PHASE INSTABILITIES OF DISTORTED HEXAGONAL PATTERNS

2001 ◽  
Vol 11 (11) ◽  
pp. 2771-2777
Author(s):  
B. PEÑA ◽  
C. PÉREZ–GARCÍA
Keyword(s):  
Analytical Study ◽  
Full Range ◽  
Amplitude Equation ◽  
Phase Equation ◽  
Stability Regions ◽  
The Stability ◽  
Phase Instabilities

We present an analytical study on the stability of distorted hexagonal patterns. From a general amplitude equation we calculate the instabilities with respect to homogeneous and longwave perturbations. The latter lead to the phase equations that permit to determine the stability regions. Slightly squeezed hexagons are locally stable in a full range of distortion angles. The stability regions obtained from the phase equation are similar to those obtained numerically by other authors [Gunaratne et al., 1994].

Theoretical Study on Instability Boundary of Rotor-Hydrodynamic Bearing Systems: Part II — Rotor With External Flexible Damped Support

2001 ◽  
Author(s):  
Zenglin Guo ◽  
R. Gordon Kirk
Keyword(s):  
Analytical Study ◽  
Theoretical Study ◽  
System Stability ◽  
Hydrodynamic Bearing ◽  
System A ◽  
Vertical Rotor ◽  
Speed Range ◽  
Stability Maps ◽  
Alternative Means ◽  
The Stability

Abstract The situation of a rotor-hydrodynamic bearing system in external flexible damped support is more complicated than that discussed before in Part I but it can become an alternative means to improve the stability of the rotor system. A model for both vertical and horizontal analysis is built first. Then, the analytical study on the vertical rotor is conducted. The results show that there might be up to four threshold speeds in this configuration that form a consecutive regional pattern taken turns by stable or unstable regions. Furthermore, the numerical calculation by MATLAB is carried out to obtain the results of the horizontal system. The stability maps for various parametric configurations are presented. It has been shown that the value of support damping has a strong effect on the first several lower threshold speeds. But it has little effect on the last top threshold speed which is mainly determined by the portion of journal mass. Within a certain range of external damping value, the first several regions of instability can be reduced or eradicated. As far as the entire stability map is concerned, there is an optimum range of value for support damping that can make the rotor have only one top threshold speed over the entire running speed range. When the support stiffness is increased, the system stability map becomes narrow which means a small support stiffness is good for broadening the range of optimum external damping.

Instability Boundary for Rotor-Hydrodynamic Bearing Systems, Part 2: Rotor With External Flexible Damped Support

2003 ◽  
Vol 125 (4) ◽  
pp. 423-426 ◽  
Author(s):  
Zenglin Guo ◽  
R. Gordon Kirk
Keyword(s):  
Analytical Study ◽  
System Stability ◽  
Regional Pattern ◽  
Hydrodynamic Bearing ◽  
System A ◽  
Vertical Rotor ◽  
Speed Range ◽  
Stability Maps ◽  
The Stability ◽  
Bearing System

A rotor-hydrodynamic bearing system having external flexible damped bearing supports is more complicated than that discussed in Part 1 but it can provide a means to improve the stability of the rotor system. A model for both vertical and horizontal analysis is developed first. Then, the analytical study on the vertical rotor is conducted. The results show that there can be up to four threshold speeds in this configuration that form a consecutive regional pattern, taking turns by stable or unstable regions. Furthermore, the numerical calculation by MATLAB is carried out to obtain the results for the horizontal system. The stability maps for various parametric configurations are presented. It has been shown that the value of support damping has a strong effect on the first several lower threshold speeds. But it has little effect on the last top threshold speed which is mainly determined by the portion of journal mass. Within a certain range of external damping value, the first several regions of instability can be reduced or eradicated. As far as the entire stability map is concerned, there is an optimum range of support damping that can make the rotor have only one top threshold speed over the entire running speed range. When the support stiffness is increased, the system stability map becomes narrow which means a small support stiffness is good for broadening the range of optimum external damping.

DDE Model of Gene Expression: A Continuum Approach

2008 ◽  
Author(s):  
Anael Verdugo ◽  
Richard H. Rand
Keyword(s):  
Gene Expression ◽  
Regulatory Network ◽  
Analytical Study ◽  
Continuum Approach ◽  
Differential Integral Equation ◽  
Gene Regulatory ◽  
The Stability ◽  
Delay Differential ◽  
Steady State Solutions ◽  
Nonlinear Delay

This paper presents an analytical study of the stability of the steady state solutions of a gene regulatory network with time delay. The system is modeled as a continuous network and takes the form of a nonlinear delay differential-integral equation coupled to an ordinary differential equation. Two examples are given in which the critical delay causing instability is computed.

