scholarly journals On maintaining the stability of the equilibrium of nonlinear oscillators under conservative perturbations

2021 ◽  
Vol 23 (3) ◽  
pp. 285-294
Author(s):  
Alexander A. Kosov
Keyword(s):  
Equilibrium Position ◽  
Arbitrary Number ◽  
Nonlinear Oscillators ◽  
General Situation ◽  
Unperturbed System ◽  
Hamiltonian Form ◽  
Homogeneous Potential ◽  
Stability And Instability ◽  
The Stability

Abstract. The problem of Yu.N. Bibikov on maintaining the stability of the equilibrium position of two interconnected nonlinear oscillators under the action of small, in a certain sense, conservative perturbing forces is considered. With different methods of reducing the system to the Hamiltonian form, some features are revealed for the case when the perturbing forces of the interaction of two oscillators are potential. The conditions for preserving the stability and instability of the equilibrium of two oscillators for the case of sufficiently small disturbing forces are obtained. The problem of maintaining the stability of the equilibrium under conservative perturbations is also considered in the more general situation of an arbitrary number of oscillators with power potentials with rational exponents, which leads to the case of a generalized homogeneous potential of an unperturbed system. The example given shows the applicability of the proposed approach in the case when the order of smallness of the perturbing forces coincides with the order of smallness of the unperturbed Hamiltonian.

The identity policy and its effect in the stability of Middle East after 2010

2019 ◽  
pp. 434
Author(s):  
Ali Hussein Kadhim Alesammi
Keyword(s):  
Middle East ◽  
International Relations ◽  
Social Construct ◽  
Stability And Instability ◽  
The Social ◽  
The Stability ◽  
International Interactions ◽  
Regional Interests ◽  
Political Groups ◽  
Identity Policy

Since 2010 Middle East have many events or what they call "Arab spring events" which it result of overthrow governments and the rise of new political groups, all of this elements was resulting of many international and regional activities and making new regional and international axles, as well as the intersections of the different regional interests, therefore this research will try to study the stability and instability in the region as an independent variable not according to the neorealism or neoliberalism theories, but according to the constructivism theory which it base their assumptions on:  "In the international relations the non-physical structures of international interactions are determined by the identities of the players, which in turn determine the interests that determine the behavior of international players." So the research questions are: 1-What is the identity policy and haw affect in international relations? 2-How the social construct affect in international relations? 3-How the elite's identities for the main actors in the Middle East affect in the regional axles?  

Stability and instability of some nonlinear dispersive solitary waves in higher dimension

1996 ◽  
Vol 126 (1) ◽  
pp. 89-112 ◽  
Author(s):  
Anne de Bouard
Keyword(s):  
Solitary Waves ◽  
Acoustic Waves ◽  
Vries Equation ◽  
Three Dimensional ◽  
Higher Dimension ◽  
Ion Acoustic Waves ◽  
Stability And Instability ◽  
Ion Acoustic ◽  
De Vries ◽  
The Stability

We study the stability of positive radially symmetric solitary waves for a three dimensional generalisation of the Korteweg de Vries equation, which describes nonlinear ion-acoustic waves in a magnetised plasma, and for a generalisation in dimension two of the Benjamin–Bona–Mahony equation.

scholarly journals Stability and Instability in the Lysogenic State of Phage Lambda

2010 ◽  
Vol 192 (22) ◽  
pp. 6064-6076 ◽  
Author(s):  
John W. Little ◽  
Christine B. Michalowski
Keyword(s):  
Intrinsic Rate ◽  
Growth Conditions ◽  
Emergent Properties ◽  
Regulatory Circuits ◽  
Stability And Instability ◽  
Natural Range ◽  
Analysis Of Stability ◽  
Stable Association ◽  
The Stability ◽  
Gene Regulatory Circuits

