scholarly journals Towards a quantitative comparison between global and local stability analysis

2017 ◽  
Vol 819 ◽  
pp. 147-164 ◽  
Author(s):  
L. Siconolfi ◽  
V. Citro ◽  
F. Giannetti ◽  
S. Camarri ◽  
P. Luchini
Keyword(s):  
Stability Analysis ◽  
Saddle Point ◽  
Global Stability ◽  
Local Stability ◽  
Correction Term ◽  
Three Dimensional ◽  
Higher Order ◽  
Order Correction ◽  
Global Stability Analysis ◽  
Local Stability Analysis

A methodology is proposed here to estimate the stability characteristics of bluff-body wakes using local analysis under the assumption of weakly non-parallel flows. In this connection, a generalisation of the classic spatio-temporal stability analysis for fully three-dimensional flows is first described. Secondly, an additional higher-order correction term with respect to the common saddle-point global frequency estimation is included in the analysis. The proposed method is first validated for the case of the flow past a circular cylinder and then applied to two fully three-dimensional flows: the boundary layer flow over a wall-mounted hemispherical body and the wake flow past a fixed sphere. In all the cases considered, both the estimated unstable eigenvalue and the spatial shape of the associated eigenmode are determined by local stability analysis, and they are compared with the reference counterparts obtained at a definitely higher computational cost by a fully three-dimensional global stability analysis. It is shown that the results of local stability analysis, when the higher-order correction term is included, are in excellent agreement with those obtained by global stability analysis. It is also shown that the retained correction term is of crucial importance in this perspective, leading to a remarkable improvement in accuracy with respect to the classical saddle-point estimation.

scholarly journals A Mathematical Modeling of Tuberculosis Dynamics with Hygiene Consciousness as a Control Strategy

2020 ◽  
pp. 38-48
Author(s):  
Phineas Z. Mawira ◽  
David M. Malonza
Keyword(s):  
Stability Analysis ◽  
Global Stability ◽  
Control Strategy ◽  
Local Stability ◽  
Equilibrium Points ◽  
Asymptotically Stable ◽  
Linear Ordinary Differential Equations ◽  
Global Stability Analysis ◽  
Local Stability Analysis ◽  
Disease Free

Tuberculosis, an airborne infectious disease, remains a major threat to public health in Kenya. In this study, we derived a system of non-linear ordinary differential equations from the SLICR mathematical model of TB to study the effects of hygiene consciousness as a control strategy against TB in Kenya. The effective basic reproduction number (R0) of the model was determined by the next generation matrix approach. We established and analyzed the equilibrium points. Using the Routh-Hurwitz criterion for local stability analysis and comparison theorem for global stability analysis, the disease-free equilibrium (DFE) was found to be locally asymptotically stable given that R0 < 1.  Also by using the Routh-Hurwitz criterion for local stability analysis and Lyapunov function and LaSalle’s invariance principle for global stability analysis, the endemic equilibrium (EE) point was found to be locally asymptotically stable given that R0 > 1. Using MATLAB ode45 solver, we simulated the model numerically and the results suggest that hygiene consciousness can helpin controlling TB disease if incorporated effectively.

scholarly journals Global stability analysis of structures and actions to control their effects

2016 ◽  
Vol 9 (2) ◽  
pp. 192-213 ◽  
Author(s):  
F. C. Freitas ◽  
L. A. R. Luchi ◽  
W. G. Ferreira
Keyword(s):  
Stability Analysis ◽  
Global Stability ◽  
Local Stability ◽  
Structural Systems ◽  
Stability Parameters ◽  
Global Stability Analysis ◽  
Basic Concepts ◽  
The Stability ◽  
Global And Local ◽  
Brazilian Standard

ABSTRACT In this moment in which civil engineering is undergoing a phase where structural projects have been developed with structural systems composed of different and complex elements, some methods and criteria are used for the purpose of evaluating important aspects with regard to global and local stability. Among them, it is necessary to mention the parameters of instability a and ?z. In this sense, this work has the objective to present the basic concepts of the instability parameters a and ?z in accordance with what is clearly defined in the Brazilian standard ABNT NBR 6118; to present the results of simulations of models in the Brazilian structural software TQS varying the stress of compression in the columns in order to relate these values with the stability parameters.

scholarly journals Local Stability Analysis of Three-dimensional Magnetically Confined Plasmas

1997 ◽  
Vol 50 (5) ◽  
pp. 921 ◽  
Author(s):  
J. L. V. Lewandowski
Keyword(s):  
Stability Analysis ◽  
Phase Angle ◽  
Local Stability ◽  
Three Dimensional ◽  
Magnetic Shear ◽  
Confined Plasmas ◽  
Fluid Displacement ◽  
Local Stability Analysis ◽  
Magnetically Confined ◽  
Magnetically Confined Plasmas

Local stability analysis of three-dimensional magnetically confined plasmas is presented using the energy principle. Fluid displacements with long parallel wavelengths by short perpendicular are retained. To lowest order in the mode fluteness the total energy density variation depends on the local magnetic shear, normal and geodesic magnetic curvatures, parallel current density, and magnetic field strength. The perpendicular fluid displacement is written in terms of a slowly-varying amplitude and a phase angle which varies rapidly in (or across) the magnetic surface. Assuming that the fluid displacement is quasi-incompressible, the solution for the phase angle is found in two limiting cases. Local stability analysis of stellarators with low or strong global magnetic shear is discussed.

scholarly journals Stability behaviour of mathematical model MERS corona virus spread in population

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3947-3960 ◽  
Author(s):  
Muhammad Tahir ◽  
Syed Shah ◽  
Gul Zaman ◽  
Tahir Khan
Keyword(s):  
Stability Analysis ◽  
Local Stability ◽  
Equilibrium Points ◽  
Reproductive Number ◽  
Virus Spread ◽  
Global Stability Analysis ◽  
Local Stability Analysis ◽  
Proposed Model ◽  
Disease Free ◽  
Model Existence

In this subsection, we first formulated the proposed model in there infectious classes and then we derived the basic key value reproductive number, R0 with the help of next generation approach. Then we obtained all the endemic equilibrium points, as well as, local stability analysis, at disease free equilibria and, at endemic equilibria of the related model and shown stable. Further the global stability analysis either, at disease free equilibria, and at endemic equilibria is discussed by constructing Lyapunov function which show the validity of the concern model exist. In the last part of the article numerical simulation is presented for the model which support the model existence with the help of RK-4 method.

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