine; Freiberger, Eva Maria; Choi, Soonja; Fitch, W Tecumseh
2014-10-01
The ability to understand and generate hierarchical structures is a crucial component of human cognition, available in language, music, mathematics and problem solving. Recursion is a particularly useful mechanism for generating complex hierarchies by means of self-embedding rules. In the visual domain, fractals are recursive structures in which simple transformation rules generate hierarchies of infinite depth. Research on how children acquire these rules can provide valuable insight into the cognitive requirements and learning constraints of recursion. Here, we used fractals to investigate the acquisition of recursion in the visual domain, and probed for correlations with grammar comprehension and general intelligence. We compared second (n=26) and fourth graders (n=26) in their ability to represent two types of rules for generating hierarchical structures: Recursive rules, on the one hand, which generate new hierarchical levels; and iterative rules, on the other hand, which merely insert items within hierarchies without generating new levels. We found that the majority of fourth graders, but not second graders, were able to represent both recursive and iterative rules. This difference was partially accounted by second graders' impairment in detecting hierarchical mistakes, and correlated with between-grade differences in grammar comprehension tasks. Empirically, recursion and iteration also differed in at least one crucial aspect: While the ability to learn recursive rules seemed to depend on the previous acquisition of simple iterative representations, the opposite was not true, i.e., children were able to acquire iterative rules before they acquired recursive representations. These results suggest that the acquisition of recursion in vision follows learning constraints similar to the acquisition of recursion in language, and that both domains share cognitive resources involved in hierarchical processing.
Kazantsev, D; Van Eyndhoven, G; Lionheart, W R B; Withers, P J; Dobson, K J; McDonald, S A; Atwood, R; Lee, P D
2015-06-13
There are many cases where one needs to limit the X-ray dose, or the number of projections, or both, for high frame rate (fast) imaging. Normally, it improves temporal resolution but reduces the spatial resolution of the reconstructed data. Fortunately, the redundancy of information in the temporal domain can be employed to improve spatial resolution. In this paper, we propose a novel regularizer for iterative reconstruction of time-lapse computed tomography. The non-local penalty term is driven by the available prior information and employs all available temporal data to improve the spatial resolution of each individual time frame. A high-resolution prior image from the same or a different imaging modality is used to enhance edges which remain stationary throughout the acquisition time while dynamic features tend to be regularized spatially. Effective computational performance together with robust improvement in spatial and temporal resolution makes the proposed method a competitive tool to state-of-the-art techniques.
Wave propagation in fractal-inspired self-similar beam lattices
Lim, Qi Jian; Wang, Pai; Koh, Soo Jin Adrian; Khoo, Eng Huat; Bertoldi, Katia
2015-11-30
We combine numerical analysis and experiments to investigate the effect of hierarchy on the propagation of elastic waves in triangular beam lattices. While the response of the triangular lattice is characterized by a locally resonant band gap, both Bragg-type and locally resonant gaps are found for the hierarchical lattice. Therefore, our results demonstrate that structural hierarchy can be exploited to introduce an additional type of band gaps, providing a robust strategy for the design of lattice-based metamaterials with hybrid band gap properties (i.e., possessing band gaps that arises from both Bragg scattering and localized resonance)
NASA Astrophysics Data System (ADS)
Bettencourt, L. M. A.; Lobo, J.; West, G. B.
2008-06-01
Cities have existed since the beginning of civilization and have always been intimately connected with humanity's cultural and technological development. Much about the human and social dynamics that takes place is cities is intuitively recognizable across time, space and culture; yet we still do not have a clear cut answer as to why cities exist or to what factors are critical to make them thrive or collapse. Here, we construct an extensive quantitative characterization of the variation of many urban indicators with city size, using large data sets for American, European and Chinese cities. We show that social and economic quantities, characterizing the creation of wealth and new ideas, show increasing returns to population scale, which appear quantitatively as a power law of city size with an exponent β≃ 1.15 > 1. Concurrently, quantities characterizing material infrastructure typically show economies of scale, namely β≃ 0.8 < 1. The existence of pervasive scaling relations across city size suggests a universal social dynamics common to all cities within an urban system. We sketch some of their general ingredients, which include the acceleration of social life and a restructuring of individual social networks as cities grow larger. We also build simple dynamical models to show that increasing returns in wealth and innovation can fuel faster than exponential growth, which inexorably lead to crises of urban organization. To avoid them we show that growth may proceed in cycles, separated by major urban adaptations, with the unintended consequence that the duration of such cycles decreases with larger urban population size and is now estimated to be shorter than a human lifetime.
