Self-similar polytropic champagne flows in HII regions
NASA Astrophysics Data System (ADS)
Hu, Ren-Yu; Lou, Yu-Qing
2008-11-01
We explore large-scale hydrodynamics of HII regions for various self-similar shock flows of a polytropic gas cloud under self-gravity and with quasi-spherical symmetry. We formulate cloud dynamics by invoking specific entropy conservation along streamlines and obtain global self-similar `champagne flows' for a conventional polytropic gas with shocks as a subclass. Molecular cloud cores are ionized and heated to high temperatures after the onset of nuclear burning of a central protostar. We model subsequent evolutionary processes in several ways and construct possible self-similar shock flow solutions. We may neglect the mass and gravity of the central protostar. The ionization and heating of the surrounding medium drive outflows in the inner cloud core and a shock travels outwards, leading to the so-called `champagne phase' with an expanding outer cloud envelope. Complementarily, we also consider the expansion of a central cavity around the centre. As the inner cloud expands plausibly due to powerful stellar winds, a cavity (i.e. `void' or `bubble') can be created around the centre, and when the cavity becomes sufficiently large, one may neglect the gravity of the central protostar. We thus present self-similar shock solutions for `champagne flows' with an expanding central void. We compare our solutions with isothermal solutions and find that the generalization to the polytropic regime brings about significant differences of the gas dynamics, especially for cases of n < 1, where n is a key scaling index in the self-similar transformation. We also compare our global polytropic self-similar solutions with numerical simulations on the expansion of HII regions. We further explore other possible dynamic evolutions of HII regions after the initiation of nuclear burning of the central protostar, for example asymptotic inflows or contractions far from the cloud centre and the ongoing infall around a central protostar. In particular, it is possible to use the downstream
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 Astrophysics Data System (ADS)
Lai, Zheng-Xuan
This research proposes Self Similar optical fiber (SSF) as a new type of optical fiber. It has a special core that consists of self similar structure. Such a structure is obtained by following the formula for generating iterated function systems (IFS) in Fractal Theory. The resulted SSF can be viewed as a true fractal object in optical fibers. In addition, the method of fabricating SSF makes it possible to generate desired structures exponentially in numbers, whereas it also allows lower scale units in the structure to be reduced in size exponentially. The invention of SSF is expected to greatly ease the production of optical fiber when a large number of small hollow structures are needed in the core of the optical fiber. This dissertation will analyze the core structure of SSF based on fractal theory. Possible properties from the structural characteristics and the corresponding applications are explained. Four SSF samples were obtained through actual fabrication in a laboratory environment. Different from traditional conductive heating fabrication system, I used an in-house designed furnace that incorporated a radiation heating method, and was equipped with automated temperature control system. The obtained samples were examined through spectrum tests. Results from the tests showed that SSF does have the optical property of delivering light in a certain wavelength range. However, SSF as a new type of optical fiber requires a systematic research to find out the theory that explains its structure and the associated optical properties. The fabrication and quality of SSF also needs to be improved for product deployment. As a start of this extensive research, this dissertation work opens the door to a very promising new area in optical fiber research.
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 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 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
Self-similar mitochondrial DNA.
Oiwa, Nestor N; Glazier, James A
2004-01-01
We show that repeated sequences, like palindromes (local repetitions) and homologies between two different nucleotide sequences (motifs along the genome), compose a self-similar (fractal) pattern in mitochondrial DNA. This self-similarity comes from the looplike structures distributed along the genome. The looplike structures generate scaling laws in a pseudorandom DNA walk constructed from the sequence, called a Lévy flight. We measure the scaling laws from the generalized fractal dimension and singularity spectrum for mitochondrial DNA walks for 35 different species. In particular, we report characteristic loop distributions for mammal mitochondrial genomes. PMID:15371639
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…
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.
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.
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.
On self-similarity of crack layer
NASA Technical Reports Server (NTRS)
Botsis, J.; Kunin, B.
1987-01-01
The crack layer (CL) theory of Chudnovsky (1986), based on principles of thermodynamics of irreversible processes, employs a crucial hypothesis of self-similarity. The self-similarity hypothesis states that the value of the damage density at a point x of the active zone at a time t coincides with that at the corresponding point in the initial (t = 0) configuration of the active zone, the correspondence being given by a time-dependent affine transformation of the space variables. In this paper, the implications of the self-similarity hypothesis for qusi-static CL propagation is investigated using polystyrene as a model material and examining the evolution of damage distribution along the trailing edge which is approximated by a straight segment perpendicular to the crack path. The results support the self-similarity hypothesis adopted by the CL theory.
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.
Self-similarity in active colloid motion
NASA Astrophysics Data System (ADS)
Constant, Colin; Sukhov, Sergey; Dogariu, Aristide
The self-similarity of displacements among randomly evolving systems has been used to describe the foraging patterns of animals and predict the growth of financial systems. At micron scales, the motion of colloidal particles can be analyzed by sampling their spatial displacement in time. For self-similar systems in equilibrium, the mean squared displacement increases linearly in time. However, external forces can take the system out of equilibrium, creating active colloidal systems, and making this evolution more complex. A moment scaling spectrum of the distribution of particle displacements quantifies the degree of self-similarity in the colloid motion. We will demonstrate that, by varying the temporal and spatial characteristics of the external forces, one can control the degree of self-similarity in active colloid motion.
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-similar evolution of the two-dimensional cylindrical magnetohydrodynamic flux rope
NASA Astrophysics Data System (ADS)
Tsui, K. H.; Tavares, M. D.
2005-12-01
One of the important features of the one-dimensional cylindrical self-similar magnetohydrodynamic (MHD) model of magnetic rope is that it oscillates about a force-free solution [Osherovich et al., 1993. Nonlinear evolution of magnetic flux ropes. 1. Low-beta limit. Journal of Geophysical Research 98, 13225 13231; Osherovich et al., 1995. Nonlinear evolution of magnetic flux ropes. 2. Finite-beta plasma. Journal of Geophysical Research 100, 12307-12318.] due to the reduced dimensionality of the system, as in laboratory Z pinch plasmas [Felber, 1982. Self-similar oscillations of a Z pinch. Physics of Fluids 25, 643 645]. However, such oscillations have never been confirmed by observations. Following the approach of Low [1982a. Self-similar magnetohydrodynamics. I. The γ=4/3 Polytrope and the Coronal transient. Astrophysical Journal 254, 796 805; 1982b. Self-similar magnetohydrodynamics. II. The expansion of a Stella envelope into a surrounding vacuum. Astrophysical Journal 261, 351 369], a two-dimensional self-similar MHD model under radial expansion is analyzed in cylindrical geometry with translational symmetry in the z-axis. Non-oscillatory solutions are established with polytropic index γ=1 and 2. For γ=2, the system is linear, and the plasma pressure is balanced by the longitudinal magnetic pressure. As for γ=1, the plasma pressure is balanced by the transverse magnetic pressure, and it is also the driving force of non-linearity that stresses the system. Due to the two-dimensional structure of the magnetic field and plasma, this model allows the possibility of an energetic magnetic cloud with a southward component impinging on Earth without raising expected magnetic storms.
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.
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 relativistic disks with pressure
NASA Astrophysics Data System (ADS)
Lemos, Jose P. S.
1989-09-01
Solutions for disks in equilibrium specified by a constant velocity of rotation and constant velocity dispersions are found. The fluid is not perfect because the stress tensor is anisotropic. These disks are self-similar if they are of infinite extent. The solutions are exact when an equal number of particles move in each sense of rotation so that there is no dragging of the inertial frames. For disks rotating with a small velocity a WKB approximation is used to obtain solutions.
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.
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.
Self-similar evolution of magnetized plasmas. I - Quasi-static solution
NASA Technical Reports Server (NTRS)
Yang, Wei-Hong
1992-01-01
The concept of linear expansion suggested by Wei-Hong (1989 and 1990), describes the self-similar evolution of a magnetic structure. Linear expansion can be represented by a single function which connects the evolving physical parameters of the plasma with their initial values in explicit forms. A general self-similar dynamic equation, therefore, is derived. As the first step toward more general consideration, the quasi-static solution is investigated in this paper. It is shown that a gamma = 4/3 polytrope may evolve through consecutive equilibria if its magnetic field expands self-similarly. The change of the energy everywhere inside the plasma equals the work done by the internal plasma pressure and magnetic field for the expansion. For the special case of an expanding force-free magnetic field, the self-similar expansion is a clean expansion. No free magnetic energy is left anywhere inside the magnetic structure. The approximation in quasi-state modeling of a pressure confined magnetized plasmoid is analyzed.
Bayesian estimation of self-similarity exponent
NASA Astrophysics Data System (ADS)
Makarava, Natallia; Benmehdi, Sabah; Holschneider, Matthias
2011-08-01
In this study we propose a Bayesian approach to the estimation of the Hurst exponent in terms of linear mixed models. Even for unevenly sampled signals and signals with gaps, our method is applicable. We test our method by using artificial fractional Brownian motion of different length and compare it with the detrended fluctuation analysis technique. The estimation of the Hurst exponent of a Rosenblatt process is shown as an example of an H-self-similar process with non-Gaussian dimensional distribution. Additionally, we perform an analysis with real data, the Dow-Jones Industrial Average closing values, and analyze its temporal variation of the Hurst exponent.
Bayesian estimation of self-similarity exponent.
Makarava, Natallia; Benmehdi, Sabah; Holschneider, Matthias
2011-08-01
In this study we propose a bayesian approach to the estimation of the Hurst exponent in terms of linear mixed models. Even for unevenly sampled signals and signals with gaps, our method is applicable. We test our method by using artificial fractional brownian motion of different length and compare it with the detrended fluctuation analysis technique. The estimation of the Hurst exponent of a Rosenblatt process is shown as an example of an H-self-similar process with non-gaussian dimensional distribution. Additionally, we perform an analysis with real data, the Dow-Jones Industrial Average closing values, and analyze its temporal variation of the Hurst exponent. PMID:21928951
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
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.
Media segmentation using self-similarity decomposition
NASA Astrophysics Data System (ADS)
Foote, Jonathan T.; Cooper, Matthew L.
2003-01-01
We present a framework for analyzing the structure of digital media streams. Though our methods work for video, text, and audio, we concentrate on detecting the structure of digital music files. In the first step, spectral data is used to construct a similarity matrix calculated from inter-frame spectral similarity.The digital audio can be robustly segmented by correlating a kernel along the diagonal of the similarity matrix. Once segmented, spectral statistics of each segment are computed. In the second step,segments are clustered based on the self-similarity of their statistics. This reveals the structure of the digital music in a set of segment boundaries and labels. Finally, the music is summarized by selecting clusters with repeated segments throughout the piece. The summaries can be customized for various applications based on the structure of the original music.
Gait Recognition Using Image Self-Similarity
NASA Astrophysics Data System (ADS)
BenAbdelkader, Chiraz; Cutler, Ross G.; Davis, Larry S.
2004-12-01
Gait is one of the few biometrics that can be measured at a distance, and is hence useful for passive surveillance as well as biometric applications. Gait recognition research is still at its infancy, however, and we have yet to solve the fundamental issue of finding gait features which at once have sufficient discrimination power and can be extracted robustly and accurately from low-resolution video. This paper describes a novel gait recognition technique based on the image self-similarity of a walking person. We contend that the similarity plot encodes a projection of gait dynamics. It is also correspondence-free, robust to segmentation noise, and works well with low-resolution video. The method is tested on multiple data sets of varying sizes and degrees of difficulty. Performance is best for fronto-parallel viewpoints, whereby a recognition rate of 98% is achieved for a data set of 6 people, and 70% for a data set of 54 people.
