Geodesic Mappings of Semi-Riemannian Manifolds with a Degenerate Metric

This article introduces the concept of geodesic mappings of manifolds with idempotent pseudo-connections. The basic equations of canonical geodesic mappings of manifolds with completely idempotent pseudo-connectivity and semi-Riemannian manifolds with a degenerate metric are obtained. It is proved that semi-Riemannian manifolds admitting concircular fields admit completely canonical geodesic mappings and form a closed class with respect to these mappings.

Study Of The Thermal Processes Dynamics In The Feedstuff Disinfection By Electric Contact Heating

The article is dedicated to the study of the heat transfer processes that occur in the feedstuff disinfection chamber that relies upon electric contact heating. The mechanism of the temperature gradient appearance, which is the main cause of the heat losses has been investigated. The basic equations of heat conduction are considered. A method is proposed for determining the key parameters of the heat transfer process. A functional diagram of the experimental setup with a description of the operation of individual units is presented. The dependence for the transient operating mode of the unit on the growth of heat losses has been established. Thermal images of different shapes of the unit dielectric chambers have been provided as well as temperature field distribution through the chamber wall.

STUDY OF SELF-SUPERPOSABLE FLUID MOTIONS IN CONFOCAL PARABOLOIDAL DUCTS

In this paper, studies have been made on some self-superposable motion of incompressible fluid is confocal Paraboloidal ducts. The boundary conditions have been neglected therefore the solutions contain a set of constants. Pressure distribution and the nature of vorticity are discussed. Tendency of irrotationality of the fluid flow is also determined. The aim of the paper is to introduce a method for solving the basic equations of fluid dynamics in confocal paraboloidal coordinates by using the property of self superposability.

MATHEMATICAL MODELING OF MICROORGANISM GROWTH (ANALYTICAL APPROACH)

This work is a report "Mathematical modeling of the growth of microorganisms", written at the suggestion of the teacher of mathematics L.S. Akinfieva in 1982, when the author was a student of the 10th grade of a specialized (with in-depth study of biology) school No. 11 in Moscow. All students of this class were asked to write reports (as a "gift for the 60th anniversary of the USSR") within the framework of the general theme "Mathematics in my future profession." The report contains the basic equations of the kinetics of growth and dying of microorganisms, as well as their consumption of a nutrient substrate (Malthus, Monod's equations, Herbert's model). In addition to the equations of microbiological kinetics themselves, some methods of obtaining their approximate solutions in the form of explicit functions (without using numerical methods) are demonstrated.

Randomness and Irreversiblity in Quantum Mechanics: A Worked Example for a Statistical Theory

The randomness of some irreversible quantum phenomena is a central question because irreversible phenomena break quantum coherence and thus yield an irreversible loss of information. The case of quantum jumps observed in the fluorescence of a single two-level atom illuminated by a quasi-resonant laser beam is a worked example where statistical interpretations of quantum mechanics still meet some difficulties because the basic equations are fully deterministic and unitary. In such a problem with two different time scales, the atom makes coherent optical Rabi oscillations between the two states, interrupted by random emissions (quasi-instantaneous) of photons where coherence is lost. To describe this system, we already proposed a novel approach, which is completed here. It amounts to putting a probability on the density matrix of the atom and deducing a general “kinetic Kolmogorov-like” equation for the evolution of the probability. In the simple case considered here, the probability only depends on a single variable θ describing the state of the atom, and p(θ,t) yields the statistical properties of the atom under the joint effects of coherent pumping and random emission of photons. We emphasize that p(θ,t) allows the description of all possible histories of the atom, as in Everett’s many-worlds interpretation of quantum mechanics. This yields solvable equations in the two-level atom case.

Mathematical description of the cavitation process in the jet apparatus

The problem of mathematical description of non-steady processes in hydrodynamic systems is currently relevant and requires early resolution. The description of cavitation as a non-steady process is one of the most important issues of hydrodynamics. In this paper, as a result of the analysis and generalization of a priori information, plus transformation of the basic equations describing cavitation processes, a number of expressions are obtained that reflect the behavior of the incompressible fluid main flow in a jet apparatus, taking into account the conduct of hydrodynamic cavitation in it. To create a cavitation process mathematical description, it is proposed to apply an empirical formula for determining the ejected flow pressure. The newly developed mathematical dependencies can be used in the design of jet devices (ejectors, cavitators, ejectors-cavitators) for various purposes in both marine and stationary coastal technological systems for processing fluid media. In particular, it is advisable to use them in the preparation and conditioning of drinking and industrial water, wastewater and oily water purification, etc.

STUDY OF SELF-SUPERPOSABLE LIQUID IN OBLATE SPHEROIDAL SHAPE

The paper studiesthe self-superposable motion of a liquid of a fluid which is incompressible in nature in oblate spheroidal shape. An incompressible fluid is defined as the fluid whose volume or density does not change with pressure. Thus, the main aim of this paper is to solve the basic equations of fluid dynamics in oblate spheroidal coordinates considering self-superposable nature of the fluid. The paper includes the study of nature of vorticity and irrotationality and has not considered the boundary conditions in theanalysis. Lastly, the paper determines the pressure distribution and the solutions contain a set of constants.

Reactive Transport: A Review of Basic Concepts with Emphasis on Biochemical Processes

Reactive transport (RT) couples bio-geo-chemical reactions and transport. RT is important to understand numerous scientific questions and solve some engineering problems. RT is highly multidisciplinary, which hinders the development of a body of knowledge shared by RT modelers and developers. The goal of this paper is to review the basic conceptual issues shared by all RT problems, so as to facilitate advance along the current frontier: biochemical reactions. To this end, we review the basic equations to point that chemical systems are controlled by the set of equilibrium reactions, which are easy to model, but whose rate is controlled by mixing. Since mixing is not properly represented by the standard advection-dispersion equation (ADE), we conclude that this equation is poor for RT. This leads us to review alternative transport formulations, and the methods to solve RT problems using both the ADE and alternative equations. Since equilibrium is easy, difficulties arise for kinetic reactions, which is especially true for biochemistry, where numerous frontiers are open (how to represent microbial communities, impact of genomics, effect of biofilms on flow and transport, etc.). We conclude with the basic 10 issues that we consider fundamental for any conceptually sound RT effort.