A Discretized Version of the Self-Similar Model for Internet Traffic

2006 ◽  
Author(s):  
Konstantinos Drakakis ◽  
Dragan Radulovic
Keyword(s):  
Internet Traffic ◽  
The Self ◽  
Similar Model ◽  
Self Similar

A self‐similar model for sedimentary rocks with application to the dielectric constant of fused glass beads

Geophysics ◽  
1981 ◽  
Vol 46 (5) ◽  
pp. 781-795 ◽  
Author(s):  
P. N. Sen ◽  
C. Scala ◽  
M. H. Cohen
Keyword(s):  
Dielectric Constant ◽  
External Field ◽  
Sedimentary Rocks ◽  
Glass Beads ◽  
The Self ◽  
Similar Model ◽  
Archie’S Law ◽  
Self Consistent ◽  
Self Similar ◽  
Coated Spheres

We develop a theory for dielectric response of water‐saturated rocks based on a realistic model of the pore space. The absence of a percolation threshold manifest in Archie’s law, porecasts, electron‐micrographs, and general theories of formation of detrital sedimentary rocks indicates that the pore spaces within such rocks remain interconnected to very low values of the porosity ϕ. In the simplest geometric model for which the conducting paths remain interconnected, each grain is envisioned to be coated with water. The dielectric constant of the assembly of water‐coated grains is obtained by a self‐consistent effective medium theory. In the dc limit, this gives Maxwell’s relation for conductivity σ of the rock [Formula: see text], where [Formula: see text] is the conductivity of water. In order to include the local environmental effects around a grain, a self‐similar model is generated by envisioning that each rock grain itself is coated with a skin made of other coated spheres; the coating at each level consists of other coated spheres. The self‐consistent complex dielectric constant [Formula: see text] is given in this model in terms of that of water [Formula: see text] and of rock [Formula: see text], by [Formula: see text] for spherical particles. This gives, in the dc limit, [Formula: see text]. For nonspherical particles, the exponent m in Archie’s law [Formula: see text] is greater than 3/2 for the plate‐like grains or cylinders with axis perpendicular to the external field and smaller than 3/2 for plates or cylindrical particles with axis parallel to the external field. Artificial rocks with a wide range of porosities were made from glass beads. We present data on the glass bead rocks for dc conductivity and the dielectric constant at 1.1 GHz. The data follow the conductivity and the dielectric responses given by the self‐similar model. The present theory fails to explain the salinity dependence of [Formula: see text] at lower frequencies.

scholarly journals Evolution of X-Ray Clusters of Galaxies with Active Protogalaxies

1998 ◽  
Vol 188 ◽  
pp. 321-322
Author(s):  
H. Saga ◽  
S. Yachi ◽  
A. Habe
Keyword(s):  
Formation Process ◽  
The Self ◽  
Radiative Cooling ◽  
Clusters Of Galaxies ◽  
Similar Model ◽  
X Ray ◽  
Metal Abundance ◽  
Self Similar ◽  
The Difference ◽  
Intracluster Gas

We consider heating due to proto galaxies in the formation process of clusters of galaxies, since much metal is observed in the intracluster gas which must be ejected from protogalaxies vir strong galactic winds and the metal abundance in the intracluster gas correlates with the fraction of early type galaxies in clusters (Arnaud 1993). We also consider radiative cooling. From the difference between the observed LX - TX relation of X-ray cluster (Hatsukade 1989), LX ∝ T2.7-3.3X, and the prediction from the self-similar model (Kaiser 1986), LX ∝ T2X, it is pointed out that physical processes which are not taken into account in the self-similar model, e.g., effect of radiative cooling, and/or effect of proto galaxy heating, play a important role in the formation process (Evrard and Henry 1991, Kaiser 1991).

scholarly journals Mathematics in Internet Traffic Data Analysis

2011 ◽  
pp. 59-67
Author(s):  
Sasmita Acharya ◽  
Sasmita Mishra ◽  
S.N. Mishra
Keyword(s):  
Spatial Scales ◽  
Internet Traffic ◽  
The Self ◽  
Traffic Data ◽  
Similar Nature ◽  
Main Research ◽  
Wide Range ◽  
Extreme Variability ◽  
Fractal Characteristics ◽  
Self Similar

The Internet traffic data have been found to possess extreme variability and bursty structures in a wide range of time-scales, so that there is no definite duration of busy or silent periods. But there is a self-similarity for which it is possible to characterize the data. The self-similar nature was first proposed by Leland et a1 [l] and subsequently established by others in a flood of research works on the subject [2]-[5]. It was then a new concept against the long believed idea of Poisson traffic. The traditional Poison model, a short ranged process, assumed the variation of data flow to be finite but the observations on Internet traffic proved otherwise. It is this large variance that leads to the self-similar nature of the data almost at all scales of resolution. Such a feature is always associated with a fractal structure of the data. The fractal characteristics can exist both in temporal and spatial scales. This was indicated by Willinger and Paxson [6], as due to the extreme variability and long range dependence in the process. Presently, one of the main research interests in the field of Internet traffic is that of prediction of data which will help a network manager to render a satisfactory quality of service. Before preparing a model of prediction, one of the important tasks is to determine its statistics. Any model to predict the future values will have to preserve these characteristics.