Kazantsev, D; Van Eyndhoven, G; Lionheart, W R B; Withers, P J; Dobson, K J; McDonald, S A; Atwood, R; Lee, P D
2015-06-13
There are many cases where one needs to limit the X-ray dose, or the number of projections, or both, for high frame rate (fast) imaging. Normally, it improves temporal resolution but reduces the spatial resolution of the reconstructed data. Fortunately, the redundancy of information in the temporal domain can be employed to improve spatial resolution. In this paper, we propose a novel regularizer for iterative reconstruction of time-lapse computed tomography. The non-local penalty term is driven by the available prior information and employs all available temporal data to improve the spatial resolution of each individual time frame. A high-resolution prior image from the same or a different imaging modality is used to enhance edges which remain stationary throughout the acquisition time while dynamic features tend to be regularized spatially. Effective computational performance together with robust improvement in spatial and temporal resolution makes the proposed method a competitive tool to state-of-the-art techniques. PMID:25939621
Power Law Behavior and Self-Similarity in Modern Industrial Accidents
NASA Astrophysics Data System (ADS)
Lopes, António M.; Tenreiro Machado, J. A.
Advances in technology have produced more and more intricate industrial systems, such as nuclear power plants, chemical centers and petroleum platforms. Such complex plants exhibit multiple interactions among smaller units and human operators, rising potentially disastrous failure, which can propagate across subsystem boundaries. This paper analyzes industrial accident data-series in the perspective of statistical physics and dynamical systems. Global data is collected from the Emergency Events Database (EM-DAT) during the time period from year 1903 up to 2012. The statistical distributions of the number of fatalities caused by industrial accidents reveal Power Law (PL) behavior. We analyze the evolution of the PL parameters over time and observe a remarkable increment in the PL exponent during the last years. PL behavior allows prediction by extrapolation over a wide range of scales. In a complementary line of thought, we compare the data using appropriate indices and use different visualization techniques to correlate and to extract relationships among industrial accident events. This study contributes to better understand the complexity of modern industrial accidents and their ruling principles.
How children perceive fractals: hierarchical self-similarity and cognitive development.
Martins, Maurício Dias; Laaha, Sabine; Freiberger, Eva Maria; Choi, Soonja; Fitch, W Tecumseh
2014-10-01
The ability to understand and generate hierarchical structures is a crucial component of human cognition, available in language, music, mathematics and problem solving. Recursion is a particularly useful mechanism for generating complex hierarchies by means of self-embedding rules. In the visual domain, fractals are recursive structures in which simple transformation rules generate hierarchies of infinite depth. Research on how children acquire these rules can provide valuable insight into the cognitive requirements and learning constraints of recursion. Here, we used fractals to investigate the acquisition of recursion in the visual domain, and probed for correlations with grammar comprehension and general intelligence. We compared second (n=26) and fourth graders (n=26) in their ability to represent two types of rules for generating hierarchical structures: Recursive rules, on the one hand, which generate new hierarchical levels; and iterative rules, on the other hand, which merely insert items within hierarchies without generating new levels. We found that the majority of fourth graders, but not second graders, were able to represent both recursive and iterative rules. This difference was partially accounted by second graders' impairment in detecting hierarchical mistakes, and correlated with between-grade differences in grammar comprehension tasks. Empirically, recursion and iteration also differed in at least one crucial aspect: While the ability to learn recursive rules seemed to depend on the previous acquisition of simple iterative representations, the opposite was not true, i.e., children were able to acquire iterative rules before they acquired recursive representations. These results suggest that the acquisition of recursion in vision follows learning constraints similar to the acquisition of recursion in language, and that both domains share cognitive resources involved in hierarchical processing. PMID:24955884
The flip-over effect in self-similar laser-induced plasma expansion
Baxter, Nathan P.; Shabanov, Sergei V.
