On hydrodynamics in the presense of strong external potential field

On the base of the Boltzmann kinetic equation, hydrodynamics of a dilute gas in the presence of the strong external potential field is investigated. First of all, a gravitational field is meant, because the consistent development of hydrodynamics in this environment is of great practical importance. In the present paper it is assumed that it is possible to neglect the influence of the field on the particle collisions. The study is based on the Chapman–Enskog method in a Bogolyubov’s formulation, which uses the idea of the functional hypothesis. Consideration is limited to steady gas states, which are subjected to a simpler experimental study. Chemical potential μ0 of the gas at the point where the external field has zero value and its temperature T are selected as the reduced description parameters of the system. In equilibrium, in the presence of the field, these values do not depend on the coordinates. It is assumed that in thehydrodynamic states T and μ0 are weakly dependent on the coordinates and therefore their gradients, considered on the scale of the free path length of the gas, are small. The kinetic equation, accounting for the functional hypothesis, gives an integro-differential equation for a gas distribution function at the hydrodynamic stage of evolution. This equation is solved in perturbation theory in gradients of T and μ0. The main approximation is analyzed for possibility of the system to be in a local equilibrium by means of comparing it with an equilibrium distribution function. Next, the distribution function is calculated in the first approximation in gradients and it is expressed in terms of solutions Ap , Bp of some first kind integral Fredholm equations. An approach to the approximate solution of these equations is discussed. The found distribution function is used to calculate the fluxes of the number of gas particles and their energy in the first order in gradients T and μ0 . Kinetic coefficients, which describe the structure of these fluxes, are introduced. Matrix elements of the operator of the linearized collision integral (integral brackets) are used for their research. It is a question of validity of the principle of symmetry of kinetic coefficients and definition of their signs.

Sexual Dimorphism and Morphological Modularity in Acanthoscelides obtectus (Say, 1831) (Coleoptera: Chrysomelidae): A Geometric Morphometric Approach

Sexual dimorphism and specific patterns of development contribute in a great manner to the direction and degree of the sexual differences in body size and shape in many insects. Using a landmark-based geometric morpohometrics approach, we investigated sex-specific morphological size and shape variation in the seed beetle, Acanthoscelides obtectus. We also tested the functional hypothesis of the two morphological modules—thorax and abdomen in both sexes. Female-biased sexual dimorphism in size was shown, while differences in shape were reflected in the wider thorax and abdomen and shorter abdomen in females in comparison to males. The functional hypothesis of a two-module body was confirmed only in females before correction for size, and in both sexes after the allometry correction. Our results indicate that reproductive function has the central role in forming the patterns of modularity. We hypothesize that high morphological integration of the abdomen in females results from intense stabilizing selection, while the more relaxed integration in males is driven by the higher intensity of sexual selection.

Lexical Tone Perception in Mandarin Chinese Speakers With Aphasia

The brain localization debate of lexical tone processing concerns functional hypothesis that lexical tone, owing to its strong linguistic features, is dominant in the left hemisphere, and acoustic hypothesis that all pitch patterns, including lexical tone, are dominant in the right hemisphere due to their acoustic features. Lexical tone as a complex signal contains acoustic components that carry linguistic, paralinguistic, and nonlinguistic information. To examine these two hypotheses, the current study adopted triplet stimuli including Chinese characters, their corresponding pinyin with a diacritic, and the four diacritics representing Chinese lexical tones. The stimuli represent the variation of lexical tone for its linguistic and acoustic features. The results of a listening task by Mandarin Chinese speakers with and without aphasia support the functional hypothesis that pitch patterns are lateralized to different hemispheres of the brain depending on their functions, with lexical tone to the left hemisphere as a function of linguistic features.

A Morphofunctional Hypothesis for Selection on EDAR V370A and Associated Elements of Sinodonty

The phenomenon of sinodonty refers to a suite of dental characters shared between East Asian and Native American populations, and most prominently to the presence of shoveled incisors. Although this syndrome is a conspicuous aspect of dental differentiation among extant human populations, elements of which have been recent subject of detailed genetic analysis, adaptive consequences of shoveled incisors and related features remains unclear. Here, I hypothesize that many of the associated differences in dentition (along with reduction in mandibular length and increases in salivary gland branching) arose in parallel with the opportunistic consumption of wild rice and millet in central and northern China, respectively, and with their subsequent domestication in the Upper Paleolithic. More efficient mastication and digestion of plant grains (and of other starchy foods obtained via broad-spectrum foraging) would potentially have been enabled by these traits, yielding greater rates of nutritional intake as wild crops were progressively domesticated. This functional hypothesis, although not mutually exclusive relative to other proposed selective factors, matches the estimated timeline in China for both origin and time to fixation of the associated allele (EDAR V370A), and is consistent with chronic energetic gain and fitness benefits independent of any assumptions for concurrent climatic conditions.

Temperature and velocity relaxation in plasma. Spectral theory approach

The electron temperature and velocity relaxation of completely ionized plasma is studied on the basis of kinetic equation obtained from the Landau equation in a generalized Lorentz model. In this model contrary to the standard one ions form an equilibrium subsystem. Relaxation processes in the system are studied on the basis of spectral theory of the collision integral operator. This leads to an exact theory of relaxation processes of component temperatures and velocities equalizing. The relation of the developed theory with the Bogolyubov method of the reduced description of nonequilibrium systems is established, because the theory contains a proof of the relevant functional hypothesis, the idea of which is the basis of the Bogolyubov method. The temperature and velocity relaxation coefficients as eigenvalues of the collision integral operator are calculated by the method of truncated expansion of its eigenfunctions in the Sonine orthogonal polynomials. The coefficients are found in one- and two-polynomial approximation. As one can expect, convergence of this expansion is slow.