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-similarity driven color demosaicking.
Buades, Antoni; Coll, Bartomeu; Morel, Jean-Michel; Sbert, Catalina
2009-06-01
Demosaicking is the process by which from a matrix of colored pixels measuring only one color component per pixel, red, green, or blue, one can infer a whole color information at each pixel. This inference requires a deep understanding of the interaction between colors, and the involvement of image local geometry. Although quite successful in making such inferences with very small relative error, state-of-the-art demosaicking methods fail when the local geometry cannot be inferred from the neighboring pixels. In such a case, which occurs when thin structures or fine periodic patterns were present in the original, state-of-the-art methods can create disturbing artifacts, known as zipper effect, blur, and color spots. The aim of this paper is to show that these artifacts can be avoided by involving the image self-similarity to infer missing colors. Detailed experiments show that a satisfactory solution can be found, even for the most critical cases. Extensive comparisons with state-of-the-art algorithms will be performed on two different classic image databases. PMID:19403366
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). PMID:20681665
Superposition of Polytropes in the Inner Heliosheath
NASA Astrophysics Data System (ADS)
Livadiotis, G.
2016-03-01
This paper presents a possible generalization of the equation of state and Bernoulli's integral when a superposition of polytropic processes applies in space and astrophysical plasmas. The theory of polytropic thermodynamic processes for a fixed polytropic index is extended for a superposition of polytropic indices. In general, the superposition may be described by any distribution of polytropic indices, but emphasis is placed on a Gaussian distribution. The polytropic density-temperature relation has been used in numerous analyses of space plasma data. This linear relation on a log-log scale is now generalized to a concave-downward parabola that is able to describe the observations better. The model of the Gaussian superposition of polytropes is successfully applied in the proton plasma of the inner heliosheath. The estimated mean polytropic index is near zero, indicating the dominance of isobaric thermodynamic processes in the sheath, similar to other previously published analyses. By computing Bernoulli's integral and applying its conservation along the equator of the inner heliosheath, the magnetic field in the inner heliosheath is estimated, B ˜ 2.29 ± 0.16 μG. The constructed normalized histogram of the values of the magnetic field is similar to that derived from a different method that uses the concept of large-scale quantization, bringing incredible insights to this novel theory.
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.
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.
Escaping the avalanche collapse in self-similar multiplexes
NASA Astrophysics Data System (ADS)
Ángeles Serrano, M.; Buzna, Ľuboš; Boguñá, Marián
2015-05-01
We deduce and discuss the implications of self-similarity for the robustness to failure of multiplexes, depending on interlayer degree correlations. First, we define self-similarity of multiplexes and we illustrate the concept in practice using the configuration model ensemble. Circumscribing robustness to survival of the mutually percolated state, we find a new explanation based on self-similarity both for the observed fragility of interconnected systems of networks and for their robustness to failure when interlayer degree correlations are present. Extending the self-similarity arguments, we show that interlayer degree correlations can change completely the global connectivity properties of self-similar multiplexes, so that they can even recover a zero percolation threshold and a continuous transition in the thermodynamic limit, qualitatively exhibiting thus the ordinary percolation properties of noninteracting networks. We confirm these results with numerical simulations.
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.
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.
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 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
Multifractal spectrum of self-similar measures with overlap
NASA Astrophysics Data System (ADS)
Bruggeman, Cameron; Hare, Kathryn E.; Mak, Cheuk Yu
2014-02-01
It is well known that the multifractal spectrum of a self-similar measure satisfying the open set condition is a closed interval. Recently, there has been interest in the overlapping case and it is known that in this case there can be isolated points. We prove that for an interesting class of self-similar measures with overlap the spectrum consists of a closed interval union together with at most two isolated points. In the case of convolutions of uniform Cantor measures we determine the end points of the interval and the isolated points. We also give an example of a related self-similar measure where the spectrum is a union of two disjoint intervals. In contrast, we prove that if one considers quotient measures of this class on the quotient group [0, 1], rather than the real line, the multifractal spectrum is a closed interval.
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
Experimental observations of self-similar plasma expansion
NASA Technical Reports Server (NTRS)
Chan, C.; Hershkowitz, N.; Ferreira, A.; Intrator, T.; Nelson, B.; Lonngren, K.
1984-01-01
The present investigation is concerned with measurements of the plasma potential profile of an expanding plasma, taking into account the demonstration of the self-similar behavior of such a plasma. The obtained experimental results are consistent with self-similar solutions reported by Crow et al. (1975). It is found that the quasi-neutrality condition breaks down early during the experiment. A consideration of the effect of charge separation is, therefore, required. Attention is given to the evolution of the potential profiles of the expanding plasma as a function of time, the accelerated ion fronts, and the sheath formation of the expanding plasma into a floating boundary.
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.
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.
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
Evaporation of droplets in a Champagne wine aerosol
NASA Astrophysics Data System (ADS)
Ghabache, Elisabeth; Liger-Belair, Gérard; Antkowiak, Arnaud; Séon, Thomas
2016-04-01
In a single glass of champagne about a million bubbles nucleate on the wall and rise towards the surface. When these bubbles reach the surface and rupture, they project a multitude of tiny droplets in the form of a particular aerosol holding a concentrate of wine aromas. Based on the model experiment of a single bubble bursting in idealized champagnes, the key features of the champagne aerosol are identified. In particular, we show that film drops, critical in sea spray for example, are here nonexistent. We then demonstrate that compared to a still wine, champagne fizz drastically enhances the transfer of liquid into the atmosphere. There, conditions on bubble radius and wine viscosity that optimize aerosol evaporation are provided. These results pave the way towards the fine tuning of flavor release during sparkling wine tasting, a major issue for the sparkling wine industry.
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.
PHOG analysis of self-similarity in aesthetic images
NASA Astrophysics Data System (ADS)
Amirshahi, Seyed Ali; Koch, Michael; Denzler, Joachim; Redies, Christoph
2012-03-01
In recent years, there have been efforts in defining the statistical properties of aesthetic photographs and artworks using computer vision techniques. However, it is still an open question how to distinguish aesthetic from non-aesthetic images with a high recognition rate. This is possibly because aesthetic perception is influenced also by a large number of cultural variables. Nevertheless, the search for statistical properties of aesthetic images has not been futile. For example, we have shown that the radially averaged power spectrum of monochrome artworks of Western and Eastern provenance falls off according to a power law with increasing spatial frequency (1/f2 characteristics). This finding implies that this particular subset of artworks possesses a Fourier power spectrum that is self-similar across different scales of spatial resolution. Other types of aesthetic images, such as cartoons, comics and mangas also display this type of self-similarity, as do photographs of complex natural scenes. Since the human visual system is adapted to encode images of natural scenes in a particular efficient way, we have argued that artists imitate these statistics in their artworks. In support of this notion, we presented results that artists portrait human faces with the self-similar Fourier statistics of complex natural scenes although real-world photographs of faces are not self-similar. In view of these previous findings, we investigated other statistical measures of self-similarity to characterize aesthetic and non-aesthetic images. In the present work, we propose a novel measure of self-similarity that is based on the Pyramid Histogram of Oriented Gradients (PHOG). For every image, we first calculate PHOG up to pyramid level 3. The similarity between the histograms of each section at a particular level is then calculated to the parent section at the previous level (or to the histogram at the ground level). The proposed approach is tested on datasets of aesthetic and
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.
Scaling and self-similarity in two-dimensional hydrodynamics.
Ercan, Ali; Kavvas, M Levent
2015-07-01
The conditions under which depth-averaged two-dimensional (2D) hydrodynamic equations system as an initial-boundary value problem (IBVP) becomes self-similar are investigated by utilizing one-parameter Lie group of point scaling transformations. Self-similarity conditions due to the 2D k-ε turbulence model are also investigated. The self-similarity conditions for the depth-averaged 2D hydrodynamics are found for the flow variables including the time, the longitudinal length, the transverse length, the water depth, the flow velocities in x- and y-directions, the bed shear stresses in x- and y-directions, the bed shear velocity, the Manning's roughness coefficient, the kinematic viscosity of the fluid, the eddy viscosity, the turbulent kinetic energy, the turbulent dissipation, and the production and the source terms in the k-ε model. By the numerical simulations, it is shown that the IBVP of depth-averaged 2D hydrodynamic flow process in a prototype domain can be self-similar with that of a scaled domain. In fact, by changing the scaling parameter and the scaling exponents of the length dimensions, one can obtain several different scaled domains. The proposed scaling relations obtained by the Lie group scaling approach may provide additional spatial, temporal, and economical flexibility in setting up physical hydraulic models in which two-dimensional flow components are important. PMID:26232977
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
Rotational properties of composite polytrope models
Rucinski, S.M.
1988-06-01
Factional radii of gyration for both the convective envelope and the radiative core have been determined using the composite-polytrope model of Rappaport et al. (1983) which describes low-mass stars by appropriately matched polytropes n(outer) = 3/2 and n(inner) = 3. Radii of gyration computed for ZAMS stars with masses of 0.4-1.2 solar masses are used to obtain ZAMS angular momenta for low-mass rapidly rotating stars in the Pleiades and Alpha Persei clusters. Results indicate that there is little chance of observing single young early G and late F type stars in rapid rotation because of the very short timescales for braking of their thin convective envelopes. 41 references.
Utilization Of Spatial Self-Similarity In Medical Image Processing
NASA Astrophysics Data System (ADS)
Kuklinski, Walter S.
1987-01-01
Many current medical image processing algorithms utilize Fourier Transform techniques that represent images as sums of translationally invariant complex exponential basis functions. Selective removal or enhancement of these translationally invariant components can be used to effect a number of image processing operations such as edge enhancement or noise attenuation. An important characteristic of many natural phenomena, including the structures of interest in medical imaging is spatial self-similarity. In this work a filtering technique that represents images as sums of scale invariant self-similar basis functions will be presented. The decomposition of a signal or image into scale invariant components can be accomplished using the Mellin Transform, which diagonalizes changes of scale in a manner analogous to the way the Fourier Transform diagonalizes translation.
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.
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.
Dynamics and processing in finite self-similar networks
DeDeo, Simon; Krakauer, David C.
2012-01-01
A common feature of biological networks is the geometrical property of self-similarity. Molecular regulatory networks through to circulatory systems, nervous systems, social systems and ecological trophic networks show self-similar connectivity at multiple scales. We analyse the relationship between topology and signalling in contrasting classes of such topologies. We find that networks differ in their ability to contain or propagate signals between arbitrary nodes in a network depending on whether they possess branching or loop-like features. Networks also differ in how they respond to noise, such that one allows for greater integration at high noise, and this performance is reversed at low noise. Surprisingly, small-world topologies, with diameters logarithmic in system size, have slower dynamical time scales, and may be less integrated (more modular) than networks with longer path lengths. All of these phenomena are essentially mesoscopic, vanishing in the infinite limit but producing strong effects at sizes and time scales relevant to biology. PMID:22378750
Ordered Self-Similar Patterns in Anisotropic Stochastic Growth.
Yao, Zhenwei; Olvera de la Cruz, Monica
2016-07-01
We propose an anisotropic stochastic growth model to rationalize the anisotropic self-assembly of supramolecules to form elongated two-dimensional ribbon structures in a recent experiment. The model exhibits distinct growth scenarios that are critically controlled by the ratio of the transverse and the longitudinal growth rate. In the regime of suppressed transverse growth, the model generates the experimentally observed elongated structures through layer-by-layer growing. We further observe the convergence of rough clusters toward smooth regular elliptic patterns by averaging over a number of independent growth processes. Remarkably, these resulting elliptic clusters are self-similar in each instantaneous moment in the growth process. Statistical analysis suggests that the realization of such ordered patterns does not rely on the delicate coordination of different parts in the cluster growth. The self-similarity phenomenon derived from this idealized model may have wider implications, notably in the designed clustering of various elementary building blocks with anisotropic interactions. PMID:27003104
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.
