基于突发分离的自相似网络流量预测

网络流量预测在网络拥塞控制及资源分配中起着至关重要的作用。对于具有自相似性的网络业务流量,由于其存在较强突发,传统预测方法的预测精度普遍较低。本文针对存在高突发的网络流量数据,提出了一种基于数据分离的流量预测方法。在预测步骤前,本方法首先通过控制图将网络流量中难以预测的突发流量进行有效的分离,从而得到突发流量和非突发流量两部分数据。之后分别采用人工神经网络和自适应模板匹配方法实现对非突发流量和突发流量的预测。最后通过对两部分预测结果的合并得到最终的预测结果。基于实际流量数据的实验结果表明:相较于传统流量预测方法,本文所提出的方法具有更高的流量预测精度。      

Self-Similar Solutions of Three-Dimensional Navier-Stokes Equation

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.     

Several Types of Similarity Solutions for the Hunter-Saxton Equation

We study separable and self-similar solutions to the HunterSaxton equation,a nonlinear wave equation which has been used to describe an instability in the director field of a nematic liquid crystal(among other applications).Essentially,we study solutions which arise from a nonlinear inhomogeneous ordinary differential equation which is obtained by an exact similarity transform for the HunterSaxton equation.For each type of solution,we are able to obtain some simple exact solutions in closed-form,and more complicated solutions through an analytical approach.We find that there is a whole family of self-similar solutions,each of which depends on an arbitrary parameter.This parameter essentially controls the manner of self-similarity and can be chosen so that the self-similar solutions agree with given initial data.The simpler solutions found constitute exact solutions to a nonlinear partial differential equation,and hence are also useful in a mathematical sense.Analytical solutions demonstrate the variety of behaviors possible within the wider family of similarity solutions.Both types of solutions cast light on self-similar phenomenon arising in the HunterSaxton equation.     

光纤中自相似脉冲研究进展

概述了光纤中自相似脉冲的最新理论与实验研究结果。对稀土元素掺杂光纤放大器、拉曼光纤放大器、光纤激光器、色散渐减光纤中自相似渐进形脉冲的演化特性作了深入细致的描述。并在此基础上对自相似脉冲在光纤通信中的应用作了介绍。展望了自相似脉冲在光纤中的应用前景,并指出了目前研究中有待解决的问题。     

Fractal Roughness Retrieval by Integrated Wavelet Transform

An integrated-wavelet-transform (IWT) approach is proposed for the study of scattering from slightly rough surfaces that manifest scaling properties over a finite domain of correlation lengths. Instead of collecting angle-resolved intensities, values of the irradiance integrated over increasing areas are used to enhance the contributions of small irradiances at large scattering angles and to reduce the coherent noise. In the case of self-similar surfaces, the scaling behavior of IWT allows investigation of the surface roughness at various length scales. For the realistic case of self-affine surfaces, IWT permits the evaluation of the scaling exponent of the autocorrelation and also offers a direct way to evaluate the necessary length scale of the surface profile.     

Flows and functional inequalities for fractional operators

This paper collects results concerning global rates and large time asymptotics of a fractional fast diffusion equation on the Euclidean space, which is deeply related with a family of fractional Gagliardo–Nirenberg–Sobolev inequalities. Generically, self-similar solutions are not optimal for the Gagliardo–Nirenberg–Sobolev inequalities, in strong contrast with usual standard fast diffusion equations based on non-fractional operators. Various aspects of the stability of the self-similar solutions and of the entropy methods like carré du champ and Rényi entropy powers methods are investigated and raise a number of open problems.     

On Vertical Diffusion of Gases in a Horizontal Reservoir

Exact and approximate solutions to vertical diffusion in gravity-stable, ideal gas mixtures in gas reservoirs, depleted oil reservoirs, or drained aquifers are presented, and characteristic times of diffusion are obtained. Our solutions also can be used to test numerical simulators that model diffusion after gas injection. First, we consider isothermal, countercurrent vertical diffusion of carbon dioxide and methane in a horizontally homogeneous reservoir. Initially, the bottom part of the reservoir, with no flow boundaries at the top and bottom, is filled with CO₂ and the upper part with CH₄. At time equal zero, the two gases begin to diffuse. We obtain the exact solution to the initial and boundary-value problem using Fourier series method. For the same problem, we also obtain an approximate solution using the integrated mass balance method. The latter solution has a particularly simple structure, provides a good approximation and retains the important features of the exact solution. Its simplicity allows one to perform calculations that are difficult and non-transparent with the Fourier series method. It also can be used to test numerical algorithms. Furthermore, we consider diffusion of CO₂ with partitioning into connate water. We show that at reservoir pressures the CO₂ retardation by water cannot be neglected. The diffusion-retardation problem is modelled by a non-linear diffusion equation whose self-similar solution is obtained. Finally, we obtain a self-similar solution to a nonlinear diffusion problem. This solution is a good approximation at early times, before the diffusing gases reach considerable concentrations at the top and bottom boundaries of the reservoir.     

A modified fractional model to describe the entire viscoelastic behavior of polybutadienes from flow to glassy regime

The dynamic mechanical behavior of a series of monodisperse polybutadienes has been investigated from the flow regime to the glassy state. Assuming a linear superposition of the entanglement and glass behavior a mathematical model of the spectrum of relaxation times is developed. It consists in a self-similar spectra for the entanglement contribution and a Fractional Maxwell Fluid (FMF) for the glassy contribution. The model closely represents the master curves of dynamic moduli over 15 logarithmic decades of frequency with three parameters for the flow regime (GN ⁰ _{N 0} and a cut-off parameter _max) and four parameters for the FMF. It is shown that one of the parameter of the FMF is similar to the power-law exponent of a self-similar spectra previously proposed in the literature to model the transition to glass.     

Unsteady one-dimensional water and steam flows through a porous medium with allowance for phase transitions

Fluid flow through a porous medium is considered with allowance for heat conduction and phase transition processes. The one-dimensional problem of the breakdown of an arbitrary discontinuity is solved with reference to the processes of combined nonisothermal water and steam flow through the porous medium. It is assumed that there are two-phase zones of water and steam flow through the porous medium to the left and right of the initial discontinuity. Six qualitatively different discontinuous solutions with internal single-phase water or steam zones are constructed and domains corresponding to each of the solutions are found in the determining parameter space. For the parameters considered a solution of the breakdown problem exists and is unique when the requirements for the existence of a discontinuity structure are satisfied [{xc1}].