Random self-similar trees and a hierarchical branching process
Kovchegov, Yevgeniy
2016-01-01
We study self-similarity in random binary rooted trees. In a well-understood case of Galton-Watson trees, a distribution is called self-similar if it is invariant with respect to the operation of pruning, which cuts the tree leaves. This only happens in the critical case (a constant process progeny), which also exhibits other special symmetries. We extend the prune-invariance set-up to a non-Markov situation and trees with edge lengths. In this general case the class of self-similar processes becomes much richer and covers a variety of practically important situations. The main result is construction of the hierarchical branching processes that satisfy various self-similarity constraints (distributional, mean, in edge-lengths) depending on the process parameters. Taking the limit of averaged stochastic dynamics, as the number of trajectories increases, we obtain a deterministic system of differential equations that describes the process evolution. This system is used to establish a phase transition that separ...
THE RANDOM SHIFT SET AND RANDOM SUB-SELF-SIMILAR SET
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
First of all the authors introduce the concepts of random sub-self-similar set and random shift set and then construct the random sub-self-similar set by a random shift set and a collection of statistical contraction operators.
Scaling of Peak Flows with Constant Flow Velocity in Random Self-Similar Networks
Mantilla, R.; Gupta, V. K.; Troutman, B. M.
2010-12-01
We present a methodology to understand the role of the statistical self-similar topology of real river networks on flow hydrographs for rainfall-runoff events. Monte Carlo generated ensembles of 1000 Random Self-similar Networks (RSNs) with geometrically distributed interior and exterior generators are created. We show how these networks emulate the statistical self-similarity present in real networks by presenting results for 30 river networks in the continental USA. Hydrographs for every link in each of these networks are obtained by numerically solving the link-based mass and momentum conservation equation under the assumption of constant flow velocity. From these simulated hydrographs for an ensemble of RSNs, the scaling parameters for the peak of the width function (β) and the hydrograph peak flow (φ) are estimated. It was found that φ > β, which supports a similar finding first reported for the Walnut Gulch basin, Arizona, and that is qualitatively different from previous results on idealized river networks (e.g. Peano Network, Mandelbrot- Viscek Network). Scaling of peak flows for individual rainfall runoff events is a new area of research that offers a path to physically understand regional scaling of flood quantiles. It addresses an important open problem in river network hydrology through studying the statistics of ensembles of multiple events in RSNs. In addition, our methodology provides a reference framework to study scaling exponents and intercepts under more complex scenarios of flow dynamics and runoff generation processes using ensembles of RSNs. Preliminary examples of such scenarios will also be given.
A self-similar process arising from a random walk with random environment in random scenery
Franke, Brice; 10.3150/09-BEJ234
2011-01-01
In this article, we merge celebrated results of Kesten and Spitzer [Z. Wahrsch. Verw. Gebiete 50 (1979) 5-25] and Kawazu and Kesten [J. Stat. Phys. 37 (1984) 561-575]. A random walk performs a motion in an i.i.d. environment and observes an i.i.d. scenery along its path. We assume that the scenery is in the domain of attraction of a stable distribution and prove that the resulting observations satisfy a limit theorem. The resulting limit process is a self-similar stochastic process with non-trivial dependencies.
Scaling of peak flows with constant flow velocity in random self-similar networks
Mantilla, R.; Gupta, V. K.; Troutman, B. M.
2011-07-01
A methodology is presented to understand the role of the statistical self-similar topology of real river networks on scaling, or power law, in peak flows for rainfall-runoff events. We created Monte Carlo generated sets of ensembles of 1000 random self-similar networks (RSNs) with geometrically distributed interior and exterior generators having parameters pi and pe, respectively. The parameter values were chosen to replicate the observed topology of real river networks. We calculated flow hydrographs in each of these networks by numerically solving the link-based mass and momentum conservation equation under the assumption of constant flow velocity. From these simulated RSNs and hydrographs, the scaling exponents β and φ characterizing power laws with respect to drainage area, and corresponding to the width functions and flow hydrographs respectively, were estimated. We found that, in general, φ > β, which supports a similar finding first reported for simulations in the river network of the Walnut Gulch basin, Arizona. Theoretical estimation of β and φ in RSNs is a complex open problem. Therefore, using results for a simpler problem associated with the expected width function and expected hydrograph for an ensemble of RSNs, we give heuristic arguments for theoretical derivations of the scaling exponents β(E) and φ(E) that depend on the Horton ratios for stream lengths and areas. These ratios in turn have a known dependence on the parameters of the geometric distributions of RSN generators. Good agreement was found between the analytically conjectured values of β(E) and φ(E) and the values estimated by the simulated ensembles of RSNs and hydrographs. The independence of the scaling exponents φ(E) and φ with respect to the value of flow velocity and runoff intensity implies an interesting connection between unit hydrograph theory and flow dynamics. Our results provide a reference framework to study scaling exponents under more complex scenarios of flow
Scaling of peak flows with constant flow velocity in random self-similar networks
Directory of Open Access Journals (Sweden)
R. Mantilla
2011-07-01
Full Text Available A methodology is presented to understand the role of the statistical self-similar topology of real river networks on scaling, or power law, in peak flows for rainfall-runoff events. We created Monte Carlo generated sets of ensembles of 1000 random self-similar networks (RSNs with geometrically distributed interior and exterior generators having parameters p_{i} and p_{e}, respectively. The parameter values were chosen to replicate the observed topology of real river networks. We calculated flow hydrographs in each of these networks by numerically solving the link-based mass and momentum conservation equation under the assumption of constant flow velocity. From these simulated RSNs and hydrographs, the scaling exponents β and φ characterizing power laws with respect to drainage area, and corresponding to the width functions and flow hydrographs respectively, were estimated. We found that, in general, φ > β, which supports a similar finding first reported for simulations in the river network of the Walnut Gulch basin, Arizona. Theoretical estimation of β and φ in RSNs is a complex open problem. Therefore, using results for a simpler problem associated with the expected width function and expected hydrograph for an ensemble of RSNs, we give heuristic arguments for theoretical derivations of the scaling exponents β^{(E} and φ^{(E} that depend on the Horton ratios for stream lengths and areas. These ratios in turn have a known dependence on the parameters of the geometric distributions of RSN generators. Good agreement was found between the analytically conjectured values of β^{(E} and φ^{(E} and the values estimated by the simulated ensembles of RSNs and hydrographs. The independence of the scaling exponents φ^{(E} and φ with respect to the value of flow velocity and runoff intensity implies an interesting connection between unit
Self-similar continuous cascades supported by random Cantor sets. Application to rainfall data
Muzy, J F
2016-01-01
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.
Random matrices, generalized zeta functions and self-similarity of zero distributions
Energy Technology Data Exchange (ETDEWEB)
Shanker, O [Bitfone Corporation, 32451 Golden Lantern Ste. 301, Laguna Niguel, CA 92677 (United States)
2006-11-10
There is growing evidence for a connection between random matrix theories used in physics and the theory of the Riemann zeta function and L-functions. The theory underlying the location of the zeros of these generalized zeta functions is one of the key unsolved problems. Physicists are interested because of the Hilbert-Polya conjecture, that the non-trivial zeros of the zeta function correspond to the eigenvalues of some positive operator. To complement the continuing theoretical work, it would be useful to study empirically the locations of the zeros by different methods. In this paper we use the rescaled range analysis to study the spacings between successive zeros of these functions. Over large ranges of the zeros the spacings have a Hurst exponent of about 0.095, using sample sizes of 10 000 zeros. This implies that the distribution has a high fractal dimension (1.9), and shows a lot of detailed structure. The distribution is of the anti-persistent fractional Brownian motion type, with a significant degree of anti-persistence. Thus, the high-order zeros of these functions show a remarkable self-similarity in their distribution, over fifteen orders of magnitude for the Riemann zeta function{exclamation_point} We find that the Hurst exponents for the random matrix theories show a different behaviour. A heuristic study of the effect of low-order primes seems to show that this effect is a promising candidate to explain the results that we observe in this study. We study the distribution of zeros for L-functions of conductors 3 and 4, and find that the distribution is similar to that of the Riemann zeta functions.
Testing Self-Similarity Through Lamperti Transformations
Lee, Myoungji
2016-07-14
Self-similar processes have been widely used in modeling real-world phenomena occurring in environmetrics, network traffic, image processing, and stock pricing, to name but a few. The estimation of the degree of self-similarity has been studied extensively, while statistical tests for self-similarity are scarce and limited to processes indexed in one dimension. This paper proposes a statistical hypothesis test procedure for self-similarity of a stochastic process indexed in one dimension and multi-self-similarity for a random field indexed in higher dimensions. If self-similarity is not rejected, our test provides a set of estimated self-similarity indexes. The key is to test stationarity of the inverse Lamperti transformations of the process. The inverse Lamperti transformation of a self-similar process is a strongly stationary process, revealing a theoretical connection between the two processes. To demonstrate the capability of our test, we test self-similarity of fractional Brownian motions and sheets, their time deformations and mixtures with Gaussian white noise, and the generalized Cauchy family. We also apply the self-similarity test to real data: annual minimum water levels of the Nile River, network traffic records, and surface heights of food wrappings. © 2016, International Biometric Society.
DEFF Research Database (Denmark)
Andersen, Allan T.; Nielsen, Bo Friis
2000-01-01
. The implications for the correlation structure when shuffling an exactly second-order self-similar process are examined. We apply the Markovian arrival process (MAP) as a tool to investigate whether general conclusions can be made with regard to the statistical implications of the shuffling experiments...
Institute of Scientific and Technical Information of China (English)
梁洪亮; 刘孝书
2003-01-01
For a physics system which exhibits memory, if memory is preserved only at points of random self-similar fractals, we define random memory functions and give the connection between the expectation of flux and the fractional integral. In particular, when memory sets degenerate to Cantor type fractals or non-random self-similar fractals our results coincide with that of Nigmatullin and Ren et al..
Universal self-similarity of propagating populations
Eliazar, Iddo; Klafter, Joseph
2010-07-01
This paper explores the universal self-similarity of propagating populations. The following general propagation model is considered: particles are randomly emitted from the origin of a d -dimensional Euclidean space and propagate randomly and independently of each other in space; all particles share a statistically common—yet arbitrary—motion pattern; each particle has its own random propagation parameters—emission epoch, motion frequency, and motion amplitude. The universally self-similar statistics of the particles’ displacements and first passage times (FPTs) are analyzed: statistics which are invariant with respect to the details of the displacement and FPT measurements and with respect to the particles’ underlying motion pattern. Analysis concludes that the universally self-similar statistics are governed by Poisson processes with power-law intensities and by the Fréchet and Weibull extreme-value laws.
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.
Davidsen, Jörn
2016-01-01
In many important systems exhibiting crackling noise --- intermittent avalanche-like 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 in particular 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 in particular clear evidence for a unified description of aftershocks and foreshocks. This may offer an improved way of time-dependent seismic hazard assessment and earthquake forecasting.
Self-similarity Driven Demosaicking
Directory of Open Access Journals (Sweden)
Antoni Buades
2011-06-01
Full Text Available Digital cameras record only one color component per pixel, red, green or blue. Demosaicking is the process by which one can infer a whole color matrix from such a matrix of values, thus interpolating the two missing color values per pixel. In this article we propose a demosaicking method based on the property of non-local self-similarity of images.
Self-Similar Collisionless Shocks
Katz, B; Waxman, E; Katz, Boaz; Keshet, Uri; Waxman, Eli
2006-01-01
Observations of gamma-ray burst afterglows suggest that the correlation length of magnetic field fluctuations downstream of relativistic non-magnetized collisionless shocks grows with distance from the shock to scales much larger than the plasma skin depth. We argue that this indicates that the plasma properties are described by a self-similar solution, and derive constraints on the scaling properties of the solution. For example, we find that the scaling of the characteristic magnetic field amplitude with distance from the shock is B \\propto D^{s_B} with -1 \\propto x^{2s_B} (for x>>D). We show that the plasma may be approximated as a combination of two self-similar components: a kinetic component of energetic particles and an MHD-like component representing "thermal" particles. We argue that the latter may be considered as infinitely conducting, in which case s_B=0 and the scalings are completely determined (e.g. dn/dE \\propto E^{-2} and B \\propto D^0). Similar claims apply to non- relativistic shocks such a...
Horton Law in Self-Similar Trees
Kovchegov, Yevgeniy; Zaliapin, Ilya
2016-04-01
Self-similarity of random trees is related to the operation of pruning. Pruning ℛ cuts the leaves and their parental edges and removes the resulting chains of degree-two nodes from a finite tree. A Horton-Strahler order of a vertex v and its parental edge is defined as the minimal number of prunings necessary to eliminate the subtree rooted at v. A branch is a group of neighboring vertices and edges of the same order. The Horton numbers 𝒩k[K] and 𝒩ij[K] are defined as the expected number of branches of order k, and the expected number of order-i branches that merged order-j branches, j > i, respectively, in a finite tree of order K. The Tokunaga coefficients are defined as Tij[K] = 𝒩ij[K]/𝒩j[K]. The pruning decreases the orders of tree vertices by unity. A rooted full binary tree is said to be mean-self-similar if its Tokunaga coefficients are invariant with respect to pruning: Tk := Ti,i+k[K]. We show that for self-similar trees, the condition limsupk→∞Tk1/k 0 and every k ≥ 1. This work is a step toward providing rigorous foundations for the Horton law that, being omnipresent in natural branching systems, has escaped so far a formal explanation.
Self-Similar Traffic In Wireless Networks
Jerjomins, R.; Petersons, E.
2005-01-01
Many studies have shown that traffic in Ethernet and other wired networks is self-similar. This paper reveals that wireless network traffic is also self-similar and long-range dependant by analyzing big amount of data captured from the wireless router.
and Models: A Self-Similar Approach
Directory of Open Access Journals (Sweden)
José Antonio Belinchón
2013-01-01
equations (FEs admit self-similar solutions. The methods employed allow us to obtain general results that are valid not only for the FRW metric, but also for all the Bianchi types as well as for the Kantowski-Sachs model (under the self-similarity hypothesis and the power-law hypothesis for the scale factors.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
We constructed a class of generalized statistically self-similar sets and give the necessary and sufficent conditions to ensure a random recursive set being a generalized statistically self-similar set. The statistically self-similar sets defined by Hutchinson ,Falconer ,Graf are the special cases of ours.
Spherically Symmetric, Self-Similar Spacetimes
Wagh, S M; Wagh, Sanjay M.; Govinder, Keshlan S.
2001-01-01
Self-similar spacetimes are of importance to cosmology and to gravitational collapse problems. We show that self-similarity or the existence of a homothetic Killing vector field for spherically symmetric spacetimes implies the separability of the spacetime metric in terms of the co-moving coordinates and that the metric is, uniquely, the one recently reported in [cqg1]. The spacetime, in general, has non-vanishing energy-flux and shear. The spacetime admits matter with any equation of state.
Burridge-Knopoff model and self-similarity
Akishin, P G; Budnik, A D; Ivanov, V V; Antoniou, I
1997-01-01
The seismic processes are well known to be self-similar in both spatial and temporal behavior. At the same time, the Burridge-Knopoff (BK) model of earthquake fault dynamics, one of the basic models of theoretical seismicity, does not posses self-similarity. In this article an extension of BK model, which directly accounts for the self-similarity of earth crust elastic properties by introducing nonlinear terms for inter-block springs of BK model, is presented. The phase space analysis of the model have shown it to behave like a system of coupled randomly kicked oscillators. The nonlinear stiffness terms cause the synchronization of collective motion and produce stronger seismic events.
Electroconvective instability of self-similar equilibria
Demekhin, E; Shtemler, Yury
2010-01-01
Stability of electro-hydrodynamic processes between ion-exchange membranes is investigated. Solutions of the equilibrium problem which represents the balance between diffusion and electro-migration are commonly described in an one-dimensional (1D) steady-state approximation. In the present work a novel class of the 1D unsteady self-similar equilibrium solution is developed asymptotically in small Debye length, epsilon, and large distance between membranes (both made dimensionless with the diffusion-layer thickness). First, the 1D unsteady family of self-similar equilibrium solutions is developed. Then, a linear stability of the self-similar solutions slowly varied with time is investigated in the limit of small epsilonand the marginal stability curves are obtained. Method of matched asymptotics is applied provided that only the outer solution is considered, ignoring the inner solutions. The success of the analysis is provided by transforming the equations to the divergent type (nabla G=0) with the patching co...
Self-similar parabolic plasmonic beams.
Davoyan, Arthur R; Turitsyn, Sergei K; Kivshar, Yuri S
2013-02-15
We demonstrate that an interplay between diffraction and defocusing nonlinearity can support stable self-similar plasmonic waves with a parabolic profile. Simplicity of a parabolic shape combined with the corresponding parabolic spatial phase distribution creates opportunities for controllable manipulation of plasmons through a combined action of diffraction and nonlinearity.
After notes on self-similarity exponent for fractal structures
Fernández-Martínez, Manuel; Caravaca Garratón, Manuel
2017-06-01
Previous works have highlighted the suitability of the concept of fractal structure, which derives from asymmetric topology, to propound generalized definitions of fractal dimension. The aim of the present article is to collect some results and approaches allowing to connect the self-similarity index and the fractal dimension of a broad spectrum of random processes. To tackle with, we shall use the concept of induced fractal structure on the image set of a sample curve. The main result in this paper states that given a sample function of a random process endowed with the induced fractal structure on its image, it holds that the self-similarity index of that function equals the inverse of its fractal dimension.
Self-similar behavior for multicomponent coagulation
Institute of Scientific and Technical Information of China (English)
杨曼丽; 卢志明; 刘宇陆
2014-01-01
Self-similar behavior for the multicomponent coagulation system is investi-gated analytically in this paper. Asymptotic self-similar solutions for the constant ker-nel, sum kernel, and product kernel are achieved by introduction of different generating functions. In these solutions, two size-scale variables are introduced to characterize the asymptotic distribution of total mass and individual masses. The result of product kernel (gelling kernel) is consistent with the Vigli-Ziff conjecture to some extent. Furthermore, the steady-state solution with injection for the constant kernel is obtained, which is again the product of a normal distribution and the scaling solution for the single variable coag-ulation.
Self-similar scalar field collapse
Banerjee, Narayan; Chakrabarti, Soumya
2017-01-01
A spherically symmetric collapsing scalar field model is discussed with a dissipative fluid which includes a heat flux. This vastly general matter distribution is analyzed at the expense of a high degree of symmetry in the space-time, that of conformal flatness and self-similarity. Indeed collapsing models terminating into a curvature singularity can be obtained. The formation of black holes or the occurrence of naked singularities depends on the initial collapsing profiles.
Self-Similar One-Dimensional Quasilattices
Boyle, Latham
2016-01-01
We study 1D quasilattices, especially self-similar ones that can be used to generate two-, three- and higher-dimensional quasicrystalline tesselations that have matching rules and invertible self-similar substitution rules (also known as inflation rules) analogous to the rules for generating Penrose tilings. The lattice positions can be expressed in a closed-form expression we call \\emph{floor form}: $x_{n} = S (n-\\alpha) + (L-S) \\lfloor \\kappa (n-\\beta) \\rfloor$, where $L > S > 0$ and $0 < \\kappa < 1$ is an irrational number. We describe three equivalent geometric constructions of these quasilattices and show how they can be subdivided into various types of equivalence classes: (i) \\emph{lattice equivalent}, where any two quasilattices in the same lattice equivalence class may be derived from one another by a local decoration/gluing rule; (ii) \\emph{self-similar}, a proper subset of lattice equivalent where, in addition, the two quasilattices are locally isomorphic; and (iii) \\emph{self-same}, a proper...
Self-similar plates: Casimir energies
Shajesh, K V; Cavero-Peláez, Inés; Parashar, Prachi
2016-01-01
We construct various self-similar configurations using parallel $\\delta$-function plates and show that it is possible to evaluate the Casimir interaction energy of these configurations using the idea of self-similarity alone. We restrict our analysis to interactions mediated by a scalar field, but the extension to electromagnetic field is immediate. Our work unveils an easy and powerful method that can be easily employed to calculate the Casimir energies of a class of self-similar configurations. As a highlight, in an example, we determine the Casimir interaction energy of a stack of parallel plates constructed by positioning $\\delta$-function plates at the points constituting the Cantor set, a prototype of a fractal. This, to our knowledge, is the first time that the Casimir energy of a fractal configuration has been reported. Remarkably, the Casimir energy of some of the configurations we consider turn out to be positive, and a few even have zero Casimir energy. For the case of positive Casimir energy that ...
I.I.D. STATISTICAL CONTRACTION OPERATORS AND STATISTICALLY SELF-SIMILAR SETS
Institute of Scientific and Technical Information of China (English)
胡迪鹤
2002-01-01
I.i.d. random sequence is the simplest but very basic one in stochastic processes, and statistically self-similar set is the simplest but very basic one in random recursive sets in the theory of random fractal. Is there any relation between i.i.d. random sequence and statistically self-similar set? This paper gives a basic theorem which tells us that the random recursive set generated by a collection of i.i.d. statistical contraction operators is always a statistically self-similar set.
Self-similar magnetohydrodynamic boundary layers
Energy Technology Data Exchange (ETDEWEB)
Nunez, Manuel; Lastra, Alberto, E-mail: mnjmhd@am.uva.e [Departamento de Analisis Matematico, Universidad de Valladolid, 47005 Valladolid (Spain)
2010-10-15
The boundary layer created by parallel flow in a magnetized fluid of high conductivity is considered in this paper. Under appropriate boundary conditions, self-similar solutions analogous to the ones studied by Blasius for the hydrodynamic problem may be found. It is proved that for these to be stable, the size of the Alfven velocity at the outer flow must be smaller than the flow velocity, a fact that has a ready physical explanation. The process by which the transverse velocity and the thickness of the layer grow with the size of the Alfven velocity is detailed.
Stability of Self-Similar Spherical Accretion
Gaite, J
2006-01-01
Spherical accretion flows are simple enough for analytical study, by solution of the corresponding fluid dynamic equations. The solutions of stationary spherical flow are due to Bondi. The questions of the choice of a physical solution and of stability have been widely discussed. The answer to these questions is very dependent on the problem of boundary conditions, which vary according to whether the accretor is a compact object or a black hole. We introduce a particular, simple form of stationary spherical flow, namely, self-similar Bondi flow, as a case with physical interest in which analytic solutions for perturbations can be found. With suitable no matter-flux-perturbation boundary conditions, we will show that acoustic modes are stable in time and have no spatial instability at r=0. Furthermore, their evolution eventually becomes ergodic-like and shows no trace of instability or of acquiring any remarkable pattern.
Hot self-similar relativistic MHD flows
Zakamska, Nadia L; Blandford, Roger D
2008-01-01
We consider axisymmetric relativistic jets with a toroidal magnetic field and an ultrarelativistic equation of state, with the goal of studying the lateral structure of jets whose pressure is matched to the pressure of the medium through which they propagate. We find all self-similar steady-state solutions of the relativistic MHD equations for this setup. One of the solutions is the case of a parabolic jet being accelerated by the pressure gradient as it propagates through a medium with pressure declining as p(z)\\propto z^{-2}. As the jet material expands due to internal pressure gradients, it runs into the ambient medium resulting in a pile-up of material along the jet boundary, while the magnetic field acts to produce a magnetic pinch along the axis of the jet. Such jets can be in a lateral pressure equilibrium only if their opening angle \\theta_j at distance z is smaller than about 1/\\gamma, where \\gamma is the characteristic bulk Lorentz-factor at this distance; otherwise, different parts of the jet canno...
Gait Recognition Using Image Self-Similarity
Directory of Open Access Journals (Sweden)
Cutler Ross G
2004-01-01
Full Text Available 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.
Self-Similar Dynamics of a Magnetized Polytropic Gas
Wang, Wei-Gang
2007-01-01
In broad astrophysical contexts of large-scale gravitational collapses and outflows and as a basis for various further astrophysical applications, we formulate and investigate a theoretical problem of self-similar MHD for a non-rotating polytropic gas of quasi-spherical symmetry permeated by a completely random magnetic field. We derive two coupled nonlinear MHD ordinary differential equations (ODEs), examine properties of the magnetosonic critical curve, obtain various asymptotic and global semi-complete similarity MHD solutions, and qualify the applicability of our results. Unique to a magnetized gas cloud, a novel asymptotic MHD solution for a collapsing core is established. Physically, the similarity MHD inflow towards the central dense core proceeds in characteristic manners before the gas material eventually encounters a strong radiating MHD shock upon impact onto the central compact object. Sufficiently far away from the central core region enshrouded by such an MHD shock, we derive regular asymptotic ...
Self-similar traffic analysis in optical burst assembly
Institute of Scientific and Technical Information of China (English)
Sui Zhicheng; Zeng Qingji; Xiao Shilin
2005-01-01
This paper investigates the traffic properties before and after assembly at edge node of Ethernet over optical burst switching (OBS) network for the first time. Burst and inter-arrival time distributions are simulated under time-based and length-based assembly schemes. Self-similar traffic Hurst parameter is compared through R/S and V/T plot. Finally three self-similar traffic generating methods are given. Simulation results demonstrate that, multi-source traffic increases self-similar degree, however after assembly, time-based scheme can decrease self-similar degree, and aggregated burst size is close to Gaussian distribution. Length-based method has no effects on the self-similarity of input traffic. RMD is fit for study of burst network with large self-similarity.
Nonexistence of self-similar singularities in ideal viscoelastic flows
Directory of Open Access Journals (Sweden)
Anthony Suen
2012-06-01
Full Text Available We prove the nonexistence of finite time self-similar singularities in an ideal viscoelastic flow in R^3. We exclude the occurrence of Leray-type self-similar singularities under suitable integrability conditions on velocity and deformation tensor. We also prove the nonexistence of asymptotically self-similar singularities in our system. The present work extends the results obtained by Chae in the case of magnetohydrodynamics (MHD.
Auditory perception of self-similarity in water sounds.
Directory of Open Access Journals (Sweden)
Maria Neimark Geffen
2011-05-01
Full Text Available Many natural signals, including environmental sounds, exhibit scale-invariant statistics: their structure is repeated at multiple scales. Such scale invariance has been identified separately across spectral and temporal correlations of natural sounds (Clarke and Voss, 1975; Attias and Schreiner, 1997; Escabi et al., 2003; Singh and Theunissen, 2003. Yet the role of scale-invariance across overall spectro-temporal structure of the sound has not been explored directly in auditory perception. Here, we identify that the sound wave of a recording of running water is a self-similar fractal, exhibiting scale-invariance not only within spectral channels, but also across the full spectral bandwidth. The auditory perception of the water sound did not change with its scale. We tested the role of scale-invariance in perception by using an artificial sound, which could be rendered scale-invariant. We generated a random chirp stimulus: an auditory signal controlled by two parameters, Q, controlling the relative, and r, controlling the absolute, temporal structure of the sound. Imposing scale-invariant statistics on the artificial sound was required for its perception as natural and water-like. Further, Q had to be restricted to a specific range for the sound to be perceived as natural. To detect self-similarity in the water sound, and identify Q, the auditory system needs to process the temporal dynamics of the waveform across spectral bands in terms of the number of cycles, rather than absolute timing. We propose a two-stage neural model implementing this computation. This computation may be carried out by circuits of neurons in the auditory cortex. The set of auditory stimuli developed in this study are particularly suitable for measurements of response properties of neurons in the auditory pathway, allowing for quantification of the effects of varying the statistics of the spectro-temporal statistical structure of the stimulus.
Local field enhancement: comparing self-similar and dimer nanoantennas
Pellegrini, Giovanni; Finazzi, Marco; Biagioni, Paolo
2016-01-01
We study the local field enhancement properties of self-similar nanolenses and compare the obtained results with the performance of standard dimer nanoantennas. We report that, despite the additional structural complexity, self-similar nanolenses are unable to provide significant improvements over the field enhancement performance of standard plasmonic dimers.
Self-similar measures on the Julia sets of polynomials
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
If the immediate basin of infinity of a polynomial P(z) contains at least one of its critical points, then there is a self-similar measure on its Julia set, and if all the critical points of P(z) lie in the immediate basin of in finity, then the self-similar measure is unique.
Escaping the avalanche collapse in self-similar multiplexes
Serrano, M Angeles; Boguna, Marian
2015-01-01
We deduce and discuss the implications of self-similarity for the stability in terms of 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 stability 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 stability attributes of noninteracting networks. We confirm these results with numerical simulations.
Self-similar motion of a Nambu-Goto string
Igata, Takahisa; Harada, Tomohiro
2016-01-01
We study the self-similar motion of a string in a self-similar spacetime by introducing the concept of a self-similar string, which is defined as the world sheet to which a homothetic vector field is tangent. It is shown that in the Nambu-Goto theory, the equations of motion for a self-similar string reduce to those for a particle. Moreover, under certain conditions such as the hypersurface orthogonality of the homothetic vector field, the equations of motion for a self-similar string simplify to the geodesic equations on a (pseudo) Riemannian space. As a concrete example, we investigate a self-similar Nambu-Goto string in a spatially flat Friedmann-Lema\\^itre-Robertson-Walker expanding universe with self-similarity, and obtain solutions of open and closed strings, which have various nontrivial configurations depending on the rate of the cosmic expansion. For instance, we obtain a circular solution that evolves linearly in the cosmic time while keeping its configuration by the balance between the effects of t...
Self-similar motion of a Nambu-Goto string
Igata, Takahisa; Houri, Tsuyoshi; Harada, Tomohiro
2016-09-01
We study the self-similar motion of a string in a self-similar spacetime by introducing the concept of a self-similar string, which is defined as the world sheet to which a homothetic vector field is tangent. It is shown that in Nambu-Goto theory, the equations of motion for a self-similar string reduce to those for a particle. Moreover, under certain conditions such as the hypersurface orthogonality of the homothetic vector field, the equations of motion for a self-similar string simplify to the geodesic equations on a (pseudo)Riemannian space. As a concrete example, we investigate a self-similar Nambu-Goto string in a spatially flat Friedmann-Lemaître-Robertson-Walker expanding universe with self-similarity and obtain solutions of open and closed strings, which have various nontrivial configurations depending on the rate of the cosmic expansion. For instance, we obtain a circular solution that evolves linearly in the cosmic time while keeping its configuration by the balance between the effects of the cosmic expansion and string tension. We also show the instability for linear radial perturbation of the circular solutions.
Discrete self similarity in filled type I strong explosions
Yalinewich, Almog; Sari, Re'em
2013-12-01
We present new solutions to the strong explosion problem in a non power law density profile. The unperturbed self similar solutions developed by Sedov, Taylor, and Von Neumann describe strong Newtonian shocks propagating into a cold gas with a density profile falling off as r-ω, where ω le 7-γ /γ +1 (filled type I solutions), and γ is the adiabatic index of the gas. The perturbations we consider are spherically symmetric and log periodic with respect to the radius. While the unperturbed solutions are continuously self similar, the log periodicity of the density perturbations leads to a discrete self similarity of the perturbations, i.e., the solution repeats itself up to a scaling at discrete time intervals. We discuss these solutions and verify them against numerical integrations of the time dependent hydrodynamic equations. This is an extension of a previous investigation on type II solutions and helps clarifying boundary conditions for perturbations to type I self similar solutions.
Fibonacci chain polynomials: Identities from self-similarity
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.
AN FFT-BASED SELF-SIMILAR TRAFFIC GENERATOR
Institute of Scientific and Technical Information of China (English)
施建俊; 薛质; 诸鸿文
2001-01-01
The self-similarity of the network traffic has great influences on the performance. But there are few analytical or even numerical solutions for such a model. So simulation becomes the most efficient method for research. Fractal Gaussian noise (FGN) is the most popularly used self-similar model. This paper presented an FGN generator based on fast Fourier transform (FFT). The study indicates that this algorithm is fairly fast and accurate.
Stable non-Gaussian self-similar processes with stationary increments
Pipiras, Vladas
2017-01-01
This book provides a self-contained presentation on the structure of a large class of stable processes, known as self-similar mixed moving averages. The authors present a way to describe and classify these processes by relating them to so-called deterministic flows. The first sections in the book review random variables, stochastic processes, and integrals, moving on to rigidity and flows, and finally ending with mixed moving averages and self-similarity. In-depth appendices are also included. This book is aimed at graduate students and researchers working in probability theory and statistics.
An Introduction to the Theory of Self-Similar Stochastic Processes
Embrechts, Paul; Maejima, Makoto
Self-similar processes such as fractional Brownian motion are stochastic processes that are invariant in distribution under suitable scaling of time and space. These processes can typically be used to model random phenomena with long-range dependence. Naturally, these processes are closely related to the notion of renormalization in statistical and high energy physics. They are also increasingly important in many other fields of application, as there are economics and finance. This paper starts with some basic aspects on self-similar processes and discusses several topics from the point of view of probability theory.
Self-similar dynamics of a magnetized polytropic gas
Wang, Wei-Gang; Lou, Yu-Qing
2007-10-01
In broad astrophysical contexts of large-scale gravitational collapses and outflows and as a basis for various further astrophysical applications, we formulate and investigate a theoretical problem of self-similar magnetohydrodynamics (MHD) for a non-rotating polytropic gas of quasi-spherical symmetry permeated by a completely random magnetic field. Within this framework, we derive two coupled nonlinear MHD ordinary differential equations (ODEs), examine properties of the magnetosonic critical curve, obtain various asymptotic and global semi-complete similarity MHD solutions, and qualify the applicability of our results. Unique to a magnetized gas cloud, a novel asymptotic MHD solution for a collapsing core is established. Physically, the similarity MHD inflow towards the central dense core proceeds in characteristic manners before the gas material eventually encounters a strong radiating MHD shock upon impact onto the central compact object. Sufficiently far away from the central core region enshrouded by such an MHD shock, we derive regular asymptotic behaviours. We study asymptotic solution behaviours in the vicinity of the magnetosonic critical curve and determine smooth MHD eigensolutions across this curve. Numerically, we construct global semi-complete similarity MHD solutions that cross the magnetosonic critical curve zero, one, and two times. For comparison, counterpart solutions in the case of an isothermal unmagnetized and magnetized gas flows are demonstrated in the present MHD framework at nearly isothermal and weakly magnetized conditions. For a polytropic index γ=1.25 or a strong magnetic field, different solution behaviours emerge. With a strong magnetic field, there exist semi-complete similarity solutions crossing the magnetosonic critical curve only once, and the MHD counterpart of expansion-wave collapse solution disappears. Also in the polytropic case of γ=1.25, we no longer observe the trend in the speed-density phase diagram of finding
On the self-similarity of nonhelical magnetohydrodynamic turbulence
Energy Technology Data Exchange (ETDEWEB)
Campanelli, Leonardo [Universita di Bari, Dipartimento di Fisica, Bari (Italy)
2016-09-15
We re-analyze the Olesen arguments on the self-similarity properties of freely evolving, nonhelical magnetohydrodynamic turbulence. We find that a necessary and sufficient condition for the kinetic and magnetic energy spectra to evolve self-similarly is that the initial velocity and magnetic field are not homogeneous functions of space of different degree, to wit, the initial energy spectra are not simple powers of the wavenumber with different slopes. If, instead, they are homogeneous functions of the same degree, the evolution is self-similar, it proceeds through selective decay, and the order of homogeneity fixes the exponents of the power laws according to which the kinetic and magnetic energies and correlation lengths evolve in time. If just one of them is homogeneous, the evolution is self-similar and such exponents are completely determined by the slope of that initial spectrum which is a power law. The latter evolves through selective decay, while the other spectrum may eventually experience an inverse transfer of energy. Finally, if the initial velocity and magnetic field are not homogeneous functions, the evolution of the energy spectra is still self-similar but, this time, the power-law exponents of energies and correlation lengths depend on a single free parameter which cannot be determined by scaling arguments. Also, in this case, an inverse transfer of energy may in principle take place during the evolution of the system. (orig.)
Discrete Self-Similarity in Type-II Strong Explosions
Oren, Yonatan; 10.1063/1.3139307
2009-01-01
We present new solutions to the strong explosion problem in a non-power law density profile. The unperturbed self-similar solutions discovered by Waxman & Shvarts describe strong Newtonian shocks propagating into a cold gas with a density profile falling off as $r^{-\\omega}$, where $\\omega>3$ (Type-II solutions). The perturbations we consider are spherically symmetric and log-periodic with respect to the radius. While the unperturbed solutions are continuously self-similar, the log-periodicity of the density perturbations leads to a discrete self-similarity of the perturbations, i.e. the solution repeats itself up to a scaling at discrete time intervals. We discuss these solutions and verify them against numerical integrations of the time dependent hydrodynamic equations. Finally we show that this method can be generalized to treat any small, spherically symmetric density perturbation by employing Fourier decomposition.
Slightly Two or Three Dimensional Self-Similar Solutions
Sari, Re'em; Yalinewich, Almog; MacFadyen, Andrew
2011-01-01
Self similarity allows for analytic or semi-analytic solutions to many hydrodynamics problems. Most of these solutions are one dimensional. Using linear perturbation theory, expanded around such a one-dimensional solution, we find self-similar hydrodynamic solutions that are two- or three-dimensional. Since the deviation from a one-dimensional solution is small, we call these slightly two-dimensional and slightly three-dimensional self-similar solutions, respectively. As an example, we treat strong spherical explosions of the second type. A strong explosion propagates into an ideal gas with negligible temperature and density profile of the form rho(r,theta,phi)=r^{-omega}[1+sigma*F(theta,phi)], where omega>3 and sigma << 1. Analytical solutions are obtained by expanding the arbitrary function F(theta,phi) in spherical harmonics. We compare our results with two dimensional numerical simulations, and find good agreement.
Investigation of Dynamics of Self-Similarly Evolving Magnetic Clouds
Dalakishvili, Giorgi; Lapenta, Giovanni; Poedts, Stefaan
2010-01-01
Magnetic clouds (MCs) are "magnetized plasma clouds" moving in the solar wind. MCs transport magnetic flux and helicity away from the Sun. These structures are not stationary but feature temporal evolution. Commonly, simplified MC models are considered. The goal of the present study is to investigate the dynamics of more general, radially expanding MCs. They are considered as cylindrically symmetric magnetic structures with low plasma {\\beta}. In order to study MC`evolution the self-similar approach method and a numerical approach are used. It is shown that the forces are balanced in the considered self-similarly evolving, cylindrically symmetric magnetic structures. Explicit analytical expressions for magnetic field, plasma velocity, density and pressure within MCs are derived. These solutions are characterized by conserved values of magnetic flux and helicity. We also investigate the dynamics of self-similarly evolving MCs by means of the numerical code "Graale". In addition, their expansion in a medium wit...
Self-similarity of complex networks and hidden metric spaces
Serrano, M Angeles; Boguna, Marian
2007-01-01
We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces. Clustering, i.e., cycles of length three, plays a crucial role in this framework as a topological reflection of the triangle inequality in the hidden geometry. We prove that a class of hidden variable models with underlying metric spaces are able to accurately reproduce the self-similarity properties that we measured in the real networks. Our findings indicate that hidden geometries underlying these real networks are a plausible explanation for their observed topologies and, in particular, for their self-similarity with respect to the degree-based renormalization.
Emergence of self-similarity in football dynamics
Kijima, Akifumi; Shima, Hiroyuki; Yamamoto, Yuji
2014-01-01
The multiplayer dynamics of a football game is analyzed to unveil self-similarities in the time evolution of player and ball positioning. Temporal fluctuations in both the team-turf boundary and the ball location are uncovered to follow the rules of fractional Brownian motion with a Hurst exponent of H=0.7. The persistence time below which self-similarity holds is found to be several tens of seconds, implying a characteristic time scale that governs far-from-equilibrium motion on a playing field.
Scattering from Rough Surfaces with Extended Self-Similarity
Institute of Scientific and Technical Information of China (English)
张延冬; 吴振森
2002-01-01
An extended self-similarity (ESS) model is developed by extending the self-similarity condition in fractional Brownian motion (FBM), then the incremental Fourier synthesis algorithm is introduced to generate ESS rough surfaces, and an estimation algorithm is presented to extract the generalized multiscale Hurst parameter, which can also be modified to estimate the Hurst parameter for FBM more accurately. Finally, the scattering coefficient from ESS rough surfaces is calculated with the scalar Kirchhoff approximation, and its variation with the parameters in the ESS model is obtained. Compared with experimental measurements, it can be concluded that the ESS model provides a good tool to model natural rough surfaces.
Self-Similar Symmetry Model and Cosmic Microwave Background
Directory of Open Access Journals (Sweden)
Tomohide eSonoda
2016-05-01
Full Text Available In this paper, we present the self-similar symmetry (SSS model that describes the hierarchical structure of the universe. The model is based on the concept of self-similarity, which explains the symmetry of the cosmic microwave background (CMB. The approximate length and time scales of the six hierarchies of the universe---grand unification, electroweak unification, the atom, the pulsar, the solar system, and the galactic system---are derived from the SSS model. In addition, the model implies that the electron mass and gravitational constant could vary with the CMB radiation temperature.
GEOMETRY AND DIMENSION OF SELF-SIMILAR SET
Institute of Scientific and Technical Information of China (English)
尹永成; 姜海益; 孙业顺
2003-01-01
The authors show that the self-similar set for a finite family of contractive similitudes (sim-ilarities, i.e., |fi(x) - fi(y)| = ai|x - y|, x,y ∈ RN, where 0 ＜ ai ＜ 1) is uniformly perfectexcept the case that it is a singleton. As a corollary, it is proved that this self-similar set haspositive Hausdorff dimension provided that it is not a singleton. And a lower bound of theupper box dimension of the uniformly perfect sets is given. Meanwhile the uniformly perfectset with Hausdorff measure zero in its Hausdorff dimension is given.
A class of self-similar hydrodynamics test problems
Energy Technology Data Exchange (ETDEWEB)
Ramsey, Scott D [Los Alamos National Laboratory; Brown, Lowell S [Los Alamos National Laboratory; Nelson, Eric M [Los Alamos National Laboratory; Alme, Marv L [Los Alamos National Laboratory
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.
A Self-Similar Dynamics in Viscous Spheres
Barreto, W.; Ovalle, J.; Rodríguez, B.
1998-01-01
We study the evolution of radiating and viscous fluid spheres assuming an additional homothetic symmetry on the spherically symmetric space-time. We match a very simple solution to the symmetry equations with the exterior one (Vaidya). We then obtain a system of two ordinary differential equations which rule the dynamics, and find a self-similar collapse which is shear-free and with a barotropic equation of state. Considering a huge set of initial self-similar dynamics states, we work out a model with an acceptable physical behavior.
A self-similar dynamics in viscous spheres
Barreto, W; Rodríguez, B
1998-01-01
We study the evolution of radiating and viscous fluid spheres assuming an additional homothetic symmetry on the spherically simmetric space--time. We match a very simple solution to the symmetry equations with the exterior one (Vaidya). We then obtain a system of two ordinary differential equations which rule the dynamics, and find a self--similar collapse which is shear--free and with a barotropic equation of state. Considering a huge set of initial self--similar dynamics states, we work out a model with an acceptable physical behavior.