2008-09-15
We present a rigorous study of a dynamical model for a nonsymmetric expansion of laser-induced plasma plumes into the vacuum. The model is used in the laser film deposition technique and for remote chemical analysis in the so-called laser-induced breakdown spectroscopy. It defines a particular class of solutions of the hydrodynamics equations when the (plasma) mass density, pressure, and temperature as functions of position have level surfaces that are ellipsoids. The time evolution of ellipsoid semiaxes is determined by the dynamical model. In this model we investigate the flip-over effect: A pancakelike shape of the plasma plume turns into a cigarlike shape and vice versa in due course of its expansion. The effect has been observed in experiments as well as in numerical simulations. In many practical cases, axially symmetric plasma plumes with the adiabatic constant of (5/3) (ideal gas) are used. For this case we prove that the flip-over effect occurs exactly once in the above dynamical model. This rigorous result agrees with the earlier experimental and numerical evidence and, hence, validates a wide applicability of the model.
The flip-over effect in self-similar laser-induced plasma expansion
NASA Astrophysics Data System (ADS)
Baxter, Nathan P.; Shabanov, Sergei V.
2008-09-01
We present a rigorous study of a dynamical model for a nonsymmetric expansion of laser-induced plasma plumes into the vacuum. The model is used in the laser film deposition technique and for remote chemical analysis in the so-called laser-induced breakdown spectroscopy. It defines a particular class of solutions of the hydrodynamics equations when the (plasma) mass density, pressure, and temperature as functions of position have level surfaces that are ellipsoids. The time evolution of ellipsoid semiaxes is determined by the dynamical model. In this model we investigate the flip-over effect: A pancakelike shape of the plasma plume turns into a cigarlike shape and vice versa in due course of its expansion. The effect has been observed in experiments as well as in numerical simulations. In many practical cases, axially symmetric plasma plumes with the adiabatic constant of 5/3 (ideal gas) are used. For this case we prove that the flip-over effect occurs exactly once in the above dynamical model. This rigorous result agrees with the earlier experimental and numerical evidence and, hence, validates a wide applicability of the model.
Self-similarity and scaling behaviour of infrared emission from radiatively heated dust - I. Theory
NASA Astrophysics Data System (ADS)
Ivezic, Zeljko; Elitzur, Moshe
1997-06-01
Dust infrared emission possesses scaling properties that yield powerful results with far-reaching observational consequences. Scaling was first noticed by Rowan-Robinson for spherical shells and is shown here to be a general property of dust emission in arbitrary geometries. Overall luminosity is never an input parameter of the radiative transfer problem; spectral shape is the only relevant property of the heating radiation when the inner boundary of the dusty region is controlled by dust sublimation. Similarly, the absolute scales of densities and distances are irrelevant; the geometry enters only through angles, relative thicknesses and aspect ratios, and the actual magnitudes of densities and distances enter only through one independent parameter, the overall optical depth. That is, as long as the overall optical depth stays the same, the system dimensions can be scaled up or down by an arbitrary factor without any effect on the radiative transfer problem. Dust properties enter only through dimensionless, normalized distributions that describe the spatial variation of density and the wavelength dependence of scattering and absorption efficiencies. Scaling enables a systematic approach to modelling and classification of IR spectra. We develop a new, fully scale-free method for solving radiative transfer, present exact numerical results, and derive approximate analytical solutions for spherical geometry, covering the entire range of parameter space relevant to observations. For a given type of grains, the spectral energy distribution (SED) is primarily controlled by the profile of the spatial dust distribution and the optical depth - each density profile produces a family of solutions, with position within the family determined by optical depth. From the model SEDs presented here, the density distribution and optical depth can be observationally determined for various sources. Scaling implies tight correlations among the SEDs of various members of the same class of sources such as young stellar objects, late-type stars, etc. In particular, all members of the same class occupy common, well-defined regions in colour-colour diagrams. The observational data corroborate the existence of these correlations.
Self-similar analysis of Vlasov-Einstein equations in spherical symmetry
Munier, A.; Burgan, J.R.; Feix, M.; Fijalkow, E.
1980-03-15
The Vlasov-Einstein system of equations is studied from the point of view of group transformations. Continuous groups are shown to generalize the usual infinitesimal treatment of the metric tensor to the case of a distribution function. Reduced equations are obtained, leading to a time-dependent analytical solution, which yields as a limiting case the Schwarzchild metric. The problem of a purely radial motion of null particles is discussed and leads to an expression for the redshift in a nonstatic, inhomogeneous spacetime.
Rényi entropy and improved equilibration rates to self-similarity for nonlinear diffusion equations
NASA Astrophysics Data System (ADS)
Carrillo, J. A.; Toscani, G.
