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.
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
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
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
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
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.
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.
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 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.
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 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
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 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.
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-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-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-similar expansion of a warm dense plasma
Djebli, Mourad; Moslem, Waleed M.
2013-07-15
The properties of an expanding plasma composed of degenerate electron fluid and non-degenerate ions are studied. For our purposes, we use fluid equations for ions together with the electron momentum equation that include quantum forces (e.g., the quantum statistical pressure, forces due to the electron-exchange and electron correlations effects) and the quasi-neutrality condition. The governing equation is written in a tractable form by using a self-similar transformation. Numerical results for typical beryllium plasma parameters revealed that, during the expansion, the ion acoustic speed decreases for both isothermal and adiabatic ion pressure. When compared with classical hydrodynamic plasma expansion model, the electrons and ions are found to initially escape faster in vacuum creating thus an intense electric field that accelerates most of the particles into the vacuum ahead of the plasma expansion. The relevancy of the present model to beryllium plasma produced by a femto-second laser is highlighted.
Self-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.
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.
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.
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.
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.
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.
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.
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.
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
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
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.
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.
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).
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.
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.
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.
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
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
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)
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
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
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.
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
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
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.
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.
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.
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.
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.
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
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 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-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.
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 "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.
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.
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.
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
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.
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.
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.
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.
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
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
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.
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.
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.
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.
Dynamics and Stability of Self-similar Pinch-off via Surface Diffusion
NASA Astrophysics Data System (ADS)
Bernoff, Andrew J.; Bertozzi, Andrea L.; Witelski, Thomas P.
1998-11-01
The motion of an interface via surface diffusion is a well-known model in the study of thin solid filaments with application to such fields as integrated circuit technology. The interface moves with a normal velocity proportional to minus the surface Laplacian of its mean curvature. This flow conserves the volume enclosed inside the surface while minimizing its surface area. A cylindrical surface is unstable to long-wave perturbations, analogous to the Rayleigh instability in fluid dynamics. The initial instability leads to a conical pinch-off of the cylinder to form isolated spheres. We examine the structure of the pinch-off, showing it has self-similar structure, using asymptotic, numerical and analytical methods. In addition to a previously known solution(Wong et al. Scripta Mater.) 39(1):55, 1998, we find a countable set of similarity solutions, each with a different cone angle. We develop a stability theory in similarity variables that selects the original similarity solution as the only linearly stable one and consequently the only observable one. We confirm this theory via numerical simulations, using self-similar adaptive mesh refinement, of the pinch-off.
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.
Self-similarity of phase-space networks of frustrated spin models and lattice gas models
NASA Astrophysics Data System (ADS)
Peng, Yi; Wang, Feng; Han, Yilong
2013-03-01
We studied the self-similar properties of the phase-spaces of two frustrated spin models and two lattice gas models. The frustrated spin models included (1) the anti-ferromagnetic Ising model on a two-dimensional triangular lattice (1a) at the ground states and (1b) above the ground states and (2) the six-vertex model. The two lattice gas models were (3) the one-dimensional lattice gas model and (4) the two-dimensional lattice gas model. The phase spaces were mapped to networks so that the fractal analysis of complex networks could be applied, i.e. the box-covering method and the cluster-growth method. These phase spaces, in turn, establish new classes of networks with unique self-similar properties. Models 1a, 2, and 3 with long-range power-law correlations in real space exhibit fractal phase spaces, while models 1b and 4 with short-range exponential correlations in real space exhibit nonfractal phase spaces. This behavior agrees with one of untested assumptions in Tsallis nonextensive statistics. Hong Kong GRC grants 601208 and 601911
Self-similar pinch-off mechanism and scaling of ferrofluid drops.
Jiang, Xiao F; Li, Huai Z
2015-12-01
The pinch off of heterogeneous ferrofluid drops at a nozzle in air was experimentally investigated with a magnetic field (downward or upward) and without a magnetic field. Compared to homogeneous drops, the self-similarity and universal scaling law were verified through modifying the initial conditions, such as the nozzle diameter, flow rate, and magnitude and direction of the magnetic fields. Two pinch-off points were observed, and the two consecutive pinch-off dynamics were characterized through scaling laws. Here our scaling exponent remains within the scope of (0.70-0.80) for the primary whereas it remains within the scope of (0.60-0.70) for the secondary pinch off, respectively, comparable to the classic range from 2/3 to 1 for homogeneous drops. The gravity-compensating and gravity-superimposing magnetic fields display a negligible effect on the exponent but determine the sequence of double pinch offs. The universal character of the self-similar pinch off is extended to a heterogeneous fluid. PMID:26764624
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 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.
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.
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).
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.
Size distribution of dust grains: A problem of self-similarity
NASA Technical Reports Server (NTRS)
Henning, TH.; Dorschner, J.; Guertler, J.
1989-01-01
Distribution functions describing the results of natural processes frequently show the shape of power laws, e.g., mass functions of stars and molecular clouds, velocity spectrum of turbulence, size distributions of asteroids, micrometeorites and also interstellar dust grains. It is an open question whether this behavior is a result simply coming about by the chosen mathematical representation of the observational data or reflects a deep-seated principle of nature. The authors suppose the latter being the case. Using a dust model consisting of silicate and graphite grains Mathis et al. (1977) showed that the interstellar extinction curve can be represented by taking a grain radii distribution of power law type n(a) varies as a(exp -p) with 3.3 less than or equal to p less than or equal to 3.6 (example 1) as a basis. A different approach to understanding power laws like that in example 1 becomes possible by the theory of self-similar processes (scale invariance). The beta model of turbulence (Frisch et al., 1978) leads in an elementary way to the concept of the self-similarity dimension D, a special case of Mandelbrot's (1977) fractal dimension. In the frame of this beta model, it is supposed that on each stage of a cascade the system decays to N clumps and that only the portion beta N remains active further on. An important feature of this model is that the active eddies become less and less space-filling. In the following, the authors assume that grain-grain collisions are such a scale-invarient process and that the remaining grains are the inactive (frozen) clumps of the cascade. In this way, a size distribution n(a) da varies as a(exp -(D+1))da (example 2) results. It seems to be highly probable that the power law character of the size distribution of interstellar dust grains is the result of a self-similarity process. We can, however, not exclude that the process leading to the interstellar grain size distribution is not fragmentation at all. It could be, e
Ultra-low-level measurements of 3H and 14C in wines and champagne
NASA Astrophysics Data System (ADS)
Scherer, U. W.; Jacobi, M.; Castillo, J.; Förstel, D. H.
Methods to measure low concentrations of tritium and radiocarbon in wine and champagne, respectively, have been tested by using liquid scintillation counting after chemical sample processing. It could be shown that tritium activity was too low to be measured by our standard low-level liquid scintillation counter, WALLAC Guardian 1414. Positive results could be achieved when using a WALLAC Quantulus. The methods will be established as standard methods to detect forgeries and to improve consumer safety.
NASA Astrophysics Data System (ADS)
Ercan, A.; Kavvas, M. L.; Haltas, I.
2014-12-01
Geophysical processes could be self-similar under certain similarity transformations at certain time and space dimensions. In this study, the conditions under which the Saint Venant equations system for unsteady open channel flow through irregular channel cross-sections becomes self-similar under various time and space scales are investigated by utilizing one-parameter Lie group of point scaling transformations. Self-similarity conditions due to the initial and boundary conditions are also investigated thoroughly in addition to the conditions due to the governing equations. The proposed scaling relations may provide additional spatial, temporal, and economical flexibility in setting up physical hydraulic models.
Polytropic scaling of a flow Z-pinch
NASA Astrophysics Data System (ADS)
Hughes, M. C.; Shumlak, U.; Nelson, B. A.; Golingo, R. P.; Claveau, E. L.; Doty, S. A.; Forbes, E. G.; Kim, B.; Ross, M. P.; Weed, J. R.
2015-11-01
The ZaP Flow Z-Pinch project investigates the use of velocity shear to mitigate MHD instabilities. The ZaP-HD experiment produces 50 cm long pinches of varying radii. The power to the experiment is split between the plasma formation and acceleration process and the pinch assembly and compression process. Once the pinch is formed, low magnetic fluctuations indicate a quiescent, long-lived pinch. The split power supply allows more control of the pinch current than previous machine iterations, with a designed range from 50 to 150 kA. Radial force balance leads to the Bennett relation which indicates that as the pinch compresses due to increasing currents, the plasma pressure and/or linear density must change. Through ion spectroscopy and digital holographic interferometry coupled with magnetic measurements of the pinch current, the components of the Bennett relation can be fully measured. A scaling relation is then assumed to follow a polytrope as the pinch pressure, initially approximately 250 kPa, increases from an initially formed state to much higher values, approaching 100 MPa. A preliminary analysis of pinch scaling is shown corroborating with other diagnostics on the machine along with extrapolations to required currents for an HEDLP machine. This work is supported by grants from the U.S. Department of Energy and the U.S. National Nuclear Security Administration.
Critical rotation of general-relativistic polytropic models revisited
NASA Astrophysics Data System (ADS)
Geroyannis, V.; Karageorgopoulos, V.
2013-09-01
We develop a perturbation method for computing the critical rotational parameter as a function of the equatorial radius of a rigidly rotating polytropic model in the "post-Newtonia approximation" (PNA). We treat our models as "initial value problems" (IVP) of ordinary differential equations in the complex plane. The computations are carried out by the code dcrkf54.f95 (Geroyannis and Valvi 2012 [P1]; modified Runge-Kutta-Fehlberg code of fourth and fifth order for solving initial value problems in the complex plane). Such a complex-plane treatment removes the syndromes appearing in this particular family of IVPs (see e.g. P1, Sec. 3) and allows continuation of the numerical integrations beyond the surface of the star. Thus all the required values of the Lane-Emden function(s) in the post-Newtonian approximation are calculated by interpolation (so avoiding any extrapolation). An interesting point is that, in our computations, we take into account the complete correction due to the gravitational term, and this issue is a remarkable difference compared to the classical PNA. We solve the generalized density as a function of the equatorial radius and find the critical rotational parameter. Our computations are extended to certain other physical characteristics (like mass, angular momentum, rotational kinetic energy, etc). We find that our method yields results comparable with those of other reliable methods. REFERENCE: V.S. Geroyannis and F.N. Valvi 2012, International Journal of Modern Physics C, 23, No 5, 1250038:1-15.
Even perturbations of the self-similar Vaidya space-time
Nolan, Brien C.; Waters, Thomas J.
2005-05-15
We study even parity metric and matter perturbations of all angular modes in self-similar Vaidya space-time. We focus on the case where the background contains a naked singularity. Initial conditions are imposed, describing a finite perturbation emerging from the portion of flat space-time preceding the matter-filled region of space-time. The most general perturbation satisfying the initial conditions is allowed to impinge upon the Cauchy horizon (CH), where the perturbation remains finite: There is no 'blue-sheet' instability. However, when the perturbation evolves through the CH and onto the second future similarity horizon of the naked singularity, divergence necessarily occurs: This surface is found to be unstable. The analysis is based on the study of individual modes following a Mellin transform of the perturbation. We present an argument that the full perturbation remains finite after resummation of the (possibly infinite number of) modes.
NASA Astrophysics Data System (ADS)
Bayerlein, Bernd; Zaslansky, Paul; Dauphin, Yannicke; Rack, Alexander; Fratzl, Peter; Zlotnikov, Igor
2014-12-01
Significant progress has been made in understanding the interaction between mineral precursors and organic components leading to material formation and structuring in biomineralizing systems. The mesostructure of biological materials, such as the outer calcitic shell of molluscs, is characterized by many parameters and the question arises as to what extent they all are, or need to be, controlled biologically. Here, we analyse the three-dimensional structure of the calcite-based prismatic layer of Pinna nobilis, the giant Mediterranean fan mussel, using high-resolution synchrotron-based microtomography. We show that the evolution of the layer is statistically self-similar and, remarkably, its morphology and mesostructure can be fully predicted using classical materials science theories for normal grain growth. These findings are a fundamental step in understanding the constraints that dictate the shape of these biogenic minerals and shed light on how biological organisms make use of thermodynamics to generate complex morphologies.
NASA Technical Reports Server (NTRS)
Golitsyn, G. S.
1977-01-01
The main results were the formulas for the mean convection velocities, of a viscous fluid and for the mean temperature difference in the bulk of the convecting fluid. These were obtained: by scaling analysis of the Boussinesq equations, by analysis of the energetics of the process, and by using similarity and dimensional arguments. The last approach defines the criteria of similarity and allows the proposition of some self-similarity hypotheses. By several simple new ways, an expression for the efficiency coefficient gamma of the thermal convection was also obtained. An analogy is pointed out between non-turbulent convection of a viscous fluid and the structure of turbulence for scales less than Kolmogorov's internal viscous microscale of turbulence.
Self-Similarity and helical symmetry in vortex generator flow simulations
NASA Astrophysics Data System (ADS)
Fernández, U.; Velte, Clara M.; Réthoré, P.-E.; Sørensen, N. N.
2014-12-01
According to experimental observations, the vortices generated by vortex generators have previously been observed to be self-similar for both the axial (uz) and azimuthal (uθ) velocity profiles. Further, the measured vortices have been observed to obey the criteria for helical symmetry. This is a powerful result, since it reduces the highly complex flow to merely four parameters. In the present work, corresponding computer simulations using Reynolds- Averaged Navier-Stokes equations have been carried out and compared to the experimental observations. The main objective of this study is to investigate how well the simulations can reproduce the physics of the flow and if the same analytical model can be applied. Using this model, parametric studies can be significantly reduced and, further, reliable simulations can substantially reduce the costs of the parametric studies themselves.
Self-similar texture modeling using FARIMA processes with applications to satellite images.
Ilow, J; Leung, H
2001-01-01
A texture model for synthetic aperture radar (SAR) images is presented. Specifically, a sea surface in satellite images is modeled using the two-dimensional (2-D) fractionally integrated autoregressive-moving average (FARIMA) process with a non-Gaussian white driving sequence. The FARIMA process is an ARMA type model which is asymptotically self-similar. It captures the long-range as well as short-range spatial dependence structure of an image with a small number of parameters. To estimate these parameters, an efficient estimation procedure based on a spectral fit is presented. Real-life ocean surveillance radar images collected by the RADARSAT sensor are used to evaluate the practicality of this FARIMA approach. Using the radial power spectral density, the new model is shown to provide a more accurate description of the SAR images than the conventional moving-average (MA), autoregressive (AR), and fractionally differenced (FD) models. PMID:18249668
Self-similarity of negative particle production from the Beam Energy Scan Program at STAR
NASA Astrophysics Data System (ADS)
Tokarev, Mikhail
2015-11-01
We present the spectra of negative charged particle production in Au + Au collisions from STAR for the first phase of the RHIC Beam Energy Scan Program measured over a wide range of collision energy sNN=7.7-200GeV, and transverse momentum of produced particle in different centralities at |η| < 0.5. The spectra demonstrate strong dependence on collision energy which enhances with pT. An indication of self-similarity of negative charged particle production in Au + Au collisions is found. The constituent energy loss as a function of energy and centrality of collisions and transverse momentum of inclusive particle was estimated in the z-scaling approach. The energy dependence of the model parameters - the fractal and fragmentation dimensions and “specific heat”, was studied.
Probing self similar structures by studying the frequency of directional changes
NASA Astrophysics Data System (ADS)
Tabei, Ali; Burov, Stanislav; Milbrandt, Andrew; Spurgeon, Kyle
It has been shown that in two and higher dimension, when the time series of individual particle trajectories exist, the distribution of relative angles of motion between successive time intervals of random motions provides information about stochastic processes, which is beyond the information obtained from studying mean squared displacement. We show that this distribution is a useful measure, which provides supplementary information about the structural properties of the media that a random walker is diffusing. We compare the behavior of this measure for common self-similar structures. We show that the distribution of relative angles is a good measure to discriminates different complex structural geometries. EPSCoR capacity building grant and UNI summer fellowship.
Self-similar formation of an inverse cascade in vibrating elastic plates
NASA Astrophysics Data System (ADS)
Düring, Gustavo; Josserand, Christophe; Rica, Sergio
2015-05-01
The dynamics of random weakly nonlinear waves is studied in the framework of vibrating thin elastic plates. Although it has been previously predicted that no stationary inverse cascade of constant wave action flux could exist in the framework of wave turbulence for elastic plates, we present substantial evidence of the existence of a time-dependent inverse cascade, opening up the possibility of self-organization for a larger class of systems. This inverse cascade transports the spectral density of the amplitude of the waves from short up to large scales, increasing the distribution of long waves despite the short-wave fluctuations. This dynamics appears to be self-similar and possesses a power-law behavior in the short-wavelength limit which significantly differs from the exponent obtained via a Kolmogorov dimensional analysis argument. Finally, we show explicitly a tendency to build a long-wave coherent structure in finite time.
Kagan, Grigory; Svyatskiy, D.; Rinderknecht, H. G.; Rosenberg, M. J.; Zylstra, A. B.; Huang, C. -K.; McDevitt, C. J.
2015-09-03
The distribution function of suprathermal ions is found to be self-similar under conditions relevant to inertial confinement fusion hot spots. By utilizing this feature, interference between the hydrodynamic instabilities and kinetic effects is for the first time assessed quantitatively to find that the instabilities substantially aggravate the fusion reactivity reduction. Thus, the ion tail depletion is also shown to lower the experimentally inferred ion temperature, a novel kinetic effect that may explain the discrepancy between the exploding pusher experiments and rad-hydro simulations and contribute to the observation that temperature inferred from DD reaction products is lower than from DT atmore » the National Ignition Facility.« less
NASA Astrophysics Data System (ADS)
Robinson, A. P. L.; Schmitz, H.; Fox, T. E.; Pasley, J.; Symes, D. R.
2015-03-01
When strong shocks interact with transverse density gradients, it is well known that vorticity deposition occurs. When two non-planar blast waves interact, a strong shock will propagate through the internal structure of each blast wave where the shock encounters such density gradients. There is therefore the potential for the resulting vorticity to produce pronounced density structures long after the passage of these shocks. If the two blast waves have evolved to the self-similar (Sedov) phase this is not a likely prospect, but for blast waves at a relatively early stage of their evolution this remains possible. We show, using 2D numerical simulations, that the interactions of two 'marginally young' blast waves can lead to strong vorticity deposition which leads to the generation of a strong protrusion and vortex ring as mass is driven into the internal structure of the weaker blast wave.
Bayerlein, Bernd; Zaslansky, Paul; Dauphin, Yannicke; Rack, Alexander; Fratzl, Peter; Zlotnikov, Igor
2014-12-01
Significant progress has been made in understanding the interaction between mineral precursors and organic components leading to material formation and structuring in biomineralizing systems. The mesostructure of biological materials, such as the outer calcitic shell of molluscs, is characterized by many parameters and the question arises as to what extent they all are, or need to be, controlled biologically. Here, we analyse the three-dimensional structure of the calcite-based prismatic layer of Pinna nobilis, the giant Mediterranean fan mussel, using high-resolution synchrotron-based microtomography. We show that the evolution of the layer is statistically self-similar and, remarkably, its morphology and mesostructure can be fully predicted using classical materials science theories for normal grain growth. These findings are a fundamental step in understanding the constraints that dictate the shape of these biogenic minerals and shed light on how biological organisms make use of thermodynamics to generate complex morphologies. PMID:25326825
Self-similarity, conservation of entropy/bits and the black hole information puzzle
NASA Astrophysics Data System (ADS)
Singleton, Douglas; Vagenas, Elias C.; Zhu, Tao
2014-05-01
John Wheeler coined the phrase "it from bit" or "bit from it" in the 1980s. However, much of the interest in the connection between information, i.e. "bits", and physical objects, i.e. "its", stems from the discovery that black holes have characteristics of thermodynamic systems having entropies and temperatures. This insight led to the information loss problem — what happens to the "bits" when the black hole has evaporated away due to the energy loss from Hawking radiation? In this essay we speculate on a radical answer to this question using the assumption of self-similarity of quantum correction to the gravitational action and the requirement that the quantum corrected entropy be well behaved in the limit when the black hole mass goes to zero.
Observation of Self-Similar Behavior of the 3D, Nonlinear Rayleigh-Taylor Instability
Sadot, O.; Smalyuk, V.A.; Delettrez, J.A.; Sangster, T.C.; Goncharov, V.N.; Meyerhofer, D.D.; Betti, R.; Shvarts, D.
2005-12-31
The Rayleigh-Taylor unstable growth of laser-seeded, 3D broadband perturbations was experimentally measured in the laser-accelerated, planar plastic foils. The first experimental observation showing the self-similar behavior of the bubble size and amplitude distributions under ablative conditions is presented. In the nonlinear regime, the modulation {sigma}{sub rms} grows as {alpha}{sub {sigma}}gt{sup 2}, where g is the foil acceleration, t is the time, and {alpha}{sub {sigma}} is constant. The number of bubbles evolves as N(t){proportional_to}({omega}t{radical}(g)+C){sup -4} and the average size evolves as <{lambda}>(t){proportional_to}{omega}{sup 2}gt{sup 2}, where C is a constant and {omega}=0.83{+-}0.1 is the measured scaled bubble-merging rate.
Self-similarity and non-Markovian behavior in traded stock volumes
NASA Astrophysics Data System (ADS)
Brown, Frank R.; Pravica, David; Bier, Martin
2015-11-01
The volume traded daily for 17 stocks is followed over a period of about half a century. We look at the volume of stocks traded in a certain time interval (day, week, month) and analyze how long that traded volume keeps monotonically increasing or decreasing. On all three times scales we find that the sequence of traded volumes behaves neither like a sequence of independent and identically distributed variables, nor like a Markov sequence. A compressed exponential survival function with the same parameters at all timescales is firmly established. A day with an increase (decrease) of traded volume is most likely followed by a day with a decrease (increase) of traded volume. We show how the apparent self-similarity results because the small day-to-day anticorrelation carries over when larger time intervals are considered. The observed small anticorrelation can be explained as a consequence of market forces and trader reactions.
Self-similar pulse-shape mode for femtosecond pulse propagation in medium with resonant nonlinearity
NASA Astrophysics Data System (ADS)
Trofimov, Vyacheslav A.; Zakharova, Irina G.; Konar, Swapan
2014-05-01
We investigate the mode of laser pulse propagation in homogeneous medium with resonant nonlinearity, at which the shape of pulse is self-similar one along some distance of propagation. We take into account a laser pulse frequency detuning from resonant frequency. Both types of sign for frequency detuning are considered. This results in appearance of a refractive index grating which induced self-action of a laser pulse. I certain cases we develop analytical solution of corresponding nonlinear eigenfunction problem of laser pulse propagation in medium for multi-photon resonance. This solution is confirmed by computer simulation of an eigenfunction problem for Schrödinger equation with considered nonlinearity. Using computer simulation, one shows a validity of existence of such kind of laser pulse propagation in a medium with resonant nonlinear response.
Scale-invariant cellular automata and self-similar Petri nets
NASA Astrophysics Data System (ADS)
Schaller, M.; Svozil, K.
2009-05-01
Two novel computing models based on an infinite tessellation of space-time are introduced. They consist of recursively coupled primitive building blocks. The first model is a scale-invariant generalization of cellular automata, whereas the second one utilizes self-similar Petri nets. Both models are capable of hypercomputations and can, for instance, “solve” the halting problem for Turing machines. These two models are closely related, as they exhibit a step-by-step equivalence for finite computations. On the other hand, they differ greatly for computations that involve an infinite number of building blocks: the first one shows indeterministic behavior, whereas the second one halts. Both models are capable of challenging our understanding of computability, causality, and space-time.
Self-Similar evolution of Richtmyer-Meshkov instability under re-shock conditions
NASA Astrophysics Data System (ADS)
Malamud, Guy; Leinov, Eli; Formoza, Asi; Sadot, Oren; Levin, Arie; Ben-Dor, Gabi; Elbaz, Yonatan; Shvarts, Dov
2011-10-01
The Richtmyer-Meshkov (RM) instability is of critical importance in inertial confinement fusion (ICF) and astrophysics. In the present work a systematic study has been made of the growth of the turbulent mixing zone (TMZ) under re-shock conditions. In this study, shock-tube experiments were done by Leinov et al. changing the re-shock arrival time, by varying the shock-tube end wall distance, as well as the shock Mach number. Using 3D direct numerical simulations as well as 3D bubble-competition model, for various initial 3D conditions, it was found that the best agreement with the experimental results is achieved when the TMZ evolution is dominated by the self-similar behavior of the bubble size and amplitude distributions. The TMZ power law at the first and second shock was deducted from the experimental and numerical data and compared with the results of the bubble competition model.
NASA Astrophysics Data System (ADS)
Zhang, Z.-Z.; Zhou, S.-G.; Zou, T.
2007-04-01
In this paper, firstly, we study analytically the topological features of a family of hierarchical lattices (HLs) from the view point of complex networks. We derive some basic properties of HLs controlled by a parameter q: scale-free degree distribution with exponent γ=2+ln 2/(ln q), null clustering coefficient, power-law behavior of grid coefficient, exponential growth of average path length (non-small-world), fractal scaling with dimension dB=ln (2q)/(ln 2), and disassortativity. Our results show that scale-free networks are not always small-world, and support the conjecture that self-similar scale-free networks are not assortative. Secondly, we define a deterministic family of graphs called small-world hierarchical lattices (SWHLs). Our construction preserves the structure of hierarchical lattices, including its degree distribution, fractal architecture, clustering coefficient, while the small-world phenomenon arises. Finally, the dynamical processes of intentional attacks and collective synchronization are studied and the comparisons between HLs and Barabási-Albert (BA) networks as well as SWHLs are shown. We find that the self-similar property of HLs and SWHLs significantly increases the robustness of such networks against targeted damage on hubs, as compared to the very vulnerable non fractal BA networks, and that HLs have poorer synchronizability than their counterparts SWHLs and BA networks. We show that degree distribution of scale-free networks does not suffice to characterize their synchronizability, and that networks with smaller average path length are not always easier to synchronize.
Co-location and Self-Similar Topologies of Urban Infrastructure Networks
NASA Astrophysics Data System (ADS)
Klinkhamer, Christopher; Zhan, Xianyuan; Ukkusuri, Satish; Elisabeth, Krueger; Paik, Kyungrock; Rao, Suresh
2016-04-01
The co-location of urban infrastructure is too obvious to be easily ignored. For reasons of practicality, reliability, and eminent domain, the spatial locations of many urban infrastructure networks, including drainage, sanitary sewers, and road networks, are well correlated. However, important questions dealing with correlations in the network topologies of differing infrastructure types remain unanswered. Here, we have extracted randomly distributed, nested subnets from the urban drainage, sanitary sewer, and road networks in two distinctly different cities: Amman, Jordan; and Indianapolis, USA. Network analyses were performed for each randomly chosen subnet (location and size), using a dual-mapping approach (Hierarchical Intersection Continuity Negotiation). Topological metrics for each infrastructure type were calculated and compared for all subnets in a given city. Despite large differences in the climate, governance, and populace of the two cities, and functional properties of the different infrastructure types, these infrastructure networks are shown to be highly spatially homogenous. Furthermore, strong correlations are found between topological metrics of differing types of surface and subsurface infrastructure networks. Also, the network topologies of each infrastructure type for both cities are shown to exhibit self-similar characteristics (i.e., power law node-degree distributions, [p(k) = ak-γ]. These findings can be used to assist city planners and engineers either expanding or retrofitting existing infrastructure, or in the case of developing countries, building new cities from the ground up. In addition, the self-similar nature of these infrastructure networks holds significant implications for the vulnerability of these critical infrastructure networks to external hazards and ways in which network resilience can be improved.
NASA Astrophysics Data System (ADS)
Niethammer, B.; Velázquez, J. J. L.
2014-10-01
We consider self-similar solutions to Smoluchowski's coagulation equation for kernels that are homogeneous of degree zero and close to constant in the sense that for . We prove that self-similar solutions with given mass are unique if is sufficiently small which is the first such uniqueness result for kernels that are not solvable. Our proof relies on a contraction argument in a norm that measures the distance of solutions with respect to the weak topology of measures.
NASA Astrophysics Data System (ADS)
Liger-Belair, G.
2002-07-01
People have long been fascinated by bubbles and foams dynamics, and since the pioneering work of Leonardo da Vinci in the early 16th century, this subject has generated a huge bibliography. However, only very recently, much interest was devoted to bubbles in Champagne wines. Small bubbles rising through the liquid, as well as a bubble ring (the so-called collar) at the periphery of a flute poured with champagne are the hallmark of this traditionally festive wine, and even there is no scientific evidence yet to connect the quality of a champagne with its effervescence, people nevertheless often make a connection between them. Therefore, since the last few years, a better understanding of the numerous parameters involved in the bubbling process has become an important stake in the champagne research area. Otherwise, in addition to these strictly enological reasons, we also feel that the area of bubble dynamics could benefit from the simple but close observation of a glass poured with champagne. In this study, our first results concerning the close observation of the three main steps of a champagne bubble's life are presented, that is, the bubble nucleation on tiny particles stuck on the glass wall (Chap. 2), the bubble ascent through the liquid (Chap. 3), and the bursting of bubbles at the free surface, which constitutes the most intriguing and visually appealing step (Chap. 4). Our results were obtained in real consuming conditions, that is, in a classical crystal flute poured with a standard commercial champagne wine. Champagne bubble nucleation proved to be a fantastic everyday example to illustrate the non-classical heterogeneous bubble nucleation process in a weakly supersaturated liquid. Contrary to a generally accepted idea, nucleation sites are not located on irregularities of the glass itself. Most of nucleation sites are located on tiny hollow and roughly cylindrical exogenous fibres coming from the surrounding air or remaining from the wiping process
Self-similar roll-up of a vortex sheet driven by a shear flow: Hyperbolic double spiral
NASA Astrophysics Data System (ADS)
Sohn, Sung-Ik
2016-06-01
In this paper, we consider the roll-up of an infinite vortex sheet and investigate its self-similar behavior. We address the question of whether the unsteady double spiral produced by the curvature singularity in finite time exhibits self-similar behavior. We find a self-similar solution of the double-spiral vortex sheet, which in fact, is a hyperbolic spiral. The radius of the spiral asymptotically grows with time and is proportional to the inverse of the angle from the spiral center. The curvature singularity plays the role of triggering spiral formation, but the source of vorticity for forming the spiral is the initial vorticity of the sheet. We show analytically that the self-similar solution satisfies the Birkhoff-Rott equation asymptotically. Numerical validation is also given by applying the blob-regularization model to the vortex sheet with a periodic perturbation. We examine various asymptotic relations among primitive variables for the spiral turns and find agreement of numerical results of the inner turns of the vortex sheet with the analytic solution. Our study clarifies contrasting results on the existence of the self-similar double-spiral of a large structure in the previous studies. Our solution also suggests the possibility of bifurcation of the self-similar solution of the double-spiral as the sheet strength varies.
NASA Astrophysics Data System (ADS)
Xie, S.; Archer, C. L.
2013-12-01
In this study, a new large-eddy simulation code, the Wind Turbine and Turbulence Simulator (WiTTS), is developed to study the wake generated from a single wind turbine in the neutral ABL. The WiTTS formulation is based on a scale-dependent Lagrangian dynamical model of the sub-grid shear stress and uses actuator lines to simulate the effects of the rotating blades. WiTTS is first tested against wind tunnel experiments and then used to study the commonly-used assumptions of self-similarity and axis-symmetry of the wake under neutral conditions for a variety of wind speeds and turbine properties. The mean velocity deficit shows good self-similarity properties following a normal distribution in the horizontal plane at the hub-height level. Self-similarity is a less valid approximation in the vertical near the ground, due to strong wind shear and ground effects. The mean velocity deficit is strongly dependent on the thrust coefficient or induction factor. A new relationship is proposed to model the mean velocity deficit along the centerline at the hub-height level to fit the LES results piecewise throughout the wake. A logarithmic function is used in the near and intermediate wake regions whereas a power function is used in the far-wake. These two functions provide a better fit to both simulated and observed wind velocity deficits than other functions previously used in wake models such as WAsP. The wind shear and impact with the ground cause an anisotropy in the expansion of the wake such that the wake grows faster horizontally than vertically. The wake deforms upon impact with the ground and spreads laterally. WiTTS is also used to study the turbulence characteristics in the wake. Aligning with the mean wind direction, the streamwise component of turbulence intensity is the dominant among the three components and thus it is further studied. The highest turbulence intensity occurs near the top-tip level. The added turbulence intensity increases fast in the near
Human-based percussion and self-similarity detection in electroacoustic music
NASA Astrophysics Data System (ADS)
Mills, John Anderson, III
Electroacoustic music is music that uses electronic technology for the compositional manipulation of sound, and is a unique genre of music for many reasons. Analyzing electroacoustic music requires special measures, some of which are integrated into the design of a preliminary percussion analysis tool set for electroacoustic music. This tool set is designed to incorporate the human processing of music and sound. Models of the human auditory periphery are used as a front end to the analysis algorithms. The audio properties of percussivity and self-similarity are chosen as the focus because these properties are computable and informative. A collection of human judgments about percussion was undertaken to acquire clearly specified, sound-event dimensions that humans use as a percussive cue. A total of 29 participants was asked to make judgments about the percussivity of 360 pairs of synthesized snare-drum sounds. The grouped results indicate that of the dimensions tested rise time is the strongest cue for percussivity. String resonance also has a strong effect, but because of the complex nature of string resonance, it is not a fundamental dimension of a sound event. Gross spectral filtering also has an effect on the judgment of percussivity but the effect is weaker than for rise time and string resonance. Gross spectral filtering also has less effect when the stronger cue of rise time is modified simultaneously. A percussivity-profile algorithm (PPA) is designed to identify those instants in pieces of music that humans also would identify as percussive. The PPA is implemented using a time-domain, channel-based approach and psychoacoustic models. The input parameters are tuned to maximize performance at matching participants' choices in the percussion-judgment collection. After the PPA is tuned, the PPA then is used to analyze pieces of electroacoustic music. Real electroacoustic music introduces new challenges for the PPA, though those same challenges might affect
Mayeda, K; Malagnini, L; Walter, W R
2007-03-16
This study is motivated by renewed interest within the seismic source community to resolve the long-standing question on energy scaling of earthquakes, specifically, 'Do earthquakes scale self-similarly or are large earthquakes dynamically different than small ones?' This question is important from a seismic hazard prediction point of view, as well as for understanding basic rupture dynamics for earthquakes. Estimating the total radiated energy (ER) from earthquakes requires significant broadband corrections for path and site effects. Moreover, source radiation pattern and directivity corrections can be equally significant and also must be accounted for. Regional studies have used a number of different methods, each with their own advantages and disadvantages. These methods include: integration of squared shear wave moment-rate spectra, direct integration of broadband velocity-squared waveforms, empirical Green's function deconvolution, and spectral ratio techniques. The later two approaches have gained popularity because adjacent or co-located events recorded at common stations have shared path and site effects, which therefore cancel. In spite of this, a number of such studies find very large amplitude variance across a network of stations. In this paper we test the extent to which narrowband coda envelopes can improve upon the traditional spectral ratio using direct phases, allowing a better comparison with theoretical models to investigate similarity. The motivation for using the coda is its stability relative to direct waves and its unique property of spatially homogenizing its energy. The local and regional coda is virtually insensitive to lateral crustal heterogeneity and source radiation pattern, and the use of the coda might allow for more stable amplitude ratios to better constrain source differences between event pairs. We first compared amplitude ratio performance between local and near-regional S and coda waves in the San Francisco Bay region for
Self-Similar Conformations and Dynamics of Non-Concatenated Entangled Ring Polymers
NASA Astrophysics Data System (ADS)
Ge, Ting
A scaling model of self-similar conformations and dynamics of non-concatenated entangled ring polymers is developed. Topological constraints force these ring polymers into compact conformations with fractal dimension D =3 that we call fractal loopy globules (FLGs). This result is based on the conjecture that the overlap parameter of loops on all length scales is equal to the Kavassalis-Noolandi number 10-20. The dynamics of entangled rings is self-similar, and proceeds as loops of increasing sizes are rearranged progressively at their respective diffusion times. The topological constraints associated with smaller rearranged loops affect the dynamics of larger loops by increasing the effective friction coefficient, but have no influence on the tubes confining larger loops. Therefore, the tube diameter defined as the average spacing between relevant topological constraints increases with time, leading to ``tube dilation''. Analysis of the primitive paths in molecular dynamics (MD) simulations suggests complete tube dilation with the tube diameter on the order of the time-dependent characteristic loop size. A characteristic loop at time t is defined as a ring section that has diffused a distance of its size during time t. We derive dynamic scaling exponents in terms of fractal dimensions of an entangled ring and the underlying primitive path and a parameter characterizing the extent of tube dilation. The results reproduce the predictions of different dynamic models of a single non-concatenated entangled ring. We demonstrate that traditional generalization of single-ring models to multi-ring dynamics is not self-consistent and develop a FLG model with self-consistent multi-ring dynamics and complete tube dilation. Various dynamic scaling exponents predicted by the self-consistent FLG model are consistent with recent computer simulations and experiments. We also perform MD simulations of nanoparticle (NP) diffusion in melts of non-concatenated entangled ring polymers
NASA Astrophysics Data System (ADS)
Lou, Yu-Qing; Hu, Xu-Yao
2016-06-01
We present a theoretical model framework for general polytropic (GP) hydrodynamic cylinder under self-gravity of infinite length with axial uniformity and axisymmetry. For self-similar dynamic solutions, we derive valuable integrals, analytic asymptotic solutions, sonic critical curves, shock conditions, and global numerical solutions with or without expansion shocks. Among others, we investigate various dynamic solutions featured with central free-fall asymptotic behaviours, corresponding to a collapsed mass string with a sustained dynamic accretion from a surrounding mass reservoir. Depending on the allowed ranges of a scaling index a < -1, such cylindrical dynamic mass accretion rate could be steady, increasing with time and decreasing with time. Physically, such a collapsed mass string or filament would break up into a sequence of sub-clumps and segments as induced by gravitational Jeans instabilities. Depending on the scales involved, such sub-clumps would evolve into collapsed objects or gravitationally bound systems. In diverse astrophysical and cosmological contexts, such a scenario can be adapted on various temporal, spatial and mass scales to form a chain of collapsed clumps and/or compact objects. Examples include the formation of chains of proto-stars, brown dwarfs and gaseous planets along molecular filaments; the formation of luminous massive stars along magnetized spiral arms and circum-nuclear starburst rings in barred spiral galaxies; the formation of chains of compact stellar objects such as white dwarfs, neutron stars, and black holes along a highly condensed mass string. On cosmological scales, one can perceive the formation of chains of galaxies, chains of galaxy clusters or even chains of supermassive and hypermassive black holes in the Universe including the early Universe. All these chains referred to above include possible binaries.