Hydrodynamic instabilities in supernova remnants - Self-similar driven waves
NASA Technical Reports Server (NTRS)
Chevalier, Roger A.; Blondin, John M.; Emmering, Robert T.
1992-01-01
An initial study aimed at elucidating the multidimensional aspects of the hydrodynamic instabilities in supernova remnants is presented. Self-similar solutions are found to exist for the interaction of a steep power-law density profile expanding into a relatively flat stationary power-law density profile. Consideration of the pressure and entropy profiles in the shocked 1D flows shows that the flows are subject to convective instability, by a local criterion. The growth rate for the instability becomes very large near the contact discontinuity between the two shocked regions. A linear analysis of the complete self-similar solutions shows that the solutions are unstable above a critical wavenumber and that the growth rate is greatest at the position of the contact discontinuity. The X-ray image of the remnant of SN 1572 (Tycho) shows emission from clumps of supernova ejecta, which is good evidence for instabilities in this remnant.
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.
Road shape recognition based on scene self-similarity
NASA Astrophysics Data System (ADS)
Postnikov, Vassili V.; Krohina, Darya A.; Prun, Victor E.
2015-02-01
A method of determining of the road shape and direction is proposed. The road can potentially have curved shape as well as be seen unclearly due to weather effects or relief features. The proposed method uses video taken from frontal camera that is rigidly placed in car as an input data. The method is based on self-similarity of typical road image, i.e. the smaller image inside the road is close to downscaled initial image.
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.
A nonlinear eigenvalue problem for self-similar spherical force-free magnetic fields
NASA Astrophysics Data System (ADS)
Lerche, I.; Low, B. C.
2014-10-01
An axisymmetric force-free magnetic field B(r, θ) in spherical coordinates is defined by a function r sin θ B φ = Q ( A ) relating its azimuthal component to its poloidal flux-function A. The power law r sin θ B φ = a A | A | 1/ n, n a positive constant, admits separable fields with A = An/(θ)rn, posing a nonlinear boundary-value problem for the constant parameter a as an eigenvalue and An(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)rn+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 discussed in the Appendix.
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
Self similarity in a model of genetic microevolution
NASA Astrophysics Data System (ADS)
Strier, Damián E.; Zanette, Damián H.
A mathematical model of genetic microevolution is presented. The model stands for a population of genotypes evolving in the genotypic space. Its dynamics is governed by a master evolution equation which takes into account both the presence of a fluctuating fitness landscape and genotypic variations of the offspring with respect to the parents. We found that, under rather general conditions, the population growth rate exhibits self-similarity. This result provides a clue to universal scaling features of evolution in the large-time scale, as observed from paleobiological evidence.
Self-similarity of wind-driven seas
NASA Astrophysics Data System (ADS)
Badulin, S. I.; Pushkarev, A. N.; Resio, D.; Zakharov, V. E.
2005-11-01
The results of theoretical and numerical study of the Hasselmann kinetic equation for deep water waves in presence of wind input and dissipation are presented. The guideline of the study: nonlinear transfer is the dominating mechanism of wind-wave evolution. In other words, the most important features of wind-driven sea could be understood in a framework of conservative Hasselmann equation while forcing and dissipation determine parameters of a solution of the conservative equation. The conservative Hasselmann equation has a rich family of self-similar solutions for duration-limited and fetch-limited wind-wave growth. These solutions are closely related to classic stationary and homogeneous weak-turbulent Kolmogorov spectra and can be considered as non-stationary and non-homogeneous generalizations of these spectra. It is shown that experimental parameterizations of wind-wave spectra (e.g. JONSWAP spectrum) that imply self-similarity give a solid basis for comparison with theoretical predictions. In particular, the self-similarity analysis predicts correctly the dependence of mean wave energy and mean frequency on wave age Cp / U10. This comparison is detailed in the extensive numerical study of duration-limited growth of wind waves. The study is based on algorithm suggested by Webb (1978) that was first realized as an operating code by Resio and Perrie (1989, 1991). This code is now updated: the new version is up to one order faster than the previous one. The new stable and reliable code makes possible to perform massive numerical simulation of the Hasselmann equation with different models of wind input and dissipation. As a result, a strong tendency of numerical solutions to self-similar behavior is shown for rather wide range of wave generation and dissipation conditions. We found very good quantitative coincidence of these solutions with available results on duration-limited growth, as well as with experimental parametrization of fetch-limited spectra JONSWAP
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.
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.
Exactly self-similar left-sided multifractal measures
NASA Astrophysics Data System (ADS)
Mandelbrot, Benoit B.; Evertsz, Carl J. G.; Hayakawa, Yoshinori
1990-10-01
We introduce and investigate a family of exactly self-similar nonrandom fractal measures, each having stretched exponentially decreasing minimum probabilities. This implies that τ(q) is not defined for q<0 and that qbottom=0 is a critical value of q. Since the partition function does not scale for all values of q, these measures are not multifractals in the restricted sense due to Frisch and Parisi [in 2 Turbulence and Predictability of Geophysical Flows and Climate Dynamics, Proceedings of the Enrico Fermi International School of Physics, edited by M. Ghil, R. Benzi, and G. Parisi (North-Holland, New York, 1985), p. 84] and to Halsey et al. [Phys. Rev. A 33, 1141 (1986)]. However, they are exactly self-similar, hence are multifractals in a much earlier and more general meaning of this notion [B. Mandelbrot, J. Fluid Mech. 62, 331 (1974)]. We show that in these measures the ``free energy'' τ(q) is singular at q=qbottom, in the sense that τ(q)=-1+cλqλ+c1q+c2q2+O(q3), where 0<λ is a ``critical'' exponent. For λ<=1, the transition in the f(α) is smooth (i.e., of infinite order), while for λ>1, the transition order is >=2. We then use a new sampling method to study problems arising in the study of such transitions in case of undersampling.
Direct simulation of a self-similar plane wake
NASA Technical Reports Server (NTRS)
Moser, Robert D.; Rogers, Michael M.
1994-01-01
Direct simulations of two time-developing turbulent wakes have been performed. Initial conditions for the simulations were obtained from two realizations of a direct simulation of a turbulent boundary layer at momentum thickness Reynolds number 670. In addition, extra two dimensional disturbances were added in one of the cases to mimic two dimensional forcing. The unforced wake is allowed to evolve long enough to attain self similarity. The mass-flux Reynolds number (equivalent to the momentum thickness Reynolds number in spatially developing wakes) is 2000, which is high enough for a short k(exp -5/3) range to be evident in the streamwise one dimensional velocity spectrum. Several turbulence statistics have been computed by averaging in space and over the self-similar period in time. The growth rate in the unforced flow is low compared to experiments, but when this growth-rate difference is accounted for, the statistics of the unforced case are in reasonable agreement with experiments. However, the forced case is significantly different. The growth rate, turbulence Reynolds number, and turbulence intensities are as much as ten times larger in the forced case. In addition, the forced flow exhibits large-scale structures similar to those observed in transitional wakes, while the unforced flow does not.
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 SOLUTIONS OF TRIAXIAL DARK MATTER HALOS
Lithwick, Yoram; Dalal, Neal
2011-06-20
We investigate the collapse and the internal structure of dark matter halos. We consider halo formation from initially scale-free perturbations, for which gravitational collapse is self-similar. Fillmore and Goldreich and Bertschinger solved the one-dimensional (i.e., spherically symmetric) case. We generalize their results by formulating the three-dimensional self-similar equations. We solve the equations numerically and analyze the similarity solutions in detail, focusing on the internal density profiles of the collapsed halos. By decomposing the total density into subprofiles of particles that collapse coevally, we identify two effects as the main determinants of the internal density structure of halos: adiabatic contraction and the shape of a subprofile shortly after collapse; the latter largely reflects the triaxiality of the subprofile. We develop a simple model that describes the results of our three-dimensional simulations. In a companion paper, we apply this model to more realistic cosmological fluctuations, and thereby explain the origin of the nearly universal (NFW-like) density profiles found in N-body simulations.
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 motion of three point vortices
NASA Astrophysics Data System (ADS)
Aref, Hassan
2010-05-01
One of the counter-intuitive results in the three-vortex problem is that the vortices can converge on and meet at a point in a finite time for certain sets of vortex circulations and for certain initial conditions. This result was already included in Gröbli's thesis of 1877 and has since been elaborated by several authors. It arises from an investigation of motions where the vortex triangle retains its shape for all time, but not its size. We revisit these self-similar motions, develop a new derivation of the initial conditions that lead to them, and derive a number of formulae pertaining to the rate of expansion or collapse and the angular frequency of rotation, some of which appear to be new. We also pursue the problem of linear stability of these motions in detail and, again, provide a number of formulae, some of which are new. In particular, we determine all eigenmodes analytically.
Self-similarity of the "1/f noise" called music.
Hsü, K J; Hsü, A
1991-04-15
Suggestions have been made that computer musicians should attempt to compose fractal music, and questions have been raised whether there is such a thing as fractal music. Voss and Clark observed that music is scaling, or 1/f noise, as analyzed on the basis of the amplitude (loudness) of the audio signals; they failed to find a fractal distribution of acoustic frequencies (music notes) in music. Analyzing Bach's and Mozart's compositions, we have shown that the incidence of the frequency intervals, or of the changes of acoustic frequency, has a fractal geometry. Fractal phenomena are characterized by scale-independency. The purpose of this investigation is to demonstrate the self-similarity of music and to explore its implications. PMID:11607178
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.
Coarsening foams robustly reach a self-similar growth regime.
Lambert, Jérôme; Mokso, Rajmund; Cantat, Isabelle; Cloetens, Peter; Glazier, James A; Graner, François; Delannay, Renaud
2010-06-18
Dry liquid foams coarsen like other diphasic systems governed by interfacial energy: gas slowly diffuses across liquid films, resulting in large bubbles growing at the expense of smaller ones which eventually shrink and disappear. A foam scatters light very effectively, preventing direct optical observation of bubble sizes and shapes in large foams. Using high speed x-ray tomography, we have produced 4D movies (i.e., 3D + time) of up to 30,000 bubbles. After a transient regime, the successive images look alike, except that the average bubble size increases as the square root of time: This scaling state is the long sought self-similar growth regime. The bubble size and face-number distributions in this regime are compared with experimental distributions for grains in crystals and with numerical simulations of foams. PMID:20867343
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-similarity and scaling in forest communities
Simini, Filippo; Anfodillo, Tommaso; Carrer, Marco; Banavar, Jayanth R.; Maritan, Amos
2010-01-01
Ecological communities exhibit pervasive patterns and interrelationships between size, abundance, and the availability of resources. We use scaling ideas to develop a unified, model-independent framework for understanding the distribution of tree sizes, their energy use, and spatial distribution in tropical forests. We demonstrate that the scaling of the tree crown at the individual level drives the forest structure when resources are fully used. Our predictions match perfectly with the scaling behavior of an exactly solvable self-similar model of a forest and are in good accord with empirical data. The range, over which pure power law behavior is observed, depends on the available amount of resources. The scaling framework can be used for assessing the effects of natural and anthropogenic disturbances on ecosystem structure and functionality. PMID:20375286
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 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.
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
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.
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
A variable polytrope index applied to planet and material models
NASA Astrophysics Data System (ADS)
Weppner, S. P.; McKelvey, J. P.; Thielen, K. D.; Zielinski, A. K.