2014-12-01
We investigate the large-time asymptotics of nonlinear diffusion equations ut = Δup in dimension n ⩾ 1, in the exponent interval p > n/(n + 2), when the initial datum u0 is of bounded second moment. Precise rates of convergence to the Barenblatt profile in terms of the relative Rényi entropy are demonstrated for finite-mass solutions defined in the whole space when they are re-normalized at each time t > 0 with respect to their own second moment, as proposed by Carrillo et al (2006 Arch. Ration. Mech. Anal. 180 127-49) and Toscani (2005 J. Evol. Eqns 5 185-203). The analysis shows that, in the range p > max((n - 1)/n, n/(n + 2)), the relative Rényi entropy exhibits a better decay, for intermediate times, with respect to the standard Ralston-Newman entropy. The result follows by a suitable use of sharp Gagliardo-Nirenberg-Sobolev inequalities considered by Dolbeault and Toscani (2013 Ann. Inst. Henri Poincare (C) Non Linear Anal. 30 917-34), and their information-theoretical proof (Savaré and Toscani 2014 IEEE Trans. Inform. Theory 60 2687-93), known as concavity of Rényi entropy power.
Isometric immersions, energy minimization and self-similar buckling in non-Euclidean elastic sheets
NASA Astrophysics Data System (ADS)
Gemmer, John; Sharon, Eran; Shearman, Toby; Venkataramani, Shankar C.
2016-04-01
The edges of torn plastic sheets and growing leaves often display hierarchical buckling patterns. We show that this complex morphology i) emerges even in zero strain configurations, and ii) is driven by a competition between the two principal curvatures, rather than between bending and stretching. We identify the key role of branch point (or “monkey saddle”) singularities in generating complex wrinkling patterns in isometric immersions, and show how they arise naturally from minimizing the elastic energy.
Social Preference in Preschoolers: Effects of Morphological Self-Similarity and Familiarity
Richter, Nadja; Tiddeman, Bernard; Haun, Daniel B. M.
2016-01-01
Adults prefer to interact with others that are similar to themselves. Even slight facial self-resemblance can elicit trust towards strangers. Here we investigate if preschoolers at the age of 5 years already use facial self-resemblance when they make social judgments about others. We found that, in the absence of any additional knowledge about prospective peers, children preferred those who look subtly like themselves over complete strangers. Thus, subtle morphological similarities trigger social preferences well before adulthood. PMID:26727132
Self similarity of turbulence and dynamo action in the largest cosmic structures
NASA Astrophysics Data System (ADS)
Miniati, Francesco; Beresnyak, Andrey
2015-08-01
Massive galaxy clusters (GC) are filled with a hot, turbulent and magnetised intra-cluster medium (ICM). They are still forming under the action of gravitational instability driving supersonic accretion flows, which partially dissipate into heat through a complex network of large scale shocks, whicle partly excite giant turbulent eddies and cascade. Amongst others turbulence amplifies magnetic energy by way of dynamo action. This pattern of gravitational energy turning kinetic, thermal, turbulent and magnetic is a basic feature of GC hydrodynamics but quantitative modelling remains a challenge. In this contribution we present results from recent high resolution numerical simulations of structure formation in which the time dependent turbulent motions of the intracluster medium of a massive galaxy cluster are resolved and their statistical properties quantified for the first time. Combined with independent state-of-theart results on turbulent dynamo we determine without adjustable parameters the thermal, turbulent and magnetic history of giant GC. I will discuss the scale free character of energy structure in the intracluster medium and how it encodes information about the efficiency of turbulent heating and dynamo action directly accessible through astronomical observations.
Petridis, Loukas; Pingali, Sai Venkatesh; Urban, Volker; Heller, William T; O'Neill, Hugh Michael; Foston, Marcus B; Ragauskas, Arthur J; Smith, Jeremy C
2011-01-01
Lignin, a major polymeric component of plant cell walls, forms aggregates in vivo and poses a barrier to cellulosic ethanol production. Here, neutron scattering experiments and molecular dynamics simulations reveal that lignin aggregates are characterized by a surface fractal dimension that is invariant under change of scale from 1 1000 A. The simulations also reveal extensive water penetration of the aggregates and heterogeneous chain dynamics corresponding to a rigid core with a fluid surface.