Distinctive Order Based Self-Similarity descriptor for multi-sensor remote sensing image matching
NASA Astrophysics Data System (ADS)
Sedaghat, Amin; Ebadi, Hamid
2015-10-01
Robust, well-distributed and accurate feature matching in multi-sensor remote sensing image is a difficult task duo to significant geometric and illumination differences. In this paper, a robust and effective image matching approach is presented for multi-sensor remote sensing images. The proposed approach consists of three main steps. In the first step, UR-SIFT (Uniform robust scale invariant feature transform) algorithm is applied for uniform and dense local feature extraction. In the second step, a novel descriptor namely Distinctive Order Based Self Similarity descriptor, DOBSS descriptor, is computed for each extracted feature. Finally, a cross matching process followed by a consistency check in the projective transformation model is performed for feature correspondence and mismatch elimination. The proposed method was successfully applied for matching various multi-sensor satellite images as: ETM+, SPOT 4, SPOT 5, ASTER, IRS, SPOT 6, QuickBird, GeoEye and Worldview sensors, and the results demonstrate its robustness and capability compared to common image matching techniques such as SIFT, PIIFD, GLOH, LIOP and LSS.
Multidimensional self-similar analytical solutions of two-phase flow in porous media
NASA Astrophysics Data System (ADS)
Fučík, Radek; Illangasekare, Tissa H.; Beneš, Michal
2016-04-01
In general, analytical solutions serve a useful purpose to obtain better insights and to verify numerical codes. For flow of two incompressible and immiscible phases in homogeneous porous media without gravity, one such method that neglects capillary pressure in the solution was first developed by Buckley and Leverett (1942). Subsequently, McWhorter and Sunada (1990) derived an exact solution for the one and two dimensional cases that factored in capillary effects. This solution used a similarity transform that allowed to reduce the governing equations into a single ordinary differential equation (ODE) that can be further integrated into an equivalent integral equation. We present a revision to McWhorter and Sunada solution by extending the self-similar solution into a general multidimensional space. Inspired by the derivation proposed by McWhorter and Sunada (1990), we integrate the resulting ODE in the third and higher dimensions into a new integral equation that can be subsequently solved iteratively by means of numerical integration. We developed implementations of the iterative schemes for one- and higher dimensional cases that can be accessed online on the authors' website.
Fast Diffusion to Self-Similarity: Complete Spectrum, Long-Time Asymptotics, and Numerology
NASA Astrophysics Data System (ADS)
Denzler, Jochen; McCann, Robert J.
2005-03-01
The complete spectrum is determined for the operator on the Sobolev space W1,2ρ(Rn) formed by closing the smooth functions of compact support with respect to the norm Here the Barenblatt profile ρ is the stationary attractor of the rescaled diffusion equation in the fast, supercritical regime m the same diffusion dynamics represent the steepest descent down an entropy E(u) on probability measures with respect to the Wasserstein distance d2. Formally, the operator H=HessρE is the Hessian of this entropy at its minimum ρ, so the spectral gap H≧α:=2-n(1-m) found below suggests the sharp rate of asymptotic convergence: from any centered initial data 0≦u(0,x) ∈ L1(Rn) with second moments. This bound improves various results in the literature, and suggests the conjecture that the self-similar solution u(t,x)=R(t)-nρ(x/R(t)) is always slowest to converge. The higher eigenfunctions which are polynomials with hypergeometric radial parts and the presence of continuous spectrum yield additional insight into the relations between symmetries of Rn and the flow. Thus the rate of convergence can be improved if we are willing to replace the distance to ρ with the distance to its nearest mass-preserving dilation (or still better, affine image). The strange numerology of the spectrum is explained in terms of the number of moments of ρ.
Dynamic neural-based buffer management for Queuing systems with self-similar characteristics.
Yousefi'zadeh, Homayoun; Jonckheere, Edmond A
2005-09-01
Buffer management in queuing systems plays an important role in addressing the tradeoff between efficiency measured in terms of overall packet loss and fairness measured in terms of individual source packet loss. Complete partitioning (CP) of a buffer with the best fairness characteristic and complete sharing (CS) of a buffer with the best efficiency characteristic are at the opposite ends of the spectrum of buffer management techniques. Dynamic partitioning buffer management techniques aim at addressing the tradeoff between efficiency and fairness. Ease of implementation is the key issue when determining the practicality of a dynamic buffer management technique. In this paper, two novel dynamic buffer management techniques for queuing systems accommodating self-similar traffic patterns are introduced. The techniques take advantage of the adaptive learning power of perceptron neural networks when applied to arriving traffic patterns of queuing systems. Relying on the water-filling approach, our proposed techniques are capable of coping with the tradeoff between packet loss and fairness issues. Computer simulations reveal that both of the proposed techniques enjoy great efficiency and fairness characteristics as well as ease of implementation. PMID:16252824
Dark energy in six nearby galaxy flows: Synthetic phase diagrams and self-similarity
NASA Astrophysics Data System (ADS)
Chernin, A. D.; Teerikorpi, P.; Dolgachev, V. P.; Kanter, A. A.; Domozhilova, L. M.; Valtonen, M. J.; Byrd, G. G.
2012-09-01
Outward flows of galaxies are observed around groups of galaxies on spatial scales of about 1 Mpc, and around galaxy clusters on scales of 10 Mpc. Using recent data from the Hubble Space Telescope (HST), we have constructed two synthetic velocity-distance phase diagrams: one for four flows on galaxy-group scales and the other for two flows on cluster scales. It has been shown that, in both cases, the antigravity produced by the cosmic dark-energy background is stronger than the gravity produced by the matter in the outflow volume. The antigravity accelerates the flows and introduces a phase attractor that is common to all scales, corresponding to a linear velocity-distance relation (the local Hubble law). As a result, the bundle of outflow trajectories mostly follow the trajectory of the attractor. A comparison of the two diagrams reveals the universal self-similar nature of the outflows: their gross phase structure in dimensionless variables is essentially independent of their physical spatial scales, which differ by approximately a factor of 10 in the two diagrams.
Self-similar inverse cascade of magnetic helicity driven by the chiral anomaly
Hirono, Yuji; Kharzeev, Dmitri E.; Yin, Yi
2015-12-28
For systems with charged chiral fermions, the imbalance of chirality in the presence of magnetic field generates an electric current—this is the chiral magnetic effect (CME). We study the dynamical real-time evolution of electromagnetic fields coupled by the anomaly to the chiral charge density and the CME current by solving the Maxwell-Chern-Simons equations. We find that the CME induces the inverse cascade of magnetic helicity toward the large distances, and that at late times this cascade becomes self-similar, with universal exponents. We also find that in terms of gauge field topology the inverse cascade represents the transition from linked electricmore » and magnetic fields (Hopfions) to the knotted configuration of magnetic field (Chandrasekhar-Kendall states). The magnetic reconnections are accompanied by the pulses of the CME current directed along the magnetic field lines. In conclusion, we devise an experimental signature of these phenomena in heavy ion collisions, and speculate about implications for condensed matter systems.« less
Spiral-driven accretion in protoplanetary discs. II. Self-similar solutions
NASA Astrophysics Data System (ADS)
Hennebelle, Patrick; Lesur, Geoffroy; Fromang, Sébastien
2016-04-01
Context. Accretion discs are ubiquitous in the Universe, and it is crucial to understand how angular momentum and mass are radially transported in these objects. Aims: Here, we study the role played by non-linear spiral patterns within hydrodynamical and non-self-gravitating accretion discs assuming that external disturbances such as infall onto the disc may trigger them. Methods: To do so, we computed self-similar solutions that describe discs in which a spiral wave propagates. These solutions present shocks and critical sonic points that were analyzed. Results: We calculated the wave structure for all allowed temperatures and for several spiral shocks. In particular, we inferred the angle of the spiral pattern, the stress it exerts on the disc, and the associated flux of mass and angular momentum as a function of temperature. We quantified the rate of angular momentum transport by means of the dimensionless α parameter. For the thickest disc we considered (corresponding to h/r values of about one-third), we found values of α as high as 0.1 that scaled with the temperature T such that α ∝ T3 / 2 ∝ (h/r)3. The spiral angle scales with the temperature as arctan(r/h). Conclusions: These solutions suggests that perturbations occurring at disc outer boundaries, such as perturbations due to infall motions, can propagate deep inside the disc and therefore should not be ignored, even when considering small radii.
Self-similar distribution of oil spills in European coastal waters
NASA Astrophysics Data System (ADS)
Redondo, Jose M; Platonov, Alexei K
2009-01-01
Marine pollution has been highlighted thanks to the advances in detection techniques as well as increasing coverage of catastrophes (e.g. the oil tankers Amoco Cadiz, Exxon Valdez, Erika, and Prestige) and of smaller oil spills from ships. The new satellite based sensors SAR and ASAR and new methods of oil spill detection and analysis coupled with self-similar statistical techniques allow surveys of environmental pollution monitoring large areas of the ocean. We present a statistical analysis of more than 700 SAR images obtained during 1996-2000, also comparing the detected small pollution events with the historical databases of great marine accidents during 1966-2004 in European coastal waters. We show that the statistical distribution of the number of oil spills as a function of their size corresponds to Zipf's law, and that the common small spills are comparable to the large accidents due to the high frequency of the smaller pollution events. Marine pollution from tankers and ships, which has been detected as oil spills between 0.01 and 100 km2, follows the marine transit routes. Multi-fractal methods are used to distinguish between natural slicks and spills, in order to estimate the oil spill index in European coastal waters, and in particular, the north-western Mediterranean Sea, which, due to the influence of local winds, shows optimal conditions for oil spill detection.
Manifold angles, the concept of self-similarity, and angle-enhanced bifurcation diagrams
NASA Astrophysics Data System (ADS)
Beims, Marcus W.; Gallas, Jason A. C.
2016-01-01
Chaos and regularity are routinely discriminated by using Lyapunov exponents distilled from the norm of orthogonalized Lyapunov vectors, propagated during the temporal evolution of the dynamics. Such exponents are mean-field-like averages that, for each degree of freedom, squeeze the whole temporal evolution complexity into just a single number. However, Lyapunov vectors also contain a step-by-step record of what exactly happens with the angles between stable and unstable manifolds during the whole evolution, a big-data information permanently erased by repeated orthogonalizations. Here, we study changes of angles between invariant subspaces as observed during temporal evolution of Hénon’s system. Such angles are calculated numerically and analytically and used to characterize self-similarity of a chaotic attractor. In addition, we show how standard tools of dynamical systems may be angle-enhanced by dressing them with informations not difficult to extract. Such angle-enhanced tools reveal unexpected and practical facts that are described in detail. For instance, we present a video showing an angle-enhanced bifurcation diagram that exposes from several perspectives the complex geometrical features underlying the attractors. We believe such findings to be generic for extended classes of systems.
Self-similarity and universality of void density profiles in simulation and SDSS data
NASA Astrophysics Data System (ADS)
Nadathur, S.; Hotchkiss, S.; Diego, J. M.; Iliev, I. T.; Gottlöber, S.; Watson, W. A.; Yepes, G.
2015-06-01
The stacked density profile of cosmic voids in the galaxy distribution provides an important tool for the use of voids for precision cosmology. We study the density profiles of voids identified using the ZOBOV watershed transform algorithm in realistic mock luminous red galaxy (LRG) catalogues from the Jubilee simulation, as well as in void catalogues constructed from the SDSS LRG and Main Galaxy samples. We compare different methods for reconstructing density profiles scaled by the void radius and show that the most commonly used method based on counts in shells and simple averaging is statistically flawed as it underestimates the density in void interiors. We provide two alternative methods that do not suffer from this effect; one based on Voronoi tessellations is also easily able to account from artefacts due to finite survey boundaries and so is more suitable when comparing simulation data to observation. Using this method, we show that the most robust voids in simulation are exactly self-similar, meaning that their average rescaled profile does not depend on the void size. Within the range of our simulation, we also find no redshift dependence of the mean profile. Comparison of the profiles obtained from simulated and real voids shows an excellent match. The mean profiles of real voids also show a universal behaviour over a wide range of galaxy luminosities, number densities and redshifts. This points to a fundamental property of the voids found by the watershed algorithm, which can be exploited in future studies of voids.
Self similarity of two point correlations in wall bounded turbulent flows
NASA Technical Reports Server (NTRS)
Hunt, J. C. R.; Moin, P.; Moser, R. D.; Spalart, P. R.
1987-01-01
The structure of turbulence at a height y from a wall is affected by the local mean shear at y, by the direct effect of the wall on the eddies, and by the action of other eddies close to or far from the wall. Some researchers believe that a single one of these mechanisms is dominant, while others believe that these effects have to be considered together. It is important to understand the relative importance of these effects in order to develop closure models, for example for the dissipation or for the Reynolds stress equation, and to understand the eddy structure of cross correlation functions and other measures. The specific objective was to examine the two point correlation, R sub vv, of the normal velocity component v near the wall in a turbulent channel flow and in a turbulent boundary layer. The preliminary results show that even in the inhomogeneous turbulent boundary layer, the two-point correlation function may have self similar forms. The results also show that the effects of shear and of blocking are equally important in the form of correlation functions for spacing normal to the wall. But for spanwise spacing, it was found that the eddy structure is quire different in these near flows. So any theory for turbulent structure must take both these effects into account.
NASA Astrophysics Data System (ADS)
Piñeiro Orioli, Asier; Boguslavski, Kirill; Berges, Jürgen
2015-07-01
We investigate universal behavior of isolated many-body systems far from equilibrium, which is relevant for a wide range of applications from ultracold quantum gases to high-energy particle physics. The universality is based on the existence of nonthermal fixed points, which represent nonequilibrium attractor solutions with self-similar scaling behavior. The corresponding dynamic universality classes turn out to be remarkably large, encompassing both relativistic as well as nonrelativistic quantum and classical systems. For the examples of nonrelativistic (Gross-Pitaevskii) and relativistic scalar field theory with quartic self-interactions, we demonstrate that infrared scaling exponents as well as scaling functions agree. We perform two independent nonperturbative calculations, first by using classical-statistical lattice simulation techniques and second by applying a vertex-resummed kinetic theory. The latter extends kinetic descriptions to the nonperturbative regime of overoccupied modes. Our results open new perspectives to learn from experiments with cold atoms aspects about the dynamics during the early stages of our universe.
Self-similar evolution of a body eroding in a fluid flow
NASA Astrophysics Data System (ADS)
Moore, Matthew N. J.; Ristroph, Leif; Childress, Stephen; Zhang, Jun; Shelley, Michael J.
2013-11-01
Erosion of solid material by flowing fluids plays an important role in shaping landforms, and in this natural context is often dictated by processes of high complexity. Here, we examine the coupled evolution of solid shape and fluid flow within the idealized setting of a cylindrical body held against a fast, unidirectional flow, and eroding under the action of fluid shear stress. Experiments and simulations both show self-similar evolution of the body, with an emerging quasi-triangular geometry that is an attractor of the shape dynamics. Our fluid erosion model, based on Prandtl boundary layer theory, yields a scaling law that accurately predicts the body's vanishing rate. Further, a class of exact solutions provides a partial prediction for the body's terminal form as one with a leading surface of uniform shear stress. Our simulations show this predicted geometry to emerge robustly from a range of different initial conditions, and allow us to explore its local stability. The sharp, faceted features of the terminal geometry defy the intuition of erosion as a globally smoothing process.
Using Self-Similarity to Simulate Meniscus Evolution Around TMV Due to Surface Diffusion
NASA Astrophysics Data System (ADS)
Potter, Richard; Zhang, Yue; Fakhraai, Zahra
It has been hypothesized that enhanced surface diffusion allows the formation of stable molecular glasses during physical vapor deposition. The improved properties of these glasses, such as increased density and kinetic stability can help improve material properties in pioneering fields of technology such as organic electronics and pharmaceutical drug delivery. While surface diffusion has been measured previously on the surfaces of organic glasses, direct measurements on the surface of vapor-deposited stable glasses has proven more challenging. This research focuses on a straightforward method for measuring the surface diffusion coefficients of molecular glasses through the use of tobacco mosaic virus (TMV) nanorods as probe particles. In conjunction, mathematical models based on the thin film equation were used to simulate fast meniscus formation around the nanorods on the glassy surface. The evolution of the meniscus is self-similar, which allows quick quantification of the diffusion coefficient, by solving the time evolution for a single experiment. Experimental data were compared and fit to these simulations to derive a quantity for the surface diffusion coefficient, Ds. Nsf-CAREER DMR-1350044.
Self-similar inverse cascade of magnetic helicity driven by the chiral anomaly
Hirono, Yuji; Kharzeev, Dmitri E.; Yin, Yi
2015-12-28
For systems with charged chiral fermions, the imbalance of chirality in the presence of magnetic field generates an electric current—this is the chiral magnetic effect (CME). We study the dynamical real-time evolution of electromagnetic fields coupled by the anomaly to the chiral charge density and the CME current by solving the Maxwell-Chern-Simons equations. We find that the CME induces the inverse cascade of magnetic helicity toward the large distances, and that at late times this cascade becomes self-similar, with universal exponents. We also find that in terms of gauge field topology the inverse cascade represents the transition from linked electric and magnetic fields (Hopfions) to the knotted configuration of magnetic field (Chandrasekhar-Kendall states). The magnetic reconnections are accompanied by the pulses of the CME current directed along the magnetic field lines. In conclusion, we devise an experimental signature of these phenomena in heavy ion collisions, and speculate about implications for condensed matter systems.
Self-similar Lagrangian hydrodynamics of beam-heated solar flare atmospheres
NASA Technical Reports Server (NTRS)
Brown, John C.; Emslie, A. Gordon
1989-01-01
The one-dimensional hydrodynamic problem in Lagrangian coordinates (Y, t) is considered for which the specific energy input Q has a power-law dependence on both Y and t, and the initial density distribution is rho(0) which is directly proportional to Y exp gamma. In regimes where the contributions of radiation, conduction, quiescent heating, and gravitational terms in the energy equation are negligible compared to those arising from Q, the problem has a self-similar solution, with the hydrodynamic variables depending only on a single independent variable which is a combination of Y, t, and the dimensional constants of the problem. It is then shown that the problem of solar flare chromospheric heating due to collisional interaction of a beam of electrons (or protons) with a power-law energy spectrum can be approximated by such forms of Q(Y, t) and rho(0)(Y), and that other terms are negligible compared to Q over a restricted regime early in the flare.
Manifold angles, the concept of self-similarity, and angle-enhanced bifurcation diagrams
Beims, Marcus W.; Gallas, Jason A. C.
2016-01-01
Chaos and regularity are routinely discriminated by using Lyapunov exponents distilled from the norm of orthogonalized Lyapunov vectors, propagated during the temporal evolution of the dynamics. Such exponents are mean-field-like averages that, for each degree of freedom, squeeze the whole temporal evolution complexity into just a single number. However, Lyapunov vectors also contain a step-by-step record of what exactly happens with the angles between stable and unstable manifolds during the whole evolution, a big-data information permanently erased by repeated orthogonalizations. Here, we study changes of angles between invariant subspaces as observed during temporal evolution of Hénon’s system. Such angles are calculated numerically and analytically and used to characterize self-similarity of a chaotic attractor. In addition, we show how standard tools of dynamical systems may be angle-enhanced by dressing them with informations not difficult to extract. Such angle-enhanced tools reveal unexpected and practical facts that are described in detail. For instance, we present a video showing an angle-enhanced bifurcation diagram that exposes from several perspectives the complex geometrical features underlying the attractors. We believe such findings to be generic for extended classes of systems. PMID:26732416
Self-similar growth of an alluvial fan fed with bimodal sediment
NASA Astrophysics Data System (ADS)
Delorme, Pauline; Voller, Vaughan; Paola, Chris; Devauchelle, Olivier; Lajeunesse, Eric; Barrier, Laurie; Métivier, François
2016-04-01
At the outlet of mountain ranges, rivers flow onto flatter lowlands. The associated change of slope causes sediment deposition. As the river is free to move laterally, it builds conical sedimentary structures called alluvial fans. Their location at the interface between erosional and depositional areas makes them valuable sedimentary archives. To decipher these sedimentary records, we need to understand the dynamics of their growth. We carried out a series of experiments to investigate the growth of alluvial fans fed with mixed sediments. The density difference between silica and coal sediments mimics a bimodal grain-size distribution in nature. The sediment and water discharges are constant during an experiment. During the run, we track the evolution of the surface pattern by digital imaging. At the end of each run, we acquire the fan topography using a scanning laser. Finally, we cut a radial cross section to visualize the sedimentary deposit. We observe there is a distinct slope break at the transition that dominates the overall curvature of the fan surface. Based on mass conservation and observations, we propose that this alluvial fan grows in a self-similar way, thus causing the transition between silica and coal deposits to be a straight line. The shape of the experimental transition accords with this prediction.
Self-Similar Random Process and Chaotic Behavior In Serrated Flow of High Entropy Alloys
NASA Astrophysics Data System (ADS)
Chen, Shuying; Yu, Liping; Ren, Jingli; Xie, Xie; Li, Xueping; Xu, Ying; Zhao, Guangfeng; Li, Peizhen; Yang, Fuqian; Ren, Yang; Liaw, Peter K.
2016-07-01
The statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, and there is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk.
SELF-SIMILAR STRUCTURE OF A HOT MAGNETIZED FLOW WITH THERMAL CONDUCTION
Ghasemnezhad, M.; Khajavi, M.; Abbassi, S.
2012-05-01
We have explored the structure of a hot magnetized accretion flow with thermal conduction. The importance of thermal conduction in hot accretion flows has been confirmed by observations of the hot gas surrounding Sgr A* and a few other nearby galactic nuclei. For a steady state structure of such accretion flows, a set of self-similar solutions is presented. In this paper, we have actually tried to re-check the solution presented by Abbassi et al. using a physical constraint. In this study, we find that Equation (29) places a new constraint that limits answers presented by Abbassi et al. In that paper, the parameter space, which is established in the new constraint, was plotted. However, the new requirement makes up only a small parameter space with physically acceptable solutions. And now in this paper, we have followed the idea with more effort and tried to find out how thermal conduction influences the structure of the disks in a physical parameter space. We have found that the existence of thermal conduction will lead to the reduction of accretion and radial and azimuthal velocities as well as the vertical thickness of the disk, which is slightly reduced. Moreover, the surface density of the disk will increase when thermal conduction becomes important in hot magnetized flow.
Viscoelastic properties of the nematode Caenorhabditis elegans, a self-similar, shear-thinning worm
Backholm, Matilda; Ryu, William S.; Dalnoki-Veress, Kari
2013-01-01
Undulatory motion is common to many creatures across many scales, from sperm to snakes. These organisms must push off against their external environment, such as a viscous medium, grains of sand, or a high-friction surface; additionally they must work to bend their own body. A full understanding of undulatory motion, and locomotion in general, requires the characterization of the material properties of the animal itself. The material properties of the model organism Caenorhabditis elegans were studied with a micromechanical experiment used to carry out a three-point bending measurement of the worm. Worms at various developmental stages (including dauer) were measured and different positions along the worm were probed. From these experiments we calculated the viscoelastic properties of the worm, including the effective spring constant and damping coefficient of bending. C. elegans moves by propagating sinusoidal waves along its body. Whereas previous viscoelastic approaches to describe the undulatory motion have used a Kelvin–Voigt model, where the elastic and viscous components are connected in parallel, our measurements show that the Maxwell model, where the elastic and viscous components are in series, is more appropriate. The viscous component of the worm was shown to be consistent with a non-Newtonian, shear-thinning fluid. We find that as the worm matures it is well described as a self-similar elastic object with a shear-thinning damping term and a stiffness that becomes smaller as one approaches the tail. PMID:23460699
Self-similar nonequilibrium dynamics of a many-body system with power-law interactions.
Gutiérrez, Ricardo; Garrahan, Juan P; Lesanovsky, Igor
2015-12-01
The influence of power-law interactions on the dynamics of many-body systems far from equilibrium is much less explored than their effect on static and thermodynamic properties. To gain insight into this problem we introduce and analyze here an out-of-equilibrium deposition process in which the deposition rate of a given particle depends as a power law on the distance to previously deposited particles. This model draws its relevance from recent experimental progress in the domain of cold atomic gases, which are studied in a setting where atoms that are excited to high-lying Rydberg states interact through power-law potentials that translate into power-law excitation rates. The out-of-equilibrium dynamics of this system turns out to be surprisingly rich. It features a self-similar evolution which leads to a characteristic power-law time dependence of observables such as the particle concentration, and results in a scale invariance of the structure factor. Our findings show that in dissipative Rydberg gases out of equilibrium the characteristic distance among excitations-often referred to as the blockade radius-is not a static but rather a dynamic quantity. PMID:26764669
Self-similar nonequilibrium dynamics of a many-body system with power-law interactions
NASA Astrophysics Data System (ADS)
Gutiérrez, Ricardo; Garrahan, Juan P.; Lesanovsky, Igor
2015-12-01
The influence of power-law interactions on the dynamics of many-body systems far from equilibrium is much less explored than their effect on static and thermodynamic properties. To gain insight into this problem we introduce and analyze here an out-of-equilibrium deposition process in which the deposition rate of a given particle depends as a power law on the distance to previously deposited particles. This model draws its relevance from recent experimental progress in the domain of cold atomic gases, which are studied in a setting where atoms that are excited to high-lying Rydberg states interact through power-law potentials that translate into power-law excitation rates. The out-of-equilibrium dynamics of this system turns out to be surprisingly rich. It features a self-similar evolution which leads to a characteristic power-law time dependence of observables such as the particle concentration, and results in a scale invariance of the structure factor. Our findings show that in dissipative Rydberg gases out of equilibrium the characteristic distance among excitations—often referred to as the blockade radius—is not a static but rather a dynamic quantity.
Self-Similar Random Process and Chaotic Behavior In Serrated Flow of High Entropy Alloys
Chen, Shuying; Yu, Liping; Ren, Jingli; Xie, Xie; Li, Xueping; Xu, Ying; Zhao, Guangfeng; Li, Peizhen; Yang, Fuqian; Ren, Yang; Liaw, Peter K.
2016-01-01
The statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, and there is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk. PMID:27435922
Self-Similar Random Process and Chaotic Behavior In Serrated Flow of High Entropy Alloys.
Chen, Shuying; Yu, Liping; Ren, Jingli; Xie, Xie; Li, Xueping; Xu, Ying; Zhao, Guangfeng; Li, Peizhen; Yang, Fuqian; Ren, Yang; Liaw, Peter K
2016-01-01
The statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, and there is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk. PMID:27435922
Nucléation, ascension et éclatement d'une bulle de champagne
NASA Astrophysics Data System (ADS)
Liger-Belair, G.
2006-03-01
People have long been fascinated by bubbles and foams dynamics, and since the pioneering work of Leonardo da Vinci in the early 16th century, this subject has generated a huge bibliography. However, only quite recently, much interest was devoted to bubbles in Champagne wines and carbonated beverages. Since the time of the benedictine monk dom Pierre Perignon (1638-1715), champagne is the wine of celebration. This fame is largely linked to the elegance of its effervescence and foaming properties. In this book, the latest results about the chemical physics behind the bubbling properties of Champagne and sparkling wines are collected and fully illustrated. The first chapter is devoted to the history of champagne and to a presentation of the tools of the physical chemistry of interfaces needed for a whole comprehension of the book. Then, the three main steps of a fleeting champagne bubble's life are presented in chronological order, that is, the bubble nucleation on the glass wall (Chap.2), the bubble ascent and growth through the liquid matrix (Chap.3), and the bursting of bubbles at the liquid surface (Chap.4), which constitutes the most intriguing, functional, and visually appealing step. L'objectif général de ce travail consacré à l'étude des processus physicochimiques liés à l'effervescence des vins de Champagne était de décortiquer les différentes étapes de la vie d'une bulle de champagne en conditions réelles de consommation, dans une flûte. Nous résumons ci-après les principaux résultats obtenus pour chacune des étapes de la vie de la bulle, depuis sa naissance sur les parois d'une flûte, jusqu'à son éclatement en surface. Nucléation À l'aide d'une caméra rapide munie d'un objectif de microscope, nous avons pu mettre à mal une idée largement répandue. Ce ne sont pas les anfractuosités de la surface du verre ou de la flûte qui sont responsable de la nucléation hétérogène des bulles, mais des particules adsorbées sur les parois du
Benke, G. |; Brandt, J.; Chen, H.; Dastangoo, S.; Miller, G.J.
1996-05-01
Recent empirical studies of traffic measurements of packet switched networks have demonstrated that actual network traffic is self-similar, or long range dependent, in nature. That is, the measured traffic is bursty over a wide range of time intervals. Furthermore, the emergence of high-speed network backbones demands the study of accurate models of aggregated traffic to assess network performance. This paper provides a method for generation of self-similar traffic, which can be used to drive network simulation models. The authors present the results of a simulation study of a two-node ATM network configuration that supports the ATM Forum`s Available Bit Rate (ABR) service. In this study, the authors compare the state of the queue at the source router at the edge of the ATM network under both Poisson and self-similar traffic loading. These findings indicate an order of magnitude increase in queue length for self-similar traffic loading as compared to Poisson loading. Moreover, when background VBR traffic is present, self-similar ABR traffic causes more congestion at the ATM switches than does Poisson traffic.
Signal-noise separation based on self-similarity testing in 1D-timeseries data
NASA Astrophysics Data System (ADS)
Bourdin, Philippe A.
2015-08-01
The continuous improvement of the resolution delivered by modern instrumentation is a cost-intensive part of any new space- or ground-based observatory. Typically, scientists later reduce the resolution of the obtained raw-data, for example in the spatial, spectral, or temporal domain, in order to suppress the effects of noise in the measurements. In practice, only simple methods are used that just smear out the noise, instead of trying to remove it, so that the noise can nomore be seen. In high-precision 1D-timeseries data, this usually results in an unwanted quality-loss and corruption of power spectra at selected frequency ranges. Novel methods exist that are based on non-local averaging, which would conserve much of the initial resolution, but these methods are so far focusing on 2D or 3D data. We present here a method specialized for 1D-timeseries, e.g. as obtained by magnetic field measurements from the recently launched MMS satellites. To identify the noise, we use a self-similarity testing and non-local averaging method in order to separate different types of noise and signals, like the instrument noise, non-correlated fluctuations in the signal from heliospheric sources, and correlated fluctuations such as harmonic waves or shock fronts. In power spectra of test data, we are able to restore significant parts of a previously know signal from a noisy measurement. This method also works for high frequencies, where the background noise may have a larger contribution to the spectral power than the signal itself. We offer an easy-to-use software tools set, which enables scientists to use this novel technique on their own noisy data. This allows to use the maximum possible capacity of the instrumental hardware and helps to enhance the quality of the obtained scientific results.
Reducing false alarms in the ICU by quantifying self-similarity of multimodal biosignals.