The Impact of Self-Similar Traffic on Network Delay
Institute of Scientific and Technical Information of China (English)
SHU Yantai; XUE Fei; JIN Zhigang; Oliver Yang
1999-01-01
The effect of self-similar traffic onthe delay of a single queue system is studied through the use of themeasured traffic and models as input process. A model-drivensimulation-based method is then proposed for the computation of meanline delay in a network design. Both the hybrid-FGN and the FARIMAalgorithms have been used to synthesize self-similar sample paths. Thecomparison results with real-traffic data sets firmly establish theusefulness of the proposed model-driven simulation-based method. Apractical database method is also introduced that helps the designer todetermine the parameters in network design. This approach mayplay an important role in network design and analysis.
PHOG analysis of self-similarity in aesthetic images
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
Naked Singularities in Spherically Symmetric, Self-Similar Spacetimes
Wagh, S M; Wagh, Sanjay M.; Govinder, Keshlan S.
2001-01-01
We show that all known naked singularities in spherically symmetric self-similar spacetimes arise as a result of singular initial matter distribution. This is a result of the peculiarity of the coordinate transformation that takes these spacetimes into a separable form. Therefore, these examples of naked singularities are of no apparent consequence to astrophysical observations or theories.
Fixed Points in Self-Similar Analysis of Time Series
Gluzman, S.; Yukalov, V. I.
1998-01-01
Two possible definitions of fixed points in the self-similar analysis of time series are considered. One definition is based on the minimal-difference condition and another, on a simple averaging. From studying stock market time series, one may conclude that these two definitions are practically equivalent. A forecast is made for the stock market indices for the end of March 1998.
Casimir energies of self-similar plate configurations
Shajesh, K. V.; Brevik, Iver; Cavero-Peláez, Inés; Parashar, Prachi
2016-09-01
We construct various self-similar configurations using parallel δ -function plates and show that it is possible to evaluate the Casimir interaction energy of these configurations using the idea of self-similarity alone. We restrict our analysis to interactions mediated by a scalar field, but the extension to the electromagnetic field is immediate. Our work unveils an easy and powerful method that can be easily employed to calculate the Casimir energies of a class of self-similar configurations. As a highlight, in an example, we determine the Casimir interaction energy of a stack of parallel plates constructed by positioning δ -function plates at the points constituting the Cantor set, a prototype of a fractal. This, to our knowledge, is the first time that the Casimir energy of a fractal configuration has been reported. Remarkably, the Casimir energy of some of the configurations we consider turn out to be positive, and a few even have zero Casimir energy. For the case of positive Casimir energy that is monotonically decreasing as the stacking parameter increases, the interpretation is that the pressure of vacuum tends to inflate the infinite stack of plates. We further support our results, derived using the idea of self-similarity alone, by rederiving them using the Green's function formalism. These expositions gives us insight into the connections between the regularization methods used in quantum field theories and regularized sums of divergent series in number theory.
Multifractal Decomposition of Statistically Self-Similar Sets
Institute of Scientific and Technical Information of China (English)
Jing Hu YU; Di He HU
2001-01-01
Let K be a statistically self-similar set defined by Graf. In this paper, we construct arandom measure p which is supported by K and study the multifractal decomposition for K with p.Under such a decomposition, we obtain the expression of the spectrum function f(α).
Length Requirement of Self-Similar Network Traffic
Institute of Scientific and Technical Information of China (English)
RAOYunhua; XUZhongyang; LIUZhenglin
2004-01-01
It is important to study the second-order character of self-similar network traffic in performance evaluation. Especially in real-time applications, traffic autocorrelation is a useful analysis tool, so how to estimate it quickly and reliably is a significant problem. In this paper,we studied the estimation and evaluation of self-similar network traffic autocorrelation structure. With the model of Fractional Gaussian noise (FGN) process, we obtained a simple variance expression of estimated autocorrelation,which is the function of Hurst parameter (H) and traffic data length. The relationship among Hurst parameter, accuracy of the estimated autocorrelation and required data length of self-similar traffic shows that the accuracy of estimated autocorrelation decreases with the increasing Hurst parameter and with the decreasing data length too. But over-long sampled data could not improve the accuracy of estimated autocorrelation remarkably. Furthermore, a sharp variety of accuracy is discovered between H > 0.75 and H < 0.75. It is a very interesting phenomenon that had not been reported before. This shows that Hurst parameter could reflect the second-order character of selfsimilarity, but it is not enough to capture all the traffic features. Experiments, which were performed with synthetical FGN traffics, confirmed the validity of our results.It can also be a reference in estimating the autocorrelation function of other self-similar processes.
Self-Affinity, Self-Similarity and Disturbance of Soil Seed Banks by Tillage.
Dias, Luís S
2013-07-05
Soil seed banks were sampled in undisturbed soil and after soil had been disturbed by tillage (tine, harrow or plough). Seeds were sorted by size and shape, and counted. Size-number distributions were fitted by power law equations that allowed the identification of self-similarity and self-affinity. Self-affinity and thus non-random size-number distribution prevailed in undisturbed soil. Self-similarity and thus randomness of size-number distribution prevailed after tillage regardless of the intensity of disturbance imposed by cultivation. The values of fractal dimensions before and after tillage were low, suggesting that short-term, short-range factors govern size-number distribution of soil seed banks.
Hierarchical Self-Similarity in Group and Crowd Behaviors
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.
Equation for self-similar singularity of Euler 3D
Pomeau, Yves
2016-01-01
The equations for a self-similar solution of an inviscid incompressible fluid are mapped into an integral equation which hopefully can be solved by iteration. It is argued that the exponent of the similarity are ruled by Kelvin's theorem of conservation of circulation. The end result is an iteration with a nonlinear term entering in a kernel given by a 3D integral (in general 3D flow) or 2D (for swirling flows), which seems to be within reach of present day computational power. Because of the slow decay of the similarity solution at large distances the total energy is diverging and recent mathematical results excluding a solution of the self-similar solution of Euler equation do not apply.
Self-similar field dependent curves for a Heusler alloy
Energy Technology Data Exchange (ETDEWEB)
Ovichi, Maryam, E-mail: movichi@gwmail.gwu.edu [Department of Electrical and Computer Engineering, The George Washington University, Washington, DC (United States); ElBidweihy, Hatem; Ghahremani, Mohammadreza; Della Torre, Edward; Bennett, Lawrence H. [Department of Electrical and Computer Engineering, The George Washington University, Washington, DC (United States); Johnson, Francis; Zou, Min [GE Global Research, Niskayuna, NY 12309 (United States)
2014-02-15
Heusler alloys feature both regular and inverse magnetocaloric effects (MCE) near room temperature as they undergo two different transitions. A temperature scaling methodology to obtain self-similar field dependent curves for materials exhibiting one first-order transition has been previously presented. In this paper, this methodology is modified and extended to obtain self-similar curves for a Ni{sub 51}Mn{sub 32.8}In{sub 16.8} Heusler alloy undergoing two transitions near room temperature. Using this method, the collapsed curve reflects the cluster compositions in the mixed-state regions. The results of characterizing the dual transitions of Heusler alloys and establishing a new model will allow the data to be better analyzed and thus more easily predicted.
Dynamics and processing in finite self-similar networks.
DeDeo, Simon; Krakauer, David C
2012-09-07
A common feature of biological networks is the geometrical property of self-similarity. Molecular regulatory networks through to circulatory systems, nervous systems, social systems and ecological trophic networks show self-similar connectivity at multiple scales. We analyse the relationship between topology and signalling in contrasting classes of such topologies. We find that networks differ in their ability to contain or propagate signals between arbitrary nodes in a network depending on whether they possess branching or loop-like features. Networks also differ in how they respond to noise, such that one allows for greater integration at high noise, and this performance is reversed at low noise. Surprisingly, small-world topologies, with diameters logarithmic in system size, have slower dynamical time scales, and may be less integrated (more modular) than networks with longer path lengths. All of these phenomena are essentially mesoscopic, vanishing in the infinite limit but producing strong effects at sizes and time scales relevant to biology.
Discrete Self Similarity in Filled Type I Strong Explosions
Yalinewich, Almog
2014-01-01
We present new solutions to the strong explosion problem in a non power law density profi{}le. The unperturbed self similar solutions developed by Sedov, Taylor and Von Neumann describe strong Newtonian shocks propagating into a cold gas with a density profile falling off as $r^{-\\omega}$, where $\\omega\\le\\frac{7-\\gamma}{\\gamma+1}$ (filled type I solutions), and $\\gamma$ is the adiabatic index of the gas. The perturbations we consider are spherically symmetric and log periodic with respect to the radius. While the unperturbed solutions are continuously self similar, the log periodicity of the density perturbations leads to a discrete self similarity of the perturbations, i.e., the solution repeats itself up to a scaling at discrete time intervals. We discuss these solutions and verify them against numerical integrations of the time dependent hydrodynamic equations. This is an extension of a previous investigation on type II solutions and helps clarifying boundary conditions for perturbations to type I self si...
Drop impact on solid surface: Short time self-similarity
Philippi, Julien; Lagrée, Pierre-Yves; Antkowiak, Arnaud
2014-11-01
Drop impact on a solid surface is a problem with many industrial or environmental applications. Many studies focused on the last stages of this phenomenon as spreading or splashing. In this study we are interested in the early stages of drop impact on solid surface. Inspired by Wagner theory developed by water entry community we shown the self-similar structure of the velocity field and the pressure field. The latter is shown to exhibit a maximum not near the impact point, but rather at the contact line. The motion of the contact line is furthermore shown to exhibit a transition from ``tank treading'' motion to pure sweeping when the lamella appears. We performed numerical simulations with the open-cource code Gerris which are in good agreement with theoretical predictions. Interestingly the inviscid self-similar impact pressure and velocities depend on the self-similar variable r /√{ t} . This allows to construct a seamless uniform analytical solution encompassing both impact and viscous effects. We predict quantitatively observables of interest, such as the evolution of total and maximum viscous shear stresses and net total force. We finally demonstrate that the structure of the flow resembles a stagnation point flow unexpectedly involving r /√{ t} .
Self-similar community structure in a network of human interactions.
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.
Persistent cyclonic structures in self-similar turbulent flows
Mininni, P D
2009-01-01
Invariance properties of a physical system govern its behavior: energy conservation in turbulence drives a wide distribution of energy among modes, as observed in geophysics, astrophysics and engineering. In hydrodynamic turbulence, the role of helicity (which measures departures from mirror symmetry) remains unclear since it does not alter this distribution. However, the interplay of rotation and helicity leads to significant differences. Using numerical simulations we show the occurence of long-lived laminar cyclonic vortices together with turbulent vortices, reminiscent of recent tornado observations. Furthermore, the small scales are completely self-similar with no deviations from Gaussianity. This result points to the discovery of a small parameter in rotating helical turbulence.
Self-similar current sheet collapse triggered by "ideal" tearing
Tenerani, Anna; Rappazzo, Antonio Franco; Pucci, Fulvia
2015-01-01
We study the onset and evolution of fast reconnection via the "ideal: tearing mode instability within a collapsing current sheet at high Lundquist numbers ($S\\gg10^4$). As the collapse proceeds, fast reconnection is triggered well before a Sweet-Parker type configuration can form: after the linear phase of the initial instability, X-points collapse and reform nonlinearly, a hierarchy of "ideal" tearing modes repeating faster and faster on current sheets at ever smaller scales. We present a simple model describing the self-similar evolution which explains both the timescale of the disruption of the initial sheet and the consequent turbulent spectra.
Self-similar solutions of NLS-type dynamical systems
Boiti, M; Pempinelli, F; Shabat, A B
1999-01-01
We study self-similar solutions of NLS-type dynamical systems. Lagrangian approach is used to show that they can be reduced to three canonical forms, which are related by Miura transformations. The fourth Painleve equation (PIV) is central in our consideration - it connects Heisenberg model, Volterra model and Toda model to each other. The connection between the rational solutions of PIV and Coulomb gas in a parabolic potential is established. We discuss also the possibility to obtain an exact solution for optical soliton i.e. of the NLS equation with time-dependent dispersion.
ELEMENTARY DENSITY BOUNDS FOR SELF-SIMILAR SETS AND APPLICATION
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Falconer[1] used the relationship between upper convex density and upper spherical density to obtain elementary density bounds for s-sets at HS-almost all points of the sets. In this paper, following Falconer[1], we first provide a basic method to estimate the lower bounds of these two classes of set densities for the self-similar s-sets satisfying the open set condition (OSC), and then obtain elementary density bounds for such fractals at all of their points. In addition, we apply the main results to the famous classical fractals and get some new density bounds.
Self-similarity and transport in the standard map
Energy Technology Data Exchange (ETDEWEB)
Benkadda, S.; Kassibrakis, S.; White, R.B. [Princeton Univ., NJ (United States). Princeton Plasma Physics Lab.; Zaslavsky, G.M. [New York Univ., NY (United States)
1996-11-01
Anomalous transport is investigated for the Standard Map. A chain of exact self similar islands in the vicinity of the period 5 accelerator island is found for a particular value of the map parameter. The transport is found to be superdiffusive with an anomalous exponent related to the characteristic temporal and spatial scaling parameters of the island chain. The value of the transport exponent is compared to the theory. The escape time distribution and Poincare recurrence distribution are found to have power-like tails and the corresponding exponents are obtained and compared to the theory.
Self-similar infall models for cold dark matter haloes
Le Delliou, Morgan Patrick
2002-04-01
How can we understand the mechanisms for relaxation and the constitution of the density profile in CDM halo formation? Can the old Self-Similar Infall Model (SSIM) be made to contain all the elements essential for this understanding? In this work, we have explored and improved the SSIM, showing it can at once explain large N-body simulations and indirect observations of real haloes alike. With the use of a carefully-crafted simple shell code, we have followed the accretion of secondary infalls in different settings, ranging from a model for mergers to a distribution of angular momentum for the shells, through the modeling of a central black hole. We did not assume self-similar accretion from initial conditions but allowed for it to develop and used coordinates that make it evident. We found self-similar accretion to appear very prominently in CDM halo formation as an intermediate stable (quasi-equilibrium) stage of Large Scale Structure formation. Dark Matter haloes density profiles are shown to be primarily influenced by non-radial motion. The merger paradigm reveals itself through the SSIM to be a secondary but non-trivial factor in those density profiles: it drives the halo profile towards a unique attractor, but the main factor for universality is still the self-similarity. The innermost density cusp flattening observed in some dwarf and Low Surface Brightness galaxies finds a natural and simple explanation in the SSIM embedding a central black hole. Relaxation in cold collisionless collapse is clarified by the SSIM. It is a continuous process involving only the newly-accreted particles for just a few dynamical times. All memory of initial energy is not lost so relaxation is only moderately violent. A sharp cut off, or population inversion, originates in initial conditions and is maintained through relaxation. It characterises moderately violent relaxation in the system's Distribution Function. Finally, the SSIM has shown this relaxation to arise from phase
ON THE SELF-SIMILARITY OF A JET IN CROSSFLOW
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The RNG k-ε turbulence model is adopted to investigate a turbulent round jet issuing into crossflow, with the Reynolds number at jet exit of Re=6000 and jet-to crossflow velocity ratio of r=8. With the CFD code, FLUENT, the relations of dimensional analysis are successfully reproduced and the calculated coefficients agree well with the experimental measurements of Wong (1991) and Chu (1996). The investigations are then taken on the velocity, stream function and vorticity at the far field of the jet. It shows that at least within the covered range herein, the jet at the far field is self-similar.
Self-Similar Hot Accretion Flow onto a Neutron Star
Medvedev, M V; Medvedev, Mikhail V.; Narayan, Ramesh
2000-01-01
We consider hot, two-temperature, viscous accretion onto a rotating, unmagnetized neutron star. We assume Coulomb coupling betweenthe protons and electrons, and free-free cooling from the electrons. We show that the accretion flow has an extended settling region which can be described by means of two analytical self-similar solutions: a two-temperature solution which is valid in an inner zone, $r10^{2.5}$. In both zones the density varies as $\\rho\\propto r^{-2}$ and the angular velocity as $\\Omega\\propto r^{-3/2}$. We solve the flow equations numerically and confirm that the analytical solutions are accurate. The self-similar settling solution differs from the advection-dominated accretion flow discussed in the context of black hole accretion. The settling flow radiates the energy dissipated by viscosity; so it is not advection-dominated. Except for the radial velocity, all other gas properties - density, angular velocity, temperature, luminosity, angular momentum flux - are independent of the mass accretion ...
Self-similarity and scaling theory of complex networks
Song, Chaoming
Scale-free networks have been studied extensively due to their relevance to many real systems as diverse as the World Wide Web (WWW), the Internet, biological and social networks. We present a novel approach to the analysis of scale-free networks, revealing that their structure is self-similar. This result is achieved by the application of a renormalization procedure which coarse-grains the system into boxes containing nodes within a given "size". Concurrently, we identify a power-law relation between the number of boxes needed to cover the network and the size of the box defining a self-similar exponent, which classifies fractal and non-fractal networks. By using the concept of renormalization as a mechanism for the growth of fractal and non-fractal modular networks, we show that the key principle that gives rise to the fractal architecture of networks is a strong effective "repulsion" between the most connected nodes (hubs) on all length scales, rendering them very dispersed. We show that a robust network comprised of functional modules, such as a cellular network, necessitates a fractal topology, suggestive of a evolutionary drive for their existence. These fundamental properties help to understand the emergence of the scale-free property in complex networks.
Accelerated expansion in a stochastic self-similar fractal universe
Energy Technology Data Exchange (ETDEWEB)
Santini, Eduardo Sergio [Centro Brasileiro de Pesquisas Fisicas-MCT, Coordenacao de Cosmologia, Relatividade e Astrofisica: ICRA-BR, Rua Dr. Xavier Sigaud 150, Urca 22290-180, Rio de Janeiro, RJ (Brazil) and Comissao Nacional de Energia Nuclear-MCT, Rua General Severiano 90, Botafogo 22290-901, Rio de Janeiro, RJ (Brazil)]. E-mail: santini@cbpf.br; Lemarchand, Guillermo Andres [Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, C.C. 8-Sucursal 25, C1425FFJ Buenos Aires (Argentina)]. E-mail: lemar@correo.uba.ar
2006-05-15
In a recent paper, a cosmological model based on El Naschie E infinity Cantorian space-time was presented [Iovane G. Varying G, accelerating universe, and other relevant consequences of a stochastic self-similar and fractal universe. Chaos, Solitons and Fractals 2004;20:657-67]. In that work, it was claimed that the present accelerated expansion of the universe can be obtained as the effect of a scaling law on Newtonian cosmology with a certain time-dependent gravitational constant (G). In the present work we show that such a cosmological model actually describes a decelerated universe. Then starting from the scenario presented in that paper, we realize a complementary approach based on an extended Friedmann model. In fact, we apply the same scaling law and a time-dependent gravitational constant, that follows from the observational constraints, to relativistic cosmology, i.e. a (extended) Friedmann's model. We are able to show that for a matter-dominated flat universe, with the scaling law and a varying G, an accelerated expansion emerges in such a way that the function luminosity distance vs redshift can be made close to the corresponding function that comes from the usual Friedmann's model supplemented with a cosmological constant, of value {omega} {sub {lambda}} {approx_equal} 0.7. Then the measurements of high redshift supernovae, could be interpreted as a consequence of the fractal self-similarity of the G varying relativistic universe.
A self-similar hierarchy of the Korean stock market
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.
On self-similar rupture of thin-film equations
Dallaston, Michael; Tseluiko, Dmitri; Zheng, Zhong; Fontelos, Marco; Kalliadasis, Serafim
2016-11-01
Many interfacial fluid dynamical settings consist of a thin film in the presence of two physical mechanisms, one stabilizing, typically surface tension, and the other one destabilizing. Examples include the Marangoni instability of a film heated from below, Rayleigh-Taylor instability of a film on a cylinder, and film dewetting due to intermolecular forces. Lubrication-type models of these phenomena lead to very similar equations for the evolution of the film thickness, differing only in the exponent of the coefficient function of the destabilizing term. However, the behavior of solutions can vary, depending on the value of this exponent. Here we report the results of analysis based on self-similarity, elements from dynamical systems theory and fully time-dependent computations. We find that branches of self-similar rupture solutions merge at critical values of the exponent, and, surprisingly, there are no stable solutions beyond the first value at which merging occurs. In this regime, time-dependent computations indicate the existence of a cascade of instabilities of increasingly short wavelengths. This work was supported by the EPSRC under Grant No. EP/K008595/1. The work of DT was partly supported by the EPSRC under Grant No. EP/K041134/1.
Self-similar ultra-relativistic jetted blast wave
Keshet, Uri
2015-01-01
Following a suggestion that a directed relativistic explosion may have a universal intermediate asymptotic, we derive a self-similar solution for an ultra-relativistic jetted blast wave. The solution involves three distinct regions: an approximately paraboloid head where the Lorentz factor $\\gamma$ exceeds $\\sim1/2$ of its maximal, nose value; a geometrically self-similar, expanding envelope slightly narrower than a paraboloid; and an axial core in which the radial flow $U$ converges inward towards the axis. Most ($\\sim 80\\%$) of the energy lies well beyond the head. Here, a radial cross section shows a maximal $\\gamma$ (separating the core and the envelope), a sign reversal in $U$, and a minimal $\\gamma$, at respectively $\\sim 1/6$, $\\sim1/4$, and $\\sim3/4$ 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 attracto...
Energy Technology Data Exchange (ETDEWEB)
Iovane, G. E-mail: iovane@diima.unisa.it
2005-02-01
A waveguiding effect is considered with respect to the large scale structure of the Universe, where the structures formation appears as if it were a classically self-similar random process at all astrophysical scales. The result is that it seems we live in an El Naschie's {epsilon}{sup (infinity)} Cantorian space-time, where gravitational lensing and waveguiding effects can explain the appearing Universe. In particular, we consider filamentary and planar large scale structures as possible refraction channels for electromagnetic radiation coming from cosmological structures. From this vision the Universe appears like a large self-similar adaptive mirrors set. Consequently, an infinite Universe is just an optical illusion that is produced by mirroring effects connected with the large scale structure of a finite and not so large Universe. Thanks to the presented analytical model supported by a numerical simulation, it is possible to explain the quasar luminosity distribution and the presence of 'twin' or 'brother' objects. More generally, the infinity and the abundance of astrophysical objects could be just a mirroring effect due to the peculiar self-similarity of the Universe.
Self-similar Champagne Flows in H II Regions
Shu, Frank H.; Lizano, Susana; Galli, Daniele; Cantó, Jorge; Laughlin, Gregory
2002-12-01
We consider the idealized expansion of an initially self-gravitating, static, singular, isothermal cloud core. For t>=0, the gas is ionized and heated to a higher uniform temperature by the formation of a luminous but massless star in its center. The approximation that the mass and gravity of the central star are negligible for the subsequent motion of the H II region holds for distances r much greater than ~100 AU and for the massive cloud cores that give rise to high-mass stars. If the initial ionization and heating are approximated to occur instantaneously at t=0, then the subsequent flow (for r>>100 AU) caused by the resulting imbalance between self-gravity and thermal pressure is self-similar. Because of the steep density profile (ρ~r-2), pressure gradients produce a shock front that travels into the cloud, accelerating the gas to supersonic velocities in what has been called the ``champagne phase.'' The expansion of the inner region at t>0 is connected to the outer envelope of the now ionized cloud core through this shock, whose strength depends on the temperature of the H II gas. In particular, we find a modified Larson-Penston (L-P) type of solution as part of the linear sequence of self-similar champagne outflows. The modification involves the proper insertion of a shock and produces the right behavior at infinity (v-->0) for an outflow of finite duration, reconciling the long-standing conflict on the correct (inflow or outflow) interpretation for the original L-P solution. For realistic heating due to a massive young central star that ionizes and heats the gas to ~104 K, we show that even the self-gravity of the ionized gas of the massive molecular cloud core can be neglected. We then study the self-similar solutions of the expansion of H II regions embedded in molecular clouds characterized by more general power-law density distributions: ρ~r-n with 3/23. We show that this happens because the model includes an origin where the pressure driving the
Self-similar spherical metrics with tangential pressure
Gair, J R
2002-01-01
A family of spherically symmetric spacetimes is discussed, which have anisotropic pressure and possess a homothetic Killing vector. The spacetimes are composed of dust with a tangential pressure provided by angular momentum of the dust particles. The solution is given implicitly by an elliptic integral and depends on four arbitrary functions. These represent the initial configurations of angular momentum, mass, energy and position of the shells. The solution is derived by imposing self-similarity in the coordinates R, the shell label, and tau, the proper time experienced by the dust. Conditions for evolution without shell crossing and a description of singularity formation are given and types of solution discussed. General properties of the solutions are illustrated by reference to a particular case, which represents a universe that exists for an infinite time, but in which every shell expands and recollapses in a finite time.
Self-similarity of proton spin and z-scaling
Tokarev, M
2015-01-01
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 A_{LL} of jet and pi0-meson production and the coefficient of polarization transfer D_{LL} measured in proton-proton collisions at sqrt s = 200 GeV at RHIC are analyzed in the framework of z-scaling. The spin-dependent fractal dimension of proton is estimated.
Self-similar breakup of a retracting liquid cone
Brasz, Frederik; Berny, Alexis; Bird, James
2016-11-01
When a fluid filament breaks up due to the Rayleigh-Plateau instability, a thin thread typically pinches off from a nearly spherical drop. Depending on its shape, this thread can break up again while it retracts to form satellite and even sub-satellite droplets. Past studies have modeled the shape of the retracting filament as a cone, yet the dynamics of nearly inviscid retracting cones are known to be stable, preventing any further filament breakup. Here we show that under certain finite perturbations, retracting conical liquid filaments can become unstable and break up into a cascade of self-similar droplets. Combining numerical simulations and experiments, we explore whether or not a conical filament is likely to break up based on cone angle and initial perturbation. We expect our results to be relevant in applications in which satellite bubbles or droplets are important, such as in modeling the flux of aerosols from the ocean to the atmosphere.
Vacuum self similar anisotropic cosmologies in $F(R)-$gravity
Apostolopoulos, Pantelis S
2016-01-01
The implications from the existence of a proper Homothetic Vector Field (HVF) on the dynamics of vacuum anisotropic models in $F(R)$ gravitational theory are studied. The fact that \\emph{every} Spatially Homogeneous vacuum model is equivalent, formally, with a \\textquotedblleft flux\\textquotedblright -free anisotropic fluid model in standard gravity and the induced power-law form of the functional $F(R)$ due to self-similarity enable us to close the system of equations. We found some new exact anisotropic solutions that arise as fixed points in the associated dynamical system. The non-existence of Kasner-like (Bianchi type I) solutions in proper $F(R)-$gravity (i.e. $R\
Global solution curves for self-similar equations
Korman, Philip
2014-10-01
We consider positive solutions of a semilinear Dirichlet problem Δu+λf(u)=0, for |x|problem. This allows us to derive results on the multiplicity of solutions, and on their Morse indices. In particular, we easily recover the classical results of D.D. Joseph and T.S. Lundgren [6] on the Gelfand problem. Surprisingly, the situation turns out to be different for the generalized Gelfand problem, where infinitely many turns are possible for any space dimension n≥3. We also derive detailed results for the equation modeling electrostatic micro-electromechanical systems (MEMS), in particular we easily recover the main result of Z. Guo and J. Wei [4], and we show that the Morse index of the solutions increases by one at each turn. We also consider the self-similar Henon's equation.
Directory of Open Access Journals (Sweden)
P. Mukherjee
2014-01-01
Full Text Available In a recent communication we reported the self-similarity in radial Walsh filters. The set of radial Walsh filters have been classified into distinct self-similar groups, where members of each group possess self-similar structures or phase sequences. It has been observed that, the axial intensity distributions in the farfield diffraction pattern of these self-similar radial Walsh filters are also self-similar. In this paper we report the self-similarity in the intensity distributions on a transverse plane in the farfield diffraction patterns of the self-similar radial Walsh filters.
Self-similar singular solution of doubly singular parabolic equation with gradient absorption term
Directory of Open Access Journals (Sweden)
Shi Peihu
2006-01-01
Full Text Available We deal with the self-similar singular solution of doubly singular parabolic equation with a gradient absorption term for , and in . By shooting and phase plane methods, we prove that when there exists self-similar singular solution, while there is no any self-similar singular solution. In case of existence, the self-similar singular solution is the self-similar very singular solutions which have compact support. Moreover, the interface relation is obtained.
Behavior near the extinction time in self-similar fragmentations I: The stable case
Goldschmidt, Christina; Haas, Bénédicte
2010-01-01
The stable fragmentation with index of self-similarity α∈[−1/2, 0) is derived by looking at the masses of the subtrees formed by discarding the parts of a (1+α)−1–stable continuum random tree below height t, for t≥0. We give a detailed limiting description of the distribution of such a fragmentation, (F(t), t≥0), as it approaches its time of extinction, ζ. In particular, we show that t1/αF((ζ−t)+) converges in distribution as t→0 to a non-trivial limit. In order to prove this, we go further a...
Locally self-similar phase diagram of the disordered Potts model on the hierarchical lattice.
Anglès d'Auriac, J-Ch; Iglói, Ferenc
2013-02-01
We study the critical behavior of the random q-state Potts model in the large-q limit on the diamond hierarchical lattice with an effective dimensionality d(eff)>2. By varying the temperature and the strength of the frustration the system has a phase transition line between the paramagnetic and the ferromagnetic phases which is controlled by four different fixed points. According to our renormalization group study the phase boundary in the vicinity of the multicritical point is self-similar; it is well represented by a logarithmic spiral. We expect an infinite number of reentrances in the thermodynamic limit; consequently one cannot define standard thermodynamic phases in this region.
On use of the alpha stable self-similar stochastic process to model aggregated VBR video traffic
Institute of Scientific and Technical Information of China (English)
Huang Tianyun
2006-01-01
The alpha stable self-similar stochastic process has been proved an effective model for high variable data traffic. A deep insight into some special issues and considerations on use of the process to model aggregated VBR video traffic is made. Different methods to estimate stability parameter α and self-similar parameter H are compared. Processes to generate the linear fractional stable noise (LFSN) and the alpha stable random variables are provided. Model construction and the quantitative comparisons with fractional Brown motion (FBM) and real traffic are also examined. Open problems and future directions are also given with thoughtful discussions.
Self-Similar Hot Accretion Flow onto a Neutron Star
Medvedev, M V
2001-01-01
We present analytical and numerical solutions which describe a hot, viscous, two-temperature accretion flow onto a neutron star or any other compact star with a surface. We assume Coulomb coupling between the protons and electrons, and free-free cooling from the electrons. Outside a thin boundary layer, where the accretion flow meets the star, we show that there is an extended settling region which is well-described by two self-similar solutions: (1) a two-temperature solution which is valid in an inner zone $r\\le10^{2.5}$ ($r$ is in Schwarzchild units), and (2) a one-temperature solution at larger radii. In both zones, $\\rho\\propto r^{-2}, \\Omega\\propto r^{-3/2}, v\\propto r^0,\\ T_p\\propto r^{-1}$; in the two-temperature zone, $T_e\\propto r^{-1/2}$. The luminosity of the settling zone arises from the rotational energy of the star as the star is braked by viscosity; hence the luminosity is independent of $\\dot M$. The settling solution is convectively and viscously stable and is unlikely to have strong winds o...
A self-similar solution for thermal disc winds
Clarke, C J
2016-01-01
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 densit...
Root Growth Optimizer with Self-Similar Propagation
Directory of Open Access Journals (Sweden)
Xiaoxian He
2015-01-01
Full Text Available Most nature-inspired algorithms simulate intelligent behaviors of animals and insects that can move spontaneously and independently. The survival wisdom of plants, as another species of biology, has been neglected to some extent even though they have evolved for a longer period of time. This paper presents a new plant-inspired algorithm which is called root growth optimizer (RGO. RGO simulates the iterative growth behaviors of plant roots to optimize continuous space search. In growing process, main roots and lateral roots, classified by fitness values, implement different strategies. Main roots carry out exploitation tasks by self-similar propagation in relatively nutrient-rich areas, while lateral roots explore other places to seek for better chance. Inhibition mechanism of plant hormones is applied to main roots in case of explosive propagation in some local optimal areas. Once resources in a location are exhausted, roots would shrink away from infertile conditions to preserve their activity. In order to validate optimization effect of the algorithm, twelve benchmark functions, including eight classic functions and four CEC2005 test functions, are tested in the experiments. We compared RGO with other existing evolutionary algorithms including artificial bee colony, particle swarm optimizer, and differential evolution algorithm. The experimental results show that RGO outperforms other algorithms on most benchmark functions.
Convergence to Self-Similar Regimes in Thin Polymer Films
Benzaquen, Michael; Salez, Thomas; Raphaël, Elie; Elie Raphaël Team; Kari Dalnoki-Veress Team
2013-03-01
The surface of a thin liquid film with nonconstant curvature is unstable, as the Laplace pressure drives a flow mediated by viscosity. Recent experiments and theory applied to stepped polymer films have shown excellent agreement and provide a technique for the study of polymer confinement, the glass transition, and slip at the fluid substrate interface to name a few. The thin film equation governs the evolution of the free surface profile in the lubrication approximation. Despite many efforts, this equation remains only partially solved. We present an analytical and numerical study of the thin film equation. Linearising this equation enables us to derive the Green's function of the problem and therefore obtain a complete set of solutions. We show that the solutions of the problem with equilibrium boundary conditions uniformly converge in time towards a first kind self-similar universal attractor. A numerical study enables us to extend our results to the nonlinear thin film equation. Laboratoire Physico-Chimie Théorique, UMR CNRS 7083 Gulliver. ESPCI, 10 rue Vauquelin, 75005, Paris, France.
Self-Similar Shocks and Winds in Galaxy Clusters
Lou, Yu-Qing; Jin, Chi-Chuan
2008-01-01
A theoretical model framework of spherical symmetry is presented for a composite astrophysical system of two polytropic fluids coupled together by gravity to explore large-scale shocks and flow dynamics in clusters of galaxies or in globular clusters. The existence of such large-scale shocks in clusters of galaxies as inferred by high-resolution X-ray and radio imaging observations implies large-scale systematic flows that are beyond usual static models for clusters of galaxies. Here, we explore self-similar two-fluid flow solutions with shocks for a hot polytropic gas flow in a cluster of galaxies in the presence of a massive dark matter (DM) flow after the initiation of a gravitational core collapse or a central AGN activity or a large-scale merging process. In particular, the possibility of DM shocks or sharp jumps of mass density and of velocity dispersion in dark matter halo is discussed and such DM shocks might be detectable through gravitational lensing effects. To examine various plausible scenarios f...
Mukherjee, P.; L. N. Hazra
2014-01-01
In a recent communication we reported the self-similarity in radial Walsh filters. The set of radial Walsh filters have been classified into distinct self-similar groups, where members of each group possess self-similar structures or phase sequences. It has been observed that, the axial intensity distributions in the farfield diffraction pattern of these self-similar radial Walsh filters are also self-similar. In this paper we report the self-similarity in the intensity distributions on a tra...
Geographical networks stochastically constructed by a self-similar tiling according to population
Hayashi, Yukio
2010-01-01
In real communication and transportation networks, the geographical positions of nodes are very important for the efficiency and the tolerance of connectivity. Considering spatially inhomogeneous positions of nodes according to a population, we introduce a multi-scale quartered (MSQ) network that is stochastically constructed by recursive subdivision of polygonal faces as a self-similar tiling. It has several advantages: the robustness of connectivity, the bounded short path lengths, and the shortest distance routing algorithm in a distributive manner. Furthermore, we show that the MSQ network is more efficient with shorter link lengths and more suitable with lower load for avoiding traffic congestion than other geographical networks which have various topologies ranging from river to scale-free networks. These results will be useful for providing an insight into the future design of ad hoc network infrastructures.
Geographical networks stochastically constructed by a self-similar tiling according to population
Hayashi, Yukio; Ono, Yasumasa
2010-07-01
In real communication and transportation networks, the geographical positions of nodes are very important for the efficiency and the tolerance of connectivity. Considering spatially inhomogeneous positions of nodes according to a population, we introduce a multiscale quartered (MSQ) network that is stochastically constructed by recursive subdivision of polygonal faces as a self-similar tiling. It has several advantages: the robustness of connectivity, the bounded short path lengths, and the shortest distance routing algorithm in a distributive manner. Furthermore, we show that the MSQ network is more efficient with shorter link lengths and more suitable with lower load for avoiding traffic congestion than other geographical networks which have various topologies ranging from river to scale-free networks. These results will be useful for providing an insight into the future design of ad hoc network infrastructures.
A self-similar solution for thermal disc winds
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.
Log-periodic oscillations for diffusion on self-similar finitely ramified structures
Padilla, L.; Mártin, H. O.; Iguain, J. L.
2010-07-01
Under certain circumstances, the time behavior of a random walk is modulated by logarithmic-periodic oscillations. Using heuristic arguments, we give a simple explanation of the origin of this modulation for diffusion on a substrate with two properties: self-similarity and finite ramification order. On these media, the time dependence of the mean-square displacement shows log-periodic modulations around a leading power law, which can be understood on the basis of a hierarchical set of diffusion constants. Both the random walk exponent and the period of oscillations are analytically obtained for a pair of examples, one is fractal and the other is nonfractal, and confirmed by Monte Carlo simulations. The last example shows that the anomalous diffusion can arise from substrates without holes of all sizes.
Measuring the self-similarity exponent in Lévy stable processes of financial time series
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
Riccati parameterized self-similar waves in tapered graded-index waveguides
Goyal, Amit; Gupta, Rama; Loomba, Shally; Kumar, C. N.
2012-10-01
We present a large family of self-similar waves by tailoring the tapering function, through Riccati parameter, in a tapered graded-index nonlinear waveguide amplifier. We show the existence of bright similaritons, self-similar Akhmediev breathers and self-similar rogue waves for generalized nonlinear Schrödinger equation with constant dispersion and nonlinearity, and a distributed gain. We illustrate the procedure to amplify the intensity of self-similar waves using isospectral Hamiltonian approach. This approach provides a handle to find analytically a wide class of tapering function and thus enabling one to control the self-similar wave structure and dynamical behavior.
SELF-SIMILAR SINGULAR SOLUTION OF A P-LAPLACIAN EVOLUTION EQUATION WITH GRADIENT ABSORPTION TERM
Institute of Scientific and Technical Information of China (English)
Shi Peihu
2004-01-01
In this paper we deal with the self-similar singular solution of the p-Laplacian evolution equation ut = div(|△u|p-2△u) - |△u|q for p ＞ 2 and q ＞ 1 in Rn × (0,∞). We prove that when p ＞ q + n/(n + 1) there exist self-similar singular solutions, while p (≤) q+n/(n+ 1) there is no any self-similar singular solution. In case of existence, the self-similar singular solutions are the self-similar very singular solutions,which have compact support. Moreover, the interface relation is obtained.
MERGING AND SPLITTING SECOND-ORDER SELF-SIMILAR PROCESSES (TRAFFICS)
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Recent traffic measurements in corporate LANs, Variable-Bit-Rate (VBR) video sources, ISDN control channels, and other communication systems, have indicated traffic behavior of self-similar nature, which has implications for design, control and analysis of high-speed networks. Merging and splitting are two basic networking operations. This paper gave the necessary and sufficient conditions for that merging of second-order self-similar traffic streams also results in a second-order self-similar stream. It shows that splitting traffic streams of the second-order self-similar stream are still self-similar streams by the independent splitting operation.
Pulse Evolution Characteristics in Self-Similar Mode-locked Fibre Laser
Institute of Scientific and Technical Information of China (English)
TU Cheng-Hou; LI Zhen; LEI Ting; LI Yong-Nan; GUO Wen-Gang; WEI Dai; ZHU Hui; ZHANG Shuang-Gen; LU Fu-Yun
2007-01-01
A self-similar mode locked fibre laser is studied based on a numerical model. By introducing a dimensionless factor k to characterize the pulse shape, the self-similar pulse evolution, formation and the temporal and spectral shape changes due to the elements in the cavity are investigated throughout the iaser cavity. The results show that in the self-similar mode locked fibre laser, self-similar pulse is first formed in the single-mode fibre, which is then amplified in the gain fibre. Gain bandwidth has a small influence on pulse shape, so high energy self-similar pulse can be obtained after amplification. Because net cavity dispersion directly influences the pulse width as well as peak power after compression by a pair of gratings, which can determine the pulse self-similar evolution, it is very important to control the net cavity dispersion to a certain range to obtain self-similar pulses.
Self-similar growth of an alluvial fan fed with bimodal sediment
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.
The Phase Transitions of Self-similar Small-world Networks
Brunson, Trent; Boettcher, Stefan
2010-03-01
A novel set of self-similar networks called Hanoi networksfootnotetextS. Boettcher, B Goncalves, Europhysics Letters 84, 30002 (2008). (HN) have been developed to study the critical phenomena of small-world networks using the renormalization group (RG). Physically, HNs contain a more desirable geometry than random small-world networks. Their structure consists of a one-dimensional backbone with a hierarchy of long-range bonds, which allows the flexibility of studying planar and non-planar networks with either a regular or exponential degree distribution. The RG and Ising model simulation results for HNs reveal unique phase transitions and non-universal behavior, which can be attributed to their hierarchical structure.footnotetextSee also http://www.physics.emory.edu/faculty/boettcher/.
Co-location and Self-Similar Topologies of Urban Infrastructure Networks
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.
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.
Institute of Scientific and Technical Information of China (English)
FENG Jie; XU WenCheng; LI ShuXian; LIU SongHao
2008-01-01
Based on the constant coefficients of Ginzburg-Landau equation that considers the influence of the doped fiber retarded time on the evolution of self-similar pulse, the parabolic asymptotic self-similar solutions were obtained by the symmetry reduc-tion algorithm.The parabolic asymptotic amplitude function, phase function, strict linear chirp function and the effective temporal pulse width of self-similar pulse are given in this paper.And these theoretical results are consistent with the numerical simulations.
THERMODYNAMIQUE DES ENSEMBLES DE CANTOR AUTOSIMILAIRES（THERMODYNAMICS OF SELF-SIMILAR CANTOR SETS）
Institute of Scientific and Technical Information of China (English)
G.MICHON; J.PEYRIERE
1994-01-01
A class of metric,compact,and totally disconnected spaces,called self-similar Cantor sets is introduced.A self-similar structure is defined to be a graph with weighted edges. The introduction of ultrametrics and quasi-isometries gives versatility to this construction. Thermodynamical functions as free energy and entropy are associated with self-similar structures. Multifractal analysis, based on a “Large Deviations” inequality and Gibbs measures, leads to a fairly general Hausdorff dimension theorem.
Chen, Shihua; Yi, Lin; Guo, Dong-Sheng; Lu, Peixiang
2005-07-01
Three novel types of self-similar solutions, termed parabolic, Hermite-Gaussian, and hybrid pulses, of the generalized nonlinear Schrödinger equation with varying dispersion, nonlinearity, and gain or absorption are obtained. The properties of the self-similar evolutions in various nonlinear media are confirmed by numerical simulations. Despite the diversity of their formations, these self-similar pulses exhibit many universal features which can facilitate significantly the achievement of well-defined linearly chirped output pulses from an optical fiber, an amplifier, or an absorption medium, under certain parametric conditions. The other intrinsic characteristics of each type of self-similar pulses are also discussed.
