New Derivation of Redshift Distance without Using Power Expansions

Here we use the flat Friedmann-Lemaitre-Robertson-Walker metric describing a spatially homogeneous and isotropic universe to derive the cosmological redshift distance in a way which differs from that which can be found in the astrophysical literature. We use the co-moving coordinate re (the subscript e indicates emission) for the place of a galaxy which is emitting photons and ra (the subscript a indicates absorption) for the place of an observer within a different galaxy on which the photons - which were traveling thru the universe - are absorbed. Therefore the real physical distance - the way of light - is calculated by D = a(t0) ra - a(te) re. Here means a(t0) the today’s (t0) scale parameter and a(te) the scale parameter at the time of emission (te) of the photons. Nobody can doubt this real travel way of light: The photons are emitted on the co-moving coordinate place re and are than traveling to the co-moving coordinate place ra. During this traveling the time is moving from te to t0 (te ≤ t0) and therefore the scale parameter is changing in the meantime from a(te) to a(t0). Using this right way of light we calculate some relevant classical cosmological equations (effects) and compare these theoretical results with some measurements of astrophysics. As one result we get e.g. the today’s Hubble parameter H0a ≈ 62.34 km/(s Mpc). This value is smaller than the Hubble parameter H0,Planck ≈ 67.66 km/(s Mpc) resulting from Planck 2018 data [12] which is discussed in the literature.

Some Issues on Crystal Plasticity Models Formulation: Motion Decomposition and Constitutive Law Variants

In this paper, kinematic relations and constitutive laws in crystal plasticity are analyzed in the context of geometric nonlinearity description and fulfillment of thermodynamic requirements in the case of elastic deformation. We consider the most popular relations: in finite form, written in terms of the unloaded configuration, and in rate form, written in terms of the current configuration. The presence of a corotational derivative in the relations formulated in terms of the current configuration testifies to the fact that the model is based on the decomposition of motion into the deformation motion and the rigid motion of a moving coordinate system, and precisely the stress rate with respect to this coordinate system is associated with the strain rate. We also examine the relations of the mesolevel model with an explicit separation of a moving coordinate system and the elastic distortion of crystallites relative to it in the deformation gradient. These relations are compared with the above formulations, which makes it possible to determine how close they are. The results of the performed analytical calculations show the equivalence or similarity (in the sense of the response determined under the same influences) of the formulation and are supported by the results of numerical calculation. It is shown that the formulation based on the decomposition of motion with an explicit separation of the moving coordinate system motion provides a theoretical framework for the transition to a similar formulation in rate form written in terms of the current configuration. The formulation of this kind is preferable for the numerical solution of boundary value problems (in a case when the current configuration and, consequently, contact boundaries, are not known a priori) used to model the technological treatment processes.

Dynamics and control of loop reactors - a review

In loop reactors the system is composed of several reactor units that are organized in a loop and the feeding takes place at one of several ports with switching of the feed port. In its simplest operation a pulse is formed and rotates around it, producing high temperatures which enable combustion of dilute streams. A limiting model with infinite number of units was derived. Rotating pulses, steady in a moving coordinate, emerge in both models when the switching to front propagation velocities ~1. But this behavior exists over a narrow domain. Simulations were conducted with generic first order Arrhenius kinetics. Experimental observations are reviewed. Outside the narrow frozen rotating pattern domain the system may exhibit multi- or quasi-periodic operation separated by domains of inactive reaction. The bifurcation set incorporates many 'finger'-like domains of complex frequency-locked solutions that allow to extend the operation domain with higher feed temperatures. Control is necessary to attain stable simple rotating frozen pattern within the narrow domains of active operation. Various tested control approaches are reviewed. Actual implementation of combustion in LR will involve several reactants of different ignition temperatures. Design and control should be aimed at producing locked fronts and avoid extinction of slower reactions.

Calculation trajectories of stealthy movement of aircraft to a specified point in detection zone of onboard Doppler radar

An onboard radar operating in the impulse–Doppler mode has the characteristic features of the detection zone. The feature lies in the fact that at every point of the detection zone an aircraft has a sector of directions such as the onboard Doppler radar will not detect it as long as it moves in these directions. This sector is called the sector of invisible motion directions of the aircraft. Because of these features, there are such trajectories that aircraft flying along them are not detected by an onboard Doppler radar, such as an AWACS radar. The article proposes a method for planning stealthy trajectories between two given points in the Doppler radar coverage area. Trajectories are selected from a parametric family of elliptical stealthy trajectories, which are ellipses in the AWACS-associated moving coordinate system. An equation is found for the characteristic parameter of the ellipse, the solution of which allows us to uniquely identify the stealthy trajectory between two given points. The conditions for the existence of stealthy trajectories passing through specified points are investigated.

Method of applied direction of mathematics in the aviation institution of higher education

The elements of the method of applied direction of mathematics in the aviation institution of higher education developed by us are considered. We use this technique in higher mathematics classes at the Flight Academy of the National Aviation University. Examples of a combination of fundamental mathematical concepts and practical methods of their application are given. We illustrate in detail the coordinate systems used in aviation. Among these systems are mobile and fixed coordinate systems. Problems of higher mathematics related to one or another coordinate system are indicated. For example, to record vector equations of motion in projections, moving coordinate systems are used, the beginning of which is located in the center of mass of the aircraft. Therefore, the study of the topic "Reflection of linear (vector) spaces" acquires a professional orientation. In particular, we present the formulas of coordinate transformations for parallel transfer and rotation of the axes. Note that the transformations of rectangular coordinate systems are used in aviation. Having considered aviation coordinate systems, the teacher is interested in students in the study of equations of motion, determination of accelerations, velocities and displacements. Methodical methods of formation of practical skills and abilities of future aviation specialists contribute to the implementation of the applied direction of mathematics. We have given some examples of methods of applied direction of mathematics in aviation in the sources that are currently published. The prospect of our research is to further improve practical approaches to solving problems of mathematical training of students of aviation institutions of higher education. This should help increase the level of methodological training of scientific and pedagogical staff of higher education institutions. At the same time, it should contribute to the improvement of methods of teaching mathematics in terms of its application. As a result, the graduate of the aviation institution of higher education must be ready for successful professional activity. Key words: applied direction of mathematics, coordinate systems in aviation, parallel transfer, rotation of axes, fundamental mathematical concepts in aviation.

Modeling Vector Fields in Space of Affine Connection

The authors have been constructed the splitting of the basic geometric images vector field (points, straights, hyperplanes and hyperguadrics) in transition from n-dimensional affine space to the space of affine connection. All invectigations have been fulfilled in the moving coordinate system of zero order.

Establishment of New Fundamental Theory in Diffusion Phenomena

Investigating the elementary process of diffusion revealed that the De Broglie hypothesis is really valid in a material and further that the Schrödinger equation is reasonably derived from the diffusion equation. The diffusion equation is thus one of the fundamental equations in physics. The problem between a moving coordinate system and a fixed coordinate system for the diffusion equation had never been discussed until recently in the history of diffusion theory. In that situation, it is revealed that investigating the problem between those coordinate systems is indispensable for understanding the diffusion phenomena. The new findings obtained here, which are revolutionary in the existing diffusion theory, will be not only dominant but also indispensable for further advance in the diffusion study.