Antink, Christoph Hoog; Leonhardt, Steffen; Walter, Marian
2016-08-01
False arrhythmia alarms pose a major threat to the quality of care in today's ICU. Thus, the PhysioNet/Computing in Cardiology Challenge 2015 aimed at reducing false alarms by exploiting multimodal cardiac signals recorded by a patient monitor. False alarms for asystole, extreme bradycardia, extreme tachycardia, ventricular flutter/fibrillation as well as ventricular tachycardia were to be reduced using two electrocardiogram channels, up to two cardiac signals of mechanical origin as well as a respiratory signal. In this paper, an approach combining multimodal rhythmicity estimation and machine learning is presented. Using standard short-time autocorrelation and robust beat-to-beat interval estimation, the signal's self-similarity is analyzed. In particular, beat intervals as well as quality measures are derived which are further quantified using basic mathematical operations (min, mean, max, etc). Moreover, methods from the realm of image processing, 2D Fourier transformation combined with principal component analysis, are employed for dimensionality reduction. Several machine learning approaches are evaluated including linear discriminant analysis and random forest. Using an alarm-independent reduction strategy, an overall false alarm reduction with a score of 65.52 in terms of the real-time scoring system of the challenge is achieved on a hidden dataset. Employing an alarm-specific strategy, an overall real-time score of 78.20 at a true positive rate of 95% and a true negative rate of 78% is achieved. While the results for some categories still need improvement, false alarms for extreme tachycardia are suppressed with 100% sensitivity and specificity. PMID:27454256
Self-similar evolution of self-gravitating viscous accretion discs
NASA Astrophysics Data System (ADS)
Illenseer, Tobias F.; Duschl, Wolfgang J.
2015-06-01
A new one-dimensional, dynamical model is proposed for geometrically thin, self-gravitating viscous accretion discs. The vertically integrated equations are simplified using the slow accretion limit and the monopole approximation with a time-dependent central point mass to account for self-gravity and accretion. It is shown that the system of partial differential equations can be reduced to a single non-linear advection diffusion equation which describes the time evolution of angular velocity. In order to solve the equation, three different turbulent viscosity prescriptions are considered. It is shown that for these parametrizations the differential equation allows for similarity transformations depending only on a single non-dimensional parameter. A detailed analysis of the similarity solutions reveals that this parameter is the initial power-law exponent of the angular velocity distribution at large radii. The radial dependence of the self-similar solutions is in most cases given by broken power laws. At small radii, the rotation law always becomes Keplerian with respect to the current central point mass. In the outer regions, the power-law exponent of the rotation law deviates from the Keplerian value and approaches asymptotically the value determined by the initial condition. It is shown that accretion discs with flatter rotation laws at large radii yield higher accretion rates. The methods are applied to self-gravitating accretion discs in active galactic nuclei. Fully self-gravitating discs are found to evolve faster than nearly Keplerian discs. The implications on supermassive black hole formation and Quasar evolution are discussed.
A Self-similar Expansion Model for Use in Solar Wind Transient Propagation Studies
NASA Astrophysics Data System (ADS)
Davies, J. A.; Harrison, R. A.; Perry, C. H.; Möstl, C.; Lugaz, N.; Rollett, T.; Davis, C. J.; Crothers, S. R.; Temmer, M.; Eyles, C. J.; Savani, N. P.
2012-05-01
Since the advent of wide-angle imaging of the inner heliosphere, a plethora of techniques have been developed to investigate the three-dimensional structure and kinematics of solar wind transients, such as coronal mass ejections, from their signatures in single- and multi-spacecraft imaging observations. These techniques, which range from the highly complex and computationally intensive to methods based on simple curve fitting, all have their inherent advantages and limitations. In the analysis of single-spacecraft imaging observations, much use has been made of the fixed phi fitting (FPF) and harmonic mean fitting (HMF) techniques, in which the solar wind transient is considered to be a radially propagating point source (fixed phi, FP, model) and a radially expanding circle anchored at Sun centre (harmonic mean, HM, model), respectively. Initially, we compare the radial speeds and propagation directions derived from application of the FPF and HMF techniques to a large set of STEREO/Heliospheric Imager (HI) observations. As the geometries on which these two techniques are founded constitute extreme descriptions of solar wind transients in terms of their extent along the line of sight, we describe a single-spacecraft fitting technique based on a more generalized model for which the FP and HM geometries form the limiting cases. In addition to providing estimates of a transient's speed and propagation direction, the self-similar expansion fitting (SSEF) technique provides, in theory, the capability to estimate the transient's angular extent in the plane orthogonal to the field of view. Using the HI observations, and also by performing a Monte Carlo simulation, we assess the potential of the SSEF technique.
Inter-relationship between scaling exponents for describing self-similar river networks
NASA Astrophysics Data System (ADS)
Yang, Soohyun; Paik, Kyungrock
2015-04-01
Natural river networks show well-known self-similar characteristics. Such characteristics are represented by various power-law relationships, e.g., between upstream length and drainage area (exponent h) (Hack, 1957), and in the exceedance probability distribution of upstream area (exponent É) (Rodriguez-Iturbe et al., 1992). It is empirically revealed that these power-law exponents are within narrow ranges. Power-law is also found in the relationship between drainage density (the total stream length divided by the total basin area) and specified source area (the minimum drainage area to form a stream head) (exponent η) (Moussa and Bocquillon, 1996). Considering that above three scaling relationships all refer to fundamental measures of 'length' and 'area' of a given drainage basin, it is natural to hypothesize plausible inter-relationship between these three scaling exponents. Indeed, Rigon et al. (1996) demonstrated the relationship between É and h. In this study, we expand this to a more general É-η-h relationship. We approach É-η relationship in an analytical manner while η-h relationship is demonstrated for six study basins in Korea. Detailed analysis and implications will be presented. References Hack, J. T. (1957). Studies of longitudinal river profiles in Virginia and Maryland. US, Geological Survey Professional Paper, 294. Moussa, R., & Bocquillon, C. (1996). Fractal analyses of tree-like channel networks from digital elevation model data. Journal of Hydrology, 187(1), 157-172. Rigon, R., Rodriguez-Iturbe, I., Maritan, A., Giacometti. A., Tarboton, D. G., & Rinaldo, A. (1996). On Hack's Law. Water Resources Research, 32(11), 3367-3374. Rodríguez-Iturbe, I., Ijjasz-Vasquez, E. J., Bras, R. L., & Tarboton, D. G. (1992). Power law distributions of discharge mass and energy in river basins. Water Resources Research, 28(4), 1089-1093.
Self-Similar Cosmologies in 5D: Spatially Flat Anisotropic Models
NASA Astrophysics Data System (ADS)
Ponce de Leon, J.
In the context of theories of the Kaluza-Klein type, with a large extra dimension, we study self-similar cosmological models in 5D that are homogeneous, anisotropic and spatially flat. The "ladder" to go between the physics in 5D and in 4D is provided by Campbell-Maagard's embedding theorems. We show that the 5D field equations RAB = 0 determine the form of the similarity variable. There are three different possibilities: homothetic, conformal and "wavelike" solutions in 5D. We derive the most general homothetic and conformal solutions to the 5D field equations. They require the extra dimension to be spacelike, and are given in terms of one arbitrary function of the similarity variable and three parameters. The Riemann tensor in 5D is not zero, except in the isotropic limit, which corresponds to the case where the parameters are equal to each other. The solutions can be used as 5D embeddings for a great variety of 4D homogeneous cosmological models, with and without matter, including the Kasner universe. Since the extra dimension is spacelike, the 5D solutions are invariant under the exchange of spatial coordinates. Therefore they also embed a family of spatially inhomogeneous models in 4D. We show that these models can be interpreted as vacuum solutions in braneworld theory. Our work (I) generalizes the 5D embeddings used for FLRW models; (II) shows that anisotropic cosmologies are, in general, curved in 5D, in contrast with FLRW models, which can always be embedded in a 5D Riemann-flat (Minkowski) manifold; and (III) reveals that anisotropic cosmologies can be curved and devoid of matter, both in 5D and in 4D, even when the metric in 5D explicitly depends on the extra coordinate, which is quite different from the isotropic case.
Numerical and Self-similar Solutions for Freezing of Non-heaving Porous Media
NASA Astrophysics Data System (ADS)
Sheshukov, A. Y.; Nieber, J. L.; Egorov, A. G.; Grant, S. A.; Iskandar, I. K.
2001-12-01
Studying the heat transfer and the water migration in porous media associated with freezing and thawing is very important in many natural environments and in environments modified by man. Energy and mass conservation laws with equilibrium thermodynamic relations are the basis for a coupled system of equations describing the coupled transport of heat and water in variably-saturated, variably-frozen porous media. These equations are solved numerically with appropriate boundary conditions and initial conditions by control volume method with the use of multigrid method as matrix solver to handle highly resolved two-dimensional domains. The developed numerical model is applicable for freezing of non-heaving variably saturated porous media, while the numerical models for freezing known to this date are capable to handle either frozen air-free conditions or frozen unsaturated condition. The semi-analytical self-similar solution for one-dimensional freezing of initially unsaturated porous medium is derived to verify the numerical model. The frozen air-free region is revealed to be always adjacent to the freezing boundary to avoid singularity in the ice content function. For a high initial water content the domain is divided on the frozen air-free zone and the unsaturated ice-free zone, while the intermediate frozen unsaturated region occurs for lower initial water content values. The possible extensions of the model to the heaving porous media are discussed. This work was supported by the Army High Performance Computing Research Center under the auspices of the Department of the Army, Army Research Laboratory cooperative agreement number DAAH04-95-2-003/contract number DAAH04-95-C-0008, the content of which does not necessarily reflect the position or the policy of the government, and no official endorsement should be inferred.
A SELF-SIMILAR EXPANSION MODEL FOR USE IN SOLAR WIND TRANSIENT PROPAGATION STUDIES
Davies, J. A.; Harrison, R. A.; Perry, C. H.; Davis, C. J.; Crothers, S. R.; Eyles, C. J.; Moestl, C.; Rollett, T.; Temmer, M.; Lugaz, N.; Savani, N. P.
2012-05-01
Since the advent of wide-angle imaging of the inner heliosphere, a plethora of techniques have been developed to investigate the three-dimensional structure and kinematics of solar wind transients, such as coronal mass ejections, from their signatures in single- and multi-spacecraft imaging observations. These techniques, which range from the highly complex and computationally intensive to methods based on simple curve fitting, all have their inherent advantages and limitations. In the analysis of single-spacecraft imaging observations, much use has been made of the fixed {phi} fitting (FPF) and harmonic mean fitting (HMF) techniques, in which the solar wind transient is considered to be a radially propagating point source (fixed {phi}, FP, model) and a radially expanding circle anchored at Sun centre (harmonic mean, HM, model), respectively. Initially, we compare the radial speeds and propagation directions derived from application of the FPF and HMF techniques to a large set of STEREO/Heliospheric Imager (HI) observations. As the geometries on which these two techniques are founded constitute extreme descriptions of solar wind transients in terms of their extent along the line of sight, we describe a single-spacecraft fitting technique based on a more generalized model for which the FP and HM geometries form the limiting cases. In addition to providing estimates of a transient's speed and propagation direction, the self-similar expansion fitting (SSEF) technique provides, in theory, the capability to estimate the transient's angular extent in the plane orthogonal to the field of view. Using the HI observations, and also by performing a Monte Carlo simulation, we assess the potential of the SSEF technique.
[Louis Maurice Champagne and the "Ecole dentaire française"].
Rousseau, Claude
2002-01-01
The Royal Edict of Louis XIV had created a new category of practitioners, "The Teeth Experts", and at the dawn of the second half of the 19th century, France had no dental school nor specific legislation. The situation worsened when many American dentists settled in France. Thus the creating of the "Ecole dentaire de Paris" in 1880 constituted a significant event which was followed by the opening of the "Ecole Dentaire de France" in 1884 and of the "Ecole Dentaire Française" in 1896. Louis Maurice Champagne will be its director from 1926. At the St Ouen Jules Vallés Market, we fortuitously discovered a framed document containing three photographs of Louis Maurice Champagne's surgery located, 3 Place de la Madeleine in Paris. Thanks to his son and through various documents, we could trace the exceptional professional carrier of this practitioner who eventually bought the "Ecole Dentaire Française" from Dr Louis-Jules Rousseau. Then, we discuss the legal frame work of the 1892 law created the "Chirurgien-dentiste" diploma and we describe the scientific and practical teaching for the "Ecole dentaire française". The operating layout of the clinical rooms is presented by opposing the ergonomic aspect of the demonstration surgery of the director and the two large operative dentistry rooms used for students. We conclude by emphasizing Louis Maurice Champagne's determination to overcome adversity which was peculiar to him as a young orphan immigrant without resources. To solve the problem of the "Chirurgien Dentiste" statute considered by its promoters as a stage of transition towards fuller reforms, we present various projects like from Dr Hulin's. This practitioner presided the Dental Section of the Medical Council Order before being voted in the first President of the "Chirurgien Dentiste" National Council Order in 1945. In 1942 he was the first to advocate a legislation based on the independence of the dental profession, still in force nowadays. PMID:12094814
Self-Similar Wave Produced by Local Perturbation of the Kelvin-Helmholtz Shear-Layer Instability
NASA Astrophysics Data System (ADS)
Hoepffner, Jérôme; Blumenthal, Ralf; Zaleski, Stéphane
2011-03-01
We show that the Kelvin-Helmholtz instability excited by a localized perturbation yields a self-similar wave. The instability of the mixing layer was first conceived by Helmholtz as the inevitable growth of any localized irregularity into a spiral, but the search and uncovering of the resulting self-similar evolution was hindered by the technical success of Kelvin’s wavelike perturbation theory. The identification of a self-similar solution is useful since its specific structure is witness of a subtle nonlinear equilibrium among the forces involved. By simulating numerically the Navier-Stokes equations, we analyze the properties of the wave: growth rate, propagation speed and the dependency of its shape upon the density ratio of the two phases of the mixing layer.
NASA Astrophysics Data System (ADS)
He, Jun-Rong; Yi, Lin
2014-06-01
We study the propagations of optical self-similar solutions in a tapered graded-index nonlinear-fiber amplifier with an external source through asymmetric twin-core fiber amplifiers. Various types of exact self-similar solutions, including the W-shaped and U-shaped solutions, trigonometric function solutions, and periodic wave solutions are found. The results show that these different types of self-similar optical structures can be generated and effectively controlled by modulating the amplitude of the source. The influences of nonlinear tunneling effects on the propagation of optical pulses are investigated as well. The obtained results may have potential applications in a tapered graded-index nonlinear-fiber amplifier with an external source.
Self-similar analysis of fluid flow and heat-mass transfer of nanofluids in boundary layer
NASA Astrophysics Data System (ADS)
Avramenko, A. A.; Blinov, D. G.; Shevchuk, I. V.
2011-08-01
Processes of heat, momentum, and concentration transport in a boundary layer of a nanofluid near a flat wall were studied. The study was performed by means of numerical analysis of boundary layer equations in a self-similar form. Self-similar forms of these equations were obtained based on symmetry properties (Lie groups). In doing so, dependence of physical properties (viscosity, thermal conductivity, and diffusion coefficient) on concentration of nanofluids and temperature were taken into account. Effects of concentration of the nano-particles on velocity and temperature profiles, as well as on the relative Nusselt numbers and skin-friction coefficients, were elucidated.
Growth of river delta networks: Thresholds, periodicity, aging and self similarity (Invited)
NASA Astrophysics Data System (ADS)
Jerolmack, D. J.; Reitz, M. D.
2010-12-01
channel locations. A lobe is abandoned (avulsion) when every point on the shoreline has built out to the threshold slope. These dynamics result in self-similar (quasi-)radial growth of fan lobes, which can be described using a simple geometric model. Together, this work provides a complete description of the statistical spatio-temporal dynamics of fan growth. Experimental fan behavior agrees well with natural systems, even though laboratory fans exclude stochastically-varying boundary conditions and fluid turbulence effects. Thus, temporal and spatial patterns of depositional channel systems appear to be a robust result of mass conservation and transport thresholds.
NASA Astrophysics Data System (ADS)
Lee, Y.; Ma, K.; Yen, Y.
2013-12-01
The work of finite fault slip models have been done in several earthquake events. We compiled the finite fault slip models of 19 earthquakes in Taiwan within the magnitude range from Mw=4.56 to 7.69 which include different fault types. We analyzed the distribution of slip on the fault surface to get the scaling relation of slip values, and found the scaling relation can be shown as Rs=10^(a+n(Rd)) (where Rd is (d/dm) as the ratio of slip, d, to the average of the effective slip, dm, Rs is A/Ae as the ratio of the fault area, A, where slip d>R_d×d_m to the effective area, Ae. The effective area and slip were determined according to the normalization of the autocorrelation of slip in length and width. The fault slip was displayed a self-similar scaling, the scaling exponent values (n) are within n=0~-1.1 which can be relative with fractal dimension of fault slip system. The scaling exponents (n) also can be seen as a measure for the roughness degree of the slip distribution on the fault surface. For lower values of n, the gradient of the slip distribution increases, and the slip models become more heterogeneous. Based on the definition of asperity as Sa(d/dm>1.5), we also got a scaling relation between asperity and magnitude as Sa(d/dm>1.5)=1.27Mw-6.49. As found in several large earthquakes, we also observed that Sa is about 20% of Ae, where Sa is the area with the slip larger than 1.5 times of the mean slip. Very intriguing feature on the relationship of the average area ratio of the examined earthquakes (M~4.5-7.6) for Rs as function of Rd follows a fractal dimension of about 0.5, as logRs= 0.428Rd-0.078. This fractal dimension might bring some hints in understanding of earthquake rupture mechanics on fault fracturing. The correlation between the average area ratio of the examined earthquakes (M~4.5-7.6) for Rs to Rd. Rs is the ratio of the fault area where slip d>R_d×d_m to the effective area, and Rd is the ratio of slip to the average of the effective slip.
Self-protection and self-similarity of the stably-stratified geophysical turbulence
NASA Astrophysics Data System (ADS)
Zilitinkevich, Sergej; Kleeorin, Nathan; Rogachevskii, Igor
2014-05-01
Following Richardson (1920), the effect of stratification on the shear-generated geophysical turbulence is determined by the gradient Richardson number Ri = (N/S)2, where Nis the Brunt-Vaisala frequency, S = dU/dz is vertical shear of the mean wind/current velocity U, and z is vertical coordinate. The concept of Richardson-number similarity postulates that dimensionless characteristics of turbulence are universal functions of Ri. Monin and Obukhov (1954) have proposed for the atmospheric surface layer a widely recognised Monin-Obukhov similarity theory (MOST). This theory postulates that dimensionless characteristics of turbulence are fully determined by the ratio z/L, where L = -u*3/Fb is the Obukhov length scale, u* is friction velocity and Fb is vertical turbulent flux of buoyancy. Nieuwstadt (1984) has employed local,z-dependent values of Fb and u* instead of the surface values, and demonstrated applicability of such version of MOST to the almost entire stably stratified planetary boundary layer. MOST is consistent with the Ri-similarity: in the surface layer Ri is a monotonously increasing function of z/L and vice versa (e.g., Sorbjan, 2010). In the strongly unstable stratification, MOST and Ri-similarity fail because of the self-organisation of convective turbulence (Elperin et al., 2006; Zilitinkevich et al., 2006). In this paper we employ the EFB turbulence closure theory (Zilitinkevich et al, 2013) together with available experimental, LES and DNS data to explain the most puzzling feature of the stably stratified geophysical turbulence, namely, its self-protection in very stable stratification, due to the counter-gradient heat-transfer mechanism missed in the traditional theory. We also explain the self-similarity of turbulence, due to the Kolmogorov's nature of dissipation for the turbulent kinetic energy (TKE), turbulent potential energy (TPE) and turbulent fluxes of heat and momentum. In non-steady regimes, traditional similarity criteria, such as z
Leo, Marco; Cazzato, Dario; De Marco, Tommaso; Distante, Cosimo
2014-01-01
's shape that is obtained through a differential analysis of image intensities and the subsequent combination with the local variability of the appearance represented by self-similarity coefficients. The experimental evidence of the effectiveness of the method was demonstrated on challenging databases containing facial images. Moreover, its capabilities to accurately detect the centers of the eyes were also favourably compared with those of the leading state-of-the-art methods. PMID:25122452
The cometary H II regions of DR 21: Bow shocks or champagne flows or both?
NASA Astrophysics Data System (ADS)
Immer, K.; Cyganowski, C.; Reid, M. J.; Menten, K. M.
2014-03-01
We present deep Very Large Array H66α radio recombination line (RRL) observations of the two cometary H II regions in DR 21. With these sensitive data, we test the "hybrid" bow shock/champagne flow model previously proposed for the DR 21 H II regions. The ionized gas down the tail of the southern H II region is redshifted by up to ~30 km s-1 with respect to the ambient molecular gas, as expected in the hybrid scenario. The RRL velocity structure, however, reveals the presence of two velocity components in both the northern and southern H II regions. This suggests that the ionized gas is flowing along cone-like shells, swept-up by stellar winds. The observed velocity structure of the well-resolved southern H II region is most consistent with a picture that combines a stellar wind with stellar motion (as in bow shock models) along a density gradient (as in champagne flow models). The direction of the implied density gradient is consistent with that suggested by maps of dust continuum and molecular line emission in the DR 21 region. The image cubes are only available as a FITS file at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/563/A39Table 2, Fig. 4, and Appendices A and B are available in electronic form at http://www.aanda.org
NASA Astrophysics Data System (ADS)
Ullrich, Maria K.; Pope, James G.; Seward, Terry M.; Wilson, Nathaniel; Planer-Friedrich, Britta
2013-07-01
Champagne Pool, a sulfidic hot spring in New Zealand, exhibits distinct diurnal variations in antimony (Sb) and arsenic (As) concentrations, with daytime high and night-time low concentrations. To identify the underlying mobilization mechanisms, five sites along the drainage channel of Champagne Pool were sampled every 2 h during a 24 h period. Temporal variations in elemental concentrations and Sb, As, and sulfur (S) speciation were monitored in the discharging fluid. Total trace element concentrations in filtered and unfiltered samples were analyzed using ICP-MS, and Sb, As and S species were determined by IC-ICP-MS. Sulfur speciation in the drainage channel was dominated by thiosulfate and sulfide at night, while sulfate dominated during the day. The distinct diurnal changes suggest that the transformations are caused by phototrophic sulfur-oxidizing bacteria. These bacteria metabolize thiosulfate and sulfide in daylight to form sulfate and, as suggested by modeling with PhreeqC, elemental sulfur. Sulfide consumption during the day results in undersaturation of antimony sulfides, which triggers the additional release of dissolved Sb. For As, diurnal cycles were much more pronounced in speciation than in total concentrations, with di- and trithioarsenate forming at night due to excess sulfide, and monothioarsenate forming from arsenite and elemental sulfur during the day. Sulfur speciation was thus found to control Sb and As in terms of both solubility and speciation.
Liquid Carbon Dioxide Venting at the Champagne Hydrothermal Site, NW Eifuku Volcano, Mariana Arc
NASA Astrophysics Data System (ADS)
Lupton, J.; Lilley, M.; Butterfield, D.; Evans, L.; Embley, R.; Olson, E.; Proskurowski, G.; Resing, J.; Roe, K.; Greene, R.; Lebon, G.
2004-12-01
In March/April 2004, submersible dives with the remotely-operated vehicle ROPOS discovered an unusual CO2-rich hydrothermal system near the summit of NW Eifuku, a submarine volcano located at 21.49° N, 144.04° E in the northern Mariana Arc. Although several sites of hydrothermal discharge were located on NW Eifuku, the most intense venting was found at 1600-m depth at the Champagne site, slightly west of the volcano summit. The Champagne site was found to be discharging two distinct fluids into the ocean: a) several small white chimneys were emitting milky 103° C gas-rich hydrothermal fluid with at least millimolar levels of H2S and b) cold (< 4° C) droplets coated with a milky skin were rising slowly from the sediment. These droplets were later determined to consist mainly of liquid CO2, with H2S as a probable secondary component. The droplets were sticky, and did not tend to coalesce into larger droplets, even though they adhered to the ROV like clumps of grapes. The film coating the droplets was assumed to be CO2 hydrate (or clathrate) which is known to form whenever liquid CO2 contacts water under these P,T conditions. Samples of the 103° C hydrothermal fluids were collected in special gas-tight titanium sampling bottles that were able to withstand the high internal pressures created by the dissolved gases. The Champagne hydrothermal fluids contained a surprising 2.3 moles/kg of CO2, an order of magnitude higher than any CO2 values previously reported for submarine hydrothermal fluids. The overall gas composition was 87% CO2, < 0.1% CH4, < 2 ppm H2, 0.012 mM/kg 4He, with the remaining 13% (322 mM/kg) assumed to be sulfur gases (H2S, SO2, etc.). (Additional analyses planned will confirm the speciation of this sulfur gas component). The helium had R/RA = 7.3, typical of subduction zone systems (R = 3He/4He and RA = Rair). Isotopic analysis of the CO2 yielded δ 13C = -1.75 ‰ , much heavier than the -6.0 ‰ typical for carbon in MOR vent fluids. The C/3He
Self-similarity of temperature profiles in distant galaxy clusters: the quest for a universal law
NASA Astrophysics Data System (ADS)
Baldi, A.; Ettori, S.; Molendi, S.; Gastaldello, F.
2012-09-01
Context. We present the XMM-Newton temperature profiles of 12 bright (LX > 4 × 1044 erg s-1) clusters of galaxies at 0.4 < z < 0.9, having an average temperature in the range 5 ≲ kT ≲ 11 keV. Aims: The main goal of this paper is to study for the first time the temperature profiles of a sample of high-redshift clusters, to investigate their properties, and to define a universal law to describe the temperature radial profiles in galaxy clusters as a function of both cosmic time and their state of relaxation. Methods: We performed a spatially resolved spectral analysis, using Cash statistics, to measure the temperature in the intracluster medium at different radii. Results: We extracted temperature profiles for the clusters in our sample, finding that all profiles are declining toward larger radii. The normalized temperature profiles (normalized by the mean temperature T500) are found to be generally self-similar. The sample was subdivided into five cool-core (CC) and seven non cool-core (NCC) clusters by introducing a pseudo-entropy ratio σ = (TIN/TOUT) × (EMIN/EMOUT)-1/3 and defining the objects with σ < 0.6 as CC clusters and those with σ ≥ 0.6 as NCC clusters. The profiles of CC and NCC clusters differ mainly in the central regions, with the latter exhibiting a slightly flatter central profile. A significant dependence of the temperature profiles on the pseudo-entropy ratio σ is detected by fitting a function of r and σ, showing an indication that the outer part of the profiles becomes steeper for higher values of σ (i.e. transitioning toward the NCC clusters). No significant evidence of redshift evolution could be found within the redshift range sampled by our clusters (0.4 < z < 0.9). A comparison of our high-z sample with intermediate clusters at 0.1 < z < 0.3 showed how the CC and NCC cluster temperature profiles have experienced some sort of evolution. This can happen because higher z clusters are at a less advanced stage of their formation and
Models of universe with a polytropic equation of state: I. The early universe
NASA Astrophysics Data System (ADS)
Chavanis, Pierre-Henri
2014-02-01
We construct models of universe with a generalized equation of state having a linear component and a polytropic component. Concerning the linear equation of state , we assume . This equation of state describes radiation ( or pressureless matter (. Concerning the polytropic equation of state , we remain very general allowing the polytropic constant k and the polytropic index n to have arbitrary values. In this paper, we consider positive indices n > 0 . In that case, the polytropic component dominates the linear component in the early universe where the density is high. For , n = 1 and , where g/m3 is the Planck density, we obtain a model of early universe describing the transition from the vacuum energy era to the radiation era. The universe exists at any time in the past and there is no primordial singularity. However, for t < 0 , its size is less than the Planck length m. In this model, the universe undergoes an inflationary expansion with the Planck density g/m3 (vacuum energy) that brings it from the Planck size m at t = 0 to a size m at s (corresponding to about 23.3 Planck times s). For , n = 1 and , we obtain a model of early universe with a new form of primordial singularity: The universe starts at t = 0 with an infinite density and a finite radius a = a 1 . Actually, this universe becomes physical at a time s from which the velocity of sound is less than the speed of light. When , the universe enters in the radiation era and evolves like in the standard model. We describe the transition from the vacuum energy era to the radiation era by analogy with a second-order phase transition where the Planck constant ℏ plays the role of finite-size effects (the standard Big Bang theory is recovered for ℏ = 0.
Jeandet, Philippe; Heinzmann, Silke S.; Roullier-Gall, Chloé; Cilindre, Clara; Aron, Alissa; Deville, Marie Alice; Moritz, Franco; Karbowiak, Thomas; Demarville, Dominique; Brun, Cyril; Moreau, Fabienne; Michalke, Bernhard; Liger-Belair, Gérard; Witting, Michael; Lucio, Marianna; Steyer, Damien; Gougeon, Régis D.; Schmitt-Kopplin, Philippe
2015-01-01
Archaeochemistry as the application of the most recent analytical techniques to ancient samples now provides an unprecedented understanding of human culture throughout history. In this paper, we report on a multiplatform analytical investigation of 170-y-old champagne bottles found in a shipwreck at the bottom of the Baltic Sea, which provides insight into winemaking practices used at the time. Organic spectroscopy-based nontargeted metabolomics and metallomics give access to the detailed composition of these wines, revealing, for instance, unexpected chemical characteristics in terms of small ion, sugar, and acid contents as well as markers of barrel aging and Maillard reaction products. The distinct aroma composition of these ancient champagne samples, first revealed during tasting sessions, was later confirmed using state-of-the-art aroma analysis techniques. After 170 y of deep sea aging in close-to-perfect conditions, these sleeping champagne bottles awoke to tell us a chapter of the story of winemaking and to reveal their extraordinary archaeometabolome and elemental diversity in the form of chemical signatures related to each individual step of champagne production. PMID:25897020
Liger-Belair, Gérard; Bourget, Marielle; Pron, Hervé; Polidori, Guillaume; Cilindre, Clara
2012-01-01
In champagne tasting, gaseous CO(2) and volatile organic compounds progressively invade the headspace above glasses, thus progressively modifying the chemical space perceived by the consumer. Simultaneous quantification of gaseous CO(2) and ethanol was monitored through micro-gas chromatography (μGC), all along the first 15 minutes following pouring, depending on whether a volume of 100 mL of champagne was served into a flute or into a coupe. The concentration of gaseous CO(2) was found to be significantly higher above the flute than above the coupe. Moreover, a recently developed gaseous CO(2) visualization technique based on infrared imaging was performed, thus confirming this tendency. The influence of champagne temperature was also tested. As could have been expected, lowering the temperature of champagne was found to decrease ethanol vapor concentrations in the headspace of a glass. Nevertheless, and quite surprisingly, this temperature decrease had no impact on the level of gaseous CO(2) found above the glass. Those results were discussed on the basis of a multiparameter model which describes fluxes of gaseous CO(2) escaping the liquid phase into the form of bubbles. PMID:22347390
Jeandet, Philippe; Heinzmann, Silke S; Roullier-Gall, Chloé; Cilindre, Clara; Aron, Alissa; Deville, Marie Alice; Moritz, Franco; Karbowiak, Thomas; Demarville, Dominique; Brun, Cyril; Moreau, Fabienne; Michalke, Bernhard; Liger-Belair, Gérard; Witting, Michael; Lucio, Marianna; Steyer, Damien; Gougeon, Régis D; Schmitt-Kopplin, Philippe
2015-05-12
Archaeochemistry as the application of the most recent analytical techniques to ancient samples now provides an unprecedented understanding of human culture throughout history. In this paper, we report on a multiplatform analytical investigation of 170-y-old champagne bottles found in a shipwreck at the bottom of the Baltic Sea, which provides insight into winemaking practices used at the time. Organic spectroscopy-based nontargeted metabolomics and metallomics give access to the detailed composition of these wines, revealing, for instance, unexpected chemical characteristics in terms of small ion, sugar, and acid contents as well as markers of barrel aging and Maillard reaction products. The distinct aroma composition of these ancient champagne samples, first revealed during tasting sessions, was later confirmed using state-of-the-art aroma analysis techniques. After 170 y of deep sea aging in close-to-perfect conditions, these sleeping champagne bottles awoke to tell us a chapter of the story of winemaking and to reveal their extraordinary archaeometabolome and elemental diversity in the form of chemical signatures related to each individual step of champagne production. PMID:25897020
Liger-Belair, Gérard; Bourget, Marielle; Pron, Hervé; Polidori, Guillaume; Cilindre, Clara
2012-01-01
In champagne tasting, gaseous CO2 and volatile organic compounds progressively invade the headspace above glasses, thus progressively modifying the chemical space perceived by the consumer. Simultaneous quantification of gaseous CO2 and ethanol was monitored through micro-gas chromatography (μGC), all along the first 15 minutes following pouring, depending on whether a volume of 100 mL of champagne was served into a flute or into a coupe. The concentration of gaseous CO2 was found to be significantly higher above the flute than above the coupe. Moreover, a recently developed gaseous CO2 visualization technique based on infrared imaging was performed, thus confirming this tendency. The influence of champagne temperature was also tested. As could have been expected, lowering the temperature of champagne was found to decrease ethanol vapor concentrations in the headspace of a glass. Nevertheless, and quite surprisingly, this temperature decrease had no impact on the level of gaseous CO2 found above the glass. Those results were discussed on the basis of a multiparameter model which describes fluxes of gaseous CO2 escaping the liquid phase into the form of bubbles. PMID:22347390
2D Self-Similar Profile for Laser Beam Propagation in Medium with Saturating Multi-Photon Absorption
NASA Astrophysics Data System (ADS)
Trofimov, Vyacheslav A.; Lysak, Tatiana M.; Zakharova, Irina G.
2016-02-01
We study a self-similar mode of 2D laser beam propagation in media with multiphoton absorption (MA) taking into account a resonant nonlinearity and nonlinear absorption saturating. An analytical solution of the corresponding equations describing the problems under consideration is derived using an eigenvalue problem method generalization for soliton- like solution finding. The developed solution is used as incident beam profile and phase front for computer simulation of the 2D laser beam propagation. In particular, we demonstrate numerically that the laser beam propagation in a self-similar mode occurs within a certain distance, which depends on medium properties. Under certain relations between the nonlinear absorption and resonant nonlinearity, and cubic nonlinear response, we observe the super long distance of the beam propagation without any beam profile distributions.
High-power self-similar amplification seeded by a 1 GHz harmonically mode-locked Yb-fiber laser
NASA Astrophysics Data System (ADS)
Luo, Daping; Li, Wenxue; Liu, Yang; Wang, Chao; Zhu, Zhiwei; Zhang, Wenchao; Zeng, Heping
2016-08-01
We demonstrate 1 GHz, 75 W, 65 fs pulse generation through chirped-pulse and self-similar amplification of a second-harmonic mode-locked Yb fiber oscillator. To confirm the experimental results of a chirped-pulse pre-amplifier, a theoretically calculative model is designed to simulate gain narrowing in the amplification. Specifically, the Kelly sidebands generated by a seed laser experience similar evolution under both conditions. The grism-based self-similar amplifier together with a high-efficiency grating compressor contribute to high-power ultrashort pulses whose spectra are efficiently broadened to a maximum 10 dB bandwidth of 56 nm with a center wavelength of 1032.2 nm owing to self-phase modulation in a gain fiber.