2015-09-01
We introduce a new approach to a century-old assumption which enhances not only planetary interior calculations but also high-pressure material physics. We show that the polytropic index is the derivative of the bulk modulus with respect to pressure. We then augment the traditional polytrope theory by including a variable polytrope index within the confines of the Lane-Emden differential equation. To investigate the possibilities of this method, we create a high-quality universal equation of state, transforming the traditional polytrope method to a tool with the potential for excellent predictive power. The theoretical foundation of our equation of state is the same elastic observable which we found equivalent to the polytrope index, the derivative of the bulk modulus with respect to pressure. We calculate the density-pressure of six common materials up to 1018 Pa, mass-radius relationships for the same materials, and produce plausible density-radius models for the rocky planets of our Solar system. We argue that the bulk modulus and its derivatives have been underutilized in previous planet formation methods. We constrain the material surface observables for the inner core, outer core, and mantle of planet Earth in a systematic way including pressure, bulk modulus, and the polytrope index in the analysis. We believe that this variable polytrope method has the necessary apparatus to be extended further to gas giants and stars. As supplemental material we provide computer code to calculate multi-layered planets.
A variable polytrope index applied to planet and material models
NASA Astrophysics Data System (ADS)
Thielen, Kevin; Weppner, Stephen; Zielinski, Alexander
2016-01-01
We introduce a new approach to a century-old assumption which enhances not only planetary interior calculations but also high-pressure material physics. We show that the polytropic index is the derivative of the bulk modulus with respect to pressure. We then augment the traditional polytrope theory by including a variable polytrope index within the confines of the Lane-Emden differential equation. To investigate the possibilities of this method, we create a high-quality universal equation of state, transforming the traditional polytrope method to a tool with the potential for excellent predictive power. The theoretical foundation of our equation of state is the same elastic observable which we found equivalent to the polytrope index, the derivative of the bulk modulus with respect to pressure. We calculate the density-pressure of six common materials up to 1018 Pa, mass-radius relationships for the same materials, and produce plausible density-radius models for the rocky planets of our Solar system. We argue that the bulk modulus and its derivatives have been underutilized in previous planet formation methods. We constrain the material surface observables for the inner core, outer core, and mantle of planet Earth in a systematic way including pressure, bulk modulus, and the polytrope index in the analysis. We believe that this variable polytrope method has the necessary apparatus to be extended further to gas giants and stars. As supplemental material we provide computer code to calculate multi-layered planets.
Stationary spiral flow in polytropic stellar models
Pekeris, C.L.
1980-06-01
It is shown that, in addition to the static Emden solution, a self-gravitating polytropic gas has a dynamic option in which there is stationary flow along spiral trajectories wound around the surfaces of concentric tori. The motion is obtained as a solution of a partial differential equation which is satisfied by the meridional stream function, coupled with Poisson's equation and a Bernoulli-type equation for the pressure (density). The pressure is affected by the whole of the Bernoulli term rather than by the centrifugal part only, which acts for a rotating model, and it may be reduced down to zero at the center. The spiral type of flow is illustrated for an incompressible fluid (n = 0), for which an exact solution is obtained. The features of the dynamic constant-density model are discussed as a basis for future comparison with the solution for compressible models.
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.
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. PMID:26135447
Log-periodic self-similarity: an emerging financial law?
NASA Astrophysics Data System (ADS)
Drożdż, S.; Grümmer, F.; Ruf, F.; Speth, J.
2003-06-01
A hypothesis that the financial log-periodicity, cascading self-similarly through various time scales, carries signatures of a law is pursued. It is shown that the most significant historical financial events can be classified amazingly well using a single and unique value of the preferred scaling factor λ=2, which indicates that its real value should be close to this number. This applies even to a declining decelerating log-periodic phase. Crucial in this connection is identification of a “super-bubble” (bubble on bubble) phenomenon. Identifying a potential “universal” preferred scaling factor, as undertaken here, may significantly improve the predictive power of the corresponding methodology. Several more specific related results include evidence that: the real end of the high technology bubble on the stock market started (with a decelerating log-periodic draw down) in the beginning of September 2000; a parallel 2000-2002 decline seen in the Standard & Poor's 500 from the log-periodic perspective is already of the same significance as the one of the early 1930s and of the late 1970s; all this points to a much more serious global crash in around 2025, of course from a level much higher (at least one order of magnitude) than in 2000.
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.
Dyslexic and skilled reading dynamics are self-similar.
Holden, John G; Greijn, Lieke T; van Rooij, Marieke M J W; Wijnants, Maarten L; Bosman, Anna M T
2014-10-01
The shape of a word pronunciation time distribution supplies information about the dynamic interactions that support reading performance. Speeded word-naming pronunciation and response time distributions were collected from 20 sixth grade Dutch students with dyslexia and 23 age-matched controls. The participants' pronunciation times were modeled and contrasted with a lognormal inverse power-law mixture distribution. Identical contrasts were also conducted on the same participants' response time distributions derived from flanker, color-naming, and arithmetic tasks. Results indicated that children with dyslexia yield slower, broader, and more variable pronunciation time distributions than their age-matched counterparts. This difference approximated a self-similar rescaling between the two group's aggregate pronunciation time distributions. Moreover, children with dyslexia produced similar, but less prominent trends toward slower and more variable performance across the three non-reading tasks. The outcomes support a proportional continuum rather than a localized deficit account of dyslexia. The mixture distribution's success at describing the participants' pronunciation and response time distributions suggests that differences in proportional contingencies among low-level neurophysiological, perceptual, and cognitive processes likely play a prominent role in the etiology of dyslexia. PMID:25079036
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.
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.
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 axi-symmetric, 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.
A self-similar solution for thermal disc winds
NASA Astrophysics Data System (ADS)
Clarke, C. J.; Alexander, R. D.
2016-05-01
We derive a self-similar description for the 2D streamline topology and flow structure of an axi-symmetric, 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.
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.
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, $1/2\\le n\\le5$.
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.
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.
Modeling the Losses of Dissolved CO2 from Laser-Etched Champagne Glasses.
Liger-Belair, Gérard
2016-04-21
Under standard champagne tasting conditions, the complex interplay between the level of dissolved CO2 found in champagne, its temperature, the glass shape, and the bubbling rate definitely impacts champagne tasting by modifying the neuro-physicochemical mechanisms responsible for aroma release and flavor perception. On the basis of theoretical principles combining heterogeneous bubble nucleation, ascending bubble dynamics, and mass transfer equations, a global model is proposed, depending on various parameters of both the wine and the glass itself, which quantitatively provides the progressive losses of dissolved CO2 from laser-etched champagne glasses. The question of champagne temperature was closely examined, and its role on the modeled losses of dissolved CO2 was corroborated by a set of experimental data. PMID:27031022
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. PMID:19215133
Analytical solutions of the Rayleigh equation for arbitrary polytropic exponent
NASA Astrophysics Data System (ADS)
Kudryashov, Nikolay A.; Sinelshchikov, Dmitry I.
2016-06-01
The Rayleigh equation for the description of spherical gas-filled bubbles dynamics is considered. It is shown that this equation can be transformed into an equation for the elliptic function for arbitrary values of the polytropic exponent. General analytical solutions of the Rayleigh equation are studied for some particular cases, such as the isothermal case.
A varying polytropic gas universe and phase space analysis
NASA Astrophysics Data System (ADS)
Khurshudyan, M.
2016-05-01
In this paper, we will consider a phenomenological model of a dark fluid that is able to explain an accelerated expansion of our low redshift universe and the phase transition to this accelerated expanding universe. Recent developments in modern cosmology towards understanding of the accelerated expansion of the large scale universe involve various scenarios and approaches. Among these approaches, one of well-known and accepted practice is modeling of the content of our universe via dark fluid. There are various models of dark energy fluid actively studied in recent literature and polytropic gas is among them. In this work, we will consider a varying polytropic gas which is a phenomenological modification of polytropic gas. Our model of varying polytropic dark fluid has been constructed to analogue to a varying Chaplygin gas actively discussed in the literature. We will consider interacting models, where dark matter is a pressureless fluid, to have a comprehensive picture. Phase space analysis is an elegant mathematical tool to earn general understanding of large scale universe and easily see an existence of a solution to cosmological coincidence problem. Imposing some constraints on parameters of the models, we found late time attractors for each case analytically. Cosmological consequences for the obtained late time attractors are discussed.
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.
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. PMID:26496377
Study on a self-similar traffic shaping mechanism with QoS in transport networks
NASA Astrophysics Data System (ADS)
Bo, Mingxia; Lee, Peiyuan; Pan, Xiaofei; Gu, Wanyi
2005-11-01
Due to easy realization and high bandwidth utilization, SDH/WDM technology becomes the important way to carry IP traffic over the backbone network. On the other hand, the feature of the data traffic which is much different from the voice traffic is dynamic, burst and self-similar, and many proofs show that the self-similar traffic can lead to some adverse effects on the network performance due to the property of long-range dependence (LRD). For this reason it is widely recognized that self-similarity of the traffic is a significant problem as far as network engineering is concerned. So any reduction in the degree of self-similarity will be greatly beneficial. One possible strategy for mitigating the deleterious effects of the self-similarity is to reduce the burstiness of the input traffic through traffic shaping function at the edge nodes. According to this scheme, in this paper, we present a new self-similar traffic shaping mechanism with QoS in transport networks, called double threshold algorithm (DTA). Simulation results show that the proposed mechanism can effectively reduce the degree of input self-similar traffic, and performs better in the terms of network packet-loss rate and blocking probability than the non-traffic shaping schemes. At the same time it guarantees good quality of service.
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
Polytropic index of magnetosheath ions based on homogeneous MHD Bernoulli Integral
NASA Astrophysics Data System (ADS)
Pang, Xuexia; Cao, Jinbin; Ma, Yuduan
2016-03-01
This paper uses Cluster data during the period from 2001 to 2010 to study the polytropic processes of magnetosheath ions. Utilizing the method of homogeneous magnetohydrodynamic (MHD) Bernoulli integral (MBI), we first identify streamflow tubes, then use the constant of polytropic relation to guarantee that the streamflow tube experiences an unchanged polytropic process, and finally determine the polytropic index of ions in these streamflow tubes. The statistical results show that the magnetosheath is a complicated system in which the polytropic index of ions ranges from -2 to 3. The polytropic index distribution of ions is dependent on the electromagnetic energy flux perpendicular to the streamline. The median polytropic index of ions in the magnetosheath is 0.960, 0.965, and 0.974 for perpendicular electromagnetic energy ratio δE × B < 5%, δE × B < 3%, and δE × B < 1%, respectively. There are two basic polytropic processes in the magnetosheath: the dominant isothermal process and the isobaric process. When there is no exchange of electromagnetic energy between neighboring streamflow tubes, the magnetosheath ions are isothermal. However, when the perpendicular electromagnetic energy ratio increases, the isobaric polytropic process starts to emerge. The magnetosheath ion flows are highly localized because most streamflow tubes experiencing same polytropic processes last less than 60 s. Thus, the polytropic index of magnetosheath ion flows is highly variable.
Intermittency and extended self-similarity in the solar wind turbulence
NASA Technical Reports Server (NTRS)
Bruno, R.; Carbone, V.
1995-01-01
Using the satellite measurements of the velocity field in the interplanetary plasma. we present some analysis which show the presence of a self-similar intermittent state in the solar wind turbulence. We used the so called Extended Self-Similarity hypothesis, which is well visible in the solar wind turbulence, showing convincing evidences for the presence of universal anomalous scaling laws. Through the Extended Self-Similarity we are able to calculate the scaling exponents of the velocity structure functions with very small uncertainties, and we show that these scaling exponents are in very good agreement with the multifractal models describing intermittency in magnetohydrodynamic flows.