How children perceive fractals: Hierarchical self-similarity and cognitive development
Martins, Maurício Dias; Laaha, Sabine; Freiberger, Eva Maria; Choi, Soonja; Fitch, W. Tecumseh
2014-01-01
The ability to understand and generate hierarchical structures is a crucial component of human cognition, available in language, music, mathematics and problem solving. Recursion is a particularly useful mechanism for generating complex hierarchies by means of self-embedding rules. In the visual domain, fractals are recursive structures in which simple transformation rules generate hierarchies of infinite depth. Research on how children acquire these rules can provide valuable insight into the cognitive requirements and learning constraints of recursion. Here, we used fractals to investigate the acquisition of recursion in the visual domain, and probed for correlations with grammar comprehension and general intelligence. We compared second (n = 26) and fourth graders (n = 26) in their ability to represent two types of rules for generating hierarchical structures: Recursive rules, on the one hand, which generate new hierarchical levels; and iterative rules, on the other hand, which merely insert items within hierarchies without generating new levels. We found that the majority of fourth graders, but not second graders, were able to represent both recursive and iterative rules. This difference was partially accounted by second graders’ impairment in detecting hierarchical mistakes, and correlated with between-grade differences in grammar comprehension tasks. Empirically, recursion and iteration also differed in at least one crucial aspect: While the ability to learn recursive rules seemed to depend on the previous acquisition of simple iterative representations, the opposite was not true, i.e., children were able to acquire iterative rules before they acquired recursive representations. These results suggest that the acquisition of recursion in vision follows learning constraints similar to the acquisition of recursion in language, and that both domains share cognitive resources involved in hierarchical processing. PMID:24955884
NASA Astrophysics Data System (ADS)
Fouvry, Jean-Baptiste; Pichon, Christophe
2015-05-01
The main orbital signatures of the secular evolution of an isolated self-gravitating stellar Mestel disc are recovered using a dressed Fokker-Planck formalism in angle-action variables. The shot-noise-driven formation of narrow ridges of resonant orbits is recovered in the WKB limit of tightly wound transient spirals, for a tepid Toomre-stable tapered disc. The relative effect of the bulge, the halo, the disc temperature and the spectral properties of the shot noise are investigated in turn. For such galactic discs all elements seem to impact the locus and direction of the ridge. For instance, when the halo mass is decreased, we observe a transition between a regime of heating in the inner regions of the disc through the inner Lindblad resonance to a regime of radial migration of quasi-circular orbits via the corotation resonance in the outer part of the disc. The dressed secular formalism captures both the nature of collisionless systems (via their natural frequencies and susceptibility), and their nurture via the structure of the external perturbing power spectrum. Hence it provides the ideal framework in which to study their long-term evolution.
Dark matter concentrations in galactic nuclei according to polytropic models
NASA Astrophysics Data System (ADS)
Saxton, Curtis J.; Younsi, Ziri; Wu, Kinwah
2016-10-01
We calculate the radial profiles of galaxies where the nuclear region is self-gravitating, consisting of self-interacting dark matter (SIDM) with F degrees of freedom. For sufficiently high density this dark matter becomes collisional, regardless of its behaviour on galaxy scales. Our calculations show a spike in the central density profile, with properties determined by the dark matter microphysics, and the densities can reach the `mean density' of a black hole (from dividing the black hole mass by the volume enclosed by the Schwarzschild radius). For a galaxy halo of given compactness (χ ≡ 2GM/Rc2), certain values for the dark matter entropy yield a dense central object lacking an event horizon. For some soft equations of state of the SIDM (e.g. F ≳ 6), there are multiple horizonless solutions at given compactness. Although light propagates around and through a sphere composed of dark matter, it is gravitationally lensed and redshifted. While some calculations give non-singular solutions, others yield solutions with a central singularity. In all cases, the density transitions smoothly from the central body to the dark matter envelope around it, and to the galaxy's dark matter halo. We propose that pulsar timing observations will be able to distinguish between systems with a centrally dense dark matter sphere (for different equations of state) and conventional galactic nuclei that harbour a supermassive black hole.
Self-similarity in the chemical evolution of galaxies and the delay-time distribution of SNe Ia
NASA Astrophysics Data System (ADS)
Walcher, C. J.; Yates, R. M.; Minchev, I.; Chiappini, C.; Bergemann, M.; Bruzual, G.; Charlot, S.; Coelho, P. R. T.; Gallazzi, A.; Martig, M.