Measurement of Characteristic Self-Similarity and Self-Diversity for Complex Mechanical Systems
Institute of Scientific and Technical Information of China (English)
ZHOU Meili; LAI Jiangfeng
2006-01-01
Based on similarity science and complex system theory, a new concept of characteristic self-diversity and corresponding relations between self-similarity and self-diversity for complex mechanical systems are presented in this paper. Methods of system self-similarity and self-diversity measure between main system and sub-system are studied. Numerical calculations show that the characteristic self-similarity and self-diversity measure method is validity. A new theory and method of self-similarity and self-diversity measure for complexity mechanical system is presented.
Random River Fluctuations Shape the Root Profile of Riparian Plants
Perona, P.; Tron, S.; Gorla, L.; Schwarz, M.; Laio, F.; Ridolfi, L.
2015-12-01
Plant roots are recognized to play a key role in the riparian ecosystems: they contribute to the plant as well as to the streambank and bedforms stability, help to enhance the water quality of the river, and sustain the belowground biodiversity. The complexity of the root-system architecture recalls their remarkable ability to respond to environmental conditions, notably including soil heterogeneity, resource availability, and climate. In fluvial environments where nutrient availability is not a limiting factor for plant to grow, the root growth of phreatophytic plants is strongly influenced by water and oxygen availability in the soil. In this work, we demonstrate that the randomness of water table fluctuations, determined by streamflow stochastic variability, is likely to be the main driver for the root development strategy of riparian plants. A collection of root measurements from field and outdoor controlled experiments is used to demonstrate that the vertical root density distribution can be described by a simple analytical expression, whose parameters are linked to properties of soil, plant and water table fluctuations. This physically-based expression is able to predict riparian plant roots adaptability to different hydrological and pedologic scenarios in riverine environments. Hence, this model has great potential towards the comprehension of the effects of future climate and environmental changing conditions on plant adaptation and river ecomorphodynamic processes. Finally, we present an open access graphical user interface that we developed in order to estimate the vertical root distribution in fluvial environments and to make the model easily available to a wider scientific and professional audience.
A NEGATIVE ANSWER TO A CONJECTURE ON SELF-SIMILAR SETS WITH OPEN SET CONDITION
Institute of Scientific and Technical Information of China (English)
Jiandong Yin
2009-01-01
Zhou and Feng posed a conjecture on self-similar set in 2004. In this paper, a self-similar set is constructed which has a best covering but its natural covering is not a best one. Thus, we indeed give a negative answer to the conjecture.
MULTIRESOLUTION ANALYSIS, SELF-SIMILAR TILINGS AND HAAR WAVELETS ON THE HEISENBERG GROUP
Institute of Scientific and Technical Information of China (English)
Liu Heping; Liu Yu; Wang Haihui
2009-01-01
In this article, the properties of multiresolution analysis and self-similar tilings on the Heisenberg group are studied. Moreover, we establish a theory to construct an orthonormal Haar wavelet base in L~2(H~d) by using self-similar tilings for the acceptable dilations on the Heisenberg group.
Self-similar Solutions for a Transport Equation with Non-local Flux
Institute of Scientific and Technical Information of China (English)
Angel CASTRO; Diego C(O)RDOBA
2009-01-01
The authors construct self-similar solutions for an N-dimensional transport equation,where the velocity is given by the Riezs transform.These solutions imply nonuniqueness of weak solution.In addition,self-similar solution for a one-dimensional conservative equation involving the Hilbert transform is obtained.
Self-similar singular solution of doubly singular parabolic equation with gradient absorption term
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available We deal with the self-similar singular solution of doubly singular parabolic equation with a gradient absorption term u t = div ( | ∇ u m | p − 2 ∇ u m − | ∇ u | q for 1$"> p > 1 , 1$"> m ( p − 1 > 1 and 1$"> q > 1 in ℝ n × ( 0 , ∞ . By shooting and phase plane methods, we prove that when {1+n}/({1+mn}q+{mn}/({mn+1}$"> p > 1 + n / ( 1 + m n q + m n / ( m n + 1 there exists self-similar singular solution, while p ≤ n + 1 / ( 1 + m n q + m n / ( m n + 1 there is no any self-similar singular solution. In case of existence, the self-similar singular solution is the self-similar very singular solutions which have compact support. Moreover, the interface relation is obtained.
Self-similar singular solution of fast diffusion equation with gradient absorption terms
Institute of Scientific and Technical Information of China (English)
SHI Pei-hu; WANG Ming-xin
2007-01-01
The self-similar singular solution of the fast diffusion equation with nonlinear gradient absorption terms are studied. By a self-similar transformation, the self-similar solutions satisfy a boundary value problem of nonlinear ordinary differential equation (ODE). Using the shooting arguments, the existence and uniqueness of the solution to the initial data problem of the nonlinear ODE are investigated, and the solutions are classified by the region of the initial data. The necessary and sufficient condition for the existence and uniqueness of self-similar very singular solutions is obtained by investigation of the classification of the solutions. In case of existence, the self-similar singular solution is very singular solution.
Higher-order effects on self-similar parabolic pulse in the microstructured fibre amplifier
Institute of Scientific and Technical Information of China (English)
Liu Wei-Ci; Xu Wen-Cheng; Feng Jie; Chen Wei-Cheng; Li Shu-Xian; Lin Song-Hao
2008-01-01
By considering higher-order effects, the properties of self-similar parabolic pulses propagating in the microstructured fibre amplifier with a normal group-velocity dispersion have been investigated. The numerical results indicate that the higher-order effects can badly distort self-similar parabolic pulse shape and optical spectrum, and at the same time the peak shift and oscillation appear, while the pulse still reveals highly linear chirp but grows into asymmetry. The influence of different higher-order effects on self-similar parabolic pulse propagation has been analysed. It shows thatthe self-steepening plays a more important role. We can manipulate the geometrical parameters of the microstructured fibre amplifier to gain a suitable dispersion and nonlinearity coefficient which will keep high-quality self-similar parabolic pulse propagation. These results are significant for the further study of self-similar parabolic pulse propagation.
Meandering instability of air flow in a granular bed: self-similarity and fluid-solid duality
Yoshimura, Yuki; Okumura, Ko
2016-01-01
Meandering instability is familiar to everyone through river meandering or small rivulets of rain flowing down a windshield. However, its physical understanding is still premature, although it could inspire researchers in various fields, such as nonlinear science, fluid mechanics and geophysics, to resolve their long-standing problems. Here, we perform a small-scale experiment in which air flow is created in a thin granular bed to successfully find a meandering regime, together with other remarkable fluidized regimes, such as a turbulent regime. We discover that phase diagrams of the flow regimes for different types of grains can be universally presented as functions of the flow rate and the granular-bed thickness when the two quantities are properly renormalized. We further reveal that the meandering shapes are self-similar as was shown for meandering rivers. The experimental findings are explained by theory, with elucidating the physics. The theory is based on force balance, a minimum-dissipation principle,...
Gurbatov, S N
1999-01-01
The present work is devoted to the evolution of random solutions of the unforced Burgers and KPZ equations in d-dimensions in the limit of vanishing viscosity. We consider a cellular model and as initial condition assign a value for the velocity potential chosen independently within each cell. We show that the asymptotic behavior of the turbulence at large times is determined by the tail of the initial potential probability distribution function. Three classes of initial distribution leading to self-similar evolution are identified: (a) distributions with a power-law tail, (b) compactly supported potential, (c) stretched exponential tails. In class (c) we find that the mean potential (mean height of the surface) increases logarithmically with time and the 'turbulence energy' E(t) (mean square gradient of the surface) decays as 1/t times a logarithmic correction. In classes (a) and (b) we find that the changes in the mean potential and energy have a power-law time dependence. In class (c) the roughness of the ...
Self-similar characteristics of single nucleotide polymorphisms in the rice genome
Lee, Chang-Yong
2016-11-01
With single nucleotide polymorphism (SNP) data from the 3,000 rice genome project, we investigate the mutational characteristics of the rice genome from the perspective of statistical physics. From the frequency distributions of the space between adjacent SNPs, we present evidence that SNPs are not spaced randomly, but clustered across the genome. The clustering property is related to a long-range correlation in SNP locations, suggesting that a mutation occurring in a locus may affect other mutations far away along the sequence in a chromosome. In addition, the reliability of the existence of the long-range correlation is supported by the agreement between the results of two independent analysis methods. The highly-skewed and long-tailed distribution of SNP spaces is further characterized by a multi-fractal, showing that SNP spaces possess a rich structure of a statistical self-similarity. These results can be used for an optimal design of a microarray assay and a primer, as well as for genotyping quality control.
An Intrusion Alarming System Based on Self- Similarity of Network Traffic
Institute of Scientific and Technical Information of China (English)
YU Fei; ZHU Miao-liang; CHEN Yu-feng; LI Ren-fa; XU Cheng
2005-01-01
Intrusion detection system can make effective alarm for illegality of network users, which is absolutely necessarily and important to build security environment of communication base service. According to the principle that the number of network traffic can affect the degree of self-similar traffic, the paper investigates the variety of self-similarity resulted from unconventional network traffic. A network traffic model based on normal behaviors of user is proposed and the Hurst parameter of this model can be calculated. By comparing the Hurst parameter of normal traffic and the self-similar parameter, we can judge whether the network is normal or not and alarm in time.
Self-similar solutions of quasilinear parabolic equations with nonlinear gradient terms
Institute of Scientific and Technical Information of China (English)
SHI Peihu; WANG Mingxin
2004-01-01
This paper is devoted to study the classification of self-similar solutions to the m ≥ 1,p,q ＞ 0 and p + q ＞ m. For m = 1, it is shown that the very singular self-similar solution exists if and only if nq + (n + 1)p ＜ n + 2, and in case of existence, such solution is unique. For m ＞ 1, it is shown that very singular self-similar solutions exist if and only if 1 ＜ m ＜ 2 and nq + (n + 1)p ＜ 2 + mn, and such solutions have compact support if they exist. Moreover, the interface relation is obtained.
Numerical Solution of Lock-Release Gravity Current with Viscous Self-Similar Regime
Institute of Scientific and Technical Information of China (English)
张立柱; 李行伟; 陈国谦
2004-01-01
Lock-release gravity currents with a viscous self-similar regime are simulated by use of the renormalization group (RNG) k - ε model for Reynolds-stress closure. Besides the turbulent regime with initially a slumping phase of a constant current front speed and later an inviscid self-similar phase of front speed decreasing as t-1/3(where t is the time measured from release), the viscous self-similar regime is satisfactorily reproduced with front speed decreasing as t-4/5,consistent with well known experimental observations.
Radev, Dimitar; Lokshina, Izabella
2010-11-01
The paper examines self-similar (or fractal) properties of real communication network traffic data over a wide range of time scales. These self-similar properties are very different from the properties of traditional models based on Poisson and Markov-modulated Poisson processes. Advanced fractal models of sequentional generators and fixed-length sequence generators, and efficient algorithms that are used to simulate self-similar behavior of IP network traffic data are developed and applied. Numerical examples are provided; and simulation results are obtained and analyzed.
Niethammer, Barbara
2011-01-01
The existence of self-similar solutions with fat tails for Smoluchowski's coagulation equation has so far only been established for the solvable and the diagonal kernel. In this paper we prove the existence of such self-similar solutions for continuous kernels $K$ that are homogeneous of degree $\\gamma \\in (-\\infty,1)$ and satisfy $K(x,y) \\leq C (x^{\\gamma} + y^{\\gamma})$. More precisely, for any $\\rho \\in (\\gamma,1)$ we establish the existence of a continuous weak self-similar profile with decay $x^{-(1{+}\\rho)}$ as $x \\to \\infty$.
ON THE SELF-SIMILAR SOLUTIONS OF THE MAGNETO-HYDRO-DYNAMIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
He Cheng; Xin Zhouping
2009-01-01
In this paper, we show that, for the three dimensional incompressible magneto-hydro-dynamic equations, there exists only trivial backward self-similar solution in LP(R3)for p > 3, under some smallness assumption on either the kinetic energy of the self-similar solution related to the velocity field, or the magnetic field.Second, we construct a class of global unique forward self-similar solutions to the three-dimensional MHD equations with small initial data in some sense, being homogeneous of degree -1 and belonging to some Besov space, or the Lorentz space or pseudo-measure space, as motivated by the work in [5].
Self-similarity of the large-scale motions in turbulent pipe flow
Hellström, Leo; Marusic, Ivan; Smits, Alexander
2016-11-01
Townsend's attached eddy hypothesis assumes the existence of a set of energetic and geometrically self-similar eddies in the logarithmic layer in wall-bounded turbulent flows. These eddies can be completely scaled with the distance from their center to the wall. We performed stereo PIV measurements together with a proper orthogonal decomposition (POD) analysis, to address the self-similarity of the energetic motions, or eddies, in fully-developed turbulent pipe flow. The resulting modes/eddies, extracted at Reτ = 2460 , show a self-similar behavior for eddies with wall-normal length scales spanning a decade. This single length scale provides a complete description of the cross-sectional shape of the self-similar eddies. ONR Grant N00014-15-1-2402 and the Australian Research Council.
Self-Similar Force-Free Wind From an Accretion Disk
Narayan, R; Farmer, A J; Narayan, Ramesh; Kinney, Jonathan C. Mc; Farmer, Alison J.
2006-01-01
We consider a self-similar force-free wind flowing out of an infinitely thin disk located in the equatorial plane. On the disk plane, we assume that the magnetic stream function $P$ scales as $P\\propto R^\
Self-similar vortex-induced vibrations of a hanging string
Grouthier, Clement; Modarres-Sadeghi, Yahya; de Langre, Emmanuel
2013-01-01
An experimental analysis of the vortex-induced vibrations of a hanging string with variable tension along its length is presented in this paper. It is shown that standing waves develop along the hanging string. The evolution of the Strouhal number St with the Reynolds number Re first follows a trend similar to what is observed for a circular cylinder in a flow for relatively low Reynolds numbers (32
GRAPH-DIRECTED STRUCTURES OF SELF-SIMILAR SETS WITH OVERLAPS
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Some kinds of the self-similar sets with overlapping structures are studied by introducing the graph-directed constructions satisfying the open set condition that coincide with these sets. In this way, the dimensions and the measures are obtained.
Self-similar solutions with fat tails for a coagulation equation with diagonal kernel
Niethammer, Barbara
2011-01-01
We consider self-similar solutions of Smoluchowski's coagulation equation with a diagonal kernel of homogeneity $\\gamma < 1$. We show that there exists a family of second-kind self-similar solutions with power-law behavior $x^{-(1+\\rho)}$ as $x \\to \\infty$ with $\\rho \\in (\\gamma,1)$. To our knowledge this is the first example of a non-solvable kernel for which the existence of such a family has been established.
Self-similar asymptotic optical beams in semiconductor waveguides doped with quantum dots
He, Jun-Rong; Yi, Lin; Li, Hua-Mei
2017-01-01
The self-similar propagation of asymptotic optical beams in semiconductor waveguides doped with quantum dots is reported. The possibility of controlling the shape of output asymptotic optical beams is demonstrated. The analytical results are confirmed by numerical simulations. We give a possible experimental protocol to generate the obtained asymptotic parabolic beams in realistic waveguides. As a generalization to the present work, the self-similar propagation of asymptotic optical beams is proposed in a power-law nonlinear medium.
Boundary layers for self-similar viscous approximations of nonlinear hyperbolic systems
Christoforou, Cleopatra
2011-01-01
We provide a precise description of the set of residual boundary conditions generated by the self-similar viscous approximation introduced by Dafermos et al. We then apply our results, valid for both conservative and non conservative systems, to the analysis of the boundary Riemann problem and we show that, under appropriate assumptions, the limits of the self-similar and the classical vanishing viscosity approximation coincide. We require neither genuinely nonlinearity nor linear degeneracy of the characteristic fields.
Self-similar solutions for the dynamical condensation of a radiative gas layer
Iwasaki, Kazunari; Tsuribe, Toru
2008-07-01
A new self-similar solution describing the dynamical condensation of a radiative gas is investigated under a plane-parallel geometry. The dynamical condensation is caused by thermal instability. The solution is applicable to generic flow with a net cooling rate per unit volume and time ~ ρ2Tα, where ρ,T and α are the density, temperature and a free parameter, respectively. Given α, a family of self-similar solutions with one parameter η is found in which the central density and pressure evolve as follows: ρ(x = 0, t) ~ (tc - t)-η/(2-α) and P(x = 0, t) ~ (tc - t)(1-η)/(1-α), where tc is the epoch at which the central density becomes infinite. For η ~ 0 the solution describes the isochoric mode, whereas for η ~ 1 the solution describes the isobaric mode. The self-similar solutions exist in the range between the two limits; that is, for 0 1. We compare the obtained self-similar solutions with the results of one-dimensional hydrodynamical simulations. In a converging flow, the results of the numerical simulations agree well with the self-similar solutions in the high-density limit. Our self-similar solutions are applicable to the formation of interstellar clouds (HI clouds and molecular clouds) by thermal instability.
Lou, Yu-Qing; Xia, Yu-Kai
2017-05-01
We study magnetohydrodynamic (MHD) self-similar collapses and void evolution, with or without shocks, of a general polytropic quasi-spherical magnetofluid permeated by random transverse magnetic fields under the Paczynski-Wiita gravity that captures essential general relativistic effects of a Schwarzschild black hole (BH) with a growing mass. Based on the derived set of non-linear MHD ordinary differential equations, we obtain various asymptotic MHD solutions, the geometric and analytical properties of the magnetosonic critical curve (MSCC) and MHD shock jump conditions. Novel asymptotic MHD solution behaviours near the rim of central expanding voids are derived analytically. By exploring numerical global MHD solutions, we identify allowable boundary conditions at large radii that accommodate a smooth solution and show that a reasonable amount of magnetization significantly increases the mass accretion rate in the expansion-wave-collapse solution scenario. We also construct the counterparts of envelope-expansion-core-collapse solutions that cross the MSCC twice, which are found to be closely paired with a sequence of global smooth solutions satisfying a novel type of central MHD behaviours. MHD shocks with static outer and various inner flow profiles are also examined. Astrophysical applications include dynamic core collapses of magnetized massive stars and compact objects as well as formation of supermassive, hypermassive, dark matter and mixed matter BHs in the Universe, including the early Universe. Such gigantic BHs can be detected in X-ray/gamma-ray sources, quasars, ultraluminous infrared galaxies or extremely luminous infrared galaxies and dark matter overwhelmingly dominated elliptical galaxies as well as massive dark matter halos, etc. Gravitational waves and electromagnetic wave emissions in broad band (including e.g., gamma-ray bursts and fast radio bursts) can result from this type of dynamic collapses of forming BHs involving magnetized media.
A novel flux-fluctuation law for network with self-similar traffic
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.
Riccati parameterized self-similar waves in two-dimensional graded-index waveguide
Kumar De, Kanchan; Goyal, Amit; Raju, Thokala Soloman; Kumar, C. N.; Panigrahi, Prasanta K.
2015-04-01
An analytical method based on gauge-similarity transformation technique has been employed for mapping a (2+1)- dimensional variable coefficient coupled nonlinear Schrödinger equations (vc-CNLSE) with dispersion, nonlinearity and gain to standard NLSE. Under certain functional relations we construct a large family of self-similar waves in the form of bright similaritons, Akhmediev breathers and rogue waves. We report the effect of dispersion on the intensity of the solitary waves. Further, we illustrate the procedure to amplify the intensity of self-similar waves using isospectral Hamiltonian approach. This approach provides an efficient mechanism to generate analytically a wide class of tapering profiles and widths by exploiting the Riccati parameter. Equivalently, it enables one to control efficiently the self-similar wave structures and hence their evolution.
Coughlin, Eric R
2016-01-01
We present the exact solutions for the collapse of a spherically-symmetric, cold (i.e., pressureless) cloud under its own self-gravity, valid for arbitrary initial density profiles and not restricted to the realm of self-similarity. These solutions exhibit a number of remarkable features, including the self-consistent formation of and subsequent accretion onto a central point mass. A number of specific examples are provided, and we show that Penston's solution of pressureless, self-similar collapse is recovered for polytropic density profiles; importantly, however, we demonstrate that the time over which this solution holds is fleetingly narrow, implying that much of the collapse proceeds non-self-similarly. We show that our solutions can naturally incorporate turbulent pressure support, and we investigate the evolution of overdensities -- potentially generated by such turbulence -- as the collapse proceeds. Finally, we analyze the evolution of the angular velocity and magnetic fields in the limit that their ...
An Improved Modeling for Network Traffic Based on Alpha-Stable Self-similar Processes
Institute of Scientific and Technical Information of China (English)
GEXiaohu; ZHUGuangxi; ZHUYaoting
2003-01-01
This paper produces an improved model based on alpha-stable processes. First, this paper introduces the basic of self-similarity, and then the reason why the alpha-stable processes have been used for self-similar network traffic modeling is given out; Second, the research in this field is advanced, and the paper analyzes the drawback of the S4 model, which is supported by the related mathematical proof and confirmations of experiments. In order to make up for the drawback of the S4 model andaccurately describe the varieties of the heavily tailed distributions, an improved network traffic model is proposed. By comparison with simulation data (including the S4 model and the improved model) and actual data, the advantage of the improved model has been demonstrated. In the end, the significance of the self-similar network traffic model has been put forward, and the future work is discussed.
Coherent structures of a self-similar adverse pressure gradient turbulent boundary layer
Sekimoto, Atsushi; Kitsios, Vassili; Atkinson, Callum; Jiménez, Javier; Soria, Julio
2016-11-01
The turbulence statistics and structures are studied in direct numerical simulation (DNS) of a self-similar adverse pressure gradient turbulent boundary layer (APG-TBL). The self-similar APG-TBL at the verged of separation is achieved by a modification of the far-field boundary condition to produce the desired pressure gradient. The turbulence statistics in the self-similar region collapse by using the scaling of the external velocity and the displacement thickness. The coherent structures of the APG-TBL are investigated and compared to those of zero-pressure gradient case and homogeneous shear flow. The support of the ARC, NCI and Pawsey SCC funded by the Australian and Western Australian governments as well as the support of PRACE funded by the European Union are gratefully acknowledged.
Riccati generalization of self-similar solutions of nonautonomous Gross-Pitaevskii equation
Panigrahi, P. K.; Gupta, Rama; Goyal, Amit; Kumar, C. N.
2013-07-01
We present a systematic analytical approach to construct a family of self-similar waves, related through a free parameter, in quasi one-dimension Gross-Pitaevskii equation with time-varying parameters. This approach enables us to control the dynamics of dark and bright similaritons, and first- and second- order self-similar rogue waves in Bose-Einstein condensate through the modulation of time dependent trapping potential. The analysis is done for the sech2- type time-varying quadratic trapping potential for two different choices of linear potential.
Scaling in the Optical Characteristics of Aperiodic Structures with Self-Similarity Symmetry
Energy Technology Data Exchange (ETDEWEB)
Zotov, A. M.; Korolenko, P. V., E-mail: pvkorolenko@rambler.ru; Mishin, A. Yu. [Moscow State University (Russian Federation)
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.
SELF-SIMILAR SOLUTIONS OF FRACTURE DYNAMICS PROBLEMS ON AXIALLY SYMMETRY
Institute of Scientific and Technical Information of China (English)
吕念春; 程靳; 程云虹; 屈德志
2001-01-01
By the theory of complex functions, a penny-shaped crack on axially symmetric propagating problems for composite materials was studied. The general representations of the analytical solutions with arbitrary index of self-similarity were presented for fracture elastodynamics problems on axially symmetry by the ways of self-similarity under the /addershaped loads. The problerns dealt with can be transformed into Riemann-Hilbert problems and their closed analytical solutions are obtained rather simple by this method. After those analytical solutions are utilized by using the method of rotational superposition theorem in conjunction with that of Smirnov-Sobolev, the solutions of arbitrary complicated problems can be obtained.
Self-similar propagation and amplification of parabolic pulses in optical fibers.
Fermann, M E; Kruglov, V I; Thomsen, B C; Dudley, J M; Harvey, J D
2000-06-26
Ultrashort pulse propagation in high gain optical fiber amplifiers with normal dispersion is studied by self-similarity analysis of the nonlinear Schrödinger equation with gain. An exact asymptotic solution is found, corresponding to a linearly chirped parabolic pulse which propagates self-similarly subject to simple scaling rules. The solution has been confirmed by numerical simulations and experiments studying propagation in a Yb-doped fiber amplifier. Additional experiments show that the pulses remain parabolic after propagation through standard single mode fiber with normal dispersion.
Institute of Scientific and Technical Information of China (English)
Suparerk JANJARASJITT
2014-01-01
Self-similarity or scale-invariance is a fascinating characteristic found in various signals including electroencephalogram (EEG) signals. A common measure used for characterizing self-similarity or scale-invariance is the spectral exponent. In this study, a computational method for estimating the spectral exponent based on wavelet transform was examined. A series of Daubechies wavelet bases with various numbers of vanishing moments were applied to analyze the self-similar characteristics of intracranial EEG data corresponding to different pathological states of the brain, i.e., ictal and interictal states, in patients with epilepsy. The computational results show that the spectral exponents of intracranial EEG signals obtained during epileptic seizure activity tend to be higher than those obtained during non-seizure periods. This suggests that the intracranial EEG signals obtained during epileptic seizure activity tend to be more self-similar than those obtained during non-seizure periods. The computational results obtained using the wavelet-based approach were validated by comparison with results obtained using the power spectrum method.
Leonardo's rule, self-similarity and wind-induced stresses in trees
Eloy, Christophe
2011-01-01
Examining botanical trees, Leonardo da Vinci noted that the total cross-sectional area 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 with the minimum biomass.
Collapsing perfect fluid in self-similar five dimensional space-time and cosmic censorship
Ghosh, S G; Saraykar, R V
2014-01-01
We investigate the occurrence and nature of naked singularities in the gravitational collapse of a self-similar adiabatic perfect fluid in a five dimensional space-time. The naked singularities are found to be gravitationally strong in the sense of Tipler and thus violate the cosmic censorship conjecture.
Space-filling curves of self-similar sets (I): iterated function systems with order structures
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.
Doneva, M.; Nielsen, T.; Boernert, P.
2012-01-01
In this work, we present a CS reconstruction based on statistical non-local self-similarity filtering (STAINLeSS), in which the parameters are entirely determined by the noise estimation in the receive channels obtained from a standard noise measurement. The method achieves improved image quality co
Spectral scalability as a result of geometrical self-similarity in fractal multilayers
Zhukovsky, S V; Gaponenko, S V
2016-01-01
The optical spectra of fractal multilayer dielectric structures have been shown to possess spectral scalability, which has been found to be directly related to the structure's spatial (geometrical) self-similarity. Phase and amplitude scaling relations, as well as effects of finite structure size, have been derived.
CRITERIA OF STRONG TRANSIENCE FOR OPERATOR-SELF-SIMILAR MARKOV PROCESSES
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Yamamuro in [1] defines strong and weak transience of Markov processes; gives a criterion for strong transience of Feller processes; and further, discusses strong and weak transience of Ornstein-Uhlenbeck type processes. In this article, the authors weaken the Feller property of the result in [1] to weak Feller property and discuss the strong transience of operator-self-similar Markov processes.
Leonardo's Rule, Self-Similarity, and Wind-Induced Stresses in Trees
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.
Self-similar solutions for the dynamical condensation of a radiative gas layer
Iwasaki, Kazunari
2008-01-01
A new self-similar solution describing the dynamical condensation of a radiative gas is investigated under a plane-parallel geometry. The dynamical condensation is caused by thermal instability. The solution is applicable to generic flow with a net cooling rate per unit volume and time $\\propto \\rho^2 T^\\alpha$, where $\\rho$, $T$ and $\\alpha$ are density, temperature and a free parameter, respectively. Given $\\alpha$, a family of self-similar solutions with one parameter $\\eta$ is found in which the central density and pressure evolve as follows: $\\rho(x=0,t)\\propto (t_\\mathrm{c}-t)^{-\\eta/(2-\\alpha)}$ and $P(x=0,t)\\propto (t_\\mathrm{c}-t)^{(1-\\eta)/(1-\\alpha)}$, where $t_\\mathrm{c}$ is an epoch when the central density becomes infinite. For $\\eta\\sim 0$, the solution describes the isochoric mode, whereas for $\\eta\\sim1$, the solution describes the isobaric mode. The self-similar solutions exist in the range between the two limits; that is, for $01$. We compare the obtained self-similar solutions with the res...
Maeda, Hideki; Carr, B J
2007-01-01
We use a combination of numerical and analytical methods, exploiting the equations derived in an accompanying 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. We also find various kinds of self-similar wormhole solutions; these represent a Friedmann universe connected to either another Friedmann universe or some other cosmological model. These wormholes are generally traversable, where we de...
DNS of self-similar adverse pressure gradient turbulent boundary layer
Soria, Julio; Kitsios, Vassili; Sekimoto, Atsushi; Atkinson, Callum; Jiménez, Javier
2016-11-01
A direct numerical simulation (DNS) of a self-similar adverse pressure gradient (APG) turbulent boundary layer (TBL) at the verge of separation has been set-up and carried out. The DNS APG TBL has a displacement thickness based Reynolds number that ranges up to 30,000. The conditions for self-similarity and appropriate scaling will be highlighted, with the first and second order velocity statistical profiles non-dimensionalised using this scaling. The details of the DNS and the required boundary conditions that are necessary to establish this self-similar APG-TBL will be presented. The statistical properties of the self-similar adverse pressure gradient (APG) turbulent boundary layer (TBL) DNS will presented, as will the profiles of the terms in the momentum equation, spanwise/wall-normal kinetic energy spectrum and two-point correlations, which will be compared to those of a zero pressure gradient turbulent boundary layer. NCI and Pawsey SCC funded by the Australian and Western Australian governments as well as the support of PRACE funded by the European Union are gratefully acknowledged.
A steady solution for Prandtl’s self-similar vortex sheet spirals
Van Kuik, G.A.M.
2008-01-01
Prandtl's [L. Prandtl, Über die Entstehung von Wirbeln in der idealen Flüssigkeit, mit Anwendung auf die Tragflügeltheorie und andere Aufgaben, in: von Kármán, Levi-Cevita (Eds.), Vorträge aus dem Gebiete der Hydro- und Aerodynamik, Springer, Berlin, 1922] self-similar, semi-infinite, free vortex sh
Self-similarity in the equation of motion of a ship
Directory of Open Access Journals (Sweden)
Lee Gyeong Joong
2014-06-01
Full Text Available If we want to analyze the motion of a body in fluid, we should use rigid-body dynamics and fluid dynamics together. Even if the rigid-body and fluid dynamics are each self-consistent, there arises the problem of self-similar structure in the equation of motion when the two dynamics are coupled with each other. When the added mass is greater than the mass of a body, the calculated motion is divergent because of its self-similar structure. This study showed that the above problem is an inherent problem. This problem of self-similar structure may arise in the equation of motion in which the fluid dynamic forces are treated as external forces on the right hand side of the equation. A reconfiguration technique for the equation of motion using pseudo-added-mass was proposed to resolve the self-similar structure problem; specifically for the case when the fluid force is expressed by integration of the fluid pressure.
Ginzburg-Landau vortices with pinning functions and self-similar solutions in harmonic maps
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
We obtain the H1-compactness for a system of Ginzburg-Landau equations with pinning functions and prove that the vortices of its classical solutions are attracted to the minimum points of the pinning functions. As a corollary, we construct a self-similar solution in the evolution of harmonic maps.
An approximative calculation of the fractal structure in self-similar tilings
Hayashi, Yukio
2010-01-01
Fractal structures emerge from statistical and hierarchical processes in urban development or network evolution. In a class of efficient and robust geographical networks, we derive the size distribution of layered areas, and estimate the fractal dimension by using the distribution without huge computations. This method can be applied to self-similar tilings based on a stochastic process.
Geometry of River Networks; 3, Characterization of Component Connectivity
Dodds, P S; Dodds, Peter Sheridan; Rothman, Daniel H.
2000-01-01
River networks serve as a paradigmatic example of all branching networks. Essential to understanding the overall structure of river networks is a knowledge of their detailed architecture. Here we show that sub-branches are distributed exponentially in size and that they are randomly distributed in space, thereby completely characterizing the most basic level of river network description. Specifically, an averaged view of network architecture is first provided by a proposed self-similarity statement about the scaling of drainage density, a local measure of stream concentration. This scaling of drainage density is shown to imply Tokunaga's law, a description of the scaling of side branch abundance along a given stream, as well as a scaling law for stream lengths. This establishes the scaling of the length scale associated with drainage density as the basic signature of self-similarity in river networks. We then consider fluctuations in drainage density and consequently the numbers of side branches. Data is anal...
Meandering instability of air flow in a granular bed: self-similarity and fluid-solid duality
Yoshimura, Yuki; Yagisawa, Yui; Okumura, Ko
2016-12-01
Meandering instability is familiar to everyone through river meandering or small rivulets of rain flowing down a windshield. However, its physical understanding is still premature, although it could inspire researchers in various fields, such as nonlinear science, fluid mechanics and geophysics, to resolve their long-standing problems. Here, we perform a small-scale experiment in which air flow is created in a thin granular bed to successfully find a meandering regime, together with other remarkable fluidized regimes, such as a turbulent regime. We discover that phase diagrams of the flow regimes for different types of grains can be universally presented as functions of the flow rate and the granular-bed thickness when the two quantities are properly renormalized. We further reveal that the meandering shapes are self-similar as was shown for meandering rivers. The experimental findings are explained by theory, with elucidating the physics. The theory is based on force balance, a minimum-dissipation principle, and a linear-instability analysis of a continuum equation that takes into account the fluid-solid duality, i.e., the existence of fluidized and solidified regions of grains along the meandering path. The present results provide fruitful links to related issues in various fields, including fluidized bed reactors in industry.
Yu, C; Yu, Cong; Lou, Yu-Qing
2005-01-01
We investigate self-similar magnetohydrodynamic (MHD) processes in an isothermal self-gravitating fluid with a quasi-spherical symmetry and extend the envelope expansion with core collapse (EECC) solutions of Lou & Shen by incorporating a random magnetic field. Stagnation surfaces of EECC solutions that seperate core collapse and envelope expansion propagate at constant speeds either sub-magnetosonically or super-magnetosonically. Crossing the magnetosonic line twice analytically, there exists an infinite number of discrete magnetized EECC and ECCC solutions. In addition to the EECC shock solution which could change the central accretion rate, the magnetic field can also affect the core accretion rate. As the magnetic parameter $\\lambda$ increases, the core accretion rate appropriate for the MHD EWCS becomes larger. Under the frozen-in approximation, magnetic fields in the envelope expansion portion would scale as $B\\propto r^{-1}$, while in the core collapse portion they would scale as $B\\propto r^{-1/2}...
Oak Park and River Forest High School Random Access Information Center; A PACE Program. Report II.
Oak Park - River Forest High School, Oak Park, IL.
The specifications, planning, and initial development phases of the Random Access Center at the Oak Park and River Forest High School in Oak Park, Illinois, are described with particular attention to the ways that the five functional specifications and the five-part program rationale were implemented in the system design. Specifications, set out…
Self-similar oscillations of a Z pinch bounded by a magnetic multipole
Energy Technology Data Exchange (ETDEWEB)
Tendler, M.
1988-11-01
A new analytic, self-similar solution of the fluid equations with losses in a stabilized Z pinch is presented. A scaling is suggested for the net energy loss with plasma density and temperature typical for a Z pinch immersed in an external multipole magnetic field. The solution of the strongly nonlinear system of fluid equations is obtained by self-similar methods. Strongly aharmonic high frequency oscillations of the plasma parameters are found. It is emphasized that a static Z pinch cannot be stabilized by a stationary field of a magnetic multipole. Therefore the potentiality of these oscillations to affect the stability of Z pinches embedded in a magnetic multipole is investigated. The effect of the dynamic stabilization is considered by taking estimates.
Approximate self-similar solutions to a nonlinear diffusion equation with time-fractional derivative
Płociniczak, Łukasz; Okrasińska, Hanna
2013-10-01
In this paper, we consider a fractional nonlinear problem for anomalous diffusion. The diffusion coefficient we use is of power type, and hence the investigated problem generalizes the porous-medium equation. A generalization is made by introducing a fractional time derivative. We look for self-similar solutions for which the fractional setting introduces other than classical space-time scaling. The resulting similarity equations are of nonlinear integro-differential type. We approximate these equations by an expansion of the integral operator and by looking for solutions in a power function form. Our method can be easily adapted to solve various problems in self-similar diffusion. The approximations obtained give very good results in numerical analysis. Their simplicity allows for easy use in applications, as our fitting with experimental data shows. Moreover, our derivation justifies theoretically some previously used empirical models for anomalous diffusion.
Self-Similar Collapse Solutions for Cylindrical Cloud Geometries and Dynamic Equations of State
Holden, Lisa; Baxter, Benjamin; Fatuzzo, Marco
2009-01-01
A self-similar formalism for the study of the gravitational collapse of molecular gas provides an important theoretical framework from which to explore the dynamics of star formation. Motivated by the presence of elongated and filamentary structures observed in giant molecular clouds, we build upon the existing body of work on cylindrical self-similar collapse flows by including dynamic equations of state that are different from the effective equation of state that produces the initial density distribution. We focus primarily on the collapse of initial states for which the gas is at rest and everywhere overdense from its corresponding hydrostatic equilibrium profile by a factor $\\Lambda$, and apply our results toward the analysis of star formation within dense, elongated molecular cores. An important aspect of this work is the determination of the mass infall rates over a range of the parameters which define the overall state of the gas -- the overdensity parameter $\\Lambda$, the index $\\Gamma$ of the static ...
Robustness of Estimators of Long-Range Dependence and Self-Similarity under non-Gaussianity
Franzke, Christian L E; Watkins, Nicholas W; Gramacy, Robert B; Hughes, Cecilia
2011-01-01
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 usually occur together in natural systems and that the superposition of both phenomena constitute the self-similarity of a system. 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 are not robust. In particula...
Self-similar accretion in thin discs around near-extremal black holes
Compère, Geoffrey; Oliveri, Roberto
2017-07-01
Near-maximally spinning black holes display conformal symmetry in their near-horizon region, which is therefore the locus of critical phenomena. In this paper, we revisit the Novikov-Thorne accretion thin disc model and find a new self-similar radiation-dominated solution in the extremely high spin regime. Motivated by the self-consistency of the model, we require that matter flows at the sound speed at the innermost stable circular orbit (ISCO). We observe that, when the disc pressure is dominated by radiation at the ISCO, which occurs for the best-fitting Novikov-Thorne model of GRS 1915+105, the Shakura-Sunyaev viscosity parameter can be expressed in terms of the spin, mass accretion rate and radiative efficiency. We quantitatively describe how the exact thin disc solution approaches the self-similar solution in the vicinity of the ISCO and for increasing spins.
Self-Similar Blowup Solutions to the 2-Component Degasperis-Procesi Shallow Water System
Yuen, Manwai
2010-01-01
In this article, we study the self-similar solutions of the 2-component Degasperis-Procesi water system:% [c]{c}% \\rho_{t}+k_{2}u\\rho_{x}+(k_{1}+k_{2})\\rho u_{x}=0 u_{t}-u_{xxt}+4uu_{x}-3u_{x}u_{xx}-uu_{xxx}+k_{3}\\rho\\rho_{x}=0. By the separation method, we can obtain a class of self-similar solutions,% [c]{c}% \\rho(t,x)=\\max(\\frac{f(\\eta)}{a(4t)^{(k_{1}+k_{2})/4}},\\text{}0),\\text{}u(t,x)=\\frac{\\overset{\\cdot}{a}(4t)}{a(4t)}x \\overset{\\cdot\\cdot}{a}(s)-\\frac{\\xi}{4a(s)^{\\kappa}}=0,\\text{}a(0)=a_{0}% \
A stable self-similar singularity of evaporating drops: ellipsoidal collapse to a point
Fontelos, Marco A; Hwang, Hyung Ju
2014-01-01
We study the problem of evaporating drops contracting to a point. Going back to Maxwell and Langmuir, the existence of a spherical solution for which evaporating drops collapse to a point in a self-similar manner is well established in the physical literature. The diameter of the drop follows the so-called $D^{2}$ law: the second power of the drop-diameter decays linearly in time. In this study we provide a complete mathematical proof of this classical law. We prove that evaporating drops which are initially small perturbations of a sphere collapse to a point and the shape of the drop converges to a self-similar ellipsoid whose center, orientation, and semi-axes are determined by the initial shape.
On the Minkowski Measurability of Self-Similar Fractals in R^d
Deniz, Ali; Ozdemir, Yunus; Ratiu, Andrei V; Ureyen, A Ersin
2010-01-01
M. Lapidus and C. Pomerance (1990-1993) and K.J. Falconer (1995) proved that a self-similar fractal in $\\mathbb{R}$ is Minkowski-measurable iff it is of non-lattice type. D. Gatzouras (1999) proved that a self-similar fractal in $\\mathbb{R}^d$ is Minkowski measurable if it is of non-lattice type (though the actual computation of the content is intractable with his approach) and conjectured that it is not Minkowski measurable if it is of lattice type. Under mild conditions we prove this conjecture and in the non-lattice case we improve his result in the sense that we express the content of the fractal in terms of the residue of the associated $\\zeta$-function at the Minkowski-dimension.
Disappearance of a spout: self-similar scaling in viscous withdrawal
Zhang, Wendy
2002-11-01
Inspired by recent experiments (Cohen & Nagel, PRL, 2002) showing that steady flow past an interface between two layers of viscous liquids can draw out a thin tendril of fluid (a spout) above a critical flow rate, we present a long-wavelength model of axisymmetric, viscous withdrawal from a fluid-filled nozzle. The model suggests that the fluid interface develops a steady-state singularity as the exterior fluid withdrawal rate is increased pass a critical rate. In addition, the critical withdrawal rate does not depend on the viscosity contrast when the nozzle fluid is much less viscous than the exterior fluid. At the the critical withdrawal rate, the volume flux is zero, corresponding to a spout of zero thickness. At flow rates slightly above critical withdrawal rate, the steady-state spout profiles can be self-similar, with a scaling exponent determined by an interplay of local self-similarity and macroscopic boundary conditions.
Phase transitions for the multifractal analysis of self-similar measures
Testud, B.
2006-05-01
We are interested in the multifractal analysis of a class of self-similar measures with overlaps. This class, for which we obtain explicit formulae for the Lq-spectrum, τ(q), as well as the singularity spectrum f(α), is sufficiently large to point out new phenomena in the multifractal structure of self-similar measures. We show that, unlike in the classical quasi-Bernoulli case, the Lq-spectrum, τ(q), of the measures studied can have an arbitrarily large number of non-differentiability points (phase transitions). These singularities occur only for the negative values of q and yield to measures that do not satisfy the usual multifractal formalism. The weak quasi-Bernoulli property is the key point of most of the arguments.