Effect of self-similar traffic on the performance and buffer requirements of ATM ABR edge devices
Dastangoo, S.; Miller, G.J.; Chen, H.; Brandt, J.
1996-02-05
Previous studies demonstrated that Ethemet local area network traffic is statistically self-similar and that the commonly used Poisson models are not able to capture the fractal characteristics of Ethemet traffic. This contribution uses simulated self-similar traffic traces from the MITRE Corporation and Sandia`s simulation software to evaluate the ABR performance of an ATM backbone. The ATM backbone interconnects Ethemet LANs via edge devices such as routers and bridges. We evaluate the overall network performance in terms of throughput, response time, fairness, and buffer requirements. Because typical edge devices perform simple forwarding functions, their usual mechanism for signaling network congestion is packet dropping. Therefore, we believe that the proper provisioning of buffer resources in ATM edge devices is crucial to the overall network performance.
NASA Technical Reports Server (NTRS)
Cox, D. P.; Edgar, R. J.
1982-01-01
Accurate approximations are presented for the self-similar structures of nonradiating blast waves with adiabatic ions, isothermal electrons, and equation ion and electron temperatures at the shock. The cases considered evolve in cavities with power law ambient densities (including the uniform density case) and have negligible external pressure. The results provide the early time asymptote for systems with shock heating of electrons and strong thermal conduction. In addition, they provide analytical results against which two fluid numerical hydrodynamic codes can be checked.
NASA Astrophysics Data System (ADS)
Pelletier, Jon D.
2013-12-01
are the type of aeolian dune associated with a relatively uniform wind direction, incomplete sand coverage of the substrate, and low vegetation cover. Here I present an analysis of the morphology and migration rates of 40 dunes in the Salton Sea dune field using historical aerial orthophotographs, airborne laser swath mapping, terrestrial laser scanning, and measurements of the aerodynamic roughness length derived from wind velocity profiles. The data demonstrate that the Salton Sea dunes deviate from self-similarity such that smaller dunes have a lower ratio of slip face height to crest height and a lower slope, on average, compared with larger dunes and that smaller dunes migrate more slowly than would be predicted based on an inverse relationship between migration rate and dune height. The lack of self-similarity in barchans has been attributed to the dependence of speed-up ratios on dune size and the presence of a finite saturation length in the physics of aeolian transport. Here I argue that deviations from self-similarity at this study site are more likely due to the systematic decrease in aerodynamic roughness length with increasing elevation on stoss slopes. The data set I developed should prove useful to the aeolian geomorphic community for the further testing of models for barchan evolution.
A Numerical Study of Self-Similarity in a Turbulent Plane Wake Using Large-Eddy Simulation
NASA Technical Reports Server (NTRS)
Ghosal, Sandip; Rogers, Michael M.
1996-01-01
Turbulent wakes are known to develop self-similarly sufficiently far downstream from obstacles that generate them. It has long been assumed that the spreading rate of the wake in the self-similar regime is independent of the details of the body generating the wake, being dependent only on the total drag (or momentum deficit). This assumption seems to be in contradiction with some recent experiments. In this study we attempt to complement these experimental investigations through a numerical study of a time-developing wake. A numerical study has the advantage of eliminating many of the uncontrolled factors present in experiments and allowing precise control of initial conditions. Large-eddy simulations employing the recently developed dynamic localization model are used to extend previous results from direct numerical simulations. The large-eddy simulation results are compared to the direct numerical simulation database, wherever such comparisons are feasible, as a check of the method. Like the experiments, the large-eddy simulations suggest that non-unique self-similar states, characterized by different spreading rates and turbulent statistics, are possible and that they can be maintained for significant time periods. The study also demonstrates the predictive capability of the dynamic localization subgrid model.
NASA Astrophysics Data System (ADS)
Ng, C. S.; Bhattacharjee, A.
A highly symmetric Euler flow, first proposed by Kida (1985), and recently simulated by Boratav and Pelz (1994) is considered. It is found that the fourth order spatial derivative of the pressure (pxxxx) at the origin is most probably positive. It is demonstrated that if pxxxx grows fast enough, there must be a finite-time singularity (FTS). For a random energy spectrum E(k) ∞ k-v, a FTS can occur if the spectral index v<3. Furthermore, a positive pxxxx has the dynamical consequence of reducing the third derivative of the velocity uxxx at the origin. Since the expectation value of uxxx is zero for a random distribution of energy, an ever decreasing uxxx means that the Kida flow has an intrinsic tendency to deviate from a random state. By assuming that uxxx reaches the minimum value for a given spectral profile, the velocity and pressure are found to have locally self-similar forms similar in shape to what are found in numerical simulations. Such a quasi self-similar solution relaxes the requirement for FTS to v<6. A special self-similar solution that satisfies Kelvin's circulation theorem and exhibits a FTS is found for v=2.
Lancia, L; Giribono, A; Vassura, L; Chiaramello, M; Riconda, C; Weber, S; Castan, A; Chatelain, A; Frank, A; Gangolf, T; Quinn, M N; Fuchs, J; Marquès, J-R
2016-02-19
Plasma-based laser amplification is considered as a possible way to overcome the technological limits of present day laser systems and achieve exawatt laser pulses. Efficient amplification of a picosecond laser pulse by stimulated Brillouin scattering (SBS) of a pump pulse in a plasma requires to reach the self-similar regime of the strongly coupled (SC) SBS. In this Letter, we report on the first observation of the signatures of the transition from linear to self-similar regimes of SC-SBS, so far only predicted by theory and simulations. With a new fully head-on collision geometry, subpicosecond pulses are amplified by a factor of 5 with energy transfers of few tens of mJ. We observe pulse shortening, frequency spectrum broadening, and down-shifting for increasing gain, signatures of SC-SBS amplification entering the self-similar regime. This is also confirmed by the power law dependence of the gain on the amplification length: doubling the interaction length increases the gain by a factor 1.4. Pump backward Raman scattering (BRS) on SC-SBS amplification has been measured for the first time, showing a strong decrease of the BRS amplitude and frequency bandwidth when SBS seed amplification occurs. PMID:26943539
NASA Astrophysics Data System (ADS)
Lancia, L.; Giribono, A.; Vassura, L.; Chiaramello, M.; Riconda, C.; Weber, S.; Castan, A.; Chatelain, A.; Frank, A.; Gangolf, T.; Quinn, M. N.; Fuchs, J.; Marquès, J.-R.
2016-02-01
Plasma-based laser amplification is considered as a possible way to overcome the technological limits of present day laser systems and achieve exawatt laser pulses. Efficient amplification of a picosecond laser pulse by stimulated Brillouin scattering (SBS) of a pump pulse in a plasma requires to reach the self-similar regime of the strongly coupled (SC) SBS. In this Letter, we report on the first observation of the signatures of the transition from linear to self-similar regimes of SC-SBS, so far only predicted by theory and simulations. With a new fully head-on collision geometry, subpicosecond pulses are amplified by a factor of 5 with energy transfers of few tens of mJ. We observe pulse shortening, frequency spectrum broadening, and down-shifting for increasing gain, signatures of SC-SBS amplification entering the self-similar regime. This is also confirmed by the power law dependence of the gain on the amplification length: doubling the interaction length increases the gain by a factor 1.4. Pump backward Raman scattering (BRS) on SC-SBS amplification has been measured for the first time, showing a strong decrease of the BRS amplitude and frequency bandwidth when SBS seed amplification occurs.
Further studies on the champagne phase of GM 24 (IRAS 17136-3617)
NASA Astrophysics Data System (ADS)
Gomez, J. F.; Torrelles, J. M.; Tapia, M.; Gomez, Y.; Rodriguez, L. F.; Roth, M.; Ho, P. T. P.
1993-05-01
The H II region associated with GM 24 has been observed with the VLA at the 3.6 and 6 cm continuum, as well as at the H92-alpha recombination line and the H2O maser line; these observations have suggested a 'champagne' flow of ionized gas. Spectral data indicate two velocity components toward GM 24 that are separated by about 10 km/sec. The weaker, extended velocity component is redshifted by about 10 km/sec relative to the velocity of the ambient molecular cloud. It is hypothesized that this velocity component constitutes emission from the ionized gas, which is breaking out of the cloud and expanding away from the direction of observation.
NASA Astrophysics Data System (ADS)
Funning, G.; Ferreira, A. M.; Weston, J. M.; Bloomfield, H.
2013-12-01
The question of how moment release in earthquakes scales to other earthquake source parameters, such as fault length and average slip, is a long-standing controversy (e.g. Scholz, 1982, 1994; Romanowicz, 1992). It is a problem that speaks to issues of earthquake source mechanics, specifically the self-similarity of earthquakes - is stress drop constant across all magnitudes? Theoretically, two end-member scaling models have been proposed - the so-called ';W-model', whereby seismic moment scales linearly with fault length, and the alternative ';L-model', where moment scales with the square of fault length. Existing data on earthquake rupture dimensions, typically from field observations or aftershock locations, do not conclusively favor one over the other. A W-model implies a constant stress drop for all earthquakes in the same tectonic setting, and therefore that earthquakes are self-similar. The L-model does not imply self-similarity, but is consistent with the idea that ';large earthquakes' (i.e. earthquakes that rupture the full thickness of the brittle upper crust) grow by increasing their rupture length, with average slip being proportional to fault length. To address this problem, we use a compilation of source parameter information from over 130 published studies of 101 individual earthquakes (Mw 4.7-9.0) studied using InSAR. There are several reasons to suggest that this information will be highly suitable for the study of earthquake scaling. The high spatial resolution and centimetric precision of InSAR data provide strong constraints on estimates of fault length and slip. In addition, in a previous study, we found good agreement between moment estimates from InSAR studies and the Global CMT catalog, derived from long-period seismic data (Weston et al., 2011). Considering events of all mechanisms together, we find a scaling relationship between moment (M0) and fault length (L), such that M0 ∝ L1.8. We find differences in this power law exponent with
NASA Astrophysics Data System (ADS)
Ruggles, Adam J.
2015-11-01
This paper presents improved statistical insight regarding the self-similar scalar mixing process of atmospheric hydrogen jets and the downstream region of under-expanded hydrogen jets. Quantitative planar laser Rayleigh scattering imaging is used to probe both jets. The self-similarity of statistical moments up to the sixth order (beyond the literature established second order) is documented in both cases. This is achieved using a novel self-similar normalization method that facilitated a degree of statistical convergence that is typically limited to continuous, point-based measurements. This demonstrates that image-based measurements of a limited number of samples can be used for self-similar scalar mixing studies. Both jets exhibit the same radial trends of these moments demonstrating that advanced atmospheric self-similarity can be applied in the analysis of under-expanded jets. Self-similar histograms away from the centerline are shown to be the combination of two distributions. The first is attributed to turbulent mixing. The second, a symmetric Poisson-type distribution centered on zero mass fraction, progressively becomes the dominant and eventually sole distribution at the edge of the jet. This distribution is attributed to shot noise-affected pure air measurements, rather than a diffusive superlayer at the jet boundary. This conclusion is reached after a rigorous measurement uncertainty analysis and inspection of pure air data collected with each hydrogen data set. A threshold based upon the measurement noise analysis is used to separate the turbulent and pure air data, and thusly estimate intermittency. Beta-distributions (four parameters) are used to accurately represent the turbulent distribution moments. This combination of measured intermittency and four-parameter beta-distributions constitutes a new, simple approach to model scalar mixing. Comparisons between global moments from the data and moments calculated using the proposed model show excellent
Effective geometry of the n=1 uniformly rotating self-gravitating polytrope
Bini, D.; Cherubini, C.; Filippi, S.; Geralico, A.
2010-08-15
The ''effective geometry'' formalism is used to study the perturbations of a perfect barotropic Newtonian self-gravitating rotating and compressible fluid coupled with gravitational backreaction. The case of a uniformly rotating polytrope with index n=1 is investigated, due to its analytical tractability. Special attention is devoted to the geometrical properties of the underlying background acoustic metric, focusing, in particular, on null geodesics as well as on the analog light cone structure.
Lin, Min-Kai
2012-07-20
Numerical calculations of the linear Rossby wave instability (RWI) in global three-dimensional (3D) disks are presented. The linearized fluid equations are solved for vertically stratified, radially structured disks with either a locally isothermal or polytropic equation of state, by decomposing the vertical dependence of the perturbed hydrodynamic quantities into Hermite and Gegenbauer polynomials, respectively. It is confirmed that the RWI operates in 3D. For perturbations with vertical dependence assumed above, there is little difference in growth rates between 3D and two-dimensional (2D) calculations. Comparison between 2D and 3D solutions of this type suggests the RWI is predominantly a 2D instability and that 3D effects, such as vertical motion, can be interpreted as a perturbative consequence of the dominant 2D flow. The vertical flow around corotation, where vortex formation is expected, is examined. In locally isothermal disks, the expected vortex center remains in approximate vertical hydrostatic equilibrium. For polytropic disks, the vortex center has positive vertical velocity, whose magnitude increases with decreasing polytropic index n.
Effects of a Piecewise Polytropic Equation of State on Turbulent Fragmentation
NASA Astrophysics Data System (ADS)
Jappsen, A.-K.; Li, Y.; Mac Low, M.-M.; Klessen, R. S.
2003-12-01
We study the effect of a piecewise polytropic equation of state on the formation of stellar clusters in turbulent, self-gravitating molecular clouds using three-dimensional, smoothed particle hydrodynamics simulations. We use the publicly available parallel code GADGET (Springel et al. 2001) in which we have implemented sink particles that can replace high-density gas cores, and with a uniform turbulent driving field. Recently several of us conducted a systematic study of the effects of a varying polytropic index γ on turbulent fragmentation. Their results showed that γ determines how strongly self-gravitating gas fragments. However in their computation, γ was left strictly constant in each simulation. In this study we extend our previous work by using a piecewise polytropic equation of state changing γ at some chosen density. We investigate if a change in γ determines the characteristic mass of the gas clump spectrum and thus perhaps the turn-over mass of the IMF. Preliminary results changing γ from 0.7 to 1.1 seem to corroborate this hypothesis, but with a weaker than expected dependence on the chosen density. We conduct a parameter study on the density at which γ changes to specify its effect on the resulting mass spectra. AKJ acknowledges support by the Kade Fellowship. M-MML acknowledges support by NSF CAREER grant AST99-85392. AKJ and RSK acknowledge support by the Emmy Noether Program of the Deutsche Forschungsgemeinschaft KL1385/1.
The ion polytropic coefficient in a collisionless sheath containing hot ions
NASA Astrophysics Data System (ADS)
Lin, Binbin; Xiang, Nong; Ou, Jing
2016-08-01
The fluid approach has been widely used to study plasma sheath dynamics. For a sheath containing hot ions whose temperature is greater than the electron's, how to truncate the fluid hierarchy chain equations while retaining to the fullest extent of the kinetic effects is always a difficult problem. In this paper, a one-dimensional, collisionless sheath containing hot ions is studied via particle-in-cell simulations. By analyzing the ion energy equation and taking the kinetic effects into account, we have shown that the ion polytropic coefficient in the vicinity of the sheath edge is approximately constant so that the state equation with the modified polytropic coefficient can be used to close the hierarchy chain of the ion fluid equations. The value of the polytropic coefficient strongly depends on the hot ion temperature and its concentration in the plasma. The semi-analytical model is given to interpret the simulation results. As an application, the kinetic effects on the ion saturation current density in the probe theory are discussed.
NASA Astrophysics Data System (ADS)
Liger-Belair, G.
2002-07-01
People have long been fascinated by bubbles and foams dynamics, and since the pioneering work of Leonardo da Vinci in the early 16th century, this subject has generated a huge bibliography. However, only very recently, much interest was devoted to bubbles in Champagne wines. Small bubbles rising through the liquid, as well as a bubble ring (the so-called collar) at the periphery of a flute poured with champagne are the hallmark of this traditionally festive wine, and even there is no scientific evidence yet to connect the quality of a champagne with its effervescence, people nevertheless often make a connection between them. Therefore, since the last few years, a better understanding of the numerous parameters involved in the bubbling process has become an important stake in the champagne research area. Otherwise, in addition to these strictly enological reasons, we also feel that the area of bubble dynamics could benefit from the simple but close observation of a glass poured with champagne. In this study, our first results concerning the close observation of the three main steps of a champagne bubble's life are presented, that is, the bubble nucleation on tiny particles stuck on the glass wall (Chap. 2), the bubble ascent through the liquid (Chap. 3), and the bursting of bubbles at the free surface, which constitutes the most intriguing and visually appealing step (Chap. 4). Our results were obtained in real consuming conditions, that is, in a classical crystal flute poured with a standard commercial champagne wine. Champagne bubble nucleation proved to be a fantastic everyday example to illustrate the non-classical heterogeneous bubble nucleation process in a weakly supersaturated liquid. Contrary to a generally accepted idea, nucleation sites are not located on irregularities of the glass itself. Most of nucleation sites are located on tiny hollow and roughly cylindrical exogenous fibres coming from the surrounding air or remaining from the wiping process
Herrero, Paula; Sáenz-Navajas, Pilar; Culleré, Laura; Ferreira, Vicente; Chatin, Amelie; Chaperon, Vincent; Litoux-Desrues, François; Escudero, Ana
2016-09-15
Five different methodologies were applied for the quantitative analysis of 86 volatile molecules in 32 Chardonnay and 30 Pinot Noir Champagne white base wines. Sensory characterization was carried out by descriptive analysis. Pinot Noir wines had more constitutive compounds while Chardonnay wines had more discriminant compounds. Only four compounds predominated in Chardonnay wines: 4-vinylphenol, guaiacol, sotolon and 4-methyl-4-mercapto-2-pentanone. Correlation studies and PLSR models were calculated with sensory and chemical variables. For Pinot Noir wines, they were not as revealing as for Chardonnay base wines. Sulfur-related compounds were suggested to be involved in tropical fruit, dried fruit and citric sensory notes. This family of compounds seemed to be responsible for discriminant sensory terms in Champagne base wines. Fermentative compounds (aromatic buffer) were found at significantly higher levels in Pinot Noir wines, which would explain the fact that these wines were more difficult to describe in comparison with Chardonnay base wines. PMID:27080902
Lee, Yik Ching; Clark, Alys R; Fuld, Matthew K; Haynes, Susan; Divekar, Abhay A; Hoffman, Eric A; Tawhai, Merryn H
2013-05-01
The pig is frequently used as an experimental model for studies of the pulmonary circulation, yet the branching and dimensional geometry of the porcine pulmonary vasculature remains poorly defined. The purposes of this study are to improve the geometric definition of the porcine pulmonary arteries and to determine whether the arterial tree exhibits self-similarity in its branching geometry. Five animals were imaged using thin slice spiral computed tomography in the prone posture during airway inflation pressure at 25 cmH2O. The luminal diameter and distance from the inlet of the left and right pulmonary arteries were measured along the left and right main arterial pathway in each lung of each animal. A further six minor pathways were measured in a single animal. The similarity in the rate of reduction of diameter with distance of all minor pathways and the two main pathways, along with similarity in the number of branches arising along the pathways, supports self-similarity in the arterial tree. The rate of reduction in diameter with distance from the inlet was not significantly different among the five animals (P > 0.48) when normalized for main pulmonary artery diameter and total main artery pathlength, which supports intersubject similarity. Other metrics to quantify the tree geometry are strikingly similar to those from airways of other quadrupeds, with the exception of a significantly larger length to diameter ratio, which is more appropriate for the vascular tree. A simplifying self-similar model for the porcine pulmonary arteries is proposed to capture the important geometric features of the arterial tree. PMID:23449941
Kiyani, K; Chapman, S C; Hnat, B; Nicol, R M
2007-05-25
We quantify the scaling of magnetic energy density in the inertial range of solar-wind turbulence seen in situ at 1 AU with respect to solar activity. At solar maximum, when the coronal magnetic field is dynamic and topologically complex, we find self-similar scaling in the solar wind, whereas at solar minimum, when the coronal fields are more ordered, we find multifractality. This quantifies the solar-wind signature that is of direct coronal origin and distinguishes it from that of local MHD turbulence, with quantitative implications for coronal heating of the solar wind. PMID:17677760
Hong Qin and Ronald C. Davidson
2011-07-19
In a linear trap confining a one-component nonneutral plasma, the external focusing force is a linear function of the configuration coordinates and/or the velocity coordinates. Linear traps include the classical Paul trap and the Penning trap, as well as the newly proposed rotating-radio- frequency traps and the Mobius accelerator. This paper describes a class of self-similar nonlinear solutions of nonneutral plasma in general time-dependent linear focusing devices, with self-consistent electrostatic field. This class of nonlinear solutions includes many known solutions as special cases.
Hug, Katrin; Maher, William A.; Stott, Matthew B.; Krikowa, Frank; Foster, Simon; Moreau, John W.
2014-01-01
Acid-sulfide hot springs are analogs of early Earth geothermal systems where microbial metal(loid) resistance likely first evolved. Arsenic is a metalloid enriched in the acid-sulfide hot spring Champagne Pool (Waiotapu, New Zealand). Arsenic speciation in Champagne Pool follows reaction paths not yet fully understood with respect to biotic contributions and coupling to biogeochemical sulfur cycling. Here we present quantitative arsenic speciation from Champagne Pool, finding arsenite dominant in the pool, rim and outflow channel (55–75% total arsenic), and dithio- and trithioarsenates ubiquitously present as 18–25% total arsenic. In the outflow channel, dimethylmonothioarsenate comprised ≤9% total arsenic, while on the outflow terrace thioarsenates were present at 55% total arsenic. We also quantified sulfide, thiosulfate, sulfate and elemental sulfur, finding sulfide and sulfate as major species in the pool and outflow terrace, respectively. Elemental sulfur concentration reached a maximum at the terrace. Phylogenetic analysis of 16S rRNA genes from metagenomic sequencing revealed the dominance of Sulfurihydrogenibium at all sites and an increased archaeal population at the rim and outflow channel. Several phylotypes were found closely related to known sulfur- and sulfide-oxidizers, as well as sulfur- and sulfate-reducers. Bioinformatic analysis revealed genes underpinning sulfur redox transformations, consistent with sulfur speciation data, and illustrating a microbial role in sulfur-dependent transformation of arsenite to thioarsenate. Metagenomic analysis also revealed genes encoding for arsenate reductase at all sites, reflecting the ubiquity of thioarsenate and a need for microbial arsenate resistance despite anoxic conditions. Absence of the arsenite oxidase gene, aio, at all sites suggests prioritization of arsenite detoxification over coupling to energy conservation. Finally, detection of methyl arsenic in the outflow channel, in conjunction with
Hug, Katrin; Maher, William A; Stott, Matthew B; Krikowa, Frank; Foster, Simon; Moreau, John W
2014-01-01
Acid-sulfide hot springs are analogs of early Earth geothermal systems where microbial metal(loid) resistance likely first evolved. Arsenic is a metalloid enriched in the acid-sulfide hot spring Champagne Pool (Waiotapu, New Zealand). Arsenic speciation in Champagne Pool follows reaction paths not yet fully understood with respect to biotic contributions and coupling to biogeochemical sulfur cycling. Here we present quantitative arsenic speciation from Champagne Pool, finding arsenite dominant in the pool, rim and outflow channel (55-75% total arsenic), and dithio- and trithioarsenates ubiquitously present as 18-25% total arsenic. In the outflow channel, dimethylmonothioarsenate comprised ≤9% total arsenic, while on the outflow terrace thioarsenates were present at 55% total arsenic. We also quantified sulfide, thiosulfate, sulfate and elemental sulfur, finding sulfide and sulfate as major species in the pool and outflow terrace, respectively. Elemental sulfur concentration reached a maximum at the terrace. Phylogenetic analysis of 16S rRNA genes from metagenomic sequencing revealed the dominance of Sulfurihydrogenibium at all sites and an increased archaeal population at the rim and outflow channel. Several phylotypes were found closely related to known sulfur- and sulfide-oxidizers, as well as sulfur- and sulfate-reducers. Bioinformatic analysis revealed genes underpinning sulfur redox transformations, consistent with sulfur speciation data, and illustrating a microbial role in sulfur-dependent transformation of arsenite to thioarsenate. Metagenomic analysis also revealed genes encoding for arsenate reductase at all sites, reflecting the ubiquity of thioarsenate and a need for microbial arsenate resistance despite anoxic conditions. Absence of the arsenite oxidase gene, aio, at all sites suggests prioritization of arsenite detoxification over coupling to energy conservation. Finally, detection of methyl arsenic in the outflow channel, in conjunction with
NASA Astrophysics Data System (ADS)
Nicolas, Bollot; Guillaume, Pierre; Gilles, Grandjean
2014-05-01
Key words : landslide, Champagne vineyards , geomorphology, geophysical data, superficial structure The Champagne region is strongly impacted by landslides. Usually inactive, these landslides suffer from partial reactivations leading to important damages, especially when they occur in the vineyards. In the Marne valley, and particularly in the center of Champagne vineyards area (Reuil), the Jacotines site is representative of such landslides since it presents typical surface characteristics widely observed in the region. However, its size, and especially its internal structure, can't be deduced from the surface analysis only. The aim of this work is to combine surface patterns analysis, geophysical data and borehole data to produce an interpretative model of the landslide. Preliminary geomorphological cartography was used for determining the influence of the landslide. From this information, geophysical investigations were carried out to image the internal structure of the landslide. Geophysical data fusion (combination of seismic and geoelectrical tomograms) was used to estimate the mechanical behavior and the fissuring pattern of the slope. Three transverse and longitudinal tomograms were used to define an heterogeneous area between 20 and 50 meters depth and a weathered zone from 0 to 10-20 meters depth. A 60 meters depth borehole on the main transverse tomogram found the shear plane and clarified the structure of the heterogeneous area as well as the uppermost weathered layer composed by debris flows resulting from partial reactivations processes.
Comparison of two landslide susceptibility assessments in the Champagne-Ardenne region (France)
NASA Astrophysics Data System (ADS)
Den Eeckhaut, M. Van; Marre, A.; Poesen, J.
2010-02-01
The vineyards of the Montagne de Reims are mostly planted on steep south-oriented cuesta fronts receiving a maximum of sun radiation. Due to the location of the vineyards on steep hillslopes, the viticultural activity is threatened by slope failures. This study attempts to better understand the spatial patterns of landslide susceptibility in the Champagne-Ardenne region by comparing a heuristic (qualitative) and a statistical (quantitative) model in a 1120 km² study area. The heuristic landslide susceptibility model was adopted from the Bureau de Recherches Géologiques et Minières, the GEGEAA - Reims University and the Comité Interprofessionnel du Vin de Champagne. In this model, expert knowledge of the region was used to assign weights to all slope classes and lithologies present in the area, but the final susceptibility map was never evaluated with the location of mapped landslides. For the statistical landslide susceptibility assessment, logistic regression was applied to a dataset of 291 'old' (Holocene) landslides. The robustness of the logistic regression model was evaluated and ROC curves were used for model calibration and validation. With regard to the variables assumed to be important environmental factors controlling landslides, the two models are in agreement. They both indicate that present and future landslides are mainly controlled by slope gradient and lithology. However, the comparison of the two landslide susceptibility maps through (1) an evaluation with the location of mapped 'old' landslides and through (2) a temporal validation with spatial data of 'recent' (1960-1999; n = 48) and 'very recent' (2000-2008; n = 46) landslides showed a better prediction capacity for the statistical model produced in this study compared to the heuristic model. In total, the statistically-derived landslide susceptibility map succeeded in correctly classifying 81.0% of the 'old' and 91.6% of the 'recent' and 'very recent' landslides. On the susceptibility map
NASA Astrophysics Data System (ADS)
Hug, K.; Krikowa, F.; Morgan, X.; Maher, W. A.; Stott, M. B.; Moreau, J. W.
2011-12-01
Arsenic is a highly toxic metalloid typically enriched in geothermal waters due to aqueous weathering of arsenic-bearing minerals. Investigation of enzymatic pathways by which thermophilic microorganisms cope with toxic arsenic levels may yield insights into the evolution of arsenic resistance mechanisms on the early Earth. At Wai-O-Tapu in the Taupo Volcanic Zone on the North Island of New Zealand, hot springs with temperatures of 30-90°C and elemental sulfur concentrations (expressed as equivalent sulfate) from 340 to 850 mg/l establish a range of environmental conditions. Total arsenic concentrations varied from 0.083 mg/l to 56 mg/l. Arsenic speciation analysis elucidated various biogeochemical arsenic transformations occurring within different springs. For example, in the Alum Cliff spring oxidizing conditions (Eh = 225 mV) were expected to stabilize dissolved arsenate (AsO43-). However, HPLC-ICPMS analyses yielded dissolved arsenate and arsenite (AsO33-) concentrations of 0.25 mg/l versus 43.3 mg/l, respectively, and point towards microbial arsenate reduction as the likely mechanism for arsenic redox transformation. 16S rRNA gene cloning of Alum Cliff DNA showed a predominantly archaeal population with the dominant clone "AC1_A1" most closely related (99% sequence similarity, NCBI BLAST°) to the uncultured Sulfolobus clone "ChP_97P" found in Champagne Pool (Childs et al., 2008). The closest isolated relative to AC1_A1 is Sulfolobus tokodaii str. TW with a sequence similarity of 94%. Arsenic speciation measurements from the Alum Cliff spring suggest that clone AC1_A1 features the arsenate reduction resistance mechanism, and we hypothesize therefore that an arsC (homolog or analog) provides this functionality. The organic arsenic species monomethylarsonic acid (MMA) and dimethylarsinic acid (DMA), detected via HPLC-ICPMS at concentrations ranging from 1 μg/l to 12 μg/l in various springs, may also implicate microbial methyl-group transfers as an active
NASA Technical Reports Server (NTRS)
Totten, T. L.; Freeman, J. W.; Arya, S.
1995-01-01
Observations of solar wind proton temperatures indicate that the solar wind is heated as it moves outward toward the orbit of Earth. This heating, which may be the results of electron heat conduction and perhaps MHD waves, has proven difficult to quantify and hence is often neglected in MHD models of the solar wind. An alternate approach to finding explicit heating terms for the MHD energy equation is to use a polytropic approximation. This paper discusses the properties of the polytropic approximation and its application to the solar wind plasma. By using data from the Helios 1 spacecraft, an empirical value for the polytropic index of the free-streaming solar wind is determined. Various corrections to the data are made to account for velocity, nonuniformity in radial sampling, and stream interaction regions. The polytropic index, as derived from proton data, is found to indepedent of speed state, within statistical error, and has an average value of 1.46. If magnetic pressure is included, the polytropic index has an average value of 1.58.
NASA Astrophysics Data System (ADS)
Balsara, Dinshaw S.; Dumbser, Michael
2015-04-01
Multidimensional Riemann solvers that have internal sub-structure in the strongly-interacting state have been formulated recently (D.S. Balsara (2012, 2014) [5,16]). Any multidimensional Riemann solver operates at the grid vertices and takes as its input all the states from its surrounding elements. It yields as its output an approximation of the strongly interacting state, as well as the numerical fluxes. The multidimensional Riemann problem produces a self-similar strongly-interacting state which is the result of several one-dimensional Riemann problems interacting with each other. To compute this strongly interacting state and its higher order moments we propose the use of a Galerkin-type formulation to compute the strongly interacting state and its higher order moments in terms of similarity variables. The use of substructure in the Riemann problem reduces numerical dissipation and, therefore, allows a better preservation of flow structures, like contact and shear waves. In this second part of a series of papers we describe how this technique is extended to unstructured triangular meshes. All necessary details for a practical computer code implementation are discussed. In particular, we explicitly present all the issues related to computational geometry. Because these Riemann solvers are Multidimensional and have Self-similar strongly-Interacting states that are obtained by Consistency with the conservation law, we call them MuSIC Riemann solvers. (A video introduction to multidimensional Riemann solvers is available on http://www.elsevier.com/xml/linking-roles/text/html". The MuSIC framework is sufficiently general to handle general nonlinear systems of hyperbolic conservation laws in multiple space dimensions. It can also accommodate all self-similar one-dimensional Riemann solvers and subsequently produces a multidimensional version of the same. In this paper we focus on unstructured triangular meshes. As examples of different systems of conservation laws we
NASA Astrophysics Data System (ADS)
Balsara, Dinshaw S.
2014-11-01
Multidimensional Riemann solvers have been formulated recently by the author (Balsara, 2010, 2012) [6,7]. They operate at the vertices of a two-dimensional mesh, taking input from all the neighboring states and yielding the resolved state and fluxes as output. The multidimensional Riemann problem produces a self-similar strongly interacting state which is the result of several one-dimensional Riemann problems interacting with each other. The prior work was restricted to the use of one-dimensional HLLC Riemann solvers as building blocks. In this paper, we formulate the problem in similarity variables. As a result, any self-similar one-dimensional Riemann solver can be used as a building block for the multidimensional Riemann solver. This paper focuses on the structure of the strongly-interacting state. (A video introduction to multidimensional Riemann solvers is available on http://www.nd.edu/~dbalsara/Numerical-PDE-Course.) In this work the strongly-interacting state is expanded in a set of basis functions that depend on the similarity variables. Consequently, the resolved state and the fluxes can be endowed with considerably richer sub-structure compared to prior work. Unlike the multidimensional HLLC Riemann solver, the need to independently specify a direction for the evolution of the contact discontinuity is eliminated. The richer sub-structure in the strongly-interacting state naturally accommodates waves that may be moving in any direction relative to the mesh, thereby minimizing mesh-imprinting. Two formulations are presented. The first formulation does not linearize the problem around a favorable state. Its derivation takes a few cues from the derivation of the multidimensional HLL Riemann solver. The second formulation identifies such a state and carries out a linearization of the fluxes about that state. This paper is the very first time that a series solution of the multidimensional Riemann problem has been presented. Explicit formulae are presented for
Champagne flutes and brandy snifters: modelling protostellar outflow-cloud chemical interfaces
NASA Astrophysics Data System (ADS)
Rollins, R. P.; Rawlings, J. M. C.; Williams, D. A.; Redman, M. P.
2014-10-01
A rich variety of molecular species has now been observed towards hot cores in star-forming regions and in the interstellar medium. An increasing body of evidence from millimetre interferometers suggests that many of these form at the interfaces between protostellar outflows and their natal molecular clouds. However, current models have remained unable to explain the origin of the observational bias towards wide-angled `brandy snifter' shaped outflows over narrower `champagne flute' shapes in carbon monoxide imaging. Furthermore, these wide-angled systems exhibit unusually high abundances of the molecular ion HCO+. We present results from a chemodynamic model of such regions where a rich chemistry arises naturally as a result of turbulent mixing between cold, dense molecular gas and the hot, ionized outflow material. The injecta drives a rich and rapid ion-neutral chemistry in qualitative and quantitative agreement with the observations. The observational bias towards wide-angled outflows is explained naturally by the geometry-dependent ion injection rate causing rapid dissociation of CO in the younger systems.