scholarly journals Hausdorff measure and Assouad dimension of generic self-conformal IFS on the line

2020 ◽  
pp. 1-31
Author(s):  
Balázs Bárány ◽  
Károly Simon ◽  
István Kolossváry ◽  
Michał Rams
Keyword(s):  
Hausdorff Measure ◽  
Similar Case ◽  
Iterated Function Systems ◽  
The Self ◽  
Dimensional Hausdorff Measure ◽  
Assouad Dimension ◽  
Iterated Function ◽  
Self Similar ◽  
Weak Separation ◽  
Topological Sense

This paper considers self-conformal iterated function systems (IFSs) on the real line whose first level cylinders overlap. In the space of self-conformal IFSs, we show that generically (in topological sense) if the attractor of such a system has Hausdorff dimension less than 1 then it has zero appropriate dimensional Hausdorff measure and its Assouad dimension is equal to 1. Our main contribution is in showing that if the cylinders intersect then the IFS generically does not satisfy the weak separation property and hence, we may apply a recent result of Angelevska, Käenmäki and Troscheit. This phenomenon holds for transversal families (in particular for the translation family) typically, in the self-similar case, in both topological and in measure theoretical sense, and in the more general self-conformal case in the topological sense.

scholarly journals Onset of the Mach Reflection of Zel’dovich–von Neumann–Döring Detonations

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 314
Author(s):  
Tianyu Jing ◽  
Huilan Ren ◽  
Jian Li
Keyword(s):  
Hot Spot ◽  
Mach Reflection ◽  
Near Field ◽  
The Self ◽  
Small Scale ◽  
Mach Stem ◽  
Self Similarity ◽  
Von Neumann ◽  
Similarity Problem ◽  
Self Similar

The present study investigates the similarity problem associated with the onset of the Mach reflection of Zel’dovich–von Neumann–Döring (ZND) detonations in the near field. The results reveal that the self-similarity in the frozen-limit regime is strictly valid only within a small scale, i.e., of the order of the induction length. The Mach reflection becomes non-self-similar during the transition of the Mach stem from “frozen” to “reactive” by coupling with the reaction zone. The triple-point trajectory first rises from the self-similar result due to compressive waves generated by the “hot spot”, and then decays after establishment of the reactive Mach stem. It is also found, by removing the restriction, that the frozen limit can be extended to a much larger distance than expected. The obtained results elucidate the physical origin of the onset of Mach reflection with chemical reactions, which has previously been observed in both experiments and numerical simulations.

On a self-similar solution for the decay of turbulent bursts

1992 ◽  
Vol 3 (4) ◽  
pp. 319-341 ◽  
Author(s):  
S. P. Hastings ◽  
L. A. Peletier
Keyword(s):  
Asymptotic Behaviour ◽  
Physical Parameter ◽  
Dimensional Analysis ◽  
Existence And Uniqueness ◽  
The Self ◽  
Similar Solution ◽  
Self Similar Solution ◽  
Eigenvalue Parameter ◽  
Self Similar ◽  
Similar Solutions

We discuss the self-similar solutions of the second kind associated with the propagation of turbulent bursts in a fluid at rest. Such solutions involve an eigenvalue parameter μ, which cannot be determined from dimensional analysis. Existence and uniqueness are established and the dependence of μ on a physical parameter λ in the problem is studied: estimates are obtained and the asymptotic behaviour as λ → ∞ is established.

Hydromagnetic effects on non-Newtonian Hiemenz flow

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Suman Sarkar ◽  
Bikash Sahoo
Keyword(s):  
Magnetic Field ◽  
Free Boundary ◽  
Existence And Uniqueness ◽  
Uniform Magnetic Field ◽  
Magnetic Parameter ◽  
Similarity Transformation ◽  
The Self ◽  
Free Boundary Value Problem ◽  
Uniqueness Of The Solution ◽  
Self Similar

Abstract The stagnation point flow of a non-Newtonian Reiner–Rivlin fluid has been studied in the presence of a uniform magnetic field. The technique of similarity transformation has been used to obtain the self-similar ordinary differential equations. In this paper, an attempt has been made to prove the existence and uniqueness of the solution of the resulting free boundary value problem. Monotonic behavior of the solution is discussed. The numerical results, shown through a table and graphs, elucidate that the flow is significantly affected by the non-Newtonian cross-viscous parameter L and the magnetic parameter M.

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