Pagnini, Gianni; Mura, Antonio; Mainardi, Francesco
2013-05-13
Two-particle dispersion is investigated in the context of anomalous diffusion. Two different modelling approaches related to time subordination are considered and unified in the framework of self-similar stochastic processes. By assuming a single-particle fractional Brownian motion and that the two-particle correlation function decreases in time with a power law, the particle relative separation density is computed for the cases with time sub-ordination directed by a unilateral M-Wright density and by an extremal Lévy stable density. Looking for advisable mathematical properties (for instance, the stationarity of the increments), the corresponding self-similar stochastic processes are represented in terms of fractional Brownian motions with stochastic variance, whose profile is modelled by using the M-Wright density or the Lévy stable density.
Self-similar expansion of solar coronal mass ejections: Implications for Lorentz self-force driving
Energy Technology Data Exchange (ETDEWEB)
Subramanian, Prasad; Arunbabu, K. P.; Mauriya, Adwiteey [Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pashan, Pune 411008 (India); Vourlidas, Angelos, E-mail: p.subramanian@iiserpune.ac.in [Space Science Division, Naval Research Laboratory, 4555 Overlook Avenue, SW Washington, DC 20375 (United States)
2014-08-01
We examine the propagation of several coronal mass ejections (CMEs) with well-observed flux rope signatures in the field of view of the SECCHI coronagraphs on board the STEREO satellites using the graduated cylindrical shell fitting method of Thernisien et al. We find that the manner in which they propagate is approximately self-similar; i.e., the ratio (κ) of the flux rope minor radius to its major radius remains approximately constant with time. We use this observation of self-similarity to draw conclusions regarding the local pitch angle (γ) of the flux rope magnetic field and the misalignment angle (χ) between the current density J and the magnetic field B. Our results suggest that the magnetic field and current configurations inside flux ropes deviate substantially from a force-free state in typical coronagraph fields of view, validating the idea of CMEs being driven by Lorentz self-forces.
Self-similar Shape Mode of Optical Pulse Propagation in Medium with non-stationary Absorption
Trofimov, Vycheslav A.; Lysak, Tatyana M.; Fedotov, Mihail V.; Prokopenko, Alexander S.
2015-03-01
We discuss laser pulse propagation with the self-similar shape in a medium with instantaneous nonlinear absorption. We consider two cases of the laser pulse propagation. First one corresponds to problem of laser-induced plasma generation in silica under action of TW laser pulse. The second one corresponds to femtosecond laser pulse propagation in medium with nanoparticles of noble metals. In both cases the mode of the self-similar shape of pulse is of interest. We discuss also a physical mechanism of non-linear acceleration or slowing-down for laser pulse propagation in a medium with nanoparticles. The last phenomena are important, in particular, for a problem of data processing of all optical method. We used analytical approach for considered problem as well as computer simulation.
Scaling and interaction of self-similar modes in models of high Reynolds number wall turbulence
Sharma, A. S.; Moarref, R.; McKeon, B. J.
2017-03-01
Previous work has established the usefulness of the resolvent operator that maps the terms nonlinear in the turbulent fluctuations to the fluctuations themselves. Further work has described the self-similarity of the resolvent arising from that of the mean velocity profile. The orthogonal modes provided by the resolvent analysis describe the wall-normal coherence of the motions and inherit that self-similarity. In this contribution, we present the implications of this similarity for the nonlinear interaction between modes with different scales and wall-normal locations. By considering the nonlinear interactions between modes, it is shown that much of the turbulence scaling behaviour in the logarithmic region can be determined from a single arbitrarily chosen reference plane. Thus, the geometric scaling of the modes is impressed upon the nonlinear interaction between modes. Implications of these observations on the self-sustaining mechanisms of wall turbulence, modelling and simulation are outlined.
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.
Self-similar and self-affine sets; measure of the intersection of two copies
Elekes, Márton; Máthé, András
2007-01-01
Let K be a self-similar or self-affine set in R^d, let \\mu be a self-similar or self-affine measure on it, and let G be the group of affine maps, similitudes, isometries or translations of R^d. Under various assumptions (such as separation conditions or we assume that the transformations are small perturbations or that K is a so called Sierpinski sponge) we prove theorems of the following types, which are closely related to each other; Non-stability: There exists a constant c 0 \\iff int_K (K\\cap g(K)) is nonempty (where int_K is interior relative to K). Extension: The measure \\mu has a G-invariant extension to R^d. Moreover, in many situations we characterize those g's for which \\mu(K\\cap g(K) > 0 holds.
Self-similarity Based Editing of 3D Surface Textures Using Height and Albedo Maps
Institute of Scientific and Technical Information of China (English)
DONG Junyu; REN Jing; CHEN Guojiang
2007-01-01
This paper presents an inexpensive method for self-similarity based editing of real-world 3D surface textures by using height and albedo maps. Unlike self-similarity based 2D texture editing approaches which only make changes to pixel color or intensity values, this technique also allows surface geometry and reflectance of the captured 3D surface textures to be edited and relit using illumination conditions and viewing angles that differ from those of the original. A single editing operation at a given location affects all similar areas and produces changes on all images of the sample rendered under different conditions. Since surface height and albedo maps can be used to describe seabed topography and geologic features, which play important roles in many oceanic processes, the proposed method can be effectively employed in applications regarding visualization and simulation of oceanic phenomena.
Providing QoS guarantees for self-similar traffic flows
Institute of Scientific and Technical Information of China (English)
Wen Jun; Zhang Rui; Lu Xianliang
2005-01-01
Provisioning network resource to meet the quality of Service (QoS) demand isa key issue for future network services. Such functions may be realized by an admission control algorithm, which determines whether or not a new traffic flow can be admitted into the network. It is widely accepted that many traffic flows have self-similar character that has detrimental influence on network performance. This characteristic has made old mathematical models invalid, and a new model must work with self-similar fractal instead. This paper applies Fractional Brownian Motion(FBM) model and integrates it into the comprehensive admission control scheme, which takes account of aggregated traffic behavior to get the statistical multiplexing performance gain. Experiment verifies that FBM model can be used to realistically describe packet traffic in modern packet networks and accurately predict their performance.
Extended self-similarity of atmospheric boundary layer wind fields in mesoscale regime: Is it real?
Kiliyanpilakkil, V P
2015-01-01
In this letter, we study the scaling properties of multi-year observed and atmospheric model-generated wind time series. We have found that the extended self-similarity holds for the observed series, and remarkably, the scaling exponents corresponding to the meoscale range closely match the well-accepted inertial-range turbulence values. However, the scaling results from the simulated time series are significantly different.
An Exactly Soluble Hierarchical Clustering Model Inverse Cascades, Self-Similarity, and Scaling
Gabrielov, A; Turcotte, D L
1999-01-01
We show how clustering as a general hierarchical dynamical process proceeds via a sequence of inverse cascades to produce self-similar scaling, as an intermediate asymptotic, which then truncates at the largest spatial scales. We show how this model can provide a general explanation for the behavior of several models that has been described as ``self-organized critical,'' including forest-fire, sandpile, and slider-block models.
Self-similar erbium-doped fiber laser with large normal dispersion.
Liu, Hui; Liu, Zhanwei; Lamb, Erin S; Wise, Frank
2014-02-15
We report a large normal dispersion erbium-doped fiber laser with self-similar pulse evolution in the gain fiber. The cavity is stabilized by the local nonlinear attractor in the gain fiber through the use of a narrow filter. Experimental results are accounted for by numerical simulations. This laser produces 3.5 nJ pulses, which can be dechirped to 70 fs with an external grating pair.
Self-similar erbium-doped fiber laser with large normal dispersion
Liu, Hui; Liu, Zhanwei; Lamb, Erin S.; Wise, Frank
2014-01-01
We report a large normal dispersion erbium-doped fiber laser with self-similar pulse evolution in the gain fiber. The cavity is stabilized by the local nonlinear attractor in the gain fiber through the use of a narrow filter. Experimental results are accounted for by numerical simulations. This laser produces 3.5 nJ pulses, which can be dechirped to 70 fs with an external grating pair.
Discrete Self-Similarity in Ultra-Relativistic Type-II Strong Explosions
Oren, Yonatan; 10.1063/1.3231838
2009-01-01
A solution to the ultra-relativistic strong explosion problem with a non-power law density gradient is delineated. We consider a blast wave expanding into a density profile falling off as a steep radial power-law with small, spherically symmetric, and log-periodic density perturbations. We find discretely self-similar solutions to the perturbation equations and compare them to numerical simulations. These results are then generalized to encompass small spherically symmetric perturbations with arbitrary profiles.
Discrete self-similarity in ultrarelativistic type-II strong explosions
Oren, Yonatan; Sari, Re'em
2009-10-01
A solution to the ultrarelativistic strong explosion problem with a nonpower law density gradient is delineated. We consider a blast wave expanding into a density profile falling off as a steep radial power law with small, spherically symmetric, and log-periodic density perturbations. We find discretely self-similar solutions to the perturbation equations and compare them to numerical simulations. These results are then generalized to encompass small spherically symmetric perturbations with arbitrary profiles.
Self-Similar Solutions of Three-Dimensional Navier-Stokes Equation
Institute of Scientific and Technical Information of China (English)
I.F. Barna
2011-01-01
In this article we will present pure three dimensional analytic solutions for the Navier-Stokes and the continuity equations in Cartesian coordinates. The key idea is the three-dimensional generalization of the well-known self-similar Ansatz of Barenblatt. A geometrical interpretation of the Ansatz is given also. The results are the Kummer functions or strongly related. Our final formula is compared with other results obtained from group theoretical approaches.
Zeng, Z. Y.; Claro, F.
2001-01-01
We study the transport of electrons in a Fibonacci magnetic superlattice produced on a two-dimensional electron gas modulated by parallel magnetic field stripes arranged in a Fibonacci sequence. Both the transmission coefficient and conductance exhibit self-similarity and the six-circle property. The presence of extended states yields a finite conductivity at infinite length, that may be detected as an abrupt change in the conductance as the Fermi energy is varied, much as a metal-insulator t...
Directory of Open Access Journals (Sweden)
Yuehai Wang
2014-01-01
Full Text Available Wireless sensor networks, in combination with image sensors, open up a grand sensing application field. It is a challenging problem to recover a high resolution (HR image from its low resolution (LR counterpart, especially for low-cost resource-constrained image sensors with limited resolution. Sparse representation-based techniques have been developed recently and increasingly to solve this ill-posed inverse problem. Most of these solutions are based on an external dictionary learned from huge image gallery, consequently needing tremendous iteration and long time to match. In this paper, we explore the self-similarity inside the image itself, and propose a new combined self-similarity superresolution (SR solution, with low computation cost and high recover performance. In the self-similarity image super resolution model (SSIR, a small size sparse dictionary is learned from the image itself by the methods such as KSVD. The most similar patch is searched and specially combined during the sparse regulation iteration. Detailed information, such as edge sharpness, is preserved more faithfully and clearly. Experiment results confirm the effectiveness and efficiency of this double self-learning method in the image super resolution.
A Uniqueness Result for Self-Similar Profiles to Smoluchowski's Coagulation Equation Revisited
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.
Accretion disk dynamics. α-viscosity in self-similar self-gravitating models
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.
Drop impact on a solid surface: short time self-similarity
Philippi, Julien; Antkowiak, Arnaud
2015-01-01
The early stages of drop impact onto a solid surface are considered. Detailed numerical simulations and detailed asymptotic analysis of the process reveal a self-similar structure both for the velocity field and the pressure field. The latter is shown to exhibit a maximum not near the impact point, but rather at the contact line. The motion of the contact line is furthermore shown to exhibit a 'tank treading' motion. These observations are apprehended at the light of a variant of Wagner theory for liquid impact. This framework offers a simple analogy where the fluid motion within the impacting drop may be viewed as the flow induced by a flat rising expanding disk. The theoretical predictions are found to be in very close agreement both qualitatively and quantitatively with the numerical observations for about three decades in time. Interestingly the inviscid self-similar impact pressure and velocities are shown to depend solely on the self-similar variables $(r/\\sqrt{t},z/\\sqrt{t})$. The structure of the boun...
Self-similar cosmological solutions with dark energy. I. Formulation and asymptotic analysis
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 0antigravity. 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.
Asymptotic self-similar solutions with a characteristic time-scale
Waxman, Eli
2010-01-01
For a wide variety of initial and boundary conditions, adiabatic one dimensional flows of an ideal gas approach self-similar behavior when the characteristic length scale over which the flow takes place, $R$, diverges or tends to zero. It is commonly assumed that self-similarity is approached since in the $R\\to\\infty(0)$ limit the flow becomes independent of any characteristic length or time scales. In this case the flow fields $f(r,t)$ must be of the form $f(r,t)=t^{\\alpha_f}F(r/R)$ with $R\\propto(\\pm t)^\\alpha$. We show that requiring the asymptotic flow to be independent only of characteristic length scales imply a more general form of self-similar solutions, $f(r,t)=R^{\\delta_f}F(r/R)$ with $\\dot{R}\\propto R^\\delta$, which includes the exponential ($\\delta=1$) solutions, $R\\propto e^{t/\\tau}$. We demonstrate that the latter, less restrictive, requirement is the physically relevant one by showing that the asymptotic behavior of accelerating blast-waves, driven by the release of energy at the center of a co...
Some topics on Ricci solitons and self-similar solutions to mean curvature flow
Futaki, Akito
2012-01-01
In this survey article, we discuss some topics on self-similar solutions to the Ricci flow and the mean curvature flow. Self-similar solutions to the Ricci flow are known as Ricci solitons. In the first part of this paper we discuss a lower diameter bound for compact manifolds with shrinking Ricci solitons. Such a bound can be obtained from an eigenvalue estimate for a twisted Laplacian, called the Witten-Laplacian. In the second part we discuss self-similar solutions to the mean curvature flow on cone manifolds. Many results have been obtained for solutions in $\\bfR^n$ or $\\bfC^n$. We see that many of them extend to cone manifolds, and in particular results on $\\bfC^n$ for special Lagrangians and self-shrinkers can be extended to toric Calabi-Yau cones. We also see that a similar lower diameter bound can be obtained for self-shrinkers to the mean curvature flow as in the case of shrinking Ricci solitons.
Self-similarities of periodic structures for a discrete model of a two-gene system
Energy Technology Data Exchange (ETDEWEB)
Souza, S.L.T. de, E-mail: thomaz@ufsj.edu.br [Departamento de Física e Matemática, Universidade Federal de São João del-Rei, Ouro Branco, MG (Brazil); Lima, A.A. [Escola de Farmácia, Universidade Federal de Ouro Preto, Ouro Preto, MG (Brazil); Caldas, I.L. [Instituto de Física, Universidade de São Paulo, São Paulo, SP (Brazil); Medrano-T, R.O. [Departamento de Ciências Exatas e da Terra, Universidade Federal de São Paulo, Diadema, SP (Brazil); Guimarães-Filho, Z.O. [Aix-Marseille Univ., CNRS PIIM UMR6633, International Institute for Fusion Science, Marseille (France)
2012-03-12
We report self-similar properties of periodic structures remarkably organized in the two-parameter space for a two-gene system, described by two-dimensional symmetric map. The map consists of difference equations derived from the chemical reactions for gene expression and regulation. We characterize the system by using Lyapunov exponents and isoperiodic diagrams identifying periodic windows, denominated Arnold tongues and shrimp-shaped structures. Period-adding sequences are observed for both periodic windows. We also identify Fibonacci-type series and Golden ratio for Arnold tongues, and period multiple-of-three windows for shrimps. -- Highlights: ► The existence of noticeable periodic windows has been reported recently for several nonlinear systems. ► The periodic window distributions appear highly organized in two-parameter space. ► We characterize self-similar properties of Arnold tongues and shrimps for a two-gene model. ► We determine the period of the Arnold tongues recognizing a Fibonacci-type sequence. ► We explore self-similar features of the shrimps identifying multiple period-three structures.
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.
Neural processing of race during imitation: self-similarity versus social status.
Losin, Elizabeth A Reynolds; Cross, Katy A; Iacoboni, Marco; Dapretto, Mirella
2014-04-01
People preferentially imitate others who are similar to them or have high social status. Such imitative biases are thought to have evolved because they increase the efficiency of cultural acquisition. Here we focused on distinguishing between self-similarity and social status as two candidate mechanisms underlying neural responses to a person's race during imitation. We used fMRI to measure neural responses when 20 African American (AA) and 20 European American (EA) young adults imitated AA, EA and Chinese American (CA) models and also passively observed their gestures and faces. We found that both AA and EA participants exhibited more activity in lateral frontoparietal and visual regions when imitating AAs compared with EAs or CAs. These results suggest that racial self-similarity is not likely to modulate neural responses to race during imitation, in contrast with findings from previous neuroimaging studies of face perception and action observation. Furthermore, AA and EA participants associated AAs with lower social status than EAs or CAs, suggesting that the social status associated with different racial groups may instead modulate neural activity during imitation of individuals from those groups. Taken together, these findings suggest that neural responses to race during imitation are driven by socially learned associations rather than self-similarity. This may reflect the adaptive role of imitation in social learning, where learning from higher status models can be more beneficial. This study provides neural evidence consistent with evolutionary theories of cultural acquisition.
Accretion disk dynamics: {\\alpha}-viscosity in self-similar self-gravitating models
Kubsch, Marcus; Duschl, W J
2016-01-01
Aims: We investigate the suitability of {\\alpha}-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 {\\alpha}-disks and derive the significant quantities. In the Keplerian part of the disk our model is consistent with standard stationary {\\alpha}-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: {\\alpha}-viscosity cannot account for the evolution of the whole mass spectrum of super-massive black holes (SMBH) in AGN. However, conside...
Self-similar solutions for the Hasselmann equation and experimental scaling of wind-wave spectra
Badulin, S. I.; Pushkarev, A. N.; Resio, D.; Zakharov, V. E.
2003-04-01
The solutions for the Hasselmann equation (kinetic equation for wind-driven waves) are studied numerically for the case of duration-limited growth and different conventional parameterizations of wave sources and sinks (Snyderet al. 1981; Plant 1982; Hsiao &Shemdin 1983; Komen, Hasselmann & Hasselmann 1984; Donelan, Pierson 1987). The strong self-similar behavior of the numerical solutions is found for all the parameterizations in a wide range of wind speeds and wave ages. Moreover, the resulting self-similar solutions are found to be surprisingly close to experimentally established approximations in magnitudes and shapes of frequency spectra. The comparison with JONSWAP modified spectra (Donelan et al. 1985) is detailed. It is found that this approximation being obtained for the case of fetch-limited growth fits quite well the corresponding spectra for the numerical duration limited solutions in a wide range of wave ages (C_p/U10 ≈ 0.4div 1.4 ). Theoretical overview of self-similar solutions for the kinetic equation is given in its relation to the experimentally observed dependencies of mean parameters (i.e. mean energy, frequency) of wind-driven waves both in cases of fetch-limited and duration limited growth. Universality features of the dependencies are treated as a result of dominating nonlinear transfer in wind-wave field. The research was conducted under the U.S. Army Corps of Engineers, RDT&E program, grant DACA 42-00-C0044, ONR grant N00014-98-1-0070 and NSF grant NDMS0072803, INTAS grant 01-234 and Russian Foundation for Basic Research 01-05-64603, 01-05-64464, 02-05-65140. This support is gratefully acknowledged.
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.
Self-Similar Earthquake Nucleation on Rate-and-State Faults
Rubin, A. M.; Ampuero, J.
2004-12-01
We obtain self-similar solutions (two-dimensional and quasi-static) for the acceleration to instability of a fixed-length patch on a fault obeying rate-and-state friction. The solution is applicable in the limit Vθ /Dc≫1, so that the evolution of the state variable is well-approximated by ˙ {θ }=Vθ /Dc. For simulations on an infinite fault with a/brate but time-varying peak and residual stresses. The nucleation length in these cases (defined as the minimum of the time-dependent size of the nucleation zone) generally increases with a/b but is very sensitive to the boundary and initial conditions. For sufficiently large values of Vθ /Dc upon localization, the nucleation zone can undergo velocity increases of many orders of magnitude before the self-similar solution becomes inapplicable; this is why this solution dominates the simulations of Dieterich [1992] even for a/b\\sim0.9. For a/b$0, so they could be applicable to faults shorter than Lν . The smallest viable nucleation zone Lmin increases in size with increasing a/b and equals Lν at a/b=0.3781. For a=0, which in the limit Vθ /Dc\\gg1 corresponds to slip-weakening behavior, L_{min} equals the universal nucleation length of 0.579G^*D_c/b\\sigma found for slip-weakening behavior by Uenishi and Rice [2003] (the slip-weakening rate is b\\sigma/D_c). The family of self-similar solutions can thus be viewed as linking the observation of Dieterich [1992] that L_\
Kagan, Grigory; Rinderknecht, H G; Rosenberg, M J; Zylstra, A B; Huang, C -K
2015-01-01
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 hydro-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 National Ignition Facility.
Dimensional analysis and self-similarity methods for engineers and scientists
Zohuri, Bahman
2015-01-01
This ground-breaking reference provides an overview of key concepts in dimensional analysis, and then pushes well beyond traditional applications in fluid mechanics to demonstrate how powerful this tool can be in solving complex problems across many diverse fields. Of particular interest is the book's coverage of dimensional analysis and self-similarity methods in nuclear and energy engineering. Numerous practical examples of dimensional problems are presented throughout, allowing readers to link the book's theoretical explanations and step-by-step mathematical solutions to practical impleme
2.5-dimensional solution of the advective accretion disk:a self-similar approach
Institute of Scientific and Technical Information of China (English)
Shubhrangshu Ghosh; Banibrata Mukhopadhyay
2009-01-01
We provide a 2.5-dimensional solution to a complete set of viscous hydrodynamical equations describing accretion-induced outflows and plausible jets around black holes/compact objects. We prescribe a self-consistent advective disk-outflow coupling model, which explicitly includes the information of vertical flux. Inter-connecting dynamics of an inflow-outflow system essentially upholds the conservation laws. We provide a set of analytical family of solutions through a self-similar approach. The flow parameters of the disk-outflow system depend strongly on the viscosity parameter α and the cooling factor f.
Prediction of oil contamination distribution in aquifers using self similar solutions
Pistiner, Arieh
2016-12-01
Oil contaminant migration in an aquifer is analyzed by applying some power law relationships between the porous medium parameters and oil saturation. Such an application generates a self-similar model whose solutions are used to analyze the effect of the porous structure and the oil properties on the oil migration in the aquifer. By using hypothetical saturation data, the model was used to find the characteristic length and time scales of the aquifer, and then to predict the temporal saturation distribution of the oil contamination in the aquifer.
Self-similar solutions for a superdiffusive heat equation with gradient nonlinearity
Directory of Open Access Journals (Sweden)
Marcelo Fernandes de Almeida
2016-09-01
Full Text Available This article studies the existence, stability, self-similarity and symmetries of solutions for a superdiffusive heat equation with superlinear and gradient nonlinear terms with initial data in new homogeneous Besov-Morrey type spaces. Unlike in previous works on such time-fractional partial differential equations of order $\\alpha\\in(1,2$, we take non null initial velocities into consideration, where new difficulties arise from. We overcome them by developing an appropriate decomposition of the two-parametric Mittag-Leffler function to obtain Mikhlin-type estimates and obtain our existence theorem.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Wavelet transform is used to analyze the scaling rule convection flow from two aspects. By utilizing the method of extended self similarity (ESS), one can find the obtained scaling exponent agrees well with the one obtained from the temperature data in a experiment of wind tunnel. And then we propose a newly defined formula based on wavelet transform, and can determine the scaling exponent ξ(q) of temperature data. The obtained results demonstrate that we can correctly extract ξ(q) by using the method which is named as wavelet transform maximum modulus (WTMM).``
Self-similar spatial structure of a streamer-free nanosecond discharge
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.
Stable Self-Similar Blow-Up Dynamics for Slightly {L^2}-Supercritical Generalized KDV Equations
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-similarity and helical symmetry in vortex generator flow simulations
DEFF Research Database (Denmark)
Fernandez, U.; Velte, Clara Marika; Réthoré, Pierre-Elouan;
2012-01-01
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 (u) velocity profiles. Further, the measured vortices have been observed to obey the criteria for helical symmetry...... 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-Similarity and helical symmetry in vortex generator flow simulations
DEFF Research Database (Denmark)
Fernandez, U.; Velte, Clara Marika; Réthoré, Pierre-Elouan;
2014-01-01
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 (uӨ) velocity profiles. Further, the measured vortices have been observed to obey the criteria for helical symmetry...... 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....
Quantum singularity structure of a class of continuously self-similar spacetimes
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.
Magnetic collimation of meridional-self-similar general relativistic MHD flows
Globus, Noemie; Sauty, Christophe; Cayatte, Véronique; Celnikier, Ludwik M.
2014-06-01
We present a model for the spine of relativistic Magnetohydrodynamics outflows in the Kerr geometry. Meridional self-similarity is invoked to derive semianalytical solutions close to the polar axis. The study of the energy conservation along a particular field line gives a simple criterion for the collimation of jets. Such parameter have already been derived in the classical case by Sauty et al. 1999 and also extended to the Schwarzschild metric by Meliani et al. 2006. We generalize the same study to the Kerr metric. We show that the rotation of the black hole increases the magnetic self-confinement.
Magnetic collimation of meridional-self-similar general relativistic MHD flows
Globus, Noemie; Cayatte, Véronique; Celnikier, Ludwik M
2014-01-01
We present a model for the spine of relativistic MHD outflows in the Kerr geometry. Meridional self-similarity is invoked to derive semi-analytical solutions close to the polar axis. The study of the energy conservation along a particular field line gives a simple criterion for the collimation of jets. Such parameter have already been derived in the classical case by Sauty et al. 1999 and also extended to the Schwarzschild metric by Meliani et al. 2006. We generalize the same study to the Kerr metric. We show that the rotation of the black hole increases the magnetic self-confinement.
Power laws and self-similar behaviour in negative ionization fronts
Energy Technology Data Exchange (ETDEWEB)
Arrayas, Manuel [Departamento de Matematicas y Fisica Aplicadas y Ciencias de la Naturaleza, Universidad Rey Juan Carlos, Tulipan s/n, 28933 Mostoles, Madrid (Spain); Fontelos, Marco A [Departamento de Matematicas, Universidad Autonoma de Madrid, 28049 Cantoblanco, Madrid (Spain); Trueba, Jose L [Departamento de Matematicas y Fisica Aplicadas y Ciencias de la Naturaleza, Universidad Rey Juan Carlos, Tulipan s/n, 28933 Mostoles, Madrid (Spain)
2006-06-09
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.
A statistical hiding algorithm based on self-similar network traffic
Institute of Scientific and Technical Information of China (English)
SHA Xue-jun; XU Yu-bin; QIANG Wei
2008-01-01
Although the encryption of network packets significantly increases privacy, the density of the traffic can still provide useful information to the observer, and maybe results in the breach of confidentiality. In this paper, we address issues related to hiding information in self-similar network, which is proved to be similar with modem communication network. And a statistical hiding algorithm is proposed for traffic padding. The figures and the comparison of Hurst Parameters before and after traffic padding, show the effective performance of the algorithm.
Topological Self-Similar Networks Introduced by Diffusion-Limited Aggregation Mechanism
Institute of Scientific and Technical Information of China (English)
YANG Lei; PEI Wen-Jiang; LI Tao; CHEUNG Yiu-Ming; HE Zhen-Ya
2008-01-01
@@ We propose a model for growing fractal networks based on the mechanisms learned from the diffusion-limited aggregation (DLA) model in fractal geometries in the viewpoint of network.By studying the DLA network,our model introduces multiplicative growth,aging and geographical preferential attachment mechanisms,whereby featuring topological self-similar property and hierarchical modularity.According to the results of theoretical analysis and simulation,the degree distribution of the proposed model shows a mixed degree distribution (i.e.,exponential and algebraic degree distribution) and the fractal dimension and clustering coefficient can be tuned by changing the values of parameters.
Gold Nanoparticle Self-Similar Chain Structure Organized by DNA Origami
Energy Technology Data Exchange (ETDEWEB)
Ding, Baoquan; Deng, Zhengtao; Yan, Hao; Cabrini, Stefano; Zuckermann, Ronald N.; Bokor, Jeffrey
2010-03-17
Here we demonstrate Au nanoparticle self-similar chain structure organized by triangle DNA origami with well-controlled orientation and <10 nm spacing. We show for the first time that a large DNA complex (origami) and multiple AuNP conjugates can be well-assembled and purified with reliable yields. The assembled structure could be used to generate high local-field enhancement. The same method can be used to precisely localize multiple components on a DNA template for potential applications in nanophotonic, nanomagnetic, and nanoelectronic devices.
Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
This paper investigates the Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets D = (r1D) ∪ (r2D + (1 + r1 - r2 - r3)/2) ∪ (r3D + 1 - r3) and E = (r1E) ∪ (r2E + 1 - r2 -r3) ∪ (r3E + 1 - r3),and proves that D and E areLipschitz equivalent if and only if there are positive integers m and n such that rm1= rn3.
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.
Self-similar solution of the subsonic radiative heat equations using a binary equation of state
Heizler, Shay I.; Shussman, Tomer; Malka, Elad
2016-01-01
Radiative subsonic heat waves, and their radiation driven shock waves, are important hydro-radiative phenomena. The high pressure, causes hot matter in the rear part of the heat wave to ablate backwards. At the front of the heat wave, this ablation pressure generates a shock wave which propagates ahead of the heat front. Although no self-similar solution of both the ablation and shock regions exists, a solution for the full problem was found in a previous work. Here, we use this model in orde...
Heat conduction: hyperbolic self-similar shock-waves in solids
Barna, Imre Ferenc
2012-01-01
Analytic solutions for cylindrical thermal waves in solid medium is given based on the nonlinear hyperbolic system of heat flux relaxation and energy conservation equations. The Fourier-Cattaneo phenomenological law is generalized where the relaxation time and heat propagation coefficient have a general power law temperature dependence. From such laws one cannot form a second order parabolic or telegraph-type equation. We consider the original non-linear hyperbolic system itself with the self-similar Ansatz for the temperature distribution and for the heat flux. As results continuous and shock-wave solutions are presented. For physical establishment numerous materials with various temperature dependent heat conduction coefficients are mentioned.
Zeng, Z. Y.; Claro, F.
2002-02-01
We study the transport of electrons in a Fibonacci magnetic superlattice produced on a two-dimensional electron gas modulated by parallel magnetic-field stripes arranged in a Fibonacci sequence. Both the transmission coefficient and conductance exhibit self similarity and the six-circle property. The presence of extended states yields a finite conductivity at infinite length, that may be detected as an abrupt change in the conductance as the Fermi energy is varied, much as a metal-insulator transition. This is a unique feature of transport in this kind of structure, arising from its inherent two-dimensional nature.
Flow rate of particles through apertures obtained from self-similar density and velocity profiles
2012-01-01
‘‘Beverloo’s law’’ is considered as the standard expression to estimate the ﬂow rate of particles through apertures. This relation was obtained by simple dimensional analysis and includes empirical parameters whose physical meaning is poorly justiﬁed. In this Letter, we study the density and velocity proﬁles in the ﬂow of particles through an aperture. We ﬁnd that, for the whole range of apertures studied, both proﬁles are self-similar. Hence, by means of the functionality obtained for the...
Zheng, Yuanjie; Hunter, Allan A; Wu, Jue; Wang, Hongzhi; Gao, Jianbin; Maguire, Maureen G; Gee, James C
2011-01-01
In this paper, we address the problem of landmark matching based retinal image registration. Two major contributions render our registration algorithm distinguished from many previous methods. One is a novel landmark-matching formulation which enables not only a joint estimation of the correspondences and transformation model but also the optimization with linear programming. The other contribution lies in the introduction of a reinforced self-similarities descriptor in characterizing the local appearance of landmarks. Theoretical analysis and a series of preliminary experimental results show both the effectiveness of our optimization scheme and the high differentiating ability of our features.
ON THE EXACT HAUSDORFF MEASURE OF A CLASS OF SELF-SIMILAR SETS SATISFYING OPEN SET CONDITION
Institute of Scientific and Technical Information of China (English)
Shaoyuan Xu; Weiyi Su; Zuoling Zhou
2008-01-01
In this paper,we provide a new effective method for computing the exact value of Hausdorff measures of a class of self-similar sets satisfying the open set condition(OSC).As applications,we discuss a self-similar Cantor set satisfying OSC and give a simple method for computing its exact Hausdorff measure.
3D simulations of disc-winds extending radially self-similar MHD models
Stute, Matthias; Vlahakis, Nektarios; Tsinganos, Kanaris; Mignone, Andrea; Massaglia, Silvano
2014-01-01
Disc-winds originating from the inner parts of accretion discs are considered as the basic component of magnetically collimated outflows. The only available analytical MHD solutions to describe disc-driven jets are those characterized by the symmetry of radial self-similarity. However, radially self-similar MHD jet models, in general, have three geometrical shortcomings, (i) a singularity at the jet axis, (ii) the necessary assumption of axisymmetry, and (iii) the non-existence of an intrinsic radial scale, i.e. the jets formally extend to radial infinity. Hence, numerical simulations are necessary to extend the analytical solutions towards the axis, by solving the full three-dimensional equations of MHD and impose a termination radius at finite radial distance. We focus here on studying the effects of relaxing the (ii) assumption of axisymmetry, i.e. of performing full 3D numerical simulations of a disc-wind crossing all magnetohydrodynamic critical surfaces. We compare the results of these runs with previou...
Self-similar fast-reaction limits for reaction-diffusion systems on unbounded domains
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.
Robustness of Estimators of Long-Range Dependence and Self-Similarity under non-Gaussianity
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.
Spectral Analysis of Multi-dimensional Self-similar Markov Processes
Modarresi, N
2009-01-01
In this paper we consider a wide sense discrete scale invariant process with scale $l>1$. We consider to have $T$ samples at each scale, and choose $\\alpha$ by the equality $l=\\alpha^T$. Our special scheme of sampling is to choose our samples at discrete points $\\alpha^k, k\\in W$. So we provide a discrete time wide sense scale invariant(DT-SI) process. We find the spectral representation of the covariance function of such DT-SI process. By providing harmonic like representation of multi-dimensional self-similar processes, spectral density function of them are presented. We also consider a discrete time scale invariance Markov(DT-SIM) process with the above scheme of sampling at points $\\alpha^k, k\\in {\\bf W}$ and show that the spectral density matrix of DT-SIM process and its associated $T$-dimensional self-similar Markov process is fully specified by $\\{R_{j}^H(1),R_{j}^H(0),j=0, 1, ..., T-1\\}$ where $R_{j}^H(\\tau)=\\mathrm{Cov}\\big(X(\\alpha^{j+\\tau}),X(\\alpha^j)\\big)$
CAN AGN FEEDBACK BREAK THE SELF-SIMILARITY OF GALAXIES, GROUPS, AND CLUSTERS?
Energy Technology Data Exchange (ETDEWEB)
Gaspari, M. [Max Planck Institute for Astrophysics, Karl-Schwarzschild-Strasse 1, D-85741 Garching (Germany); Brighenti, F. [Astronomy Department, University of Bologna, Via Ranzani 1, I-40127 Bologna (Italy); Temi, P. [Astrophysics Branch, NASA/Ames Research Center, MS 245-6, Moffett Field, CA 94035 (United States); Ettori, S., E-mail: mgaspari@mpa-garching.mpg.de [INAF, Osservatorio Astronomico di Bologna, Via Ranzani 1, I-40127 Bologna (Italy)
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.
Magnetic Helicity of Self-Similar Axisymmetric Force-free Fields
Zhang, Mei; Low, Boon Chye
2012-01-01
In this paper we continue our theoretical studies on addressing what are the possible consequences of magnetic helicity accumulation in the solar corona. Our previous studies suggest that coronal mass ejections (CMEs) are natural products of coronal evolution as a consequence of magnetic helicity accumulation and the triggering of CMEs by surface processes such as flux emergence also have their origin in magnetic helicity accumulation. Here we use the same mathematical approach to study the magnetic helicity of axisymmetric power-law force-free fields, but focus on a family whose surface flux distributions are defined by self-similar force-free fields. The semi-analytical solutions of the axisymmetric self-similar force-free fields enable us to discuss the properties of force-free fields possessing a huge amount of accumulated magnetic helicity. Our study suggests that there may be an absolute upper bound on the total magnetic helicity of all bipolar axisymmetric force-free fields. And with the increase of ac...
Relativistic Self-similar Dynamic Collapses of Black Holes in General Polytropic Spherical Clouds
Lian, Biao
2013-01-01
We study the hydrodynamic self-similar mass collapses of general polytropic (GP) spherical clouds to central Schwarzschild black holes and void evolution with or without shocks. In order to grossly capture characteristic effects of general relativity (GR) outside yet close to the event horizon of a Schwarzschild black hole and to avoid mathematical complexity, we adopt the approximation of the Paczynski-Wiita gravity to replace the simple Newtonian gravity in our model formulation. A new dimensionless parameter s appears with the physical meaning of the square of the ratio of the sound speed to the speed of light $c$. Various self-similar dynamic solutions are constructed for a polytropic index $\\gamma>4/3$. Two (for small enough $s4/3$, representing the collapse of static singular GP spheres towards the central singularity of spacetime. Such GP spherical dynamic mass collapse is shown to be highly efficient for the rapid formation of supermassive black holes (SMBHs; mass range of $10^6-10^{10}M_{\\odot}$) in ...
Self-similar cosmological solutions with dark energy I: formulation and asymptotic analysis
Harada, Tomohiro; Carr, B J
2007-01-01
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 $p=(\\gamma -1)\\mu$ with $01$). 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 {\\it genuinely} asymptotically Friedmann at large distances. We find eight classes of asymptotic behavior: Friedmann or quasi-Friedmann or quasi-static or constant-velocity at large distances, quasi-Friedmann or positive-mass singular or negative-mass singular at small distances, or quasi-Kantowski-Sachs at intermediate distances. The self-similar asymptotica...
Self-similarity of phase-space networks of frustrated spin models and lattice gas models
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
Primordial black hole formation in the early universe: critical behaviour and self-similarity
Musco, Ilia
2012-01-01
Following on after three previous papers discussing the formation of primordial black holes during the radiation-dominated era of the early universe, we present here a further investigation of the critical nature of the collapse. In particular, we focus on the long-lived intermediate state, which appears in collapses of perturbations close to the critical limit, and examine the extent to which this follows a similarity solution, as seen for critical collapse under more idealized circumstances (rather than within the context of an expanding universe, as studied here). We find that a similarity solution is indeed realised, to good approximation, for a region contained within the past light-cone of the forming black hole (and eventual singularity). The self-similarity is not exact, however, and this is explained by the presence within the light-cone of some outer matter still coupled to the expanding universe, which does not participate in the self-similarity. Our main interest, from a cosmological point of view...
QoS Analysis of a Storage System with Self-similar Input
Institute of Scientific and Technical Information of China (English)
RAOYunhua; ZOUXuecheng
2004-01-01
Packet delay, jitter and loss rate of a storage system with self-similar traffic input is analyzed, which is related to QoS (Quality of service). At first, the storage model with First in first out (FIFO) service discipline and Fractional autoregressive integrated moving average(FARIMA) traffic input which comprises Long-range dependence (LRD) and Short-range dependence (SRD) simultaneity is proposed. Then based on large deviation technique, analytic overflow probability formula of this storage model is obtained, which is related to traffic time scale. Meanwhile, packet delay and jitter analytic formulas are also obtained. Studies show that both SRD and LRD traffic will influence QoS parameters. The effect of traffic SRD on system performance at small time scales is related to storage system parameters. And when the time scale of aggregated traffic is large enough, LRD character of traffic begins to dominate the impaction on system QoS.Monte-Carlo simulations confirm the validity of the above results. Because of self-similarity in network traffic, the performance of storage system can be influenced greatly,which is quite different from that of Markov model and must be considered in network QoS provision.
Self-similar solution of the subsonic radiative heat equations using a binary equation of state
Heizler, Shay I; Malka, Elad
2016-01-01
Radiative subsonic heat waves, and their radiation driven shock waves, are important hydro-radiative phenomena. The high pressure, causes hot matter in the rear part of the heat wave to ablate backwards. At the front of the heat wave, this ablation pressure generates a shock wave which propagates ahead of the heat front. Although no self-similar solution of both the ablation and shock regions exists, a solution for the full problem was found in a previous work. Here, we use this model in order to investigate the effect of the equation of state (EOS) on the propagation of radiation driven shocks. We find that using a single ideal gas EOS for both regions, as used in previous works, yields large errors in describing the shock wave. We use the fact that the solution is composed of two different self-similar solutions, one for the ablation region and one for the shock, and apply two ideal gas EOS (binary-EOS), one for each region, by fitting a detailed tabulated EOS to power laws at different regimes. By comparin...
Discrete self-similarity and critical point behavior in fluctuations about extremal black holes
Traschen, Jennie
1994-12-01
The issues of scaling symmetry and critical point behavior are studied for fluctuations about extremal charged black holes. We consider the scattering and capture of the spherically symmetric mode of a charged, massive test field on the background spacetime of a black hole with charge Q and mass M. The spacetime geometry near the horizon of a ||Q||=M black hole has a scaling symmetry, which is absent if ||Q||scale being introduced by the surface gravity. We show that this symmetry leads to the existence of a self-similar solution for the charged field near the horizon, and further, that there is a one parameter family of discretely self-similar solutions. The scaling symmetry, or lack thereof, also shows up in correlation length scales, defined in terms of the rate at which the influence of an external source coupled to the field dies off. It is shown by constructing the Green's functions that an external source has a long range influence on the extremal background, compared to a correlation length scale which falls off exponentially fast in the ||Q||0 in the background spacetime, infinitesimal changes in the black hole area vary like Δ1/2.
Odd-parity perturbations of the self-similar LTB spacetime
Energy Technology Data Exchange (ETDEWEB)
Duffy, Emily M; Nolan, Brien C, E-mail: emilymargaret.duffy27@mail.dcu.ie, E-mail: brien.nolan@dcu.ie [School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9 (Ireland)
2011-05-21
We consider the behaviour of odd-parity perturbations of those self-similar LemaItre-Tolman-Bondi spacetimes which admit a naked singularity. We find that a perturbation which evolves from initially regular data remains finite on the Cauchy horizon. Finiteness is demonstrated by considering the behaviour of suitable energy norms of the perturbation (and pointwise values of these quantities) on natural spacelike hypersurfaces. This result holds for a general choice of initial data and initial data surface. Finally, we examine the perturbed Weyl scalars in order to provide a physical interpretation of our results. Taken on its own, this result does not support cosmic censorship; however, a full perturbation of this spacetime would include even-parity perturbations, so we cannot conclude that this spacetime is stable to all linear perturbations.
Analytic self-similar solutions of the Oberbeck-Boussinesq equations
Barna, I. F.; Mátyás, L.