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.
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).
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).
NASA Astrophysics Data System (ADS)
Vollmer, Michael; Möllmann, Klaus-Peter
2012-09-01
We 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 as well as adiabatic cooling observed upon opening a bottle of champagne.
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}.
From bubble bursting to droplet evaporation in the context of champagne aerosols
NASA Astrophysics Data System (ADS)
Seon, Thomas; Ghabache, Elisabeth; Antkowiak, Arnaud; Liger-Belair, Gerard
2015-11-01
As champagne or sparkling wine is poured into a glass, a myriad of ascending bubbles collapse and therefore radiate a multitude of tiny droplets above the free surface into the form of very characteristic and refreshing aerosols. Because these aerosols have been found to hold the organoleptic ``essence'' of champagne they are believed to play a crucial role in the flavor release in comparison with that from a flat wine for example. Based on the model experiment of a single bubble bursting in idealized champagnes, the velocity, radius and maximum height of the first jet drop following bubble collapse have been characterized, with varying bubble size and liquid properties in the context of champagne aerosols. Using the experimental results and simple theoretical models for drop and surface evaporation, we show that bubble bursting aerosols drastically enhance the transfer of liquid in the atmosphere with respect to a flat liquid surface. Contrary to popular opinion, we exhibit that small bubbles are negative in terms of aroma release, and we underline bubble radii enabling to optimize the droplet height and evaporation in the whole range of champagne properties. These results pave the road to the fine tuning of champagne aroma diffusion, a major issue of the sparkling wine industry.
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.
Determination of the polytropic index in the plasma sheet
Baumjohann, W.; Paschmann, G.
1989-04-01
Using eight months of magnetotail plasma data, we have done a statistical survey on the relation between ion density and pressure in the Earth's plasmasheet. More than 270,000 spin averaged (4.5s) samples of ion density and thermal pressure obtained in the central plasma sheet and the plasma sheet boundary layer were cross-correlated in order to obtain typical values of the polytropic index ..gamma.. for different tail regions and disturbance conditions. The plasma sheet ion population behaves, on average, adiabatically both in the central plasma sheet and the plasma sheet boundary layer. However, a polytropic index of about 1.4 for the quiet plamsa sheet indicates that the latter behaves like a poorly insulated vessel. Hence, there seems to be no quiet time magnetotail equilibrium (''ground state''), but rather continuous cooling until new enegy is entering from the outside. copyright American Geophysical Union 1989
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.
Polytropic equation of state and primordial quantum fluctuations
NASA Astrophysics Data System (ADS)
Freitas, R. C.; Gonçalves, S. V. B.
2014-12-01
We study the primordial Universe in a cosmological model where inflation is driven by a fluid with a polytropic equation of state . We calculate the dynamics of the scalar factor and build a Universe with constant density at the origin. We also find the equivalent scalar field that could create such an equation of state and calculate the corresponding slow-roll parameters. We calculate the scalar perturbations, the scalar power spectrum, and the spectral index.
Self-similar PDFs in the inertial range of solar wind turbulence
NASA Astrophysics Data System (ADS)
Podesta, J.
2006-05-01
In solar wind turbulence, the probability distribution functions (PDFs) of time delayed velocity differences δ vj(τ)= vj(t+τ)-vj(t) and magnetic field differences δ Bj(τ)= Bj(t+τ)-Bj(t) are not self-similar, even when the time scale τ is restricted to the inertial range of the turbulence (approximately the range extending from 10 s to 104 s). An interesting study of solar wind data by Hnat, Chapman, and Rowlands [2003] suggests that even though the PDFs for the individual vector components are not self similar, the PDFs for the mass density ρ, kinetic energy density ρ v2=ρ v· v, and magnetic energy density B2=B· B, are all self-similar in the inertial range. In an attempt to confirm this claim, a similar analysis is performed using all available data from the Wind and ACE spacecraft---data acquired in the ecliptic plane near 1 AU. The analysis utilizes the largest data sets available in order to adequately resolve the tails of the probability distributions. The results of this study indicate that: (1) The first order PDF of Δ B2(τ)= B2(t+τ)-B2(t) appears to exhibit self-similar behavior in the inertial range. (2) The first order PDFs of proton density npand kinetic energy density npv2 do not exhibit self-similar behavior in the inertial range. (3) The first order PDF of kinetic energy density measured relative to the mean flow np(v-v¯)2 appears to be self-similar in the inertial range, that is, it is self-similar to within the error bars of the measurement. Larger data sets and more precise measurements are required to further validate these results although, at the moment, Wind and ACE are the largest and highest quality solar wind data sets available. Theoretical implications of these results for solar wind modeling are also discussed.
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
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
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.
DNS of self-similar adverse pressure gradient turbulent boundary layer at incipient separation
NASA Astrophysics Data System (ADS)
Soria, Julio; Kitsios, Vassili; Atkinson, Callum; Sillero, Juan; Borrell, Guillem; Gungar, Ayse; Jimenez, Javier
2015-11-01
A direct numerical simulation of a self-similar adverse pressure gradient turbulent boundary layer (APG-TBL) flow at incipient separation has been carried out. The maximum Reynolds number based on the momentum thickness, Reδ2 , reached in this DNS is 6,500. A wall-normal far-field boundary condition to effect the desired APG that will lead to the desired self-similar flow at the verge of separation has been developed. The self-similar analysis of the mean turbulent boundary layer equations yields the necessary conditions for a self-similar mean flow to exists. These conditions are tested using the DNS APG-TBL data base. First and second order statistics of the velocity across the APG-TBL are also presented in the light of the self-similar analysis results and compared to the results of a zero pressure gradient turbulent boundary layer DNS with similar mean inflow characteristics as the APG-TBL. The support of the ARC, NCI and Pawsey SCC funded by the Australian and Western Australian governments as well as the support of PRACE funded by the European Union are gratefully acknowledged.
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.
Exploiting the self-similar nature of Raman and Brillouin amplification
NASA Astrophysics Data System (ADS)
Trines, R.; Alves, E. P.; Fonseca, R. A.; Silva, L. O.; Webb, E.; Fiuza, F.; Cairns, R. A.; Bingham, R.; Norreys, P.
2015-11-01
Raman and Brillouin amplification are two schemes for amplifying and compressing short laser pulses in plasma. Depending on the laser and plasma configurations, these schemes could potentially deliver the high-energy high-power pulses needed for inertial confinement fusion, especially fast-ignition fusion. Analytical self-similar models for both Raman and Brillouin amplification have already been derived, but the consequences of this self-similar behavior are little known and hardly ever put to good use. In this talk, we will give an overview of the self-similar laws that govern the evolution of the probe pulse in Raman and Brillouin amplification, and show how these laws can be exploited, in particular regarding the parameters of the initial probe pulse, to control the properties of the final amplified probe and improve the efficiency of the process.
Self-similar motions of self-gravitating gas in stars
Bogoyavlenskii, O.I.
1986-05-10
In this work the stellar explosion model is studied on the basis of a complete investigation of the three-dimensional dynamic system describing the self-similar solutions in classical gas dynamics with gravitation taken into account by the methods of the qualitative theory of dynamic systems. The problem of the self-similar centripetal accretion of a self-gravitating gas and the problem of the motion of a converging shock wave are also solved on the basis of this investigation. The methods of this work are a further development of the methods used before in the study of uniform cosmological models and self-similar solutions in the general theory of relativity, in the study of the motion of gravitating gas ellipsoids, and in the investigation of the dynamics of perturbations of some completely integrable systems and hydrodynamic systems.
Self-similarities in one-dimensional periodic and quasiperiodic systems
NASA Astrophysics Data System (ADS)
Odagaki, T.; Aoyama, Hideaki
1989-01-01
We find hyperinflation rules for periodic and quasiperiodic systems in one dimension which consist of two components and are characterized by a single-parameter α. Applying hyperinflation rules, we analyze the diffraction pattern and physical properties described by a class of transfer matrices in SL(2,C). We show that the diffraction pattern is self-similar in the wave-vector-α space. We also show that the product of transfer matrices has self-similar structure in its asymptotic behavior in the space spanned by α and parameters in the matrices, which gives rise to self-similarity in various physical properties such as transmission coefficient, conductivity, heat conductivity, effective impedance, and spectral diffusion. Possible experiments are also discussed.
Self-similar transmission properties of aperiodic Cantor potentials in gapped graphene
NASA Astrophysics Data System (ADS)
Rodríguez-González, Rogelio; Rodríguez-Vargas, Isaac; Díaz-Guerrero, Dan Sidney; Gaggero-Sager, Luis Manuel
2016-01-01
We investigate the transmission properties of quasiperiodic or aperiodic structures based on graphene arranged according to the Cantor sequence. In particular, we have found self-similar behaviour in the transmission spectra, and most importantly, we have calculated the scalability of the spectra. To do this, we implement and propose scaling rules for each one of the fundamental parameters: generation number, height of the barriers and length of the system. With this in mind we have been able to reproduce the reference transmission spectrum, applying the appropriate scaling rule, by means of the scaled transmission spectrum. These scaling rules are valid for both normal and oblique incidence, and as far as we can see the basic ingredients to obtain self-similar characteristics are: relativistic Dirac electrons, a self-similar structure and the non-conservation of the pseudo-spin.
Self-Similar Solutions for a Fractional Thin Film Equation Governing Hydraulic Fractures
NASA Astrophysics Data System (ADS)
Imbert, C.; Mellet, A.
2015-12-01
In this paper, self-similar solutions for a fractional thin film equation governing hydraulic fractures are constructed. One of the boundary conditions, which accounts for the energy required to break the rock, involves the toughness coefficient K ≥ 0. Mathematically, this condition plays the same role as the contact angle condition in the thin film equation. We consider two situations: The zero toughness ( K = 0) and the finite toughness K ∈ (0, ∞) cases. In the first case, we prove the existence of self-similar solutions with constant mass. In the second case, we prove that for all K > 0 there exists an injection rate for the fluid such that self-similar solutions exist.
Horton and Tokunaga self-similarity for multiplicative coalescent: numerical approach
NASA Astrophysics Data System (ADS)
Tejedor, A.; Zaliapin, I.
2012-12-01
The Horton and Tokunaga branching laws provide a convenient and powerful framework for studying self-similarity in branching structures represented by random tree graphs. The Horton self-similarity, described by the Horton exponent R, is a weaker property that addresses the principal branching in a tree; it is a counterpart of the power-law size distribution for elements of a branching system. The stronger Tokunaga self-similarity, parameterized by a positive pair (a, c), addresses so-called side branching and implies that different hierarchical levels of a tree have the same statistical structure. The Horton and Tokunaga self-similarity have been empirically established in numerous observed and modeled systems and proven for the following paradigmatic models: (i) the critical binary Galton-Watson branching process with finite progeny, also known in hydrology as Shreve's random topology model, (ii) level-set tree representation of white noise and (iii) random walk, and (iv) Kingman's coalescent process. This work addresses the problem of testing the Tokunaga self-similarity hypothesis and statistical estimation of Horton and Tokunaga parameters in a single finite tree. We use critical binary Galton-Watson trees to illustrate and quantify finite-size effects that influence estimation as well as compare among estimation techniques based on regression and maximum likelihood approaches. Next, we apply the developed testing and estimation procedure to study the multiplicative coalescent process. The results of our numerical experiments suggest that the multiplicative coalescent is Tokunaga self-similar with parameters (a, c) = (1, 2), the same as that for the critical binary Galton-Watson process and level-set tree representation of a random walk.