ABSTRACT Complex gene regulatory circuits exhibit emergent properties that are difficult to predict from the behavior of the components. One such property is the stability of regulatory states. Here we analyze the stability of the lysogenic state of phage λ. In this state, the virus maintains a stable association with the host, and the lytic functions of the virus are repressed by the viral CI repressor. This state readily switches to the lytic pathway when the host SOS system is induced. A low level of SOS-dependent switching occurs without an overt stimulus. We found that the intrinsic rate of switching to the lytic pathway, measured in a host lacking the SOS response, was almost undetectably low, probably less than 10−8/generation. We surmise that this low rate has not been selected directly during evolution but results from optimizing the rate of switching in a wild-type host over the natural range of SOS-inducing conditions. We also analyzed a mutant, λprm240, in which the promoter controlling CI expression was weakened, rendering lysogens unstable. Strikingly, the intrinsic stability of λprm240 lysogens depended markedly on the growth conditions; lysogens grown in minimal medium were nearly stable but switched at high rates when grown in rich medium. These effects on stability likely reflect corresponding effects on the strength of the prm240 promoter, measured in an uncoupled assay system. Several derivatives of λprm240 with altered stabilities were characterized. This mutant and its derivatives afford a model system for further analysis of stability.

Double-diffusive instabilities in a vertical slot

1999 ◽  
Vol 392 ◽  
pp. 213-232 ◽  
Author(s):  
OLIVER S. KERR ◽  
KIT YEE TANG
Keyword(s):  
Temperature Difference ◽  
Salinity Gradient ◽  
Stability Boundary ◽  
Large Temperature ◽  
Vertical Slot ◽  
Stability And Instability ◽  
Heat Diffusivity ◽  
Prandtl Numbers ◽  
The Stability ◽  
Double Diffusive

A fluid stably stratified by a salinity gradient and enclosed between two vertical boundaries can become unstable when it is subjected to a temperature difference between the walls. The linear stability of such a fluid in a vertical slot is investigated. Errors in earlier results are found, confirming recent results of Young & Rosner (1998). Four different asymptotic regimes on the stability boundary are identified. One of these, the limit of a strong salinity gradient, has previously been analysed. The analyses of the separate asymptotic limits of weak salinity gradient, large temperature difference and small wavenumber are also given. These four cases make up much of the total boundary between stability and instability for double-diffusive instabilities in a vertical slot, and so most of this boundary can be mapped out for general Prandtl numbers and salt/heat diffusivity ratios using these results.

scholarly journals STABILITY AND INSTABILITY OF AN OUTDOOR ILLUMINATION INSTALLATION

2004 ◽  
Vol 12 (4) ◽  
pp. 115-119
Author(s):  
Klaus-Dieter Fröhner ◽  
Ze Li
Keyword(s):  
Human Performance ◽  
Night Shift ◽  
Lighting Design ◽  
Work Efficiency ◽  
Safety And Health ◽  
Stability And Instability ◽  
Visual Tasks ◽  
And Performance ◽  
The Stability

Stability and instability are very important for the layout of real world processes concerning safety and health esp. when planned by scientists. The long‐term investigation of stability was carried out for the last ten years on the basis of the installation and the evaluation of an ergonomically designed outdoor illumination. In the depicted dynamic situation the lighting design influences directly visual discomfort and human performance and in the end stability and instability. The improvement of the adaptation of luminance and its influence on the visual tasks after the rearrangement are presented and discussed. The effective factors on the visual capability and performance of workers, work efficiency and potential accidents in the night shift, and furthermore the accelerators and barriers for the stability of the project are analysed and discussed.

scholarly journals Stability of Soliton Solutions For A PT- Symmetric NLDC Considering High-Order Dispersion and Nonlinear Effects Simultaneously

2021 ◽  
Author(s):  
Lida Safaei ◽  
Mohsen Hatami ◽  
Mahmood Borhani Zarandi
Keyword(s):  
Communication Systems ◽  
Exact Analytical Solution ◽  
Nonlinear Effects ◽  
High Order ◽  
Order Effects ◽  
Coupled Equations ◽  
Solitary Solutions ◽  
Stability And Instability ◽  
The Stability ◽  
Order Dispersion