2015-09-01
In this article we will present pure two-dimensional analytic solutions for the coupled non-compressible Newtoniain Navier-Stokes --- with Boussinesq approximation --- and the heat conduction equation. The system was investigated from E.N. Lorenz half a century ago with Fourier series and pioneered the way to the paradigm of chaos. We present a novel analysis of the same system where the key idea is the two-dimensional generalization of the well-known self-similar Ansatz of Barenblatt which will be interpreted in a geometrical way. The results, the pressure, temperature and velocity fields are all analytic and can be expressed with the help of the error functions. The temperature field has a strongly damped oscillating behavior which is an interesting feature.
Possible Implications of a Vortex Gas Model and Self-Similarity for Tornadogenesis and Maintenance
Dokken, Doug; Shvartsman, Misha; Běl\\'\\ik, Pavel; Potvin, Corey; Dahl, Brittany; McGover, Amy
2014-01-01
We describe tornado genesis and maintenance using the 3-dimensional vortex gas model presented in Chorin (1994). High-energy vortices with negative temperature in the sense of Onsager (1949) play an important role in the model. We speculate that the formation of high-temperature vortices is related to the helicity inherited as they form or tilt into the vertical. We also exploit the notion of self-similarity to justify power laws derived from observations of weak and strong tornadoes presented in Cai (2005), Wurman and Gill (2000), and Wurman and Alexander (2005). Analysis of a Bryan Cloud Model (CM1) simulation of a tornadic supercell reveals scaling consistent with the observational studies.
Analytic self-similar solutions of the Oberbeck-Boussinesq equations
Barna, I F
2015-01-01
In this article we will present pure two-dimensional analytic solutions for the coupled non-compressible Newtoniain Navier-Stokes --- with Boussinesq approximation --- and the heat conduction equation. The system was investigated from E.N. Lorenz half a century ago with Fourier series and pioneered the way to the paradigm of chaos. We present a novel analysis of the same system where the key idea is the two-dimensional generalization of the well-known self-similar Ansatz of Barenblatt which will be interpreted in a geometrical way. The results, the pressure, temperature and velocity fields are all analytic and can be expressed with the help of the error functions. The temperature field has a strongly damped oscillating behavior which is an interesting feature.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The problem of state space explosion is still an outstanding challenge in Markovian performance analysis for multiserver multiqueue (MSMQ) systems. The system behavior of a MSMQ system is described using stochastic high-level Petri net (SHLPN) models, and an approximate performance analysis technique is proposed based on decomposition and refinement methods as well as iteration technique. A real MSMQ system, Web-server cluster, is investigated. The performance of an integrated scheme of request dispatching and scheduling is analyzed with both Poisson and self-similar request arrivals. The study shows that the approximate analysis technique significantly reduces the complexity of the model solution and is also efficient for accuracy of numerical results.
Self-similarity, conservation of entropy/bits and the black hole information puzzle
Energy Technology Data Exchange (ETDEWEB)
Singleton, Douglas [Department of Physics, California State University Fresno,2345 East San Ramon Avenue M/S MH37, Fresno, CA 93740-8031 (United States); Department of Physics, Institut Teknologi Bandung,Jalan Ganesha 10, Bandung 40132 (Indonesia); Vagenas, Elias C. [Theoretical Physics Group, Department of Physics, Kuwait University,P.O. Box 5969, Safat 13060 (Kuwait); Zhu, Tao [GCAP-CASPER, Physics Department, Baylor University,One Bear Place, # 97316, Waco, TX 76798-7316 (United States); Institute for Advanced Physics & Mathematics, Zhejiang University of Technology,18 Chao-Wang Rd, Hangzhou, 310032 (China)
2014-05-19
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.
Differing self-similarity in light scattering spectra: A potential tool for pre-cancer detection
Ghosh, Sayantan; Purwar, Harsh; Jagtap, Jaidip; Pradhan, Asima; Ghosh, Nirmalya; Panigrahi, Prasanta K
2011-01-01
The fluctuations in the elastic light scattering spectra of normal and dysplastic human cervical tissues analyzed through wavelet transform based techniques reveal clear signatures of self-similar behavior in the spectral fluctuations. Significant differences in the power law behavior ascertained through the scaling exponent was observed in these tissues. The strong dependence of the elastic light scattering on the size distribution of the scatterers manifests in the angular variation of the scaling exponent. Interestingly, the spectral fluctuations in both these tissues showed multi-fractality (non-stationarity in fluctuations), the degree of multi-fractality being marginally higher in the case of dysplastic tissues. These findings using the multi-resolution analysis capability of the discrete wavelet transform can contribute to the recent surge in the exploration for non-invasive optical tools for pre-cancer detection.
Bianchi VI{sub 0} and III models: self-similar approach
Energy Technology Data Exchange (ETDEWEB)
Belinchon, Jose Antonio, E-mail: abelcal@ciccp.e [Departamento de Fisica, ETS Arquitectura, UPM, Av. Juan de Herrera 4, Madrid 28040 (Spain)
2009-09-07
We study several cosmological models with Bianchi VI{sub 0} and III symmetries under the self-similar approach. We find new solutions for the 'classical' perfect fluid model as well as for the vacuum model although they are really restrictive for the equation of state. We also study a perfect fluid model with time-varying constants, G and LAMBDA. As in other studied models we find that the behaviour of G and LAMBDA are related. If G behaves as a growing time function then LAMBDA is a positive decreasing time function but if G is decreasing then LAMBDA{sub 0} is negative. We end by studying a massive cosmic string model, putting special emphasis in calculating the numerical values of the equations of state. We show that there is no SS solution for a string model with time-varying constants.
Self-similar accelerative propagation of expanding wrinkled flames and explosion triggering.
Akkerman, V'yacheslav; Law, Chung K; Bychkov, Vitaly
2011-02-01
The formulation of Taylor on the self-similar propagation of an expanding spherical piston with constant velocity was extended to an instability-wrinkled deflagration front undergoing acceleration with R(F)∝t(α), where R(F) is the instantaneous flame radius, t the time, and α a constant exponent. The formulation describes radial compression waves pushed by the front, trajectories of gas particles, and the explosion condition in the gas upstream of the front. The instant and position of explosion are determined for a given reaction mechanism. For a step-function induction time, analytic formulas for the explosion time and position are derived, showing their dependence on the reaction and flow parameters including thermal expansion, specific heat ratio, and acceleration of the front.
Directory of Open Access Journals (Sweden)
Gianni Pagnini
2012-01-01
inhomogeneity and nonstationarity properties of the medium. For instance, when this superposition is applied to the time-fractional diffusion process, the resulting Master Equation emerges to be the governing equation of the Erdélyi-Kober fractional diffusion, that describes the evolution of the marginal distribution of the so-called generalized grey Brownian motion. This motion is a parametric class of stochastic processes that provides models for both fast and slow anomalous diffusion: it is made up of self-similar processes with stationary increments and depends on two real parameters. The class includes the fractional Brownian motion, the time-fractional diffusion stochastic processes, and the standard Brownian motion. In this framework, the M-Wright function (known also as Mainardi function emerges as a natural generalization of the Gaussian distribution, recovering the same key role of the Gaussian density for the standard and the fractional Brownian motion.
A fully nonlinear iterative solution method for self-similar potential flows with a free boundary
Iafrati, Alessandro
2013-01-01
An iterative solution method for fully nonlinear boundary value problems governing self-similar flows with a free boundary is presented. Specifically, the method is developed for application to water entry problems, which can be studied under the assumptions of an ideal and incompressible fluid with negligible gravity and surface tension effects. The approach is based on a pseudo time stepping procedure, which uses a boundary integral equation method for the solution of the Laplace problem governing the velocity potential at each iteration. In order to demonstrate the flexibility and the capabilities of the approach, several applications are presented: the classical wedge entry problem, which is also used for a validation of the approach, the block sliding along an inclined sea bed, the vertical water entry of a flat plate and the ditching of an inclined plate. The solution procedure is also applied to cases in which the body surface is either porous or perforated. Comparisons with numerical or experimental d...
Self-similar Evolution of Self-Gravitating Viscous Accretion Discs
Illenseer, Tobias F
2015-01-01
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 sma...
Self-similar prior and wavelet bases for hidden incompressible turbulent motion
Héas, Patrick; Kadri-Harouna, Souleymane
2013-01-01
This work is concerned with the ill-posed inverse problem of estimating turbulent flows from the observation of an image sequence. From a Bayesian perspective, a divergence-free isotropic fractional Brownian motion (fBm) is chosen as a prior model for instantaneous turbulent velocity fields. This self-similar prior characterizes accurately second-order statistics of velocity fields in incompressible isotropic turbulence. Nevertheless, the associated maximum a posteriori involves a fractional Laplacian operator which is delicate to implement in practice. To deal with this issue, we propose to decompose the divergent-free fBm on well-chosen wavelet bases. As a first alternative, we propose to design wavelets as whitening filters. We show that these filters are fractional Laplacian wavelets composed with the Leray projector. As a second alternative, we use a divergence-free wavelet basis, which takes implicitly into account the incompressibility constraint arising from physics. Although the latter decomposition ...
Self-similarity and universality of void density profiles in simulation and SDSS data
Nadathur, S; Diego, J M; Iliev, I T; Gottlöber, S; Watson, W A; Yepes, G
2014-01-01
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 voids in simulation are exactly self-similar, meaning that their avera...
Self-similar inverse cascade of magnetic helicity driven by the chiral anomaly
Hirono, Yuji; Yin, Yi
2015-01-01
For systems with charged chiral fermions, the imbalance of chirality in the presence of magnetic field generates an electric current - this is the Chiral Magnetic Effect (CME). We study the dynamical real-time evolution of electromagnetic fields coupled by the anomaly to the chiral charge density and the CME current by solving the Maxwell-Chern-Simons equations. We find that the CME induces the inverse cascade of magnetic helicity towards the large distances, and that at late times this cascade becomes self-similar, with universal exponents. We also find that in terms of gauge field topology the inverse cascade represents the transition from linked electric and magnetic fields (Hopfions) to the knotted configuration of magnetic field (Chandrasekhar-Kendall states). The magnetic reconnections are accompanied by the pulses of the CME current directed along the magnetic field lines. We devise an experimental signature of these phenomena in heavy ion collisions, and speculate about implications for condensed matt...
Self-Similar Evolution of Cosmic-Ray-Modified Quasi-Parallel Plane Shocks
Kang, Hyesung
2007-01-01
Using an improved version of the previously introduced CRASH (Cosmic Ray Acceleration SHock) code, we have calculated the time evolution of cosmic-ray (CR) modified quasi-parallel plane shocks for Bohm-like diffusion, including self-consistent models of Alfven wave drift and dissipation, along with thermal leakage injection of CRs. The new simulations follow evolution of the CR distribution to much higher energies than our previous study, providing a better examination of evolutionary and asymptotic behaviors. The postshock CR pressure becomes constant after quick initial adjustment, since the evolution of the CR partial pressure expressed in terms of a momentum similarity variable is self-similar. The shock precursor, which scales as the diffusion length of the highest energy CRs, subsequently broadens approximately linearly with time, independent of diffusion model, so long as CRs continue to be accelerated to ever-higher energies. This means the nonlinear shock structure can be described approximately in t...
Hard state of the urban canopy layer turbulence and its self-similar multiplicative cascade models
Institute of Scientific and Technical Information of China (English)
HU; Fei; CHENG; Xueling; ZHAO; Songnian; QUAN; Lihong
2005-01-01
It is found by experiment that under the thermal convection condition, the temperature fluctuation in the urban canopy layer turbulence has the hard state character, and the temperature difference between two points has the exponential probability density function distribution. At the same time, the turbulent energy dissipation rate fits the log-normal distribution, and is in accord with the hypothesis proposed by Kolmogorov in 1962 and lots of reported experimental results. In this paper, the scaling law of hard state temperature n order structure function is educed by the self-similar multiplicative cascade models. The theory formula is Sn = n/3μ{n(n+6)/72+[2lnn!-nln2]/2ln6}, and μ Is intermittent exponent. The formula can fit the experimental results up to order 8 exponents, is superior to the predictions by the Kolmogorov theory, the β And log-normal model.
Local self-similarity descriptor for point-of-interest reconstruction of real-world scenes
Gao, Xianglu; Wan, Weibing; Zhao, Qunfei; Zhang, Xianmin
2015-08-01
Scene reconstruction is utilized commonly in close-range photogrammetry, with diverse applications in fields such as industry, biology, and aerospace industries. Presented surfaces or wireframe three-dimensional (3D) model reconstruction applications are either too complex or too inflexible to accommodate various types of real-world scenes, however. This paper proposes an algorithm for acquiring point-of-interest (referred to throughout the study as POI) coordinates in 3D space, based on multi-view geometry and a local self-similarity descriptor. After reconstructing several POIs specified by a user, a concise and flexible target object measurement method, which obtains the distance between POIs, is described in detail. The proposed technique is able to measure targets with high accuracy even in the presence of obstacles and non-Lambertian surfaces. The method is so flexible that target objects can be measured with a handheld digital camera. Experimental results further demonstrate the effectiveness of the algorithm.
Self-similarity of far wake behind tandem of two disks
DEFF Research Database (Denmark)
Okulov, Valery; Litvinov, I. V.; Naumov, I. V.
2017-01-01
In this work we used digital particle image visualization (PIV) to experimentally establish the self-similarity of far wake behind a tandem of two disks of a diameter D (300 mm) with a common axis along the incident flow. The research was performed in a water flume (Re ≈ 2 · 105) with variation...... the tandem exceeded the corresponding value for a single disk, being independent of the distance between the disks (L = 4–8D). The velocity fluctuations behind the tandem did not differ much from the level of fluctuations in the case of a single disk up to a distance of forty calibers downstream, where...... the wake ceased to differ from the background of natural turbulent fluctuations of the incident flow. It has been found that the position of the second disk in the tandem affects the energy loss in the wake due to its expansion but does not influence the decay. The revealed patterns in the wake development...
Self-similarity of negative particle production from the Beam Energy Scan Program at STAR
Tokarev, M V
2015-01-01
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 sqrt s{NN}=7.7-200 GeV, and transverse momentum of produced particle in different centralities at |eta|<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.
Flow Rate of Particles through Apertures Obtained from Self-Similar Density and Velocity Profiles
Janda, Alvaro; Zuriguel, Iker; Maza, Diego
2012-06-01
“Beverloo’s law” is considered as the standard expression to estimate the flow rate of particles through apertures. This relation was obtained by simple dimensional analysis and includes empirical parameters whose physical meaning is poorly justified. In this Letter, we study the density and velocity profiles in the flow of particles through an aperture. We find that, for the whole range of apertures studied, both profiles are self-similar. Hence, by means of the functionality obtained for them the mass flow rate is calculated. The comparison of this expression with the Beverloo’s one reveals some differences which are crucial to understanding the mechanism that governs the flow of particles through orifices.
Methods of construction and study of Frankl system self-similar solutions in the hyperbolic case
Shemyakina, T.; Alekseenkκo, S.
2016-11-01
Self-similar solution of the Frankl system in the hyperbolic case was found. The Frankl system is a system of mixed type equations. Under certain conditions, it describes a model of the membrane theory of shells. The Frankl system describes a stationary irrotational motion of an ideal gas in the transition vicinity from subsonic to supersonic speeds. We find a sufficient condition on the initial data that guarantees existence of a global classical solution continued from a local solution. The proof of the nonlocal solvability of the problem in the original variables is based on the additional argument method. It allowed justify and construct a numerical solution. Numerical experiments were carried out for model examples of the Frankl system.
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.
Self-Similar Solutions for Viscous and Resistive Advection Dominated Accretion Flows
Indian Academy of Sciences (India)
Kazem Faghei
2012-03-01
In this paper, self-similar solutions of resistive advection dominated accretion flows (ADAF) in the presence of a pure azimuthal magnetic field are investigated. The mechanism of energy dissipation is assumed to be the viscosity and the magnetic diffusivity due to turbulence in the accretion flow. It is assumed that the magnetic diffusivity and the kinematic viscosity are not constant and vary by position and -prescription is used for them. In order to solve the integrated equations that govern the behavior of the accretion flow, a self-similar method is used. The solutions show that the structure of accretion flow depends on the magnetic field and the magnetic diffusivity. As the radial infall velocity and the temperature of the flow increase by magnetic diffusivity, the rotational velocity decreases. Also, the rotational velocity for all selected values of magnetic diffusivity and magnetic field is sub-Keplerian. The solutions show that there is a certain amount of magnetic field for which rotational velocity of the flow becomes zero. This amount of the magnetic field depends upon the gas properties of the disc, such as adiabatic index and viscosity, magnetic diffusivity, and advection parameters. The mass accretion rate increases by adding the magnetic diffusivity and the solutions show that in high magnetic pressure, the ratio of the mass accretion rate to the Bondi accretion rate is reduced with an increase in magnetic pressure. Also, the study of Lundquist and magnetic Reynolds numbers based on resistivity indicates that the linear growth of magnetorotational instability (MRI) of the flow reduces by resistivity. This property is qualitatively consistent with resistive magnetohydrodynamics (MHD) simulations.
Agnati, Luigi F; Baluska, Frantisek; Barlow, Peter W; Guidolin, Diego
2009-11-01
From a structural standpoint, living organisms are organized like a nest of Russian matryoshka dolls, in which structures are buried within one another. From a temporal point of view, this type of organization is the result of a history comprised of a set of time backcloths which have accompanied the passage of living matter from its origins up to the present day. The aim of the present paper is to indicate a possible course of this 'passage through time, and suggest how today's complexity has been reached by living organisms. This investigation will employ three conceptual tools, namely the Mosaic, Self-Similarity Logic, and the Biological Attraction principles. Self-Similarity Logic indicates the self-consistency by which elements of a living system interact, irrespective of the spatiotemporal level under consideration. The term Mosaic indicates how, from the same set of elements assembled according to different patterns, it is possible to arrive at completely different constructions: hence, each system becomes endowed with different emergent properties. The Biological Attraction principle states that there is an inherent drive for association and merging of compatible elements at all levels of biological complexity. By analogy with the gravitation law in physics, biological attraction is based on the evidence that each living organism creates an attractive field around itself. This field acts as a sphere of influence that actively attracts similar fields of other biological systems, thereby modifying salient features of the interacting organisms. Three specific organizational levels of living matter, namely the molecular, cellular, and supracellular levels, have been considered in order to analyse and illustrate the interpretative as well as the predictive roles of each of these three explanatory principles.
DEFF Research Database (Denmark)
Andersen, Allan T.; Nielsen, Bo Friis
1997-01-01
We present a modelling framework and a fitting method for modelling second order self-similar behaviour with the Markovian arrival process (MAP). The fitting method is based on fitting to the autocorrelation function of counts a second order self-similar process. It is shown that with this fitting...... algorithm it is possible closely to match the autocorrelation function of counts for a second order self-similar process over 3-5 time-scales with 8-16 state MAPs with a very simple structure, i.e. a superposition of 3 and 4 interrupted Poisson processes (IPP) respectively and a Poisson process. The fitting...
Institute of Scientific and Technical Information of China (English)
ZHANG Di; ZHANG Min; YE Pei-da
2006-01-01
This article explores the short-range dependence (SRD) and the long-range dependence (LRD) of self-similar traffic generated by the fractal-binomial-noise-driven Poisson process (FBNDP) model and lays emphasis on the former. By simulation, the SRD decaying trends with the increase of Hurst value and peak rate are obtained, respectively. After a comprehensive analysis of accuracy of self-similarity intensity,the optimal range of peak rate is determined by taking into account the time cost, the accuracy of self-similarity intensity,and the effect of SRD.
Estimates for the resolvent kernel of the Laplacian on p.c.f. self similar fractals and blowups
Rogers, Luke G
2010-01-01
We provide a method for obtaining upper estimates of the resolvent kernel of the Laplacian on a post-critically finite self-similar fractal that relies on a self-similar series decomposition of the resolvent. Decay estimates on the positive real axis are proved by analyzing functions satisfying an interior eigenfunction condition with positive eigenvalue. These lead to estimates on the complement of the negative real axis via the Phragmen-Lindelof theorem. Applications are given to kernels for functions of the Laplacian, including the heat kernel, and to proving the existence of a self-similar series decomposition for the Laplacian resolvent on fractal blowups.
Improved river flow and random sample consensus for curve lane detection
Directory of Open Access Journals (Sweden)
Huachun Tan
2015-07-01
Full Text Available Accurate and robust lane detection, especially the curve lane detection, is the premise of lane departure warning system and forward collision warning system. In this article, an algorithm based on improved river flow and random sample consensus is proposed to detect curve lane under challenging conditions including the dashed lane markings and vehicle occlusion. The curve lanes are modeled as hyperbola pair. To determine the coefficient of curvature, an improved river flow method is presented to search feature points in the far vision field guided by the results of detected straight lines in near vision field or the curved lines from the last frame, which can connect dashed lane markings or obscured lane markings. As a result, it is robust on dashed lane markings and vehicle occlusion conditions. Then, random sample consensus is utilized to calculate the curvature, which can eliminate noisy feature points obtained from improved river flow. The experimental results show that the proposed method can accurately detect lane under challenging conditions.
Institute of Scientific and Technical Information of China (English)
WU Lei
2009-01-01
@@ Recently, Feng et al. claimed that "they have found the asymptotic self-similar parabolic solutions in gain medium of the normal GVD", where the evolution of optical pulses is governed by the following Ginzburg-Landau equation (GLE):[1
Directory of Open Access Journals (Sweden)
Hailong Ye
2015-04-01
Full Text Available Uniqueness of self-similar very singular solutions with compact support are proved for the non-Newtonian polytropic filtration equation with gradient absorption $$ \\frac{\\partial u}{\\partial t} =\\hbox{div}(|\
Oodaira, Hiroshi
1989-01-01
A large deviations result is obtained for a class of self-similar processes represented by multiple Wiener integrals, which includes the limit processes appearing in functional "non-central" limit theorems.
Self-similar structures in a 2D parameter-space of an inductorless Chua's circuit
Energy Technology Data Exchange (ETDEWEB)
Albuquerque, Holokx A. [Departamento de Fisica, Universidade do Estado de Santa Catarina, 89223-100 Joinville (Brazil)], E-mail: dfi2haa@joinville.udesc.br; Rubinger, Rero M. [Departamento de Fisica e Quimica, Universidade Federal de Itajuba, 37500-903 Itajuba (Brazil); Rech, Paulo C. [Departamento de Fisica, Universidade do Estado de Santa Catarina, 89223-100 Joinville (Brazil)
2008-06-30
In a 2D parameter-space of an inductorless Chua's circuit model, we carried out numerical investigations and observed self-similar stability structures embedded in a sea of chaos, known until recently just in discrete-time models, namely, shrimps. We showed that those structures are self-similar and organize themselves in a period-adding bifurcation cascade in a region of the parameter-space.
Directory of Open Access Journals (Sweden)
Bennaceur-Doumaz Djamila
2016-06-01
Full Text Available The expansion of semi-infinite laser produced plasma into vacuum is analyzed with a hydrodynamic model for cold ions assuming electrons modeled by a kappa-type distribution. Self-similar analytic expressions for the potential, velocity, and density of the plasma have been derived. It is shown that nonthermal energetic electrons have the role of accelerating the self-similar expansion.
Energy Technology Data Exchange (ETDEWEB)
Lau, Erwin T.; Nagai, Daisuke; Avestruz, Camille [Department of Physics, Yale University, New Haven, CT 06520 (United States); Nelson, Kaylea [Yale Center for Astronomy and Astrophysics, Yale University, New Haven, CT 06520 (United States); Vikhlinin, Alexey, E-mail: erwin.lau@yale.edu [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States)
2015-06-10
Galaxy clusters exhibit remarkable self-similar behavior which allows us to establish simple scaling relationships between observable quantities and cluster masses, making galaxy clusters useful cosmological probes. Recent X-ray observations suggested that self-similarity may be broken in the outskirts of galaxy clusters. In this work, we analyze a mass-limited sample of massive galaxy clusters from the Omega500 cosmological hydrodynamic simulation to investigate the self-similarity of the diffuse X-ray emitting intracluster medium (ICM) in the outskirts of galaxy clusters. We find that the self-similarity of the outer ICM profiles is better preserved if they are normalized with respect to the mean density of the universe, while the inner profiles are more self-similar when normalized using the critical density. However, the outer ICM profiles as well as the location of accretion shock around clusters are sensitive to their mass accretion rate, which causes the apparent breaking of self-similarity in cluster outskirts. We also find that the collisional gas does not follow the distribution of collisionless dark matter (DM) perfectly in the infall regions of galaxy clusters, leading to 10% departures in the gas-to-DM density ratio from the cosmic mean value. Our results have a number implications for interpreting observations of galaxy clusters in X-ray and through the Sunyaev–Zel’dovich effect, and their applications to cosmology.
Human-based percussion and self-similarity detection in electroacoustic music
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
Self-similar variables and the problem of nonlocal electron heat conductivity
Energy Technology Data Exchange (ETDEWEB)
Krasheninnikov, S.I.; Bakunin, O.G. [Massachusetts Inst. of Tech., Cambridge, MA (United States). Plasma Fusion Center]|[Kurchatov Inst. of Atomic Energy, Moscow (Russian Federation)
1993-10-01
Self-similar solutions of the collisional electron kinetic equation are obtained for the plasmas with one (1D) and three (3D) dimensional plasma parameter inhomogeneities and arbitrary Z{sub eff}. For the plasma parameter profiles characterized by the ratio of the mean free path of thermal electrons with respect to electron-electron collisions, {gamma}{sub T}, to the scale length of electron temperature variation, L, one obtains a criterion for determining the effect that tail particles with motion of the non-diffusive type have on the electron heat conductivity. For these conditions it is shown that the use of a {open_quotes}symmetrized{close_quotes} kinetic equation for the investigation of the strong nonlocal effect of suprathermal electrons on the electron heat conductivity is only possible at sufficiently high Z{sub eff} (Z{sub eff} {ge} (L/{gamma}{sub T}){sup 1/2}). In the case of 3D inhomogeneous plasma (spherical symmetry), the effect of the tail electrons on the heat transport is less pronounced since they are spread across the radius r.
Composite self-similar solutions for relativistic shocks: The transition to cold fluid temperatures
Energy Technology Data Exchange (ETDEWEB)
Pan, Margaret [School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540 (United States); Sari, Re' em [California Institute of Technology, MS 130-33, Pasadena, California 91125 (United States) and Racah Institute of Physics, Hebrew University, Jerusalem 91904 (Israel)
2009-11-15
The flow resulting from a strong ultrarelativistic shock moving through a stellar envelope with a polytropelike density profile has been studied analytically and numerically at early times while the fluid temperature is relativistic--that is, just before and after the shock breaks out of the star. Such a flow should expand and accelerate as its internal energy is converted to bulk kinetic energy; at late enough times, the assumption of relativistic temperatures becomes invalid. Here we present a new self-similar solution for the postbreakout flow when the accelerating fluid has bulk kinetic Lorentz factors much larger than unity but is cooling through p/n of order unity to subrelativistic temperatures. This solution gives a relation between a fluid element's terminal Lorentz factor and that element's Lorentz factor just after it is shocked. Our numerical integrations agree well with the solution. While our solution assumes a planar flow, we show that corrections due to spherical geometry are important only for extremely fast ejecta originating in a region very close to the stellar surface. This region grows if the shock becomes relativistic deeper in the star.
Composite self-similar solutions for relativistic shocks: the transition to cold fluid temperatures
Pan, Margaret
2008-01-01
The flow resulting from a strong ultrarelativistic shock moving through a stellar envelope with a polytrope-like density profile has been studied analytically and numerically at early times while the fluid temperature is relativistic--that is, just before and just after the shock breaks out of the star. Such a flow should expand and accelerate as its internal energy is converted to bulk kinetic energy; at late enough times, the assumption of relativistic temperatures becomes invalid. Here we present a new self-similar solution for the post-breakout flow when the accelerating fluid has bulk kinetic Lorentz factors much larger than unity but is cooling through $p/n$ of order unity to subrelativistic temperatures. This solution gives a relation between a fluid element's terminal Lorentz factor and that element's Lorentz factor just after it is shocked. Our numerical integrations agree well with the solution. While our solution assumes a planar flow, we show that corrections due to spherical geometry are importan...
A nonlinear self-similar solution to barotropic flow over rapidly varying topography
Ibanez, Ruy; Kuehl, Joseph
2016-11-01
Beginning from the Shallow Water Equations (SWE), a nonlinear self-similar analytic solution is derived for barotropic flow over rapidly varying topography. We study conditions relevant to the ocean slope where the flow is dominated by Earth's rotation and topography. Attention is paid to the northern Gulf of Mexico slope with application to pollutant dispersion and the Norwegian Coastal Current which sheds eddies into the Lofoten Basin that are believe to influence deep water formation. The solution is found to extend the topographic β-plume solution (Kuehl 2014, GRL) in two ways: 1) The solution is valid for intensifying jets. 2) The influence of nonlinear advection is included. The SWE are scaled to the case of a topographically controlled jet, then solved by introducing a similarity variable η = Cxy . The nonlinear solution, valid for topographies h =h0 - αxy3 , takes the form of the Lambert W Function for velocity. The linear solution, valid for topographies h =h0 - αxyγ , takes the form of the Error Function for transport. Kuehl's results considered the case - 1 <= γ < 1 which admits expanding jets, while the new result consider the case γ < - 1 which admits intensifying jets.
Self-Similarity in Population Dynamics: Surname Distributions and Genealogical Trees
Directory of Open Access Journals (Sweden)
Paolo Rossi
2015-01-01
Full Text Available The frequency distribution of surnames turns out to be a relevant issue not only in historical demography but also in population biology, and especially in genetics, since surnames tend to behave like neutral genes and propagate like Y chromosomes. The stochastic dynamics leading to the observed scale-invariant distributions has been studied as a Yule process, as a branching phenomenon and also by field-theoretical renormalization group techniques. In the absence of mutations the theoretical models are in good agreement with empirical evidence, but when mutations are present a discrepancy between the theoretical and the experimental exponents is observed. Hints for the possible origin of the mismatch are discussed, with some emphasis on the difference between the asymptotic frequency distribution of a full population and the frequency distributions observed in its samples. A precise connection is established between surname distributions and the statistical properties of genealogical trees. Ancestors tables, being obviously self-similar, may be investigated theoretically by renormalization group techniques, but they can also be studied empirically by exploiting the large online genealogical databases concerning European nobility.
Directory of Open Access Journals (Sweden)
Geoff Boeing
2016-11-01
Full Text Available Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be very simple, yet they produce completely unpredictable and divergent behavior. Systems of nonlinear equations are difficult to solve analytically, and scientists have relied heavily on visual and qualitative approaches to discover and analyze the dynamics of nonlinearity. Indeed, few fields have drawn as heavily from visualization methods for their seminal innovations: from strange attractors, to bifurcation diagrams, to cobweb plots, to phase diagrams and embedding. Although the social sciences are increasingly studying these types of systems, seminal concepts remain murky or loosely adopted. This article has three aims. First, it argues for several visualization methods to critically analyze and understand the behavior of nonlinear dynamical systems. Second, it uses these visualizations to introduce the foundations of nonlinear dynamics, chaos, fractals, self-similarity and the limits of prediction. Finally, it presents Pynamical, an open-source Python package to easily visualize and explore nonlinear dynamical systems’ behavior.
Landau-Ginzburg Limit of Black Hole's Quantum Portrait: Self Similarity and Critical Exponent
Dvali, Gia
2012-01-01
Recently we have suggested that the microscopic quantum description of a black hole is an overpacked self-sustained Bose-condensate of N weakly-interacting soft gravitons, which obeys the rules of 't Hooft's large-N physics. In this note we derive an effective Landau-Ginzburg Lagrangian for the condensate and show that it becomes an exact description in a semi-classical limit that serves as the black hole analog of 't Hooft's planar limit. The role of a weakly-coupled Landau-Ginzburg order parameter is played by N. This description consistently reproduces the known properties of black holes in semi-classical limit. Hawking radiation, as the quantum depletion of the condensate, is described by the slow-roll of the field N. In the semiclassical limit, where black holes of arbitrarily small size are allowed, the equation of depletion is self similar leading to a scaling law for the black hole size with critical exponent 1/3.
Self-Similar Blowup Solutions to the 2-Component Camassa-Holm Equations
Yuen, Manwai
2010-01-01
In this article, we study the self-similar solutions of the 2-component Camassa-Holm equations% \\begin{equation} \\left\\{ \\begin{array} [c]{c}% \\rho_{t}+u\\rho_{x}+\\rho u_{x}=0,\\\\ m_{t}+2um_{x}+um_{x}+\\sigma\\rho\\rho_{x}=0, \\end{array} \\right. \\end{equation} with \\begin{equation} m=u-\\alpha^{2}u_{xx}. \\end{equation} By the separation method, we can obtain a class of blowup or global solutions for $\\sigma=1$ or $-1$. In particular, for the integrable system with $\\sigma=1$, we have the collapsing solutions:% \\begin{equation} \\left\\{ \\begin{array} [c]{c}% \\rho(t,x)=\\left\\{ \\begin{array} [c]{c}% \\frac{f\\left( \\eta\\right) }{a(3t)^{1/3}},\\text{ for }\\eta^{2}<-\\xi\\alpha ^{2},\\\\ 0,\\text{ for }\\eta^{2}\\geq-\\xi\\alpha^{2}% \\end{array} \\right. ,u(t,x)=\\frac{\\overset{\\cdot}{a}(3t)}{a(3t)}x,\\\\ \\overset{\\cdot\\cdot}{a}(s)-\\frac{\\xi}{3a(s)^{1/3}}=0,\\text{ }a(0)=a_{0}% <0,\\text{ }\\overset{\\cdot}{a}(0)=a_{1},\\\\ f(\\eta)=\\frac{1}{\\xi}\\sqrt{\\xi\\eta^{2}+\\left( \\xi\\alpha\\right) ^{2}}, \\end{array} \\right. \\end{equation} where $\\e...
Spiral-driven accretion in protoplanetary discs - II Self-similar solutions
Hennebelle, Patrick; Fromang, Sébastien
2016-01-01
Accretion discs are ubiquitous in the universe and it is a crucial issue to understand how angular momentum and mass are being radially transported in these objects. Here, we study the role played by non-linear spiral patterns within hydrodynamical and non self-gravitating accretion disc assuming that external disturbances such as infall onto the disc may trigger them. To do so, we computed self-similar solutions that describe discs in which a spiral wave propagates. Such solutions present both shocks and critical sonic points that we carefully analyze. For all allowed temperatures and for several spiral shocks, we calculated the wave structure. In particular we inferred the angle of the spiral patern, the stress it exerts on the disc as well as 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 $\\alpha$ parameter. For the thickest disc we considered (corresponding to $h/r$ values of about 1/3), we f...
Muniandy, S V; Lim, S C
2001-04-01
Fractional Brownian motion (FBM) is widely used in the modeling of phenomena with power spectral density of power-law type. However, FBM has its limitation since it can only describe phenomena with monofractal structure or a uniform degree of irregularity characterized by the constant Holder exponent. For more realistic modeling, it is necessary to take into consideration the local variation of irregularity, with the Holder exponent allowed to vary with time (or space). One way to achieve such a generalization is to extend the standard FBM to multifractional Brownian motion (MBM) indexed by a Holder exponent that is a function of time. This paper proposes an alternative generalization to MBM based on the FBM defined by the Riemann-Liouville type of fractional integral. The local properties of the Riemann-Liouville MBM (RLMBM) are studied and they are found to be similar to that of the standard MBM. A numerical scheme to simulate the locally self-similar sample paths of the RLMBM for various types of time-varying Holder exponents is given. The local scaling exponents are estimated based on the local growth of the variance and the wavelet scalogram methods. Finally, an example of the possible applications of RLMBM in the modeling of multifractal time series is illustrated.
Self-similar distribution of oil spills in European coastal waters
Energy Technology Data Exchange (ETDEWEB)
Redondo, Jose M; Platonov, Alexei K [Departament de Fisica Aplicada, Universidad Politecnica de Catalunya C/ J G Salgado s/n, Campus Nord, Modul B-4, E-08034, Barcelona (Spain)], E-mail: redondo@fa.upc.es
2009-01-15
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 km{sup 2}, 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.
Self-similar fragmentation regulated by magnetic fields in a region forming massive stars
Li, Hua-Bai; Yuen, Ka Ho; Otto, Frank; Leung, Po Kin; Sridharan, T. K.; Zhang, Qizhou; Liu, Hauyu; Tang, Ya-Wen; Qiu, Keping
2015-04-01
Most molecular clouds are filamentary or elongated. For those forming low-mass stars (8 solar masses). But whether the core field morphologies are inherited from the intercloud medium or governed by cloud turbulence is unknown, as is the effect of magnetic fields on cloud fragmentation at scales of 10 to 0.1 parsecs. Here we report magnetic-field maps inferred from polarimetric observations of NGC 6334, a region forming massive stars, on the 100 to 0.01 parsec scale. NGC 6334 hosts young star-forming sites where fields are not severely affected by stellar feedback, and their directions do not change much over the entire scale range. This means that the fields are dynamically important. The ordered fields lead to a self-similar gas fragmentation: at all scales, there exist elongated gas structures nearly perpendicular to the fields. Many gas elongations have density peaks near the ends, which symmetrically pinch the fields. The field strength is proportional to the 0.4th power of the density, which is an indication of anisotropic gas contractions along the field. We conclude that magnetic fields have a crucial role in the fragmentation of NGC 6334.
Self-Similar Hot Accretion Flow onto a Rotating Neutron Star Structure and Stability
Medvedev, M V; Medvedev, Mikhail; Narayan, Ramesh
2001-01-01
We present analytical and numerical solutions which describe a hot, viscous, two-temperature accretion flow onto a rotating neutron star or any other rotating compact star with a surface. We assume Coulomb coupling between the protons and electrons, and free-free cooling from the electrons. Outside a thin boundary layer, where the accretion flow meets the star, we show that there is an extended settling region which is well-described by two self-similar solutions: (i) a two-temperature solution which is valid in an inner zone $r\\le10^{2.5}$ ($r$ is in Schwarzchild units), and (ii) a one-temperature solution at larger radii. In both zones, $\\rho\\propto r^{-2}, \\Omega\\propto r^{-3/2}, v\\propto r^0, T_p\\propto r^{-1}$; in the two-temperature zone, $T_e\\propto r^{-1/2}$. The luminosity of the settling zone arises from the rotational energy of the star as the star is braked by viscosity. Hence the luminosity and the flow parameters (density, temperature, angular velocity) are independent of $\\dot M$. The settling ...
Self-similar solutions with compactly supported profile of some nonlinear Schrodinger equations
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Pascal Begout
2014-04-01
Full Text Available ``Sharp localized'' solutions (i.e. with compact support for each given time t of a singular nonlinear type Schr\\"odinger equation in the whole space $\\mathbb{R}^N$ are constructed here under the assumption that they have a self-similar structure. It requires the assumption that the external forcing term satisfies that $\\mathbf{f}(t,x=t^{-(\\mathbf{p}-2/2}\\mathbf{F}(t^{-1/2}x$ for some complex exponent $\\mathbf{p}$ and for some profile function $\\mathbf{F}$ which is assumed to be with compact support in $\\mathbb{R}^N$. We show the existence of solutions of the form $\\mathbf{u}(t,x=t^{\\mathbf{p}/2}\\mathbf{U}(t^{-1/2}x$, with a profile $\\mathbf{U}$, which also has compact support in $\\mathbb{R}^N$. The proof of the localization of the support of the profile $\\mathbf{U}$ uses some suitable energy method applied to the stationary problem satisfied by $\\mathbf{U}$ after some unknown transformation.
Self-similarity of temperature profiles in distant galaxy clusters: the quest for a universal law
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 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 0.4 has been attempted. We were able to define the closest possible relation to a universal law for the temperature profiles of galaxy clusters at 0.1 < z < 0.9, showing a dependence on both the relaxation state of the clusters and the redshift. Appendix A is only available in electronic form at http://www.aanda.org
Experimentation and direct numerical simulation of self-similar convergent detonation wave
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Bozier O.
2011-01-01
Full Text Available The propagation of self similar convergent detonation wave in TATB-based explosive composition was studied both experimentally and numerically. The device constists in a 50 mm cylinder of TATB surrounded by an HMX tube. The detonation in HMX overdrives the detonation in TATB which adapts to the propagation velocity with a convergent front at centerline. We measured a curvature of κ = −21.2 m−1 for propagation velocity of 8750 m/s, which extends the knowledge of the (Dn,κ law. A wide ranged EOS/reaction rate model inspired from previous work of Wescott et al. was calibrated to reproduce both the run-to-detonation distance and the newly extended (Dn,κ law for the 1D sligthly curved detonation theory. 2D Direct Numerical Simulations (DNS were made on fine resolved mesh grid for the experimental configuration and for various driver velocities. The simulation reproduces the experimental data both qualitatively (overall detonation structure and quantitatively (κ = −25.4 m−1.
Dark energy in six nearby galaxy flows: Synthetic phase diagrams and self-similarity
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.
Lévy Flights and Self-Similar Exploratory Behaviour of Termite Workers: Beyond Model Fitting
Miramontes, Octavio; DeSouza, Og; Paiva, Leticia Ribeiro; Marins, Alessandra; Orozco, Sirio
2014-01-01
Animal movements have been related to optimal foraging strategies where self-similar trajectories are central. Most of the experimental studies done so far have focused mainly on fitting statistical models to data in order to test for movement patterns described by power-laws. Here we show by analyzing over half a million movement displacements that isolated termite workers actually exhibit a range of very interesting dynamical properties –including Lévy flights– in their exploratory behaviour. Going beyond the current trend of statistical model fitting alone, our study analyses anomalous diffusion and structure functions to estimate values of the scaling exponents describing displacement statistics. We evince the fractal nature of the movement patterns and show how the scaling exponents describing termite space exploration intriguingly comply with mathematical relations found in the physics of transport phenomena. By doing this, we rescue a rich variety of physical and biological phenomenology that can be potentially important and meaningful for the study of complex animal behavior and, in particular, for the study of how patterns of exploratory behaviour of individual social insects may impact not only their feeding demands but also nestmate encounter patterns and, hence, their dynamics at the social scale. PMID:25353958
Levy flights and self-similar exploratory behaviour of termite workers: beyond model fitting.
Directory of Open Access Journals (Sweden)
Octavio Miramontes
Full Text Available Animal movements have been related to optimal foraging strategies where self-similar trajectories are central. Most of the experimental studies done so far have focused mainly on fitting statistical models to data in order to test for movement patterns described by power-laws. Here we show by analyzing over half a million movement displacements that isolated termite workers actually exhibit a range of very interesting dynamical properties--including Lévy flights--in their exploratory behaviour. Going beyond the current trend of statistical model fitting alone, our study analyses anomalous diffusion and structure functions to estimate values of the scaling exponents describing displacement statistics. We evince the fractal nature of the movement patterns and show how the scaling exponents describing termite space exploration intriguingly comply with mathematical relations found in the physics of transport phenomena. By doing this, we rescue a rich variety of physical and biological phenomenology that can be potentially important and meaningful for the study of complex animal behavior and, in particular, for the study of how patterns of exploratory behaviour of individual social insects may impact not only their feeding demands but also nestmate encounter patterns and, hence, their dynamics at the social scale.