Scaling in the Optical Characteristics of Aperiodic Structures with Self-Similarity Symmetry
Zotov, A. M.; Korolenko, P. V. Mishin, A. Yu.
2010-11-15
The properties of diffraction gratings and multilayered systems constructed using 1D models of quasicrystals are considered based on numerical simulation. It is shown that there is a direct relationship between the self-similarity symmetry of quasicrystals and scaling in the characteristics of the above-mentioned optical devices. The degree of structural correspondence between the graphical representations of the geometric properties of crystals, light diffraction patterns of gratings, and the transmission spectra of multilayered systems is estimated. It is shown that certain types of self-similarity symmetry make the characteristics of aperiodic diffraction gratings highly stable to a change in the size ratio of forming elements.
Failure of self-similarity for large (Mw > 81/4) earthquakes.
Hartzell, S.H.; Heaton, T.H.
1988-01-01
Compares teleseismic P-wave records for earthquakes in the magnitude range from 6.0-9.5 with synthetics for a self-similar, omega 2 source model and conclude that the energy radiated by very large earthquakes (Mw > 81/4) is not self-similar to that radiated from smaller earthquakes (Mw < 81/4). Furthermore, in the period band from 2 sec to several tens of seconds, it is concluded that large subduction earthquakes have an average spectral decay rate of omega -1.5. This spectral decay rate is consistent with a previously noted tendency of the omega 2 model to overestimate Ms for large earthquakes.-Authors
Modeling the self-similarity in complex networks based on Coulomb's law
NASA Astrophysics Data System (ADS)
Zhang, Haixin; Wei, Daijun; Hu, Yong; Lan, Xin; Deng, Yong
2016-06-01
Recently, self-similarity of complex networks have attracted much attention. Fractal dimension of complex network is an open issue. Hub repulsion plays an important role in fractal topologies. This paper models the repulsion among the nodes in the complex networks in calculation of the fractal dimension of the networks. Coulomb's law is adopted to represent the repulse between two nodes of the network quantitatively. A new method to calculate the fractal dimension of complex networks is proposed. The Sierpinski triangle network and some real complex networks are investigated. The results are illustrated to show that the new model of self-similarity of complex networks is reasonable and efficient.
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.
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
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.
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.
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.
NASA Astrophysics Data System (ADS)
Vamoş, Călin; Crăciun, Maria; Suciu, Nicolae
2015-10-01
Fractional Brownian motion (fBm) is a nonstationary self-similar continuous stochastic process used to model many natural phenomena. A realization of the fBm can be numerically approximated by discrete paths which do not entirely preserve the self-similarity. We investigate the self-similarity at different time scales by decomposing the discrete paths of fBm into intrinsic components. The decomposition is realized by an automatic numerical algorithm based on successive smoothings stopped when the maximum monotonic variation of the averaged time series is reached. The spectral properties of the intrinsic components are analyzed through the monotony spectrum defined as the graph of the amplitudes of the monotonic segments with respect to their lengths (characteristic times). We show that, at intermediate time scales, the mean amplitude of the intrinsic components of discrete fBms scales with the mean characteristic time as a power law identical to that of the corresponding continuous fBm. As an application we consider hydrological time series of the transverse component of the transport process generated as a superposition of diffusive movements on advective transport in random velocity fields. We found that the transverse component has a rich structure of scales, which is not revealed by the analysis of the global variance, and that its intrinsic components may be self-similar only in particular cases.
Local Self-Similarity and Finite-Time Singularity in a High-Symmetry Euler Flow
NASA Astrophysics Data System (ADS)
Ng, C. S.; Bhattacharjee, A.
1997-11-01
The dynamical consequence of a positive fourth-order pressure derivative (p_xxxx) at the origin [C. S. Ng and A. Bhattacharjee, Phys. Rev. E 54 1530, 1996] in a high-symmetry Euler flow (the Kida flow) is considered. It is shown that the third order spatial derivative u_xxx of the x component of the velocity u at the origin is always decreasing in this situation. By assuming that u_xxx always attains a minimum possible value consistent with a given spectral profile, it is found that the flow is locally self-similar near the origin and collapses as energy cascades to Fourier modes with higher wavenumbers k. Moreover, it is found that the self-similar p(x) and u(x) profiles (as well as their derivatives) near the origin are very similar in shape to what were found in numerical simulations [O. N. Boratav and R. B. Pelz, Phys. Fluids 6 2757, 1994]. It is shown that a finite-time singularity (FTS) must appear in this case if the spectral index ν of the energy spectrum E(k) ∝ k^-ν of the locally self-similar flow is less than 6. A self-similar solution satisfying the Kelvin's theorem of circulation trivially has ν = 2 with vortex filaments and a FTS.
Influence of heterogeneity on second-kind self-similar solutions for viscous gravity currents
Zheng, Zhong; Christov, Ivan C.; Stone, Howard A.
2014-04-16
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
Influence of heterogeneity on second-kind self-similar solutions for viscous gravity currents
Zheng, Zhong; Christov, Ivan C.; Stone, Howard A.
2014-04-16
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.
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.
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.
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.
A proof for the mode stability of a self-similar wave map
NASA Astrophysics Data System (ADS)
Costin, O.; Donninger, R.; Xia, X.
2016-08-01
We study the fundamental self-similar solution to the SU(2) sigma model, found by Shatah and Turok–Spergel. We give a rigorous proof for its mode stability. Based on earlier results by the second author, the present paper constitutes the last building block for a completely rigorous proof of the nonlinear stability of the Shatah–Turok–Spergel wave map.
Effect of ingress buffering on self-similarity of optical burst traffic
NASA Astrophysics Data System (ADS)
Huang, Rui; Zaruba, Gergely V.
2003-10-01
Recently, optical burst switching and aggregated optical packet switching have gained significant exposure as possible future mechanisms for routing aggregated IP traffic over all-optical core networks. However, the limited buffering capacity in all-optical networks presents a major challenge, as current IP traffic displays strong self-similar properties. Reducing the burst loss rate of such long-range dependent traffic can be costly requiring a significant increase in either the network bandwidth or the buffer size of optical cross connects. In this paper, we revisit the possibility of using buffers to reduce self-similarity before the traffic is routed onto the all-optical core. The aim of this paper is to increase the understanding of the effect of packet/burst aggregation on the self-similarity measure of the traffic. In particular, we implement a simple burst assembly mechanism with two parameters, the maximum burst length L and the maximum burst delay d, so that incoming traffic is smoothed with a guaranteed delay bound. Unlike previous works, we simulate the burst assembler using more realistic input traffic sources, and analyze the results using both R/S plot and discrete wavelet analysis methods. Our detailed results show that buffering indeed reduces traffic self-similarity (an area of research controversy) when parameters L and d are set appropriately.
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.
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.
Polytropic index of central plasma sheet ions based on MHD Bernoulli integral
NASA Astrophysics Data System (ADS)
Pang, Xuexia; Cao, Jinbin; Liu, Wenlong; Ma, Yuduan; Lu, Haoyu; Yang, Junying; Li, Liuyuan; Liu, Xu; Wang, Jing; Wang, Tieyan; Yu, Jiang
2015-06-01
This paper uses the data of Cluster from 2001 to 2009 to study the polytropic processes of central plasma sheet (CPS) ions. We first adopt the approach of MHD Bernoulli integral (MBI) to identify homogeneous streamflow tubes (quasi-invariant MBI regions) and then calculate the polytropic index of ions for those streamflow tubes whose outward electromagnetic energy ratios δ < 0.05. The central plasma sheet is actually a complicated system, which comprises many streamflow tubes with different polytropic relations and the transition layers in between. The polytropic indexes of the CPS ions range from 0.1 to 1.8 and have a quasi-Gaussian distribution. The median polytropic index is 0.93 for AE < 200 nT and 0.91 for AE ≥ 200 nT. Thus, there is no obvious difference between the polytropic indexes of the quiet time and the substorm time CPS ions, which suggests that the thinning and thickening processes of plasma sheet during substorm times do not change obviously the polytropic relation of the CPS ions. The statistical analysis using different δ (δ < 0.05, 0.025, and 0.01) shows that the outward emission of electromagnetic energy is an effective cooling mechanism and can make the polytropic index to decrease and shift toward isobaric. It is inferred that the CPS ions as a whole much likely behave in a way between isobaric and isothermal.
Rayleigh Taylor turbulence: self-similar analysis and direct numerical simulations
NASA Astrophysics Data System (ADS)
Ristorcelli, J. R.; Clark, T. T.
2004-05-01
Direct numerical simulations and a self-similar analysis of the single-fluid Boussinesq Rayleigh Taylor instability and transition to turbulence are used to investigate Rayleigh Taylor turbulence. The Schmidt, Atwood and bulk Reynolds numbers are Sc {=} 1, A {=} 0.01, Re {≤} 3000. High-Reynolds-number moment self-similarity, consistent with the the energy cascade interpretation of dissipation, is used to analyse the DNS results. The mixing layer width obeys a differential equation with solution h(t;C_o,h_0) {=} fourth C_o Agt(2+) sqrt{AgC_o}h(1/2) _0 t+h_0; the result for h(t;C_o,h_0) is a rigorous consequence of only one ansatz, self-similarity. It indicates an intermediate time regime in which the growth is linear and the importance of a virtual origin. At long time the well-known h ˜ fourth C_o Agt(2) scaling dominates. The self-similar analysis indicates that the asymptotic growth rate is not universal. The scalings of the second-order moments, their dissipations, and production dissipation ratios, are obtained and compared to the DNS. The flow is not self-similar in a conventional sense there is no single length scale that scales the flow. The moment similarity method produces three different scalings for the turbulence energy-containing length scale, ℓ, the Taylor microscale, la, and the Kolmogorov dissipation scale, eta. The DNS and the self-similar analysis are in accord showing ℓ {˜} Agt(2) , ⪉ {˜} t(1/2) and eta {˜} (({A(2g^2}/{nu^3})t)(-1/4)) achieving self-similar behaviour within three initial eddy turnovers of the inception of the turbulence growth phase at bulk Reynolds numbers in the range of Re = 800 1000 depending on initial conditions. A picture of a turbulence in which the largest scales grow, asymptotically, as t(2) and the smallest scales decrease as t(-1/4) , emerges. As a consequence the bandwidth of the turbulence spectrum grows as t(9/4) and is consistent with the R_t(3/4) Kolmogorov scaling law of fully developed stationary
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.
Radar meteors range distribution model. III. Ablation, shape-density and self-similarity parameters
NASA Astrophysics Data System (ADS)
Pecinová, D.; Pecina, P.
2007-10-01
The theoretical radar meteors Range Distribution of the overdense echoes developed by Pecinová and Pecina (2007 a) is applied here to observed range distributions of meteors belonging to the Quadrantid, Perseid, Leonid, Geminid, γ Draconid (Giacobinid), ζ Perseid and β Taurid streams to study the variability of the shape-density, ablation, and self-similarity parameters of meteoroids of these streams. We have found in accordance with results of photographical observations that ablation parameter σ is higher for members of showers of clearly cometary origin, and is lower for Geminid and daytime shower meteoroids. Levin's self-similarity parameter μ was found to be much greater than the classical value 2/3 for all investigated streams with the exception of Geminids, for which the value found is almost classical, i.e. 0.66 ± 0.01. The method of getting μ by means of fitting the light curve of faint TV meteors is also suggested.