Theoretical investigation of the interfacial stability of inviscid fluids in motion, considering surface tension

1972 ◽  
Vol 54 (1) ◽  
pp. 129-141 ◽  
Author(s):  
Jan Berghmans
Keyword(s):  
Surface Tension ◽  
Analytical Study ◽  
Minimum Free Energy ◽  
Gas Jet ◽  
Interfacial Stability ◽  
Viscous Effects ◽  
Inertia Effects ◽  
Inviscid Fluids ◽  
The Stability

The present work is an analytical study of the stability of interfaces between fluids in motion, special attention being given to the role of surface tension without consideration of viscous effects. A variational approach based upon the principle of minimum free energy, which was first formulated for stagnant fluids, is applied to fluids in motion. This generalization is possible if viscous and inertia effects are unimportant as far as stability is concerned. One stability problem is studied in detail: a gas jet impinging on a free liquid. The analytical results obtained by this variational technique lie within the range of accuracy (15%) of the experimental results for this gas-jet problem. The method is very general and therefore can be applied to quite a number of interface stability problems.

scholarly journals Analytical study of the stability of a two-ball automatic balancer

2009 ◽  
Vol 23 (3) ◽  
pp. 884-896 ◽  
Author(s):  
Chung-Jen Lu ◽  
Ming-Cheng Wang ◽  
Shih-Hsuan Huang
Keyword(s):  
Analytical Study ◽  
The Stability

scholarly journals Analytical study of auto-balancing within the framework of the flat model of a rotor and an auto-balancer with a single cargo

2021 ◽  
Vol 2 (7 (110)) ◽  
pp. 66-73
Author(s):  
Gennadiy Filimonikhin ◽  
Lubov Olijnichenko ◽  
Guntis Strautmanis ◽  
Antonina Haleeva ◽  
Vasyl Hruban ◽  
...  
Keyword(s):  
Differential Equations ◽  
Analytical Study ◽  
Rotation Axis ◽  
Equations Of Motion ◽  
The Third ◽  
Rotor Imbalance ◽  
Small Resistance ◽  
The Stability ◽  
Resistance Forces ◽  
Rotor Model

This paper reports the analytically established conditions for the onset of auto-balancing for the case of a flat rotor model on isotropic elastic-viscous supports and an auto-balancer with a single load. The rotor is statically unbalanced, the rotation axis is vertical. The auto-balancer has a single cargo – a pendulum, a ball, or a roller. The balancing capacity of the cargo is equal to the rotor imbalance. The physical-mathematical model of the system is described. The differential equations of motion are recorded in dimensionless form relative to the coordinate system that rotates synchronously with the rotor. The so-called main movement has been found; in it, the cargo synchronously rotates with the rotor and balances it. The differential equations of motion are linearized in the neighborhood of the main movement. A characteristic equation has been constructed. It helped investigate the stability of the main movement (an auto-balancing mode) for the cases of the absence and presence of resistance forces in the system. It was established that in the absence of resistance forces in the system: – the rotor has three characteristic rotational speeds, and the first always coincides with the resonance frequency; – auto-balancing occurs when the rotor rotates at speeds between the first and second ones, and above the third characteristic speed; – the value of the second and third characteristic speeds is significantly influenced by the ratio of weight to the mass of the system; – the second and third characteristic speeds monotonously increase with an increase in the ratio of cargo weight to the mass of the system. Resistance forces significantly affect both the values of the second and third characteristic speeds and the conditions of their existence. Small resistance forces do not change the quality behavior of the system. With high resistance forces, the number of characteristic speeds decreases to one. The paper reports the results applicable to an auto-balancer with many cargoes when it balances the imbalance that equals the balancing capacity of the auto-balancer

scholarly journals Need of Legal, Administrative and Judicial Reforms in Pakistan to Combat Money Laundering and Terrorism Financing: An Analytical Study

2020 ◽  
Vol 3 (1) ◽  
pp. 91-100
Author(s):  
Khalil Haider ◽  
Naureen Akhtar
Keyword(s):  
Money Laundering ◽  
Analytical Study ◽  
Economic Prosperity ◽  
Financial Systems ◽  
Global Problems ◽  
Terrorism Financing ◽  
Financing Of Terrorism ◽  
The Stability ◽  
Combat Money Laundering

The main objective of this article is to discuss, review and analyze money laundering and terrorism financing simultaneously as both share common incentives, line of action and executing strategies. Money laundering and financing of terrorism are global problems which not only threaten security but also compromise the stability, transparency and efficiency of financial systems, thus undermining economic prosperity and peace of a country. This research defines and expounds the terms ‘money laundering’ and ‘terrorism financing’, and common strategies to execute both of these criminal activities. It also analyzes the current predicament of legal, administrative and judicial skeleton of Pakistan which makes the country more vulnerable to money laundering and terrorism financing. Furthermore, it would also provide its readers with the most needed reforms in the all-over blueprint of the country, and imperative amendments to make the Anti-money Laundering Act, 2010 and the Anti-terrorism Act, 1997 more efficacious to encounter money laundering and terrorism financing in one fell swoop.

Sign in / Sign up

Export Citation Format

Share Document