Optimal design of self-similar serpentine interconnects embedded in stretchable electronics
Dong, Wentao; Zhu, Chen; Ye, Dong; Huang, YongAn
2017-06-01
The order-2 self-similar serpentine interconnects (SSIs) that joint rigid, functional devices can ensure mechanical integrity and stretchability in electronic systems under large deformations. However, the conventional design and analysis aim merely at the freestanding order-2 SSIs. The paper studies the design law and the stretchability of order-2 SSI that are bonded onto the polydimethylsiloxane (PDMS) substrate in stretchable electronics through analytical modeling, finite element method (FEM), and experiments. The scale law formula is built to predict the stretchability of the order-2 SSI with geometry parameters based on FEM simulation results. The out-of-plane and in-plane bending strains during lateral postbuckling processes are proportional to the thickness and width of the order-2 SSI, respectively. The stretchability of order-2 SSI decreases with the increasing ratio β of order-2 space L 2 to order-1 space L 1, and it would be approximate to the stretchability of order-1 serpentine interconnect when β > 32. The optimized order-2 SSI is demonstrated in stretchable electronics application with high stretchability.
Unraveling the Rank-Size Rule with Self-Similar Hierarchies
Chen, Yanguang
2011-01-01
Many scientists are interested in but puzzled by the various inverse power laws with a negative exponent 1 such as the rank-size rule. The rank-size rule is a very simple scaling law followed by many observations of the ubiquitous empirical patterns in physical and social systems. Where there is a rank-size distribution, there will be a hierarchy with cascade structure. However, the equivalence relation between the rank-size rule and the hierarchical scaling law remains to be mathematically demonstrated and empirically testified. In this paper, theoretical derivation, mathematical experiments, and empirical analysis are employed to show that the rank-size rule is equivalent in theory to the hierarchical scaling law (the Nn principle). Abstracting an ordered set of quantities in the form {1, 1/2,..., 1/k,...} from the rank-size rule, I prove a geometric subdivision theorem of the harmonic sequence (k=1, 2, 3,...). By the theorem, the rank-size distribution can be transformed into a self-similar hierarchy, thus...
Self-Similar Models for the Mass Profiles of Early-type Lens Galaxies
Rusin, D; Keeton, C R
2003-01-01
We introduce a self-similar mass model for early-type galaxies, and constrain it using the aperture mass-radius relations determined from the geometries of 22 gravitational lenses. The model consists of two components: a concentrated component which traces the light distribution, and a more extended power-law component (rho propto r^-n) which represents the dark matter. We find that lens galaxies have total mass profiles which are nearly isothermal, or slightly steeper, on the several-kiloparsec radial scale spanned by the lensed images. In the limit of a single-component, power-law radial profile, the model implies n=2.07+/-0.13, consistent with isothermal (n=2). Models in which mass traces light are excluded at >99 percent confidence. An n=1 cusp (such as the Navarro-Frenk-White profile) requires a projected dark matter mass fraction of f_cdm = 0.22+/-0.10 inside 2 effective radii. These are the best statistical constraints yet obtained on the mass profiles of lenses, and provide clear evidence for a small ...
Using Self-Similarity to Simulate Meniscus Evolution Around TMV Due to Surface Diffusion
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.
Viscoelastic properties of the nematode Caenorhabditis elegans, a self-similar, shear-thinning worm.
Backholm, Matilda; Ryu, William S; Dalnoki-Veress, Kari
2013-03-19
Undulatory motion is common to many creatures across many scales, from sperm to snakes. These organisms must push off against their external environment, such as a viscous medium, grains of sand, or a high-friction surface; additionally they must work to bend their own body. A full understanding of undulatory motion, and locomotion in general, requires the characterization of the material properties of the animal itself. The material properties of the model organism Caenorhabditis elegans were studied with a micromechanical experiment used to carry out a three-point bending measurement of the worm. Worms at various developmental stages (including dauer) were measured and different positions along the worm were probed. From these experiments we calculated the viscoelastic properties of the worm, including the effective spring constant and damping coefficient of bending. C. elegans moves by propagating sinusoidal waves along its body. Whereas previous viscoelastic approaches to describe the undulatory motion have used a Kelvin-Voigt model, where the elastic and viscous components are connected in parallel, our measurements show that the Maxwell model, where the elastic and viscous components are in series, is more appropriate. The viscous component of the worm was shown to be consistent with a non-Newtonian, shear-thinning fluid. We find that as the worm matures it is well described as a self-similar elastic object with a shear-thinning damping term and a stiffness that becomes smaller as one approaches the tail.
Distinctive Order Based Self-Similarity descriptor for multi-sensor remote sensing image matching
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.
An accurate algorithm to calculate the Hurst exponent of self-similar processes
Energy Technology Data Exchange (ETDEWEB)
Fernández-Martínez, M., E-mail: fmm124@ual.es [Department of Mathematics, Faculty of Science, Universidad de Almería, 04120 Almería (Spain); Sánchez-Granero, M.A., E-mail: misanche@ual.es [Department of Mathematics, Faculty of Science, Universidad de Almería, 04120 Almería (Spain); Trinidad Segovia, J.E., E-mail: jetrini@ual.es [Department of Accounting and Finance, Faculty of Economics and Business, Universidad de Almería, 04120 Almería (Spain); Román-Sánchez, I.M., E-mail: iroman@ual.es [Department of Accounting and Finance, Faculty of Economics and Business, Universidad de Almería, 04120 Almería (Spain)
2014-06-27
In this paper, we introduce a new approach which generalizes the GM2 algorithm (introduced in Sánchez-Granero et al. (2008) [52]) as well as fractal dimension algorithms (FD1, FD2 and FD3) (first appeared in Sánchez-Granero et al. (2012) [51]), providing an accurate algorithm to calculate the Hurst exponent of self-similar processes. We prove that this algorithm performs properly in the case of short time series when fractional Brownian motions and Lévy stable motions are considered. We conclude the paper with a dynamic study of the Hurst exponent evolution in the S and P500 index stocks. - Highlights: • We provide a new approach to properly calculate the Hurst exponent. • This generalizes FD algorithms and GM2, introduced previously by the authors. • This method (FD4) results especially appropriate for short time series. • FD4 may be used in both unifractal and multifractal contexts. • As an empirical application, we show that S and P500 stocks improved their efficiency.
Morgan, Brandon; Olson, Britton; White, Justin; McFarland, Jacob
2016-11-01
High-fidelity large eddy simulation (LES) of a low-Atwood number (A = 0.05) Rayleigh-Taylor mixing layer is performed using the tenth-order compact difference code Miranda. An initial multimode perturbation spectrum is specified in Fourier space as a function of mesh resolution such that a database of results is obtained in which each successive level of increased grid resolution corresponds approximately to one additional doubling of the mixing layer width, or generation. The database is then analyzed to determine approximate requirements for self-similarity, and a new metric is proposed to quantify how far a given simulation is from the limit of self-similarity. It is determined that the present database reaches a high degree of self-similarity after approximately 4.5 generations. Finally, self-similar turbulence profiles from the LES database are compared with one-dimensional simulations using the k- L- a and BHR-2 Reynolds-averaged Navier-Stokes (RANS) models. The k- L- a model, which is calibrated to reproduce a quadratic turbulence kinetic energy profile for a self-similar mixing layer, is found to be in better agreement with the LES than BHR-2 results. This work was preformed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344.
Dallaston, Michael C; Tseluiko, Dmitri; Kalliadasis, Serafim
2016-01-01
The formation of iterated structures, such as satellite and sub-satellite drops, filaments, bubbles, etc is a common phenomenon in free surface flows. We provide a computational and theoretical study of the origin of these patterns in the case of thin films of viscous fluids subject to long-range molecular forces. Iterated structures appear as a consequence of discrete self-similarity, where patterns repeat themselves, subject to rescaling, periodically in a logarithmic time scale. The result is an infinite sequence of ridges and filaments with similarity properties. The character of these discretely self-similar solutions as the result of a Hopf bifurcation from ordinarily self-similar solutions is also described.
Self-similar wave produced by local perturbation of the Kelvin-Helmholtz shear-layer instability.
Hoepffner, Jérôme; Blumenthal, Ralf; Zaleski, Stéphane
2011-03-11
We show that the Kelvin-Helmholtz instability excited by a localized perturbation yields a self-similar wave. The instability of the mixing layer was first conceived by Helmholtz as the inevitable growth of any localized irregularity into a spiral, but the search and uncovering of the resulting self-similar evolution was hindered by the technical success of Kelvin's wavelike perturbation theory. The identification of a self-similar solution is useful since its specific structure is witness of a subtle nonlinear equilibrium among the forces involved. By simulating numerically the Navier-Stokes equations, we analyze the properties of the wave: growth rate, propagation speed and the dependency of its shape upon the density ratio of the two phases of the mixing layer.
Biswas, Piyali; Biswas, Abhijit; Pal, Bishnu P
2016-01-01
We numerically demonstrate self-similar propagation of parabolic optical pulses through a highly nonlinear and passive specialty photonic bandgap fiber at 2.8 micron. In this context, we have proposed a scheme endowed with a rapidly varying, but of nearly-mean-zero longitudinal dispersion and modulated nonlinear profile in order to achieve self-similarity of the formed parabolic pulse propagating over longer distances. To implement the proposed scheme, we have designed a segmented bandgap fiber with suitably tapered counterparts to realize such customized dispersion with chalchogenide glass materials. A self-similar parabolic pulse with full-width-at-half-maxima of 4.12 ps and energy of ~ 39 pJ as been achieved at the output. Along with a linear chirp spanning over the entire pulse duration, 3dB spectral broadening of about 38 nm at the output has been reported.
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.
Self-similarity and scaling transitions during rupture of thin free films of Newtonian fluids
Thete, Sumeet Suresh; Anthony, Christopher; Doshi, Pankaj; Harris, Michael T.; Basaran, Osman A.
2016-09-01
Rupture of thin liquid films is crucial in many industrial applications and nature such as foam stability in oil-gas separation units, coating flows, polymer processing, and tear films in the eye. In some of these situations, a liquid film may have two free surfaces (referred to here as a free film or a sheet) as opposed to a film deposited on a solid substrate that has one free surface. The rupture of such a free film or a sheet of a Newtonian fluid is analyzed under the competing influences of inertia, viscous stress, van der Waals pressure, and capillary pressure by solving a system of spatially one-dimensional evolution equations for film thickness and lateral velocity. The dynamics close to the space-time singularity where the film ruptures is asymptotically self-similar and, therefore, the problem is also analyzed by reducing the transient partial differential evolution equations to a corresponding set of ordinary differential equations in similarity space. For sheets with negligible inertia, it is shown that the dominant balance of forces involves solely viscous and van der Waals forces, with capillary force remaining negligible throughout the thinning process in a viscous regime. On the other hand, for a sheet of an inviscid fluid for which the effect of viscosity is negligible, it is shown that the dominant balance of forces is between inertial, capillary, and van der Waals forces as the film evolves towards rupture in an inertial regime. Real fluids, however, have finite viscosity. Hence, for real fluids, it is further shown that the viscous and the inertial regimes are only transitory and can only describe the initial thinning dynamics of highly viscous and slightly viscous sheets, respectively. Moreover, regardless of the fluid's viscosity, it is shown that for sheets that initially thin in either of these two regimes, their dynamics transition to a late stage or final inertial-viscous regime in which inertial, viscous, and van der Waals forces balance
Self-protection and self-similarity of the stably-stratified geophysical turbulence
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
Directory of Open Access Journals (Sweden)
Marco Leo
representation of the eye'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.
Collapsing Scalar Field with Kinematic Self-Similarity of the Second Kind in 2+1 Gravity
Chan, R; Rocha, J F V; Wang, A; Wang, Anzhong
2004-01-01
All the 2+1-dimensional circularly symmetric solutions with kinematic self-similarity of the second kind to the Einstein-massless-scalar field equations are found and their local and global properties are studied. It is found that some of them represent gravitational collapse of a massless scalar field, in which black holes are always formed.
Self-similarity matrix based slow-time feature extraction for human target in high-resolution radar
He, Y.; Aubry, P.; Le Chevalier, F.; Yarovoy, A.
2014-01-01
A new approach is proposed to extract the slow-time feature of human motion in high-resolution radars. The approach is based on the self-similarity matrix (SSM) of the radar signals. The Mutual Information is used as a measure of similarity. The SSMs of different radar signals (high-resolution range
The Tutte polynomial of an infinite family of outerplanar, small-world and self-similar graphs
Liao, Yunhua; Fang, Aixiang; Hou, Yaoping
2013-10-01
In this paper we recursively describe the Tutte polynomial of an infinite family of outerplanar, small-world and self-similar graphs. In particular, we study the Abelian Sandpile Model on these graphs and obtain the generating function of the recurrent configurations. Further, we give some exact analytical expression for the Tutte polynomial at several special points
The self-similar, non-linear evolution of rotating magnetic flux ropes
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C. J. Farrugia
Full Text Available We study, in the ideal MHD approximation, the non-linear evolution of cylindrical magnetic flux tubes differentially rotating about their symmetry axis. Our force balance consists of inertial terms, which include the centrifugal force, the gradient of the axial magnetic pressure, the magnetic pinch force and the gradient of the gas pressure. We employ the "separable" class of self-similar magnetic fields, defined recently. Taking the gas to be a polytrope, we reduce the problem to a single, ordinary differential equation for the evolution function. In general, two regimes of evolution are possible; expansion and oscillation. We investigate the specific effect rotation has on these two modes of evolution. We focus on critical values of the flux rope parameters and show that rotation can suppress the oscillatory mode. We estimate the critical value of the angular velocity Ω_{crit}, above which the magnetic flux rope always expands, regardless of the value of the initial energy. Studying small-amplitude oscillations of the rope, we find that torsional oscillations are superimposed on the rotation and that they have a frequency equal to that of the radial oscillations. By setting the axial component of the magnetic field to zero, we study small-amplitude oscillations of a rigidly rotating pinch. We find that the frequency of oscillation ω is inversely proportional to the angular velocity of rotation Ω; the product ωΩbeing proportional to the inverse square of the Alfvén time. The period of large-amplitude oscillations of a rotating flux rope of low beta increases exponentially with the energy of the equivalent 1D oscillator. With respect to large-amplitude oscillations of a non-rotating flux rope, the only change brought about by rotation is to introduce a multiplicative factor greater than unity, which further increases the period. This multiplicative factor depends on the ratio of the azimuthal speed to the Alfvén speed
Transformation and Self-Similarity Properties of Gamma and Weibull Fragment Size Distributions
2015-12-01
Monte Carlo Estimates of the Distributions of the Random Polygons of the Voronoi Tessellation with Respect to a Poisson Process, Journal of...BELVOIR, VA 22060-6201 ATTN: DTIC/ OCA DEPARTMENT OF DEFENSE CONTRACTORS QUANTERION SOLUTIONS, INC. 1680 TEXAS STREET, SE KIRTLAND AFB, NM 87117-5669 ATTN: DTRIAC
Self-similar solutions for some nonlinear evolution equations: KdV, mKdV and Burgers equations
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S.A. El-Wakil
2016-02-01
Full Text Available A method for solving three types of nonlinear evolution equations namely KdV, modified KdV and Burgers equations, with self-similar solutions is presented. The method employs ideas from symmetry reduction to space and time variables and similarity reductions for nonlinear evolution equations are performed. The obtained self-similar solutions of KdV and mKdV equations are related to Bessel and Airy functions whereas those of Burgers equation are related to the error and Hermite functions. These solutions appear as new types of solitary, shock and periodic waves. Also, the method can be applied to other nonlinear evolution equations in mathematical physics.
Scaling and interaction of self-similar modes in models of high-Reynolds number wall turbulence
Sharma, A S; McKeon, B J
2016-01-01
Previous work has established the usefulness of the resolvent operator that maps the terms nonlinear in the turbulent fluctuations to the fluctuations themselves. Further work has described the self-similarity of the resolvent arising from that of the mean velocity profile. The orthogonal modes provided by the resolvent analysis describe the wall-normal coherence of the motions and inherit that self-similarity. In this contribution, we present the implications of this similarity for the nonlinear interaction between modes with different scales and wall-normal locations. By considering the nonlinear interactions between modes, it is shown that much of the turbulence scaling behaviour in the logarithmic region can be determined from a single arbitrarily chosen reference plane. Thus, the geometric scaling of the modes is impressed upon the nonlinear interaction between modes. Implications of these observations on the self-sustaining mechanisms of wall turbulence, modelling and simulation are outlined.
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Giuseppe Vitiello
2014-05-01
Full Text Available In electrodynamics there is a mutual exchange of energy and momentum between the matter field and the electromagnetic field and the total energy and momentum are conserved. For a constant magnetic field and harmonic scalar potential, electrodynamics is shown to be isomorph to a system of damped/amplified harmonic oscillators. These can be described by squeezed coherent states which in turn are isomorph to self-similar fractal structures. Under the said conditions of constant magnetic field and harmonic scalar potential, electrodynamics is thus isomorph to fractal self-similar structures and squeezed coherent states. At a quantum level, dissipation induces noncommutative geometry with the squeezing parameter playing a relevant role. Ubiquity of fractals in Nature and relevance of coherent states and electromagnetic interaction point to a unified, integrated vision of Nature.
Gor, G Yu
2009-01-01
The paper presents an analytical description of the growth of a two-component bubble in a binary liquid-gas solution. We obtain asymptotic self-similar time dependence of the bubble radius and analytical expressions for the non-steady profiles of dissolved gases around the bubble. We show that the necessary condition for the self-similar regime of bubble growth is the constant, steady-state composition of the bubble. The equation for the steady-state composition is obtained. We reveal the dependence of the steady-state composition on the solubility laws of the bubble components. Besides, the universal, independent from the solubility laws, expressions for the steady-state composition are obtained for the case of strong supersaturations, which are typical for the homogeneous nucleation of a bubble.
Smoller, Joel
2012-01-01
We prove that the Einstein equations in Standard Schwarzschild Coordinates close to form a system of three ordinary differential equations for a family of spherically symmetric, self-similar expansion waves, and the critical ($k=0$) Friedmann universe associated with the pure radiation phase of the Standard Model of Cosmology (FRW), is embedded as a single point in this family. Removing a scaling law and imposing regularity at the center, we prove that the family reduces to an implicitly defined one parameter family of distinct spacetimes determined by the value of a new {\\it acceleration parameter} $a$, such that $a=1$ corresponds to FRW. We prove that all self-similar spacetimes in the family are distinct from the non-critical $k\
Perez, H.; Zheltikov, A. M.
2017-01-01
We examine the influence of the structural self-similarity of the kagome lattice on the defect modes and waveguiding properties of hollow-core kagome-cladding fibers. We show that the guidance of such fibers is influenced by photonic band gaps (PBGs) which appear for a subset of the kagome lattice. Using these insights, we provide design considerations to further decrease loss in kagome-clad fibers.
Gorobets, Y. I.; Gorobets, Y.; Kulish, V. V.
2017-01-01
In the paper, spin waves in a uniaxial two-sublattice antiferromagnet are investigated. A new class of self-similar solutions of the Landau-Lifshitz equation is obtained and, therefore, a new type of spin waves is described. Examples of solutions of the found class are presented. New type of solution admits both linear and non-linear spin waves, including solitons. Space transformations used in the solution are mathematically analogous to the relativistic transformations.
Log-periodic oscillations in the specific heat behaviour for self-similar Ising type spin systems
Khamzin, A. A.; Nigmatullin, R. R.; Popov, I. I.; Zhelifonov, M. P.
2012-11-01
The self-similar model of spin-system of the Ising type is formulated. The thermodynamic properties of this model are considered. Analytically and numerically the specific heat of this system is calculated in the nearest neighbor approximation (only the influence of two neighboring spins was taken into account). It is shown that in temperature dependence of the specific heat the log-periodic oscillations are appeared. These oscillations are imposed on the expected power-law dependence.
On the behaviour of non-radial null geodesics in self-similar Tolman-Bondi collapse
Ortiz, Néstor; Zannias, Thomas
2015-01-01
Motivated by recent work on the structure of the singularity in inhomogeneous Tolman-Bondi collapse models, we investigate the behaviour of null geodesics in the particular case where the collapse is self-similar. The presence of the homothetic Killing vector field implies that the geodesic equation can be described by an integrable Hamiltonian system, and exploiting this fact we provide a full qualitative picture for its phase flow.
Mukherjee, P; Hazra, L N
2014-02-01
Pupil plane filtering by radial Walsh filters is a convenient technique for tailoring the axial intensity distribution near the focal plane of a rotationally symmetric imaging system. Radial Walsh filters, derived from radial Walsh functions, form a set of orthogonal phase filters that take on values either 0 or π phase, corresponding to +1 or -1 values of the radial Walsh functions over prespecified annular regions of the circular filter. Order of these filters is given by the number of zero-crossings, or equivalently phase transitions within the domain over which the set is defined. In general, radial Walsh filters are binary phase zone plates, each of them demonstrating distinct focusing characteristics. The set of radial Walsh filters can be classified into distinct groups, where the members of each group possess self-similar structures. Self-similarity can also be observed in the corresponding axial intensity distributions. These observations provide valuable clues in tackling the inverse problem of synthesis of phase filter in accordance with prespecified axial intensity distributions. This paper reports our observations on self-similarity in radial Walsh filters of various orders and corresponding axial intensity distributions.
Implication of the polarization force on the self-similar expansion of a dusty plasma into vacuum
Bentabet, Karima; Tribeche, Mouloud
2017-01-01
The effects of the polarization force on the self-similar expansion into vacuum of an unmagnetized, collisionless dusty plasma are addressed. It is found that the polarization force may drastically influence the general trends of the self-similar expansion. It is noticed that when the polarization force dominates over the electrical one, the self-similar expansion of the dusty plasma cannot set in because the net force experienced by the dust grains is not a restoring force. Dust wave breaking and inherent dust bunching then occur preventing therefore the expansion of the dust grains. For any value of the polarization parameter R ranging from zero to a critical value Rcr , the sound-speed increases as the dust number density increases. As R increases, the values of the plasma sound-speed are shifted towards higher values before decreasing beyond the critical value Rcr . As R increases from zero to Rc, the plasma expansion becomes faster compared to those of the other cases, and larger velocities are communicated to the dust grains. This is attributed to the fact that as R increases from 0 to Rcr , the electrostatic potential and thus the electric field are sustained over a larger distance allowing therefore the dust particles to expand over a much farther distance.
Ruggles, Adam; Pickett, Lyle; Frank, Jonathan
2014-11-01
Many real world combustion devices model fuel scalar mixing by assuming the self-similar argument established in atmospheric free jets. This allows simple prediction of the mean and rms fuel scalar fields to describe the mixing. This approach has been adopted in super critical liquid injections found in diesel engines where the liquid behaves as a dense fluid. The effect of pressure ratio (injection to ambient) when the ambient is greater than atmospheric pressure, upon the self-similar collapse has not been well characterized, particularly the effect upon mixing constants, jet spreading rates, and virtual origins. Changes in these self-similar parameters control the reproduction of the scalar mixing statistics. This experiment investigates the steady state mixing of high pressure ethylene jets in a pressurized pure nitrogen environment for various pressure ratios and jet orifice diameters. Quantitative laser Rayleigh scattering imaging was performed utilizing a calibration procedure to account for the pressure effects upon scattering interference within the high-pressure vessel.
A Study of Wavelet Analysis and Data Extraction from Second-Order Self-Similar Time Series
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Leopoldo Estrada Vargas
2013-01-01
Full Text Available Statistical analysis and synthesis of self-similar discrete time signals are presented. The analysis equation is formally defined through a special family of basis functions of which the simplest case matches the Haar wavelet. The original discrete time series is synthesized without loss by a linear combination of the basis functions after some scaling, displacement, and phase shift. The decomposition is then used to synthesize a new second-order self-similar signal with a different Hurst index than the original. The components are also used to describe the behavior of the estimated mean and variance of self-similar discrete time series. It is shown that the sample mean, although it is unbiased, provides less information about the process mean as its Hurst index is higher. It is also demonstrated that the classical variance estimator is biased and that the widely accepted aggregated variance-based estimator of the Hurst index results biased not due to its nature (which is being unbiased and has minimal variance but to flaws in its implementation. Using the proposed decomposition, the correct estimation of the Variance Plot is described, as well as its close association with the popular Logscale Diagram.
Interfacial stability and self-similar rupture of evaporating liquid layers under vapor recoil
Wei, Tao; Duan, Fei
2016-12-01
We investigate interfacial stability of an evaporating viscous liquid layer above/below a horizontal heated substrate in the framework of a long-wave model that accounts for surface tension, positive/negative gravity, and evaporation effects of mass loss and vapor recoil. With the time-dependent linear stability analysis, it is found that the interface instability is enhanced by vapor recoil with time using an effective growth rate. The destabilizing mechanism of vapor thrust competes with the stabilizing surface tension, and the effects of the latter are not asymptotically negligible near rupture, reflected by a rescaled effective interfacial pressure. A two-dimensional nonlinear evolution is investigated for the quasi-equilibrium evaporating layers with different evaporative conditions for Rayleigh-Taylor unstable and sessile layers. For weak mass loss and strong vapor recoil, the well-defined capillary ridges emerge around a deepening narrow valley with increasing wavelength under a positive gravity, while, on the basis of initial condition, main and secondary droplets are either coalesced partially or separated by a sharp dry-out point under a negative gravity. The rupture location depends strongly on the characteristics of a given initial condition, except for the random perturbation. For both the cases, an increase in the modified evaporation number tends to reduce the rupture time tr and droplet thickness remarkably. Similarity analysis along with numerical strategy is presented for the final stage of touch-down dynamics, determined by a physical balance between the vapor recoil and capillary force. The evaporation-driven rupture with a significant vapor recoil and negligible mass loss is shown to contain a countably infinite number of similarity solutions whose horizontal and vertical length scales behave as (tr - t)1/2 and (tr - t)1/3. The first similarity solution represents a stable single-point rupture.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This paper proposes a distributed denial-of-service attack detection method based on self similar and wavelet analysis. This method adopts an optimized transmission control protocol cookie technology for filter optimization in order to accurately detect and efficiently filter the traffic of distributed denial-of-service attack. This paper presents the design of our software, and describes all important algorithms of detection and filtering. Experimental results showed that our method has only a low delay to detect abnormal traffic of distributed denial-of-service attacks, and with a high percentage of filtering.
Sarwe, S B; Sarwe, Sanjay B.
2004-01-01
We study five dimensional(5D) spherically symmetric self-similar perfect fluid space-time with adiabatic equation of state, considering all the families of future directed non-spacelike geodesics. The space-time admits globally strong curvature naked singularities in the sense of Tipler and thus violates the cosmic censorship conjecture provided a certain algebraic equation has real positive roots. We further show that it is the weak energy condition (WEC) that is necessary for visibility of singularities for a finite period of time and for singularities to be gravitationally strong. We, also, match the solution to 5D Schwarzschild solution using the junction conditions.
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.
Institute of Scientific and Technical Information of China (English)
Dipak Ghosh; Argha Deb; Samabrata Sarkar; Prabir Kumar Haldar
2006-01-01
@@ The intermittent fluctuation of target evaporated particles is studied in both ring-like and jet-like events emitted in 32S-emulsion interactions at 200 AGeV within the framework of multi-dimensional factorial moment methodology using the concept of the Hurst exponent. It is observed that the intermittent fluctuation in the ring-like event is self-similar, whereas in the jet-like event fluctuation is self-affine. However, study indicates that the strength of fluctuation in the ring-like events is much stronger than that in the jet-like events.
Energy Technology Data Exchange (ETDEWEB)
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.
SELF-SIMILAR SOLUTIONS AND BLOW-UP PHENOMENA FOR A TWO-COMPONENT SHALLOW WATER SYSTEM
Institute of Scientific and Technical Information of China (English)
Shouming ZHOU; Chunlai MU; Liangchen WANG
2013-01-01
In this article,we consider a two-component nonlinear shallow water system,which includes the famous 2-component Camassa-Holm and Degasperis-Procesi equations as special cases.The local well-posedess for this equations is established.Some sufficient conditions for blow-up of the solutions in finite time are given.Moreover,by separation method,the self-similar solutions for the nonlinear shallow water equations are obtained,and which local or global behavior can be determined by the corresponding Emden equation.
Random forest models for the probable biological condition of streams and rivers in the USA
The National Rivers and Streams Assessment (NRSA) is a probability based survey conducted by the US Environmental Protection Agency and its state and tribal partners. It provides information on the ecological condition of the rivers and streams in the conterminous USA, and the ex...
The Simple Map for a Single-null Divertor Tokamak: How to Look for Self-Similarity in Chaos
Nguyen, Christina; Ali, Halima; Punjabi, Alkesh
2000-10-01
The movement of magnetic field lines inside a single-null divertor tokamak can be described by the Simple Map^1. The Simple Map in the Poincaré Surface of Section is given by the equations: X_1=X_0-KY_0(1-Y_0) and Y_1=Y_0+KX_1. In these equations, K remains constant at 0.60. However, the values for X0 and Y0 are changed. These values are changed so that we can zoom into chaos. Chaos lies between the region (0,0.997) and (0,1). In chaos, there lies order. As we zoom into chaos, we again find chaos and order that looks like the original good surfaces and chaos. This phenomenon is called self-similarity. Self-similarity can occur for an infinite number of times if one magnifies into the chaotic region. For this work, we write a program in a computer language called Fortran 77 and Gnuplot. This work is supported by US DOE OFES. Ms. Christina Nguyen is a HU CFRT Summer Fusion High School Workshop Scholar from Andrew Hill High School in California. She is supported by NASA SHARP Plus Program. 1. Punjabi A, Verma A and Boozer A, Phys Rev Lett 69 3322 (1992) and J Plasma Phys 52 91 (1994)
Robustness of Estimators of Long-range Dependence and Self-Similarity for Non-Gaussian Datasets.
Watkins, N. W.; Franzke, C. L. E.; Graves, T.; Gramacy, R. B.; Hughes, C.
2012-04-01
Evidence for long-range dependence and non-Gaussianity is ubiquitous in many natural systems like ecosystems, biological systems and climate. However, it is not always appreciated that both phenomena frequently occur together in natural systems, and that self-similarity of a system can result from the superposition of both phenomena. These features, which are common in complex systems, impact the attribution of trends and the occurrence and clustering of extremes. The risk assessment of systems posessing these properties will lead to different outcomes (e.g. return periods) than the more common assumption of independence of extremes. We discuss two paradigmatic models which can simultaneously account for long-range dependence and non-Gaussianity: Autoregressive Fractional Integrated Moving Average (ARFIMA) and Linear Fractional Stable Motion (LFSM). The statistical properties of estimators for long-range dependence and self-similarity are critically assessed as applied to these models. It is seen that the most popular estimators are not robust. In particular, they can be biased in the presence of important features of many natural systems like annual cycles, trends and multiplicative noise. [Related paper in press, Phil. Trans. Roy. Soc. A; preprint at arXiv:1101.5018
Banerjee, A.; Coplan, M. A.
2009-12-01
We analyze solar wind and interplanetary magnetic field data to study scaling properties of kinetic and magnetic energy density as a function of solar cycle and distance from the sun. In his original theory on turbulence, Kolmogorov predicted that in the inertial range the fluctuations in velocity differences should be self-similar. Analysis of solar wind data showed this not to be the case. On the other hand B. Hnat et.al.(Geophys. Res. Lett., 29 (10), 1446, 2002) and J.J Podesta (J. Geophys. Res., 111, A09105, 2006) showed that fluctuations in kinetic and magnetic energy density are approximately self-similar. We extend this analysis using data from the SWE and MFI experiments on the WIND spacecraft (at 1AU) during solar minimum (2006) and solar maximum (2001) and VHM/FGM experiment on the Ulysses spacecraft (1AU to 5AU). We calculate the cumulative distribution function (CDF) of the time delayed differences in kinetic and magnetic energy density and present a method through which the scaling exponent can be reliably calculated from the CDFs, instead of using structure functions which are very sensitive to large fluctuations. We compare the scaling exponents derived from the CDFs to the ones calculated from structure functions and study the rescaling properties of CDFs.
Yang, Xiang I A; Marusic, Ivan; Biferale, Luca
2016-01-01
In wall-bounded turbulence, the moment generating functions (MGFs) of the streamwise velocity fluctuations $\\left$ develop power-law scaling as a function of the wall normal distance $z/\\delta$. Here $u$ is the streamwise velocity fluctuation, $+$ indicates normalization in wall units (averaged friction velocity), $z$ is the distance from the wall, $q$ is an independent variable and $\\delta$ is the boundary layer thickness. Previous work has shown that this power-law scaling exists in the log-region {\\small $3Re_\\tau^{0.5}\\lesssim z^+$, $z\\lesssim 0.15\\delta$}, where $Re_\\tau$ is the friction velocity-based Reynolds numbers. Here we present empirical evidence that this self-similar scaling can be extended, including bulk and viscosity-affected regions $30
Donets, E E; Boyadjiev, T L
2003-01-01
We study both analytically and numerically a coupled system of spherically symmetric SU(2) Yang-Mills-dilaton equation in 3+1 Minkowski space-time. It has been found that the system admits a hidden scale invariance which becomes transparent if a special ansatz for the dilaton field is used. This choice corresponds to transition to a frame rotated in the $\\ln r-t$ plane at a definite angle. We find an infinite countable family of self-similar solutions which can be parametrized by the $N$ - the number of zeros of the relevant Yang-Mills function. According to the performed linear perturbation analysis, the lowest solution with N=0 only occurred to be stable. The Cauchy problem has been solved numerically for a wide range of smooth finite energy initial data. It has been found that if the initial data exceed some threshold, the resulting solutions in a compact region shrinking to the origin, attain the lowest N=0 stable self-similar profile, which can pretend to be a global stable attractor in the Cauchy proble...
Dallaston, M. C.; Tseluiko, D.; Zheng, Z.; Fontelos, M. A.; Kalliadasis, S.
2017-07-01
A thin liquid film coating a planar horizontal substrate may be unstable to perturbations in the film thickness due to unfavourable intermolecular interactions between the liquid and the substrate, which may lead to finite-time rupture. The self-similar nature of the rupture has been studied before by utilising the standard lubrication approximation along with the Derjaguin (or disjoining) pressure formalism used to account for the intermolecular interactions, and a particular form of the disjoining pressure with exponent n = 3 has been used, namely, \\Pi(h)\\propto -1/h3 , where h is the film thickness. In the present study, we use a numerical continuation method to compute discrete solutions to self-similar rupture for a general disjoining pressure exponent n (not necessarily equal to 3), which has not been previously performed. We focus on axisymmetric point-rupture solutions and show for the first time that pairs of solution branches merge as n decreases, starting at nc ≈ 1.485 . We verify that this observation also holds true for plane-symmetric line-rupture solutions for which the critical value turns out to be slightly larger than for the axisymmetric case, n_cplane≈ 1.499 . Computation of the full time-dependent problem also demonstrates the loss of stable similarity solutions and the subsequent onset of cascading, increasingly small structures.
Dallaston, Michael C; Zheng, Zhong; Fontelos, Marco A; Kalliadasis, Serafim
2016-01-01
A thin liquid film coating a planar horizontal substrate may be unstable to perturbations in the film thickness due to unfavourable intermolecular interactions between the liquid and the substrate, which may lead to finite-time rupture. The self-similar nature of the rupture has been studied before by utilizing the standard lubrication approximation along with the Derjaguin (or disjoining) pressure formalism used to account for the intermolecular interactions, and a particular form of the disjoining pressure with exponent $n=3$ has been used, namely, $\\Pi(h)\\propto -1/h^{3}$, where $h$ is the film thickness. In the present study, we use a numerical continuation method to compute discrete solutions to self-similar rupture for a general disjoining pressure exponent $n$. We focus on axisymmetric point-rupture solutions and show that pairs of solution branches merge as $n$ decreases, leading to a critical value $n_c \\approx 1.485$ below which stable similarity solutions do not appear to exist. We verify that this...
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.
Directory of Open Access Journals (Sweden)
Tobias Hacker
2012-04-01
Full Text Available The integral boundary layer system (IBL with spatially periodic coefficients arises as a long wave approximation for the flow of a viscous incompressible fluid down a wavy inclined plane. The Nusselt-like stationary solution of the IBL is linearly at best marginally stable; i.e., it has essential spectrum at least up to the imaginary axis. Nevertheless, in this stable case we show that localized perturbations of the ground state decay in a self-similar way. The proof uses the renormalization group method in Bloch variables and the fact that in the stable case the Burgers equation is the amplitude equation for long waves of small amplitude in the IBL. It is the first time that such a proof is given for a quasilinear PDE with spatially periodic coefficients.
Zhang, Xuefeng
2015-01-01
Motivated by cosmic censorship in general relativity and string theory, we extend Christodoulou's celebrated examples of naked singularity formation in the Einstein-massless scalar field system to include a positive or negative scalar potential of exponential forms, i.e., $V(\\phi)=\\pm\\exp(2\\phi/\\kappa)$ with a parameter $\\kappa$. Under spherical symmetry and a self-similar ansatz depending on $\\kappa$, we derive a 3-dimensional autonomous system of first-order ordinary differential equations, which incorporates the equations for massless scalar fields as a special case. Local behavior of the phase space is studied analytically with global solutions constructed numerically. Within the 3-dimensional solution manifold, we observe, for the negative potentials, naked singularity formation from nonsingular initial data for $\\kappa^2<1$. Meanwhile, transitions between solutions containing naked singularities and black holes are also identified. However, when the potential is taken positive, numerical evolutions r...
Hébert-Dufresne, Laurent; Marceau, Vincent; Noël, Pierre-André; Dubé, Louis J
2011-01-01
Many complex systems have been shown to share universal properties of organization, such as scale independence, modularity and self-similarity. We borrow tools from statistical physics in order to study structural preferential attachment (SPA), a recently proposed growth principle for the emergence of the aforementioned properties. We study the corresponding stochastic process in terms of its time evolution, its asymptotic behaviour and the scaling properties of its statistical steady state. Moreover, approximations are introduced to facilitate the reproduction of real systems, mainly complex networks, using SPA. Finally, we investigate a particular behaviour observed in the stochastic process, the peloton dynamics, and show how it predicts some features of real growing systems using prose samples as an example.
Krawiecki, A; Matyjaskiewicz, S; Holyst, J A
2003-01-01
The origin of log-periodic oscillations around the power-law trend of the escape probability from a precritical attractor and of the noise-free stochastic multiresonance, found in numerical simulations in chaotic systems close to crises is discussed. It is shown that multiple maxima of the spectral power amplification vs. the control parameter result from a fractal structure of a precritical attractor colliding with a possibly fractal basin of attraction at the crisis point. Qualitative explanation of the multiresonance, based on a concept of fractal self-similarity, or discrete-scale invariance, is given and compared with numerical results and analytic theory using a simple geometric models of the colliding fractal sets.
Large mass self-similar solutions of the parabolic-parabolic Keller-Segel model of chemotaxis.
Biler, Piotr; Corrias, Lucilla; Dolbeault, Jean
2011-07-01
In two space dimensions, the parabolic-parabolic Keller-Segel system shares many properties with the parabolic-elliptic Keller-Segel system. In particular, solutions globally exist in both cases as long as their mass is less than a critical threshold M(c). However, this threshold is not as clear in the parabolic-parabolic case as it is in the parabolic-elliptic case, in which solutions with mass above M(c) always blow up. Here we study forward self-similar solutions of the parabolic-parabolic Keller-Segel system and prove that, in some cases, such solutions globally exist even if their total mass is above M(c), which is forbidden in the parabolic-elliptic case.
Energy Technology Data Exchange (ETDEWEB)
Churchill, Christopher W.; Trujillo-Gomez, Sebastian; Nielsen, Nikole M. [New Mexico State University, Las Cruces, NM 88003 (United States); Kacprzak, Glenn G. [Swinburne University of Technology, Victoria 3122 (Australia)
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.
Lin, Gaojian; Chandrasekaran, Prashant; Lv, Cunjing; Zhang, Qiuting; Tang, Yichao; Han, Lin; Yin, Jie
2017-08-09
Smart window has immense potential for energy savings in architectural and vehicular applications, while most studies focus on the tunability of a single property of optical transmittance. Here we explore harnessing dynamically tunable hierarchical wrinkles for design of a potential multifunctional smart window with combined structural color and water droplet transport control. The self-similar hierarchical wrinkles with both nanoscale and microscale features are generated on a prestrained poly(dimethylsiloxane) elastomer through sequential strain release and multistep oxygen plasma treatment. We show that the hierarchically wrinkled elastomer displays both opaqueness and iridescent structural color. We find that restretching/releasing the elastomer leads to the reversible and repeatable switch from opaqueness to transparency, arising from the flattening of large wrinkles (micrometer scale), while a nonvanishing structural color occurs due to the nondisappearing small wrinkles (nanoscale). The unique features of combined reversible large wrinkles and irreversible small wrinkles during hierarchical wrinkling are well reproduced by corresponding finite element simulation. The criteria for generating self-similar hierarchical wrinkles is revealed through a simplified theoretical model and validated by experiments. In addition to its tunable optical property, we further show its ability in control of water droplet transport on demand through mechanical stretching and release. We find that an initially pinned water droplet on the tilted hierarchically wrinkled surface starts to slide when the surface is stretched, and becomes pinned again upon strain release. Such a process is reversible and repeatable. The hierarchically wrinkled surface could find broad potential applications not only in multifunctional smart windows with additional features of aesthetics and water collection, but in microfluidics, design of slippery surfaces, and directional water transportation.
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.
Gusev, A A
2008-01-01
High-frequency (HF) seismic radiation of large earthquakes is approximately represented by P wave trains recorded at teleseismic distances. Observed envelopes of such signals look random and intermittent, suggesting non-trivial stochastic structure. Variogram and spectral analyses were applied to instant power calculated from band-filtered observed P-wave signals from eight large (Mw=7.6-9.2) earthquakes, with 8-30 records per event and eight non-overvlapping frequency bands analyzed (total frequency range 0.6-6.2 Hz, bandwidth 0.7 Hz). Estimates for both variograms and power spectra look linear in log-log scale, suggesting in most cases self-similar correlation structure of the signal. The range for the individual-event values of the Hurst exponent H is 0.71-0.80 (averaged over bands and stations) when estimated from variograms, and 0.78-0.83 when estimated from spectra. No systematic dependence on station or frequency band was noticed. The values of H around 0.8 may be characteristic for large earthquakes i...
Institute of Scientific and Technical Information of China (English)
朱海平
2012-01-01
We construct analytical self-similar solutions for the generalized （3＋1）-dimensional nonlinear Schrdinger equation with polynomial nonlinearity of arbitrary order. As an example, we list self-similar solutions of quintic nonlinear Schrdinger equation with distributed dispersion and distributed linear gain, including bright similariton solution, fractional and combined Jacobian elliptic function solutions. Moreover, we discuss self-similar evolutional dynamic behaviors of these solutions in the dispersion decreasing fiber and the periodic distributed amplification system.
