scholarly journals Амплитудно-частотные и фазово-частотные характеристики вынужденных колебаний нелинейного дробного осциллятора

2019 ◽  
Vol 45 (13) ◽  
pp. 25
Author(s):  
Р.И. Паровик
Keyword(s):  
Computer Simulation ◽  
Quality Factor ◽  
Fractional Derivatives ◽  
Model Equation ◽  
Oscillatory System ◽  
Forced Oscillations ◽  
Control Parameters ◽  
System A ◽  
Fractional Oscillator

In the work, using the amplitude-frequency (AFC) and phase-frequency characteristics (PFC) of forced oscillations of a non-linear fractional oscillator, their connection with the orders of fractional derivatives, which are included in its model equation, is substantiated. It is shown, using computer simulation, that the orders of fractional derivatives are related to the quality factor of an oscillatory system. A decrease in the higher order (“fractional” inertia) leads to a decrease in the quality factor, and a decrease in the lower order (“fractional” friction) leads to an increase in the quality factor. Therefore, we come to two mechanisms for controlling the Q of the oscillatory system, where the orders of fractional derivatives play the role of control parameters.

scholarly journals Frequency characteristics of the fractional oscillator Van der Pol

2019 ◽  
Vol 127 ◽  
pp. 02010
Author(s):  
Roman Parovik
Keyword(s):  
Quality Factor ◽  
Harmonic Balance ◽  
Fractional Derivatives ◽  
Harmonic Balance Method ◽  
Oscillatory System ◽  
Frequency Characteristics ◽  
Van Der Pol ◽  
Fractional Oscillator ◽  
Analytical Formulas ◽  
Frequency Phase

Into this paper, the amplitude-frequency and phase-frequency characteristics of the Van der Polar fractional oscillator are studied in order to establish their relationship with the orders of fractional derivatives included in the model equation. Using the harmonic balance method, analytical formulas were obtained for the amplitude-frequency, phase-frequency characteristics, as well as the quality factor – the energy characteristic of the oscillatory system. It was shown that the quality factor depends on the orders of fractional derivatives, and change in their values can lead to both an increase and a decrease in the quality factor.

scholarly journals Анализ добротности вынужденных колебаний дробного линейного осциллятора

2020 ◽  
Vol 90 (7) ◽  
pp. 1059
Author(s):  
Р.И. Паровик
Keyword(s):  
Quality Factor ◽  
Frequency Characteristic ◽  
Fractional Derivatives ◽  
Harmonic Balance Method ◽  
Forced Oscillations ◽  
Oscillatory Process ◽  
Fractional Oscillator ◽  
Analytical Formulas ◽  
Derivatives Of ◽  
Fractional Orders

Using the harmonic balance method, analytical formulas are obtained for calculating the amplitude-frequency and phase-frequency characteristics, as well as the quality factor of the forced oscillations of a linear fractional oscillator. It was established that the characteristics under study depend on the dissipative properties of the medium - memory effects, which are described by derivatives of fractional orders. It is shown that fractional orders affect the attenuation of the oscillatory process and are associated with its quality factor. The calculated curves of the characteristics of the forced oscillations of a linear linear fractional oscillator showed that fractional orders can be considered as control parameters of the oscillatory process in a dissipative medium. Key words: quality factor, amplitude-frequency characteristic, phase-frequency characteristic, fractional derivatives, memory.

scholarly journals Mathematical Modeling of Linear Fractional Oscillators

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1879 ◽  
Author(s):  
Roman Parovik
Keyword(s):  
Cauchy Problem ◽  
Fractional Derivatives ◽  
Model Equation ◽  
Initial Conditions ◽  
Memory Function ◽  
Analytical Formula ◽  
Forced Oscillations ◽  
Caputo Fractional Derivatives ◽  
Specific Test ◽  
The Cauchy Problem

