Research of Self-Oscillating Processes in the Zone of Interaction of an Elastic Tire with a Solid Support Base

When two bodies interact in contact, self-oscillations or relaxation vibrations can occur, which are vibrations of parts of bodies relative to each other. The study of the processes occurring in the zone of an elastic tire interaction with a solid support base is of particular interest, since they directly affect the safety of movement of wheeled vehicles. The aim of the work is to study the conditions for the occurrence of self-oscillating processes in the zone of interaction of an elastic tire with a solid support base in three rolling modes: traction, driven, and braking. It has been established that the appearance of a self-oscillating mode in the zone of interaction of an elastic tire with a solid support base is a useful diagnostic feature providing recognition of the development of the process of losing adhesion of a wheel with a support base when the rear axle skids at early stages.

The dialectics of cyclicity in the development of law.

The dialectic of cyclicity in the system of dual natural and positive law, as the transition from one opposite to another, involution to evolution, quantitative transformations into qualitative and actually regular cyclicity of crises and stability in the legal system is studied. The dialectic of cyclicity in law occurs as constant oscillating processes of transition from one opposite to another, natural law into positive, involution into evolution, quantity into quality, crisis into stability, and development in a circle gradually turns into a spiral. Defining and substantiating the phases and stages of the cycle allows us to demonstrate the development of a particular cycle and the driving mechanisms of this transformation – the laws of dialectics, in particular, the unity and struggle of opposites in law, the transition from quantity to quality, denial of the old and so on. Oscillatory processes are manifested in opposites of phases and stages of cycles, and small cycles of development of law are embedded in large ones, where each cycle is part of a larger cycle, and that in turn is even larger, and so on. The end of one cycle leads to the transformation of the legal system and its manifestation in a new form and content at a new level of the spiral of development. Ways to overcome the crisis in the legal system should be sought, first of all, in the updated methodological principles of cyclicality in jurisprudence based on the ideas of natural law, based on the principles and laws of dialectics, laws of philosophy of law, and in combination with other branches of modern knowledge.

Review of Advanced Implementation of Doppler Backscattering Method in Globus-M

Doppler backscattering (DBS) is a microwave diagnostics method typically used to study the plasma rotation velocity. Apart from conventional techniques, more advanced forms of DBS implementation were suggested on Globus-M. More specifically the study of a variety of oscillating processes was performed using DBS. In this review we present a detailed description of all of the methods and techniques employed in Globus-M alongside results obtained using DBS in all the years up until the shutdown of the tokamak. These include research similar to that done on other devices into the properties of such phenomena like geodesic acoustic modes or limit cycle oscillations, along with innovative works regarding the detection and investigation of Alfven eigenmodes and filaments that were the first of their kind and that provided important and novel results. Apart from that, the specific aspects of DBS application on a spherical tokamak are discussed. An in-depth look into the gradual change and improvement of the DBS diagnostics on Globus-M is also presented in this paper.

Modeling Cell Energy Metabolism as Weighted Networks of Non-autonomous Oscillators

Networks of oscillating processes are a common occurrence in living systems. This is as true as anywhere in the energy metabolism of individual cells. Exchanges of molecules and common regulation operate throughout the metabolic processes of glycolysis and oxidative phosphorylation, making the consideration of each of these as a network a natural step. Oscillations are similarly ubiquitous within these processes, and the frequencies of these oscillations are never truly constant. These features make this system an ideal example with which to discuss an alternative approach to modeling living systems, which focuses on their thermodynamically open, oscillating, non-linear and non-autonomous nature. We implement this approach in developing a model of non-autonomous Kuramoto oscillators in two all-to-all weighted networks coupled to one another, and themselves driven by non-autonomous oscillators. Each component represents a metabolic process, the networks acting as the glycolytic and oxidative phosphorylative processes, and the drivers as glucose and oxygen supply. We analyse the effect of these features on the synchronization dynamics within the model, and present a comparison between this model, experimental data on the glycolysis of HeLa cells, and a comparatively mainstream model of this experiment. In the former, we find that the introduction of oscillator networks significantly increases the proportion of the model's parameter space that features some form of synchronization, indicating a greater ability of the processes to resist external perturbations, a crucial behavior in biological settings. For the latter, we analyse the oscillations of the experiment, finding a characteristic frequency of 0.01–0.02 Hz. We further demonstrate that an output of the model comparable to the measurements of the experiment oscillates in a manner similar to the measured data, achieving this with fewer parameters and greater flexibility than the comparable model.

Experimental Investigation of Plow-Chopping Unit

The article presents research results of a machine-tractor unit that performs two technological operations simultaneously: (i) chopping plant residues (sunflower stubble); (ii) covering the chopped stubble with the soil. The first operation is carried out with a front-mounted plant residues chopper, and the second one is carried out with a rear-mounted plough. The chopper’s working devices are rotated by the tractor’s front power take-off (PTO), which has two operating modes: 540 and 1000 rpm. It was determined that to reduce the dynamic load in the drive of the chopper’s plant residues working devices, to chop these residues qualitatively, and then to cover them with the soil, the tractor’s front PTO should be adjusted to a speed of 1000 rpm. With this mode of the chopper’s working device’s rotation, the difference in its vertical vibrations’ dispersion and the tractor front axle’s oscillations is insignificant. The variance of the plowing depth vibrations (1.44 cm2), changing aperiodically in the frequency range of 0–2.5 Hz, is not accidentally less than the variance of irregularities vibrations of the longitudinal field profile (2.75 cm2). The plough draft resistant oscillations of the plow-chopping unit had the least impaction at the plowing depth oscillations. The proof of this is the small value of the cross correlation function; for such oscillating processes as ‘plough draft resistance—plowing depth’, it was equal to 0.22, which is 3.4 times less than for oscillating processes ‘surface’s longitudinal profile—plowing depth’. The number of chopped particles less than 15 cm in length increased by 1.5 times, and the number of particles longer than 30 cm decreased by 3 times. With the complete incorporation of plant residues into the soil, their non-chopped part did not exceed 1%.