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
From nucleotides to DNA analysis by a SERS substrate of a self similar chain of silver nanospheres
Coluccio, M L
2015-11-01
In this work we realized a device of silver nanostructures designed so that they have a great ability to sustain the surface-enhanced Raman scattering effect. The nanostructures were silver self-similar chains of three nanospheres, having constant ratios between their diameters and between their reciprocal distances. They were realized by electron beam lithography, to write the pattern, and by silver electroless deposition technique, to fill it with the metal. The obtained device showed the capability to increase the Raman signal coming from the gap between the two smallest nanospheres (whose size is around 10 nm) and so it allows the detection of biomolecules fallen into this hot spot. In particular, oligonucleotides with 6 DNA bases, deposited on these devices with a drop coating method, gave a Raman spectrum characterized by a clear fingerprint coming from the hot spot and, with the help of a fitting method, also oligonucleotides of 9 bases, which are less than 3 nm long, were resolved. In conclusion the silver nanolens results in a SERS device able to measure all the molecules, or part of them, held into the hot spot of the nanolenses, and thus it could be a future instrument with which to analyze DNA portions.
CoMaLit-IV. Evolution and self-similarity of scaling relations with the galaxy cluster mass
Sereno, Mauro
2015-01-01
The scaling of observable properties of galaxy clusters with mass evolves with time. Assessing the role of the evolution is crucial to study the formation and evolution of massive halos and to avoid biases in the calibration. We present a general method to infer the mass and the redshift dependence, and the time-evolving intrinsic scatter of the mass-observable relations. The procedure self-calibrates the redshift dependent completeness function of the sample. The intrinsic scatter in the mass estimates used to calibrate the relation is considered too. We apply the method to the scaling of mass M_Delta versus line of sight galaxy velocity dispersion sigma_v, optical richness, X-ray luminosity, L_X, and Sunyaev-Zel'dovich signal. Masses were calibrated with weak lensing measurements. The measured relations are in good agreement with time and mass dependencies predicted in the self-similar scenario of structure formation. The lone exception is the L_X-M_Delta relation whose time evolution is negative in agreeme...
Churchill, Christopher W; Nielsen, Nikole M; Kacprzak, Glenn G
2013-01-01
In Churchill et al., we used halo abundance matching applied to 182 galaxies in the MAGIICAT MgII Absorption-Galaxy Catalog (Nielsen et al.) and showed that the mean MgII 2796 equivalent width follows a tight inverse-square power law, W_r(2796) ~ (D/R_vir)^-2, with projected location relative to the galaxy virial radius and that the MgII absorption covering fraction is invariant with galaxy virial mass, M_h, over the range 10.7 < M_h/M_solar < 13.9. In this work, we explore multivariate relationships between W_r(2796), virial mass, impact parameter, virial radius, and the theoretical cooling radius that further elucidate self-similarity in the cool/warm (T=10^{4-4.5} K) circumgalactic medium (CGM) with virial mass. We show that virial mass determines the extent and strength of the MgII absorbing gas such that the mean W_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_vir, ...
Volpes, L
2015-01-01
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 03 April 2010 CME 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 use 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, show good agreement with Advanced Composition Explorer (ACE) measurements. The shock standoff distance $[\\Delta]$, the density compression $[\\frac{\\rho_d}{\\rho_u}]$ and the Mach number $[M]$ are calculated combining the results obtained for the CME and shock kinematics with models for the shock location. Their values are extrapolated to $\\textrm{L}_1$ and compared to in-situ data. The in-situ standoff distance is obtained from ACE solar-wind measurements, and t...
Orban, Chris
2011-01-01
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 \\xi_L(r)=(r_0/r)^{n+3} of an underlying self-similar model with initial power spectrum P(k)=A k^n. 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 \\sigma_8=4-12 for r_bao = 100 Mpc/h). In all cases, non-linear evolution flattens and broadens the BAO bump in \\xi(r) while approximately preserving its area. This evolution resembles a "diffusion" process in which the bump width \\sigma_bao is the quadrature sum of the linear theory width and a length proportional to the rms relative displacement \\Sigma_pair(r_bao}) of particle pairs separated by...
Junginger, Andrej; Duvenbeck, Lennart; Feldmaier, Matthias; Main, Jörg; Wunner, Günter; Hernandez, Rigoberto
2017-08-01
In chemical or physical reaction dynamics, it is essential to distinguish precisely between reactants and products for all times. This task is especially demanding in time-dependent or driven systems because therein the dividing surface (DS) between these states often exhibits a nontrivial time-dependence. The so-called transition state (TS) trajectory has been seen to define a DS which is free of recrossings in a large number of one-dimensional reactions across time-dependent barriers and thus, allows one to determine exact reaction rates. A fundamental challenge to applying this method is the construction of the TS trajectory itself. The minimization of Lagrangian descriptors (LDs) provides a general and powerful scheme to obtain that trajectory even when perturbation theory fails. Both approaches encounter possible breakdowns when the overall potential is bounded, admitting the possibility of returns to the barrier long after the trajectories have reached the product or reactant wells. Such global dynamics cannot be captured by perturbation theory. Meanwhile, in the LD-DS approach, it leads to the emergence of additional local minima which make it difficult to extract the optimal branch associated with the desired TS trajectory. In this work, we illustrate this behavior for a time-dependent double-well potential revealing a self-similar structure of the LD, and we demonstrate how the reflections and side-minima can be addressed by an appropriate modification of the LD associated with the direct rate across the barrier.
A class of dust-like self-similar solutions of the massless Einstein-Vlasov system
Rendall, Alan D
2010-01-01
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 s...
Markoff, Sera; Ceccobello, Chiara; Heemskerk, Martin; Cavecchi, Yuri; Polko, Peter; Meier, David
2017-08-01
Jets are ubiquitous and reveal themselves at different scales and redshifts, showing an extreme diversity in energetics, shapes and emission. Indeed jets are found to be characteristic features of black hole systems, such as X-ray binaries (XRBs) and active galactic nuclei (AGN), as well as of young stellar objects (YSOs) and gamma-ray bursts (GRBs). Observations suggest that jets are an energetically important component of the system that hosts them, because the jet power appears to be comparable to the accretion power. Significant evidence has been found of the impact of jets not only in the immediate proximity of the central object, but as well on their surrounding environment, where they deposit the energy extracted from the accretion flow. Moreover, the inflow/outflow system produces radiation over the entire electromagnetic spectrum, from radio to X-rays. Therefore it is a compelling problem to be solved and deeply understood. I present a new integration scheme to solve radial self-similar, stationary, axisymmetric relativistic magneto-hydro-dynamics (MHD) equations describing collimated, relativistic outflows crossing smoothly all the singular points (the Alfvén point and the modified slow/fast points). For the first time, the integration can be performed all the way from the disk mid-plane to downstream of the modified fast point. I will discuss an ensemble of jet solutions showing diverse jet dynamics (jet Lorentz factor ~ 1-10) and geometric properties (i.e. shock height ~ 103 - 107 gravitational radii), which makes our model suitable for application to many different systems where a relativistic jet is launched.
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.
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 develop power-law scaling as a function of the wall normal distance z /δ . Here u is the streamwise velocity fluctuation, + indicates normalization in wall units (averaged friction velocity), z is the distance from the wall, q is an independent variable, and δ is the boundary layer thickness. Previous work has shown that this power-law scaling exists in the log-region 3 Reτ0.5≲z+,z ≲0.15 δ where Reτ is the friction velocity-based Reynolds number. Here we present empirical evidence that this self-similar scaling can be extended, including bulk and viscosity-affected regions 30 reference value, qo. ESS also improves the scaling properties, leading to more precise measurements of the scaling exponents. The analysis is based on hot-wire measurements from boundary layers at Reτ ranging from 2700 to 13 000 from the Melbourne High-Reynolds-Number-Turbulent-Boundary-Layer-Wind-Tunnel. Furthermore, we investigate the scalings of the filtered, large-scale velocity fluctuations uzL and of the remaining small-scale component, uzS=uz-uzL . The scaling of uzL falls within the conventionally defined log region and depends on a scale that is proportional to l+˜Reτ1/2 ; the scaling of uzS extends over a much wider range from z+≈30 to z ≈0.5 δ . Last, we present a theoretical construction of two multiplicative processes for uzL and uzS that reproduce the empirical findings concerning the scalings properties as functions of z+ and in the ESS sense.
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.
Directory of Open Access Journals (Sweden)
Morel Mathieu
2016-01-01
Full Text Available The OECD report “Boosting Resilience through Innovative Risk Governance” examines the efforts of OECD countries to prevent or reduce future disaster impacts, and highlights several key areas where improvements can be made. International collaboration is insufficiently utilised to address shocks that have increasingly global consequences. Institutional design plays a significant role in facilitating or hampering the engagement and investments of governmental and non-governmental stakeholders in disaster risk prevention and mitigation. To inform the design of “better” institutions, the OECD proposes the application of a diagnostic framework that helps governments identify institutional shortcomings and take actions to improve them. The goal of the case study on the Rhone River is to conduct an analysis of the progress, achievements and existing challenges in designing and implementing disaster risk reduction strategies through the Rhone Plan from a comparative perspective across a set of selected countries of this study, like Austria and Switzerland, will inform how to improve institutional frameworks governing risk prevention and mitigation. The case study will be used to identify examples of successful practice taking into account their specific country contexts, and analyse their potential for policy transfer.
Wu, Menghong; Yang, Changbao; Zhang, Yanhong; Lin, Nan
2017-05-01
Based on the platform of RS and GIS, random forest progression model is used for study driving force of wetland change in western Liaohe river basin, five influencing factors which include elevation, slope, temperature, precipitation and population density are chosen to establish random forest progression model about the wetland change and the driving factors. Using the the mean value of the prediction accuracy outside the bag calculated by the model to evaluate the importance of the variables. The result indicates that the coefficient of partial correlation between precipitation and wetland density is the largest among the five influencing factors, followed by temperature, population density, elevation and slope is smallest. The influence of natural factors on the change of wetland density is mainly reflected in precipitation and temperature factors, and the precipitation is obviously higher than that of temperature, under the influence of human factors, the influence of population density factor on wetland density is higher than that of elevation and slope factor. The result shows that in the past 40 years, the human activities in the study area have increased the density of wetland to some extent, but it is not the main factor.
Directory of Open Access Journals (Sweden)
Bruce T. Milne
2017-05-01
Full Text Available Stream networks are branched structures wherein water and energy move between land and atmosphere, modulated by evapotranspiration and its interaction with the gravitational dissipation of potential energy as runoff. These actions vary among climates characterized by Budyko theory, yet have not been integrated with Horton scaling, the ubiquitous pattern of eco-hydrological variation among Strahler streams that populate river basins. From Budyko theory, we reveal optimum entropy coincident with high biodiversity. Basins on either side of optimum respond in opposite ways to precipitation, which we evaluated for the classic Hubbard Brook experiment in New Hampshire and for the Whitewater River basin in Kansas. We demonstrate that Horton ratios are equivalent to Lagrange multipliers used in the extremum function leading to Shannon information entropy being maximal, subject to constraints. Properties of stream networks vary with constraints and inter-annual variation in water balance that challenge vegetation to match expected resource supply throughout the network. The entropy-Horton framework informs questions of biodiversity, resilience to perturbations in water supply, changes in potential evapotranspiration, and land use changes that move ecosystems away from optimal entropy with concomitant loss of productivity and biodiversity.
Directory of Open Access Journals (Sweden)
Jin-Ying Zhuang
Full Text Available Attractiveness judgment in the context of mate preferences is thought to reflect an assessment of mate quality in relation to an absolute scale of genetic fitness and a relative scale of self-similarity. In this study, subjects judged the attractiveness and trustworthiness of faces in composite images that were manipulated to produce self-similar (self-resemblance and dissimilar (other-resemblance images. Males differentiated between self- and other-resemblance as well as among different degrees of self-resemblance in their attractiveness ratings; females did not. Specifically, in Experiment 1, using a morphing technique, we created previously unseen face images possessing different degrees (0%, 30%, 40%, or 50% of incorporation of the subject's images (different degrees of self-resemblance and found that males preferred images that were closer to average (0% rather than more self-similar, whereas females showed no preference for any degree of self-similarity. In Experiment 2, we added a pro-social question about trustworthiness. We replicated the Experiment 1 attractiveness rating results and further found that males differentiated between self- and other-resemblance for the same degree of composites; women did not. Both males and females showed a similar preference for self-resemblances when judging trustworthiness. In conclusion, only males factored self-resemblance into their attractiveness ratings of opposite-sex individuals in a manner consistent with cues of reproductive fitness, although both sexes favored self-resemblance when judging trustworthiness.
Modeling and simulation of self-similar traffic based on FBM model%基于FBM模型的自相似流量建模仿真
Institute of Scientific and Technical Information of China (English)
卢颖; 裴承艳; 陈子辰; 康凤举
2011-01-01
Network traffic models are important basis of network programming and performance evaluation. The conventional models are mostly based on Poisson model and Markovian franc model,which is only Short-Range Dependence. With the continuous development of network services, studies found that the actual network traffic has a long-range dependence （LRD） now and in a very long time , which is a kind of self-similarity. In this paper, the RMD and Fourier algorithm were adopted to simulate and analyze FBM model, a self-similar model. They generated the necessary sequence of self-similar traffic. Then the article uses R/S method and variance-time method to verify Hurst value of the generated sequence of self-similar traffic in order to verify the self-similarity of the self-similar traffic sequence. The existence of self-similarity is verified by experiments, and the advantage and disadvantage of RMD and Fourier algorithm are analyzed.%网络流量建模是网络规划与性能评价的重要基础。传统的业务模型大多基于泊松模型和马尔可夫排队模型，只具有短程相关性，随着网络业务的不断研究发现，实际网络业务流在很长的时间范围内都具有长程相关性，即一种自相似性。本文采用RMD算法和Fourier变换法对网络流量的自相似模型-FBM模型进行了建模及仿真研究，生成了所需的自相似流量序列。然后分别采用R／S法和方差时间图法对其进行自相似参数检测。结果验证了仿真算法所产生的序列存在着自相似性，并同时对RMD算法和Fourier变换法的优缺点进行了分析。
The quantization of river network morphology based on the Tokunaga network
Institute of Scientific and Technical Information of China (English)
2009-01-01
River network morphology not only reflects the structure of river stream but also has great effects on hydrological process, soil erosion, river evolution, and watershed topography. Here we propose and define a new sequence of self-similar networks and corresponding parameters for the generated Tokunaga network. We also discuss the topological and numerical characteristics of self-similar networks with different iteration rules by utilizing links and fractal dimension. Application results indicate that the proposed method could be used to generate river network, which is much consistent with natural river network. The proposed parameter λ could well reflect the river network morphology.
Gordon, Peter V
2012-01-01
This paper deals with the long-time behavior of solutions of nonlinear reaction-diffusion equations describing formation of morphogen gradients, the concentration fields of molecules acting as spatial regulators of cell differentiation in developing tissues. For the considered class of models, we establish existence of a new type of ultra-singular self-similar solutions. These solutions arise as limits of the solutions of the initial value problem with zero initial data and infinitely strong source at the boundary. We prove existence and uniqueness of such solutions in the suitable weighted energy spaces. Moreover, we prove that the obtained self-similar solutions are the long-time limits of the solutions of the initial value problem with zero initial data and a time-independent boundary source.
Xue, Liutang
2016-11-01
Motivated by the numerical simulation and the study on several 1D models, we consider the locally self-similar singular solutions for the surface quasi-geostrophic equation with decaying or non-decaying blowup profiles. Based on a suitable local Lp-inequality in terms of the profile and the bootstrapping method, we show some exclusion results and derive the asymptotic behavior of the possible blowup profiles.
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.
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.
Directory of Open Access Journals (Sweden)
Martin eBouda
2016-02-01
Full Text Available Fractal dimension (FD, estimated by box-counting, is a metric used to characterise 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 quantisation 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 characterise 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 digitised in 3D and subjected to box-counts. A pattern search algorithm was used to minimise QE by optimising 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 minimising 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 digitisations 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
Institute of Scientific and Technical Information of China (English)
张雪媛; 王永刚; 张琼
2013-01-01
针对网络流量自相似程度判别方法较少和应用分数布朗运动(FBM)进行自相似流量模拟时可能会产生负值流量等问题,给出一种基于多阶矩的自相似流量判别方法和改进FBM模型的自相似流量模拟方法.首先通过分析样本矩的数学式,在分形矩分析的基础上得到一种多阶矩的自相似判别方法,然后对经典的随机中点置位(RMD)算法进行改进,最后对Bellcore和LBL实验室采集的真实流量数据进行自相似判别和模拟,仿真验证实验结果表明该方法的有效性.%To deal with the difficulties of lacking the discrimination method of network's traffic self-similarity and producing negative traffic based on classical Fractal Brown Motion (FBM), a discrimination method was proposed based on multiple order moment and a generation method was provided based on modified FBM model. Firstly, the mathematical formula of sample moment was studied. The discrimination method of self-similarity traffic was obtained on account of fractal moment analysis. Secondly, the classical Random Midpoint Displacement ( RMD) algorithm was modified. At last, taking account of the real traffic of Bellcore and LBL, the discrimination method and generation method were given. The comparison of the simulation results with the actual experimental data proves that the method is feasible.
存储系统负载自相似性研究综述%Survey of Studies on Self-similarity in Storage System Workload
Institute of Scientific and Technical Information of China (English)
邹强; 程强
2013-01-01
I/O突发是造成I/O瓶颈的一个主要原因,研究I/O负载中普遍存在的突发性并对负载进行精确合成,对存储系统设计及其性能评价具有重要意义.对实际I/O负载的研究表明,传统的泊松假定难以准确地描述长时间范围内的I/O突发行为.研究发现,I/O突发在不同时间尺度下具有相似性,即I/O负载具有自相似性,因此,自相似模型被用来刻画I/O负载中的长相关性.针对I/O负载自相似参数估计,总结了各种常用的时域和频域估值方法.着重对已有的I/O负载合成模型进行了剖析,讨论了各种自相似模型、多分形模型以及alpha稳定模型的特点.探讨了有待解决的开放性问题,并对I/O负载自相似性研究的发展趋势进行了展望.上述工作将对存储负载的自相似性研究提供有益参考.%I/O bursty is one of the main reasons causing I/O bottleneck, so, it is significant for designing storage system and evaluating system performance to study and accurately synthesize the ubiquitous bursty in I/O workload. Research results show that the traditional poisson assumption is difficult to describe the I/O-burstiness behavior well at the long-term time scales,and I/O bursty exhibits the similarity at different time scales,i. e. ,self-similarity. So, self-similar models are used to characterize the long-range dependence in I/O workloads. Aimed at the Hurst parameter estimate, this paper summarized the time-domain and frequency-domain estimators usually used to estimate the degree of self-similarity in storage workloads. After that,some existing models synthesizing I/O workloads were examined, thereinto, the characteristics of self-similar, multi-fractal and alpha-stable models were discussed. After summarizing the unresolved problems , this paper explored the future trend of the study on self-similarity in I/O workloads. The above work will provide a valuable reference for pushing the research on self-similarity in storage
Energy Technology Data Exchange (ETDEWEB)
Filipov, L.G.
1984-01-01
A generalized nonlinear equation with self-similar solutions is developed for time-dependent disk accretion around quasars and active galactic nuclei. The equation accounts for viscous shear stress and opacity, and is based on a model defined by Shakura and Sunyaev (1973, 1977) describing disk accretion. Recurrent X ray bursts are demonstrated to result from continual gas accretion onto the accumulating disk of a neutron star with a strong magnetic field. The gas could also form a boundary layer around a white dwarf and produce X rays, as evidenced by observational data on Cir X-1. 15 references.
Shi, Xun
2016-01-01
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 $\\gamma \\approx 5/3$ 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 $\\sim 1.1-1.2$, are captured by the self-similar spherical collapse model, and are insensitive to the mass accretion history.
Directory of Open Access Journals (Sweden)
S. Borazjani
2014-01-01
Full Text Available Analytical solutions for one-dimensional two-phase multicomponent flows in porous media describe processes of enhanced oil recovery, environmental flows of waste disposal, and contaminant propagation in subterranean reservoirs and water management in aquifers. We derive the exact solution for 3×3 hyperbolic system of conservation laws that corresponds to two-phase four-component flow in porous media where sorption of the third component depends on its own concentration in water and also on the fourth component concentration. Using the potential function as an independent variable instead of time allows splitting the initial system to 2×2 system for concentrations and one scalar hyperbolic equation for phase saturation, which allows for full integration of non-self-similar problem with wave interactions.
Self-similar hydrodynamic flow in the laser light to x-ray conversion layer of a laser-heated solid
Energy Technology Data Exchange (ETDEWEB)
Oparin, A.M.; Sigel, R. [Max-Planck-Institut fuer Quantenoptik, D-85748 Garching (Germany)
1995-08-01
Intense short-wavelength laser light may be converted into thermal soft x rays in the dense plasma formed by irradiation of a solid high-{ital Z} material. Under certain conditions, the hydrodynamic flow in the conversion layer is self-similar, and profiles of the hydrodynamic variables may be readily calculated by solving the appropriate hydrodynamic equations. It is found that the structure of the conversion layer depends on the type of equilibrium that determines the atomic physics processes of radiation emission. Varying the conditions between the limits of local thermodynamic equilibrium (LTE) and coronal equilibrium (CE) shows, that in the latter case, the radiation comes mainly from a thin layer in the dense part of the conversion layer. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
基于网络自相似性的DDoS攻击检测%DDoS Attack Detection Based on the Self-similar Network
Institute of Scientific and Technical Information of China (English)
张冬梅; 李浩; 胡金鱼
2014-01-01
虽然目前在危害Internet的安全中，分布式拒绝服务即DDOS已经成为重要的隐患之一，但是由于对DDOS攻击进行防范、检测和反击的研究工作还没有取得实质性的重大突破，因此，目前还没有一种有效的方法来准确及时的预测DDOS攻击的发生。本文提出一种根据网络业务自相似性，通过实时建模和动态分析检测拒绝服务攻击发生前后网络流量自相似性参数Hurst的变化来检测DDoS攻击。通过仿真试验，该方法能够快速准确的检测出DDoS攻击的发生。%Although the harmfulness of Internet security, distributed denial of service DDOS has become one of the important potential danger, but because of the work of prevention, detection and response to DDOS attacks have not achieved a major breakthrough, there is not an efficient way to predict DDOS attacks accurately and timely. This paper presents a self similarity based on network traffic, by real-time modeling and dynamic analysis to detect denial of service attacks occurred before and after the self similar network traffic changes of parameters of Hurst to detect DDoS attacks. Through the simulation test, the method can quickly and accurately detect the occurrence of DDoS attack.
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
Kukushkin, A. B.; Rantsev-Kartinov, V. A.
2003-10-01
The phenomenon of skeletal structures (tubules, cartwheels, and their simple combinations) formerly found in laboratory plasmas, is extended to atmospheric and cosmic phenomena (Phys. Lett. A 306, 175, Dec. 2002). The long-lived filaments in plasmas have been suggested (1998) to possess a skeleton self-assembled during electric breakdown from wildly produced nanodust. The proof-of-concept studies revealed the skeletal structures in (1) plasmas in tokamaks, Z-pinches, plasma focus (in the range 0.01-10 cm), including the electric breakdown stage of discharge, (2) dust deposits in tokamak (10 nm - 10 microns), (3) hailstones (1-10 cm), tornado (10 m -1 km), (4) a wide class of objects in space (10^11-10^23 cm). The similarity of, and the trend toward self-similarity in, skeletal structures suggest all them to possess a fractal condensed matter of particular topology of the fractal. Here we discuss probable role of skeletal structures in the fast nonlocal transport of energy in strongly localized severe weather phenomena (tornado) and laboratory plasmas.
Kushnir, Doron
2010-01-01
Shock waves driven by the release of energy at the center of a cold ideal gas sphere of initial density rho\\propto r^{-omega} approach a self-similar (SLS) behavior, with velocity \\dot{R}\\propto R^delta, as R->\\infty. For omega>3 the solutions are of the second type, i.e. delta is determined by the requirement that the flow should include a sonic point. No solution satisfying this requirement exists, however, in the 3\\leq omega\\leq omega_{g}(gamma) "gap" (omega_{g}=3.26 for adiabatic index gamma=5/3). We argue that second type solutions should not be required in general to include a sonic point. Rather, it is sufficient to require the existence of a characteristic line r_c(t), such that the energy in the region r_c(t)\\infty, and an asymptotic solution given by the SLS solution at r_c(t)omega_g, and the latter identifies delta=0 solutions as the asymptotic solutions for 3\\leq omega\\leq omega_{g} (as suggested by Gruzinov 2003). In these solutions, r_c is a C_0 characteristic. It is difficult to check, using nu...
Nath, G.
2012-01-01
A self-similar solution is obtained for one dimensional adiabatic flow behind a cylindrical shock wave propagating in a rotating dusty gas in presence of heat conduction and radiation heat flux with increasing energy. The dusty gas is assumed to be a mixture of non-ideal (or perfect) gas and small solid particles, in which solid particles are continuously distributed. It is assumed that the equilibrium flow-condition is maintained and variable energy input is continuously supplied by the piston (or inner expanding surface). The heat conduction is expressed in terms of Fourier's law and the radiation is considered to be of the diffusion type for an optically thick grey gas model. The thermal conductivity K and the absorption coefficient αR are assumed to vary with temperature only. In order to obtain the similarity solutions the initial density of the ambient medium is assumed to be constant and the angular velocity of the ambient medium is assumed to be decreasing as the distance from the axis increases. The effects of the variation of the heat transfer parameters and non-idealness of the gas in the mixture are investigated. The effects of an increase in (i) the mass concentration of solid particles in the mixture and (ii) the ratio of the density of solid particles to the initial density of the gas on the flow variables are also investigated.
Directory of Open Access Journals (Sweden)
Selina eVåge
2015-12-01
Full Text Available 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.
Memory Function and Fractional Intergral Associated to the Random Self—similar Fractal
Institute of Scientific and Technical Information of China (English)
LIANGHong-liang; Hong-liang; LIUXiao-shu
2003-01-01
For a physics system which exhibits memory,if memory is preserved only at points of random self-similar fractals,we define random memory functions and give the connection between the expectation of flux and the fractional integral.In particular,when memory sets degenerate to Cantor type fractals or non-random self-similar fractals our results coincide with that of Nigmatullin and Ren et al.
Energy Technology Data Exchange (ETDEWEB)
Davies, J. A.; Perry, C. H.; Harrison, R. A. [RAL Space, Rutherford Appleton Laboratory, Harwell Oxford, OX11 0QX (United Kingdom); Trines, R. M. G. M. [Central Laser Facility, Rutherford Appleton Laboratory, Harwell Oxford, OX11 0QX (United Kingdom); Lugaz, N. [Space Science Centre, University of New Hampshire, Durham, NH 03824 (United States); Möstl, C. [Space Science Laboratory, University of California, Berkeley, CA 94720 (United States); Liu, Y. D. [State Key Laboratory of Space Weather, National Space Science Centre, Chinese Academy of Sciences, Beijing 100190 (China); Steed, K., E-mail: jackie.davies@stfc.ac.uk [Centre for mathematical Plasma Astrophysics, KU Leuven, B-3001 Leuven (Belgium)
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.
Wang, Sijia; Liu, Bowen; Song, Youjian; Hu, Minglie
2016-04-01
We report on a simple passive scheme to reduce the intensity noise of high-power nonlinear fiber amplifiers by use of the spectral-breathing parabolic evolution of the pulse amplification with an optimized negative initial chirp. In this way, the influences of amplified spontaneous emission (ASE) on the amplifier intensity noise can be efficiently suppressed, owing to the lower overall pulse chirp, shorter spectral broadening distance, as well as the asymptotic attractive nature of self-similar pulse amplification. Systematic characterizations of the relative intensity noise (RIN) of a free-running nonlinear Yb-doped fiber amplifier are performed over a series of initial pulse parameters. Experiments show that the measured amplifier RIN increases respect to the decreased input pulse energy, due to the increased amount of ASE noise. For pulse amplification with a proper negative initial chirp, the increase of RIN is found to be smaller than with a positive initial chirp, confirming the ASE noise tolerance of the proposed spectral-breathing parabolic amplification scheme. At the maximum output average power of 27W (25-dB amplification gain), the incorporation of an optimum negative initial chirp (-0.84 chirp parameter) leads to a considerable amplifier root-mean-square (rms) RIN reduction of ~20.5% (integrated from 10 Hz to 10 MHz Fourier frequency). The minimum amplifier rms RIN of 0.025% (integrated from 1 kHz to 5 MHz Fourier frequency) is obtained along with the transform-limited compressed pulse duration of 55fs. To our knowledge, the demonstrated intensity noise performance is the lowest RIN level measured from highpower free-running femtosecond fiber amplifiers.
Quist, M.C.; Gerow, K.G.; Bower, M.R.; Hubert, W.A.
2006-01-01
Native fishes of the upper Colorado River basin (UCRB) have declined in distribution and abundance due to habitat degradation and interactions with normative fishes. Consequently, monitoring populations of both native and nonnative fishes is important for conservation of native species. We used data collected from Muddy Creek, Wyoming (2003-2004), to compare sample size estimates using a random and a fixed-site sampling design to monitor changes in catch per unit effort (CPUE) of native bluehead suckers Catostomus discobolus, flannelmouth suckers C. latipinnis, roundtail chub Gila robusta, and speckled dace Rhinichthys osculus, as well as nonnative creek chub Semotilus atromaculatus and white suckers C. commersonii. When one-pass backpack electrofishing was used, detection of 10% or 25% changes in CPUE (fish/100 m) at 60% statistical power required 50-1,000 randomly sampled reaches among species regardless of sampling design. However, use of a fixed-site sampling design with 25-50 reaches greatly enhanced the ability to detect changes in CPUE. The addition of seining did not appreciably reduce required effort. When detection of 25-50% changes in CPUE of native and nonnative fishes is acceptable, we recommend establishment of 25-50 fixed reaches sampled by one-pass electrofishing in Muddy Creek. Because Muddy Creek has habitat and fish assemblages characteristic of other headwater streams in the UCRB, our results are likely to apply to many other streams in the basin. ?? Copyright by the American Fisheries Society 2006.
Institute of Scientific and Technical Information of China (English)
胡严; 刘星成; 张光昭
2001-01-01
传统的业务模型大多基于Poisson模型或其改进形式，假定业务突发长度显负指数分布.近期真实网络流量分析表明很多信息源会产生在多时间尺度下具有自相似特性的信息流.该性质显著地影响宽带网的流量控制及其排队分析．合成可控制的自相似业务流是进行仿真的第一步.实现了一个快速RMD算法的自相似流生成器；估计了产生的自相似流的Hurst参数；估计了两个或多个自相似流叠加后的流的Hurst参数；利用一种打乱算法成功地去掉了自相似流的长相关性.%The conventional models are mostly based on Poisson models or their improved versions.It is assumed that the distribution of burst length is exponential. Recent traffic analyses of a lot of networks have shown that many traffic sources produce traffic streams that are self-similar over several time scales. This character has severe impact on flow control and queuing analysis in broadband networks. A self-similar traffic stream generator using a high-speed RMD algorthm has been implemented. The Hurst parameters are estimated for those self-similar traffic streams from the generator and several superposed self-similar traffic streams.The autocorrelation structure of the self-similar traffic is destroyed by shuffling algorithm.
Institute of Scientific and Technical Information of China (English)
石佩虎
2004-01-01
研究了p-拉普拉斯发展方程ut＝div(up-2u)-uq 的自相似奇性解, 其中1＜p＜2, q＞1, (x, t)∈Rn×(0, ∞). 证明了当1＜q＜p-n/(n+1)时方程存在惟一的自相似强奇性解.%This paper investigates the self-similar singular solution of the p-Laplacian evolution equation with the nonlinear gradient absorption terms ut＝div(up-2u)-uq for 1＜p＜2 and q＞1 in Rn×(0, ∞). It has been proved that when 1＜q＜p-n/(n+1) there exists a unique self-similar very singular solution.
Institute of Scientific and Technical Information of China (English)
张少武; 易林
2009-01-01
在获得一个含变化3.5阶非线性、弱非局域性、增益及非线性增益的广义薛定谔方程的自相似解的基础上,采用数值方法研究了解的稳定性.结果表明,在同时具有或没有非局域性和5阶非线性的介质中可以形成与传播自相似波;而且当相位参数远离士～1/2时,非局域度和累积衍射将极大影响自相似波的稳定性.%Exact self-similar solution of a generalized nonlinear Schrodinger equation with varying cubic-quintic nonlinearity, weakly nonlocality, gain and nonlinear gain was obtained. The stability of the solution was studied numerically. The results show that the self-similar solitary wave can exist and propagate in the media with or without both nonlocality and quintic nonlinearity, and that the stability of the self-similar solitary wave is drastically influenced by the degree of nonlocality and the cumulative diffraction under the condition that the phase parameter is far from ±√2
Winstral, A. H.; Marks, D. G.
2012-12-01
This study presents an analysis of eleven years of manually sampled snow depth and SWE data at the drift-dominated Reynolds Mountain East catchment (0.36 km^2) in southwestern Idaho, U.S.A. The dataset includes eleven mid-winter surveys and ten surveys that targeted peak accumulation in the early spring. Depths were sampled on the same 30-meter grid covering the entire catchment in each survey. Densities were sampled at a coarser resolution using a depth-stratified random sampling scheme. In 19 of the 21 surveys, snow density increased with increasing depth until an upper limit was attained in the drifts. The coefficient of variation (CV) for mid-winter snow depths varied from 0.46 to 0.75 and was significantly related to seasonal wind speeds (p = 0.02). Energy inputs, correlated inversely to accumulation rates in this catchment, caused variability to increase as melt increased through the season. The CV for all three surveys that took place after peak accumulation exceeded 1.0. Inter-seasonal distributions were strongly correlated - correlation coefficients ranged from 0.70 to 0.97 with a mean of 0.84. An index site with similar site characteristics to NRCS Snotel sites gave reasonable approximations of average catchment SWE in drier years, however as snowfall increased this site increasingly over-estimated basin-wide SWE. Though others have found snow distributions to be reasonably approximated by two-parameter lognormal distributions, Kolmogorov-Smirnov goodness of fit tests rejected this hypothesis (p < 0.01) in 20 of the 21 observed distributions.
Institute of Scientific and Technical Information of China (English)
李莉苹; 张爱玲
2011-01-01
The self-similar evolution of an initial Gaussian pulse propagating in a nonlinearity increasing fiber (NIF) with an exponential nonlinearity profile is studied theoretically and numerically. As well as the dispersion decreasing fiber with normal group velocity dispersion (ND-DDF with a hyperbolic dispersion profile) , the NIF is also equivalent to a fiber amplifier, which can generate a parabolic self-similar pulse with strictly linear chirp. Furthermore, the impacts of two equivalent ways of ND-DDF and NIF on characteristics of the self-similar evolution are studied. The theoretical and simulation results show that: 1) the equivalent gain determines the results of self-similar evolution while the equivalent method determines the process speed; 2) with the same equivalent gain, the initial pulses in ND-DDF and NIF both evolve into the same parabolic self-similar pulse, but the process of NIF is more efficient, needing a shorter fiber length; 3) the relationship of fiber lengths of NIF and ND-DDF is to make the two fibers have the same "effective amplification".%采用理论推导和数值模拟相结合的方法研究了脉冲在指数渐增的非线性渐增光纤(NIF)中的自相似演化.结果表明,与双曲渐减的正色散渐减光纤(ND-DDF)类似,利用指数渐增的NIF也可获得具有严格线性凋啾的抛物线型自相似脉冲.同时深人研究了ND-DDF和NIF两种增益等效方式对自相似演化特性的影响,结果表明:1)等效增益决定了脉冲自相似演化的结果,等效方式决定了脉冲自相似演化进程快慢;2)在具有相等的等效增益条件下,脉冲在指数渐增NIF和双曲渐减ND-DDF中演化为相同的自相似脉冲,但是前者对脉冲的自相似演化更高效,即前者实现自相似演化所需光纤长度更短;3)两种增益等效方式所需光纤长度的关系是使得各自具有相同的光纤"有效放大因子".
Anisotropic Fractional Brownian Random Fields as White Noise Functionals
Institute of Scientific and Technical Information of China (English)
Zhi-yuan Huang; Chu-jin Li
2005-01-01
This investigation aims at a new construction of anisotropic fractional Brownisn random fields by the white noise approach. Moreover, we investigate its distribution and sample properties (stationariness of increments, self-similarity, sample continuity) which will furnish some useful views to future applications.
Institute of Scientific and Technical Information of China (English)
蒋加伏; 赵怡
2015-01-01
The traditional human action recognition algorithm tends to focus on solving a certain behavior recognition,it cannot be generalized.So,this paper put forward a kind of Local evidence RBF algorithm based high-level characteristic self similarity fusion for human behavior recognition.Firstly,the time-dependent generalized self similarity concept and the spa-tio-temporal interest point optical flow based local features extraction method were used to construct the human behavior description based on self similar matrix.Secondly,after independent individual behavior recognition in the use of SVM algo-rithm,the evidence theory based high level feature fusion was used to realize the optimization for classification of structure, which can improve the accuracy of classification.Simulation results show that the proposed scheme can significantly improve the efficiency and accuracy for human action recognition.%针对传统人体动作识别算法，往往重点解决某一类行为识别，不具有通用性的问题，提出一种局部证据 RBF人体行为高层特征自相似融合识别算法。首先，借用随时间变化的广义自相似性概念，利用时空兴趣点光流场局部特征提取方法，构建基于自相似矩阵的人体行为局部特征描述；其次，在使用 SVM算法进行独立个体行为识别后，利用所提出的证据理论 RBF(Radial Basis Function)高层特征融合，实现分类结构优化，从而提高分类准确度；仿真实验表明，所提方案能够明显提高人体行为识别算法效率和识别准确率。
De Vries, M.
1993-01-01
One dimension models - basic eauations, analytical models, numberical models. One dimensional models -suspended load, roughness and resistance of river beds. Solving river problems - tools, flood mitigation, bank protection.
Institute of Scientific and Technical Information of China (English)
代昆玉; 胡滨; 王翔
2011-01-01
网络蠕虫攻击是一种危害巨大且难以防御的网络攻击方式.传统的基于特征匹配的蠕虫检测方法受限于对蠕虫特征值的提取,无法检测未知类型蠕虫的攻击.在此将表征网络流量自相性的Hurst参数应用到蠕虫攻击检测.通过时Hurst参数的变化来检测未知类型蠕虫的攻击.实验表明该方法能有效检测到网络中采用主动扫描方式传播的未知类型蠕虫攻击行为.%Internet worms attack is harmful and difficult to defend.The traditional detection method based on feature matching is not suitable for detecting the attack launched by unknown worms since it requires worms'feature extraction in advance.The Hurst parameter of network flow self-similarity is applied to the detection of worms attack.The attack of the unknown worms is detected by changing the Hurst parameter.Experimental result shows that unknown worms' attacks can be detected efficiently.
基于自相似流量检测的DDoS攻击及防御研究%Research on DDoS Attack and Defense based on Network Self-similarity Detecting
Institute of Scientific and Technical Information of China (English)
黄长慧; 王海珍; 陈思
2014-01-01
DDoS attack is a widely-used and most dangerous attack mode of Internet. It takes availability of network service as the target. This paper introduces the principle of DDoS attack, and focus on methods of network self-similarity in detecting DDoS Attack. Finally, the methods of DDoS attack are analyzed comprehensively.%DDoS攻击是目前互联网中应用最广泛，也是危害性最大的一种攻击方式，以破坏网络服务的可用性为目标。文章首先介绍了DDoS的攻击原理，并重点对DDoS的攻击方式和基于自相似网络流量的DDoS攻击检测方式进行研究，最后针对目前DDoS攻击的防御方式进行了全面解析。
DEFF Research Database (Denmark)
Gorm Hansen, Louise Lyngfeldt
explores translocal connections through ethnographic fieldwork at a global water conference and preliminary fieldwork at chosen locations on China's Nu River. The Nu River is one of the last undammed rivers in Asia and runs through China close to the Chinese-Burmese border, then flows into the Andaman Sea...
L q dimensions and projections of random measures
Galicer, Daniel; Saglietti, Santiago; Shmerkin, Pablo; Yavicoli, Alexia
2016-09-01
We prove preservation of L q dimensions (for 1) under all orthogonal projections for a class of random measures on the plane, which includes (deterministic) homogeneous self-similar measures and a well-known family of measures supported on 1-variable fractals as special cases. We prove a similar result for certain convolutions, extending a result of Nazarov, Peres and Shmerkin. Recently many related results have been obtained for Hausdorff dimension, but much less is known for L q dimensions.
DEFF Research Database (Denmark)
2016-01-01
River nomads is a movie about people on the move. The documentary film explores the lifestyle of a group of nomadic fishermen whose mobility has been the recipe of success and troubles. Engaged in trade and travel, twice a year the river nomads form impressive convoys of majestic pirogues and set...... and liberated lifestyle and the breath-taking landscapes and vistas offered by the Niger River. River Nomads is also a personal account of the Kebbawa’s way of life and their current struggles as nomadic folk living in a world divided by borders and ruled by bureaucrats....
VANDENBERG, IP
1991-01-01
We present a mathematical model for the ''river-phenomenon'': striking concentrations of trajectories of ordinary differential equations. This model of ''macroscopic rivers'' is formulated within nonstandard analysis, and stated in terms of macroscopes and singular perturbations. For a subclass, the
On the local time of random processes in random scenery
Castell, Fabienne; Pène, Françoise; Schapira, Bruno
2012-01-01
Random walks in random scenery are processes defined by $Z_n:=\\sum_{k=1}^n\\xi_{X_1+...+X_k}$, where basically $(X_k,k\\ge 1)$ and $(\\xi_y,y\\in\\mathbb Z)$ are two independent sequences of i.i.d. random variables. We assume here that $X_1$ is $\\ZZ$-valued, centered and with finite moments of all orders. We also assume that $\\xi_0$ is $\\ZZ$-valued, centered and square integrable. In this case H. Kesten and F. Spitzer proved that $(n^{-3/4}Z_{[nt]},t\\ge 0)$ converges in distribution as $n\\to \\infty$ toward some self-similar process $(\\Delta_t,t\\ge 0)$ called Brownian motion in random scenery. In a previous paper, we established that ${\\mathbb P}(Z_n=0)$ behaves asymptotically like a constant times $n^{-3/4}$, as $n\\to \\infty$. We extend here this local limit theorem: we give a precise asymptotic result for the probability for $Z$ to return to zero simultaneously at several times. As a byproduct of our computations, we show that $\\Delta$ admits a bi-continuous version of its local time process which is locally H\\"o...
