Abstract:
The spatial local anomalies of the concentration ratios for isotopes ^{143}Nd/^{144}Nd (or εNd) and ^{87}Sr/^{86}S in Lukkulaisvaara intrusion (North Karelia) were discovered. The physical mechanisms and the descriptions of the effect of an arising of those anomalies were developed and presented. The base of the proposed mechanisms is the phenomena of the migration (diffusion) of components, due to the (T, P (or D)) gradients. The description of the processes of an arising of the gradients of a temperature (T), of a pressure (P) and of a deformation (D) in the layered inhomogeneous intrusion during its formation and evolution, were obtained. It was shown that the gradients can induce the spatial redistribution of the chemical elements and their isotopes in the intrusion. The redistribution, in turn, can lead to the observed spatial concentration anomalies for these components. It was first obtained the expressions for the diffusion additions to the isotope’s parameter ε (εNd, in part).

Abstract:
On the basis of a three-dimensional non stationary model of a convective cloud with detailed description of dynamic, thermodynamic and microphysical processes, numerical experiments were conducted to study the formation of parameters of convective clouds under unstable stratification of the atmosphere. Numerical experiments have been carried out to study the formation of convective processes in the atmosphere. The thermo hydrodynamic parameters in the zone of a thunderstorm cloud are determined, and regions with a vortex motion of air are identified. The main flows feeding the convective cloud in the mature stage are determined. Due to the means of visualization, the areas of formation and growth of precipitation particles are identified. In a three-dimensional form, the interaction of dynamic and thermodynamic processes is analyzed. The interaction of fields is manifested in the form of deformation of fields of thermodynamic parameters under the influence of dynamic processes. Trajectories of air streams around a cloud and the trajectories of drops in a cloud are determined. The results of numerical experiments confirm that dynamic processes significantly influence the formation of fields of thermodynamic parameters in the cloud, which also determine the course of microphysical processes and the nature of the growth of precipitation particles.

Abstract:
Many researchers use the estimation method of exposure doses due to natural radioactivity adopted by UNSCEAR equation, which is based on an infinite plan source modeling. The results in most cases are acceptable within acceptable accuracy and error. However, in many cases, this approach cannot be applied e.g., for more complicated source geometry, composition, radioactivity distribution and so on. In previous situations, simulation and modeling are needed for exposure dose calculation to get more acceptable and accurate results. In the present work, modeling and recalculation of exposure dose rate are performed for an important previous published study about Hammam Pharaon. The study is selected because of its special physical characterization parameters and possible effects on Egyptian tourism. The effects of radionuclides distribution with soils and source composition, density, and geometry as recommended by NCRP 129 have been taken into consideration. The results for depth profile calculation show the conformation with the NCRP 129, which indicates a reduction in the free air exposure dose due to the fact that the above soil covered the active slab by 20% - 25% for 1 cm cover-up to 95% - 100% for 30 cm cover. In addition, the effect of density variation in dose rate is studied. A comparison with previous results has been performed.

Abstract:
The state of the physics of convective clouds and cloud seeding is discussed briefly. It is noted that at the present time there is a transition from the stage of investigation of “elementary” processes in the clouds to the stage of studying the formation of macro- and microstructural characteristics of clouds as a whole, taking into account their system properties. The main directions of the development of cloud physics at the upcoming stage of its development are discussed. The paper points out that one of these areas is the determination of the structure-forming factors for the clouds and the study of their influence on their formation and evolution. It is noted that one of such factors is the interaction of clouds with their surrounding atmosphere, and the main method of studying its role in the processes of cloud formation is mathematical modeling. A three-dimensional nonstationary model of convective clouds is presented with a detailed account of the processes of thermohydrodynamics and microphysics, which is used for research. The results of modeling the influence of the wind field structure in the atmosphere on the formation and evolution of clouds are presented. It is shown that the dynamic characteristics of the atmosphere have a significant effect on the formation of macro- and microstructural characteristics of convective clouds: the more complex the structure of the wind field in the atmosphere (i.e., the more intense the interaction of the atmosphere and the cloud), the less powerful the clouds are formed.