Mathematical Analysis of Some Reaction Networks Inducing Biological Growth/Decay Functions.

In this work, we study some characteristics of sigmoidal growth/decay functions that are solutions of dynamical systems. In addition, the studied dynamical systems have a realization in terms of reaction networks that are closely related to the Gompertzian and logistic type growth models. Apart from the growing species, the studied reaction networks involve an additional species interpreted as an environmental resource. The reaction network formulation of the proposed models hints for the intrinsic mechanism of the modeled growth process and can be used for analyzing evolutionary measured data when testing various appropriate models, especially when studying growth processes in life sciences. The proposed reaction network realization of Gompertz growth model can be interpreted from the perspective of demographic and socio-economic sciences. The reaction network approach clearly explains the intimate links between the Gompertz model and the Verhulst logistic model. There are shown reversible reactions which complete the already known non-reversible ones. It is also demonstrated that the proposed approach can be applied in oscillating processes and social-science events. The paper is richly illustrated with numerical computations and computer simulations performed by algorithms using the computer algebra system Mathematica.

Suppression of the instrumental disturbance effect by locally invariant scaling of the physical model of spacecraft angular stabilization

The study introduces a method of ground conditions physical modeling of the spacecraft motion around a fixed axis. On a natural scale of parameters and variables, the dynamic modes under consideration can be implemented only with an extremely small amount of kinetic energy dissipation. The feasible minimum friction for a test bed of simple design significantly exceeds the required values. In current modes of economical limit cycles, the characteristics of the simulated process are distorted so much that the physical modeling test bed is unsuitable for practical use. The solution to this problem is usually sought by complicating the design of the test bed through the use of air or magnetic suspension. The paper proposes an innovative method of “invariant scaling”, based on the principle of dynamic similarity of self-oscillating processes. Its application makes it possible to drastically reduce the effect of friction on the characteristics of physically modeled modes during ground developmental testing of control algorithms. Computer modeling with the use of this method has confirmed its high efficiency. It has been shown analytically and numerically that the modeling accuracy can be radically improved. An example of reducing the modeling error by 200 times is given.

ПРОГНОЗУВАННЯ ТРАЄКТОРІЇ НАЦІОНАЛЬНОГО ЕКОНОМІЧНОГО РОЗВИТКУ МЕТОДАМИ ГАРМОНІЙНОГО І СПЕКТРАЛЬНОГО АНАЛІЗУ

Improving of the methodological tools for the national economies behavior’s forecasting in the context of increasing the validity and analytical characteristics of state economic strategies in conditions of high volatility, lack of trend stability and non-stationary dynamics of external and internal socio-economic processes by implementing interdisciplinary methods of Fourier analysis and their adaptation to the specifics of the socio-economic systems’ functioning and development. Methodology. The forecasting’s targeting as an important independent stage in the process of analytical assessment of the balance of development is performed on the basis of structuring, division into stages, systematization, and grouping. Justification of the interdisciplinary approach for forecasting of national economic system’s development is carried out by methods of analysis and synthesis, comparison and practical testing. Establishment of the economic dynamics’ structural regularities and forecasting of a trajectory of national economy development are executed by harmonic and spectral analysis of the dynamic systems’ fluctuating processes. The results. The paper’s attention is focused on the specific features of macroeconomic dynamics’ time series as a basis for the forecasting of national economies development, namely their short duration, non-stationary, aperiodic, polyharmonic and their impact on the formation of adequate methodological support for forecasting. The possibility and efficiency of spectral and harmonic methods using for analysis oscillating processes of national economic system’s development are substantiated. A harmonic model of Ukraine's economic development’s trajectory during 1991-2020 is formed, which allowed to analyze the fluctuating component of the macroeconomic indicators’ dynamics on the basis of actual data that included all the initial information contained in the time series. By distinguishing economic cycles, their amplitude-frequency characteristics, the current phase of Ukrainian economy’s development is characterized. On the basis of the economic dynamics’ model, being used the indicator of annual GDP growth, forecasting is executed and short-term, average-term and long-term tendencies Ukraine’s economy’s development are established. Scientific novelty. The extending of theoretical and methodological tools for forecasting of main trends in national economies, based on harmonic and spectral analysis, is allowed to form a structural approach to the analysis of economic dynamics in the context of selection of its decisive harmonics and basing on their characteristics to make conclusions about the current level and projected national economic systems’ development. Practical significance. The adapted and regulated procedure of harmonic and spectral analysis of socio-economic systems’ oscillating processes became the basis for forecasting the level, rates and proportions of national economic systems development.

Quantum-Relativistic Effects at the Nanolevel: Analysis of the Mean Square Deviation of Position with a new Analytical Model

In this paper I present new results about the quantum-relativistic form of the mean squaredeviation of position related to a recently appeared Drude-Lorentz-like model alreadyperformed in classical and quantum way, named DS model. The model gives preciseinformations about the distance traveled by a carrier (electrons, ions, etc.) inside ananostructure in the hypothesis of quantum effects and relativistic velocity. It has a widescale range of applicability; I consider the nanoscale in this paper, but the model holdsfrom sub-pico-level to macro-level because of the presence of a gauge factor, making itapplicable to all oscillating processes in Nature. Examples of application and suggestions complete the paper.