EFFECTS OF POISSON’S RATIO ON SCALING LAW IN HERTZIAN FRACTURE

In this paper the Auerbach＇s scaling law of Hertzian fracture induced by a spherical indenter pressing on a brittle solid is studied. In the analysis, the singular integral equation method is used to analyze the fracture behavior of the Hertzian contact problem. The results show that the Auerbach＇s constant sensitively depends on the Poisson＇s ratio, and the effective Auerbach＇s domain is also determined for a given value of the Poisson＇s ratio.     

A second order explicit finite element scheme to multidimensional conservation laws and its convergence

A second order explicit finite element scheme is given for the numerical computation to multi-dimensional scalar conservation laws.L ^p convergence to entropy solutions is proved under some usual conditions. For two-dimensional problems, uniform mesh, and sufficiently smooth solutions a second order error estimate inL ² is proved under a stronger condition, Δt≤Ch ^2/4     

Reynolds Number Effect on the Grid Turbulence Degeneration Law

A comprehensive experimental investigation of the effect of the Reynolds number on the degeneration law for turbulence generated by biplanar and wicker grids is carried out over a wide range of the grid geometry parameters and the flow velocity. It is established that an increase in the flow velocity leads to an increase in the turbulence intensity at a given distance from the biplanar grid and a decrease in the turbulence decay rate downstream of the grid. An empirical relation between the turbulence intensity behind the grid, on the one hand, and the relative distance x/M from the grid and the Reynolds number based on the grid rod diameter and the flow velocity at the grid mesh center, on the other hand, is proposed. For the same relative distance x/M from the grid the intensity of wicker-grid turbulence is higher than in the case of the flow past a biplanar grid.     

应力互换定律与平衡条件的等价性

本文从空间一般的情形证明了应力互换定律是微体平衡的充分必要条件,即证明了应力互换定律与平衡条件的等价性,从而揭示了应力互换定律的实质。     

Permeability Tensor for Heterogeneous Porous Medium of Fibre Type

A theoretical model which allows us to determine the permeability of a fibrous porous medium is proposed. Fibres are assumed to be parallel and nonuniform in space and material with a low volume fraction of fibres is considered. The model includes two geometric parameters: the diameter of fibres and the diameter of caverns or fissures inside the bundle of fibres. The tensor of permeability of the porous medium is determined based upon a generalized cell model. The components of permeability tensor depend on two parameters which are determined using experimental data and least-squares approximation. The influence of the geometric parameters on components of permeability tensor is discussed.     

Effects of the method of identification of the diffusion coefficient on accuracy of modeling bound water transfer in wood

An alternative approach to determining the bound water diffusion coefficient is proposed. It comprises a method for solving the inverse diffusion problem, an improved algorithm for the bound-constrained optimization as well as an alternative submodel for the diffusion coefficient’s dependency on the bound water content. Identification of the diffusion coefficient for Scots pine wood (Pinus sylvestris L.) using the proposed inverse approach is presented. The accuracy of predicting the diffusion process with the use of the coefficient values determined by traditional sorption methods as well as by the inverse modeling approach is quantified. The similarity approach is used and the local and global relative errors are calculated. The results show that the inverse method provides valuable data on the bound water diffusion coefficient as well as on the boundary condition. The results of the identification can significantly improve the accuracy of mass transfer modeling as studied for drying processes in wood.     

Quadratic systems of conservation laws with generic behavior at infinity

We identify quadratic systems of conservation laws with generic behavior at infinity, where the genericity conditions derive naturally when studying weak solutions of conservation laws. Namely, we identify quadratic models for which the vector field associated with the viscosity admissibility criterion has properties at infinity that are true for an open and dense subset of the set of all planar quadratic vector fields in the metric associated with the Euclidian space of coefficients. We determine the boundaries of the regions containing, generic models in the parameter space of coefficients of quadratic models. We show that when crossing the boundaries of nongeneric models transversally, the Poincaré compactification of the corresponding vector field undergoes either a saddle node or a transcritical bifurcation at infinity. For quadratic models with a bounded elliptic region we calculate the loci of nongeneric models assuming the viscosity matrix to be the identity. We obtain a two-parameter normal form for such models and show that the boundaries that determine generic models in the two-dimensional parameter space correspond to the Schaeffer-Shearer classification of models with an isolated umbilic point. Since the loci of nongeneric models are invariant under the equivalence transformations that preserve weak solutions of conservation laws, understanding their behavior at infinity promises to provide an insight into a general classification of quadratic conservation laws.     

二维槽道湍流的标度律分析

对不同Reynolds数的二维不可压槽道湍流（即二维槽道流动的扰动饱和态）进行了标度律分析.指出二维槽道湍流中存在明显的标度律及扩展自相似性;分析了标度指数随着流动Reynolds数的变化,指出随着Reynolds数的增长,标度指数的奇异性并没有减小的趋势;由此推测充分发展的二维槽道湍流的标度指数也是奇异的、将所得计算值和余振苏等人的SL标度律预测值相比较,认为余等人的SL标度律公式能很好描述二维湍流.     

Transmission of a spherical sound wave through a single-leaf wall: Mass law for spherical wave incidence

This paper examines the sound insulation of a single-leaf wall driven by a spherical wave. The transmitted sound field of an infinite elastic plate under a spherical wave incidence is theoretically analyzed and insulation mechanisms are considered. The displacement of the plate is formulated using the Hankel transform in wavenumber space and the transmitted sound pressure in the far-field is obtained by Rayleigh’s formula in an explicit closed form. Moreover, a reduction index is also derived in a closed form by introducing an approximation into the vibration characteristics of the plate. Deterioration of the insulation performance under the spherical wave incidence is caused by an apparent decrease of wall impedance that depends on the directivity of the transmitted sound wave. The mass law for a spherical wave incidence is different from that for a normal plane wave incidence: doubling the weight of the wall or the frequency gives an increase of 3 dB (c.f. 6 dB for a normal plane wave incidence), which is also smaller than the field incidence mass law.     

Anomalous power law decay in solvation dynamics of DNA: a mode coupling theory analysis of ion contribution

Several time dependent fluorescence Stokes shift (TDFSS) experiments have reported a slow power law decay in the hydration dynamics of a DNA molecule. Such a power law has neither been observed in computer simulations nor in some other TDFSS experiments. Here we observe that a slow decay may originate from collective ion contribution because in experiments DNA is immersed in a buffer solution, and also from groove bound water and lastly from DNA dynamics itself. In this work we first express the solvation time correlation function in terms of dynamic structure factors of the solution. We use mode coupling theory to calculate analytically the time dependence of collective ionic contribution. A power law decay in seen to originate from an interplay between long-range probe–ion direct correlation function and ion–ion dynamic structure factor. Although the power law decay is reminiscent of Debye–Falkenhagen effect, yet solvation dynamics is dominated by ion atmosphere relaxation times at longer length scales (small wave number) than in electrolyte friction. We further discuss why this power law may not originate from water motions which have been computed by molecular dynamics simulations. Finally, we propose several experiments to check the prediction of the present theoretical work.