Search

Copyright of Studia Geophysica & Geodaetica is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Studia Geophysica & Geodaetica is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Studia Geophysica & Geodaetica is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Studia Geophysica & Geodaetica is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Studia Geophysica & Geodaetica is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Studia Geophysica & Geodaetica is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

An analysis of the equation for geodetic distance is presented, based on the condition of integrability of the equation for the covariant derivative of the velocity of an admixture particle in a fluid and on the assumption that the motion is taking place in a compact varieta along trajectories close to geodesics. A pattern of state is thus obtained in the neighbourhood of equilibirum state in the appropriate space of states, and we decide about its stability in the sense of the Lyapunovian theory of stability of the quiescent condition. The conditions of integrability are also considered with regard to the metric in conformal Euclidean (conformally flat) form. [ABSTRACT FROM AUTHOR]

The law of the self-preservation of the power spectrum is the result of the covariant formulation of the law of motion of particles of a fluid and of the non-stationary metric of the space of configurations, induced by their velocity field. The initial concept is the covariant derivative of the vector of the mean velocity of the particle of the fluid. As a tensor of the second order we select it so that it contains the Lagrangean characteristics of motion-two-point correlation tensors of the second order and expressions generated by specifying it. [ABSTRACT FROM AUTHOR]

With the aid of elementary methods of the theory of dimensionality we approach the problem of existence of invariants in the process of mixing particles of a passive admixture in a field of turbulence. [ABSTRACT FROM AUTHOR]

The progressive development of the theory of turbulence is based on the formalism of characteristic functionals. Drawing on an incomplete analogy between the Hopf equation for these functionals and the equation for the quantized boson field, a system of fundamental principles of the theory of turbulence is proposed. This represents a set of statements which can be used in an attempt to classify the theory in the sense of its algebraization and, therefore, also its axiomatization. [ABSTRACT FROM AUTHOR]

The efforts to axiomatize the theory of turbulent diffusion, founded on the theory of Markovian random processes, are based on the principal logical algebraic aspects of the concept of modelling. [ABSTRACT FROM AUTHOR]

The problem of the motion of a particle in a field of turbulence is formulated with the aid of analytical methods of mechanics. The equation of energy balance for the interaction of the field and particle is obtained from the mathematical structure, the real counterpart of which is the equation of a dynamic system with mixing (discrete model). [ABSTRACT FROM AUTHOR]

The concept of the metric theory of particle transfer in a random field of velocities the problem of turbulent diffusion is the result of a suitable connection of a certain computational theoretical model of the endomorphism of Lebesgue's space L and the concept of the action of the field of velocities on the particle in its abstract form. The metric theory of this phenomenon is part of the general metric theory of dynamic systems, i.e. the ergodic theory. The adjective 'suitable' means that we are introducing certain relations between the said concepts. The essence of these concepts is in that we require that the relations, describing the nature of the field-particle interaction, be a realistic counterpart to the appropriate endomorphism T of space L. This endomorphism is closely associated with Kolmogorov's automorphism and with the automorphism with a positive enthropy. We are pointing out the close relation between the T-representation, the equations of motion of the particle in a random field of velocities, the canonic transformations and the fundamental model of stochasticity of Hamiltonian systems. [ABSTRACT FROM AUTHOR]

(Part I): The metric theory of turbulent diffusion is a metric theory of transport in a random velocity field. This method of description is founded on the general theory of representation with an invariant measure, a part of which is also formed by the endomorphisms of Lebesgue's space. With the help of a certain class of these representations, which form a theoretical computation model of the transport phenomenon, the equations of motion of the particle are established. The main purpose of the deliberations, contained in Part I of this paper, is an outline of the theory which explains in particular the topological (less so the algebraic) properties of the process in the sense of our endeavour for a more abstract approach to the theory of transport phenomena. Attention is concentrated on these properties not only in treating some of the problems of the metric theory of dynamic systems, but also in interpreting the fundamental concept of the theory of instability, e.g., the divergence of geodesic flows. [ABSTRACT FROM AUTHOR]

Copyright of Studia Geophysica & Geodaetica is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Studia Geophysica & Geodaetica is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Studia Geophysica & Geodaetica is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Studia Geophysica & Geodaetica is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Studia Geophysica & Geodaetica is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Studia Geophysica & Geodaetica is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Studia Geophysica & Geodaetica is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)