2016-10-01
Recent improvements in the age dating of stellar populations and single stars allow us to study the ages and abundance of stars and galaxies with unprecedented accuracy. We here compare the relation between age and α-element abundances for stars in the solar neighborhood to that of local, early-type galaxies. We find these two relations to be very similar. Both fall into two regimes with a shallow slope for ages younger than ~9 Gyr and a steeper slope for ages older than that value. This quantitative similarity seems surprising because of the different types of galaxies and scales involved. For the sample of early-type galaxies we also show that the data are inconsistent with literature delay-time distributions of either single- or double-Gaussian shape. The data are consistent with a power-law delay-time distribution. We thus confirm that the delay-time distribution inferred for the Milky Way from chemical evolution arguments must also apply to massive early-type galaxies. We also offer a tentative explanation for the seeming universality of the age-[α/Fe] relation: it is the manifestation of averaging different stellar populations with varying chemical evolution histories.
Self-Similar, Self-Replicating Critical Layers and Vortices in the Accretion Disk around a Protostar
NASA Astrophysics Data System (ADS)
Pei, S.; Jiang, C.; Hassanzadeh, P.; Marcus, P. S.
2012-12-01
Rotation, linearly-stable vertical (z) density stratification, and horizontal shear allow protoplanetary disks to form a new type of critical layer. In a Boussinesq Cartesian approximation of the disk, these critical layers are neutral eigenmodes with streamwise x (azimuthal) wavenumber k and temporal frequency s, and they form at cross-stream y (radial) locations, such that: s/k-V(y)=±N/k, where N is the Brunt-Väisälä frequency and V(y)=σy is the streamwise velocity with linear shear σ. These critical layers have singular vertical velocities Vz. The Coriolis parameter, couples with the vertical derivative of Vz to produce vortex layers at the critical layers. These vortex layers roll up into new vortices, which in turn create new critical layers and so on filling space with a lattice of vortices. Here we show two types of self-replicating lattices of vortices by plotting the vertical vorticity. The first type is shown in Fig. 1. The initial condition is a single vortex at the origin indicated by the red box. This vortex produces critical layers with s=0 at y=±N/(kσ). These critical layers grow and roll-up into vortices and self-replicate to form a lattice of vortices. A second type of vortex lattice is shown in Fig. 2. The initial condition consists of a vortex pair at the origin separated in y by distance Δ indicated by the red box. Due to V(y) these vortices advect past each other at a well-defined frequency with s≠0. This causes new vortices to be formed in pairs, with the vortices in each pair separated by Δ. Thus, this process also self-replicates and ends up filling the domain with regularly spaced pairs of vortices.
Coluccio, Maria Laura; Gentile, Francesco; Das, Gobind; Nicastri, Annalisa; Perri, Angela Mena; Candeloro, Patrizio; Perozziello, Gerardo; Proietti Zaccaria, Remo; Gongora, Juan Sebastian Totero; Alrasheed, Salma; Fratalocchi, Andrea; Limongi, Tania; Cuda, Giovanni; Di Fabrizio, Enzo
2015-09-01
Control of the architecture and electromagnetic behavior of nanostructures offers the possibility of designing and fabricating sensors that, owing to their intrinsic behavior, provide solutions to new problems in various fields. We show detection of peptides in multicomponent mixtures derived from human samples for early diagnosis of breast cancer. The architecture of sensors is based on a matrix array where pixels constitute a plasmonic device showing a strong electric field enhancement localized in an area of a few square nanometers. The method allows detection of single point mutations in peptides composing the BRCA1 protein. The sensitivity demonstrated falls in the picomolar (10(-12) M) range. The success of this approach is a result of accurate design and fabrication control. The residual roughness introduced by fabrication was taken into account in optical modeling and was a further contributing factor in plasmon localization, increasing the sensitivity and selectivity of the sensors. This methodology developed for breast cancer detection can be considered a general strategy that is applicable to various pathologies and other chemical analytical cases where complex mixtures have to be resolved in their constitutive components.