Abstract:
The first justified theory of solid state was proposed by Grüneisen in the year 1912 and was based on the virial theorem. The forces of interaction between two atoms were assumed as changing with distance between them according to inverse power laws. But only virial theorem is insufficient to deduce the equation of state, so this author has introduced some relations, which are correct, when the forces linearly depend on displacement of atoms. But with such law of interaction the phase transitions cannot take place. Debye received Grüneisen equation in another way. He deduced the expression for thermocapacity, using Plank formula for energy of harmonic vibrator. Taking into account the dependence of atomic vibration frequency from distance between atoms, when the forces of interaction are anharmonic, he received the equation of state, which in classical limit turns to Grüneisen equation. The question, formulated by Debye is—How can we come to phase transitions, when Plank formula for harmonic vibrator was used? Debye solved this question not perfectly, because he was born to small anharmonicity. In the presented work a chain of atoms is considered, and their movement is analysed by means of relations, equivalent to virial theorem and theorem of Lucas (disappearing of mean force). Both are the results of variation principle of Hamilton. The Grüneisen equation for low temperature (not very low, where quantum expression for energy is essential) was obtained, and a family of isotherms and isobars are drown, which show the existence of spinodals, where phase transitions occur. So, Grüneisen equation is an equation of state for low temperatures.

Abstract:
In this work the problem of rewinding of a tape with constant speed is
considered. Considering that drums represent bodies of variable weight, the equations
of motion of system are formulated. Taking into account parametrical clearing
of system of servo-constraints, the structure of force of reaction of
servo-constraints which provides steady realization of servo-constraints (a
constancy of linear speed of a tape) is defined. For realization of
servo-constraints, it is offered to build digital watching system (DWS) and the
full system of equations of DWS is formed. Laws of change of the operating
influences, systems providing stability under the relation of the variety
defined of servo-constraints are defined.

Abstract:
The anharmonic vibrator, whose expression of potential energy contains second and third powers of coordinates, is treated on the basis of dynamical procedure, which presents the state of motion by means of mean position and mean amplitude of vibration. The divergent statistical integral comes here not into consideration. The free energy is represented through mean atomic displacement and developed in power series, retaining fourth degree. The graphs show that at certain temperature, the minimum in free energy disappears, and the atom escapes from the potential pit. A simple atomic model that represents this phenomenon is proposed and the influence of model dimension and pressure on melting temperature will be presented.

Abstract:
In this paper we are concerned with the oscillation
criteria of second order non-linear homogeneous differential equation. Example
have been given to illustrate the results.

Abstract:
On the base of a vibrator atomic model the mechanical and thermal properties of the object are analyzed. The potential energy of the vibrator is represented by means of positive term with coordinate deflection in second power and negative term with deflection in fourth power. With the use of dynamical procedure of calculation, which permits to calculate mean deflection and root mean square amplitude of vibrations, the dependence of applied force from mean amplitude and temperature is calculated. This dependence shows a maximum (or minimum, when the direction of force is reversed), the height of which diminishes with rising temperature. When the force reaches the value of the maximum, the object does not elastic counteract to the force, and gliding begins. It is also considered a vibrator with positive term, containing the deflection in second power and a term, where the deflection treats in third power (Boguslawski vibrator). Exact calculations of the dependence of the force from the temperature in adiabatic process, where the entropy is maintained constant, shows that it is represented by means of a curve with a maximum, so that stretching leads to cooling till the point of maximum is reached.

Abstract:
The purpose of the research is to develop a dynamical theory of phase transitions in crystalline structures, when except for temperature, the pressure is acting. So, the phase diagram temperature-pressure (dimensions) must be constructed. In general case, it is a complicated question, which can be solved for simple models of crystal, as three atomic models, introduced in the work of Frenkel [1]. In this model, three identical atoms are placed on the straight line and interact with the forces, which can be described by the expression, given in the article of Lennard-Jones [2]. Such simple model may have success, when the crystalline structure is simple, which consists of one type of atoms, for example: carbon. The model was generalized to cubic cell model with a moving atom in the inner part of the cell. The rigorous calculation of phase diagram for transition graphite-diamond shows some similarity with results of numerous experimental investigations (which are not discussed here). So, the way of phase diagram calculation may attract attention.