Abstract In this paper, we analytically solve the coupled equations of a PT -Symmetric NLDC by considering high-order dispersion and nonlinear effects (Raman Scattering and self-steeping) simultaneously in normal dispersion regime. To the best of knowledge no works has been done in previous studies to decoupled these equations and obtain an exact analytical solution. The new exact bright solitary solutions are derived. In addition, to study the stability and instability of these propagated solitons in a PT -Symmetric NLDC, perturbation theory is used. Numerical methods are applied to find perturbed eigenvalues and eigenfunctions. The Stability of obtained four perturbed eigenvalues and perturbed eigenfunctions for a PT -Symmetric NLDC equations regard to high-order effects are examined. Using these results and simulating the propagation of perturbed temporal bright solitons through PT -Symmetric NLDC show that perturbed solitons are mostly stable. This means that high-order dispersion and nonlinear effects canceled each other and do not affected the propagated solitons. Furthermore, the evolution of perturbed solitons energies match well the previous results and con rmed the stability of these solitons in a PT -Symmetric NLDC. As seen the energies of pulses in bar and cross behave in two manner 1) the exchange of energy is happened in some periods, but the shape of each pulse in bar and cross is preserved. Therefore, the solitons under this eigenfunction perturbation are mostly stable. 2) the evolution of energy in the bar and cross, demonstrate that there is no changes in their energies and they remain constant. It is straightforward to show that in spite of considering high-order effects, the perturbed soliton conserve the shape and it remain stable. The deliverables of this article not only demonstrate a novel approach to ultra-fast pulses, solitons and optical couplers, but more fundamentally, they could give insight for improving the new medical equipments technologies, enabling innovations in nonlinear optics and their usage in designing new communication systems and Photonic devices.

scholarly journals Stability analysis of magnetic fluids in the presence of an oblique field and mass and heat transfer

2020 ◽  
Vol 330 ◽  
pp. 01035
Author(s):  
Rabah Djeghiour ◽  
Bachir Meziani
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Magnetic Fluids ◽  
Physical Parameters ◽  
Stability Diagrams ◽  
Stability And Instability ◽  
Mass And Heat Transfer ◽  
Model Equations ◽  
The Stability ◽  
Oblique Magnetic Field

In this paper, we investigate an analysis of the stability of a basic flow of streaming magnetic fluids in the presence of an oblique magnetic field is made. We have use the linear analysis of modified Kelvin-Helmholtz instability by the addition of the influence of mass transfer and heat across the interface. Problems equations model is presented where nonlinear terms are neglected in model equations as well as the boundary conditions. In the case of a oblique magnetic field, the dispersion relation is obtained and discussed both analytically and numerically and the stability diagrams are also obtained. It is found that the effect of the field depends strongly on the choice of some physical parameters of the system. Regions of stability and instability are identified. It is found that the mass and heat transfer parameter has a destabilizing influence regardless of the mechanism of the field.

PREFERENTIAL MATING IN SYMMETRIC MULTILOCUS SYSTEMS: STABILITY CONDITIONS OF THE CENTRAL EQUILIBRIUM

Genetics ◽  
1982 ◽  
Vol 100 (1) ◽  
pp. 137-147
Author(s):  
S Karlin ◽  
J Raper
Keyword(s):  
Sexual Selection ◽  
Arbitrary Number ◽  
Sexual Attractiveness ◽  
Stability Conditions ◽  
Heterozygous State ◽  
Mating Pattern ◽  
Viability Selection ◽  
Class A ◽  
The Stability ◽  
Central Equilibrium

ABSTRACT Several multilocus models that incorporate both preferential mating and viability selection are studied. Specifically, a class of symmetric heterozygosity models are considered that assign individuals to phenotypic classes according to which loci are in heterozygous state regardless of the actual allelic content. Otherwise, an arbitrary number of loci, number of alleles per locus, and arbitrary recombination scheme, viability parameters and preferential mating pattern based on phenotypes are allowed. The conditions for the stability of a central polymorphism are indicated and interpreted. The effects of viability and preference selection may be summarized in a single quantity for each phenotypic class, a generalized fitness. Preferential assortative mating alone can produce stability for a central polymorphism as in the case of viability selection when sexual attractiveness or general fitness increases with higher levels of heterozygosity. The situation is more complex with sexual selection.

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