Coluccio, Maria Laura; Gentile, Francesco; Das, Gobind; Nicastri, Annalisa; Perri, Angela Mena; Candeloro, Patrizio; Perozziello, Gerardo; Proietti Zaccaria, Remo; Gongora, Juan Sebastian Totero; Alrasheed, Salma; Fratalocchi, Andrea; Limongi, Tania; Cuda, Giovanni; Di Fabrizio, Enzo
2015-01-01
Control of the architecture and electromagnetic behavior of nanostructures offers the possibility of designing and fabricating sensors that, owing to their intrinsic behavior, provide solutions to new problems in various fields. We show detection of peptides in multicomponent mixtures derived from human samples for early diagnosis of breast cancer. The architecture of sensors is based on a matrix array where pixels constitute a plasmonic device showing a strong electric field enhancement localized in an area of a few square nanometers. The method allows detection of single point mutations in peptides composing the BRCA1 protein. The sensitivity demonstrated falls in the picomolar (10−12 M) range. The success of this approach is a result of accurate design and fabrication control. The residual roughness introduced by fabrication was taken into account in optical modeling and was a further contributing factor in plasmon localization, increasing the sensitivity and selectivity of the sensors. This methodology developed for breast cancer detection can be considered a general strategy that is applicable to various pathologies and other chemical analytical cases where complex mixtures have to be resolved in their constitutive components. PMID:26601267
Kukushkin, A. B.; Rantsev-Kartinov, V. A.
2009-07-26
The hypotheses for self-assembling of a fractal condensed matter in electric discharges and the probable role of a skeletal matter in the long-lived filamentary structures in fusion devices is studied in two directions. First, we append previous collection of respective data with recent evidences for skeletal structuring in peripheral plasmas and dust deposits in fusion and material test devices. Second, we demonstrate, via numerical modelling, the possibility of coaxial tubular structuring formation in a system of electric current filaments composed of magnetized, electrically conducting thin rods (nanodust), with an accent on self-reduction of spatial dimensionality of structuring and on the role of magnetic
NASA Astrophysics Data System (ADS)
Kulikovskii, A. G.; Chugainova, A. P.; Shargatov, V. A.
2016-07-01
Solutions of the Riemann problem for a generalized Hopf equation are studied. The solutions are constructed using a sequence of non-overturning Riemann waves and shock waves with stable stationary and nonstationary structures.
ERIC Educational Resources Information Center
Vollmer, Michael; Mollmann, Klaus-Peter
2012-01-01
The recent introduction of inexpensive high-speed cameras offers a new experimental approach to many simple but fast-occurring events in physics. In this paper, the authors present two simple demonstration experiments recorded with high-speed cameras in the fields of gas dynamics and thermal physics. The experiments feature vapour pressure effects…
Dorangeon, P H; Quereux, C; Wahl, P
1989-12-01
In 92,130 pregnancies followed between 1980 and 1987, 48 cases of hyperthyroidism were reported including 38 Grave's diseases, 5 toxic adenomas, 4 multinodules goiters. In comparing the results with those mentioned in the literature, a number of conclusions may be reached. In case of hyperthyroidism treated before the pregnancy or discovered at the beginning, there is, in every other case, an aggravation at the end of the first trimester, then a stabilization in the 2nd or 3rd trimester and finally an aggravation in the post-partum period. There is a high rate of abortions (35 p. cent), a delayed intra-uterine growth in half of the cases. The problem of the treatment is of paramount importance; there is no problem with Beta-blockers but the SAT are not without danger: risk of hypothyroidism and fetal goiter, but also risk of maternal hypothyroidism. From the 15th week, the doses should therefore be decreased, and sometimes the treatment discontinued and replaced with Beta-blockers. The best SAT drug during pregnancy is the propylthioracile which is the least likely to cross the fetal barrier. Surgery is only exceptionally indicated. In a woman who is cured from her Grave's disease, recurrences are always possible, and also fetal hyperthyroidism caused by crossing of thyreostimulins immunoglobins, even in case of maternal euthyroidism. PMID:2696063
The energy balance of plasmoids in the solar atmosphere
NASA Technical Reports Server (NTRS)
Cargill, P. J.; Pneuman, G. W.