In this work, based on Newton’s second law, taking into account heredity, an equation is derived for a linear hereditary oscillator (LHO). Then, by choosing a power-law memory function, the transition to a model equation with Gerasimov–Caputo fractional derivatives is carried out. For the resulting model equation, local initial conditions are set (the Cauchy problem). Numerical methods for solving the Cauchy problem using an explicit non-local finite-difference scheme (ENFDS) and the Adams–Bashforth–Moulton (ABM) method are considered. An analysis of the errors of the methods is carried out on specific test examples. It is shown that the ABM method is more accurate and converges faster to an exact solution than the ENFDS method. Forced oscillations of linear fractional oscillators (LFO) are investigated. Using the ABM method, the amplitude–frequency characteristics (AFC) were constructed, which were compared with the AFC obtained by the analytical formula. The Q-factor of the LFO is investigated. It is shown that the orders of fractional derivatives are responsible for the intensity of energy dissipation in fractional vibrational systems. Specific mathematical models of LFOs are considered: a fractional analogue of the harmonic oscillator, fractional oscillators of Mathieu and Airy. Oscillograms and phase trajectories were constructed using the ABM method for various values of the parameters included in the model equation. The interpretation of the simulation results is carried out.

scholarly journals STUDY OF THE SINGULAR POINTS OF THE FRACTIONAL OSCILLATOR VAN DER POL-DUFFING

2019 ◽  
pp. 47-54
Author(s):  
Е.Р. Новикова
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Oscillatory System ◽  
Memory Effects ◽  
Oscillatory Process ◽  
Van Der Pol ◽  
Phase Trajectories ◽  
Fractional Oscillator

В работе проводится исследование на асимптотическую устойчивость точек покоя дробного осциллятора Ван дер ПоляДуффинга. Дробный осциллятор Ван дер Поля Дуффинга представляет собой колебательную систему двух дифференциальных уравнений с производными дробных порядков в смысле ГерасимоваКапуто. Порядки дробных производных характеризуют свойства среды (эффекты памяти), в которой происходит колебательный процесс и могут быть одинаковыми (соизмеримыми) или разными (несоизмеримыми). С помощью теорем для соизмеримой и несоизмеримой систем на конкретных примерах исследуется асимптотическая устойчивость точек покоя дробного осциллятора Ван дер ПоляДуффинга. Результаты исследований были подтверждены с помощью построения соответствующих осциллограмм и фазовых траекторий A study is conducted on the asymptotic stability of the rest points of the fractional oscillator Van der PolDuffing. The fractional van der PolDuffing oscillator is an oscillatory system of two differential equations with fractional order derivatives in the sense of GerasimovCaputo. The orders of fractional derivatives characterize the properties of the medium (memory effects) in which the oscillatory process takes place and can be the same (commensurate) or different (incommensurable). Using theorems for commensurable and incommensurable systems, the asymptotic stability of the rest points of the fractional van der PolDuffing oscillator is investigated with concrete examples. The results of the studies were confirmed by constructing the appropriate waveforms and phase trajectories.

scholarly journals Mathematical Model of Fractional Duffing Oscillator with Variable Memory

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2063
Author(s):  
Valentine Kim ◽  
Roman Parovik
Keyword(s):  
Mathematical Model ◽  
Fractional Derivative ◽  
Quality Factor ◽  
Numerical Scheme ◽  
Duffing Oscillator ◽  
Harmonic Balance Method ◽  
Forced Oscillations ◽  
Model Parameters ◽  
Liouville Type ◽  
Fractional Oscillator

The article investigates a mathematical model of the Duffing oscillator with a variable fractional order derivative of the Riemann–Liouville type. The study of the model is carried out using a numerical scheme based on the approximation of the fractional derivative of the Riemann–Liouville type by a discrete analog—the fractional derivative of Grunwald–Letnikov. The adequacy of the numerical scheme is verified using specific examples. Using a numerical algorithm, oscillograms and phase trajectories are constructed depending on the values of the model parameters. Chaotic regimes of the Duffing fractional oscillator are investigated using the Wolf–Bennetin algorithm. The forced oscillations of the Duffing fractional oscillator are investigated using the harmonic balance method. Analytical formulas for the amplitude-frequency, phase-frequency characteristics, and also the quality factor are obtained. It is shown that the fractional Duffing oscillator possesses different modes: regular, chaotic, multi-periodic. The relationship between the order of the fractional derivative and the quality factor of the oscillatory system is established.

