Rarefaction

Abstract: The shock‐wave propagation characteristics of polymethyl methacrylate (PMMA), fused silica, and sapphire were measured for both compressive and rarefaction waves using plate‐impact experiments and interferometer instrumentation techniques The peak stress levels in the experiments were 22, 65, and 120 kbar, respectively The high‐resolution measurements of the stress wave profiles showed the PMMA to be a complex material whose wave propagation is influenced by nonlinearity, strain‐rate dependence, and elastic‐plastic effects in which plastic working increases the zero‐pressure volume of the material The fused silica is very well characterized as a nonlinear elastic material having the interesting property of propagating stable rarefaction shock waves The sapphire was nearly linear elastic to 120 kbar The use of these three transparent materials as ``windows'' in laser interferometer instrumented shock‐wave studies of other materials is discussed The effect of the shock‐induced variation of the index o

Abstract: increase, unless the pertinent loci are otherwise selected. The second objection stems from the observation that too-weak balancing selection still leaves the population open to loss of variability by drift. But with the present model there is no need to postulate low selection intensity so, at least theoretically, drift becomes less of a problem. Loci, or linkage groups conforming in their demographic characteristics to the Charlesworth-Giesel model, will thus be maintained in a polymorphic state at little or no cost. In addition, any linkage (Franklin and Lewontin 1970) contributes to maintenance of heterozygosity of the rest of the genoiue. The result is perpetuation of population variability and adaptability.

Abstract: The Riemann problem for two-dimensional gas dynamics with isentropic or polytropic gas is considered. The initial data is constant in each quadrant and chosen so that only a rarefaction wave, shock wave, or slip line connects two neighboring constant initial states. With this restriction sixteen (respectively, fifteen) genuinely different wave combinations for isentropic (respectively, polytropic) gas exist. For each configuration the numerical solution is analyzed and illustrated by contour plots. Additionally, the required relations for the initial data and the symmetry properties of the solutions are given. The chosen calculations correspond closely to the cases studied by T. Zhang and Y. Zheng [SIAM J. Math. Anal., 21 (1990), pp. 593–630], so that the analytical theory can be directly compared to our numerical study.

Abstract: --The common practice of expressing community structure in terms of indices of diversity and evenness involves a serious loss of information. Differences attributable to the accumulation of species with increasing area are ignored, differences in the density of individuals are often masked by other factors, and many combinations of species richness and relative abundance can produce the same value of the index. As an alternative we suggest (1) comparing species richness by standardizing samples either to equal numbers of individuals or to the number of individuals expected on equal-sized plots, and (2) expressing the relative abundance of species as a graph of their relative abundances arranged in a decreasing array. We present an analysis of bird census data based on the proposed methods, and we include comparisons with applications of four indices commonly used in ecology, the Shannon-Weaver index of diversity, the J' evenness index, the inverse of Simpson's measure of concentration, and Hill's evenness index. For 37 Breeding Bird Censuses taken in various terrestrial habitats across the United States and Canada, the proposed methods reveal some very general relationships about the organization of bird communities in different habitats. Equal-sized areas of mature deciduous forest and secondgrowth habitats may be equally species rich (14-24 species with •> 1 breeding territory per 6 ha); the density of individuals (territorial pairs) is generally higher in deciduous forest habitats, and the relative abundance of bird species shows more dominance (less evenness) in the deciduous forest. Mixed coniferous-deciduous forests and dense young deciduous forests have fewer species than mature eastern deciduous forests or second-growth abitats (9-16 and 7-10 species per 6 ha, respectively), although the density of individuals is approximately equal to that in second-growth habitats. Coniferous forests are species-poor (5-8 per 6 ha), and the density of territorial pairs is low (8-12 per 6 ha compared with 40-70 in deciduous forests). Although the proposed methods require assumptions that need to be evaluated carefully, we are optimistic that they will have other useful applications in the analysis of arian communities. Received 8 October 1980, accepted 15 April 1981. A large literature has developed in ecology presenting descriptive analyses of biotic assemblages (Dennis et al. 1979, Patil and Taille 1979). Although one should not infer mechanisms of community regulation from such studies (Pielou 1975), certain patterns recur in vertebrate communities in different habitats (Palmgren 1930, Udvardy 1957, MacArthur and MacArthur 1961, Williams 1964, MacArthur 1964, Karr and Roth 1971, Wiens 1973, Willson 1974), climates (Bock and Lepthien 1974, Rotenberry 1978), seasons (Rotenberry et al. 1979), and geographic areas (Pianka 1966, Recher 1969, Karr 1971, Tramer 1974, Cody 1975, Short 1979). One methodological problem with much of this literature and with community ecology generally since the early 1960's is the expression of community structure in terms of indices of diversity and evenness. Indices such as H' [-5; p/log Pi] (Shannon and Weaver 1949, Margalef 1958) and J' [H'/log s] (Pielou 1966a) confound important parameters that should be defined as precisely as possible and examined separately before communities are compared. These are (1) the number of species (species richness), (2) their relative abundance (evenness), (3) the number of individuals or territorial pairs, and (4) the area sampled. To combine any of these variables into a single statistic assures that the relative effects of the contributing parameters cannot be determined. The same value of the index can result from various com785 The Auk 98: 785-800. October 1981 786 JAMES AND RATHBUN [Auk, Vol. 98 binations of values of the parameters (Pielou 1975). Here, we recommend that data be standardized to either equal numbers of individuals (in this case, territorial pairs) or equal-sized areas before comparisons are attempted. We propose that rarefaction and relative abundance curves be used as an alternative to diversity indices. In addition to clarifying components of biological interest, these methods avoid many of the mathematical deficiencies of the application of indices. We will examine the community structure of a large set of breeding bird censuses on the basis of the traditional methods and then present four graphic displays of the results of rarefactions (Figs. 1-3) and relative abundance curves (Fig. 4).

Abstract: A first-order relationship between changes in area and shock strength is derived for the case of a shock moving through a small area change in a channel. By integration of this relationship the area of the channel is obtained as a function of the shock strength in closed form. This result is interpreted as giving the average strength of a shock at a given time as it moves along a channel of arbitrary shape.By suitable choices of the shape of the channel, descriptions of converging cylindrical and spherical shocks are obtained. These descriptions are found to be in close agreement with the similarity solutions valid near the points of collapse of the shocks. The reason for such good agreement is examined.