Some remarks to the derivation of the “generalized Lippmann equation”

In the present communication, an attempt is made to demonstrate (once again) some of the problems with the derivation of the “generalized Lippmann equation” considered to be valid by many researchers for solid electrodes and to address the problems in the framework of the Gibbs model of the interface by using only the basic principles of thermodynamics. By surveying the relevant literature, it has been shown that during the derivation of the equation, it was completely ignored that the Gibbs-Duhem equation (i.e., the electrocapillary equation) is a mathematical consequence which follows directly from the homogeneous degree one property of the corresponding thermodynamic potential function; consequently, the resulting expression cannot be correct. Some alternative approaches have also been considered. The adequacy of the open system and the partly closed system approach has been critically discussed, together with the possibility of introducing new thermodynamic potential functions.

Analysing the Role of Environmental Stresses on Species Richness and the Process of Hierarchical Structuring of Species Abundances in Marine Gastropods communities at Suva (Fiji Islands)

Anthropogenic environmental stresses, especially physio-chemical pollution, are causing steadily increasing threat to many ecosystems, among which coastal marine communities in tropical shallow waters are especially sensitive. In particular, species-rich marine gastropod assemblages are doomed to bear sharp drops in species diversity when exposed to pollutants released offshore. Yet, the details of the process of decline in species diversity remain to be addressed and analysed more deeply. By addressing a series of previously reported inventories of marine gastropod communities along a sharp gradient of pollution along southern coast at Suva (Fiji Archipelago), I first confirm the already recognised trend towards both a severe decrease in species richness and a strong increase of the unevenness in species abundance distribution, as a response to incremental pollution. Yet, the last trend – increased unevenness – reveals being essentially the purely mathematical consequence of the concomitant decline in species richness. In fact, the genuine intensity of the process of hierarchical structuring of species abundances proves remaining virtually unaffected by environmental degradation, contrary to what has been generally thought so far. Also, another unexpected aspect of the decline in species richness with growing pollution is that this decline is far from being primarily restricted to the set of rarest species; in fact, the originally abundant species are also largely implied in this decline. Moreover, considering separately the two co-occurring feeding guilds, it is shown that herbivores and carnivores are substantially involved the same in the drop in species diversity; as a result, their relative contributions in the community do not seem markedly contrasted by growing pollution. In another respect, a recently proposed paradigmatic hypothesis is supported, according to which the herbivore-guild has quite less numerous species with more unevenly distributed abundances, as compared to the carnivore-guild. Yet, once again, this increased unevenness is essentially the purely mathematical consequence of the concomitant decline in species richness; the genuine intensity of the process of hierarchical structuring of species abundances does remain substantially unchanged. At last, a comparatively extremely high sensitivity to pollution is highlighted for the emblematic genus Conus, which suffers, here, a dramatic drop in species diversity.

The boundary integral formulation of Stokes flows includes slender-body theory

The incompressible Stokes equations can classically be recast in a boundary integral (BI) representation, which provides a general method to solve low-Reynolds-number problems analytically and computationally. Alternatively, one can solve the Stokes equations by using an appropriate distribution of flow singularities of the right strength within the boundary, a method that is particularly useful to describe the dynamics of long slender objects for which the numerical implementation of the BI representation becomes cumbersome. While the BI approach is a mathematical consequence of the Stokes equations, the singularity method involves making judicious guesses that can only be justified a posteriori. In this paper, we use matched asymptotic expansions to derive an algebraically accurate slender-body theory directly from the BI representation able to handle arbitrary surface velocities and surface tractions. This expansion procedure leads to sets of uncoupled linear equations and to a single one-dimensional integral equation identical to that derived by Keller & Rubinow (J. Fluid Mech., vol. 75, 1976, p. 705) and Johnson (J. Fluid Mech., vol. 99, 1979, p. 411) using the singularity method. Hence, we show that it is a mathematical consequence of the BI approach that the leading-order flow around a slender body can be represented using a distribution of singularities along its centreline. Furthermore, when derived from either the single-layer or the double-layer modified BI representation, general slender solutions are only possible in certain types of flow, in accordance with the limitations of these representations.

THREE-DIMENSIONAL MAGNETOGRADIENT WAVES IN THE UPPER ATMOSPHERE

General dispersion equation has been obtained for three-dimensional electromagnetic planetary waves, from which follows, as particular case Khantadze results in one-dimension case. It was shown that partial magnetic field line freezing-in as in one-dimension case lead to the excitation of both “fast” and “slow” planetary waves, in two-liquid approximation (i.e. at ion drag by neutral particles) they are represent oscillations of magnetized electrons and partially magnetized ions in E region of the ionosphere. In F region of the ionosphere using one-liquid approximation only “fast” planetary wave will be generated representing oscillation of medium as a whole. Hence, it was shown that three-dimension magnetogradient planetary waves are exist in all components of the ionosphere, and as exact solutions, with well-known slow short-wave MHD waves, are simple mathematical consequence of the MHD equations for the ionosphere.

VEROAD: A Viscoelastic Multilayer Computer Program

The mathematical principles and derivation of a linear viscoelastic multilayer computer program are described. The principles of the derivation apply equally to conventional linear elastic programs. The practical consequences of the viscous material properties for the mathematical derivation have been solved by Fourier transformation; another mathematical consequence is that complex calculus was inevitable. The program is called VEROAD, (viscoelastic road analysis Delft). The program's primary extension is that the analyzed material can be vis-coelastic. Consequences of this extension are numerous: calculation from physical material properties of quantities such as time-dependent displacements, stresses and strains, permanent deformations, and dissipated energies is made possible. All these quantities depend on velocity of traffic, which is explicitly included in the calculations. The material model assumes the bulk modulus to be elastic and the shear modulus to be viscoelastic. The latter follows Burger's model. For illustrative purposes some mechanical analyses of asphaltic road structures are carried out, with emphasis on the distribution of stresses, strains, (permanent) deformations, and dissipated energies.

On the Dangers of Averaging Across Subjects When Using Multidimensional Scaling or the Similarity-Choice Model

When ratings of judged similarity or frequencies of stimulus identification are averaged across subjects, the psychological structure of the data is fundamentally changed. Regardless of the structure of the individual-subject data, the averaged similarity data will likely be well fit by a standard multidimensional scaling model, and the averaged identification data will likely be well fit by the similarity-choice model. In fact, both models often provide excellent fits to averaged data, even if they fail to fit the data of each individual subject. Thus, a good fit of either model to averaged data cannot be taken as evidence that the model describes the psychological structure that characterizes individual subjects. We hypothesize that these effects are due to the increased symmetry that is a mathematical consequence of the averaging operation.

Prediction of an Individual Speech Pattern from Dyadic Interaction

One mathematical consequence of a Markov model of conversational rhythm is tested empirically. It is that monologue represents a special case of dialogue in which one participant is silent (or absent). The interaction parameters unique to dialogue indeed contribute little if any information to the prediction of noninteractive speech rhythms. They are nevertheless essential if one wishes to regenerate the dyadic system via the concatenation of monologue sequences.