Is there pain in champagne? Semantic involvement of words within words during sense-making.
van Alphen, Petra M; van Berkum, Jos J A
2010-11-01
In an ERP experiment, we examined whether listeners, when making sense of spoken utterances, take into account the meaning of spurious words that are embedded in longer words, either at their onsets (e.g., pie in pirate) or at their offsets (e.g., pain in champagne). In the experiment, Dutch listeners heard Dutch words with initial or final embeddings presented in a sentence context that did or did not support the meaning of the embedded word, while equally supporting the longer carrier word. The N400 at the carrier words was modulated by the semantic fit of the embedded words, indicating that listeners briefly relate the meaning of initial- and final-embedded words to the sentential context, even though these words were not intended by the speaker. These findings help us understand the dynamics of initial sense-making and its link to lexical activation. In addition, they shed new light on the role of lexical competition and the debate concerning the lexical activation of final-embedded words. PMID:19702463
Natural oxygenation of Champagne wine during ageing on lees: A metabolomics picture of hormesis.
Roullier-Gall, Chloé; Witting, Michael; Moritz, Franco; Gil, Ryan B; Goffette, Delphine; Valade, Michel; Schmitt-Kopplin, Philippe; Gougeon, Régis D
2016-07-15
The oxygenation of Champagne wine after 4 and 6 years of aging on lees in bottle was investigated by FTICR-MS and UPLC-Q-TOF-MS. Three levels of permeability were considered for the stoppers, ranging from 0.2 to 1.8 mg/L/year of oxygen transfer rate. Our results confirmed a good repeatability of ultra-high resolution FTICR-MS, both in terms of m/z and coefficient of variation of peak intensities among biological replicates. Vintages appeared to be the most discriminated features, and metabolite annotations suggested that the oldest wines (2006) were characterized by a higher sensitivity towards oxygenation. Within each vintage, the oxygenation mechanisms appeared to be different for low and high ingresses of oxygen, in agreement with the hormesis character of wine oxygenation. In the particular case of single variety wines and for a given level of stopper permeability, our results also showed that variety discrimination could be easily achieved among wines. PMID:26948607
NASA Astrophysics Data System (ADS)
Renard, F.; JeannéE, N.
2008-11-01
This paper presents a flexible and general methodology that combines hydrogeological and geostatistical modeling techniques to estimate a set of transmissivity fields and their influence on flow and transport. The methodology may be applied to any case with only hydraulic head observations, even if most of them are concentrated inside a small part of the entire domain of interest. It is applied here to the case of the Champagne chalk aquifer (France), where it is shown to be very efficient. The methodology is decomposed in three independent parts. First, a reference head distribution is constructed by kriging in order to constrain the inverse problem. As hydraulic heads and elevations are correlated, a smoothed digital elevation model is used as external drift. The inverse problem is then solved by using a simplified pilot point method with an efficient and easy-to-use minimization algorithm. Finally, geostatistical simulations combined with flow simulations lead to a set of acceptable transmissivity fields. The induced uncertainty is evaluated by calculating tracer concentrations, pointing out areas where flow behavior is uncertain and where new borings would be advantageously drilled.
NASA Technical Reports Server (NTRS)
Lerche, I.; Low, B. C.
1980-01-01
Exact analytic solutions for the static equilibrium of a gravitating plasma polytrope in the presence of magnetic fields are presented. The means of generating various equilibrium configurations to illustrate directly the complex physical relationships between pressure, magnetic fields, and gravity in self-gravitating systems is demonstrated. One of the solutions is used to model interstellar clouds suspended by magnetic fields against the galactic gravity such as may be formed by the Parker (1966) instability. It is concluded that the pinching effect of closed loops of magnetic fields in the clouds may be a dominant agent in further collapsing the clouds following their formation.
Surface curvature singularities of polytropic spheres in Palatini f (R ,T ) gravity
NASA Astrophysics Data System (ADS)
Barrientos O., José; Rubilar, Guillermo F.
2016-01-01
We consider Palatini f (R ,T ) gravity models, similar to those introduced by Harko et al. (2012), where the gravitational Lagrangian is given by an arbitrary function of the curvature scalar R and of the trace of the energy-momentum tensor T . Interior spherical static solutions are studied considering the model of matter given by a perfect fluid configuration and a polytropic equation of state. We analyze the curvature singularities found previously for Palatini f (R ) gravity and discuss the possibility to remove them in some particular f (R ,T ) models. We show that it is possible to construct a restricted family of models for which these singularities are not present.
MICRO-SIGMOIDS AS PROGENITORS OF CORONAL JETS: IS ERUPTIVE ACTIVITY SELF-SIMILARLY MULTI-SCALED?
Raouafi, N.-E.; Rust, D. M.; Bernasconi, P. N.; Georgoulis, M. K.
2010-08-01
Observations from the X-ray telescope (XRT) on Hinode are used to study the nature of X-ray-bright points, sources of coronal jets. Several jet events in the coronal holes are found to erupt from small-scale, S-shaped bright regions. This finding suggests that coronal micro-sigmoids may well be progenitors of coronal jets. Moreover, the presence of these structures may explain numerous observed characteristics of jets such as helical structures, apparent transverse motions, and shapes. Analogous to large-scale sigmoids giving rise to coronal mass ejections (CMEs), a promising future task would perhaps be to investigate whether solar eruptive activity, from coronal jets to CMEs, is self-similar in terms of properties and instability mechanisms.
Waters, Thomas J.; Nolan, Brien C.
2009-04-15
In this paper we consider gauge invariant linear perturbations of the metric and matter tensors describing the self-similar Lemaitre-Tolman-Bondi (timelike dust) spacetime containing a naked singularity. We decompose the angular part of the perturbation in terms of spherical harmonics and perform a Mellin transform to reduce the perturbation equations to a set of ordinary differential equations with singular points. We fix initial data so the perturbation is finite on the axis and the past null cone of the singularity, and follow the perturbation modes up to the Cauchy horizon. There we argue that certain scalars formed from the modes of the perturbation remain finite, indicating linear stability of the Cauchy horizon.
NASA Astrophysics Data System (ADS)
Chatterjee, Subhasri; Das, Nandan K.; Kumar, Satish; Mohapatra, Sonali; Pradhan, Asima; Panigrahi, Prasanta K.; Ghosh, Nirmalya
2013-02-01
Multi-resolution analysis on the spatial refractive index inhomogeneities in the connective tissue regions of human cervix reveals clear signature of multifractality. We have thus developed an inverse analysis strategy for extraction and quantification of the multifractality of spatial refractive index fluctuations from the recorded light scattering signal. The method is based on Fourier domain pre-processing of light scattering data using Born approximation, and its subsequent analysis through Multifractal Detrended Fluctuation Analysis model. The method has been validated on several mono- and multi-fractal scattering objects whose self-similar properties are user controlled and known a-priori. Following successful validation, this approach has initially been explored for differentiating between different grades of precancerous human cervical tissues.
Semirational and symbiotic self-similar rogue waves in a (2+1)-dimensional graded-index waveguide
NASA Astrophysics Data System (ADS)
De, Kanchan Kumar; Soloman Raju, Thokala; Kumar, C. N.; Panigrahi, Prasanta K.
2016-07-01
We have investigated the (?)-dimensional variable coefficient-coupled nonlinear Schrödinger equation (vc-CNLSE) in a graded-index waveguide. Similarity transformations are used to convert the vc-CNLSE into constant coefficient CNLSE. Under certain functional constraints we could extract semirational, multi-parametric solution of the associated Manakov system. This family of solutions include known Peregrine soliton, mixture of either bright soliton and rogue wave or dark soliton and rogue wave or breather and rogue wave. Under a distinct set of self-phase modulation and cross-phase modulation coefficients we could establish symbiotic existence of different soliton pairs as solutions. These soliton pairs may constitute of one bright and a dark soliton, two bright solitons or two dark solitons. Finally, when two wave components are directly proportional, we find bright and dark similaritons, self-similar breathers, and rogue waves as different solutions.
NASA Astrophysics Data System (ADS)
Fortuna, Ismael; Thomas, Gilberto L.; de Almeida, Rita M. C.; Graner, François
2012-06-01
We study the topology and geometry of two-dimensional coarsening foam with an arbitrary liquid fraction. To interpolate between the dry limit described by von Neumann’s law and the wet limit described by Marqusee’s equation, the relevant bubble characteristics are the Plateau border radius and a new variable: the effective number of sides. We propose an equation for the individual bubble growth rate as the weighted sum of the growth through bubble-bubble interfaces and through bubble-Plateau border interfaces. The resulting prediction is successfully tested, without an adjustable parameter, using extensive bidimensional Potts model simulations. The simulations also show that a self-similar growth regime is observed at any liquid fraction, and they also determine how the average size growth exponent, side number distribution, and relative size distribution interpolate between the extreme limits. Applications include concentrated emulsions, grains in polycrystals, and other domains with coarsening that is driven by curvature.
NASA Astrophysics Data System (ADS)
Ponce de Leon, J.
2008-03-01
In this paper we find the most general self-similar, homogeneous and isotropic, Ricci-flat cosmologies in 5D. These cosmologies show a number of interesting features: (i) the field equations allow a complete integration in terms of one arbitrary function of the similarity variable, and a free parameter; (ii) the three-dimensional spatial surfaces are flat; (iii) the extra dimension is spacelike; (iv) the general solution is Riemann-flat in 5D but curved in 4D, which means that an observer confined to 4D spacetime can relate this curvature to the presence of matter, as determined by the Einstein equations in 4D. We show that these cosmologies can be interpreted, or used, as 5D Riemann-flat embeddings for spatially flat FRW cosmologies in 4D. In this interpretation our universe arises as a topological separation from an empty 5D Minkowski space, as envisaged by Zeldovich.
Self-similar pulse evolution in a fiber laser with a comb-like dispersion-decreasing fiber.
Tang, Yuxing; Liu, Zhanwei; Fu, Walter; Wise, Frank W
2016-05-15
We demonstrate an erbium fiber laser with self-similar pulse evolution inside a comb-like dispersion-decreasing fiber. We show numerically and experimentally that the comb-like dispersion-decreasing fiber works as well as an ideal one, and offers major practical advantages. The existence of a nonlinear attractor is verified by the invariant pulse chirp over a wide range of net cavity dispersion in experiments. The laser generates 1.3 nJ pulses with parabolic shapes and linear chirps, which can be dechirped to 37 fs. Comb-like dispersion-decreasing fiber should enable the generation of high-energy few-cycle pulses directly from a fiber oscillator. PMID:27176985
NASA Astrophysics Data System (ADS)
Rodríguez-Bermúdez, Germán; Sánchez-Granero, Miguel Ángel; García-Laencina, Pedro J.; Fernández-Martínez, Manuel; Serna, José; Roca-Dorda, Joaquín
2015-12-01
A Brain Computer Interface (BCI) system is a tool not requiring any muscle action to transmit information. Acquisition, preprocessing, feature extraction (FE), and classification of electroencephalograph (EEG) signals constitute the main steps of a motor imagery BCI. Among them, FE becomes crucial for BCI, since the underlying EEG knowledge must be properly extracted into a feature vector. Linear approaches have been widely applied to FE in BCI, whereas nonlinear tools are not so common in literature. Thus, the main goal of this paper is to check whether some Hurst exponent and fractal dimension based estimators become valid indicators to FE in motor imagery BCI. The final results obtained were not optimal as expected, which may be due to the fact that the nature of the analyzed EEG signals in these motor imagery tasks were not self-similar enough.
NASA Astrophysics Data System (ADS)
Churchill, Christopher W.; Trujillo-Gomez, Sebastian; Nielsen, Nikole M.; Kacprzak, Glenn G.
2013-12-01
In Churchill et al., we used halo abundance matching applied to 182 galaxies in the Mg II Absorber-Galaxy Catalog (MAGIICAT) and showed that the mean Mg II λ2796 equivalent width follows a tight inverse-square power law, Wr (2796)vprop(D/R vir)-2, with projected location relative to the galaxy virial radius and that the Mg II absorption covering fraction is effectively invariant with galaxy virial mass, M h, over the range 10.7 <= log M h/M ⊙ <= 13.9. In this work, we explore multivariate relationships between Wr (2796), virial mass, impact parameter, virial radius, and the theoretical cooling radius that further elucidate self-similarity in the cool/warm (T = 104-104.5 K) circumgalactic medium (CGM) with virial mass. We show that virial mass determines the extent and strength of the Mg II absorbing gas such that the mean Wr (2796) increases with virial mass at fixed distance while decreasing with galactocentric distance for fixed virial mass. The majority of the absorbing gas resides within D ~= 0.3 R vir, independent of both virial mass and minimum absorption threshold; inside this region, and perhaps also in the region 0.3 < D/R vir <= 1, the mean Wr (2796) is independent of virial mass. Contrary to absorber-galaxy cross-correlation studies, we show there is no anti-correlation between Wr (2796) and virial mass. We discuss how simulations and theory constrained by observations support self-similarity of the cool/warm CGM via the physics governing star formation, gas-phase metal enrichment, recycling efficiency of galactic scale winds, filament and merger accretion, and overdensity of local environment as a function of virial mass.
Churchill, Christopher W.; Trujillo-Gomez, Sebastian; Nielsen, Nikole M.; Kacprzak, Glenn G.
2013-12-10
In Churchill et al., we used halo abundance matching applied to 182 galaxies in the Mg II Absorber-Galaxy Catalog (MAGIICAT) and showed that the mean Mg II λ2796 equivalent width follows a tight inverse-square power law, W{sub r} (2796)∝(D/R {sub vir}){sup –2}, with projected location relative to the galaxy virial radius and that the Mg II absorption covering fraction is effectively invariant with galaxy virial mass, M {sub h}, over the range 10.7 ≤ log M {sub h}/M {sub ☉} ≤ 13.9. In this work, we explore multivariate relationships between W{sub r} (2796), virial mass, impact parameter, virial radius, and the theoretical cooling radius that further elucidate self-similarity in the cool/warm (T = 10{sup 4}-10{sup 4.5} K) circumgalactic medium (CGM) with virial mass. We show that virial mass determines the extent and strength of the Mg II absorbing gas such that the mean W{sub r} (2796) increases with virial mass at fixed distance while decreasing with galactocentric distance for fixed virial mass. The majority of the absorbing gas resides within D ≅ 0.3 R {sub vir}, independent of both virial mass and minimum absorption threshold; inside this region, and perhaps also in the region 0.3 < D/R {sub vir} ≤ 1, the mean W{sub r} (2796) is independent of virial mass. Contrary to absorber-galaxy cross-correlation studies, we show there is no anti-correlation between W{sub r} (2796) and virial mass. We discuss how simulations and theory constrained by observations support self-similarity of the cool/warm CGM via the physics governing star formation, gas-phase metal enrichment, recycling efficiency of galactic scale winds, filament and merger accretion, and overdensity of local environment as a function of virial mass.
NASA Astrophysics Data System (ADS)
Conti, Caroline; Nunes, Paulo; Ducla Soares, Luís.
2013-09-01
Holoscopic imaging, also known as integral imaging, has been recently attracting the attention of the research community, as a promising glassless 3D technology due to its ability to create a more realistic depth illusion than the current stereoscopic or multiview solutions. However, in order to gradually introduce this technology into the consumer market and to efficiently deliver 3D holoscopic content to end-users, backward compatibility with legacy displays is essential. Consequently, to enable 3D holoscopic content to be delivered and presented on legacy displays, a display scalable 3D holoscopic coding approach is required. Hence, this paper presents a display scalable architecture for 3D holoscopic video coding with a three-layer approach, where each layer represents a different level of display scalability: Layer 0 - a single 2D view; Layer 1 - 3D stereo or multiview; and Layer 2 - the full 3D holoscopic content. In this context, a prediction method is proposed, which combines inter-layer prediction, aiming to exploit the existing redundancy between the multiview and the 3D holoscopic layers, with self-similarity compensated prediction (previously proposed by the authors for non-scalable 3D holoscopic video coding), aiming to exploit the spatial redundancy inherent to the 3D holoscopic enhancement layer. Experimental results show that the proposed combined prediction can improve significantly the rate-distortion performance of scalable 3D holoscopic video coding with respect to the authors' previously proposed solutions, where only inter-layer or only self-similarity prediction is used.
NASA Astrophysics Data System (ADS)
Balsara, Dinshaw S.; Vides, Jeaniffer; Gurski, Katharine; Nkonga, Boniface; Dumbser, Michael; Garain, Sudip; Audit, Edouard
2016-01-01
Just as the quality of a one-dimensional approximate Riemann solver is improved by the inclusion of internal sub-structure, the quality of a multidimensional Riemann solver is also similarly improved. Such multidimensional Riemann problems arise when multiple states come together at the vertex of a mesh. The interaction of the resulting one-dimensional Riemann problems gives rise to a strongly-interacting state. We wish to endow this strongly-interacting state with physically-motivated sub-structure. The self-similar formulation of Balsara [16] proves especially useful for this purpose. While that work is based on a Galerkin projection, in this paper we present an analogous self-similar formulation that is based on a different interpretation. In the present formulation, we interpret the shock jumps at the boundary of the strongly-interacting state quite literally. The enforcement of the shock jump conditions is done with a least squares projection (Vides, Nkonga and Audit [67]). With that interpretation, we again show that the multidimensional Riemann solver can be endowed with sub-structure. However, we find that the most efficient implementation arises when we use a flux vector splitting and a least squares projection. An alternative formulation that is based on the full characteristic matrices is also presented. The multidimensional Riemann solvers that are demonstrated here use one-dimensional HLLC Riemann solvers as building blocks. Several stringent test problems drawn from hydrodynamics and MHD are presented to show that the method works. Results from structured and unstructured meshes demonstrate the versatility of our method. The reader is also invited to watch a video introduction to multidimensional Riemann solvers on http://www.nd.edu/~dbalsara/Numerical-PDE-Course.
CO2 volume fluxes outgassing from champagne glasses in tasting conditions: flute versus coupe.
Liger-Belair, Gérard; Villaume, Sandra; Cilindre, Clara; Polidori, Guillaume; Jeandet, Philippe
2009-06-10
Measurements of CO(2) fluxes outgassing from glasses containing a standard Champagne wine initially holding about 11.5 g L(-1) of dissolved CO(2) were presented, in tasting conditions, during the first 10 min following the pouring process. Experiments were performed at room temperature, with a flute and a coupe, respectively. The progressive loss of dissolved CO(2) concentration with time was found to be significantly higher in the coupe than in the flute, which finally constitutes the first analytical proof that the flute prolongs the drink's chill and helps it to retain its effervescence in contrast with the coupe. Moreover, CO(2) volume fluxes outgassing from the coupe were found to be much higher in the coupe than in the flute in the early moments following pouring, whereas this tendency reverses from about 3 min after pouring. Correlations were proposed between CO(2) volume fluxes outgassing from the flute and the coupe and their continuously decreasing dissolved CO(2) concentration. The contribution of effervescence to the global kinetics of CO(2) release was discussed and modeled by use of results developed over recent years. Due to a much shallower liquid level in the coupe, bubbles collapsing at the free surface of the coupe were found to be significantly smaller than those collapsing at the free surface of the flute, and CO(2) volume fluxes released by collapsing bubbles only were found to be approximately 60% smaller in the coupe than in the flute. Finally, the contributions of gas discharge by invisible diffusion through the free surface areas of the flute and coupe were also approached and compared for each type of drinking vessel. PMID:19419170
NASA Astrophysics Data System (ADS)
Yang, X. I. A.; Meneveau, C.; Marusic, I.; Biferale, L.
2016-08-01
In wall-bounded turbulence, the moment generating functions (MGFs) of the streamwise velocity fluctuations
NASA Astrophysics Data System (ADS)
Testik, F. Y.; Ungarish, M.
2016-05-01
Self-similar propagation of gravity currents through vegetation-like obstruction arrays was elucidated. We conducted a theoretical analysis by using an approximate model for one-layer and two-layer situations. This model incorporates a balance between the driving buoyancy (i.e., pressure) force and the resisting obstruction-induced drag force that is proportional to |" separators=" u | λ (where |" separators=" u | —speed in the layer and λ —a constant). We focused our attention on solutions with λ ≥ 1. We considered both gravity currents in a deep ambient fluid (including both continuous-flux release currents and constant-volume currents) and lock-exchange currents and demonstrated that a variety of such flows are governed by physically acceptable similarity solutions. For gravity currents in a deep ambient fluid, our theoretical analysis revealed four distinct classes of similarity solutions. Class I solutions predict gravity currents with a triangular profile (i.e., linear current interface with a constant negative slope) and a front/nose position that is a linear function of time. The physical presence of such self-similar currents was reported in recent experimental observations for currents sustained by a continuous-flux release source. We showed that theoretical predictions of Class I solutions capture the behavior of these experimental currents well. Class II solutions predict gravity currents with a non-linear profile/interface and a constant height at the source. Though physically acceptable, we could not relate this class of solutions to presently known currents. Class III solutions correspond to constant-volume currents and predict a linear increase of velocity within the current toward the nose. We discussed this class of similarity solutions using previously reported experimental observations of such currents. Class IV solutions cover the rest of the parameter domain for all other continuous-flux release gravity currents (except those that
NASA Astrophysics Data System (ADS)
Krasnyuk, I. B.; Taranets, R. M.; Yurchenko, V. M.
2011-04-01
We examine the response to an external magnetic field by a multi-layer superconductor with an electrical resistance ρff(b)αbσ, where b is the dimensionless magnetic induction and σ is a parameter characterizing the ratio of the pinning activation energy to the energy of thermal fluctuations. When σ > 1 the sample is in the vortex glass phase, when 0 < σ < 1, it is in the vortex liquid phase, and a vortex glass to vortex liquid phase transition takes place at σ = 1. In the vortex glass phase, the magnetic field penetrates into the superconductor in the form of a self-similar wave. At all times it penetrates to a finite depth and its front moves at a finite velocity which depends on the parameters of the problem, such as the rate of pumping by the external magnetic field. In the vortex liquid phase the magnetic field penetrates to an infinite depth. Thus, the magnetic field penetrates to an infinite depth in the superconductor during a transition from the vortex glass phase into the vortex liquid phase.
NASA Astrophysics Data System (ADS)
Bhat, Pradeep P.; Appathurai, Santosh; Harris, Michael T.; Basaran, Osman A.
2012-08-01
A characteristic feature of pinch-off of fluid threads is the formation of drops connected to thinning filaments. This phenomenon is encountered in a number of widely used applications requiring the production of drops such as electronics microfabrication via inkjet printing, spray coating/drying, and microarraying. In pinch-off of viscoelastic fluid threads, the region that connects the drops to the filaments develops into a sharp corner. Recently, Clasen et al. [J. Fluid Mech. 556, 283-308 (2006)], 10.1017/S0022112006009633 showed that such a corner evolves self-similarly. They, however, neglected the capillary pressure in the drop. A modified similarity solution is presented here that incorporates the drop capillary-pressure term, and transient simulations of corner region profiles are shown to converge onto the new similarity solution better than that of Clasen et al. Indeed, the new similarity solution is valid in all the three regions: the drop, the corner, and the filament regions. Similarity solutions, so obtained, are particularly useful in capillary-breakup rheometry where they are employed to estimate a fluid's extensional viscosity—a material property of viscoelastic fluids that influences greatly the drop formation process.
Jirauschek, Christian; Ilday, F. Oemer
2011-06-15
A semianalytic theory for the pulse dynamics in similariton amplifiers and lasers is presented, based on a model pulse with adaptive shape. By changing a single parameter, this test function can be continuously tweaked between a pure Gaussian and a pure parabolic profile and can even represent sech-like pulses, the shape of a soliton. This approach allows us to describe the pulse evolution in the self-similar and other regimes of optical propagation. Employing the method of moments, the evolution equations for the characteristic pulse parameters are derived from the governing nonlinear Schroedinger or Ginzburg-Landau equation. Due to its greatly reduced complexity, this description allows for extensive parameter optimization, and can aid intuitive understanding of the dynamics. As an application of this approach, we model a soliton-similariton laser and validate the results against numerical simulations. This constitutes a semianalytic model of the soliton-similariton laser. Due to the versatility of the model pulse, it can also prove useful in other application areas.
A Class of Dust-Like Self-Similar Solutions of the Massless Einstein-Vlasov System
NASA Astrophysics Data System (ADS)
Rendall, Alan D.; Velázquez, Juan J. L.
2011-07-01
In this paper the existence of a class of self-similar solutions of the Einstein-Vlasov system is proved. The initial data for these solutions are not smooth, with their particle density being supported in a submanifold of codimension one. They can be thought of as intermediate between smooth solutions of the Einstein-Vlasov system and dust. The motivation for studying them is to obtain insights into possible violation of weak cosmic censorship by solutions of the Einstein-Vlasov system. By assuming a suitable form of the unknowns it is shown that the existence question can be reduced to that of the existence of a certain type of solution of a four-dimensional system of ordinary differential equations depending on two parameters. This solution starts at a particular point $P_0$ and converges to a stationary solution $P_1$ as the independent variable tends to infinity. The existence proof is based on a shooting argument and involves relating the dynamics of solutions of the four-dimensional system to that of solutions of certain two- and three-dimensional systems obtained from it by limiting processes.
Application of a Self-Similar Pressure Profile to Sunyaev-Zeldovich Effect Data from Galaxy Clusters
NASA Technical Reports Server (NTRS)
Mroczkowski, Tony; Bonamente, Max; Carlstrom, John E.; Culverhouse, Thomas L.; Greer, Christopher; Hawkins, David; Hennessy, Ryan; Joy, Marshall; Lamb, James W.; Leitch, Erik M.; Loh, Michael; Maughan, Ben; Marrone, Daniel P.; Miller, Amber; Muchovej, Stephen; Nagai, Daisuke; Pryke, Clem; Sharp, Matthew; Woody, David
2009-01-01
We investigate the utility of a new, self-similar pressure profile for fitting Sunyaev-Zel'dovich (SZ) effect observations of galaxy clusters. Current SZ imaging instruments-such as the Sunyaev-Zel'dovich Array (SZA)- are capable of probing clusters over a large range in a physical scale. A model is therefore required that can accurately describe a cluster's pressure profile over a broad range of radii from the core of the cluster out to a significant fraction of the virial radius. In the analysis presented here, we fit a radial pressure profile derived from simulations and detailed X-ray analysis of relaxed clusters to SZA observations of three clusters with exceptionally high-quality X-ray data: A1835, A1914, and CL J1226.9+3332. From the joint analysis of the SZ and X-ray data, we derive physical properties such as gas mass, total mass, gas fraction and the intrinsic, integrated Compton y-parameter. We find that parameters derived from the joint fit to the SZ and X-ray data agree well with a detailed, independent X-ray-only analysis of the same clusters. In particular, we find that, when combined with X-ray imaging data, this new pressure profile yields an independent electron radial temperature profile that is in good agreement with spectroscopic X-ray measurements.
Prajapati, R. P.; Chhajlani, R. K.; Soni, G. D.
2008-06-15
The effects of uniform rotation, finite electrical resistivity, electron inertia, and Hall current on the self-gravitational instability of anisotropic pressure plasma with generalized polytrope laws have been studied. A general dispersion relation is obtained with the help of the relevant linearized perturbed magnetohydrodynamic (MHD) equations incorporating the relevant contributions of various effects of the problem using the method of normal mode analysis. The general dispersion relation is further reduced for the special cases of rotation; i.e., parallel and perpendicular to the direction of the magnetic field. The longitudinal and transverse modes of propagation are discussed separately for investigation of condition of instability. The effects of rotation, Hall current, finite electron inertia, and polytropic indices are discussed on the gravitational, ''firehose,'' and ''mirror'' instabilities. The numerical calculations have been performed to obtain the dependence of the growth rate of the gravitational unstable mode on the various physical parameters involved. The finite electrical resistivity, rotation, and Hall current have a stabilizing influence on the growth rate of the unstable mode of wave propagation. The finite electrical resistivity removes the effect of magnetic field and polytropic index from the condition of instability in the transverse mode of propagation for both the cases of rotation. It is also found that the Jeans criterion of gravitational instability depends upon rotation, electron inertia, and polytropic indices. In the case of transverse mode of propagation with the axis of rotation parallel to the magnetic field, it is observed that the region of instability and the value of the critical Jeans wavenumber are larger for the Chew-Goldberger-Low set of equations in comparison with the MHD set of equations. The stability of the system is discussed by applying Routh-Hurwitz criterion. The inclusion of rotation or Hall current or both
NASA Astrophysics Data System (ADS)
Gao, Lan
2014-10-01
The Rayleigh-Taylor (RT) instability has been extensively studied because of its relevance to ignition target designs in inertial confinement fusion, material strength studies in high energy density physics, and astrophysical systems. This talk presents the first measurements of magnetic field generation by the nonlinear RT instability in laser-accelerated planar foils using ultrafast proton radiography at the OMEGA EP Laser System. Thin plastic foils were irradiated with 4-kJ, 2.5-ns laser pulses at focused laser intensities of ~1014 W /cm2. Target modulations were seeded by laser nonuniformities and amplified during the target-acceleration phase by the RT instability growth. A high-energy proton beam tracked the hydrodynamic evolution of the target and mapped the magnetic field spatial distribution with high spatial and temporal resolution. The experimental data show self-similar behavior in the growing cellular magnetic field structures. The calculated magnetic cell-merging rate is consistent with the value determined by earlier x-ray measurements, linking the cellular magnetic field structures with the RT bubble and spike growth. The results are consistent with two-dimensional magnetohydrodynamic simulations, showing MG-level magnetic field generation in the laser-driven foil. The work could benefit the understanding of magnetic-seed-field generation in high energy density plasmas and the flow-driven processes that induce global magnetic structures prior to their turbulent amplification by the dynamo process. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0001944.
NASA Astrophysics Data System (ADS)
Volpes, L.; Bothmer, V.
2015-10-01
We present an application of the stereoscopic self-similar-expansion model (SSSEM) to Solar Terrestrial Relations Observatory (STEREO)/ Sun-Earth Connection Coronal and Heliospheric Investigation (SECCHI) observations of the CME on 3 April 2010 and its associated shock. The aim is to verify whether CME-driven shock parameters can be inferred from the analysis of j-maps. For this purpose, we used the SSSEM to derive the CME and the shock kinematics. Arrival times and speeds, inferred assuming either propagation at constant speed or with uniform deceleration, agree well with Advanced Composition Explorer (ACE) measurements. The shock standoff distance [Δ], the density compression [ρd/ρu], and the Mach number [M] were calculated by combining the results obtained for the CME and shock kinematics with models for the shock location. Their values were extrapolated to L1 and compared to in-situ data. The in-situ standoff distance was obtained from ACE solar-wind measurements, and the Mach number and compression ratio were provided by the interplanetary shock database of the Harvard-Smithsonian Center for Astrophysics. They are ρd/ρu =2.84 and M = 2.2. The best fit to observations was obtained when the SSSEM half-width λ= 40°, and the CME and shock propagate with uniform deceleration. In this case we found Δ= 23 R_{⊙}, ρd/ρu =2.61, and M = 2.93. The study shows that CME-driven shock parameters can be estimated from the analysis of time-elongation plots and can be used to predict their in-situ values.
Lidz, B.H.; Brock, J.C.; Nagle, D.B.
2008-01-01
A recently developed remote-sensing instrument acquires high-quality digital photographs in shallow-marine settings within water depths of 15 m. The technology, known as the Along-Track Reef-Imaging System, provides remarkably clear, georeferenced imagery that allows visual interpretation of benthic class (substrates, organisms) for mapping coral reef habitats, as intended. Unforeseen, however, are functions new to the initial technologic purpose: interpr??table evidence for real-time biogeologic processes and for perception of scaled-up skeletal self-similarity of scleractinian microstructure. Florida reef sea trials lacked the grid structure required to map contiguous habitat and submarine topography. Thus, only general observations could be made relative to times and sites of imagery. Degradation of corals was nearly universal; absence of reef fish was profound. However, ???1% of more than 23,600 sea-trial images examined provided visual evidence for local environs and processes. Clarity in many images was so exceptional that small tracks left by organisms traversing fine-grained carbonate sand were visible. Other images revealed a compelling sense, not yet fully understood, of the microscopic wall structure characteristic of scleractinian corals. Conclusions drawn from classifiable images are that demersal marine animals, where imaged, are oblivious to the equipment and that the technology has strong capabilities beyond mapping habitat. Imagery acquired along predetermined transects that cross a variety of geomorphic features within depth limits will ( 1) facilitate construction of accurate contour maps of habitat and bathymetry without need for ground-truthing, (2) contain a strong geologic component of interpreted real-time processes as they relate to imaged topography and regional geomorphology, and (3) allow cost-effective monitoring of regional- and local-scale changes in an ecosystem by use of existing-image global-positioning system coordinates to re
NASA Astrophysics Data System (ADS)
Dauenhauer, Eric C.; Majdalani, Joseph
2003-06-01
This article describes a self-similarity solution of the Navier-Stokes equations for a laminar, incompressible, and time-dependent flow that develops within a channel possessing permeable, moving walls. The case considered here pertains to a channel that exhibits either injection or suction across two opposing porous walls while undergoing uniform expansion or contraction. Instances of direct application include the modeling of pulsating diaphragms, sweat cooling or heating, isotope separation, filtration, paper manufacturing, irrigation, and the grain regression during solid propellant combustion. To start, the stream function and the vorticity equation are used in concert to yield a partial differential equation that lends itself to a similarity transformation. Following this similarity transformation, the original problem is reduced to solving a fourth-order differential equation in one similarity variable η that combines both space and time dimensions. Since two of the four auxiliary conditions are of the boundary value type, a numerical solution becomes dependent upon two initial guesses. In order to achieve convergence, the governing equation is first transformed into a function of three variables: The two guesses and η. At the outset, a suitable numerical algorithm is applied by solving the resulting set of twelve first-order ordinary differential equations with two unspecified start-up conditions. In seeking the two unknown initial guesses, the rapidly converging inverse Jacobian method is applied in an iterative fashion. Numerical results are later used to ascertain a deeper understanding of the flow character. The numerical scheme enables us to extend the solution range to physical settings not considered in previous studies. Moreover, the numerical approach broadens the scope to cover both suction and injection cases occurring with simultaneous wall motion.
