Quantitative analysis method for laminar-turbulence transition process of mechanical seal by a catastrophic model

Fluid flow regime has an important influence on the lubrication performance of mechanical seal. A novel method is proposed to analyze the flow regime transition quantitatively based on a cusp catastrophic model with dimensionless analysis. Furthermore, from this method, a turbulence transition factor is derived strictly to describe the turbulent transition process of mechanical seal, which is verified by the published results. Then this factor is applied to hydrodynamic lubrication mechanical seal to analyze the influence of flow regime on sealing performance. The results indicate that the performance parameters of mechanical seal are greatly influenced by the transition of fluid flow regime, and the stability of mechanical seal decreases in the transition to turbulent flow. The novel method of flow regime transition analysis provides a new insight into the turbulence model.

Mathematical modeling of the mosaic of forest systems

In the article a small review of the main mathematical models describing the mosaic dynamics of forest communities is given: catastrophic model, the Tuzinkevich model, the Hahyama model and gap-models.

A Nonlinear Catastrophic Model of Isolated Rock Pillar Instability and its Chaotic Behaviour Based on Material Properties

A cusp catastrophic model of rock pillar instability was developed under uniaxial stress conditions, based on the assumptive softening constitutive relations under static mechanics. The static criterion of rock pillar instability is derived. The dynamical nonlinear differential equation under nonequilibrium state followed by the cusp catastrophic model is introduced. The characteristics of rock pillars chaotic evaluation are studied under the change of linear stiffness. The results show that the rock pillars motion is chaotic when the linear stiffness is in a certain interval, which are proved by the calculated max Lyapunov exponent.

Model Analysis for Comprehensive Transportation Structure Evolution Based on Catastrophe Theory

The cusp catastrophic model based on catastrophe theory is presented to analyze the development pattern evolution of comprehensive transportation system (CTS for short). By establishing cusp catastastrophe model of development pattern we obtain that the construction of comprehensive transportation system should include two parts, the first part is the stock optimization and the second part is the increment construction. With the increment construction as the turning point, promoting the fast optimization of the stock should be the basic principles of the construction and development of CTS.

Application of Catastrophe Theory in Surrounding Rock Stability

Surrounding rock system of underground engineering is highly nonlinear, and there is no unified cognition for its stability criteria. Introduces the basic principle of catastrophe theory, focusing on the cusp catastrophic model, build a simplified mechanical model for the surrounding rock, and the instability of surrounding rock of the cusp catastrophic model is obtained. In practical engineering, it is show that catastrophe theory is an effective method to study the instability problem of the tunnel.

Catastrophic Model of Water Inrush from Coal Mine Floor

The water inrush from coal mine floor is a typical catastrophic process. A catastrophic theory is applied to water bursting in pit footwall for the first time. Through the research on lost stabilization of energy in the floor system of coal mine, a cusp catastrophic model applied to forecast water bursting from coal mine floor is put forward. The formulas of the critical stress, the strain and the released energy of the floor are developed when the floor system lost stabilization. So a new theory approach is offered for the forecast of water inrush from coal mine floor.