ABSTRACT
We introduce here a new index of diversity based on consideration of reasonable propositions that such an index should have in order to represent diversity. The behaviour of the index is compared with that of the Gini-Simpson diversity index, and is found to predict more realistic values of diversity for small communities, in particular when each species is equally represented and for small communities. The index correctly provides a measure of true diversity that is equal to the species richness across all values of species and organism numbers when all species are equally represented, as well as Hill's more stringent 'doubling' criterion when they are not. In addition, a new graphical interpretation is introduced that permits a straightforward visual comparison of pairs of indices across a wide range within a parameter space based on species and organism numbers.
Subject(s)
BiodiversityABSTRACT
An analysis introduced by the authors in 2011 examining the robustness of the isovolume method for the calibration of the respiratory inductive plethysmograph based on the connected cylinders particular model of Konno and Mead's generalized two-compartment model of respiration is extended. It is demonstrated that extending this to a more physically realistic geometrical model, termed the connected prismatic elliptical segments model, does not enhance the earlier analysis, and that the analysis can easily be proven to cover all area-based transduction sensors, irrespective of the actual geometry of the compartments.
Subject(s)
Models, Biological , Monitoring, Physiologic/methods , RespirationABSTRACT
An analytical formalism developed previously to examine the robustness of the isovolume calibration technique for non-invasive respiratory monitoring devices based on measurements of torso circumference (e.g. fibre-optic respiratory plethysmography) is extended here to techniques based on area measurement (e.g. respiratory inductive plethysmography), and the results are compared. The earlier perturbation approach is adopted, and an exact method is also presented. It is demonstrated that the area-based techniques have less dependence on the cylindrical compartmental parameters of radius and height, and are independent of compartmental volume if height variations are negligible, in contrast to circumference-based techniques. It is also demonstrated that both the area- and the circumference-based techniques provide similar inferences of volume when calibrated using the isovolume method under reasonable assumptions for the dimensions of the compartments that constitute a model of the torso.
Subject(s)
Models, Biological , Monitoring, Physiologic/methods , Respiration , CalibrationABSTRACT
Thermodynamic properties of one-dimensional lattice models exhibiting entropy-driven phase transformations are discussed in quantum and classical regimes. Motivated by the multistability of compounds exhibiting photoinduced phase transitions, we consider systems with asymmetric, double, and triple well on-site potential. One finds that among a variety of regimes, quantum versus classical, discrete versus continuum, a key feature is asymmetry distinguished as a "shift" type and "shape" type in limiting cases. The behavior of the specific heat indicates one phase transformation in a "shift" type and a sequence of two phase transformations in "shape"-type systems. Future analysis in higher dimensions should allow us to identify which of these entropy-driven phase transformations would evolve into phase transitions of the first order.
ABSTRACT
Classical thermodynamics of the (1+1)-dimensional asymmetric double sinh-Gordon system is investigated. The pseudo-Schrödinger equation resulting from the transfer integral method is solved numerically and within the semiclassical approximation; the exact results are also given at several temperatures. It is found that the specific heat exhibits a characteristic hump resembling a similar one observed in the systems with a symmetric potential; in some structures, extremely narrow and extremely high peak is developed. The interpretation for this behavior is given.
ABSTRACT
It is shown that the nontopological (bell-shaped) solitary waves in the asymmetric straight phi(4) model are unstable and correspond to saddle points of the potential energy of the continuous system. Their lifetime is estimated. In the discrete model, the potential energy landscape becomes rough: bell-shaped configurations may become stable. The potential energy function is analyzed around the bell-shaped configurations. A dynamical scenario for the decay of the metastable state in a discrete system, related to spontaneous energy localization, is shown.
