scholarly journals A geometric approach to the modelling of critical phenomena for a spray combustion model

2018 ◽  
Vol 209 ◽  
pp. 00014
Author(s):  
Elena Shchepakina
Keyword(s):  
Critical Phenomena ◽  
Invariant Manifolds ◽  
Asymptotic Expression ◽  
Critical Phenomenon ◽  
Relaxation Times ◽  
Combustible Mixture ◽  
Critical Regime ◽  
Combustion Model ◽  
Sharp Change ◽  
Singularly Perturbed Systems

The paper is devoted to the modelling of the critical phenomena in multiscale combustion models. Such models are usually described by singularly perturbed systems of differential equations to reflect the significant distinction in characteristic relaxation times of different physicochemical processes. The paper proposes an approach for modelling of critical phenomena on the basis of the geometric asymptotic method of invariant manifolds. The critical phenomenon means as a sharp change in the dynamics of the process under consideration. As an illustration of this approach a dynamic model of fuel spray ignition and combustion is considered. The realizability conditions for the critical regime is obtained in the form of the asymptotic expression for the control parameter. The main feature of the critical regime is that during it the temperature of the combustible mixture can reach a high value within the framework of a safe process. It is shown that the critical regime plays the role of a watershed between the slow combustion regimes and the thermal explosion.

Analysis on Critical Phenomena of a Hysteretic System

2003 ◽  
Author(s):  
Z. Chen ◽  
Z. Q. Wu ◽  
P. Yu
Keyword(s):  
Critical Phenomena ◽  
Nonlinear Dynamical Systems ◽  
Critical Phenomenon ◽  
External Forcing ◽  
Restoring Force ◽  
Nonlinear Dynamical ◽  
Hysteretic Property ◽  
Nonlinear Mechanical System ◽  
Hysteretic Damper ◽  
New Finding

In this paper, a nonlinear mechanical system with external forcing is investigated to study the critical phenomena of the system. The system involves a von der Pol type damping and a hysteretic damper representing a restoring force. Numerical simulations are used to show that under an external exciting force, the hysteretic restoring force may not follow the routes described by a conventional form of piecewise function, but exhibit some irregular behavior. We call this unusual situation the critical phenomenon of the system. Simulations results suggest that a device with hysteretic property (e.g., the damper considered in this paper) may change its typical characteristics under external forcing. This new finding may enhance the study of nonlinear dynamical systems with hysteretic property under external excitement.

CRITICAL PHENOMENON INDUCED BY NOISE IN THE BTW SANDPILE

Fractals ◽  
2009 ◽  
Vol 17 (02) ◽  
pp. 227-232
Author(s):  
LIUJUN CHEN ◽  
WEITING CHEN ◽  
ZENGRU DI ◽  
DAHUI WANG
Keyword(s):  
Critical Phenomena ◽  
Critical Phenomenon ◽  
Internal Noise ◽  
Critical States ◽  
Self Organized ◽  
Self Organized Criticality

The behavior of sandpile far from self-organized critical states (SOCS) is investigated in this paper. The results indicate that noise plays an important role in the critical phenomenon. The critical phenomena are detected in sandpile far from SOCS when external or internal noise is applied. In contrast to self-organized criticality, the exponent of avalanche distribution in sandpile far from SOCS increases with the distance of the sandpile from SOCS. At the same time, the exponent of avalanche distribution in a sandpile far from SOCS is consistent with some real systems such as earthquake.

scholarly journals Study of critical phenomena in economic systems using a model of damped oscillations

2019 ◽  
Vol 65 ◽  
pp. 06008 ◽  
Author(s):  
Hanna Danylchuk ◽  
Liubov Kibalnyk ◽  
Olexandr Serdiuk
Keyword(s):  
Critical Phenomena ◽  
Initial Phase ◽  
Wavelet Coefficient ◽  
Critical Phenomenon ◽  
Damping Coefficient ◽  
Economic Systems ◽  
Prediction Horizon ◽  
Damped Oscillations ◽  
Conducting Research ◽  
Two Parameters

The article describes the construction of a model for the analysis and forecasting of critical phenomena in economic systems based on the equation of the damped oscillations. The model of the damped oscillations based on the analysis of wavelet coefficient energy allows identifying critical phenomena, in the first place, crashes. Two parameters of the model, the initial phase and the damping coefficient, are the most appropriate for the analysis and prediction of the critical events in the economic systems. The sequence of steps for conducting research is presented and the possibility to automate the process of predicting critical phenomena is described. Critical phenomenon can be predicted based on the initial phase and the damping coefficient, the prediction horizon depends on the scale at which the model of the damped oscillations was constructed. The study of the results of the model is based on the known crashes and shocks given in the work.

scholarly journals Combustion waves

1997 ◽  
Vol 38 (4) ◽  
pp. 464-476 ◽  
Author(s):  
R. O. Weber ◽  
S. D. Watt
Keyword(s):  
Critical Phenomena ◽  
Stable Equilibrium ◽  
Travelling Waves ◽  
Stable State ◽  
Critical Parameters ◽  
Spontaneous Ignition ◽  
Combustion Model ◽  
Centre Manifold ◽  
Centre Manifold Reduction ◽  
Manifold Reduction

AbstractFinding critical phenomena in two-dimensional combustion is normally done numerically. By using a centre-manifold reduction, we can find a reduced equation in one dimension. Once we have found the reduced equation, it is simpler to find critical phenomena. We consider two different problems. One is spontaneous ignition. We compare our results with known critical parameters to give some validity to our reduction technique. We also look at a combustion model with three equilibrium states. For this model, the possible transitions can occur as travelling waves between the unstable to either of the stable equilibrium or from one stable to the other stable state. For the latter transition, the direction of the transition tells us whether we have an extinction or ignition wave. We find the critical parameters when the direction of the wave changes.

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