scholarly journals DEFORMATIONS OF DYNAMICS ASSOCIATED TO THE CHIRAL POTTS MODEL

1992 ◽  
Vol 06 (22) ◽  
pp. 3575-3584 ◽  
Author(s):  
M.P. BELLON ◽  
J-M. MAILLARD ◽  
G. ROLLET ◽  
C-M. VIALLET
Keyword(s):  
Finite Order ◽  
Potts Model ◽  
Discrete Groups ◽  
Chiral Potts Model ◽  
Potts Models ◽  
Deformation Parameters ◽  
Fermat Number ◽  
Non Linear ◽  
The Stability

We describe deformations of non-linear (birational) representations of discrete groups generated by involutions, having their origin in the theory of the symmetric five-state Potts model. One of the deformation parameters can be seen as the number q of states of a chiral Potts models. This analogy becomes exact when q is a Fermat number. We analyze the stability of the corresponding dynamics, with a particular attention to orbits of finite order.

MULTICOMPONENT CHIRAL POTTS MODELS

1992 ◽  
Vol 07 (supp01b) ◽  
pp. 1007-1023 ◽  
Author(s):  
HELEN AU-YANG ◽  
JACQUES H. H. PERK
Keyword(s):  
Potts Model ◽  
Lattice Site ◽  
Nearest Neighbor ◽  
Composite Model ◽  
Dual Lattice ◽  
Chiral Potts Model ◽  
Potts Models ◽  
Spin Interactions ◽  
Composite Models ◽  
Relative Prime

It is shown that an (Nρ,Nσ) chiral Potts model, which is a generalization of the Ashkin-Teller model and consists of two chiral Potts models which are coupled together by four-spin interactions, can always be mapped to a single chiral Potts model of NρNσ states if Nρ and Nσ are relative prime. Moreover, if on every lattice site there are d spins with Nρ,…,Nσ states, respectively, similar mappings exist: If there are chiral two-spin interactions between nearest neighbor spins of the same kind and if the d sublattices are coupled together by chiral 2j-spin interactions for j≤d between the j pairs of spins, this defines a composite (Nρ,…,Nσ) state chiral Potts model. If (Ni,Nj)=1, for i≠j, i,j=1,…,d, then the composite model with (Nρ,…,Nσ) states can be mapped into a [Formula: see text]-state chiral Potts model. Finally, it is shown that if one or more of the spins of a unit cell sits on the dual lattice whereas the other spins sit on the original lattice, so that this is a generalization of the eight-vertex model in the spin language, such a mapping also exists. This mean that results obtained for the chiral Potts models can be used for many such composite models.

Investigation of the stability of periodic motions in a nonlinear automatic control system based on the fast fourier transform

2003 ◽  
Vol 3 ◽  
pp. 297-307
Author(s):  
V.V. Denisov
Keyword(s):  
Fourier Transform ◽  
Control System ◽  
Automatic Control ◽  
Fast Fourier Transform ◽  
Automatic Control System ◽  
Resonance Phenomenon ◽  
Periodic Motions ◽  
Multiply Connected ◽  
Non Linear ◽  
The Stability

An approach to the study of the stability of non-linear multiply connected systems of automatic control by means of a fast Fourier transform and the resonance phenomenon is considered.

A novel approach for the stability problem in non-linear dynamical systems

2003 ◽  
Vol 155 (1) ◽  
pp. 21-30 ◽  
Author(s):  
Tarcı́sio M. Rocha Filho ◽  
Iram M. Gléria ◽  
Annibal Figueiredo
Keyword(s):  
Dynamical Systems ◽  
Stability Problem ◽  
Linear Dynamical Systems ◽  
Novel Approach ◽  
Non Linear ◽  
The Stability

Non-linear stability analysis of micropolar fluid lubricated journal bearings with turbulent effect

2019 ◽  
Vol 71 (1) ◽  
pp. 31-39
Author(s):  
Subrata Das ◽  
Sisir Kumar Guha
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Micropolar Fluid ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Turbulent Regime ◽  
Content Type ◽  
Non Linear ◽  
The Stability ◽  
Bearing System

