scholarly journals Modeling of the criterion for predicting the loss of stability of discrete systems

2021 ◽  
Vol 9 (4) ◽  
pp. 96-100
Author(s):  
Vladimir Kulikov ◽  
Viktor Evstratov
Keyword(s):  
Life Cycle ◽  
Discrete System ◽  
Discrete Systems ◽  
Loss Of Stability ◽  
External Influences ◽  
Future State ◽  
Operation Process ◽  
Internal Properties ◽  
The Stability ◽  
External Forces

The paper proposes a method for determining the estimated parameter of the stability state of discrete systems exposed to external influences. As a rule, the loss of stability of the first and second kind leads to a problematic operation process throughout the life cycle, or even the destruction of the system. Hence the requirements of a certain rigidity to the designed and operated systems in order to ensure their geometric immutability. At the same time, in practice, there are no naturally deformable systems from external influences. The paper sets and solves the problem of determining the stability parameter, with the help of which, even before the stage of loss of stability, it is possible to predict the future state of a discrete system, i.e. to predict whether it (the system) has sufficient internal properties to return to a stable position at any exit from the preliminary state of equilibrium due to the influence of external forces.

scholarly journals ALGORITHM AND SOFTWARE FOR CALCULATING THE STABILITY OF THE FORM OF EQUILIBRIUM OF DISCRETE SYSTEMS

2019 ◽  
Vol 13 (3) ◽  
pp. 44-49
Author(s):  
A.A. SHKURUPIY ◽  
A.N. PASCHENKO ◽  
P.B. MYTROFANOV
Keyword(s):  
Discrete Systems ◽  
Stability Loss ◽  
Transcendental Equation ◽  
Loss Of Stability ◽  
Displacement Method ◽  
Software Complex ◽  
Complex Functions ◽  
Transcendental Functions ◽  
The Stability ◽  
Theoretical Mechanics

The paper presents an algorithm for calculating the stability of the form of equilibrium of the first kind of compressed discrete systems by the method of displacements in combination with themethods of iterations and bisection. The use of the displacement method in combination with the iteration and bisection methods makes it possible to effectively determine the minimum critical stress or strain at the first bifurcation and their corresponding form of loss of stability, both for statically determined and statically undetectable systems. This approach, using matrixforms, makes it possible to significantly simplify the calculations of the analytical condition for the loss of stability of compressed discrete systems (the stability loss equation), which has high orders, as well as to construct the form of loss of stability corresponding to a critical load, that is, to solve the problem of loss of stability of equilibrium. The calculation of the compressed discrete system on the stability of the form of equilibrium actually reduces to the solution of the difficultly described nonlinear transcendental equation, which is the equation of loss of stability. The difficulty lies in the absence of an analytical solution of such an equation due to the presence of complex functions of Zhukovsky, which have transcendental functions in their structure. Such solution can be performed only with the use of numerical methods. This algorithm for calculating the loss of equilibrium of the first kind of compressed discrete systems by displacement in combination with the methods of iteration and bisection is implemented in the software complex "Persist" for a PC in Windows OS. The program was approbated and implemented in theeducational process at the Department of Structural and Theoretical Mechanics of the Poltava National Technical Yuri Kondratyuk University during the training of specialists in engineering specialties.

Central Asia: International Relations As A Factor Of Regional Stability And Integration

2020 ◽  
Vol 02 (10) ◽  
pp. 135-140
Author(s):  
B.O. Berdiyev ◽  
Keyword(s):  
International Relations ◽  
Central Asia ◽  
Interethnic Relations ◽  
Regional Stability ◽  
External Influences ◽  
The Stability

The article is devoted to the issues of interethnic relations in Central Asia, the need for integration and cooperation between states, external influences, information impacts on the peoples of the region, border issues, overpopulation, ethnic issues and their impact on the stability of the region.

scholarly journals Stability of Nonlinear Autonomous Quadratic Discrete Systems in the Critical Case

2010 ◽  
Vol 2010 ◽  
pp. 1-23 ◽  
Author(s):  
Josef Diblík ◽  
Denys Ya. Khusainov ◽  
Irina V. Grytsay ◽  
Zdenĕk Šmarda
Keyword(s):  
Lyapunov Functions ◽  
Critical Case ◽  
Autonomous Systems ◽  
Discrete Systems ◽  
Simple Eigenvalue ◽  
Discrete Equations ◽  
The Matrix ◽  
The Stability ◽  
Important Characterization

Many processes are mathematically simulated by systems of discrete equations with quadratic right-hand sides. Their stability is thought of as a very important characterization of the process. In this paper, the method of Lyapunov functions is used to derive classes of stable quadratic discrete autonomous systems in a critical case in the presence of a simple eigenvalueλ=1of the matrix of linear terms. In addition to the stability investigation, we also estimate stability domains.

