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1.
In this work the results of the statistical topometric analysis of fracture surfaces of soda-lime-silica glass with and without ionic exchange treatment are reported. In this case, the mechanism of substitution is K+-Na+. atomic force microscopy (AFM) was employed to record the topometric data from the fracture surface. The roughness exponent (ζ) and the correlation length (ξ) were calculated by the variable bandwidth method. The analysis for both glasses (subjected and non-subjected to ionic exchange) for ζ shows a value ∼0.8, this value agrees well with that reported in the literature for rapid crack propagation in a variety of materials. The correlation length shows different values for each condition. These results, along with those of microhardness indentations suggest that the self-affine correlation length is influenced by the complex interactions of the stress field of microcracks with that resulting from the collective behavior of the point defects introduced by the strengthening mechanism of ionic exchange. 相似文献
2.
The finite-size corrections, central chargesc, and scaling dimensionsx of tricritical hard squares and critical hard hexagons are calculated analytically. This is achieved by solving the special functional equation or inversion identity satisfied by the commuting row transfer matrices of these lattice models at criticality. The results are expressed in terms of Rogers dilogarithms. For tricritical hard squares we obtainc=7/10,x=3/40, 1/5, 7/8, 6/5 and for hard hexagons we obtainc=4/5,x=2/15, 4/5, 17/15, 4/3, 9/5, in accord with the predictions of conformal and modular invariance. 相似文献
3.
P. -M. Binder 《Journal of statistical physics》1992,67(3-4):827-832
Average first-passage times for a single-variable stochastic model with a critical fixed point at the origin are computed by exact enumeration. The numerical measurements show excellent agreement with analytical results. The scaling function approaches the predicted asymptotic dependence. 相似文献
4.
Scaling impacted structures 总被引:1,自引:0,他引:1
Summary The problem of non-scalability of structures under impact loads caused by strain-rate effects is solved in this article by properly correcting the impact velocity. The technique relies on the use of an alternative dimensionless basis, together with a mathematical model which allows the calculation of a correction factor for the impact velocity. This new velocity, when applied to the model, makes it to assure the satisfaction of the scaling laws. The indirect similitude method detailed here is applied to two strain-rate sensitive structures, a double plate under in-plane impact and a beam subjected to a blast load. The results show a very good agreement so that the model and a prototype made from strain rate sensitive materials behave the same.accepted for publication 3 March 2004 相似文献
5.
C. Mitrescu G.L. Stephens 《Journal of Quantitative Spectroscopy & Radiative Transfer》2004,86(4):387-394
The present paper shows how the well-known similarity and scaling concepts are properties of the radiative transfer equation and not specifically of the degree of anisotropy of the phase function. It is shown that the key assumption regarding the angular dependence of the radiative field is essential in determining both the value for the parameter used to scale the radiative transfer, as well as the number of streams used in calculating the radiances for various atmospheric problems. Simulations performed on realistic type of cirrus clouds, characterized by strongly anisotropic functions, demonstrates the superior computational advantage for accurately simulating radiances. A new approach for determining the scaling parameter is introduced. 相似文献
6.
The behavior of three-dimensional bond fluctuation model chains tethered on an adsorbing flat surface was simulated by the Monte Carlo method. The dependence of the number of surface contacts M on the interaction strength e and the chain length N was investigated by a finite-size scaling law M = N[a0 + a1N1/vk + O((N 1/vk)2)] for e near the critical adsorption point ec, i.e., k ≡(e-ec)/ec closes to 0. The critical adsorption point was estimated to be ec = 0.93, and the exponents 61542; = 0.49 and 1/v= 0.57. 相似文献
7.
利用蒙特卡洛模拟方法对线形链和星形键在亚浓溶液区的标度律作了验证与讨论。我们的计算结果证明线形链渗透压Π与体积分数Φ在亚浓溶液区的标度规律是与德热纳的理论结果相一致的。同时还证明了星形链在亚浓溶液区具有与线形链相同的标度行为。 相似文献
8.
9.
J. A. Yan 《Applied Mathematics and Optimization》1995,31(2):137-153
Some sharp results about Weiner and Wick products of whitenoise functionals are obtained. Using the inequality of Wick products we show to what extent scaling transformations, translations, and Sobolev differentiations can be performed on white-noise functionals.This work was supported by the National Natural Science Foundation of China. This paper is an enlargement and revised version of the paper entitled Products and Transforms of White-Noise Functionals (preprint, 1990). 相似文献
10.
Asymmetric scaling of a square matrixA 0 is a matrix of the formXAX
–1 whereX is a nonnegative, nonsingular, diagonal matrix having the same dimension ofA. Anasymmetric scaling of a rectangular matrixB 0 is a matrix of the formXBY
–1 whereX andY are nonnegative, nonsingular, diagonal matrices having appropriate dimensions. We consider two objectives in selecting a symmetric scaling of a given matrix. The first is to select a scalingA of a given matrixA such that the maximal absolute value of the elements ofA is lesser or equal that of any other corresponding scaling ofA. The second is to select a scalingB of a given matrixB such that the maximal absolute value of ratios of nonzero elements ofB is lesser or equal that of any other corresponding scaling ofB. We also consider the problem of finding an optimal asymmetric scaling under the maximal ratio criterion (the maximal element criterion is, of course, trivial in this case). We show that these problems can be converted to parametric network problems which can be solved by corresponding algorithms.This research was supported by NSF Grant ECS-83-10213. 相似文献