Purpose The purpose of this paper is to investigate the effect of turbulence on the stability characteristics of finite hydrodynamic journal bearing lubricated with micropolar fluid. Design/methodology/approach The non-dimensional transient Reynolds equation has been solved to obtain the non-dimensional pressure field which in turn used to obtain the load carrying capacity of the bearing. The second-order equations of motion applicable for journal bearing system have been solved using fourth-order Runge–Kutta method to obtain the stability characteristics. Findings It has been observed that turbulence has adverse effect on stability and the whirl ratio at laminar flow condition has the lowest value. Practical implications The paper provides the stability characteristics of the finite journal bearing lubricated with micropolar fluid operating in turbulent regime which is very common in practical applications. Originality/value Non-linear stability analysis of micropolar fluid lubricated journal bearing operating in turbulent regime has not been reported in literatures so far. This paper is an effort to address the problem of non-linear stability of journal bearings under micropolar lubrication with turbulent effect. The results obtained provide useful information for designing the journal bearing system for high speed applications.

Non-linear dynamic analysis of bearing—rotor system lubricating with couple stress fluid

2008 ◽  
Vol 222 (4) ◽  
pp. 599-616 ◽  
Author(s):  
C-W Chang-Jian ◽  
C-K Chen
Keyword(s):  
Dynamic Analysis ◽  
Chaotic Motion ◽  
Couple Stress ◽  
Couple Stress Fluid ◽  
Speed Ratio ◽  
Non Linear ◽  
System Life ◽  
The Stability ◽  
Suitable System ◽  
Bearing System

The current study performs a dynamic analysis of a rotor supported by two couple stress fluid film journal bearings with non-linear suspension. The dynamics of the rotor centre and bearing centre are studied. The analysis of the rotor—bearing system is investigated under the assumptions of a couple-stress lubricant and a short journal bearing approximation. The displacements in the horizontal and vertical directions are considered for various non-dimensional speed ratios. The analysis methods employed in this study include the dynamic trajectories of the rotor centre and the bearing centre, Poincaré maps, and bifurcation diagrams. The Lyapunov exponent analysis is also used to identify the onset of chaotic motion. Numerical results show that the stability of the system varies with the non-dimensional speed ratios. Specifically, it is found that the system is quasi-periodic at a small speed ratio ( s = 0.5). At speed ratios of s = 0.6–0.7, the system is periodic. At s = 0.8–1.9, the system is quasi-periodic, but the system is periodic at s = 2.0–2.6. However, the system exhibits chaotic motion at the speed ratios s = 2.7–2.74. At the speed ratios s = 2.75–3.16, the system becomes periodic. At s = 3.17–3.30, the system is unstable. The Poincaré map has a particular form at s = 3.17, indicative of a chaotic motion. At s = 3.31–6.0, the system finally becomes periodic. The results also confirm that the stability of the system varies with the non-dimensional speed ratios s and l∗. The results of this study allow suitable system parameters to be defined such that undesirable behaviour of the rotor centre can be avoided and the bearing system life extended as a result.

A Dynamical Model for Studying the Stability of Thermo-Solutal Convection Under the Effect of Vertical Vibration

2005 ◽  
Author(s):  
Y. P. Razi ◽  
M. Mojtabi ◽  
K. Maliwan ◽  
M. C. Charrier-Mojtabi ◽  
A. Mojtabi
Keyword(s):  
Stability Analysis ◽  
Mechanical Vibration ◽  
Stability Limit ◽  
Lewis Number ◽  
Vertical Vibration ◽  
Wave Number ◽  
Dimensionless Wave Number ◽  
Non Linear ◽  
Linear Differential ◽  
The Stability

This paper concerns the thermal stability analysis of porous layer saturated by a binary fluid under the influence of mechanical vibration. The linear stability analysis of this thermal system leads us to study the following damped coupled Mathieu equations: BH¨+B(π2+k2)+1H˙+(π2+k2)−k2k2+π2RaT(1+Rsinω*t*)H=k2k2+π2(NRaT)(1+Rsinω*t*)Fε*BF¨+Bπ2+k2Le+ε*F˙+π2+k2Le−k2k2+π2NRaT(1+Rsinω*t*)F=k2k2+π2RaT(1+Rsinω*t*)H where RaT is thermal Rayleigh number, R is acceleration ratio (bω2/g), Le is the Lewis number, k is the dimensionless wave-number, ε* is normalized porosity and N is the buoyancy ratio (H and F are perturbations of temperature and concentration fields). In the follow up, the non-linear behavior of the problem is studied via a generalization of the Lorenz model (five coupled non-linear differential equations with periodic coefficients). In the presence or absence of gravity, the stability limit for the onset of stationary as well as Hopf bifurcations is determined.

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