Nonstationary Response of a Two-Degrees-of-Freedom Nonlinear Ship Model Under Modulated Excitation

1995 ◽  
Author(s):  
Ruigui Pan ◽  
Huw G. Davies
Keyword(s):  
Degrees Of Freedom ◽  
Stability Boundary ◽  
Period Doubling ◽  
Approximate Solutions ◽  
Loss Of Stability ◽  
Two Degrees Of Freedom ◽  
Ship Model ◽  
Nonstationary Response ◽  
Period 2 ◽  
The Stability

Abstract Nonstationary response of a two-degrees-of-freedom system with quadratic coupling under a time varying modulated amplitude sinusoidal excitation is studied. The nonlinearly coupled pitch and roll ship model is based on Nayfeh, Mook and Marshall’s work for the case of stationary excitation. The ship model has a 2:1 internal resonance and is excited near the resonance of the pitch mode. The modulated excitation (F0 + F1 cos ωt) cosQt is used to model a narrow band sea-wave excitation. The response demonstrates a variety of bifurcations, loss of stability, and chaos phenomena that are not present in the stationary case. We consider here the periodically modulated response. Chaotic response of the system is discussed in a separate paper. Several approximate solutions, under both small and large modulating amplitudes F1, are obtained and compared with the exact one. The stability of an exact solution with one mode having zero amplitude is studied. Loss of stability in this case involves either a rapid transition from one of two stable (in the stationary sense) branches to another, or a period doubling bifurcation. From Floquet theory, various stability boundary diagrams are obtained in F1 and F0 parameter space which can be used to predict the various transition phenomena and the period-2 bifurcations. The study shows that both the modulation parameters F1 and ω (the modulating frequency) have great effect on the stability boundaries. Because of the modulation, the stable area is greatly expanded, and the stationary bifurcation point can be exceeded without loss of stability. Decreasing ω can make the stability boundary very complicated. For very small ω the response can make periodic transitions between the two (pseudo) stable solutions.

scholarly journals Telomeric G-Quadruplexes: From Human to Tetrahymena Repeats

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Erika Demkovičová ◽  
Ľuboš Bauer ◽  
Petra Krafčíková ◽  
Katarína Tlučková ◽  
Petra Tóthova ◽  
...  
Keyword(s):  
Life Cycle ◽  
Base Substitution ◽  
Telomeric Dna ◽  
Purine Base ◽  
Telomeric Sequences ◽  
G Quadruplex ◽  
The Stability ◽  
Scientific Value ◽  
The Relationship ◽  
Adenine Base

The human telomeric and protozoal telomeric sequences differ only in one purine base in their repeats; TTAGGG in telomeric sequences; and TTGGGG in protozoal sequences. In this study, the relationship between G-quadruplexes formed from these repeats and their derivatives is analyzed and compared. The human telomeric DNA sequence G3(T2AG3)3 and related sequences in which each adenine base has been systematically replaced by a guanine were investigated; the result is Tetrahymena repeats. The substitution does not affect the formation of G-quadruplexes but may cause differences in topology. The results also show that the stability of the substituted derivatives increased in sequences with greater number of substitutions. In addition, most of the sequences containing imperfections in repeats which were analyzed in this study also occur in human and Tetrahymena genomes. Generally, the presence of G-quadruplex structures in any organism is a source of limitations during the life cycle. Therefore, a fuller understanding of the influence of base substitution on the structural variability of G-quadruplexes would be of considerable scientific value.

scholarly journals Personality Traits Across the Life Cycle: Disentangling Age, Period, and Cohort Effects

2021 ◽  
Author(s):  
Bernd Fitzenberger ◽  
Gary Mena ◽  
Jan Nimczik ◽  
Uwe Sunde
Keyword(s):  
Life Cycle ◽  
Personality Traits ◽  
Economic Outcomes ◽  
Cohort Effects ◽  
Specification Tests ◽  
Age Patterns ◽  
Age Profile ◽  
Time Periods ◽  
The Stability

Abstract Economists increasingly recognise the importance of personality traits for socio-economic outcomes, but little is known about the stability of these traits over the life cycle. Existing empirical contributions typically focus on age patterns and disregard cohort and period influences. This paper contributes novel evidence for the separability of age, period, and cohort effects for a broad range of personality traits based on systematic specification tests for disentangling age, period and cohort influences. Our estimates document that for different cohorts, the evolution of personality traits across the life cycle follows a stable, though non-constant, age profile, while there are sizeable differences across time periods.