The density structure and star formation rate of non-isothermal polytropic turbulence
NASA Astrophysics Data System (ADS)
Federrath, Christoph; Banerjee, Supratik
2015-04-01
The interstellar medium of galaxies is governed by supersonic turbulence, which likely controls the star formation rate (SFR) and the initial mass function (IMF). Interstellar turbulence is non-universal, with a wide range of Mach numbers, magnetic fields strengths and driving mechanisms. Although some of these parameters were explored, most previous works assumed that the gas is isothermal. However, we know that cold molecular clouds form out of the warm atomic medium, with the gas passing through chemical and thermodynamic phases that are not isothermal. Here we determine the role of temperature variations by modelling non-isothermal turbulence with a polytropic equation of state (EOS), where pressure and temperature are functions of gas density, P˜ ρ ^Γ, T ˜ ρΓ - 1. We use grid resolutions of 20483 cells and compare polytropic exponents Γ = 0.7 (soft EOS), Γ = 1 (isothermal EOS) and Γ = 5/3 (stiff EOS). We find a complex network of non-isothermal filaments with more small-scale fragmentation occurring for Γ < 1, while Γ > 1 smoothes out density contrasts. The density probability distribution function (PDF) is significantly affected by temperature variations, with a power-law tail developing at low densities for Γ > 1. In contrast, the PDF becomes closer to a lognormal distribution for Γ ≲ 1. We derive and test a new density variance-Mach number relation that takes Γ into account. This new relation is relevant for theoretical models of the SFR and IMF, because it determines the dense gas mass fraction of a cloud, from which stars form. We derive the SFR as a function of Γ and find that it decreases by a factor of ˜5 from Γ = 0.7 to 5/3.
Hsiang, Wei-Wei; Chang, Chia-Hao; Cheng, Chien-Po; Lai, Yinchieh
2009-07-01
We report the first (to our knowledge) experimental observation of passive synchronization between a 1.03 microm self-similar pulse and a 1.56 microm bound-soliton bunch in a two-color mode-locked fiber laser. The self-similar pulse can form an effective potential well of several picoseconds to trap the copropagating bound solitons in the shared-fiber section. Such synchronization mechanism is supported by the experimental evidence of smaller time separation between the bound solitons under synchronization. In addition, the self-similar pulse and bound solitons can still remain locked under the periodic collision of another 1.56 microm unlocked pulse train. PMID:19571968
NASA Astrophysics Data System (ADS)
Kierkels, A. H. M.; Velázquez, J. J. L.
2016-06-01
We construct a family of self-similar solutions with fat tails to a quadratic kinetic equation. This equation describes the long time behaviour of weak solutions with finite mass to the weak turbulence equation associated to the nonlinear Schrödinger equation. The solutions that we construct have finite mass, but infinite energy. In Kierkels and Velázquez (J Stat Phys 159:668-712, 2015) self-similar solutions with finite mass and energy were constructed. Here we prove upper and lower exponential bounds on the tails of these solutions.
Zhao, Jian; Li, Wenxue; Wang, Chao; Liu, Yang; Zeng, Heping
2014-12-29
We report on the generation of 80-W average power 38-fs laser pulse from a 2-m polarization-maintaining large-mode-area photonic crystal fiber amplifier with high pump absorption coefficient. The pre-chirping management was demonstrated to play a key role on the self-similar amplification. The achieved spectral bandwidth and compressed pulse duration were determined by the interplay between self-phase modulation and finite gain bandwidth. The power scaling in the self-similar fiber amplifier system was eventually limited by the onset of stimulated Raman scattering. PMID:25607187
NASA Astrophysics Data System (ADS)
Kierkels, A. H. M.; Velázquez, J. J. L.
2016-04-01
We construct a family of self-similar solutions with fat tails to a quadratic kinetic equation. This equation describes the long time behaviour of weak solutions with finite mass to the weak turbulence equation associated to the nonlinear Schrödinger equation. The solutions that we construct have finite mass, but infinite energy. In Kierkels and Velázquez (J Stat Phys 159:668-712, 2015) self-similar solutions with finite mass and energy were constructed. Here we prove upper and lower exponential bounds on the tails of these solutions.
NASA Astrophysics Data System (ADS)
Orban, Chris; Weinberg, David H.
2011-09-01
Motivated by cosmological surveys that demand accurate theoretical modeling of the baryon acoustic oscillation (BAO) feature in galaxy clustering, we analyze N-body simulations in which a BAO-like Gaussian bump modulates the linear theory correlation function ξL(r)=(r0/r)n+3 of an underlying self-similar model with initial power spectrum P(k)=Akn. These simulations test physical and analytic descriptions of BAO evolution far beyond the range of most studies, since we consider a range of underlying power spectra (n=-0.5, -1, -1.5) and evolve simulations to large effective correlation amplitudes (equivalent to σ8=4-12 for rbao=100h-1Mpc). In all cases, nonlinear evolution flattens and broadens the BAO bump in ξ(r) while approximately preserving its area. This evolution resembles a diffusion process in which the bump width σbao is the quadrature sum of the linear theory width and a length proportional to the rms relative displacement Σpair(rbao) of particle pairs separated by rbao. For n=-0.5 and n=-1, we find no detectable shift of the location of the BAO peak, but the peak in the n=-1.5 model shifts steadily to smaller scales, following rpeak/rbao=1-1.08(r0/rbao)1.5. The perturbation theory scheme of McDonald (2007) [P. McDonald, Phys. Rev. DPRVDAQ1550-7998 75, 043514 (2007).10.1103/PhysRevD.75.043514] and, to a lesser extent, standard 1-loop perturbation theory are fairly successful at explaining the nonlinear evolution of the Fourier power spectrum of our models. Analytic models also explain why the ξ(r) peak shifts much more for n=-1.5 than for n≥-1, though no ab initio model we have examined reproduces all of our numerical results. Simulations with Lbox=10rbao and Lbox=20rbao yield consistent results for ξ(r) at the BAO scale, provided one corrects for the integral constraint imposed by the uniform density box.
NASA Technical Reports Server (NTRS)
Sittler, E. C., Jr.; Scudder, J. D.
1979-01-01
Empirical evidence is presented that solar wind thermal electrons obey a polytrope law with polytrope index gamma = 1.175 plus or minus 0.03. The Voyager 2 and Mariner 10 data used as evidence are compared and discussed. The theoretical predictions that solar wind thermal electrons in the asymptotic solar wind should obey a polytrope law with polytrope index gamma = 1.16 plus or minus. The widespread impressions in the literature that solar wind electrons behave more like an isothermal than adiabatic gas, and the arguments that Coulomb collisions are the dominant stochastic process shaping observed electron distribution functions in the solar wind are reexamined, reviewed and evaluated. The assignment of the interplanetary potential as equal to approximately seven times the temperature of the thermal electrons is discussed.
NASA Astrophysics Data System (ADS)
Yang, Bin; Zhong, Wei-Ping; Belić, Milivoj R.
2010-05-01
We study analytically and numerically the propagation of spatial solitons in a two-dimensional strongly nonlocal nonlinear medium. Exact analytical solutions in the form of self-similar spatial solitons are obtained involving higher-order Hermite-Gaussian functions. Our theoretical predictions provide new insights into the low-energy spatial soliton transmission with high fidelity.
Spence, H.E.; Kivelson, M.G.
1990-08-15
The polytropic index is obtained as a function of distance along the midnight meridian in the terrestrial magnetotail. As our purpose is to establish the effects of the finite width of the magnetotail, we use a simple theoretical model of plasma sheet convection, i.e., two-dimensional field structure and adiabatic inward convection of a uniform distant tail source. Particle orbits are treated independently for portions of the phase space distribution on shells of constant energy. On the midnight meridian, the moments of the distribution are parameterized by tau, the ratio of half the cross-tail potential energy to the characteristic Maxwellian energy of a distant down-tail plasma source. We infer from the model the plasma pressure, P, and the number density, n, along the midnight meridian as a function of tau. P and n define locally an effective polytropic index. Gamma ranges between 5/3 and 1, depending on the value of tau and on geocentric distance. The qualitative differences between the recent empirical determinations of the polytropic index by Baumjohann and Paschmann and Huang et al. may be accounted for in part by this simple model.
Spence, H.E. ); Kivelson, M.G. )
1990-04-01
The authors have obtained the polytropic index as a function of distance along the midnight meridian in the terrestrial magnetotail. As their purpose is to establish the effects of the finite width of the magnetotail, they use a simple theoretical model of plasma sheet convection, i.e., 2-dimensional (2D) field structure and adiabatic inward convection of a uniform distant tail source. Particle orbits are treated independently for portions of the phase space distribution on shells of constant energy. On the midnight meridian, the moments of the distribution are parameterized by {tau}, the ratio of half the crosstail potential energy to the characteristic maxwellian energy of a distant downtail plasma source. They infer from the model the plasma pressure, P, and the number density, n, along the midnight meridian as a function of {tau}. P and n define locally an effective polytropic index, {gamma}. They find that {gamma} ranges between 5/3 and 1, depending on the value of {tau} and on geocentric distance. They suggest that the qualitative differences between the recent empirical determinations of the polytropic index by Baumjohann et al. (1989) and Huang et al. (1989) may be accounted for in part by this simple model.
Battini, J L; Heard, J M; Danos, O
1992-01-01
The envelope glycoproteins (SU) of mammalian type C retroviruses possess an amino-terminal domain of about 200 residues, which is involved in binding a cell surface receptor. In this domain, highly conserved amino acid sequences are interrupted by two segments of variable length and sequence, VRA and VRB. We have studied the role of these variable regions in receptor recognition and binding by constructing chimeric molecules in which portions of the amino-terminal domains from amphotropic (4070A), xenotropic (NZB), and polytropic (MCF 247) murine leukemia virus SU proteins were permuted. These chimeras, which exchanged either one or two variable regions, were expressed at the surface of replication-defective viral particles by a pseudotyping assay. Wild-type or recombinant env genes were transfected into a cell line producing Moloney murine leukemia virus particles devoid of envelope glycoproteins in which a retrovirus vector genome carrying an Escherichia coli lacZ gene was packaged. The host range and sensitivity to interference of pseudotyped virions were assayed, and we observed which permutations resulted in receptor switch or loss of function. Our results indicate that the determinants of receptor choice are found within the just 120 amino acids of SU proteins. Downstream sequences contribute to the stabilization of the receptor-specific structure. PMID:1310758
NASA Astrophysics Data System (ADS)
Kim, Jeong-Gyu; Kim, Woong-Tae; Seo, Young Min; Hong, Seung Soo
2012-12-01
We investigate the gravitational instability (GI) of rotating, vertically stratified, pressure-confined, polytropic gas disks using a linear stability analysis as well as analytic approximations. The disks are initially in vertical hydrostatic equilibrium and bounded by a constant external pressure. We find that the GI of a pressure-confined disk is in general a mixed mode of the conventional Jeans and distortional instabilities, and is thus an unstable version of acoustic-surface-gravity waves. The Jeans mode dominates in weakly confined disks or disks with rigid boundaries. On the other hand, when the disk has free boundaries and is strongly pressure confined, the mixed GI is dominated by the distortional mode that is surface-gravity waves driven unstable under their own gravity and thus incompressible. We demonstrate that the Jeans mode is gravity-modified acoustic waves rather than inertial waves and that inertial waves are almost unaffected by self-gravity. We derive an analytic expression for the effective sound speed c eff of acoustic-surface-gravity waves. We also find expressions for the gravity reduction factors relative to a razor-thin counterpart that are appropriate for the Jeans and distortional modes. The usual razor-thin dispersion relation, after correcting for c eff and the reduction factors, closely matches the numerical results obtained by solving a full set of linearized equations. The effective sound speed generalizes the Toomre stability parameter of the Jeans mode to allow for the mixed GI of vertically stratified, pressure-confined disks.
NASA Technical Reports Server (NTRS)
Lerche, I.
1978-01-01
One-dimensional self-similar isothermal flow behind a blast wave propagating in a medium whose density varies with distance is investigated for the cases of one-dimensional and two-dimensional flow. The isothermal flow model is adopted as an alternative to adiabatic models of self-similar flow, which neglect heat flux. The topology of the one-dimensional flow solutions, the singularities, and the influence of boundary conditions are discussed; the instability of the isothermal blast waves against nonself-similar perturbations is also considered. The number of critical points in the two-dimensional solutions is found to vary from the number in the one-dimensional problem.
NASA Astrophysics Data System (ADS)
Harrington, Rebecca M.; Kwiatek, Grzegorz; Moran, Seth C.
2015-07-01
We analyze a group of 6073 low-frequency earthquakes recorded during a week-long temporary deployment of broadband seismometers at distances of less than 3 km from the crater at Mount St. Helens in September of 2006. We estimate the seismic moment (M0) and spectral corner frequency (f0) using a spectral ratio approach for events with a high signal-to-noise (SNR) ratio that have a cross-correlation coefficient of 0.8 or greater with at least five other events. A cluster analysis of cross-correlation values indicates that the group of 421 events meeting the SNR and cross-correlation criteria forms eight event families that exhibit largely self-similar scaling. We estimate the M0 and f0 values of the 421 events and calculate their static stress drop and scaled energy (ER/M0) values. The estimated values suggest self-similar scaling within families, as well as between five of eight families (i.e., M0∝f0-3 and ER/M0∝ constant). We speculate that differences in scaled energy values for the two families with variable scaling may result from a lack of resolution in the velocity model. The observation of self-similar scaling is the first of its kind for such a large group of low-frequency volcanic tectonic events occurring during a single active dome extrusion eruption.
NASA Astrophysics Data System (ADS)
Gerlich, Nikolas; Rostek, Stefan
2015-09-01
We derive a heuristic method to estimate the degree of self-similarity and serial correlation in financial time series. Especially, we propagate the use of a tailor-made selection of different estimation techniques that are used in various fields of time series analysis but until now have not consequently found their way into the finance literature. Following the idea of portfolio diversification, we show that considerable improvements with respect to robustness and unbiasedness can be achieved by using a basket of estimation methods. With this methodological toolbox at hand, we investigate real market data to show that noticeable deviations from the assumptions of constant self-similarity and absence of serial correlation occur during certain periods. On the one hand, this may shed a new light on seemingly ambiguous scientific findings concerning serial correlation of financial time series. On the other hand, a proven time-changing degree of self-similarity may help to explain high-volatility clusters of stock price indices.
Harrington, Rebecca M.; Kwiatek, Grzegorz; Moran, Seth C.
2015-01-01
We analyze a group of 6073 low-frequency earthquakes recorded during a week-long temporary deployment of broadband seismometers at distances of less than 3 km from the crater at Mount St. Helens in September of 2006. We estimate the seismic moment (M0) and spectral corner frequency (f0) using a spectral ratio approach for events with a high signal-to-noise (SNR) ratio that have a cross-correlation coefficient of 0.8 or greater with at least five other events. A cluster analysis of cross-correlation values indicates that the group of 421 events meeting the SNR and cross-correlation criteria forms eight event families that exhibit largely self-similar scaling. We estimate the M0 and f0 values of the 421 events and calculate their static stress drop and scaled energy (ER/M0) values. The estimated values suggest self-similar scaling within families, as well as between five of eight families (i.e., and constant). We speculate that differences in scaled energy values for the two families with variable scaling may result from a lack of resolution in the velocity model. The observation of self-similar scaling is the first of its kind for such a large group of low-frequency volcanic tectonic events occurring during a single active dome extrusion eruption.
Bouda, Martin; Caplan, Joshua S.; Saiers, James E.
2016-01-01
Fractal dimension (FD), estimated by box-counting, is a metric used to characterize plant anatomical complexity or space-filling characteristic for a variety of purposes. The vast majority of published studies fail to evaluate the assumption of statistical self-similarity, which underpins the validity of the procedure. The box-counting procedure is also subject to error arising from arbitrary grid placement, known as quantization error (QE), which is strictly positive and varies as a function of scale, making it problematic for the procedure's slope estimation step. Previous studies either ignore QE or employ inefficient brute-force grid translations to reduce it. The goals of this study were to characterize the effect of QE due to translation and rotation on FD estimates, to provide an efficient method of reducing QE, and to evaluate the assumption of statistical self-similarity of coarse root datasets typical of those used in recent trait studies. Coarse root systems of 36 shrubs were digitized in 3D and subjected to box-counts. A pattern search algorithm was used to minimize QE by optimizing grid placement and its efficiency was compared to the brute force method. The degree of statistical self-similarity was evaluated using linear regression residuals and local slope estimates. QE, due to both grid position and orientation, was a significant source of error in FD estimates, but pattern search provided an efficient means of minimizing it. Pattern search had higher initial computational cost but converged on lower error values more efficiently than the commonly employed brute force method. Our representations of coarse root system digitizations did not exhibit details over a sufficient range of scales to be considered statistically self-similar and informatively approximated as fractals, suggesting a lack of sufficient ramification of the coarse root systems for reiteration to be thought of as a dominant force in their development. FD estimates did not
Bouda, Martin; Caplan, Joshua S; Saiers, James E
2016-01-01
Fractal dimension (FD), estimated by box-counting, is a metric used to characterize plant anatomical complexity or space-filling characteristic for a variety of purposes. The vast majority of published studies fail to evaluate the assumption of statistical self-similarity, which underpins the validity of the procedure. The box-counting procedure is also subject to error arising from arbitrary grid placement, known as quantization error (QE), which is strictly positive and varies as a function of scale, making it problematic for the procedure's slope estimation step. Previous studies either ignore QE or employ inefficient brute-force grid translations to reduce it. The goals of this study were to characterize the effect of QE due to translation and rotation on FD estimates, to provide an efficient method of reducing QE, and to evaluate the assumption of statistical self-similarity of coarse root datasets typical of those used in recent trait studies. Coarse root systems of 36 shrubs were digitized in 3D and subjected to box-counts. A pattern search algorithm was used to minimize QE by optimizing grid placement and its efficiency was compared to the brute force method. The degree of statistical self-similarity was evaluated using linear regression residuals and local slope estimates. QE, due to both grid position and orientation, was a significant source of error in FD estimates, but pattern search provided an efficient means of minimizing it. Pattern search had higher initial computational cost but converged on lower error values more efficiently than the commonly employed brute force method. Our representations of coarse root system digitizations did not exhibit details over a sufficient range of scales to be considered statistically self-similar and informatively approximated as fractals, suggesting a lack of sufficient ramification of the coarse root systems for reiteration to be thought of as a dominant force in their development. FD estimates did not
Kim, Jeong-Gyu; Kim, Woong-Tae; Seo, Young Min; Hong, Seung Soo E-mail: wkim@astro.snu.ac.kr E-mail: sshong@astro.snu.ac.kr
2012-12-20
We investigate the gravitational instability (GI) of rotating, vertically stratified, pressure-confined, polytropic gas disks using a linear stability analysis as well as analytic approximations. The disks are initially in vertical hydrostatic equilibrium and bounded by a constant external pressure. We find that the GI of a pressure-confined disk is in general a mixed mode of the conventional Jeans and distortional instabilities, and is thus an unstable version of acoustic-surface-gravity waves. The Jeans mode dominates in weakly confined disks or disks with rigid boundaries. On the other hand, when the disk has free boundaries and is strongly pressure confined, the mixed GI is dominated by the distortional mode that is surface-gravity waves driven unstable under their own gravity and thus incompressible. We demonstrate that the Jeans mode is gravity-modified acoustic waves rather than inertial waves and that inertial waves are almost unaffected by self-gravity. We derive an analytic expression for the effective sound speed c{sub eff} of acoustic-surface-gravity waves. We also find expressions for the gravity reduction factors relative to a razor-thin counterpart that are appropriate for the Jeans and distortional modes. The usual razor-thin dispersion relation, after correcting for c{sub eff} and the reduction factors, closely matches the numerical results obtained by solving a full set of linearized equations. The effective sound speed generalizes the Toomre stability parameter of the Jeans mode to allow for the mixed GI of vertically stratified, pressure-confined disks.
NASA Astrophysics Data System (ADS)
Harko, T.; Mak, M. K.
2016-09-01
Obtaining exact solutions of the spherically symmetric general relativistic gravitational field equations describing the interior structure of an isotropic fluid sphere is a long standing problem in theoretical and mathematical physics. The usual approach to this problem consists mainly in the numerical investigation of the Tolman-Oppenheimer-Volkoff and of the mass continuity equations, which describes the hydrostatic stability of the dense stars. In the present paper we introduce an alternative approach for the study of the relativistic fluid sphere, based on the relativistic mass equation, obtained by eliminating the energy density in the Tolman-Oppenheimer-Volkoff equation. Despite its apparent complexity, the relativistic mass equation can be solved exactly by using a power series representation for the mass, and the Cauchy convolution for infinite power series. We obtain exact series solutions for general relativistic dense astrophysical objects described by the linear barotropic and the polytropic equations of state, respectively. For the polytropic case we obtain the exact power series solution corresponding to arbitrary values of the polytropic index n. The explicit form of the solution is presented for the polytropic index n=1, and for the indexes n=1/2 and n=1/5, respectively. The case of n=3 is also considered. In each case the exact power series solution is compared with the exact numerical solutions, which are reproduced by the power series solutions truncated to seven terms only. The power series representations of the geometric and physical properties of the linear barotropic and polytropic stars are also obtained.
NASA Astrophysics Data System (ADS)
Geroyannis, Vassilis; Tzelati, Eleftheria
In this paper we compute general-relativistic polytropic models simulating rigidly rotating, pulsating neutron stars. These relativistic compact objects, with a radius of $\\sim 10 \\, \\mathrm{km}$ and mass between $\\sim 1.4$ and $3.2$ solar masses, are closely related to pulsars. We emphasize on computing the change in the pulsation eigenfrequencies owing to a rigid rotation, which, in turn, is a decisive issue for studying stability of such objects. In our computations, we keep rotational perturbation terms of up to second order in the angular velocity.
Batra, Karuna; Mitra, Sugata; Subbarao, D.; Sharma, R.P.; Uma, R.
2005-01-01
The task for the present study is to make an investigation of self-similarity in a self-focusing laser beam both theoretically and numerically using graphical user interface based interactive computer simulation model in MATLAB (matrix laboratory) software in the presence of saturating ponderomotive force based and relativistic electron quiver based plasma nonlinearities. The corresponding eigenvalue problem is solved analytically using the standard eikonal formalism and the underlying dynamics of self-focusing is dictated by the corrected paraxial theory for slow self-focusing. The results are also compared with computer simulation of self-focusing by the direct fast Fourier transform based spectral methods. It is found that the self-similar solution obtained analytically oscillates around the true numerical solution equating it at regular intervals. The simulation results are the main ones although a feasible semianalytical theory under many assumptions is given to understand the process. The self-similar profiles are called as self-organized profiles (not in a strict sense), which are found to be close to Laguerre-Gaussian curves for all the modes, the shape being conserved. This terminology is chosen because it has already been shown from a phase space analysis that the width of an initially Gaussian beam undergoes periodic oscillations that are damped when any absorption is added in the model, i.e., the beam width converges to a constant value. The research paper also tabulates the specific values of the normalized phase shift for solutions decaying to zero at large transverse distances for first three modes which can, however, be extended to higher order modes.
NASA Astrophysics Data System (ADS)
Sarkar, Sanjay
2016-01-01
The present work deals with the accretion of two interacting fluids: dark matter and a hypothetical fluid as the holographic dark energy components onto wormhole in a non-flat FRW universe. First of all, following Cruz et al. (Phys. Lett. B 669, 271 2008), we obtained an exact solution of the Einstein's field equations. Solution describes effectively the actual acceleration and indicates a big rip type future singularity of the universe. After that we have studied the evolution of the mass of wormhole embedded in this FRW universe in order to reproduce a stable universe protected against future-time singularity. We found that the accretion of these dark components leads to a gradual increase of wormhole mass. It is also observed that contrary to the case as shown by Cruz et al. (Phys. Lett. B 669, 271 2008), the big rip singularity of the universe with a divergent Hubble parameter of this dark energy model may be avoided by a big trip. We have established a correspondence between the holographic dark energy with the polytropic gas dark energy model and obtained the potential as well as dynamics of the scalar field which describes the polytropic cosmology.
NASA Astrophysics Data System (ADS)
Nitta, Shin-ya
2010-08-01
We applied the "self-similar evolutionary model" of magnetic reconnection to simple pre-flare reconnection events driven by flux emergence as the first step in inspecting the realizability of the reconnection events predicted by this model. Previous works paid scant attention to the dependence of the magnetic Reynolds number (R*em) on reconnection events. We aim to clarify how the pre-flare phase of reconnection events in the high R*em range that is frequently encountered in astrophysical applications is observed. We clarify that (1) the time variation of the emission measure distribution strongly depends on R*em, (2) the expected light curve for sufficiently low R*em shows a long lifetime property while that for high R*em shows an impulsive property, and (3) in the case of recurrent small reconnection events on the same loop, the released magnetic energy scale is inversely correlated to the rear-end speed of the moving bright point along the loop. Note that other reconnection models cannot totally explain integration of these properties. If evidence of phenomena with these properties can be detected from, e.g., the Hinode observation, it strongly supports the validity of the self-similar reconnection model.
NASA Astrophysics Data System (ADS)
Jin, Y.; Gu, S.; Bennett, L. H.; Della Torre, E.; Provenzano, V.; Zhao, Q.
2012-04-01
A temperature scaling methodology to obtain a self-similar field dependence (∂M/∂T)H curve for metamagnetic material exhibiting first-order ferro-to-paramagnetic transitions is presented. The methodology extends Franco's transformation by (i) performing the scaling methodology on the (∂M/∂T)H curve instead of the ΔSM(T,H) curve and (ii) redefining the arbitrary temperature references, Tr1 and Tr2, used by Franco, by employing the physical constants TFM and TPM, which can be determined from the (∂2M/∂T2)H curves. (∂M/∂T)H of the metamagnetic material, Gd5Si2Ge2, exhibiting first-order ferro-to-paramagnetic transition is shown as an example. Applying the new modified Franco's transformation, Gd5Si2Ge2's (∂M/∂T)H curves collapse onto a self-similar curve with a low index of dispersion. The collapsed curve is asymmetrical with a negative skewness, which reflects the intrinsic transition differences in the mixed-state region.
NASA Astrophysics Data System (ADS)
Huesca, Margarita; Merino-de-Miguel, Silvia; Eklundh, Lars; Litago, Javier; Cicuéndez, Victor; Rodríguez-Rastrero, Manuel; Ustin, Susan L.; Palacios-Orueta, Alicia
2015-12-01
Remote sensing (RS) time series are an excellent operative source for information about the land surface across several scales and different levels of landscape heterogeneity. Ustin and Gamon (2010) proposed the new concept of "optical types" (OT), meaning "optically distinguishable functional types", as a way to better understand remote sensing signals related to the actual functional behavior of species that share common physiognomic forms but differ in functionality. Whereas the OT approach seems to be promising and consistent with ecological theory as a way to monitor vegetation derived from RS, it received little implementation. This work presents a method for implementing the OT concept for efficient monitoring of ecosystems based on RS time series. We propose relying on an ecosystem's repetitive pattern in the temporal domain (self-similarity) to assess its dynamics. Based on this approach, our main hypothesis is that distinct dynamics are intrinsic to a specific OT. Self-similarity level in the temporal domain within a broadleaf forest class was quantitatively assessed using the auto-correlation function (ACF), from statistical time series analysis. A vector comparison classification method, spectral angle mapper, and principal component analysis were used to identify general patterns related to forest dynamics. Phenological metrics derived from MODIS NDVI time series using the TIMESAT software, together with information from the National Forest Map were used to explain the different dynamics found. Results showed significant and highly stable self-similarity patterns in OTs that corresponded to forests under non-moisture-limited environments with an adaptation strategy based on a strong phenological synchrony with climate seasonality. These forests are characterized by dense closed canopy deciduous forests associated with high productivity and low biodiversity in terms of dominant species. Forests in transitional areas were associated with patterns of less
NASA Astrophysics Data System (ADS)
van den Eeckhaut, M.; Marre, A.; Poesen, J.
2009-04-01
The vineyards of the Champagne region are planted on steep south-oriented cuesta fronts receiving a maximum of sun radiation. However, due to the location of the vineyards on steep hillslopes, the viticultural activity is threatened by slope failures. In this study we attempt to better understand the spatial variability of landslides by comparing two techniques for landslide susceptibility assessment in a 1120 km² study area in the Champagne Ardenne. The first landslide susceptibility map was derived from an heuristic model adopted from the Bureau de Recherches Géologiques et Minières, geomorphologists of Reims University and the Comité Interprofessionnel du Vin de Champagne. In this qualitative model expert knowledge of the Champagne region was used to assign weights to all slope classes and lithologies located in the area. The second landslide susceptibility map was developed in this study by the application of a statistical model, logistic regression, to a calibration dataset of ‘old' (Holocene) landslides. This map was successfully evaluated using ROC curves and κ values. Both models indicate that present and future landslides are mainly controlled by slope gradient and lithology. However, the comparison of the two landslide susceptibility maps through (1) evaluation with the location of mapped ‘old' (Holocene) landslides and through (2) temporal validation with spatial data of ‘recent' (between forty and ten years old) and ‘very recent' (less than ten years old) landslides showed that the statistical model produced in this study allowed better prediction of sites already affected by landslides. In total the statistically-derived susceptibility map succeeded in correctly classifying 83.2% of the ‘old' and 84.0% of the ‘recent' and ‘very recent' landslides. The heuristic model on the other hand classified only 50.6% of the ‘old' and 58.5% of the ‘recent' and ‘very recent' landslides correctly as unstable. Taking into account the
NASA Astrophysics Data System (ADS)
Kocharovsky, V. V.; Kocharovsky, Vl. V.; Tarasov, S. V.
2016-01-01
The analytical theory of Bose-Einstein condensation of an ideal gas in mesoscopic systems has been briefly reviewed in application to traps with arbitrary shapes and dimension. This theory describes the phases of the classical gas and the formed Bose-Einstein condensate, as well as the entire vicinity of the phase transition point. The statistics and thermodynamics of Bose-Einstein condensation have been studied in detail, including their self-similar structure in the critical region, transition to the thermodynamic limit, effect of boundary conditions on the properties of a system, and nonequivalence of the description of Bose-Einstein condensation in different statistical ensembles. The complete classification of universality classes of Bose-Einstein condensation has been given.
NASA Astrophysics Data System (ADS)
Yan, Kun
2007-04-01
In this paper, by discussing the basic hypotheses about the continuous orbit and discrete orbit in two research directions of the background medium theory for celestial body motion, the concrete equation forms and their summary of the theoretic frame of celestial body motion are introduced. Future more, by discussing the general form of Binet's equation of celestial body motion orbit and it's solution of the advance of the perihelion of planets, the relations and differences between the continuous orbit theory and Newton's gravitation theory and Einstein's general relativity are given. And by discussing the fractional-dimension expanded equation for the celestial body motion orbits, the concrete equations and the prophesy data of discrete orbit or stable orbits of celestial bodies which included the planets in the Solar system, satellites in the Uranian system, satellites in the Earth system and satellites obtaining the Moon obtaining from discrete orbit theory are given too. Especially, as the preliminary exploration and inference to the gravitation curve of celestial bodies in broadly range, the concept for the ideal black hole with trend to infinite in mass density difficult to be formed by gravitation only is explored. By discussing the position hypothesis of fractional-dimension derivative about general function and the formula form the hypothesis of fractional-dimension derivative about power function, the concrete equation formulas of fractional-dimension derivative, differential and integral are described distinctly further, and the difference between the fractional-dimension derivative and the fractional-order derivative are given too. Subsequently, the concrete forms of measure calculation equations of self-similar fractal obtaining by based on the definition of form in fractional-dimension calculus about general fractal measure are discussed again, and the differences with Hausdorff measure method or the covering method at present are given. By applying
NASA Technical Reports Server (NTRS)
Ghosh, S.; Matthaeus, W. H.
1992-01-01
Theory suggests that three distinct types of turbulence can occur in the low Mach number limit of polytropic flow: nearly incompressible flows dominated by vorticity, nearly pure acoustic turbulence dominated by compression, and flows characterized by near statistical equipartition of vorticity and compressions. Distinctions between these kinds of turbulence are investigated here by direct numerical simulation of two-dimensional compressible hydrodynamic turbulence. Dynamical scalings of density fluctuations, examination of the ratio of transverse to longitudinal velocity fluctuations, and spectral decomposition of the fluctuations are employed to distinguish the nature of these low Mach number solutions. A strong dependence on the initial data is observed, as well as a tendency for enhanced effects of compressibility at later times and at higher wave numbers, as suggested by theories of nearly incompressible flows.
Kong, Dali; Zhang, Keke; Schubert, Gerald; Anderson, John E-mail: K.Zhang@exeter.ac.uk
2013-02-15
We present a new three-dimensional numerical method for calculating the non-spherical shape and internal structure of a model of a rapidly rotating gaseous body with a polytropic index of unity. The calculation is based on a finite-element method and accounts for the full effects of rotation. After validating the numerical approach against the asymptotic solution of Chandrasekhar that is valid only for a slowly rotating gaseous body, we apply it to models of Jupiter and a rapidly rotating, highly flattened star ({alpha} Eridani). In the case of Jupiter, the two-dimensional distributions of density and pressure are determined via a hybrid inverse approach by adjusting an a priori unknown coefficient in the equation of state until the model shape matches the observed shape of Jupiter. After obtaining the two-dimensional distribution of density, we then compute the zonal gravity coefficients and the total mass from the non-spherical model that takes full account of rotation-induced shape change. Our non-spherical model with a polytropic index of unity is able to produce the known mass of Jupiter with about 4% accuracy and the zonal gravitational coefficient J {sub 2} of Jupiter with better than 2% accuracy, a reasonable result considering that there is only one parameter in the model. For {alpha} Eridani, we calculate its rotationally distorted shape and internal structure based on the observationally deduced rotation rate and size of the star by using a similar hybrid inverse approach. Our model of the star closely approximates the observed flattening.
NASA Astrophysics Data System (ADS)
Xavier, Morvan; Christophe, Naisse; Issa Oumarou, Malam; Jean-François, Desprats; Anne, Combaud; Olivier, Cerdan
2015-04-01
In the literature, grass cover is often considered to be one of the best methods of limiting runoff in the vineyards; But results can vary, especially when the plot area is <2 m². However, in any study to our knowledge, the way grass cover is structured in the inter-row is taken into account to explain the variability of runoff and soil loss. The objective of this study, conducted in Champagne vineyards in France, was to quantify the influence of the cultivation practices in the inter-rows of vines and determine the influence of the density of the grass cover in the wheel tracks on the surface runoff and soil erosion in experimental plots of 0.25 m2 under simulated rainfall. Three types of ground cover were studied. In the bark-and-vine-prunings plots, the runoff coefficient ranged from 1.3 to 4.0% and soil losses were <1 g/m²/h. In the bare soil plot, the highest runoff coefficient of the study was found (80.0%) and soil losses reached 7.4 g/m²/h. In the grass cover plots, the runoff coefficient and amount of eroded soil were highly variable: the runoff coefficients ranged from 0.4 to 77.0%, and soil losses were between less than 1 and 13.4 g/m²/h. Soil type, soil moisture, slope and agricultural practices did not account for the variability. In fact, the density of grass cover in the wheel tracks explained a portion of this variability. The lack of grass in the centre of the inter-row allowed for a preferential flow and created an erosion line in the wheel tracks where the soil was compacted. This study showed that grass cover in a vineyard was not necessarily sufficient to reduce surface runoff and prevent soil erosion. To be effective, the grass cover must be dense enough in the wheel tracks of agricultural machinery to avoid runoff coefficients close to those achieved with bare soil.