Edgington, Eugene
2007-01-01
Statistical Tests That Do Not Require Random Sampling Randomization Tests Numerical Examples Randomization Tests and Nonrandom Samples The Prevalence of Nonrandom Samples in Experiments The Irrelevance of Random Samples for the Typical Experiment Generalizing from Nonrandom Samples Intelligibility Respect for the Validity of Randomization Tests Versatility Practicality Precursors of Randomization Tests Other Applications of Permutation Tests Questions and Exercises Notes References Randomized Experiments Unique Benefits of Experiments Experimentation without Mani
Relationship to the River: The Case of the Muar River Community
Directory of Open Access Journals (Sweden)
Bahaman A. Samah
2011-01-01
Full Text Available Problem statement: Muar River which located in Johor, is an important river in Malaysia. Previously Muar River had a huge influence on the socio-economic status of the community. It has been used as the sources of income, protein and as well as the major mode of transportation for the community and traders. However, does the Muar River still has that influences on this modern day? The answer of this pertinent question will fulfill the main objective of this study which is to discover Muar River relationship with its surrounding community. Approach: In addition to relationship with the river, this quantitative study was conducted to determine the Muar River community agreement towards initiative to develop the river. A total of 300 respondents from 19 villages along Muar River were selected based on the simple random sampling. Results: Based on the analysis of the results, it can be concluded that Muar River still has a lot to offer to its surrounding community especially for the recreational activities (fish and prawn fishing. A large majority of Muar River community have a moderate and high level of agreement towards the river development. Further analysis performed revealed that income per month, number of household, age, distance to Muar River and period of staying in the areas had significant relationships with agreement towards river development. Conclusion/Recommendations: It is recommended that additional recreational facilities can be added, events at national and international level especially on fish and prawn fishing can be held at Muar River and campaign on the importance of river development and the danger of river pollution can be conducted.
Institute of Scientific and Technical Information of China (English)
罗光春; 林夏; 卢显良; 张骏
2003-01-01
This paper presents a new method of DDoS Intrude Detection Based on Self-Similarity of Network Traffics based on analysis of parameter of self-similar, which includes Hurst parameter, Holder parameter (Time variable function H(t)), we do research on the affect of H parameter change brought by DDoS attack. And we discover the DDoS attack can be detected in some extent by measure the change of H parameter, as it showed by the research result this network traffic based method can detected DDoS attack and is more reliable on the recognition of all kinds of DDoS attack than any other method based on character recognition.
Institute of Scientific and Technical Information of China (English)
GUO TieXin; CHEN XinXiang
2009-01-01
The purpose of this paper is to provide a random duality theory for the further development of the theory of random conjugate spaces for random normed modules.First,the complicated stratification structure of a module over the algebra L(μ,K) frequently makes our investigations into random duality theory considerably different from the corresponding ones into classical duality theory,thus in this paper we have to first begin in overcoming several substantial obstacles to the study of stratification structure on random locally convex modules.Then,we give the representation theorem of weakly continuous canonical module homomorphisms,the theorem of existence of random Mackey structure,and the random bipolar theorem with respect to a regular random duality pair together with some important random compatible invariants.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The purpose of this paper is to provide a random duality theory for the further development of the theory of random conjugate spaces for random normed modules. First, the complicated stratification structure of a module over the algebra L(μ, K) frequently makes our investigations into random duality theory considerably difierent from the corresponding ones into classical duality theory, thus in this paper we have to first begin in overcoming several substantial obstacles to the study of stratification structure on random locally convex modules. Then, we give the representation theorem of weakly continuous canonical module homomorphisms, the theorem of existence of random Mackey structure, and the random bipolar theorem with respect to a regular random duality pair together with some important random compatible invariants.
Measuring the fractal dimension of an optical random walk
Savo, Romolo; Svensson, Tomas; Vynck, Kevin; Wiersma, Diederik S
2013-01-01
Random walks often grasp the essence of transport processes in complex systems, representing a model for a large variety of phenomena, from human travel, to molecular kinetics, to the propagation of light and sound in disordered media. Transport is generally driven by the topology of the system, which can range from a simply random distribution of scattering elements, to very rich self-similar structures like random fractals. In this context the fractal dimension of the random walk trajectory, $d_\\mathrm{w}$, crucially determines the nature of the resulting transport process and provides information on the way the spatial evolution scales with time. In living cells and turbulent flow it has been possible to study anomalous dynamics showing $d_\\mathrm{w}\
Characterization of river flow fluctuations via horizontal visibility graphs
Braga, A C; Costa, L S; Ribeiro, A A; de Jesus, M M A; Tateishi, A A; Ribeiro, H V
2015-01-01
We report on a large-scale characterization of river discharges by employing the network framework of the horizontal visibility graph. By mapping daily time series from 141 different stations of 53 Brazilian rivers into complex networks, we present an useful approach for investigating the dynamics of river flows. We verified that the degree distributions of these networks were well described by exponential functions, where the characteristic exponents are almost always larger than the value obtained for random time series. The faster-than-random decay of the degree distributions is an another evidence that the fluctuation dynamics underlying the river discharges has a longe-range correlated nature. We further investigated the evolution of the river discharges by tracking the values of the characteristic exponents (of the degree distribution) and the global clustering coefficients of the networks over the years. We show that the river discharges in several stations have evolved to become more or less correlate...
Directory of Open Access Journals (Sweden)
Ginno Millán Naveas
2010-04-01
Full Text Available En este trabajo se presentan los fundamentos de un proyecto de investigación sobre el modelado de redes de computadoras con mecanismo de control de acceso al medio, según el estándar IEEE 802.3-2005, empleando los postulados de la teoría de conjuntos autosimilares para establecer el nivel de impacto que poseen las correlaciones temporales con dependencia de largo alcance sobre el rendimiento de tales redes. Se postula una nueva forma de estimar grados de autosimilaridad basada en una variación del estimador de Whittle.The foundation of a research project about a model of computer networks with media access control mechanism based on the IEEE standard 802.3-2005 is presented. The model draws from the theory of self-similar sets for establishing the impact level that the long-range-dependent temporary correlations have on the performance of such networks. A new method for the estimation of self-similar levels based on a variation of the Whittle estimator is postulated.
Hausdorff dimension of self-similar sets with overlaps
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
We provide a simple formula to compute the Hausdorff dimension of the attractor of an overlapping iterated function system of contractive similarities satisfying a certain collection of assumptions. This formula is obtained by associating a non-overlapping infinite iterated function system to an iterated function system satisfying our assumptions and using the results of Moran to compute the Hausdorff dimension of the attractor of this infinite iterated function system, thus showing that the Hausdorff dimension of the attractor of this infinite iterated function system agrees with that of the attractor of the original iterated function system. Our methods are applicable to some iterated function systems that do not satisfy the finite type condition recently introduced by Ngai and Wang.
The Relationship between Virtual Self Similarity and Social Anxiety
Directory of Open Access Journals (Sweden)
Laura eAymerich-Franch
2014-11-01
Full Text Available 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.
The Cosmic Foam and the Self-Similar Cluster Distribution
Van de Weygaert, R
1999-01-01
Voronoi Tessellations form an attractive and versatile geometrical asymptotic model for the foamlike cosmic distribution of matter and galaxies. In the Voronoi model the vertices are identified with clusters of galaxies. For a substantial range out to a scale in the order of the cellsize, their spatial two-point correlation function is a power-law with a slope $\\gamma \\approx 1.95$. This study presents recent results showing that subsets of vertices selected on the basis of their ``richness'', i.e. inflow volume, retain this power-law correlation behaviour. Interestingly, they do so with a ``clustering length'' $r_{\\rm o}$ that is exactly linearly proportional to the average inter-vertex distance in the sample, thus forming a realization of the Szalay-Schramm prescription. For the geometry and structural patterns even more significant is the finding tessellation vertices display a similar linear increase for their correlation length $r_{\\rm a}$, the coherence length at which $\\xi(r_{\\rm a})=0$. Such patterns ...
Brine transport in porous media self-similar solutions
C.J. van Duijn (Hans); L.A. Peletier (Bert); R.J. Schotting
1996-01-01
textabstractIn this paper we analyze a model for brine transport in porous media, which includes a mass balance for the fluid, a mass balance for salt, Darcy's law and an equation of state, which relates the fluid density to the salt mass fraction. This model incorporates the effect of local volume
Hausdorff dimension of self-similar sets with overlaps
Institute of Scientific and Technical Information of China (English)
DENG QiRong; John HARDING; HU TianYou
2009-01-01
We provide a simple formula to compute the Hausdorff dimension of the attractor of an overlapping iterated function system of contractive similarities satisfying a certain collection of assumptions. This formula is obtained by associating a non-overlapping infinite iterated function system to an iterated function system satisfying our assumptions and using the results of Moran to compute the Hausdorff dimension of the attractor of this infinite iterated function system,thus showing that the Hausdorff dimension of the attractor of this infinite iterated function system agrees with that of the attractor of the original iterated function system.Our methods are applicable to some iterated function systems that do not satisfy the finite type condition recently introduced by Ngai and Wang.
Self-similar motion of three point vortices
DEFF Research Database (Denmark)
Aref, Hassan
2010-01-01
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 Groumlbli's thesis of 1877 and has since been...
Analysis of self-similar solutions of multidimensional conservation laws
Energy Technology Data Exchange (ETDEWEB)
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.
Time inversion, Self-similar evolution, and Issue of time
Datta, D P
2001-01-01
We investigate the question, "how does time flow?" and show that time may change by inversions as well. We discuss its implications to a simple class of linear systems. Instead of introducing any unphysical behaviour, inversions can lead to a new multi- time scale evolutionary path for the linear system exhibiting late time stochastic fluctuations. We explain how stochastic behaviour is injected into the linear system as a combined effect of an uncertainty in the definition of inversion and the irrationality of the golden mean number. We also give an ansatz for the nonlinear stochastic behaviour of (fractal) time which facilitates us to estimate the late and short time limits of a two-time correlation function relevant for the stochastic fluctuations in linear systems. These fluctuations are shown to enjoy generic 1/f spectrum. The implicit functional definition of the fractal time is shown to satisfy the differential equation dx=dt. We also discuss the relevance of intrinsic time in the present formalism, st...
Self-similar energetics in large clusters of galaxies
Miniati, Francesco
2015-01-01
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 [1], while residual transonic flows create giant turbulent eddies and cascades [2,3]. Turbulence heats the intra-cluster medium [4] and also amplifies magnetic energy by way of dynamo action [5-8]. 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 a...
Self-Similar Fluid Dynamic Limits for the Broadwell System
1992-10-01
bounded variation such that f" -+ f pointwise on the reals. The function f is a local Maxwellian, that is f3 = flf2 for a.e. C, and satisfies the balance... bounded variation . The functions f’- admit constant values f+ outside [-1, 1i; therefore, first f’" ---+ f pointwise on (-oo, o0), and second f(ý) = f- for...2.4) 23 Thus (2.1) holds in the sense of distributions and, because fi, f2 are of bounded variation , it also holds in the sense of measures. Passing
Self-similar two-particle separation model
DEFF Research Database (Denmark)
Lüthi, Beat; Berg, Jacob; Ott, Søren
2007-01-01
We present a new stochastic model for relative two-particle separation in turbulence. Inspired by material line stretching, we suggest that a similar process also occurs beyond the viscous range, with time scaling according to the longitudinal second-order structure function S2(r), e.g.; in the i......We present a new stochastic model for relative two-particle separation in turbulence. Inspired by material line stretching, we suggest that a similar process also occurs beyond the viscous range, with time scaling according to the longitudinal second-order structure function S2(r), e.......g.; in the inertial range as epsilon−1/3r2/3. Particle separation is modeled as a Gaussian process without invoking information of Eulerian acceleration statistics or of precise shapes of Eulerian velocity distribution functions. The time scale is a function of S2(r) and thus of the Lagrangian evolving separation....... The model predictions agree with numerical and experimental results for various initial particle separations. We present model results for fixed time and fixed scale statistics. We find that for the Richardson-Obukhov law, i.e., =gepsilont3, to hold and to also be observed in experiments, high Reynolds...
Self-similar solutions for the foam drainage equation
Zitha, P.L.J.; Vermolen, F.J.
2003-01-01
The travelling wave solutions of the equation for foam drainage in porous media are developed taking into account the mass conservation criterion. The existence of traveling wave solutions is also discussed. Finally, numerical solutions are obtained using a finite difference scheme together with the
Dwarf and Normal Spiral Galaxies: are they Self-Similar?
Directory of Open Access Journals (Sweden)
Ana María Hidalgo Gámez
2004-01-01
Full Text Available En el presente estudio se ha tratado de comprobar si las galaxias espirales enanas constituyen un grupo diferente a las clásicas o por el contrario no son más que la cola de distribución de éstas. Para ello, lo primero ha sido establecer una lista de todas aquellas galaxias que tienen estructura espiral y pequeño tamaño. Después se ha buscado información acerca del color, luminosidad, morfología y características espectrales de estas galaxias. A partir de esta información se puede concluir que hay indicios más que suficientes para decir que las galaxias espirales enanas difieren de las espirales clásicas en algunas propiedades importantes como son la existencia de un gradiente en metalicidad y la frecuencia de las barras. De todas formas, son necesarias más observaciones de calidad para poder dar una respuesta definitiva.
Self-similar and fractal design for stretchable electronics
Rogers, John A.; Fan, Jonathan; Yeo, Woon-Hong; Su, Yewang; Huang, Yonggang; Zhang, Yihui
2017-04-04
The present invention provides electronic circuits, devices and device components including one or more stretchable components, such as stretchable electrical interconnects, electrodes and/or semiconductor components. Stretchability of some of the present systems is achieved via a materials level integration of stretchable metallic or semiconducting structures with soft, elastomeric materials in a configuration allowing for elastic deformations to occur in a repeatable and well-defined way. The stretchable device geometries and hard-soft materials integration approaches of the invention provide a combination of advance electronic function and compliant mechanics supporting a broad range of device applications including sensing, actuation, power storage and communications.
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.
Self-similar solutions to isothermal shock problems
Deschner, Stephan C; Duschl, Wolfgang J
2016-01-01
We investigate exact solutions for isothermal shock problems in different one-dimensional geometries. These solutions are given as analytical expressions if possible, or are computed using standard numerical methods for solving ordinary differential equations. We test the numerical solutions against the analytical expressions to verify the correctness of all numerical algorithms. We use similarity methods to derive a system of ordinary differential equations (ODE) yielding exact solutions for power law density distributions as initial conditions. Further, the system of ODEs accounts for implosion problems (IP) as well as explosion problems (EP) by changing the initial or boundary conditions, respectively. Taking genuinely isothermal approximations into account leads to additional insights of EPs in contrast to earlier models. We neglect a constant initial energy contribution but introduce a parameter to adjust the initial mass distribution of the system. Moreover, we show that due to this parameter a constant...
Self-similar and fractal design for stretchable electronics
Energy Technology Data Exchange (ETDEWEB)
Rogers, John A.; Fan, Jonathan; Yeo, Woon-Hong; Su, Yewang; Huang, Yonggang; Zhang, Yihui
2017-04-04
The present invention provides electronic circuits, devices and device components including one or more stretchable components, such as stretchable electrical interconnects, electrodes and/or semiconductor components. Stretchability of some of the present systems is achieved via a materials level integration of stretchable metallic or semiconducting structures with soft, elastomeric materials in a configuration allowing for elastic deformations to occur in a repeatable and well-defined way. The stretchable device geometries and hard-soft materials integration approaches of the invention provide a combination of advance electronic function and compliant mechanics supporting a broad range of device applications including sensing, actuation, power storage and communications.
Dissolved oxygen and water temperature dynamics in lowland rivers over various timescales
Directory of Open Access Journals (Sweden)
Rajwa-Kuligiewicz Agnieszka
2015-12-01
Full Text Available The impact of floodplain hydrology on the in-stream dissolved oxygen dynamics and the relation between dissolved oxygen and water temperature are investigated. This has been done by examining the time series of dissolved oxygen and water temperature coupled with meteorological and hydrological data obtained from two lowland rivers having contrasting hydrological settings. Spectral analysis of long-term oxygen variations in a vegetated river revealed a distinct scaling regime with slope ‘–1’ indicating a self-similar behaviour. Identical slopes were obtained for water temperature and water level. The same power-law behaviour was observed for an unvegetated river at small timescales revealing the underlying scaling behaviour of dissolved oxygen regime for different types of rivers and over various time scales. The results have shown that the oxygenation of a vegetated river is strongly related to its thermal regime and flow conditions. Moreover, analysis of short-term fluctuations in the unvegetated river demonstrated that physical factors such as rainfall and backwaters play a substantial role in the functioning of this ecosystem. Finally, the results show that the relation between water temperature and dissolved oxygen concentration at the diurnal timescale exhibits a looping behaviour on the variable plot. The findings of this study provide an insight into the sensitivity of rivers to changing hydro-physical conditions and can be useful in the assessment of environmental variability.
Stephanov, M A; Wettig, T
2005-01-01
We review elementary properties of random matrices and discuss widely used mathematical methods for both hermitian and nonhermitian random matrix ensembles. Applications to a wide range of physics problems are summarized. This paper originally appeared as an article in the Wiley Encyclopedia of Electrical and Electronics Engineering.
ajansen; kwhitefoot; panteltje1; edprochak; sudhakar, the
2014-07-01
In reply to the physicsworld.com news story “How to make a quantum random-number generator from a mobile phone” (16 May, http://ow.ly/xFiYc, see also p5), which describes a way of delivering random numbers by counting the number of photons that impinge on each of the individual pixels in the camera of a Nokia N9 smartphone.
Modeling and statistical analysis of non-Gaussian random fields with heavy-tailed distributions
Nezhadhaghighi, Mohsen Ghasemi; Nakhlband, Abbas
2017-04-01
In this paper, we investigate and develop an alternative approach to the numerical analysis and characterization of random fluctuations with the heavy-tailed probability distribution function (PDF), such as turbulent heat flow and solar flare fluctuations. We identify the heavy-tailed random fluctuations based on the scaling properties of the tail exponent of the PDF, power-law growth of q th order correlation function, and the self-similar properties of the contour lines in two-dimensional random fields. Moreover, this work leads to a substitution for the fractional Edwards-Wilkinson (EW) equation that works in the presence of μ -stable Lévy noise. Our proposed model explains the configuration dynamics of the systems with heavy-tailed correlated random fluctuations. We also present an alternative solution to the fractional EW equation in the presence of μ -stable Lévy noise in the steady state, which is implemented numerically, using the μ -stable fractional Lévy motion. Based on the analysis of the self-similar properties of contour loops, we numerically show that the scaling properties of contour loop ensembles can qualitatively and quantitatively distinguish non-Gaussian random fields from Gaussian random fluctuations.
Mehta, Madan Lal
1990-01-01
Since the publication of Random Matrices (Academic Press, 1967) so many new results have emerged both in theory and in applications, that this edition is almost completely revised to reflect the developments. For example, the theory of matrices with quaternion elements was developed to compute certain multiple integrals, and the inverse scattering theory was used to derive asymptotic results. The discovery of Selberg's 1944 paper on a multiple integral also gave rise to hundreds of recent publications. This book presents a coherent and detailed analytical treatment of random matrices, leading
Energy Technology Data Exchange (ETDEWEB)
CARR,ROBERT D.; VEMPALA,SANTOSH
2000-01-25
The authors present a new technique for the design of approximation algorithms that can be viewed as a generalization of randomized rounding. They derive new or improved approximation guarantees for a class of generalized congestion problems such as multicast congestion, multiple TSP etc. Their main mathematical tool is a structural decomposition theorem related to the integrality gap of a relaxation.
River Data Package for Hanford Assessments
Energy Technology Data Exchange (ETDEWEB)
Rakowski, Cynthia L.; Guensch, Gregory R.; Patton, Gregory W.
2006-08-01
This data package documents the technical basis for selecting physical and hydraulic parameters and input values that will be used in river modeling for Hanford assessments. This work was originally conducted as part of the Characterization of Systems Task of the Groundwater Remediation Project managed by Fluor Hanford, Inc. and revised as part of the Characterization of Systems Project managed by PNNL for DOE. The river data package provides calculations of flow and transport in the Columbia River system. The module is based on the legacy code for the Modular Aquatic Simulation System II (MASS2), which is a two-dimensional, depth-averaged model that provides the capability to simulate the lateral (bank-to-bank) variation of flow and contaminants. It simulates river hydrodynamics (water velocities and surface elevations), sediment transport, contaminant transport, biotic transport, and sediment-contaminant interaction, including both suspended sediments and bed sediments. This document presents the data assembled to run the river module components for the section of the Columbia River from Vernita Bridge to the confluence with the Yakima River. MASS2 requires data on the river flow rate, downstream water surface elevation, groundwater influx and contaminants flux, background concentrations of contaminants, channel bathymetry, and the bed and suspended sediment properties. Stochastic variability for some input parameters such as partition coefficient (kd) values and background radionuclide concentrations is generated by the Environmental Stochastic Preprocessor. River flow is randomized on a yearly basis. At this time, the conceptual model does not incorporate extreme flooding (for example, 50 to 100 years) or dam removal scenarios.
River Morphology and River Channel Changes
Institute of Scientific and Technical Information of China (English)
CHANG Howard H
2008-01-01
River morphology has been a subject of great challenge to scientists and engineers who recognize that any effort with regard to river engineering must be based on a proper understanding of the morphological features involved and the responses to the imposed changes. In this paper,an overview of river morphology is presented from the geomorphic viewpoint. Included in the scope are the regime concept, river channel classification, thresholds in river morphology, and geomor-phic analysis of river responses. Analytical approach to river morphology based on the physical principles for the hydraulics of flow and sediment transport processes is also presented. The appli-cation of analytical river morphology is demonstrated by an example. Modeling is the modern tech-nique to determine both short-term and long-term river channel responses to any change in the en-vironment. The physical foundation of fluvial process-response must be applied in formatting a mathematical model. A brief introduction of the mathematical model FLUVIAL-12 is described.
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
THE 400-kilometer Qingjiang River, second tributary of the Yangtze River in Hubei Province, has a drainage area of 17,000 square kilometers. Its advantageous natural conditions have made it a key water power development project.
US Fish and Wildlife Service, Department of the Interior — The Illinois River National Wildlife and Fish Refuges Complex stretches along 124 miles of the Illinois River in west central Illinois. The Complex includes three...
Allegheny County / City of Pittsburgh / Western PA Regional Data Center — This dataset contains locations of major rivers that flow through Allegheny County. These shapes have been taken from the Hydrology dataset. The Ohio River,...
Iowa's Sovereign Meandered Rivers
Iowa State University GIS Support and Research Facility — This data set depicts Iowa's Meandered Rivers. These rivers are deemed sovereign land & therefore require any person wishing to conduct construction activities...
Tapiero, Charles S.; Vallois, Pierre
2016-11-01
The premise of this paper is that a fractional probability distribution is based on fractional operators and the fractional (Hurst) index used that alters the classical setting of random variables. For example, a random variable defined by its density function might not have a fractional density function defined in its conventional sense. Practically, it implies that a distribution's granularity defined by a fractional kernel may have properties that differ due to the fractional index used and the fractional calculus applied to define it. The purpose of this paper is to consider an application of fractional calculus to define the fractional density function of a random variable. In addition, we provide and prove a number of results, defining the functional forms of these distributions as well as their existence. In particular, we define fractional probability distributions for increasing and decreasing functions that are right continuous. Examples are used to motivate the usefulness of a statistical approach to fractional calculus and its application to economic and financial problems. In conclusion, this paper is a preliminary attempt to construct statistical fractional models. Due to the breadth and the extent of such problems, this paper may be considered as an initial attempt to do so.
Gurau, Razvan
2017-01-01
Written by the creator of the modern theory of random tensors, this book is the first self-contained introductory text to this rapidly developing theory. Starting from notions familiar to the average researcher or PhD student in mathematical or theoretical physics, the book presents in detail the theory and its applications to physics. The recent detections of the Higgs boson at the LHC and gravitational waves at LIGO mark new milestones in Physics confirming long standing predictions of Quantum Field Theory and General Relativity. These two experimental results only reinforce today the need to find an underlying common framework of the two: the elusive theory of Quantum Gravity. Over the past thirty years, several alternatives have been proposed as theories of Quantum Gravity, chief among them String Theory. While these theories are yet to be tested experimentally, key lessons have already been learned. Whatever the theory of Quantum Gravity may be, it must incorporate random geometry in one form or another....
Random functions and turbulence
Panchev, S
1971-01-01
International Series of Monographs in Natural Philosophy, Volume 32: Random Functions and Turbulence focuses on the use of random functions as mathematical methods. The manuscript first offers information on the elements of the theory of random functions. Topics include determination of statistical moments by characteristic functions; functional transformations of random variables; multidimensional random variables with spherical symmetry; and random variables and distribution functions. The book then discusses random processes and random fields, including stationarity and ergodicity of random
Wild and scenic river reports: Alagnak River
US Fish and Wildlife Service, Department of the Interior — The Alagnak and its major tributary the Novianuk River and their immediate surroundings possess the qualities necessary for inclusion in the National Wild and Scenic...
Institute of Scientific and Technical Information of China (English)
1995-01-01
THE Yellow River is the Mother River of China. In the hearts of the Chinese people, it is not just an ancient river measuring 4,845 kilometers long that passes through nine provinces and regions, but also a symbol. The poets say that the waterway is the image of ancient China. Thephilosophers say the river is the shadow of a dragon. The river
Gayton, D.
2001-01-01
Metadata only record This perspective piece examines the history and geography of the Columbia River and some current ecosystem management issues related to hydroelectric development on the river. Once the greatest salmon producer in the word, the Columbia has, according to the author, become a "ghost river," with its salmon runs reduced to remnants, and its ecological integrity hanging in the balance. The author suggests that British Columbians have much to lose, both biologically and cul...
DEFF Research Database (Denmark)
Wessels, Josepha Ivanka
2015-01-01
Currently there is no coherent or sustainable water cooperation among the five states—Israel, Jordan, Lebanon, Palestinian territories and Syria—that share the Jordan River. Why do people not cooperate on sustainable river basin management, even if it seems the most rational course from...... to illustrate hydropolitics in praxis, because the political future of this particular area in many respects affects the sustainable future of the Jordan River Basin and the entire Levant....
Long-time behavior of a Hele-Shaw type problem in random media
Pozar, Norbert
2010-01-01
We study the long-time behavior of an exterior Hele-Shaw problem in random media with a free boundary velocity that depends on position in dimensions $n \\geq 2$. A natural rescaling of solutions that is compatible with the evolution of the free boundary leads to homogenization of the free boundary velocity. By studying a limit obstacle problem for a Hele-Shaw system with a point source, we are able to show uniform convergence of the rescaled solution to a self-similar limit profile and we deduce that the rescaled free boundary uniformly approaches a sphere.
Bennett, J
2002-01-01
Rivers provide society with numerous returns. These relate to both the passive and extractive uses of the resources embodied in river environments. Some returns are manifest in the form of financial gains whilst others are non-monetary. For instance, rivers are a source of monetary income for those who harvest their fish. The water flowing in rivers is extracted for drinking and to water crops and livestock that in turn yield monetary profits. However, rivers are also the source of non-monetary values arising from biological diversity. People who use them for recreation (picnicking, swimming, boating) also receive non-monetary returns. The use of rivers to yield these returns has had negative consequences. With extraction for financial return has come diminished water quantity and quality. The result has been a diminished capacity of rivers to yield (non-extractive) environmental returns and to continue to provide extractive values. A river is like any other asset. With use, the value of an asset depreciates because its productivity declines. In order to maintain the productive capacity of their assets, managers put aside from their profits depreciation reserves that can be invested in the repair or replacement of those assets. Society now faces a situation in which its river assets have depreciated in terms of their capacity to provide monetary and non-monetary returns. An investment in river "repair" is required. But, investment means that society gives up something now in order to achieve some benefit in the future. Society thus has to grapple wih the choice between investing in river health and other investments--such as in hospitals, schools, defence etc. - as well as between investing in river health and current consumption--such as on clothes, food, cars etc. A commonly used aid for investment decision making in the public sector is benefit cost analysis. However, its usefulness in tackling the river investment problem is restricted because it requires all
Vermont Center for Geographic Information — River corridors are delineated to provide for the least erosive meandering and floodplain geometry toward which a river will evolve over time. River corridor maps...
Random fixed points and random differential inclusions
Directory of Open Access Journals (Sweden)
Nikolaos S. Papageorgiou
1988-01-01
Full Text Available In this paper, first, we study random best approximations to random sets, using fixed point techniques, obtaining this way stochastic analogues of earlier deterministic results by Browder-Petryshyn, KyFan and Reich. Then we prove two fixed point theorems for random multifunctions with stochastic domain that satisfy certain tangential conditions. Finally we consider a random differential inclusion with upper semicontinuous orientor field and establish the existence of random solutions.
Raptor-Powerline Mortality Data, Snake River Birds of Prey Conservation Area - 1999-2005
U.S. Geological Survey, Department of the Interior — This data set is a spreadsheet resulting from monthly searches for dead birds along randomly selected power line segments in and near the Snake River Birds of Prey...
Raptor-Powerline Mortality Data, Snake River Birds of Prey Conservation Area - 1999-2005
Oak Ridge National Laboratory — This data set is a spreadsheet resulting from monthly searches for dead birds along randomly selected power line segments in and near the Snake River Birds of Prey...
Microbial Ecoenzymatic Stoichiometry as an Indicator of Nutrient Limitation in US Streams and Rivers
We compared microbial ecoenzymatic activity at 2122 randomly-selected stream and river sites across the conterminous US. The sites were evenly distributed between wadeable and non-wadeable streams and rivers. Sites were aggregated into nine larger physiographic provinces for stat...
Microbial Ecoenzymatic Stoichiometry as an Indicator of Nutrient Limitation in US Streams and Rivers
We compared microbial ecoenzymatic activity at 2122 randomly-selected stream and river sites across the conterminous US. The sites were evenly distributed between wadeable and non-wadeable streams and rivers. Sites were aggregated into nine larger physiographic provinces for stat...
Modelling river dune development
Paarlberg, Andries; Weerts, H.J.T.; Dohmen-Janssen, Catarine M.; Ritsema, I.L; Hulscher, Suzanne J.M.H.; van Os, A.G.; Termes, A.P.P.
2005-01-01
Since river dunes influence flow resistance, predictions of dune dimensions are required to make accurate water level predictions. A model approach to simulate developing river dunes is presented. The model is set-up to be appropriate, i.e. as simple as possible, but with sufficient accuracy for
Hoitink, A.J.F.; Jay, D.A.
2016-01-01
Tidal rivers are a vital and little studied nexus between physical oceanography and hydrology. It is only in the last few decades that substantial research efforts have been focused on the interactions of river discharge with tidal waves and storm surges into regions beyond the limit of salinity
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Concerned about the effects of increasing water scarcity on economic development, China hopes a new law will save the Yellow River The first day of August marked what could be a new page in the history of China's long-suffering "mother river." That day, a regulation took effect that for the first time in histo-
Characterization of river flow fluctuations via horizontal visibility graphs
Braga, A. C.; Alves, L. G. A.; Costa, L. S.; Ribeiro, A. A.; de Jesus, M. M. A.; Tateishi, A. A.; Ribeiro, H. V.
2016-02-01
We report on a large-scale characterization of river discharges by employing the network framework of the horizontal visibility graph. By mapping daily time series from 141 different stations of 53 Brazilian rivers into complex networks, we present a useful approach for investigating the dynamics of river flows. We verified that the degree distributions of these networks were well described by exponential functions, where the characteristic exponents are almost always larger than the value obtained for random time series. The faster-than-random decay of the degree distributions is an another evidence that the fluctuation dynamics underlying the river discharges has a long-range correlated nature. We further investigated the evolution of the river discharges by tracking the values of the characteristic exponents (of the degree distribution) and the global clustering coefficients of the networks over the years. We show that the river discharges in several stations have evolved to become more or less correlated (and displaying more or less complex internal network structures) over the years, a behavior that could be related to changes in the climate system and other man-made phenomena.
Modeling sediment transport in river networks
Wang, Xu-Ming; Hao, Rui; Huo, Jie; Zhang, Jin-Feng
2008-11-01
A dynamical model is proposed to study sediment transport in river networks. A river can be divided into segments by the injection of branch streams of higher rank. The model is based on the fact that in a real river, the sediment-carrying capability of the stream in the ith segment may be modulated by the undergone state, which may be erosion or sedimentation, of the i-1th and ith segments, and also influenced by that of the ith injecting branch of higher rank. We select a database about the upper-middle reach of the Yellow River in the lower-water season to test the model. The result shows that the data, produced by averaging the erosion or sedimentation over the preceding transient process, are in good agreement with the observed average in a month. With this model, the steady state after transience can be predicted, and it indicates a scaling law that the quantity of erosion or sedimentation exponentially depends on the number of the segments along the reach of the channel. Our investigation suggests that fluctuation of the stream flow due to random rainfall will prevent this steady state from occurring. This is owing to the phenomenon that the varying trend of the quantity of erosion or sedimentation is opposite to that of sediment-carrying capability of the stream.
2007-01-01
The Mackenzie River in the Northwest Territories, Canada, with its headstreams the Peace and Finley, is the longest river in North America at 4241 km, and drains an area of 1,805,000 square km. The large marshy delta provides habitat for migrating Snow Geese, Tundra Swans, Brant, and other waterfowl. The estuary is a calving area for Beluga whales. The Mackenzie (previously the Disappointment River) was named after Alexander Mackenzie who travelled the river while trying to reach the Pacific in 1789. The image was acquired on August 4, 2005, covers an area of 55.8 x 55.8 km, and is located at 68.6 degrees north latitude, 134.7 degrees west longitude. The U.S. science team is located at NASA's Jet Propulsion Laboratory, Pasadena, Calif. The Terra mission is part of NASA's Science Mission Directorate.
Earth Data Analysis Center, University of New Mexico — This map layer portrays the linear federally-owned land features (i.e., national parkways, wild and scenic rivers, etc.) of the United States, Puerto Rico, and the...
Seizilles, Grégoire; Devauchelle, Olivier; Lajeunesse, Éric; Métivier, François
2014-05-01
A viscous fluid flowing over fine plastic grains spontaneously channelizes into a few centimeters-wide river. After reaching its equilibrium shape, this stable laboratory flume is able to carry a steady load of sediments, like many alluvial rivers. When the sediment discharge vanishes, the river size, shape and slope fit the threshold theory proposed by Glover and Florey (1951), which assumes that the Shields parameter is critical on the channel bed. As the sediment discharge is increased, the river widens and flattens. Surprisingly, the aspect ratio of its cross section depends on the sediment discharge only, regardless of the water discharge. We propose a theoretical interpretation of these findings based on the balance between gravity, which pulls particles towards the center of the channel, and the diffusion of bedload particles, which pushes them away from areas of intense bedload.
US Fish and Wildlife Service, Department of the Interior — A survey of white-fronted goose (Anser albifrons) and Canada goose (Branta canadensis) broods was conducted on 58 3/8 miles of the Dulbi River in Alaska. Four...
Skjern River Restoration Counterfactual
DEFF Research Database (Denmark)
Clemmensen, Thomas Juel
2014-01-01
In 2003 the Skjern River Restoration Project in Denmark was awarded the prestigious Europa Nostra Prize for ‘conserving the European cultural heritage’ (Danish Nature Agency 2005). In this case, however, it seems that the conservation of one cultural heritage came at the expense of another cultural...... of Dissonance in Nature Restoration’, Journal of Landscape Architecture 2/2014: 58-67. Danish Nature Agency (2005), Skjern Å: Ådalens historie. De store projekter. Det nye landskab og naturen. På tur i ådalen [The Skjern River: The History of the River Delta. The Big Projects. The New Landscape and Nature...... heritage. While the meanders of the Skjern River were reconstructed according to its assumed course in 1870s, the embanked canal, which was the main feature and symbol of a comprehensive cultivation project from the 1960s, was deconstructed and reduced to incomprehensible traces of the past. Not only did...
US Fish and Wildlife Service, Department of the Interior — In this study, undertaken as an independent project at Bellport High School, the authors have attempted to provide a historical description of the Carmans River area...
US Fish and Wildlife Service, Department of the Interior — This document is an analysis and summary of progress toward achieving the interim management objectives for the Russian River during the 1979 season. Additionally,...
Brown, R.; Pasternack, G. B.
2011-12-01
The description of fluvial form has evolved from anecdotal descriptions to artistic renderings to 2D plots of cross section or longitudinal profiles and more recently 3D digital models. Synthetic river valleys, artificial 3D topographic models of river topography, have a plethora of potential applications in fluvial geomorphology, and the earth sciences in general, as well as in computer science and ecology. Synthetic river channels have existed implicitly since approximately the 1970s and can be simulated from a variety of approaches spanning the artistic and numerical. An objective method of synthesizing 3D stream topography based on reach scale attributes would be valuable for sizing 3D flumes in the physical and numerical realms, as initial input topography for morphodynamic models, stream restoration design, historical reconstruction, and mechanistic testing of interactions of channel geometric elements. Quite simply - simulation of synthetic channel geometry of prescribed conditions can allow systematic evaluation of the dominant relationships between river flow and geometry. A new model, the control curve method, is presented that uses hierarchically scaled parametric curves in over-lapping 2D planes to create synthetic river valleys. The approach is able to simulate 3D stream geometry from paired 2D descriptions and can allow experimental insight into form-process relationships in addition to visualizing past measurements of channel form that are limited to two dimension descriptions. Results are presented that illustrate the models ability to simulate fluvial topography representative of real world rivers as well as how channel geometric elements can be adjusted. The testing of synthetic river valleys would open up a wealth of knowledge as to why some 3D attributes of river channels are more prevalent than others as well as bridging the gap between the 2D descriptions that have dominated fluvial geomorphology the past century and modern, more complete, 3D
Discrete random walk models for space-time fractional diffusion
Energy Technology Data Exchange (ETDEWEB)
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo
2002-11-01
A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order {alpha} is part of (0,2] and skewness {theta} (module{theta}{<=}{l_brace}{alpha},2-{alpha}{r_brace}), and the first-order time derivative with a Caputo derivative of order {beta} is part of (0,1]. Such evolution equation implies for the flux a fractional Fick's law which accounts for spatial and temporal non-locality. The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process that we view as a generalized diffusion process. By adopting appropriate finite-difference schemes of solution, we generate models of random walk discrete in space and time suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation.
Random broadcast on random geometric graphs
Energy Technology Data Exchange (ETDEWEB)
Bradonjic, Milan [Los Alamos National Laboratory; Elsasser, Robert [UNIV OF PADERBORN; Friedrich, Tobias [ICSI/BERKELEY; Sauerwald, Tomas [ICSI/BERKELEY
2009-01-01
In this work, we consider the random broadcast time on random geometric graphs (RGGs). The classic random broadcast model, also known as push algorithm, is defined as: starting with one informed node, in each succeeding round every informed node chooses one of its neighbors uniformly at random and informs it. We consider the random broadcast time on RGGs, when with high probability: (i) RGG is connected, (ii) when there exists the giant component in RGG. We show that the random broadcast time is bounded by {Omicron}({radical} n + diam(component)), where diam(component) is a diameter of the entire graph, or the giant component, for the regimes (i), or (ii), respectively. In other words, for both regimes, we derive the broadcast time to be {Theta}(diam(G)), which is asymptotically optimal.
Completely random signed measures
DEFF Research Database (Denmark)
Hellmund, Gunnar
Completely random signed measures are defined, characterized and related to Lévy random measures and Lévy bases.......Completely random signed measures are defined, characterized and related to Lévy random measures and Lévy bases....
Combination of fractional Brownian random field and lacunarity for iris recognition
Liu, Kai; Zhou, Weidong; Wang, Yu
2011-10-01
Feature extraction plays a vital role in iris recognition, affecting the performance of iris recognition algorithm strongly. In this paper, we present an individual recognition algorithm using fractal dimension based on fractional Brownian random field and lacunarity in feature extraction. Making use of the fractal feature of iris, such as self-similarity and random patterns, fractal dimension can extract texture information effectively. Lacunarity overcomes the limitation of fractal dimension that fractal sets with different textures may share the same fractal dimension value. The combination of fractal dimension and lacunarity makes the feature extraction more comprehensive and distinguishable. The experimental results show that this recognition algorithm can obtain great performance on CASIA 1.0 iris database
Wind River: A Wild and Scenic River Analysis: Preliminary draft
US Fish and Wildlife Service, Department of the Interior — The Wind River meets the criteria for inclusion in the National Wild and Scenic Rivers System. Subject to valid existing rights, the minerals in Federal lands which...
Kisaralik River: A wild and scenic river analysis
US Fish and Wildlife Service, Department of the Interior — The Kisaralik River from and including Kisaralik Lake to the west boundary of TSN, R65W meets the criteria established by the Wild and Scenic Rivers Act for...
Study on the Reutilization of River Sediment
Institute of Scientific and Technical Information of China (English)
LIU Gui-yun; JIANG Pei-hua; XI Dan-li
2002-01-01
Main components and properties of river sediment are introduced. Secondary pollution of river sediments to the water quality of the river is clarified. The methods of the reutilization of river sediment are elucidated.
2010-10-01
... 50 Wildlife and Fisheries 7 2010-10-01 2010-10-01 false Critical habitat for Snake River sockeye salmon, Snake River fall chinook salmon, and Snake River spring/summer chinook salmon. 226.205 Section... Snake River sockeye salmon, Snake River fall chinook salmon, and Snake River spring/summer...
2010-07-01
... 33 Navigation and Navigable Waters 3 2010-07-01 2010-07-01 false Red Lake River, Minn.; logging regulations for portion of river above Thief River Falls. 207.380 Section 207.380 Navigation and Navigable... Red Lake River, Minn.; logging regulations for portion of river above Thief River Falls. (a)...
33 CFR 117.734 - Navesink River (Swimming River).
2010-07-01
... 33 Navigation and Navigable Waters 1 2010-07-01 2010-07-01 false Navesink River (Swimming River). 117.734 Section 117.734 Navigation and Navigable Waters COAST GUARD, DEPARTMENT OF HOMELAND SECURITY... (Swimming River). The Oceanic Bridge, mile 4.5, shall open on signal; except that, from December 1 through...
2002-01-01
This image of the northern portion of the Nile River was captured by MISR's nadir camera on January 30, 2001 (Terra orbit 5956). The Nile is the longest river in the world, extending for about 6700 kilometers from its headwaters in the highlands of eastern Africa. At the apex of the fertile Nile River Delta is the Egyptian capital city of Cairo. To the west are the Great Pyramids of Giza. North of here the Nile branches into two distributaries, the Rosetta to the west and the Damietta to the east. Also visible in this image is the Suez Canal, a shipping waterway connecting Port Said on the Mediterranean Sea with the Gulf of Suez. The Gulf is an arm of the Red Sea, and is located on the righthand side of the picture. Image credit: NASA/GSFC/LaRC/JPL, MISR Team.
U.S. Environmental Protection Agency — PFAS concentrations in river and drinking water in and around the Haw River in North Carolina. This dataset is associated with the following publication: Sun, M., E....