Mathematical modeling of the dissolving and deposition processes during solution seepage in a porous medium

A mathematical model that describes solution seepage in a porous medium and the processes of mineral dissolving and secondary deposition is proposed. Self-similar solutions describing the motion of the leading and trailing fronts, that is, the boundaries of the complete-dissolving zone, are determined. The main features of the processes under consideration are studied and numerical calculations are performed. It is shown that the model describes well the experimental data on mineral leaching by sulfate solutions. The dynamics of mineral extraction from productive solutions in a medium with a nonuniformacidity distribution are investigated. It is shown that, in the elevated-PH zones, the mineral is dissolved; whereas, in the low-acidity zones, secondary deposition of the mineral occurs. In the latter case, after the work has been completed, the bed may contain more or less considerable mineral resources, depending on the extent of the low-PH zone and its proximity to an extraction well.     

基于LFSN自相似流量模型的随机突发边界分析

基于线形分形稳定噪声(LFSN)的网络业务流模型可以很好地描述流量的自相似和重尾特性,对这种模型的随机突发边界进行理论推导,得出较现有文献更为普遍的结论,尤其是其随机上界更为精确,因此在随机网络演算分析中有着重要意义.同时基于对一般LFSN过程的快速模拟,设计了一种独特的实验方法,得到突发边界随机分布的估计值,验证了理论推导的正确性.     

Riemann problems for three-dimensional combustion models

We investigate Chapman-Jouguet models in three-dimensional space by means of generalized char- acteristic analysis. The interaction of detonation, shock waves and contact discontinuity is discussed intensively in this paper. If contact discontinuity appears, the structure of global solutions becomes complex. We deal with this problem when strength of detonation is small.     

SOLUTIONS OF A SYSTEM OF FORCED BURGERS EQUATION IN TERMS OF GENERALIZED LAGUERRE POLYNOMIALS

In this article, we obtain explicit solutions of a linear PDE subject to a class of radial square integrable functions with a monotonically increasing weight function |x|n-1eβ|x|2/2,β≥ 0, x ∈ Rn. This linear PDE is obtained from a system of forced Burgers equation via the Cole-Hopf transformation. For any spatial dimension n 1, the solution is expressed in terms of a family of weighted generalized Laguerre polynomials. We also discuss the large time behaviour of the solution of the system of forced Burgers equation.     

Solutions of a system of forced burgers equation in terms of generalized laguerre polynomials

In this article, we obtain explicit solutions of a linear PDE subject to a class of radial square integrable functions with a monotonically increasing weight function |x|ⁿ⁻¹eβ|x|²/2,${\left|x\right|}^{n-1}{e}^{\beta {\left|x\right|}^2}/2,$, β≥0, x ∈?n$\beta \ge 0,\hspace{0.17em}x\hspace{0.17em}\in {?}^n$. This linear PDE is obtained from a system of forced Burgers equation via the Cole-Hopf transformation. For any spatial dimension n > 1, the solution is expressed in terms of a family of weighted generalized Laguerre polynomials. We also discuss the large time behaviour of the solution of the system of forced Burgers equation.     

Quantization dimension for infinite self-similar probabilities

The quantization dimension function for a probability measure induced by a set of infinite contractive similarity mappings and a given probability vector is determined. A relationship between the quantization dimension function and the temperature function of the thermodynamic formalism arising in multifractal analysis is established. The result in this paper is an infinite extension of Graf and Luschgy [S. Graf, H. Luschgy, The quantization dimension of self-similar probabilities, Math. Nachr. 241 (2002) 103-109].     

FRACTAL PROPERTIES OF STATISTICALLY SELF-SIMILAR SETS I

In this paper,authors compute the Packing dimension of statistically selfsimilar sets and obtaine the dimension and dimension distribution of statistically selfsimilar measure.     

自相似业务下视频服务器的接纳控制

VOD 系统中,有限的磁盘 I/O 带宽或缓存空间往往成为系统的瓶颈。针对这一问题,提出了自相似业务下视频服务器的接纳控制算法。该算法运用等效带宽理论,通过在线测量系统所剩资源和周期容限的幅度变化来实时调节调度周期的大小,使得系统所剩资源达到动态的“等量”平衡。仿真结果表明,该算法不但简化了接纳过程,节约了系统资源,提高了算法的可实现性,而且系统的接纳率比 Lee,Yeom 所提算法的接纳率提高了 15%,并且还可根据系统的 QoS 参数灵活调整接纳率。     

分析重尾ON/OFF源功率谱密度的TAM近似法

经过十年的研究，发现电信网络业务流量显示自相似和长相关性。传统模型不能很好的仿真网络特性，而重尾分布的ON／OFF模型能够很好地解释计算机网络业务流量的自相似性的形成机理，它的功率谱密度(PSD)成为判断其突发性的有效手段。本文在Laevens K的基础上，结合Harris CM提出的TAM方法，提出一种计算重尾ON／OFF源的PSD的TAM近似法，并通过MATLAB仿真得到PSD曲线，符合其长相关特性，证明了该方法的有效性。