A scaling limit for the length of the longest cycle in a sparse random digraph

We discuss the length of the longest directed cycle in the sparse random digraph , constant. We show that for large there exists a function such that a.s. The function where is a polynomial in . We are only able to explicitly give the values , although we could in principle compute any .     

POD enriched boundary models and their optimal stabilisation

Modes obtained using the Proper Orthogonal Decomposition are used as boundary enrichment functions within a variational multiscale method for the stochastically forced Burgers equation. Initially, large increases in accuracy are obtained using the enrichment functions without stabilisation terms. Then, optimal coefficients for the stabilisation parameter τ of the unresolved scale model are calibrated using a goal‐oriented model‐constrained optimisation technique, resulting in further improvements. As both the determination of the enrichment functions and the optimisation of the coefficients requires high‐accuracy reference data, a scaling procedure is introduced to allow their use over range of conditions. Numerical experiments confirm that the scaling procedure is effective. Copyright © 2014 John Wiley & Sons, Ltd.     

Dimensional scaling of flame propagation in discrete particulate clouds

The critical dimension necessary for a flame to propagate in suspensions of fuel particles in oxidiser is studied analytically and numerically. Two types of models are considered: First, a continuum model, wherein the individual particulate sources are not resolved and the heat release is assumed spatially uniform, is solved via conventional finite difference techniques. Second, a discrete source model, wherein the heat diffusion from individual sources is modelled via superposition of the Green's function of each source, is employed to examine the influence of the random, discrete nature of the media. Heat transfer to cold, isothermal walls and to a layer of inert gas surrounding the reactive medium are considered as the loss mechanisms. Both cylindrical and rectangular (slab) geometries of the reactive medium are considered, and the flame speed is measured as a function of the diameter and thickness of the domains, respectively. In the continuum model with inert gas confinement, a universal scaling of critical diameter to critical thickness near 2:1 is found. In the discrete source model, as the time scale of heat release of the sources is made small compared to the interparticle diffusion time, the geometric scaling between cylinders and slabs exhibits values greater than 2:1. The ability of the flame in the discrete regime to propagate in thinner slabs than predicted by continuum scaling is attributed to the flame being able to exploit local fluctuations in concentration across the slab to sustain propagation. As the heat release time of the sources is increased, the discrete source model reverts back to results consistent with the continuum model. Implications of these results for experiments are discussed.     

分数阶尺度函数的分解与重构算法

引入分数阶多分辨分析与分数阶尺度函数的概念.运用时频分析方法与分数阶小波变换,研究了分数阶正交小波的构造方法,得到分数阶正交小波存在的充要条件.给出分数阶尺度函数与小波的分解与重构算法,算法比经典的尺度函数与小波的分解与重构算法更具有一般性.     

Phase Behavior of Methane-Pentane Mixture in Bulk and in Porous Media

The adiabatic calorimetry method is used to measure the isochoric heat capacity and the dew-bubble curves for the methane-normal pentane mixtures in bulk for three different mixture compositions of n-pentane. The near-critical behavior of the mixture heat capacity indicates that at low n-pentane concentrations, this system is close to the special point of the critical locus. The effect of porous medium has been investigated for one of the mixtures studied in bulk. It has been shown that in porous medium the essential shift of the dew-bubble curve takes place. In our opinion this shift is caused by the formation of wetting film on the surface of porous medium. The estimation of film thickness resulting from the data obtained yields the value 7–8 nm.     

Scaling Immiscible Displacements in Porous Media with Horizontal Wells

Despite the increase in horizontal well applications, scaling fluid displacement in porous medium with horizontal wells is yet to be fully investigated. Determining the conditions under which horizontal wells may lead to better oil recovery is of great importance to the petroleum industry. In this paper, a numerical sensitivity study was performed for several well configurations. The study is performed in order to reveal the functional relationships between the scaling groups governing the displacement and the performance of immiscible displacements in homogeneous reservoirs produced by horizontal wells. These relationships can be used as a quick prediction tool for the fractional oil recovery for any combinations of the scaling groups, thus eliminating the need for the expensive fine-mesh simulations. In addition, they provide the condition under which a horizontal well configuration may yield better recovery performance. These results have potential applications in modeling immiscible displacements and in the scaling of laboratory displacements to field conditions.     

湍流最高激发态的局部结构及其绝对标度律

通过对湍流层次结构模型中提出的最高激发态的进一步研究发现，最高激发态 存在绝对标度律，且该绝对标度律是由信号中最强耗散涨落的局部结构产生的，并由此推测 出局部强间歇结构一般具有绝对标度的结论.     

Size effect upon grained materials tensile strength: The increase of the statistical dispersion at the smaller scales

The present paper provides a statistical model to the size effect on grained materials tensile strength; it is based on an Extreme Value Theory approach. Since the weakest link in grained materials is usually represented by the interface between the matrix and the aggregates, it is assumed that the flaw distribution can be represented by the aggregate distribution, expressed as a probability density function (pdf) of the grain diameters. Under the hypothesis that the strength of the material depends on the largest flaw, the tensile strength is computed as a function of the specimen size. In this way, two remarkable results are obtained: (i) a size effect for the average tensile strength that substantially agrees with the multifractal scaling law (MFSL) proposed by the first author and (ii) an increase of scatter of the tensile strength values when testing small specimens. Both these trends are confirmed by experimental data available in the literature.     

微电子机械系统中的若干固体力学问题

简述了微电子机械系统若干固体力学问题研究的现状，包括：微构件材料的基本力学性能；微构件的力学分析与计算；微系统的失效分析研究；微系统的驱动等，并阐述了微系统力学问题中涉及的表面效应和尺度效应，提出了微系统多类型力作用，多种因素交叉，多学科耦合，非线性突出的特点和研究方向。     

Percolation theory approach to transport phenomena in porous media

The percolation theory approach to static and dynamic properties of the single- and two-phase fluid flow in porous media is described. Using percolation cluster scaling laws, one can obtain functional relations between the saturation fraction of a given phase and the capillary pressure, the relative permeability, and the dispersion coefficient, in drainage and imbibition processes. In addition, the scale dependency of the transport coefficient is shown to be an outcome of the fractal nature of pore space and of the random flow pattern of the fluids or contaminant.