Added Fluid Mass and the Equations of Motion of a Parachute

1983 ◽  
Vol 34 (3) ◽  
pp. 226-242 ◽  
Author(s):  
John A. Eaton
Keyword(s):  
Equations Of Motion ◽  
Added Mass ◽  
Unsteady Forces ◽  
Fluid Mass ◽  
Mass Tensor ◽  
Body Shapes ◽  
The Stability ◽  
External Forces ◽  
Six Degree Of Freedom ◽  
Nonlinear Solutions

SummaryWhile it has long been known that added fluid mass may be important in the dynamics of parachutes, due to inadequate or incorrect derivation and/or implementation of the added mass tensor its full significance in the stability of parachutes has yet to be appreciated. The concept of added mass is outlined and some general conditions for its significance are presented. Its implementation in the parachute equations of motion is reviewed, and the equations used in previous treatments are shown to be erroneous. A general method for finding the equivalent external forces and moments due to added mass is given, and the correct, anisotropic forms of the added mass tensor are derived for the six degree-of-freedom motion in an ideal fluid of rigid body shapes with planar-, twofold- and axisymmetry, These derivations may also be useful in dynamic stability studies of other low relative density bodies such as airships, balloons, submarines and torpedoes. Full nonlinear solutions of the equations of motion for the axisymmetric parachute have been obtained, and results indicate that added mass effects are more significant than previously predicted. In particular, the component of added mass along the axis of symmetry has a strong influence on stability. Better data on unsteady forces and moments on parachutes are needed.

Assembling Industrial Ecosystems for a Knowledge City

2012 ◽  
Vol 4 (3) ◽  
pp. 38-51 ◽  
Author(s):  
Carlos Scheel ◽  
Nathalíe Galeano
Keyword(s):  
Life Cycle ◽  
Well Being ◽  
Sustainable Construction ◽  
Wealth Creation ◽  
Developing Regions ◽  
Knowledge Based ◽  
Knowledge Based Economy ◽  
Synergistic Approach ◽  
External Forces ◽  
Industrial Life Cycle

Economic forces and industrialization are determinant factors in wealth creation; however, an important part of the equation has been omitted by most of the industrial and social players, especially in developing countries. The business cycle’s impact on the environment, on the life cycle assessment, and on the biocapacity of the earth has had a tremendous effect on the equilibrium of all the sub-systems (economic, social, and environmental resources). Based on these systemic requirements, a synergistic approach involving all the stakeholders has been collated and a systemic framework, the Sustainable WIT Model has been developed, and is designed to build “sustainable clusters of high value, globally competitive industries” for developing regions. This paper discusses how the Sustainable WIT Model has been applied to one of the most important industries currently having an impact on economic, social, and environmental ecosystems worldwide - the sustainable construction industry - in a region where it is creating suitable conditions for a city to become part of a knowledge-based economy. The SWIT Model considers the economic growth of the industrial life cycle as a priority, but also includes other external forces that have previously been ignored, such as societal impact, human well-being, and bio capacity, in such a way that the sustainability cycle can be economically viable.

scholarly journals Dynamics of a Discretization Physiological Control System

2007 ◽  
Vol 2007 ◽  
pp. 1-16 ◽  
Author(s):  
Xiaohua Ding ◽  
Huan Su
Keyword(s):  
Control System ◽  
Discrete System ◽  
Numerical Results ◽  
Positive Equilibrium ◽  
Hopf Bifurcations ◽  
Physiological Control ◽  
Midpoint Rule ◽  
The Stability ◽  
Stability Of The Solution

We study the dynamics of solutions of discrete physiological control system obtained by Midpoint rule. It is shown that a sequence of Hopf bifurcations occurs at the positive equilibrium as the delay increases and we analyze the stability of the solution of the discrete system and calculate the direction of the Hopf bifurcations. The numerical results are presented.

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