Showing papers on "Rarefaction published in 1981"

Rarefaction, Relative Abundance, and Diversity of Avian Communities

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).

Rarefaction Ion Acoustic Solitons in Two-Electron-Temperature Plasma

Abstract: This paper shows that rarefaction ion acoustic solitons appear in a two-electron-temperature plasma. And also it presents general conditions and physical mechanism for existence of the rarefaction solitons. It is found that finite amplitude rarefaction and compression solitons coexist in a plasma within a certain parameter region.

Fast ion production by suprathermal electrons in laser fusion plasmas

Abstract: The acceleration of ions by two isothermal species of electrons, thermal and suprathermal, in a laser‐fusion plasma is investigated. The disassembly of an initially stationary plasma slab, including charge separation effects, is described. Before the rarefaction wave has penetrated appreciably into the slab, an interior Debye sheath which separates the suprathermal and thermal electrons, as well as an exterior sheath at the ion‐vacuum interface is found. As the rarefaction approaches the center of the slab, the dynamics is modified due to the conservation of species number and total energy. The energetics of the long‐time evolution is described by a quasi‐neutral similarity solution appropriate to finite two‐electron species systems.

Stimulated and spontaneous emission of acoustic waves from shock fronts

Abstract: In certain materials, shock waves of sufficient intensity spontaneously emit transverse rarefaction waves and are therefore unstable. A criterion is derived by calculating the relative amplitudes of reflected acoustic waves incident on the shock from behind. This criterion is found to delimit the conditions under which both acoustic amplification and acoustic emission can occur; it agrees with earlier results by Kontorovich.

Stability of interface and shock wave driven by initial pressure discontinuity

Abstract: The flow arising from an initial pressure discontinuity across a perturbed interface of two ideal gases is studied using analytical and numerical methods. In particular, the stability of the shock wave, the interface, and the rarefaction wave in the resulting flow are investigated. The equations of motion and the initial and boundary conditions are linearized for small perturbations, and a Fourier analysis is made in the lateral direction. The equations are then solved by the method of characteristics. The results show that the interface is unstable and its perturbations asymptotically acquire a constant rate of growth. The shock wave is stable and has rapidly damped oscillations, which appear to be unaffected by the instability of the interface.

A three-fluid model for critical surface structure in laser-plasma systems

Abstract: A simple three‐fluid model has been developed to describe the critical surface structure for cases in which an abrupt density jump causes resonant absorption to be the dominant absorption mechanism. In this model, ions, thermal electrons, and superthermal electrons interact in a rarefaction wave induced by the three‐temperature equation of state and the ponderomotive force of the laser beam. Scaling laws from particle‐in‐cell calculations are used to simulate the effects of resonant absorption. The three temperatures characterizing the problem result in four distinct laser intensity regimes. Simple expressions are derived for the induced static potential, ion velocity, density, and temperature in three of these regimes. It is shown that these results agree with recent two‐dimensional simulation studies. The model provides a critical surface momentum flux condition well‐suited for implementation in a one‐dimensional implosion code.

The development of central peaks in lunar craters

Abstract: From a consideration of equations describing the supersonic impact of a solid body on to a solid target, the difference between final crater depth and distance vertically below the original impact at which the rarefaction wave front, resulting from the reflection of the backward propagating shock wave in the meteorite, first intersects the forward travelling shock wave front in the target has been determined. A correlation between this difference and the height of central peak features in the majority of fresh lunar craters has been established. On the basis of this, it is proposed that the intersection of these two wave fronts locally inhibits the ejection of material from behind the shock front during the excavation phase of crater formation, leading to the appearance of a centrally located peak of uplifted material. Subsequent post-impact development of the interior morphological features has been shown to be consistent with the size-scale of development of complex crater features on the lunar and other planetary surfaces. By considering only craters which exhibit this correlation, a scaling between peak height and impact energy has been derived.

Rarefaction shocks in spherical geometry

Abstract: The uniform density region that develops behind a rarefaction shock in planar geometry (and attaches downstream to the outer expansion flow) is shown to be modified by geometric divergence into a region of self‐similar flow with nonvanishing gradients. A single set of equations is derived that describes both shock and similarity flow. The longest gradient scale length in the transition region is shown to vary linearly with the radius at the shock.

A uniformly accurate description of finite amplitude sound radiation from a harmonically vibrating planar boundary

Abstract: The velocity potential for the two‐dimensional, finite amplitude acoustic waves induced by harmonic excitation on a region in an infinite baffle was obtained by the author (1980). That analysis, which represented the response in terms of a continuous spectrum of wavenumbers parallel to the boundary, was valid only for limited distances from the boundary. The current analysis employs the perturbation method of renormalization to derive expressions for the pressure and particle velocity that are uniformly accurate up to the location where a shock forms. The response consists of radiative and evanescent waves, with nonlinearity being significant only for the former. The solution is described as inversions of Fourier cosine transforms which feature a straining transformation of the space–time coordinates. A quantitative example for the case of an intense high‐frequency excitation is shown to lead to a sound beam in which the nonlinear distortion is asymmetrical between the compression and rarefaction phases.

Beyond three decades of continuous research at UTIAS on shock tubes and waves

Abstract: : Analytical and experimental research on nonstationary shock waves, rarefaction waves and contact surfaces has been conducted continuously since 1948. Some unique facilities were used to study the properties of planar, cylindrical and spherical shock waves and their interactions. Investigations were also performed on shock-wave structure and boundary layers in ionizing argon, water-vapor condensation in rarefaction waves, magnetogasdynamic flows, and the regions of regular and various types of Mach reflections of oblique shock waves. Explosively-driven implosions have been employed as drivers for projectile launchers and shock tubes, and as a means of producing industrial-type diamonds from graphite, and fusion plasmas in deuterium. The effects of sonic-boom on humans, animals and structures have also formed an important part of the investigations. More recently, interest has focused on shock waves in dusty gases, the viscous and vibrational structure of weak spherical blast waves in air, and oblique shock-wave reflections. In all of these studies instrumentation and computational methods have played a very important role. A brief survey of this work is given with some perspectives on future research.

Some Factors Influencing the Transition from Deflagration to Detonation

Abstract: A viable supported shock wave has a definite structure. Such a shock moving into cold unburned explosive loses energy at first faster than energy is locally recruited from exothermic reactions. However, as time goes on, this situation monotonically changes and energy is paid back at an increasing rate until a maximum in the released energy is reached. At this point the Chapman-Jouguet surface is passing over the position in question and a rarefaction wave sets in. If enough energy has been concentrated at the shock front the shock wave will persist through the explosive, otherwise the detonation will fail. A blow on unburned materials is an ideal way to build the gradient for a self supporting shock wave since it automatically sets up the appropriate monotonically increasing energy release.