Discrimination of sedimentary facies by association analysis

The ability of association analysis to discriminate sedimentary facies was tested on Purdy's modal analyses of modern sediments of the Great Bahama Bank. Purdy's data set has served in the past as a standard reference for evaluating various multivariate classification algorithms. In order to adapt Purdy's data to association analysis, the percent abundance of the 12 constituents was converted to binary form by dichotomizing each variable on its mean value. The results obtained by association analysis are virtually identical to those obtained by Purdy and other authors. The same four main sedimentary facies were discriminated; 86% of the samples were identically classified (97% when misclassified borderline cases are counted as matches); the total partition variance of the classification is only negligibly greater (4%); and the grouping of the variables yielded the same four groups. The rank order of the three division-attributes responsible for the sample classification is fines, oolites, and corals. Association analysis has been employed by other authors to differentiate meaningful facies groups in studies of ancient reef carbonates, modern reef sediments, and heavy minerals in stream sediments. In all these studies, the results were found to be compatible with those obtained by using the continuous quantitative measurements, indicating that qualitative binary data may often be sufficient for the purpose of facies discrimination in many branches of geology and that association analysis is an effective method for this purpose.     

Studies on wind environment around high buildings in urban areas

High buildings or architectural complex in urban areas remarkably distort the urban surface wind fields. As the air flow approaches,local strong wind may appear around the buildings. The strong wind makes the pedestrians on sidewalks, entrances and terrace very uncomfortable and causes the pedestrian level wind environment problem. In this studies, hot-wire wind measurement, wind scouring in wind tunnel and numerical computation were carried out to evaluate the wind environment of tall buildings in the prevailing flow conditions in Beijing areas. The results obtained by three techniques were compared and mutually verified. The conclusions drawn from three approaches agree with each other. Also the advantages and limitations of each method were analyzed. It is suggested that the combination of different techniques may produce better assessment of wind environment around high buildings.     

3D viscous-spring artificial boundary in time domain

After a brief review of studies on artificial boundaries in dynamic soil-structure interaction, a three-dimensional viscous-spring artificial boundary （VSAB） in the time domain is developed in this paper. First, the 3D VSAB equations in the normal and tangential directions are derived based on the elastic wave motion theory. Secondly, a numerical simulation technique of wave motion equations along with the VSAB condition in the time domain is studied. Finally, numerical examples of some classical elastic wave motion problems are presented and the results are compared with the associated theoretical solutions, demonstrating that high precision and adequate stability can be achieved by using the proposed 3D VSAB. The proposed 3D VSAB can be conveniently incorporated in the general finite element program, which is commonly used to study dynamic soil-structure interaction problems.     

The general solution of the HENON–HEILES problem

The general solution of the Henon–Heiles system is approximated inside a domain of the (x, C) of initial conditions (C is the energy constant). The method applied is that described by Poincaré as ‘the only “crack” permitting penetration into the non-integrable problems’ and involves calculation of a dense set of families of periodic solutions that covers the solution space of the problem. In the case of the Henon–Heiles potential we calculated the families of periodic solutions that re-enter after 1–108 oscillations. The density of the set of such families is defined by a pre-assigned parameter ε (Poincaré parameter), which ascertains that at least one periodic solution is computed and available within a distance ε from any point of the domain (x, C) for which the approximate general solution computed. The approximate general solution presented here corresponds to ε = 0.07. The same solution is further improved by “zooming” into four square sub-domain of (x, C), i.e. by computing sufficient number of families that reduce the density parameter to ε = 0.003. Further zooming to reduce the density parameter, say to ε = 10⁻⁶, or even smaller, although easily performable in both areas occupied by stable as well as unstable solutions, was found unnecessary. The stability of all members of each and all families computed was calculated and presented in this paper for both the large solution domain and for the sub-domains. The correspondence between areas of the approximate general solution occupied by stable periodic solutions and Poincaré sections with well-aligned section points and also correspondence between areas occupied by unstable solutions and Poincaré sections with randomly scattered section points is shown by calculating such sections. All calculations were performed using the Runge-Kutta (R-K) 8th order direct integration method and the large output received, consisting of many thousands of families is saved as “Atlas of the General Solution of the Henon–Heiles Problem,” including their stability and is available at request. It is concluded that approximation of the general solution of this system is straightforward and that the chaotic character of its Poincaré sections imposes no limitations or difficulties.