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
Random Vortex-Street Model for a Self-Similar Plane Turbulent Jet
NASA Astrophysics Data System (ADS)
L'Vov, Victor S.; Pomyalov, Anna; Procaccia, Itamar; Govindarajan, Rama
2008-08-01
We ask what determines the (small) angle of turbulent jets. To answer this question we first construct a deterministic vortex-street model representing the large-scale structure in a self-similar plane turbulent jet. Without adjustable parameters the model reproduces the mean velocity profiles and the transverse positions of the large-scale structures, including their mean sweeping velocities, in a quantitative agreement with experiments. Nevertheless, the exact self-similar arrangement of the vortices (or any other deterministic model) necessarily leads to a collapse of the jet angle. The observed (small) angle results from a competition between vortex sweeping tending to strongly collapse the jet and randomness in the vortex structure, with the latter resulting in a weak spreading of the jet.
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.
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 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
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.
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.
On the role of self-similarity in component-based software.
Elwasif, Wael; Armstrong, Robert C.; Bernholdt, David E.; Allan, Benjamin A.
2005-03-01
This is a speculative work meant to stimulate discussion about the role of subsumability in self-similar software structures for computational simulations. As in natural phenomena, self-similar features in framework structures allow the size and complexity of code to grow without bound and still maintain apparent coherence. As in crystal growth, the coherence may be maintained by the application of a repeated pattern, or patterns may, as in fluid mechanical turbulence, be scaled by size and nested. Examples of these kinds of patterns applied to component systems in particular will be given. Conclusions and questions for discussion will be drawn regarding the applicability of these ideas to component architectures, complexity, and scientific computing.
Complete description of all self-similar models driven by Lévy stable noise.
Weron, Aleksander; Burnecki, Krzysztof; Mercik, Szymon; Weron, Karina
2005-01-01
A canonical decomposition of H-self-similar Lévy symmetric alpha-stable processes is presented. The resulting components completely described by both deterministic kernels and the corresponding stochastic integral with respect to the Lévy symmetric alpha-stable motion are shown to be related to the dissipative and conservative parts of the dynamics. This result provides stochastic analysis tools for study the anomalous diffusion phenomena in the Langevin equation framework. For example, a simple computer test for testing the origins of self-similarity is implemented for four real empirical time series recorded from different physical systems: an ionic current flow through a single channel in a biological membrane, an energy of solar flares, a seismic electric signal recorded during seismic Earth activity, and foreign exchange rate daily returns. PMID:15697664
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.
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.
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
Self-Similarity of Jet and Top-Quark Production at Tevatron and Lhc
NASA Astrophysics Data System (ADS)
Tokarev, M. V.; Dedovich, T. G.; Zborovský, I.
2015-03-01
Self-similarity of jet and top-quark production in bar pp and ρρ collisions at √ s = 630 - 8000GeV is studied in the framework of z-scaling. Inclusive transverse momentum spectra measured by the CDF and DØ Collaborations at the Tevatron and the CMS, ATLAS, ALICE Collaborations at the LHC are analyzed. New results on asymptotic behavior of scaling function ψ(z) for jet production are presented and discussed. Universality of the shape of ψ(z) over a wide range of masses and different flavor contents of hadrons is verified. The obtained results are considered as confirmation of self-similarity of jet production, fractality of hadron structure and locality of constituent interactions at small scales.
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.
The non-integer operation associated to random variation sets of the self-similar set
NASA Astrophysics Data System (ADS)
Ren, Fu-Yao; Liang, Jin-Rong
2000-10-01
When memory sets are random variation sets of the self-similar set and the total number of remaining states in each stage of the division of this set is normalized to unity, the corresponding flux and fractional integral are “robust” and stable under some conditions. This answers an open problem proposed by Alian Le Mehaute et al. in their book entitled Irreversibilitê Temporel et Geometrie Fractale.
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.
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. PMID:18233821
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.
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.
2016-06-01
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 -ɛ ≤ K(x,y)-2 ≤ ɛ 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 {C}{setminus } (-∞ ,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 ɛ 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 → ∞.
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. PMID:24146005
A New Look at Self-Similarity in Strained Plane Wakes. 1.3
NASA Technical Reports Server (NTRS)
Rogers, Michael M.; Mansour, Nagi N. (Technical Monitor)
2001-01-01
In early experiments, A. J. Reynolds and J. F. Keffer sought to determine whether plane wakes of circular cylinders, when strained by a wind tunnel of varying cross-section, evolved in accordance with an analytically derived self-similar solution. As pointed out by Reynolds, for the strain geometry considered this self-similar solution indicated exponential growth of the viscous term in the mean momentum equation, a result which he interpreted as suggesting that such wakes would eventually relaminarize. The experimental results were found not to agree with the similarity theory and recent direct numerical simulations confirm this. However, a more general self-similar analysis of the kind suggested by W. K. George is found to lead to families of possible similarity solutions, some of which do indeed describe the observed flaw behavior. These equilibrium similarity solutions result from creating a balance in the governing equations by grouping certain terms. For these solutions the viscous terms can be retained in the analysis.
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
Elastic-wave transmission through self-similar anisotropic Cantor-like multilayers
NASA Astrophysics Data System (ADS)
Ponge, M.-F.; Jacob, X.; Gibiat, V.
2016-04-01
Through the study of elastic wave propagation in Cantor-like anisotropic multilayers, this work analyzes the influence of medium geometry on the transmission of elastic waves to yield a better understanding of the connection between topological ordering and physical properties. Cantor-like multilayers, whose homothetic dimension is modified by changing the length of the central segment, are made of one anisotropic material with two orientations. The influence of the combination of self-similarity and anisotropy on the global transmission is investigated by means of iteration order, homothetic dimension and layer orientations. The propagation is described by the stiffness matrix algorithm. The results reveal that the homothetic dimension scales the resonance frequencies and the frequency ranges of the pseudo band gaps, and that layer orientation influences the speed of quasi-transverse waves to enhance the effect of self-similarity. Finally, an extensive study on various frequency ranges is conducted. It is demonstrated that self-similarity may be used to tune the position and the width of the pseudo band gaps to minimize the global acoustic transmission.
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-similar occurrence of massless Dirac particles in graphene under magnetic field
NASA Astrophysics Data System (ADS)
Rhim, Jun-Won; Park, Kwon
2013-03-01
Intricate interplay between the periodicity of the lattice structure and that of the cyclotron motion gives rise to a well-known self-similar fractal structure of the Hofstadter butterfly for an electron moving in lattice under magnetic field. Evolving from the n = 0 Landau level, the central band of the Hofstadter butterfly is especially interesting since it may hold a key to the mysteries of the fractional quantum Hall effect in graphene. In this paper, we develop an effective Hamiltonian method that can be used to provide an accurate analytic description of the central Hofstadter band in the weak-field regime. One of the most important discoveries obtained in this work is that massless Dirac particles always exist inside the central Hofstadter band no matter how small the magnetic flux may become. In other words, with its bandwidth broadened by the lattice effect, the n = 0 Landau level contains massless Dirac particles within itself. In fact, by carefully analyzing the self-similar recursive pattern of the central Hofstadter band, we conclude that massless Dirac particles should occur under arbitrary magnetic field. As a corollary, the central Hofstadter band also contains a self-similar structure of recursive Landau levels associated with such massless Dirac particles.
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.
Self-similar cosmological solutions with dark energy. I. Formulation and asymptotic analysis
Harada, Tomohiro; Maeda, Hideki; Carr, B. J.
2008-01-15
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=({gamma}-1){mu} with 0<{gamma}<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 ({gamma}>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<{gamma}<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 "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
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.
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.
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
Liger-Belair, Gérard; Villaume, Sandra
2011-04-27
Measurements of dissolved CO(2) concentrations from Champagne bottles initially holding the same CO(2) level after having been elaborated (close to 11.5 g L(-1)), but having experienced different periods of aging after having been corked with natural cork stoppers, were done. Losses of dissolved CO(2) close to 3.5 g L(-1) experienced by the oldest Champagne samples aged for about 75 months were reported. This very significant loss of dissolved CO(2) was logically interpreted as a consequence of the continuous diffusion of gaseous CO(2) through the pores of the cork stopper. By combining the diffusion principle through a porous medium with Henry's law (which links the solubility of a gas species in a liquid medium with its partial pressure in the vapor phase), a multiparameter model was built that provides the dissolved CO(2) content found in Champagne during its whole aging period. Both Champagne temperature and bottle volume were found to be key parameters with regard to the kinetics of CO(2) losses through the cork. PMID:21413811
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.
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.
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
Missense Mutation in Exon 2 of SLC36A1 Responsible for Champagne Dilution in Horses
Cook, Deborah; Brooks, Samantha; Bellone, Rebecca; Bailey, Ernest
2008-01-01
Champagne coat color in horses is controlled by a single, autosomal-dominant gene (CH). The phenotype produced by this gene is valued by many horse breeders, but can be difficult to distinguish from the effect produced by the Cream coat color dilution gene (CR). Three sires and their families segregating for CH were tested by genome scanning with microsatellite markers. The CH gene was mapped within a 6 cM region on horse chromosome 14 (LOD = 11.74 for θ = 0.00). Four candidate genes were identified within the region, namely SPARC [Secreted protein, acidic, cysteine-rich (osteonectin)], SLC36A1 (Solute Carrier 36 family A1), SLC36A2 (Solute Carrier 36 family A2), and SLC36A3 (Solute Carrier 36 family A3). SLC36A3 was not expressed in skin tissue and therefore not considered further. The other three genes were sequenced in homozygotes for CH and homozygotes for the absence of the dilution allele (ch). SLC36A1 had a nucleotide substitution in exon 2 for horses with the champagne phenotype, which resulted in a transition from a threonine amino acid to an arginine amino acid (T63R). The association of the single nucleotide polymorphism (SNP) with the champagne dilution phenotype was complete, as determined by the presence of the nucleotide variant among all 85 horses with the champagne dilution phenotype and its absence among all 97 horses without the champagne phenotype. This is the first description of a phenotype associated with the SLC36A1 gene. PMID:18802473
Some non-linear interactions in polytropic gas cosmology: phase space analysis
NASA Astrophysics Data System (ADS)
Khurshudyan, Martiros
2015-11-01
There are various cosmological models with polytropic equation of state associated to dark energy. Polytropic EoS has important applications in astrophysics, therefore a study of it on cosmological framework continues to be interesting. From the other hand, there are various forms of interactions phenomenologically involved into the darkness of the universe able to solve important cosmological problems. This is a motivation for us to perform a phase space analysis of various cosmological scenarios where non-linear interacting polytropic gas models are involved. Dark matter is taken to be a pressureless fluid.
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. PMID:23060344
Self-similar occurrence of massless Dirac particles in graphene under a magnetic field
NASA Astrophysics Data System (ADS)
Rhim, Jun-Won; Park, Kwon
2012-12-01
Intricate interplay between the periodicity of the lattice structure and that of the cyclotron motion gives rise to a well-known self-similar fractal structure of the energy eigenvalue, known as the Hofstadter butterfly, for an electron moving in lattice under magnetic field. Connected with the n=0 Landau level, the central band of the Hofstadter butterfly is especially interesting in the honeycomb lattice. While the entire Hofstadter butterfly can be in principle obtained by solving Harper's equations numerically, the weak-field limit, most relevant for experiment, is intractable owing to the fact that the size of the Hamiltonian matrix, which needs to be diagonalized, diverges. In this paper, we develop an effective Hamiltonian method that can be used to provide an accurate analytic description of the central Hofstadter band in the weak-field regime. One of the most important discoveries obtained in this work is that massless Dirac particles always exist inside the central Hofstadter band no matter how small the magnetic flux may become. In other words, with its bandwidth broadened by the lattice effect, the n=0 Landau level contains massless Dirac particles within itself. In fact, by carefully analyzing the self-similar recursive pattern of the central Hofstadter band, we conclude that massless Dirac particles should occur under arbitrary magnetic field. As a corollary, the central Hofstadter band also contains a self-similar structure of recursive Landau levels associated with such massless Dirac particles. To assess the experimental feasibility of observing massless Dirac particles inside the central Hofstadter band, we compute the width of the central Hofstadter band as a function of magnetic field in the weak-field regime.