1986-01-01
The properties of an isolated magnetized plasmoid in a nonuniform magnetic field such as arises in stellar atmospheres are studied. The work of Pneuman and Cargill (1985) on the so-called melon-seed effect is extended to include an equation describing the energy balance, so giving a unified picture of the shape, motion, and energetics of the plasmoid. Three treatments of plasmoid energy balance are considered: (1) a polytropic law, (P = about N to the gamma); (2) one in which the plasmoid cools radiatively; and (3) one in which a heating function proportional to the local density balances the radiation. For a gamma = 4/3 polytrope the evolution is self-similar, so that the plasmoid maintains its shape as it moves out from the stellar surface. If gamma is less than 4/3, the final shape is a long thin cigar-shaped body, whereas if gamma is greater than or equal to 4/3, it ultimately becomes self-similar. In cases with radiation and also with heating, the ultimate shape of the plasmoid is determined by whether its gas or magnetic pressure dominate. The former is equivalent to the gamma-less-than-4/3 polytrope, and the latter to the gamma-greater-than-4/3 one. If radiation alone is present, the plasmoid cools rapidly and subsequently evolves self-similarly. If heating balances radiation initially, then the plasmoid heats up as it moves out, but, if the ratio of the transit of time of Alfven waves across it is much less than the radiative cooling time, it ultimately evolves as a gamma = 5/3 polytrope. In each case the plasmoid can be ejected to large distances (several radii) in a stellar atmosphere, for a reasonable choice of surface parameters.
Stability Analysis of the Viscous Polytropic Dark Energy Model in Einstein Cosmology
NASA Astrophysics Data System (ADS)
Wang, Yue-Yi; Chen, Ju-Hua; Wang, Yong-Jiu
2016-10-01
Not Available Supported by the National Natural Science Foundation of China under Grant No 10873004, the State Key Development Program for Basic Research Program of China under Grant No 2010CB832803, and the Program for Changjiang Scholars and Innovative Research Team in University under Grant No IRT0964.
NASA Astrophysics Data System (ADS)
Witzke, V.; Silvers, L. J.; Favier, B.
2016-08-01
Shear flows are ubiquitous in astrophysical objects including planetary and stellar interiors, where their dynamics can have significant impact on thermo-chemical processes. Investigating the complex dynamics of shear flows requires numerical calculations that provide a long time evolution of the system. To achieve a sufficiently long lifetime in a local numerical model the system has to be forced externally. However, at present, there exist several different forcing methods to sustain large-scale shear flows in local models. In this paper we examine and compare various methods used in the literature in order to resolve their respective applicability and limitations. These techniques are compared during the exponential growth phase of a shear flow instability, such as the Kelvin-Helmholtz (KH) instability, and some are examined during the subsequent non-linear evolution. A linear stability analysis provides reference for the growth rate of the most unstable modes in the system and a detailed analysis of the energetics provides a comprehensive understanding of the energy exchange during the system's evolution. Finally, we discuss the pros and cons of each forcing method and their relation with natural mechanisms generating shear flows.
Existence results for viscous polytropic fluids with degenerate viscosity coefficients and vacuum
NASA Astrophysics Data System (ADS)
Zhu, Shengguo
2015-07-01
In this paper, we considered the isentropic Navier-Stokes equations for compressible fluids with density-dependent viscosities in R3. These systems come from the Boltzmann equations through the Chapman-Enskog expansion to the second order, cf. [17], and are degenerate when vacuum appears. We firstly establish the existence of the unique local regular solution (see Definition 1.1 or [11]) when the initial data are arbitrarily large with vacuum at least appearing in the far field. Moreover it is interesting to show that we couldn't obtain any global regular solution satisfying that the L∞ norm of u decays to zero as time t goes to infinity.
NASA Astrophysics Data System (ADS)
Witzke, V.; Silvers, L. J.; Favier, B.
2016-11-01
Shear flows are ubiquitous in astrophysical objects including planetary and stellar interiors, where their dynamics can have significant impact on thermochemical processes. Investigating the complex dynamics of shear flows requires numerical calculations that provide a long-time evolution of the system. To achieve a sufficiently long lifetime in a local numerical model, the system has to be forced externally. However, at present, there exist several different forcing methods to sustain large-scale shear flows in local models. In this paper, we examine and compare various methods used in the literature in order to resolve their respective applicability and limitations. These techniques are compared during the exponential growth phase of a shear flow instability, such as the Kelvin-Helmholtz (KH) instability, and some are examined during the subsequent non-linear evolution. A linear stability analysis provides reference for the growth rate of the most unstable modes in the system and a detailed analysis of the energetics provides a comprehensive understanding of the energy exchange during the system's evolution. Finally, we discuss the pros and cons of each forcing method and their relation with natural mechanisms generating shear flows.