Cassibry, J. T.; Cortez, R. J.; Hsu, S. C.; Witherspoon, F. D.
2009-11-15
Plasma liner driven magnetoinertial fusion (PLMIF) is a fusion energy concept that utilizes an imploding plasma liner to shock heat and compress a magnetized target plasma to fusion conditions. The fusion burn fraction is linearly proportional to the confinement (or ''dwell'') time of the liner-target system at peak compression, and therefore it is important to estimate the dwell time accurately in order to assess the fusion energy yield and gain. In this work, the dwell time has been estimated using the exact solution to a self-similar converging shock model. The dwell time was found to be determined by the sum of the outgoing shock and rarefaction times through the plasma liner at peak compression, and for chosen PLMIF conditions the dwell time was on the order of 1 {mu}s. In addition, we show that the engineering gain, i.e., the total energy extracted as electricity (from fusion plus expanded liner energy) divided by the electrical energy required to implode the liner, exceeds unity for a wide range of liner thicknesses and specific heat ratios.
Våge, Selina; Thingstad, T. Frede
2015-01-01
Trophic interactions are highly complex and modern sequencing techniques reveal enormous biodiversity across multiple scales in marine microbial communities. Within the chemically and physically relatively homogeneous pelagic environment, this calls for an explanation beyond spatial and temporal heterogeneity. Based on observations of simple parasite-host and predator-prey interactions occurring at different trophic levels and levels of phylogenetic resolution, we present a theoretical perspective on this enormous biodiversity, discussing in particular self-similar aspects of pelagic microbial food web organization. Fractal methods have been used to describe a variety of natural phenomena, with studies of habitat structures being an application in ecology. In contrast to mathematical fractals where pattern generating rules are readily known, however, identifying mechanisms that lead to natural fractals is not straight-forward. Here we put forward the hypothesis that trophic interactions between pelagic microbes may be organized in a fractal-like manner, with the emergent network resembling the structure of the Sierpinski triangle. We discuss a mechanism that could be underlying the formation of repeated patterns at different trophic levels and discuss how this may help understand characteristic biomass size-spectra that hint at scale-invariant properties of the pelagic environment. If the idea of simple underlying principles leading to a fractal-like organization of the pelagic food web could be formalized, this would extend an ecologists mindset on how biological complexity could be accounted for. It may furthermore benefit ecosystem modeling by facilitating adequate model resolution across multiple scales. PMID:26648929
Kalocsai, A.G.
1992-12-31
An asymptotic analysis is presented for two distinct and independent problems: (I) Wave propagation in dispersive optical media with quadratic nonlinearity (II) Hypersonic flows with three dimensional self-similarity. In the optics problem, we at first study single and multiple input propagating waves at frequencies away from dielectric resonances. Here we compare the Slowly Varying Envelope Approximation to the Method of Multiple Scales and show that the Method of Multiple Scales is a superior technique that can be applied self consistently to any perturbation order which in turn predicts new physical effects. For the single slowly modulated input wave problem, under appropriate conditions, we shown that at the O({epsilon}{sup 2}) perturbation, we obtain the cubic nonlinear Schrodinger equation. This means that for the single input wave propagating in a quadratic nonlinear medium, self-modulation effects and soliton behavior may be observed depending on the boundary conditions. For the single input wave near a classical dielectric resonance, we find that the wave number becomes amplitude dependent. The method of multiple scales is replaced by Whitham`s averaged Lagrangian. We derive the associated modulated envelope equations. We investigate an effective medium regime and the full nonlinear problem. The hypersonic flow problem requires the use of asymptotic matching that arises from the geometry from the problem. Here the pressure field and lift to drag C{sup 3/2}{sub L}/C{sub D} is evaluated for a wide delta wing with small power law curvature. Use is made of Hypersonic Small Disturbance Theory and three dimensional power law similarity. It is shown that an improvement for C{sup 3/2}{sub L}/C{sub D} occurs for wings with power law curvatures greater than one, when compared to flat delta wings. This improvement in performance agrees qualitatively with other types of concave wings.
Koch, Patrick M.; Ho, Paul T. P.; Tang, Ya-Wen
2012-03-01
Dust polarization observational results are analyzed for the high-mass star formation region W51 from the largest parent cloud ({approx}2 pc, James Clerk Maxwell Telescope) to the large-scale envelope ({approx}0.5 pc, BIMA array) down to the collapsing core e2 ({approx}60 mpc, Submillimeter Array). Magnetic field and dust emission gradient orientations reveal a correlation which becomes increasingly more tight with higher resolution. The previously developed polarization-intensity-gradient method is applied in order to quantify the magnetic field significance. This technique provides a way to estimate the local magnetic field force compared to gravity without the need of any mass or field strength measurements, solely making use of measured angles which reflect the geometrical imprint of the various forces. All three data sets clearly show regions with distinct features in the field-to-gravity force ratio. Azimuthally averaged radial profiles of this force ratio reveal a transition from a field dominance at larger distances to a gravity dominance closer to the emission peaks. Normalizing these profiles to a characteristic core scale points toward self-similarity. Furthermore, the polarization-intensity-gradient method is linked to the mass-to-flux ratio, providing a new approach to estimate the latter one without mass and field strength inputs. A transition from a magnetically supercritical to a subcritical state as a function of distance from the emission peak is found for the e2 core. Finally, based on the measured radius-dependent field-to-gravity force ratio we derive a modified star formation efficiency with a diluted gravity force. Compared to a standard (free-fall) efficiency, the observed field is capable of reducing the efficiency down to 10% or less.
Davies, J. A.; Perry, C. H.; Harrison, R. A.; Trines, R. M. G. M.; Lugaz, N.; Möstl, C.; Liu, Y. D.; Steed, K.
2013-11-10
The twin-spacecraft STEREO mission has enabled simultaneous white-light imaging of the solar corona and inner heliosphere from multiple vantage points. This has led to the development of numerous stereoscopic techniques to investigate the three-dimensional structure and kinematics of solar wind transients such as coronal mass ejections (CMEs). Two such methods—triangulation and the tangent to a sphere—can be used to determine time profiles of the propagation direction and radial distance (and thereby radial speed) of a solar wind transient as it travels through the inner heliosphere, based on its time-elongation profile viewed by two observers. These techniques are founded on the assumption that the transient can be characterized as a point source (fixed φ, FP, approximation) or a circle attached to Sun-center (harmonic mean, HM, approximation), respectively. These geometries constitute extreme descriptions of solar wind transients, in terms of their cross-sectional extent. Here, we present the stereoscopic expressions necessary to derive propagation direction and radial distance/speed profiles of such transients based on the more generalized self-similar expansion (SSE) geometry, for which the FP and HM geometries form the limiting cases; our implementation of these equations is termed the stereoscopic SSE method. We apply the technique to two Earth-directed CMEs from different phases of the STEREO mission, the well-studied event of 2008 December and a more recent event from 2012 March. The latter CME was fast, with an initial speed exceeding 2000 km s{sup –1}, and highly geoeffective, in stark contrast to the slow and ineffectual 2008 December CME.
NASA Astrophysics Data System (ADS)
Davies, J. A.; Perry, C. H.; Trines, R. M. G. M.; Harrison, R. A.; Lugaz, N.; Möstl, C.; Liu, Y. D.; Steed, K.
2013-11-01
The twin-spacecraft STEREO mission has enabled simultaneous white-light imaging of the solar corona and inner heliosphere from multiple vantage points. This has led to the development of numerous stereoscopic techniques to investigate the three-dimensional structure and kinematics of solar wind transients such as coronal mass ejections (CMEs). Two such methods—triangulation and the tangent to a sphere—can be used to determine time profiles of the propagation direction and radial distance (and thereby radial speed) of a solar wind transient as it travels through the inner heliosphere, based on its time-elongation profile viewed by two observers. These techniques are founded on the assumption that the transient can be characterized as a point source (fixed phi, FP, approximation) or a circle attached to Sun-center (harmonic mean, HM, approximation), respectively. These geometries constitute extreme descriptions of solar wind transients, in terms of their cross-sectional extent. Here, we present the stereoscopic expressions necessary to derive propagation direction and radial distance/speed profiles of such transients based on the more generalized self-similar expansion (SSE) geometry, for which the FP and HM geometries form the limiting cases; our implementation of these equations is termed the stereoscopic SSE method. We apply the technique to two Earth-directed CMEs from different phases of the STEREO mission, the well-studied event of 2008 December and a more recent event from 2012 March. The latter CME was fast, with an initial speed exceeding 2000 km s-1, and highly geoeffective, in stark contrast to the slow and ineffectual 2008 December CME.
NASA Astrophysics Data System (ADS)
Zhang, Keke; Kong, D.; Schubert, G.; Anderson, J.
2012-10-01
An accurate calculation of the rotationally distorted shape and internal structure of Jupiter is required to understand the high-precision gravitational field that will be measured by the Juno spacecraft now on its way to Jupiter. We present a three-dimensional non-spherical numerical calculation of the shape and internal structure of a model of Jupiter with a polytropic index of unity. The calculation is based on a finite element method and accounts for the full effects of rotation. After validating the numerical approach against the asymptotic solution of Chandrasekhar (1933) that is valid only for a slowly rotating gaseous planet, we apply it to a model of Jupiter whose rapid rotation causes a significant departure from spherical geometry. The two-dimensional distribution of the density and the pressure within Jupiter is then determined via a hybrid inverse approach by matching the a priori unknown coefficient in the equation of state to the observed shape of Jupiter. After obtaining the two-dimensional distribution of Jupiter's density, we then compute the zonal gravity coefficients and the total mass from the non-spherical Jupiter model that takes full account of rotation-induced shape changes. Our non-spherical model with a polytrope of unit index is able to produce the known mass and zonal gravitational coefficients of Jupiter. Chandrasekhar, S. 1933, The equilibrium of distorted polytropes, MNRAS 93, 390
NASA Astrophysics Data System (ADS)
Chaverra, Eliana; Mach, Patryk; Sarbach, Olivier
2016-05-01
We analyze the properties of a polytropic fluid that is radially accreted into a Schwarzschild black hole. The case where the adiabatic index γ lies in the range of 1\\lt γ ≤slant 5/3 has been treated in previous work. In this article, we analyze the complementary range of 5/3\\lt γ ≤slant 2. To this purpose, the problem is cast into an appropriate Hamiltonian dynamical system, whose phase flow is analyzed. While, for 1\\lt γ ≤slant 5/3, the solutions are always characterized by the presence of a unique critical saddle point, we show that, when 5/3\\lt γ ≤slant 2, an additional critical point might appear, which is a center point. For the parametrization used in this paper, we prove that, whenever this additional critical point appears, there is a homoclinic orbit. Solutions corresponding to homoclinic orbits differ from standard transonic solutions with vanishing asymptotic velocities in two aspects: they are local (i.e., they cannot be continued to arbitrarily large radii); the dependence of the density or the value of the velocity on the radius is not monotonic.
NASA Astrophysics Data System (ADS)
Smolinski, Gregory J.
Of interest to the analytical study of Mach stem heights is the shock patterns that form in a simple inlet flow. A simple inlet flow is defined as a flow in which the inlet height is of such a size such that the incident wave does not interact with the expansion fan, and that the inlet wedge face is small enough that a reflected shock does not impinge upon it. The condition for which the incident wave intersects the leading edge of the expansion fan, and for the case where a reflected wave intersects the trailing edge of the inlet wedge were found in the form of a ratio between the inlet height and wedge face length. The various wave angle limits for both cases were also studied and presented. Once the limits for a simple inlet flow were defined, the problem of solving for Mach stem heights was studied. Quantitatively, past analytical studies were able to achieve moderate success at predicting stem heights for a very limited range of Mach numbers. Inherent to a quantitative study regarding Mach stems is the lack of a physical length scale. Therefore, the present study approached the problem of Mach Reflections in a qualitative way. The self-similar aspects of the Mach stem were revealed and a solution for Mach stems was found. The explicit dependence of the Mach stem on the freestream Mach number, wedge angle, and ratio of specific heats were noted. Additionally, the theoretical lower and upper limits of the Regular and Mach Reflection flowfields were studied. In addition to solving qualitatively for Mach stem heights, a study was done on the stability of the shock waves pertaining to the reflection patterns that form. In the region betaN ≤ beta ≤ beta D it is possible for either a Regular Reflection or a Mach Reflection to form for a given freestream Mach number. Of practical interest, besides the stability of the shock pattern, is the transition from a Regular Reflection to a Mach Reflection and vice versa. The transition between the two reflection patterns
Renard, D; Lavenant-Gourgeon, L; Lapp, A; Nigen, M; Sanchez, C
2014-11-01
particles differing in dimensions. The secondary structures content of control and enzyme-treated AGPs were similar, highlighting both the high rigidity of the protein backbone and the overall symmetry of AGP. This conclusion was reinforced by the more compact structures found when AGP was intact compare to the more elongated structures found when AGP was enzymatically cleaved. Finally, the structural similarities found in enzyme-treated AGP together with the theoretical calculations to analytically probe the type of branching would suggest that AGP would be made of a self-similar assembly of two types of building blocks, the second being a five-fold repetition of the first one, for which palindromic amino acid sequence would ensure a self-ordering of carbohydrate moieties along the polypeptide chains. The cleavage would therefore lead to hydrolysed building blocks with similar secondary structures and conformations whatever the enzyme used. PMID:25129794
Durisen, R.H.; Gingold, R.A.; Tohline, J.E.; Boss, A.P.
1986-06-01
The effectiveness of three different hydrodynamics models is evaluated for the analysis of the effects of fission instabilities in rapidly rotating, equilibrium flows. The instabilities arise in nonaxisymmetric Kelvin modes as rotational energy in the flow increases, which may occur in the formation of close binary stars and planets when the fluid proto-object contracts quasi-isostatically. Two finite-difference, donor-cell methods and a smoothed particle hydrodynamics (SPH) code are examined, using a polytropic index of 3/2 and ratios of total rotational kinetic energy to gravitational energy of 0.33 and 0.38. The models show that dynamic bar instabilities with the 3/2 polytropic index do not yield detached binaries and multiple systems. Ejected mass and angular momentum form two trailing spiral arms that become a disk or ring around the central remnant. The SPH code yields the same data as the finite difference codes but with less computational effort and without acceptable fluid constraints in low density regions. Methods for improving both types of codes are discussed. 68 references.
NASA Astrophysics Data System (ADS)
Stollsteiner, P.; Bessiere, H.; Nicolas, J.; Allier, D.; Berthet, O.
2015-04-01
This article is based on a BRGM study on piezometric indicators, threshold values of discharge and groundwater levels for the assessment of potentially-exploitable water resources of chalky watersheds. A method for estimating low water levels based on groundwater levels is presented from three examples representing chalk aquifers with different cycles: annual, combined and interannual. The first is located in Picardy and the two others in the Champagne-Ardennes region. Piezometers with annual cycles, used in these examples, are supposed to be representative of the aquifer hydro-dynamics. Except for multi-annual systems, the analysis between discharge measurements at a hydrometric station and groundwater levels measured at a piezometer representative of the main aquifer, leads to relatively precise and satisfactory relationships within a chalky context. These relationships may be useful for monitoring, validation, extension or reconstruction of the low water flow data. On the one hand, they allow definition of the piezometric levels corresponding to the different alert thresholds of river discharges. On the other hand, they clarify the proportions of low surface water flow from runoff or drainage of the aquifer. Finally, these correlations give an assessment of the minimum flow for the coming weeks. However, these correlations cannot be used to optimize the value of the exploitable water resource because it seems to be difficult to integrate the value of the effective rainfall that could occur during the draining period. Moreover, in the case of multi-annual systems, the solution is to attempt a comprehensive system modelling and, if it is satisfactory, using the simulated values to get rid of parasites or running the model for forecasting purposes.
NASA Technical Reports Server (NTRS)
Gosling, J. T.; Riley, P.; Skoug, R. M.
2001-01-01
We strongly disagree with the essence of the Osherovich (hereafter Osherovich) comment on one of our papers. The following paragraphs provide the basis of our disagreement and elaborate on why we believe that none of the concluding statements in his Comment are true. Our most important point is that one can apply the model developed by Osherovich and colleagues to real data obtained at a single point in space to determine the polytropic index within magnetic clouds if and only if the highly idealized assumptions of that model conform to physical reality. There is good reason to believe that those assumptions do not provide an accurate physical description of real magnetic clouds in the spherically expanding solar wind.
NASA Astrophysics Data System (ADS)
Tirani, M. D.; Maleki, M.; Kajani, M. T.
2014-11-01
A numerical method for solving the Lane-Emden equations of the polytropic index α when 4.75 ≤ α ≤ 5 is introduced. The method is based upon nonclassical Gauss-Radau collocation points and Freud type weights. Nonclassical orthogonal polynomials, nonclassical Radau points and weighted interpolation are introduced and are utilized in the interval [0,1]. A smooth, strictly monotonic transformation is used to map the infinite domain x ∈ [0,∞) onto a half-open interval t ∈ [0,1). The resulting problem on the finite interval is then transcribed to a system of nonlinear algebraic equations using collocation. The method is easy to implement and yields very accurate results.
Alter, Harvey J.; Mikovits, Judy A.; Switzer, William M.; Ruscetti, Francis W.; Lo, Shyh-Ching; Klimas, Nancy; Komaroff, Anthony L.; Montoya, Jose G.; Bateman, Lucinda; Levine, Susan; Peterson, Daniel; Levin, Bruce; Hanson, Maureen R.; Genfi, Afia; Bhat, Meera; Zheng, HaoQiang; Wang, Richard; Li, Bingjie; Hung, Guo-Chiuan; Lee, Li Ling; Sameroff, Stephen; Heneine, Walid; Coffin, John; Hornig, Mady; Lipkin, W. Ian
2012-01-01
ABSTRACT The disabling disorder known as chronic fatigue syndrome or myalgic encephalomyelitis (CFS/ME) has been linked in two independent studies to infection with xenotropic murine leukemia virus-related virus (XMRV) and polytropic murine leukemia virus (pMLV). Although the associations were not confirmed in subsequent studies by other investigators, patients continue to question the consensus of the scientific community in rejecting the validity of the association. Here we report blinded analysis of peripheral blood from a rigorously characterized, geographically diverse population of 147 patients with CFS/ME and 146 healthy subjects by the investigators describing the original association. This analysis reveals no evidence of either XMRV or pMLV infection. PMID:22991430
NASA Astrophysics Data System (ADS)
2011-01-01
Particle Physics: ATLAS unveils mural at CERN Prize: Corti Trust invites essay entries Astrophysics: CERN holds cosmic-ray conference Researchers in Residence: Lord Winston returns to school Music: ATLAS scientists record physics music Conference: Champagne flows at Reims event Competition: Students triumph at physics olympiad Teaching: Physics proves popular in Japanese schools Forthcoming Events
2011-01-01
In 2009, a newly discovered human retrovirus, xenotropic murine leukemia virus (MuLV)-related virus (XMRV), was reported by Lombardi et al. in 67% of persons from the US with chronic fatigue syndrome (CFS) by PCR detection of gag sequences. Although six subsequent studies have been negative for XMRV, CFS was defined more broadly using only the CDC or Oxford criteria and samples from the US were limited in geographic diversity, both potentially reducing the chances of identifying XMRV positive CFS cases. A seventh study recently found polytropic MuLV sequences, but not XMRV, in a high proportion of persons with CFS. Here we tested blood specimens from 45 CFS cases and 42 persons without CFS from over 20 states in the United States for both XMRV and MuLV. The CFS patients all had a minimum of 6 months of post-exertional malaise and a high degree of disability, the same key symptoms described in the Lombardi et al. study. Using highly sensitive and generic DNA and RNA PCR tests, and a new Western blot assay employing purified whole XMRV as antigen, we found no evidence of XMRV or MuLV in all 45 CFS cases and in the 42 persons without CFS. Our findings, together with previous negative reports, do not suggest an association of XMRV or MuLV in the majority of CFS cases. PMID:21342521
The Relationship between Virtual Self Similarity and Social Anxiety
Aymerich-Franch, Laura; Kizilcec, René F.; Bailenson, Jeremy N.
2014-01-01
In virtual reality (VR), it is possible to embody avatars that are dissimilar to the physical self. We examined whether embodying a dissimilar self in VR would decrease anxiety in a public speaking situation. We report the results of an observational pilot study and two laboratory experiments. In the pilot study (N = 252), participants chose an avatar to use in a public speaking task. Trait public speaking anxiety correlated with avatar preference, such that anxious individuals preferred dissimilar self-representations. In Study 1 (N = 82), differences in anxiety during a speech in front of a virtual audience were compared among participants embodying an assigned avatar whose face was identical to their real self, an assigned avatar whose face was other than their real face, or embodied an avatar of their choice. Anxiety differences were not significant, but there was a trend for lower anxiety with the assigned dissimilar avatar compared to the avatar looking like the real self. Study 2 (N = 105) was designed to explicate that trend, and further investigated anxiety differences with an assigned self or dissimilar avatar. The assigned dissimilar avatar reduced anxiety relative to the assigned self avatar for one measure of anxiety. We discuss implications for theories of self-representation as well as for applied uses of VR to treat social anxiety. PMID:25477810
Theory of Self-Similar Oscillatory Finite-Time Singularities
NASA Astrophysics Data System (ADS)
Sornette, D.; Ide, K.
A simple two-dimensional system is introduced which suggests a qualitative dynamical relationship between (1) stock market prices in the presence of nonlinear trend-followers and nonlinear value investors, (2) the world human population with a competition between a population-dependent growth rate and a nonlinear dependence on a finite carrying capacity and (3) the failure of materials subjected to a time-varying stress with a competition between positive geometrical feedback on the damage variable and nonlinear healing. Our model keeps three key ingredients (inertia, nonlinear positive and negative feedbacks) that compete to give rise to singularities in finite time decorated by accelerating oscillations.
A multicomponent self-similar characterization of rainfall fluctuations
Kumar, P.; Foufoula-Georgiou, E.
1996-12-31
Issues of scaling characteristics in spatial rainfall have attracted increasing attention over the last decade. Several models based on simple/multi scaling and multifractal ideas have been put forth and parameter estimation techniques developed for the hypothesized models. Simulations based on these models have realistic resemblance to {open_quotes}generic rainfall fields{close_quotes}. In this research we analyze rainfall data for scaling characteristics without an a priori assumed model. We look at the behavior of rainfall fluctuations obtained at several scales, via orthogonal wavelet transform of the data, to infer the precise nature of scaling exhibited by spatial rainfall. The essential idea behind the analysis is to segregate large scale (long wavelength) features from small scale features and study them independently of each other. The hypothesis is set forward that rainfall might exhibit scaling in small scale fluctuations, if at all, and at large scale this behavior will break down to accommodate the effects of external factors affecting the particular rain producing mechanism. The validity of this hypothesis is examined. In addition we define and estimate parameters that characterize the spatial dependence of the rainfall fluctuations and we use these parameters, estimated for several frames (in time), to relate to and identify the evolutionary nature of rainfall. These parameters and the type of scaling show significant variation from one rainfall field to another.
Self-similar equilibration of strongly interacting systems from holography
NASA Astrophysics Data System (ADS)
Bakas, Ioannis; Skenderis, Kostas; Withers, Benjamin
2016-05-01
We study the equilibration of a class of far-from-equilibrium strongly interacting systems using gauge-gravity duality. The systems we analyze are 2 +1 dimensional and have a four-dimensional gravitational dual. A prototype example of a system we analyze is the equilibration of a two-dimensional fluid which is translational invariant in one direction and is attached to two different heat baths with different temperatures at infinity in the other direction. We realize such setup in gauge-gravity duality by joining two semi-infinite asymptotically anti-de Sitter (AdS) black branes of different temperatures, which subsequently evolve towards equilibrium by emitting gravitational radiation towards the boundary of AdS. At sufficiently late times the solution converges to a similarity solution, which is only sensitive to the left and right equilibrium states and not to the details of the initial conditions. This attractor solution not only incorporates the growing region of equilibrated plasma but also the outwardly propagating transition regions, and can be constructed by solving a single ordinary differential equation.
Self-similarity and self-inversion of quasicrystals
NASA Astrophysics Data System (ADS)
Madison, A. E.
2014-08-01
The discovery of quasicrystals played a revolutionary role in the condensed matter science and forced to renounce the dogma of the classical crystallography that the regular filling of the space by identical blocks is reduced solely to the Fedorov space groups. It is shown that aperiodic crystals, apart from the similarity, exhibit the self-inversion property. In a broadened sense, the self-inversion implies the possible composition of the inversion with translations, rotations, and homothety, whereas pure reflection by itself in a circle can be absent as an independent symmetry element. It is demonstrated that the symmetry of aperiodic tilings is described by Schottky groups (which belong to a particular type of Kleinian groups generated by the linear fractional Möbius transformations); in the theory of aperiodic crystals, the Schottky groups play the same role that the Fedorov groups play in the theory of crystal lattices. The local matching rules for the Penrose fractal tiling are derived, the problem of choice of the fundamental region of the group of motions of a quasicrystal is discussed, and the relation between the symmetry of aperiodic tilings and the symmetry of constructive fractals is analyzed.
Material combustion in oxidant flows: Self-similar solutions
NASA Astrophysics Data System (ADS)
Tyurenkova, V. V.; Smirnova, M. N.
2016-03-01
The paper presents exact solution for the problem of condensed material surface burning in a flow of oxidant in the case of steady flame over fuel layer. The solution is obtained within the frame of assumption of fuel gasification and gas phase chemical reacting in a diffusion flame. The regression rate of the material surface in the turbulent and laminar flow regimes is studied. The zones corresponding to kinetic and diffusion regime are determined.
Psychoanalysis and dynamical systems theory: prediction and self similarity.
Galatzer-Levy, R M
1995-01-01
The theory of dynamical systems (sometimes called chaos theory) has emerged in the past two decades as a powerful tool for understanding the evolution of complex systems. Attempts to develop psychoanalysis along the lines of nineteenth century physical science have proven unsatisfactory. The theory of dynamical systems provides another route for development. It suggests that prediction should aim at describing the overall evolution of systems and that the possibilities for such evolution are broader than classical theory suggested. It also shows that complex systems often involve structures that repeat basic features on several different levels of observation. This suggests a method for systematically exploring the overly rich data of psychoanalysis. PMID:8926326
MRI Superresolution Using Self-Similarity and Image Priors
Manjón, José V.; Coupé, Pierrick; Buades, Antonio; Collins, D. Louis; Robles, Montserrat
2010-01-01
In Magnetic Resonance Imaging typical clinical settings, both low- and high-resolution images of different types are routinarily acquired. In some cases, the acquired low-resolution images have to be upsampled to match with other high-resolution images for posterior analysis or postprocessing such as registration or multimodal segmentation. However, classical interpolation techniques are not able to recover the high-frequency information lost during the acquisition process. In the present paper, a new superresolution method is proposed to reconstruct high-resolution images from the low-resolution ones using information from coplanar high resolution images acquired of the same subject. Furthermore, the reconstruction process is constrained to be physically plausible with the MR acquisition model that allows a meaningful interpretation of the results. Experiments on synthetic and real data are supplied to show the effectiveness of the proposed approach. A comparison with classical state-of-the-art interpolation techniques is presented to demonstrate the improved performance of the proposed methodology. PMID:21197094
Honeycomb phononic crystals with self-similar hierarchy
NASA Astrophysics Data System (ADS)
Mousanezhad, Davood; Babaee, Sahab; Ghosh, Ranajay; Mahdi, Elsadig; Bertoldi, Katia; Vaziri, Ashkan
2015-09-01
We highlight the effect of structural hierarchy and deformation on band structure and wave-propagation behavior of two-dimensional phononic crystals. Our results show that the topological hierarchical architecture and instability-induced pattern transformations of the structure under compression can be effectively used to tune the band gaps and directionality of phononic crystals. The work provides insights into the role of structural organization and hierarchy in regulating the dynamic behavior of phononic crystals, and opportunities for developing tunable phononic devices.
Self-similarity and scaling of thermal shock fractures.
Tarasovs, S; Ghassemi, A
2014-07-01
The problem of crack pattern formation due to thermal shock loading at the surface of half space is solved numerically using the two-dimensional boundary element method. The results of numerical simulations with 100-200 random simultaneously growing and interacting cracks are used to obtain scaling relations for crack length and spacing. The numerical results predict that such a process of pattern formation with quasistatic crack growth is not stable and at some point the excess energy leads to unstable propagation of one of the longest cracks. This single-crack scenario should be understood in a local sense. There could be other unstable cracks far away that together can form a new pattern. The onset of instability has also been determined from numerical results. PMID:25122311
Analysis of self-similar solutions of multidimensional conservation laws
Keyfitz, Barbara
2014-02-15
This project focused on analysis of multidimensional conservation laws, specifically on extensions to the study of self-siminar solutions, a project initiated by the PI. In addition, progress was made on an approach to studying conservation laws of very low regularity; in this research, the context was a novel problem in chromatography. Two graduate students in mathematics were supported during the grant period, and have almost completed their thesis research.
Dyslexic and Skilled Reading Dynamics Are Self-Similar
ERIC Educational Resources Information Center
Holden, John G.; Greijn, Lieke T.; van Rooij, Marieke M. J. W.; Wijnants, Maarten L.; Bosman, Anna M. T.
2014-01-01
The shape of a word pronunciation time distribution supplies information about the dynamic interactions that support reading performance. Speeded word-naming pronunciation and response time distributions were collected from 20 sixth grade Dutch students with dyslexia and 23 age-matched controls. The participants' pronunciation times were…
Self-similarity patterns of precipitation in the Iberian Peninsula
NASA Astrophysics Data System (ADS)
Morata, A.; Martín, M. L.; Luna, M. Y.; Valero, F.
2006-05-01
An objective classification of the precipitation field over the Iberian Peninsula and the Balearic Islands is obtained. Data are derived from a high-resolution daily precipitation dataset obtained from in-situ measurements. The dataset, Iberian monthly Precipitation Dataset (IPD), consists of monthly precipitation data over a 25 km × 25 km grid from 1st January 1961 to 31st December 2003. Therefore, 960 data series over the Iberian Peninsula and the Balearic Islands are disposed over the grid for 43-year period. Multi-resolution wavelet analysis is used to extract similar information in the precipitation field at different timescales. An objective classification of the obtained wavelet coefficient series is carried out by means of the Kohonen’s neural network, also named Self-Organizing Map (SOM). SOM is formed by an unsupervised learning algorithm that may be used to find clusters of similar events in the input data and is able to identify some underlying dynamic structures of the multi-dimensional datasets. SOM is applied to the wavelet coefficients for intramonthly, intermonthly and interannual oscillations, obtaining self-organised maps which objectively identify similar zones of precipitation behaviour over the Iberian Peninsula. The homogeneity of the patterns is also studied by means of non-parametric correlations, energy scalograms and tests of significance. The intramonthly, intermonthly and interannual waves resulted in seven, five and three SOM patterns, respectively. As timescale increases, the wavelet series coefficients tend to be highly clustered. The results indicate that as the oscillation frequencies decrease, the Iberian precipitation behaves more linearly.
Analysis of Self-Similar Solutions of Multidimensional Conservation Laws
Tesdall, Allen M.
2012-08-31
This project brought large-scale, advanced methods for numerical solution of PDE to bear on the two-dimensional Riemann problem, and obtained numerical solution of problem. This numerical solution allowed us to describe key features of the solution. Analysis was combined with numerical solution to explain these numerical results. High-resolution, large-scale numerical computations show for the first time that a shock forms strictly in the supersonic region. Numerical solutions appear to show the disappearance of a diffracting shock at a sonic line.
Biotinidase deficiency and our champagne legacy.
Wolf, Barry
2016-09-10
Biotinidase is the enzyme that is necessary for the recycling of the vitamin, biotin. Biotinidase deficiency is an autosomal recessively inherited metabolic disorder. If untreated, individuals with biotinidase deficiency usually develop neurological and cutaneous symptoms that can result in coma or death. Symptomatic individuals can be markedly improved by treating them with pharmacological doses of biotin; however, some clinical features may be irreversible. Fortunately, essentially all symptoms can be prevented if treatment is initiated at birth or before the symptoms develop. Because of this, the disorder is currently screened for in newborns in all states in the United States and in many countries around the world. This is the story of one laboratory's work in bringing basic science research from the discovery of the disorder to its translation into clinical medicine and its impact on the individuals with the disorder and their families. PMID:26456103
Polytropic relationship in interplanetary magnetic clouds
NASA Technical Reports Server (NTRS)
Osherovich, V. A.; Farrugia, C. J.; Burlaga, L. F.; Lepping, R. P.; Fainberg, J.; Stone, R. G.
1993-01-01
High time-resolution data from the ISEE 3 and IMP 8 spacecraft are presented for the magnetic field and the proton and electron populations of a number of magnetic clouds, in order to investigate such clouds' thermodynamics and the relationship between their magnetic and thermodynamic structures. It is judged on the basis of these data that while the magnetic flield of the cloud expands, the ions are cooled. Hot electrons are trapped by the magnetic field in the magnetic cloud's core. These conditions are favorable for the generation of ion-acoustic waves.
Does shaking increase the pressure inside a bottle of champagne?
Vreme, A; Pouligny, B; Nadal, F; Liger-Belair, G
2015-02-01
Colas, beers and sparkling wines are all concentrated solutions of carbon dioxide in aqueous solvents. Any such carbonated liquid is ordinarily conditioned inside a closed bottle or a metal can as a liquid-gas 2-phase system. At thermodynamic equilibrium, the partial pressure of carbon-dioxide in the gas phase and its concentration in the liquid are proportional (Henry's law). In practical conditions and use (transport, opening of the container, exterior temperature change, etc.), Henry's equilibrium can be perturbed. The goal of this paper is to describe and understand how the system responds to such perturbations and evolves towards a new equilibrium state. Formally, we investigate the dynamics around Henry's equilibrium of a closed system, through dedicated experiments and modeling. We focus on the response to a sudden pressure change and to mechanical shaking (the latter point inspired the article's title). Observations are rationalized through basic considerations including molecular diffusion, bubble dynamics (based on Epstein-Plesset theory) and chemi-convective hydrodynamic instabilities. PMID:25463174
Building a Champagne Network on a Beer Budget
ERIC Educational Resources Information Center
Dolan, Jon; Pederson, Curt
2004-01-01
Oregon State University's demand for bandwidth to support scientific collaboration and research continues to grow exponentially, while state funding declines due to hard economic times. The challenge faced by these authors was to find creative yet fiscally responsible ways to meet OSU's bandwidth demands. Looking at their options for high-capacity…
Rényi entropy and improved equilibration rates to self-similarity for nonlinear diffusion equations
NASA Astrophysics Data System (ADS)
Carrillo, J. A.; Toscani, G.
