Inside Singularity Sets of Random Gibbs Measures

We evaluate the scale at which the multifractal structure of some random Gibbs measures becomes discernible. The value of this scale is obtained through what we call the growth speed in Hölder singularity sets of a Borel measure. This growth speed yields new information on the multifractal behavior of the rescaled copies involved in the structure of statistically self-similar Gibbs measures. Our results are useful to understand the multifractal nature of various heterogeneous jump processes.     

EXPERIMENTAL EVIDENCE OF THE SELF-SIMILARITY AND LONG-RANGE CORRELATIONS OF THE EDGE FLUCTUATIONS IN HT-6M TOKAMAK

To better understand long-time-scale transport dynamics, the rescaled range analysis techniques, the autocorrelation function (ACF) and the probability distribution function (PDF) are used to investigate long-range dependences in edge plasma fluctuations in HT-6M tokamak. The results reveal the self-similar characters of the electrostatic fluctuations with self-similarity parameters (Hurst exponent) ranging from 0.64 to 0.79, taking into consideration the {\vec E}_r×{\vec B} rotation-sheared effect. Fluctuation ACFs of both the ion saturation current and the floating potential, as well as PDF of the turbulence-induced particle flux, have two distinct time scales. One corresponds to the decorrelation time scale of local fluctuations (μs) and the other lasts to the order of the confinement time (ms). All these experimental results suggest that some of the mechanisms of the underlying turbulence are consistent with plasma transport as characterized by self-organized criticality(SOC).     

Extended Sobolev and Hilbert spaces and approximate stationary solutions for electronic systems within the non-linear Schrödinger equation

The definition of Sobolev spaces, which has already been shown to be a convenient way to set up the Schrödinger equation for approximate stationary solutions within extended Hilbert spaces, is readily generalized in order to express, in a similar way, the so-called non-linear Schrödinger equation (NLSE). The unavoidable theory, related to extended Hilbert and Sobolev spaces, is previously described in order to design the formalism inherent to the approximate NLSE. Afterwards the nature of the NLSE stationary solutions is discussed. The procedure uses as a basic tool an implied N-electron quantum self-similarity measure, provided with the structure of an overlap-like measure form, involving the integral of the fourth power of the N-electron wavefunction. Computation of this theoretical element is sketched and a two-electron case is developed as an illustrative example within the LCAO MO framework. The N-electron Slater determinant situation is also presented under the additional help of the nested sums formalism. It is shown afterwards that addition of second order gradient terms on the extended wavefunction provides variation of mass with velocity corrections into the energy expression. Finally, use into the Hamilton operator of exponential terms depending on the density functions in the extended Hilbert spaces formalism provides the theory with a general structure.     

Gravitational collapse with standard and dark energy in the teleparallel equivalent of general relativity

A perfect fluid with self-similarity of the second kind is studied within the framework of the teleparallel equivalent of general relativity(TEGR).A spacetime which is not asymptotically flat is derived.The energy conditions of this spacetime are studied.It is shown that after some time the strong energy condition is not enough to satisfy showing a transition from standard matter to dark energy.The singularities of this solution are discussed.     

ANALYSIS ON PSEUDO-STEADY INDENTATION CREEP

Theoretical analysis and finite element （FE） simulation have been carried out for a constant specific load rate （CSLR） indentation creep test. Analytical results indicate that both the representative stress and the indentation strain rate become constant after a transient period. Moreover, the FE simulation reveals that both the contours of equivalent stress and equivalent plastic strain rate underneath the indenter evolve with geometrical self-similarity. This suggests that pseudo-steady indentation creep occurs in the region beneath the indenter. The representative points in the region are defined as the ones with the equivalent stress equal to the representative stress. In addition, it is revealed that the proportionality between indentation strain rate and equivalent plastic strain rate holds at the representative points during the pseudo-steady indentation creep of a power law material. A control volume （CV） beneath the indenter, which governs the indenter velocity, is identified. The size of the CV at the indented surface is approximately 2.5 times the size of the impression. The stress exponent for creep can be obtained from the pseudosteady indentation creep data. These results demonstrate that the CSLR testing technique can be used to evaluate creep parameters with the same accuracy as conventional uniaxial creep tests.     

Fields with Exceptional Tangent Fields

The asymptotic self-similarity property describes the local structure of a random field. In this paper, we introduce a locally asymptotically self-similar second order field X_H, whose local structures at x=0 and at x0 are very far from each other. More precisely, whereas its tangent field at x0 is a Fractional Brownian Motion, its tangent field at x=0 is a Fractional Stable Motion. In addition, X_H, is asymptotically self-similar at infinity with a Gaussian field, which is not a Fractional Brownian Motion, as tangent field. Then, its trajectories regularity is studied. Finally, the Hausdorff dimension of its graphs is given.     

Simulation of Weakly Self-Similar Stationary Increment $${\text{Sub}}_{\varphi } {\left( \Omega \right)}$$-Processes: A Series Expansion Approach

We consider simulation of -processes that are weakly selfsimilar with stationary increments in the sense that they have the covariance function

Small and Large Time Scale Analysis of a Network Traffic Model

Empirical studies of the internet and WAN traffic data have observed multifractal behavior at time scales below a few hundred milliseconds. There have been some attempts to model this phenomenon, but there is no model to connect the small time scale behavior with behavior observed at large time scales of bigger than a few hundred milliseconds. There have been separate analyses of models for high speed data transmissions, which show that appropriate approximations to large time scale behavior of cumulative traffic are either fractional Brownian motion or stable Lévy motion, depending on the input rates assumed. This paper tries to bridge this gap and develops and analyzes a model offering an explanation of both the small and large time scale behavior of a network traffic model based on the infinite source Poisson model. Previous studies of this model have usually assumed that transmission rates are constant and deterministic. We consider a nonconstant, multifractal, random transmission rate at the user level which results in cumulative traffic exhibiting multifractal behavior on small time scales and self-similar behavior on large time scales.     

On the Self-Decomposability of Euler's Gamma Function

Let be Euler's Gamma function. We prove that, for all 0, > 0, > 0, > 0, the function (( + iz)/() ^{i z)} , z R ¹, is a self-decomposable characteristic function from the Thorin class and derive its explicit canonical form. Similarly to [1], we also describe several classes of Lévy-type stochastic processes related to .