The SORS Decision-Making Support System: A statistical tool for better policy making in the Republic of Serbia

2021 ◽  
pp. 1-11
Author(s):  
Miladin Kovačević ◽  
Katarina Stančić
Keyword(s):  
Policy Making ◽  
Modern Society ◽  
Monitoring And Evaluation ◽  
Public Debate ◽  
Statistical Tool ◽  
The Public ◽  
System A ◽  
The Republic ◽  
Trusted Data

Modern society is witnessing a data revolution which necessarily entails changes to the overall behavior of citizens, governments and companies. This is a big challenge and an opportunity for National Statistics Offices (NSOs). Especially after the outbreak of COVID-19, when the public debate about the number of mortalities and tested and infected persons escalated, trusted data is required more than ever. Which data can modern society trust? Are modern societies being subjected to opinion rather than fact? This paper introduces a new statistical tool to facilitate policy-making based on trusted statistics. Using economic indicators to illustrate implementation, the new statistical tool is shown to be a flexible instrument for analysis, monitoring and evaluation of the economic situation in the Republic of Serbia. By taking a role in public policy management, the tool can be used to transform the NSO’s role in the statistical system into an active participant in public debate in contrast to the previous traditional, usually passive role of collecting, processing and publishing data. The tool supports the integration of statistics into public policies and connects the knowledge and expertise of official statisticians on one side with political decision makers on the other.

scholarly journals Prenatal and Perinatal Environmental Influences Shaping the Neonatal Immune System: A Focus on Asthma and Allergy Origins

2021 ◽  
Vol 18 (8) ◽  
pp. 3962
Author(s):  
Azahara María García-Serna ◽  
Elena Martín-Orozco ◽  
Trinidad Hernández-Caselles ◽  
Eva Morales
Keyword(s):  
Immune System ◽  
Immune Cell ◽  
Mode Of Delivery ◽  
Environmental Influences ◽  
Pet Ownership ◽  
System A ◽  
Neonatal Immune System ◽  
Chemical Factors ◽  
Asthma And Allergy

It is suggested that programming of the immune system starts before birth and is shaped by environmental influences acting during critical windows of susceptibility for human development. Prenatal and perinatal exposure to physiological, biological, physical, or chemical factors can trigger permanent, irreversible changes to the developing immune system, which may be reflected in cord blood of neonates. The aim of this narrative review is to summarize the evidence on the role of the prenatal and perinatal environment, including season of birth, mode of delivery, exposure to common allergens, a farming environment, pet ownership, and exposure to tobacco smoking and pollutants, in shaping the immune cell populations and cytokines at birth in humans. We also discuss how reported disruptions in the immune system at birth might contribute to the development of asthma and related allergic manifestations later in life.

scholarly journals The Relevance of the SH2 Domain for c-Src Functionality in Triple-Negative Breast Cancer Cells

Cancers ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 462
Author(s):  
Víctor Mayoral-Varo ◽  
María Pilar Sánchez-Bailón ◽  
Annarica Calcabrini ◽  
Marta García-Hernández ◽  
Valerio Frezza ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Triple Negative Breast Cancer ◽  
Triple Negative ◽  
Sh2 Domain ◽  
Model Systems ◽  
System A ◽  
Promising Therapeutic Target ◽  
Relevant Role ◽  
Inactivating Mutation

The role of Src family kinases (SFKs) in human tumors has been always associated with tyrosine kinase activity and much less attention has been given to the SH2 and SH3 adapter domains. Here, we studied the role of the c-Src-SH2 domain in triple-negative breast cancer (TNBC). To this end, SUM159PT and MDA-MB-231 human cell lines were employed as model systems. These cells conditionally expressed, under tetracycline control (Tet-On system), a c-Src variant with point-inactivating mutation of the SH2 adapter domain (R175L). The expression of this mutant reduced the self-renewal capability of the enriched population of breast cancer stem cells (BCSCs), demonstrating the importance of the SH2 adapter domain of c-Src in the mammary gland carcinogenesis. In addition, the analysis of anchorage-independent growth, proliferation, migration, and invasiveness, all processes associated with tumorigenesis, showed that the SH2 domain of c-Src plays a very relevant role in their regulation. Furthermore, the transfection of two different aptamers directed to SH2-c-Src in both SUM159PT and MDA-MB-231 cells induced inhibition of their proliferation, migration, and invasiveness, strengthening the hypothesis that this domain is highly involved in TNBC tumorigenesis. Therefore, the SH2 domain of c-Src could be a promising therapeutic target and combined treatments with inhibitors of c-Src kinase enzymatic activity may represent a new therapeutic strategy for patients with TNBC, whose prognosis is currently very negative.

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