Stirring by blinking rotlets in a bounded Stokes flow

A blinking rotlet model is used for the analysis of stirring in a Stokes flow in a rectangular domain. After the two-dimensional biharmonic equation is solved analytically, the associated velocity field of a pair of blinking rotlets positioned symmetrically on the y -axis, is used studying the stirring qualities of this blinking rotlet model. Contour kinematic simulations are performed in order to obtain information about the chaotic behaviour of a blob of passive tracer material put in this flow field

New classes of exact solutions of three-dimensional Navier-Stokes equations

New classes of exact solutions of the three-dimensional unsteady Navier-Stokes equations containing arbitrary functions and parameters are described. Various periodic and other solutions, which are expressed through elementary functions are obtained. The general physical interpretation and classification of solutions is given.Comment: 11 page

Jacobi multipliers, non-local symmetries and nonlinear oscillators

Constants of motion, Lagrangians and Hamiltonians admitted by a family of relevant nonlinear oscillators are derived using a geometric formalism. The theory of the Jacobi last multiplier allows us to find Lagrangian descriptions and constants of the motion. An application of the jet bundle formulation of symmetries of differential equations is presented in the second part of the paper. After a short review of the general formalism, the particular case of non-local symmetries is studied in detail by making use of an extended formalism. The theory is related to some results previously obtained by Krasil'shchi, Vinogradov and coworkers. Finally the existence of non-local symmetries for such two nonlinear oscillators is proved.Comment: 20 page

Устойчивость сперматогенеза и проявления отбора на клеточном и индивидуальном уровнях у незрелых представителей Pelophylax esculentus complex

Pelophylax esculentus is an interspecific hybrid which reproduces hemiclonally by crossing with the parental species (P. ridibundus or P. lessonae). The structure of hemiclonal population systems is of great interest. The majority of investigations into populations of water frogs deal with samples of mature animals, while subadults are less studied. We collected a random sample of 73 small water frogs from three localities in the Siverskyi Donets River floodplain. All frogs were measured, injected with colchicines and killed after anesthesia. We determined the species specifity, sex, age and ploidy of every individual. In addition, we measured testis length and studied the germ cells of all males by means of karyological analysis. We calculated the portion of triploids in the largest subsample from the vicinity of the Biological Station of V.N. Karazin Kharkiv National University and carried out a meta-analysis of previous publications dealing with composition of green frog samples from this locality. The proportion of triploids in our sample appeared to be approximately the same as 12 years ago. However, this proportion in our sample differed significantly from that obtained in recent samples of green frogs belonging to other age groups (adults and metamorphs) from the same locality. The share of triploids of P. esculentus is the lowest in the sample of metamorphs. This proportion increases in froglets because of early death of representatives of parental species which originated from hybrid-hybrid crossing. Then the number of triploids among adult P. esculentus individuals declines again probably because of their lower viability compared to diploids. We have revealed that subadult diploids have erythrocytes smaller than 28 microns, while triploids’ erythrocytes exceed 27 microns. Therefore, in borderline cases true ploidy could be determined only by the karyological technique. The average ratio between testis length and body length appeared to be larger in the parental species than in both diploid and triploid hybrids. Karyological analysis has revealed that P. esculentus had significantly lower portions of spermatocytes I with normal karyotype (13 bivalents) in the testis in comparison with P. ridibundus, but this value increases in adult hybrids. We suggest that increasing of spermatogenesis stability in adult frogs as opposed to subadults might be the consequence of both selection of germ cell lines in the testis and more frequent survival of individuals with stable gametogenesis. Исследована случайная выборка неполовозрелых зеленых лягушек из Северско-Донецкого центра разнообразия Pelophylax esculentus complex. У каждой особи определяли пол, возраст (методом скелетохронологии), плоидность и принадлежность к P. esculentus или P. ridibundus, а также измеряли длину тела и длину семенников у самцов. По мазкам крови определяли среднюю длину эритроцитов. Из семенников изготавливали кариологические препараты, по которым описывали кариотипы клеток во время митотических и мейотических делений. Проведен метаанализ результатов данной и предшествовавших работ, в которых определяли состав выборок зеленых лягушек пойме р. Северский Донец в окрестностях Биологической станции Харьковского национального университета имени В.Н. Каразина. Доля триплоидных P. esculentus ниже всего у метаморфов, повышается (вследствие гибели представителей родительского вида, появляющихся от скрещивания гибридов) у незрелых особей и снижается (из-за большей смертности триплоидов) у половозрелых особей. Диплоидные лягушки имеют длину эритроцитов менее 28 мкм, триплоидные – более 27 мкм; в диапазоне 27–28 мкм по длине эритроцитов установить плоидность невозможно. Незрелые P. esculentus имеют тенденцию к задержке развития гонад и значимо большее количество аномальных кариотипов в митозе и мейозе, чем P. ridibundus. Повышение устойчивости сперматогенеза у половозрелых лягушек по сравнению с незрелыми может быть следствием как отбора клеточных линий внутри семенников, так и преимущественного выживания особей с относительно более устойчивым гаметогенезом.Исследована случайная выборка неполовозрелых зеленых лягушек из Северско-Донецкого центра разнообразия Pelophylax esculentus complex. У каждой особи определяли пол, возраст (методом скелетохронологии), плоидность и принадлежность к P. esculentus или P. ridibundus, а также измеряли длину тела и длину семенников у самцов. По мазкам крови определяли среднюю длину эритроцитов. Из семенников изготавливали кариологические препараты, по которым описывали кариотипы клеток во время митотических и мейотических делений. Проведен метаанализ результатов данной и предшествовавших работ, в которых определяли состав выборок зеленых лягушек пойме р. Северский Донец в окрестностях Биологической станции Харьковского национального университета имени В.Н. Каразина. Доля триплоидных P. esculentus ниже всего у метаморфов, повышается (вследствие гибели представителей родительского вида, появляющихся от скрещивания гибридов) у незрелых особей и снижается (из-за большей смертности триплоидов) у половозрелых особей. Диплоидные лягушки имеют длину эритроцитов менее 28 мкм, триплоидные – более 27 мкм; в диапазоне 27–28 мкм по длине эритроцитов установить плоидность невозможно. Незрелые P. esculentus имеют тенденцию к задержке развития гонад и значимо большее количество аномальных кариотипов в митозе и мейозе, чем P. ridibundus. Повышение устойчивости сперматогенеза у половозрелых лягушек по сравнению с незрелыми может быть следствием как отбора клеточных линий внутри семенников, так и преимущественного выживания особей с относительно более устойчивым гаметогенезом