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.
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 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)].
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 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.
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
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
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.
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.
Self-similar continuous cascades supported by random Cantor sets: Application to rainfall data
NASA Astrophysics Data System (ADS)
Muzy, Jean-François; Baïle, Rachel
2016-05-01
We introduce a variant of continuous random cascade models that extends former constructions introduced by Barral-Mandelbrot and Bacry-Muzy in the sense that they can be supported by sets of arbitrary fractal dimension. The so-introduced sets are exactly self-similar stationary versions of random Cantor sets formerly introduced by Mandelbrot as "random cutouts." We discuss the main mathematical properties of our construction and compute its scaling properties. We then illustrate our purpose on several numerical examples and we consider a possible application to rainfall data. We notably show that our model allows us to reproduce remarkably the distribution of dry period durations.
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
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.
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.
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.
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
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.
Self-similar community structure in a network of human interactions
NASA Astrophysics Data System (ADS)
Guimerà, R.; Danon, L.; Díaz-Guilera, A.; Giralt, F.; Arenas, A.
2003-12-01
We propose a procedure for analyzing and characterizing complex networks. We apply this to the social network as constructed from email communications within a medium sized university with about 1700 employees. Email networks provide an accurate and nonintrusive description of the flow of information within human organizations. Our results reveal the self-organization of the network into a state where the distribution of community sizes is self-similar. This suggests that a universal mechanism, responsible for emergence of scaling in other self-organized complex systems, as, for instance, river networks, could also be the underlying driving force in the formation and evolution of social networks.
NASA Astrophysics Data System (ADS)
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.
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.
Quantum resolution of timelike singularities in spherically symmetric, self-similar spacetimes
NASA Astrophysics Data System (ADS)
Konkowski, Deborah; Helliwell, Thomas; Williams, Jon
2015-04-01
A definition of quantum singularity for the case of static spacetimes has recently been extended to conformally static spacetimes. Here the theory behind quantum singularities in conformally static spacetimes is reviewed, and then applied to a class of spherically symmetric, self-similar spacetimes. We use solutions of the massless Klein-Gordon equation as test fields. In this way we find the ranges of metric parameters for which classical timelike singularities in these spacetimes are resolved quantum mechanically, in the sense that the Hamiltonian operator is essentially self-adjoint, so the evolution of quantum wave packets lacks the usual ambiguity associated with scattering off singulartities.
Power laws and self-similar behaviour in negative ionization fronts
NASA Astrophysics Data System (ADS)
Arrayás, Manuel; Fontelos, Marco A.; Trueba, José L.
2006-06-01
We study anode-directed ionization fronts in curved geometries. An electric shielding factor determines the behaviour of the electric field and the charged particle densities. From a minimal streamer model, a Burgers type equation which governs the dynamics of the electric shielding factor is obtained when electron diffusion is neglected. A Lagrangian formulation is then derived to analyse the ionization fronts. Power laws for the velocity and the amplitude of streamer fronts are found numerically and calculated analytically by using the shielding factor formulation. The phenomenon of geometrical diffusion is explained and clarified, and a universal self-similar asymptotic behaviour is derived.
NASA Astrophysics Data System (ADS)
de La Torre, A.; Alexander, P.; Cornejo, J.
2003-02-01
With the assumption of a polytropic evolution for the lifting gas, the response of an ascending open atmospheric balloon to a monochromatic gravity wave is specified among other parameters by the heat balance with the surrounding air. If one considers the bubble of gas inside the open balloon as a thermodynamic system in contact through the balloon skin with a uniform thermal source (isothermic atmosphere), a relationship between the skin thermal conductivity and the polytropic index for the lifting gas [hydrogen (H2) or helium (He)] may be found. The results for both gases are extended to the case of a typical tropospheric linearly decreasing temperature profile. Constant and variable balloon skin thicknesses are studied for both background temperature profiles. The polytropic index is found to be lower for the changing skin and shows a sensitive difference between the two temperature profiles. The relationship between the thermal conductivity and polytropic index becomes abrupt only when the latter approaches the isothermal or adiabatic values.
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.
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.
Tunable rainbow trapped in a self-similar liquid crystal waveguide
NASA Astrophysics Data System (ADS)
Hu, Qing; Wang, Si-Hui; Xu, Di-Hu; Zhou, Yu; Peng, Ru-Wen; Wang, Mu
2012-02-01
We have investigated the optical propagation through a self-similar dielectric waveguide, where a hollow core is surrounded by a coaxial Thue-Morse multilayer. It is found that due to the self-similar furcation feature in the photonic band structure, the transmission multibands are achieved. And different frequency ranges of the transmission modes can be selectively guided and spatially confined along the waveguide. Consequently, a rainbow can be trapped in the waveguide. Then by infiltrating liquid crystal into the cladding layers, the transmission modes and rainbow trapping can be tuned by altering the temperature. And transverse electric (TE) and transverse magnetic (TM) polarizations present different propagating features. The attenuation and energy density distributions of different modes in the waveguide are also discussed. The finding can be applied to designing miniaturized compact photonic devices, such as a spectroscopy on a chip, color-sorters on a chip, and photon sorters for spectral imaging. Reference: Qing Hu, Jin-Zhu Zhao, Ru-Wen Peng, Feng Gao, Rui-Li Zhang, and Mu Wang, Appl. Phys. Lett. (2010) 96, 161101; and Qing Hu, Ru-Wen Peng, Si-Hui Wang, and Mu Wang, manuscript prepared(2011).
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.
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.
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 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.
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.
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.
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.
Lie Algebraic Analysis of Thin Film Marangoni Flows: Multiplicity of Self-Similar Solutions
NASA Astrophysics Data System (ADS)
Nicolaou, Zachary; Troian, Sandra
The rapid advance of an insoluble surfactant monolayer on a thin liquid film of higher surface tension is controlled by distinct flow regimes characterized by the relative strength of viscous, Marangoni and capillary forces. Such flows play a critical role in human pulmonary and ocular systems. During the past quarter century, researchers have focused exclusively on self-similar solutions to the governing pair of nonlinear PDEs for the film thickness, H (r /ta) , and surface concentration, Γ (r /ta) /tb , in the limit where the Marangoni or capillary terms vanish, where r denotes the spatial variable, t is time, and a and b are fractional exponents. Using Lie algebraic techniques, we demonstrate for the first time the existence of several embedded symmetries in this system of equations which yield multiple self-similar solutions describing more complex scaling behavior, even when all three forces are incorporated. A special and previously unrecognized subset of these solutions reveals the dynamical behavior of film thinning and surfactant distribution near the origin, which ultimately meters the downstream flow. Finite element simulations confirm the suite of scaling exponents obtained analytically.
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.
Shear flow over a self-similar expanding pulmonary alveolus during rhythmical breathing
NASA Astrophysics Data System (ADS)
Haber, S.; Butler, J. P.; Brenner, H.; Emanuel, I.; Tsuda, A.
2000-02-01
Alternating shear flow over a self-similar, rhythmically expanding hemispherical depression is investigated. It provides a fluid-mechanical model for an alveolated respiratory unit, by means of which the effect of lung rhythmical expansion on gas mixing as well as aerosol dispersion and deposition can be studied. The flow is assumed to be very slow and governed by the quasi-steady linear Stokes equations. Consequently, superposition of the following two cases provides an easy route toward characterizing the aforementioned flow field. The first case treats the flow field that is generated by a rhythmically expanding spherical cap (the alveolus). The cap is attached at its rim to a circular opening in an expanding unbounded plane bounding a semi-infinite fluid region. The rate of expansion of the cap and the plane are chosen such as to maintain the system's configurational self-similarity. The second case addresses the flow disturbance that is generated by an alternating shear flow encountering a rigid hemispherical cavity in a plane bounding a semi-infinite fluid domain.
Self-similar turbulent boundary layer with imposed pressure gradient. Four flow regimes
NASA Astrophysics Data System (ADS)
Vigdorovich, I. I.
2014-11-01
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{/p -1/3} + O(Re{/p -2/3}), where Re p is the Reynolds number based on longitudinal pressure gradient. The theoretical results are in good agreement with experimental data.
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-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.
Statistical self-similarity of width function maxima with implications to floods
Veitzer, S.A.; Gupta, V.K.
2001-01-01
Recently a new theory of random self-similar river networks, called the RSN model, was introduced to explain empirical observations regarding the scaling properties of distributions of various topologic and geometric variables in natural basins. The RSN model predicts that such variables exhibit statistical simple scaling, when indexed by Horton-Strahler order. The average side tributary structure of RSN networks also exhibits Tokunaga-type self-similarity which is widely observed in nature. We examine the scaling structure of distributions of the maximum of the width function for RSNs for nested, complete Strahler basins by performing ensemble simulations. The maximum of the width function exhibits distributional simple scaling, when indexed by Horton-Strahler order, for both RSNs and natural river networks extracted from digital elevation models (DEMs). We also test a powerlaw relationship between Horton ratios for the maximum of the width function and drainage areas. These results represent first steps in formulating a comprehensive physical statistical theory of floods at multiple space-time scales for RSNs as discrete hierarchical branching structures. ?? 2001 Published by Elsevier Science Ltd.
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.
Asymptotics of Self-similar Solutions to Coagulation Equations with Product Kernel
NASA Astrophysics Data System (ADS)
McLeod, J. B.; Niethammer, B.; Velázquez, J. J. L.
2011-07-01
We consider mass-conserving self-similar solutions for Smoluchowski's coagulation equation with kernel K( ξ, η)=( ξη) λ with λ∈(0,1/2). It is known that such self-similar solutions g( x) satisfy that x -1+2 λ g( x) is bounded above and below as x→0. In this paper we describe in detail via formal asymptotics the qualitative behavior of a suitably rescaled function h( x)= h λ x -1+2 λ g( x) in the limit λ→0. It turns out that h ˜ 1+ C x^{λ/2} \\cos(sqrt{λ} log x) as x→0. As x becomes larger h develops peaks of height 1/ λ that are separated by large regions where h is small. Finally, h converges to zero exponentially fast as x→∞. Our analysis is based on different approximations of a nonlocal operator, that reduces the original equation in certain regimes to a system of ODE.
Robustness of Estimators of Long-Range Dependence and Self-Similarity under non-Gaussianity
NASA Astrophysics Data System (ADS)
Franzke, C.; Watkins, N. W.; Graves, T.; Gramacy, R.; Hughes, C.
2011-12-01
Long-range dependence and non-Gaussianity are ubiquitous in many natural systems like ecosystems, biological systems and climate. However, it is not always appreciated that both phenomena may occur together in natural systems and that self-similarity in a system can be a superposition of both phenomena. These features, which are common in complex systems, impact the attribution of trends and the occurrence and clustering of extremes. The risk assessment of systems with these properties will lead to different outcomes (e.g. return periods) than the more common assumption of independence of extremes. Two paradigmatic models are discussed which can simultaneously account for long-range dependence and non-Gaussianity: Autoregressive Fractional Integrated Moving Average (ARFIMA) and Linear Fractional Stable Motion (LFSM). Statistical properties of estimators for long-range dependence and self-similarity are critically assessed. It is found that the most popular estimators can be biased in the presence of important features of many natural systems like trends and multiplicative noise. Also the long-range dependence and non-Gaussianity of two typical natural time series are discussed.
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.
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.
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.