2014-12-01
We investigate the large-time asymptotics of nonlinear diffusion equations ut = Δup in dimension n ⩾ 1, in the exponent interval p > n/(n + 2), when the initial datum u0 is of bounded second moment. Precise rates of convergence to the Barenblatt profile in terms of the relative Rényi entropy are demonstrated for finite-mass solutions defined in the whole space when they are re-normalized at each time t > 0 with respect to their own second moment, as proposed by Carrillo et al (2006 Arch. Ration. Mech. Anal. 180 127-49) and Toscani (2005 J. Evol. Eqns 5 185-203). The analysis shows that, in the range p > max((n - 1)/n, n/(n + 2)), the relative Rényi entropy exhibits a better decay, for intermediate times, with respect to the standard Ralston-Newman entropy. The result follows by a suitable use of sharp Gagliardo-Nirenberg-Sobolev inequalities considered by Dolbeault and Toscani (2013 Ann. Inst. Henri Poincare (C) Non Linear Anal. 30 917-34), and their information-theoretical proof (Savaré and Toscani 2014 IEEE Trans. Inform. Theory 60 2687-93), known as concavity of Rényi entropy power.
Self-similarity and scaling behaviour of infrared emission from radiatively heated dust - I. Theory
NASA Astrophysics Data System (ADS)
Ivezic, Zeljko; Elitzur, Moshe
1997-06-01
Dust infrared emission possesses scaling properties that yield powerful results with far-reaching observational consequences. Scaling was first noticed by Rowan-Robinson for spherical shells and is shown here to be a general property of dust emission in arbitrary geometries. Overall luminosity is never an input parameter of the radiative transfer problem; spectral shape is the only relevant property of the heating radiation when the inner boundary of the dusty region is controlled by dust sublimation. Similarly, the absolute scales of densities and distances are irrelevant; the geometry enters only through angles, relative thicknesses and aspect ratios, and the actual magnitudes of densities and distances enter only through one independent parameter, the overall optical depth. That is, as long as the overall optical depth stays the same, the system dimensions can be scaled up or down by an arbitrary factor without any effect on the radiative transfer problem. Dust properties enter only through dimensionless, normalized distributions that describe the spatial variation of density and the wavelength dependence of scattering and absorption efficiencies. Scaling enables a systematic approach to modelling and classification of IR spectra. We develop a new, fully scale-free method for solving radiative transfer, present exact numerical results, and derive approximate analytical solutions for spherical geometry, covering the entire range of parameter space relevant to observations. For a given type of grains, the spectral energy distribution (SED) is primarily controlled by the profile of the spatial dust distribution and the optical depth - each density profile produces a family of solutions, with position within the family determined by optical depth. From the model SEDs presented here, the density distribution and optical depth can be observationally determined for various sources. Scaling implies tight correlations among the SEDs of various members of the same class of sources such as young stellar objects, late-type stars, etc. In particular, all members of the same class occupy common, well-defined regions in colour-colour diagrams. The observational data corroborate the existence of these correlations.
Self-Similar Magneto-Electric Nanocircuit Technology for Probabilistic Inference Engines
NASA Astrophysics Data System (ADS)
Khasanvis, Santosh; Li, Mingyu; Rahman, Mostafizur; Salehi-Fashami, Mohammad; Biswas, Ayan K.; Atulasimha, Jayasimha; Bandyopadhyay, Supriyo; Moritz, Csaba Andras
2015-11-01
Probabilistic graphical models are powerful mathematical formalisms for machine learning and reasoning under uncertainty that are widely used for cognitive computing. However they cannot be employed efficiently for large problems (with variables in the order of 100K or larger) on conventional systems, due to inefficiencies resulting from layers of abstraction and separation of logic and memory in CMOS implementations. In this paper, we present a magneto-electric probabilistic technology framework for implementing probabilistic reasoning functions. The technology leverages Straintronic Magneto-Tunneling Junction (S-MTJ) devices in a novel mixed-signal circuit framework for direct computations on probabilities while enabling in-memory computations with persistence. Initial evaluations of the Bayesian likelihood estimation operation occurring during Bayesian Network inference indicate up to 127x lower area, 214x lower active power, and 70x lower latency compared to an equivalent 45nm CMOS Boolean implementation.
Current interruption limit and resistance of the self-similar electric arc
NASA Astrophysics Data System (ADS)
Christen, Thomas; Seeger, Martin
2005-05-01
A model for the axially blown cylindrical arc is derived. In contrast to earlier theories, the model is gauge invariant with respect to energy, which is crucial for investigating current interruption. We determine from our model the dependence of the maximum interruptible current rate, (dI/dt)L, on the pressure, on the parallel capacitance, and on the line impedance for an SF6 arc. (dI/dt)L scales, approximately independent of the gas type, with the square root of the pressure. The arc resistance, at current zero with current rate equal to (dI/dt)L, is pressure independent. As a consequence, the arc resistance at current zero can serve as a figure of merit for the interruption performance of gas circuit breakers.
Variable step random walks, self-similar distributions, and pricing of options (Invited Paper)
NASA Astrophysics Data System (ADS)
Gunaratne, Gemunu H.; McCauley, Joseph L.
2005-05-01
A new theory for pricing of options is presented. It is based on the assumption that successive movements depend on the value of the return. The solution to the Fokker-Planck equation is shown to be an asymmetric exponential distribution, similar to those observed in intra-day currency markets. The "volatility smile", used by traders to correct the Black-Scholes pricing is shown to be a heuristic mechanism to implement options pricing formulae derived from our theory.
NASA Astrophysics Data System (ADS)
Fouvry, Jean-Baptiste; Pichon, Christophe
2015-05-01
The main orbital signatures of the secular evolution of an isolated self-gravitating stellar Mestel disc are recovered using a dressed Fokker-Planck formalism in angle-action variables. The shot-noise-driven formation of narrow ridges of resonant orbits is recovered in the WKB limit of tightly wound transient spirals, for a tepid Toomre-stable tapered disc. The relative effect of the bulge, the halo, the disc temperature and the spectral properties of the shot noise are investigated in turn. For such galactic discs all elements seem to impact the locus and direction of the ridge. For instance, when the halo mass is decreased, we observe a transition between a regime of heating in the inner regions of the disc through the inner Lindblad resonance to a regime of radial migration of quasi-circular orbits via the corotation resonance in the outer part of the disc. The dressed secular formalism captures both the nature of collisionless systems (via their natural frequencies and susceptibility), and their nurture via the structure of the external perturbing power spectrum. Hence it provides the ideal framework in which to study their long-term evolution.
Wave propagation in fractal-inspired self-similar beam lattices
Lim, Qi Jian; Wang, Pai; Koh, Soo Jin Adrian; Khoo, Eng Huat; Bertoldi, Katia
2015-11-30
We combine numerical analysis and experiments to investigate the effect of hierarchy on the propagation of elastic waves in triangular beam lattices. While the response of the triangular lattice is characterized by a locally resonant band gap, both Bragg-type and locally resonant gaps are found for the hierarchical lattice. Therefore, our results demonstrate that structural hierarchy can be exploited to introduce an additional type of band gaps, providing a robust strategy for the design of lattice-based metamaterials with hybrid band gap properties (i.e., possessing band gaps that arises from both Bragg scattering and localized resonance)
Kazantsev, D.; Van Eyndhoven, G.; Lionheart, W. R. B.; Withers, P. J.; Dobson, K. J.; McDonald, S. A.; Atwood, R.; Lee, P. D.
2015-01-01
There are many cases where one needs to limit the X-ray dose, or the number of projections, or both, for high frame rate (fast) imaging. Normally, it improves temporal resolution but reduces the spatial resolution of the reconstructed data. Fortunately, the redundancy of information in the temporal domain can be employed to improve spatial resolution. In this paper, we propose a novel regularizer for iterative reconstruction of time-lapse computed tomography. The non-local penalty term is driven by the available prior information and employs all available temporal data to improve the spatial resolution of each individual time frame. A high-resolution prior image from the same or a different imaging modality is used to enhance edges which remain stationary throughout the acquisition time while dynamic features tend to be regularized spatially. Effective computational performance together with robust improvement in spatial and temporal resolution makes the proposed method a competitive tool to state-of-the-art techniques. PMID:25939621
Kazantsev, D; Van Eyndhoven, G; Lionheart, W R B; Withers, P J; Dobson, K J; McDonald, S A; Atwood, R; Lee, P D
2015-06-13
There are many cases where one needs to limit the X-ray dose, or the number of projections, or both, for high frame rate (fast) imaging. Normally, it improves temporal resolution but reduces the spatial resolution of the reconstructed data. Fortunately, the redundancy of information in the temporal domain can be employed to improve spatial resolution. In this paper, we propose a novel regularizer for iterative reconstruction of time-lapse computed tomography. The non-local penalty term is driven by the available prior information and employs all available temporal data to improve the spatial resolution of each individual time frame. A high-resolution prior image from the same or a different imaging modality is used to enhance edges which remain stationary throughout the acquisition time while dynamic features tend to be regularized spatially. Effective computational performance together with robust improvement in spatial and temporal resolution makes the proposed method a competitive tool to state-of-the-art techniques. PMID:25939621
An Automated Self-similarity Analysis of the Pulmonary Tree of the Sprague-Dawley Rat
Einstein, Daniel R.; Neradilak, Blazej; Pollisar, Nayak; Minard, Kevin R.; Wallis, Chris; Fanucchi, Michelle; Carson, James P.; Kuprat, Andrew P.; Kabilan, Senthil; Jacob, Richard E.; Corley, Richard A.
2009-01-01
We present the results of an automated analysis of the morphometry of the pulmonary airway trees of the Sprague Dawley rat. Our work is motivated by a need to inform lower-dimensional mathematical models in order to prescribe realistic boundary conditions for multiscale hybrid models of rat lung mechanics. Silicone casts were made from three age-matched, male Sprague Dawley rats, immersed in a gel containing a contrast agent and subsequently imaged with magnetic resonance (MR). From a segmentation of this data, we extracted a connected graph, representing the airway centerline. Segment statistics (lengths and diameters) were derived from this graph. To validate this MR imaging/digital analysis method, airway segment measurements were compared to nearly one thousand measurements collected by hand using an optical microscope from one of the rat lung casts. To evaluate the reproducibility of the MR imaging/digital analysis method, two lung casts were each imaged three times with randomized orientations in the MR bore. Diameters and lengths of randomly selected airways were compared among each of the repeated imaging datasets to estimate the variability. Finally, we analyzed the morphometry of the airway tree by assembling individual airway segments into structures that span multiple generations, which we call branches. We show that branches not segments are the fundamental repeating unit in the rat lung and develop simple mathematical relationships describing these structures for the entire lung. Our analysis shows that airway diameters and lengths have both a deterministic and stochastic character. PMID:18951511
Social Preference in Preschoolers: Effects of Morphological Self-Similarity and Familiarity.
Richter, Nadja; Tiddeman, Bernard; Haun, Daniel B M
2016-01-01
Adults prefer to interact with others that are similar to themselves. Even slight facial self-resemblance can elicit trust towards strangers. Here we investigate if preschoolers at the age of 5 years already use facial self-resemblance when they make social judgments about others. We found that, in the absence of any additional knowledge about prospective peers, children preferred those who look subtly like themselves over complete strangers. Thus, subtle morphological similarities trigger social preferences well before adulthood. PMID:26727132
NASA Astrophysics Data System (ADS)
Ushenko, V. O.
2012-10-01
This work presents the possibility of phase tomography of optical-anisotropic multilayered biological structures. The superposition approach of polarization manifestation of optical anisotropy of polycrystalline protein networks is proposed. The optical model of polycrystalline networks of biological tissues protein fibrils is presented. The technique of phase tomography based on determining the coordinate distributions of Mueller-matrix elements of biological tissues is suggested. The results of investigating the interrelation between the values of statistical (statistical moments of the 1st- 4th order) parameters are presented. They characterize the coordinate distributions of phase shifts of biological tissue layer of different optical thickness and the degree of muscle dystrophy.
How children perceive fractals: hierarchical self-similarity and cognitive development.
Martins, Maurício Dias; Laaha, Sabine; Freiberger, Eva Maria; Choi, Soonja; Fitch, W Tecumseh
2014-10-01
The ability to understand and generate hierarchical structures is a crucial component of human cognition, available in language, music, mathematics and problem solving. Recursion is a particularly useful mechanism for generating complex hierarchies by means of self-embedding rules. In the visual domain, fractals are recursive structures in which simple transformation rules generate hierarchies of infinite depth. Research on how children acquire these rules can provide valuable insight into the cognitive requirements and learning constraints of recursion. Here, we used fractals to investigate the acquisition of recursion in the visual domain, and probed for correlations with grammar comprehension and general intelligence. We compared second (n=26) and fourth graders (n=26) in their ability to represent two types of rules for generating hierarchical structures: Recursive rules, on the one hand, which generate new hierarchical levels; and iterative rules, on the other hand, which merely insert items within hierarchies without generating new levels. We found that the majority of fourth graders, but not second graders, were able to represent both recursive and iterative rules. This difference was partially accounted by second graders' impairment in detecting hierarchical mistakes, and correlated with between-grade differences in grammar comprehension tasks. Empirically, recursion and iteration also differed in at least one crucial aspect: While the ability to learn recursive rules seemed to depend on the previous acquisition of simple iterative representations, the opposite was not true, i.e., children were able to acquire iterative rules before they acquired recursive representations. These results suggest that the acquisition of recursion in vision follows learning constraints similar to the acquisition of recursion in language, and that both domains share cognitive resources involved in hierarchical processing. PMID:24955884
Isometric immersions, energy minimization and self-similar buckling in non-Euclidean elastic sheets
NASA Astrophysics Data System (ADS)
Gemmer, John; Sharon, Eran; Shearman, Toby; Venkataramani, Shankar C.
2016-04-01
The edges of torn plastic sheets and growing leaves often display hierarchical buckling patterns. We show that this complex morphology i) emerges even in zero strain configurations, and ii) is driven by a competition between the two principal curvatures, rather than between bending and stretching. We identify the key role of branch point (or “monkey saddle”) singularities in generating complex wrinkling patterns in isometric immersions, and show how they arise naturally from minimizing the elastic energy.
Petridis, Loukas; Pingali, Sai Venkatesh; Urban, Volker; Heller, William T; O'Neill, Hugh Michael; Foston, Marcus B; Ragauskas, Arthur J; Smith, Jeremy C
2011-01-01
Lignin, a major polymeric component of plant cell walls, forms aggregates in vivo and poses a barrier to cellulosic ethanol production. Here, neutron scattering experiments and molecular dynamics simulations reveal that lignin aggregates are characterized by a surface fractal dimension that is invariant under change of scale from 1 1000 A. The simulations also reveal extensive water penetration of the aggregates and heterogeneous chain dynamics corresponding to a rigid core with a fluid surface.
Self similarity of turbulence and dynamo action in the largest cosmic structures
NASA Astrophysics Data System (ADS)
Miniati, Francesco; Beresnyak, Andrey
2015-08-01
Massive galaxy clusters (GC) are filled with a hot, turbulent and magnetised intra-cluster medium (ICM). They are still forming under the action of gravitational instability driving supersonic accretion flows, which partially dissipate into heat through a complex network of large scale shocks, whicle partly excite giant turbulent eddies and cascade. Amongst others turbulence amplifies magnetic energy by way of dynamo action. This pattern of gravitational energy turning kinetic, thermal, turbulent and magnetic is a basic feature of GC hydrodynamics but quantitative modelling remains a challenge. In this contribution we present results from recent high resolution numerical simulations of structure formation in which the time dependent turbulent motions of the intracluster medium of a massive galaxy cluster are resolved and their statistical properties quantified for the first time. Combined with independent state-of-theart results on turbulent dynamo we determine without adjustable parameters the thermal, turbulent and magnetic history of giant GC. I will discuss the scale free character of energy structure in the intracluster medium and how it encodes information about the efficiency of turbulent heating and dynamo action directly accessible through astronomical observations.
ERIC Educational Resources Information Center
Monroe, Charles; Newman, John
2005-01-01
This simple example demonstrates the physical significance of similarity solutions and the utility of dimensional and asymptotic analysis of partial differential equations. A procedure to determine the existence of similarity solutions is proposed and subsequently applied to transient constant-flux heat transfer. Short-time expressions follow from…
Self-similar rupture of thin free films of power law fluids
NASA Astrophysics Data System (ADS)
Thete, Sumeet; Anthony, Christopher; Basaran, Osman; Doshi, Pankaj
2015-11-01
Rupture of a thin sheet (free film) of a power law fluid under the competing influences of destabilizing van der Waals pressure (vdWP) and stabilizing surface tension pressure (STP) is analyzed. In such a fluid, viscosity is not constant but decreases with the deformation rate raised to the n - 1 power where 0 < n <= 1 is the power law exponent (n = 1 for a Newtonian fluid). It is shown that when 1 > n > 6 / 7 , film rupture occurs under a balance between vdWP, inertial stress (IS), and viscous stress (VS), and the film thickness decreases as τ n / 3 and the lateral length scale as τ 1 - n / 2 where τ is time remaining to rupture. When n < 6 / 7 , the dominant balance changes so that VS becomes negligible and the film ruptures under the competition between vdWP, IS, and STP. In this new regime, film thickness and lateral length vary as τ 2 / 7 and τ 4 / 7.
Self-similar rupture of thin free films of power-law fluids
NASA Astrophysics Data System (ADS)
Thete, Sumeet Suresh; Anthony, Christopher; Basaran, Osman A.; Doshi, Pankaj
2015-08-01
The rupture of a thin free film of a power-law fluid under the competing influences of destabilizing van der Waals pressure and stabilizing surface tension pressure is analyzed. In such a fluid, viscosity decreases with the deformation rate raised to the n -1 power where 0
Evidence for non-self-similarity of microearthquakes recorded at a Taiwan borehole seismometer array
NASA Astrophysics Data System (ADS)
Lin, Yen-Yu; Ma, Kuo-Fong; Kanamori, Hiroo; Song, Teh-Ru Alex; Lapusta, Nadia; Tsai, Victor C.
2016-04-01
We investigate the relationship between seismic moment M0 and source duration tw of microearthquakes by using high-quality seismic data recorded with a vertical borehole array installed in central Taiwan. We apply a waveform cross-correlation method to the three-component records and identify several event clusters with high waveform similarity, with event magnitudes ranging from 0.3 to 2.0. Three clusters-Clusters A, B, and C-contain 11, 8, and 6 events with similar waveforms, respectively. To determine how M0 scales with tw, we remove path effects by using a path-averaged Q. The results indicate a nearly constant tw for events within each cluster, regardless of M0, with mean values of tw being 0.058, 0.056, and 0.034 s for Clusters A, B, and C, respectively. Constant tw, independent of M0, violates the commonly used scaling relation {t_w} ∝ M_0^{1/3}. This constant duration may arise either because all events in a cluster are hosted on the same isolated seismogenic patch, or because the events are driven by external factors of constant duration, such as fluid injections into the fault zone. It may also be related to the earthquake nucleation size.
How children perceive fractals: Hierarchical self-similarity and cognitive development
Martins, Maurício Dias; Laaha, Sabine; Freiberger, Eva Maria; Choi, Soonja; Fitch, W. Tecumseh
2014-01-01
The ability to understand and generate hierarchical structures is a crucial component of human cognition, available in language, music, mathematics and problem solving. Recursion is a particularly useful mechanism for generating complex hierarchies by means of self-embedding rules. In the visual domain, fractals are recursive structures in which simple transformation rules generate hierarchies of infinite depth. Research on how children acquire these rules can provide valuable insight into the cognitive requirements and learning constraints of recursion. Here, we used fractals to investigate the acquisition of recursion in the visual domain, and probed for correlations with grammar comprehension and general intelligence. We compared second (n = 26) and fourth graders (n = 26) in their ability to represent two types of rules for generating hierarchical structures: Recursive rules, on the one hand, which generate new hierarchical levels; and iterative rules, on the other hand, which merely insert items within hierarchies without generating new levels. We found that the majority of fourth graders, but not second graders, were able to represent both recursive and iterative rules. This difference was partially accounted by second graders’ impairment in detecting hierarchical mistakes, and correlated with between-grade differences in grammar comprehension tasks. Empirically, recursion and iteration also differed in at least one crucial aspect: While the ability to learn recursive rules seemed to depend on the previous acquisition of simple iterative representations, the opposite was not true, i.e., children were able to acquire iterative rules before they acquired recursive representations. These results suggest that the acquisition of recursion in vision follows learning constraints similar to the acquisition of recursion in language, and that both domains share cognitive resources involved in hierarchical processing. PMID:24955884
NASA Astrophysics Data System (ADS)
Bettencourt, L. M. A.; Lobo, J.; West, G. B.
2008-06-01
Cities have existed since the beginning of civilization and have always been intimately connected with humanity's cultural and technological development. Much about the human and social dynamics that takes place is cities is intuitively recognizable across time, space and culture; yet we still do not have a clear cut answer as to why cities exist or to what factors are critical to make them thrive or collapse. Here, we construct an extensive quantitative characterization of the variation of many urban indicators with city size, using large data sets for American, European and Chinese cities. We show that social and economic quantities, characterizing the creation of wealth and new ideas, show increasing returns to population scale, which appear quantitatively as a power law of city size with an exponent β≃ 1.15 > 1. Concurrently, quantities characterizing material infrastructure typically show economies of scale, namely β≃ 0.8 < 1. The existence of pervasive scaling relations across city size suggests a universal social dynamics common to all cities within an urban system. We sketch some of their general ingredients, which include the acceleration of social life and a restructuring of individual social networks as cities grow larger. We also build simple dynamical models to show that increasing returns in wealth and innovation can fuel faster than exponential growth, which inexorably lead to crises of urban organization. To avoid them we show that growth may proceed in cycles, separated by major urban adaptations, with the unintended consequence that the duration of such cycles decreases with larger urban population size and is now estimated to be shorter than a human lifetime.
Record-Breaking Intervals: Detecting Trends in the Incidence of Self-Similar Earthquake Sequences
NASA Astrophysics Data System (ADS)
Yoder, Mark R.; Rundle, John B.
2015-08-01
We introduce a method of resolving temporal incidence trends in earthquake sequences. We have developed a catalog partitioning method based on canonical earthquake scaling relationships, and have further developed a metric based on record-breaking interval (RBI) statistics to resolve increasing and decreasing seismicity in time series of earthquakes. We calculated the RBI metric over fixed-length sequences of earthquake intervals and showed that the length of those sequences is related to the magnitude of the earthquake to which the method is sensitive—longer sequences resolve large earthquakes, shorter sequences resolve small-magnitude events. This sequence length effectively constitutes a local temporal catalog constraint, and we show that spatial constraints can be defined from rupture length scaling. We have applied the method to several high-profile earthquakes and have shown that it consistently resolves aftershock sequences after a period of accelerating seismicity before the targeted mainshock. The method also suggests a minimum detectable (forecastable) mainshock magnitude on the basis of the catalog's minimum completeness magnitude.
Burgers equation with self-similar gaussian initial data: Tail probabilities
NASA Astrophysics Data System (ADS)
Molchan, G. M.
1996-09-01
The statistical properties of solutions of the one-dimensional Burgers equation in the limit of vanishing viscosity are considered when the initial velocity potential is fractional Brownian motion (FBM). We establish the asymptotic power-law order for log-probability of large values, both velocity and shock (amplitude of velocity discontinuity). This confirms the conjecture of U. Frisch and his collaborators. Rigorous results for this problem were previously derived for the case of Brownian motion using Markov techniques. Our approach is based on the intrinsic properties of FBM and the theory of extreme values for Gaussian processes.
Burgers equation with self-similar gaussian initial data: Tail probabilities
NASA Astrophysics Data System (ADS)
Molchan, G. M.
1997-09-01
The statistical properties of solutions of the one-dimensional Burgers equation in the limit of vanishing viscosity are considered when the initial velocity potential is fractional Brownian motion (FBM). We establish the asymptotic power-law order for log-probability of large values, both velocity and shock (amplitude of velocity discontinuity). This confirms the conjecture of U. Frisch and his collaborators. Rigorous results for this problem were previously derived for the case of Brownian motion using Markov techniques. Our approach is based on the intrinsic properties of FBM and the theory of extreme values for Gaussian processes.
Video compressed sensing using iterative self-similarity modeling and residual reconstruction
NASA Astrophysics Data System (ADS)
Kim, Yookyung; Oh, Han; Bilgin, Ali
2013-04-01
Compressed sensing (CS) has great potential for use in video data acquisition and storage because it makes it unnecessary to collect an enormous amount of data and to perform the computationally demanding compression process. We propose an effective CS algorithm for video that consists of two iterative stages. In the first stage, frames containing the dominant structure are estimated. These frames are obtained by thresholding the coefficients of similar blocks. In the second stage, refined residual frames are reconstructed from the original measurements and the measurements corresponding to the frames estimated in the first stage. These two stages are iterated until convergence. The proposed algorithm exhibits superior subjective image quality and significantly improves the peak-signal-to-noise ratio and the structural similarity index measure compared to other state-of-the-art CS algorithms.
Annealed Ising model with site dilution on self-similar structures
NASA Astrophysics Data System (ADS)
Silva, V. S. T.; Andrade, R. F. S.; Salinas, S. R.
2014-11-01
We consider an Ising model on the triangular Apollonian network (AN), with a thermalized distribution of vacant sites. The statistical problem is formulated in a grand canonical ensemble, in terms of the temperature T and a chemical potential μ associated with the concentration of active magnetic sites. We use a well-known transfer-matrix method, with a number of adaptations, to write recursion relations between successive generations of this hierarchical structure. We also investigate the analogous model on the diamond hierarchical lattice (DHL). From the numerical analysis of the recursion relations, we obtain various thermodynamic quantities. In the μ →∞ limit, we reproduce the results for the uniform models: in the AN, the system is magnetically ordered at all temperatures, while in the DHL there is a ferromagnetic-paramagnetic transition at a finite value of T . Magnetic ordering, however, is shown to disappear for sufficiently large negative values of the chemical potential.
Evidence for non-self-similarity of microearthquakes recorded at a Taiwan borehole seismometer array
NASA Astrophysics Data System (ADS)
Lin, Yen-Yu; Ma, Kuo-Fong; Kanamori, Hiroo; Song, Teh-Ru Alex; Lapusta, Nadia; Tsai, Victor C.
2016-08-01
We investigate the relationship between seismic moment M0 and source duration tw of microearthquakes by using high-quality seismic data recorded with a vertical borehole array installed in central Taiwan. We apply a waveform cross-correlation method to the three-component records and identify several event clusters with high waveform similarity, with event magnitudes ranging from 0.3 to 2.0. Three clusters-Clusters A, B and C-contain 11, 8 and 6 events with similar waveforms, respectively. To determine how M0 scales with tw, we remove path effects by using a path-averaged Q. The results indicate a nearly constant tw for events within each cluster, regardless of M0, with mean values of tw being 0.058, 0.056 and 0.034 s for Clusters A, B and C, respectively. Constant tw, independent of M0, violates the commonly used scaling relation {t_w} ∝ M_0^{1/3}. This constant duration may arise either because all events in a cluster are hosted on the same isolated seismogenic patch, or because the events are driven by external factors of constant duration, such as fluid injections into the fault zone. It may also be related to the earthquake nucleation size.
Social Preference in Preschoolers: Effects of Morphological Self-Similarity and Familiarity
Richter, Nadja; Tiddeman, Bernard; Haun, Daniel B. M.
2016-01-01
Adults prefer to interact with others that are similar to themselves. Even slight facial self-resemblance can elicit trust towards strangers. Here we investigate if preschoolers at the age of 5 years already use facial self-resemblance when they make social judgments about others. We found that, in the absence of any additional knowledge about prospective peers, children preferred those who look subtly like themselves over complete strangers. Thus, subtle morphological similarities trigger social preferences well before adulthood. PMID:26727132
2014-01-01
Background In 2009, a retrospective study reported the detection of xenotropic murine leukemia virus-related virus (XMRV) in clinical isolates derived from individuals with chronic fatigue syndrome or myalgic encephalomyelitis (CFS). While many efforts to confirm this observation failed, one report detected polytropic murine leukemia virus (pMLV), instead of XMRV. In both studies, Polymerase Chain Reaction (PCR)-based methods were employed which could provide the basis for the development of a practical diagnostic tool. To confirm these studies, we hypothesized that the ability to detect these viruses will not only depend upon the technical details of the methods employed but also on the criteria used to diagnose CFS and the availability of well characterized clinical isolates. Methods A repository of clinical isolates from geographically distinct sites was generated by the collection of fresh blood samples from well characterized CFS and healthy subjects. Molecular techniques were used to generate assay positive controls and to determine the lower limit of detection (LLOD) for murine retroviral and Intracisternal A particle (Cell 12(4):963-72, 1977) detection methods. Results We report the establishment of a repository of well-defined, clinical isolates from five, geographically distinct regions of the US, the comparative determination of the LLODs and validation efforts for the previously reported detection methods and the results of an effort to confirm the association of these retroviral signatures in isolates from individuals with CFS in a blinded, multi-site, prospective study. We detected various, murine retroviral DNA signatures but were unable to resolve a difference in the incidence of their detection between isolates from CFS (5/72; 6.7%) and healthy (2/37; 5.4%) subjects (Fisher’s Exact Test, p-value = 1). The observed sequences appeared to reflect the detection of endogenous murine retroviral DNA, which was not identical to either XMRV or p
Pang, Judy; Ice, Gene E; Liu, W.
2010-01-01
We report on novel 3D spatially resolved X-ray diffraction microscopy studies of self-affine behavior in deformed single crystals. This study extends surface profile measurements of self-affined morphology changes in single crystals during deformation to include local lattice rotations and sub-surface behavior. Investigations were made on the spatial correlation of the local lattice rotations in 8% tensile deformed Cu single crystals oriented with [1 2 3], [1 1 1] and [0 0 1] axes parallel to the tensile axis. The nondestructive depth-resolved measurements were made over a length scale of one to hundreds of micrometers. Self-affined correlation was found both at the surface and below the surface of the samples. A universal exponent for the power-law similar to that observed with surface profile methods is found at the surface of all samples but crystallographically sensitive changes are observed as a function of depth. Correlation lengths of the self-affine behavior vary with the [1 2 3] crystal exhibiting the longest self-affine length scale of 70 m with only 18 m for the [1 1 1] and [0 0 1] crystals. These measurements illuminate the transition from surface-like to bulk-like deformation behavior and provide new quantitative information to guide emerging models of self-organized structures in plasticity.
Kukushkin, A. B.; Rantsev-Kartinov, V. A.
2009-07-26
The hypotheses for self-assembling of a fractal condensed matter in electric discharges and the probable role of a skeletal matter in the long-lived filamentary structures in fusion devices is studied in two directions. First, we append previous collection of respective data with recent evidences for skeletal structuring in peripheral plasmas and dust deposits in fusion and material test devices. Second, we demonstrate, via numerical modelling, the possibility of coaxial tubular structuring formation in a system of electric current filaments composed of magnetized, electrically conducting thin rods (nanodust), with an accent on self-reduction of spatial dimensionality of structuring and on the role of magnetic
NASA Astrophysics Data System (ADS)
Kulikovskii, A. G.; Chugainova, A. P.; Shargatov, V. A.
2016-07-01
Solutions of the Riemann problem for a generalized Hopf equation are studied. The solutions are constructed using a sequence of non-overturning Riemann waves and shock waves with stable stationary and nonstationary structures.
Coluccio, Maria Laura; Gentile, Francesco; Das, Gobind; Nicastri, Annalisa; Perri, Angela Mena; Candeloro, Patrizio; Perozziello, Gerardo; Proietti Zaccaria, Remo; Gongora, Juan Sebastian Totero; Alrasheed, Salma; Fratalocchi, Andrea; Limongi, Tania; Cuda, Giovanni; Di Fabrizio, Enzo
2015-01-01
Control of the architecture and electromagnetic behavior of nanostructures offers the possibility of designing and fabricating sensors that, owing to their intrinsic behavior, provide solutions to new problems in various fields. We show detection of peptides in multicomponent mixtures derived from human samples for early diagnosis of breast cancer. The architecture of sensors is based on a matrix array where pixels constitute a plasmonic device showing a strong electric field enhancement localized in an area of a few square nanometers. The method allows detection of single point mutations in peptides composing the BRCA1 protein. The sensitivity demonstrated falls in the picomolar (10−12 M) range. The success of this approach is a result of accurate design and fabrication control. The residual roughness introduced by fabrication was taken into account in optical modeling and was a further contributing factor in plasmon localization, increasing the sensitivity and selectivity of the sensors. This methodology developed for breast cancer detection can be considered a general strategy that is applicable to various pathologies and other chemical analytical cases where complex mixtures have to be resolved in their constitutive components. PMID:26601267
NASA Astrophysics Data System (ADS)
Nath, G.
2014-07-01
Similarity solutions are obtained for one-dimensional unsteady isothermal and adiabatic flows behind a strong exponential cylindrical shock wave propagating in a rotational axisymmetric dusty gas, which has variable azimuthal and axial fluid velocities. The shock wave is driven by a piston moving with time according to an exponential law. Similarity solutions exist only when the surrounding medium is of constant density. The azimuthal and axial components of the fluid velocity in the ambient medium are assumed to obey exponential laws. The dusty gas is assumed to be a mixture of small solid particles and a perfect gas. To obtain some essential features of the shock propagation, small solid particles are considered as a pseudo-fluid; it is assumed that the equilibrium flow conditions are maintained in the flow field, and that the viscous stresses and heat conduction in the mixture are negligible. Solutions are obtained for the cases when the flow between the shock and the piston is either isothermal or adiabatic, by taking into account the components of the vorticity vector. It is found that the assumption of zero temperature gradient results in a profound change in the density distribution as compared to that for the adiabatic case. The effects of the variation of the mass concentration of solid particles in the mixture , and the ratio of the density of solid particles to the initial density of the gas are investigated. A comparison between the solutions for the isothermal and adiabatic cases is also made.
Giri, Bapun K; Mitra, Chiranjit; Panigrahi, Prasanta K; Iyengar, A N Sekar
2014-12-01
The multiscale dynamics of glow discharge plasma is analysed through wavelet transform, whose scale dependent variable window size aptly captures both transients and non-stationary periodic behavior. The optimal time-frequency localization ability of the continuous Morlet wavelet is found to identify the scale dependent periodic modulations efficiently, as also the emergence of neutral turbulence and dissipation, whereas the discrete Daubechies basis set has been used for detrending the temporal behavior to reveal the multi-fractality of the underlying dynamics. The scaling exponents and the Hurst exponent have been estimated through wavelet based detrended fluctuation analysis, and also Fourier methods and rescale range analysis. PMID:25554055