Lie symmetry analysis and exact solutions of the quasi-geostrophic two-layer problem

The quasi-geostrophic two-layer model is of superior interest in dynamic meteorology since it is one of the easiest ways to study baroclinic processes in geophysical fluid dynamics. The complete set of point symmetries of the two-layer equations is determined. An optimal set of one- and two-dimensional inequivalent subalgebras of the maximal Lie invariance algebra is constructed. On the basis of these subalgebras we exhaustively carry out group-invariant reduction and compute various classes of exact solutions. Where possible, reference to the physical meaning of the exact solutions is given. In particular, the well-known baroclinic Rossby wave solutions in the two-layer model are rediscovered.Comment: Extended version, 24 pages, 1 figur

Experiment for Testing Special Relativity Theory

An experiment aimed at testing special relativity via a comparison of the velocity of a non matter particle (annihilation photon) with the velocity of the matter particle (Compton electron) produced by the second annihilation photon from the decay Na-22(beta^+)Ne-22 is proposed.Comment: 7 pages, 1 figure, Report on the Conference of Nuclear Physics Division of Russian Academy of Science "Physics of Fundamental Interactions", ITEP, Moscow, November 26-30, 200

Dynamics of Vortex Pair in Radial Flow

The problem of vortex pair motion in two-dimensional plane radial flow is solved. Under certain conditions for flow parameters, the vortex pair can reverse its motion within a bounded region. The vortex-pair translational velocity decreases or increases after passing through the source/sink region, depending on whether the flow is diverging or converging, respectively. The rotational motion of two corotating vortexes in a quiescent environment transforms into motion along a logarithmic spiral in the presence of radial flow. The problem may have applications in astrophysics and geophysics.Comment: 13 pages, 9 figure

Sustainable coexistence of the parental species and hemiclonal interspecific hybrids is provided by the variety of ontogenetic strategies

Factors determining the sustainability of Hemiclonal Population Systems in which the interspecies hybrids Pelophylax esculentus complex coexist with members of parental species were studied using a combination of empirical data and computer simulation modeling. The empirical data demonstrates the existence of different intrapopulation strategies by partitioning a sample of individuals into two groups on the basis of their body size at a given age and comparing selected groups in terms of factors such as growth rate, life span, females’ fecundity and the age at which breeding commences. Then by using simulation modeling, we study the probable importance of intrapopulation ontogenetic strategies for the stability of Pelophylax esculentus complex HPS