Self-similarity of electrostatic fluctuations in a linear magnetised plasma system

In this Letter the long-range time correlations present in the fluctuation data in presence of electrostatic instability in a magnetised dc discharge plasma is presented. The electrostatic instability is generated due to the effect of crossed electric and magnetic field (E×B flow) and has intermediate frequency ranging from 50 to 100 MHz. Hurst exponent, the self-similarity parameter is calculated with the help of different statistical methods suggested by many researchers to determine the long-range time correlation present in fluctuation dynamics in the plasma column. The fluctuation in the ion saturation current is measured by a Langmuir probe for the study and the measurement is done both radially and axially in the plasma system. Estimated results clearly expose the self-similar character of the fluctuations with self-similarity parameters having values from 0.65 to 0.90 through the presence of long-range time correlation.     

Generation of excellent self-similar pulses in a dispersion-decreasing fiber

Pulses compression has been widely studied for a long time. In order to generate excellent self-similar pulses in a dispersion-decreasing optical fiber with normal group-velocity dispersion, the influence of initial pulse parameters on the properties of the self-similar parabolic pulses interaction are firstly investigated in the paper. We find that the phase of sinusoidal fit and asymptotic dark soliton change according to the changing of initial phase difference. Meanwhile, increasing the full-width at half-maximum and input energy or decreasing time-delay properly, the interaction between self-similar pulses enhances accordingly, which makes the interaction length shorter and reduce the lose of energy, resulting in high energy output. The results are beneficial in experimental studies by adjusting the initial parameters of pulses to generate high-quality self-similar pulse. It is important for Dense Wavelength Division Multiplexing (DWDM) transmission system which is in heavy demands of light source in wide-range wavelength.     

On the extended self similarity and the form function

In this work some investigations on the properties of the so calledform function which characterizes the scaling behavior of the small scales fluctuations in a turbulent flow are presented. The present analysis is based on previous experimental measurements in homogeneous and non-homogeneous grid-generated turbulence at low Re. The universality properties of the form function are investigated in the frame of the Extended Self Similarity (ESS) form of scaling.

---

Sommario Nel presente lavoro viene presentato uno studio riguardante le proprietà della cosiddetta funzione di forma che caratterizza le leggi di scala delle fluttuazioni di velocità in un flusso turbolento. L'analisi é basata su precedenti misure sperimentali effettuate in flussi turbolenti generati da griglie a bassi Re ed in condizioni omogenee e non omogenee. Le proprietá di universalitá della funzione di forma sono studiate nell'ambito della cosiddetta Extended Self-Similarity.

     

Selbstähnlichkeit am Beispiel des Aggregationsprozesses von Amphiphilen

The micelle aggregation-process of amphiphiles is described under the viewpoint of self-similarity nearby the critical point. The results allow a deeper insight in the nature of the critical micelle concentration.

     

Strong convergence towards homogeneous cooling states for dissipative Maxwell models

We show the propagation of regularity, uniformly in time, for the scaled solutions of the inelastic Maxwell model for small inelasticity. This result together with the weak convergence towards the homogeneous cooling state present in the literature implies the strong convergence in Sobolev norms and in the L¹ norm towards it depending on the regularity of the initial data. The strategy of the proof is based on a precise control of the growth of the Fisher information for the inelastic Boltzmann equation. Moreover, as an application we obtain a bound in the L¹ distance between the homogeneous cooling state and the corresponding Maxwellian distribution vanishing as the inelasticity goes to zero.     

A self-similar premixed turbulent flame model

This paper is devoted to premixed combustion modelling in turbulent flow. First, we derive a model for the turbulent flame velocity based on the observed self-similarity of the turbulent flame. The model uses the local flame brush width as a fundamental parameter and, therefore, we show how it can be retrieved for numerical implementation. The diffusive property of the brush width is treated in such a way as to theoretically let the brush have a clearly defined boundary propagating at finite velocity. The model, implemented in Star-CD CFD software through user programming, is then numerically tested on three configurations for which another model, the Turbulent Flame Closure model, is known to give very good agreement. Some effects of numerics are commented and results for both models are compared. While based on very different approaches the two models lead to substantially similar results. In this way, we have shown that the local brush width can effectively be used, giving an additional degree of freedom for premixed turbulent combustion modelling.     

Small and Large Scale Asymptotics of some Lévy Stochastic Integrals

We provide general conditions for normalized, time-scaled stochastic integrals of independently scattered, Lévy random measures to converge to a limit. These integrals appear in many applied problems, for example, in connection to models for Internet traffic, where both large scale and small scale asymptotics are considered. Our result is a handy tool for checking such convergence. Numerous examples are provided as illustration. Somewhat surprisingly, there are examples where rescaling towards large times scales yields a Gaussian limit and where rescaling towards small time scales yields an infinite variance stable limit, and there are examples where the opposite occurs: a Gaussian limit appears when one converges towards small time scales and an infinite variance stable limit occurs when one converges towards large time scales.      

模糊分形及其在级配骨料研究中的应用

结合模糊集理论和分形理论提出了模糊分形集的概念,将分形论的应用范围从清晰现象推广到了模糊现象领域。模糊分形系统大量存在于自然界中,例如海岸线、混凝土的断裂表面、级配骨料的粒度分布等。级配骨料的分形特征具有模糊性,模糊分维是其粒度分布复杂程度的度量。文中给出模糊分形集在级配骨料研究中的应用实例。     

Complexity of hierarchical ensembles

Within the framework of generalized combinatorial approaches, complexity is determined as a disorder measure for hierarchical statistical ensembles related to Cayley trees possessing arbitrary branching and number of levels. With strengthening hierarchical coupling, the complexity is shown to increase monotonically to the limit value that grows with tree branching. In contrast to the temperature dependence of thermodynamic entropy, the complexity is reduced by the variance of hierarchical statistical ensemble if the branching exponent does not exceed the gold mean. Time dependencies are found for both the probability distribution over ensemble states and the related complexity. The latter is found explicitly for self-similar ensemble and generalized for arbitrary hierarchical trees.