The Study of Chamber Rockburst by the CUSP Model of Catastrophe Theory

By means of CUSP model of catastrophe theory. this paper has studied thephysics process of rockburst occured on circular chamber. The present paper has nolonly described the instability process of rockburst more deeply. but also got the crilicaldepth of plastic softening area of chamber that is valuable in the controlling engineering of rockburst. the chamber displacement jump and energy liberation have been derived. the influence of rock parameters on the rockburst has been discussed .

Catastrophe Theory Models for Stress-dependent Behaviour in a NiTi Shape Memory Alloy

The measurements by Huibin XU et al of the stress-dependence ot hysteresis in a NiTi shape memo ry alloy are modeled by catastrophe theory. The cusp catastrophe is used with the strain as the behaviour variable and the control parameters being functions of the stress and the temperature. A two constant model is found to be preferred to a four constant model.

Stability of interbed for salt cavern gas storage in solution mining considering cusp displacement catastrophe theory

Cusp displacement catastrophe theory can be introduced to propose a new method about instability failure of the interbed for gas storage cavern in bedded salt in solution mining.We can calculate initial fracture drawing pace of this interbed to obtain 2D and 3D gas storage shapes at this time.Moreover,Stability evaluation of strength reduction finite element method(FEM)based on this catastrophe theory can used to evaluate this interbed stability after initial fracture.A specific example is simulated to obtain the influence of the interbed depth,cavern internal pressure,and cavern building time on stability safety factor(SSF).The results indicate:the value of SSF will be lower with the increase of cavern building time in solution mining and the increase of interbed depth and also this value remains a rise with the increase of cavern internal pressure Especially,we can conclude that the second-fracture of the interbed may take place when this pressure is lower than 6 MPa or after 6 days later of the interbed after initial fracture.According to above analysis,some effective measures,namely elevating the tube up to the top of the interbed,or changing the circulation of in-and-out lines,can be introduced to avoid the negative effects when the secondfracture of the interbed may occur.

Development of a wheat aphid population dynamics model based on cusp catastrophe theory

Aphids are a major global wheat,pest that can cause considerable loss of yield.Modeling of aphid population dynamics is an integral part of management strategies to manage or control aphid populations.In this paper,first,a wheat aphid population dynamics model was developed based on a logistic model and theⅠlollingⅢfunctional response,which includes three factors:temperature,natural enemies and insecticide.Second,this model fitted with a cusp catastrophe model to describe how abrupt changes in the wheat aphid population were influenced by these factors,Finally,the system was validated with field data from 2016 to 2018.The bifurcation set of the cusp catastrophe model was deemod to be the quantified dynamic control threshold,so an outbreak of aphid's population can be explained according to the variation of control variables.In short,this aphid population model was successfully validated on survey data,which can be used to guide the prevention and control of aphids.

Modeling and simulation of voluntary employee turnover using catastrophe theory: A case study on a manufacturing enterprise in China

The Lewisian turning-point obviously increase the labor costs of Chinese manufacturing firms,it made the employee turnover to become the key problem that how to keep the enterprise human resource stability.Here,the conceptual catastrophe model of employee turnover is built from the new perspective of empirical study and catastrophe theory.In particular,we developed a parameter estimation method of the Cusp catastrophe model based on qualitative simulation and fuzzy math,and then to demonstrate the rationality and robustness of this method by a practical case on a manufacturing enterprise.In the end,a series of virtual experiments are carried out for the employee turnover in the period of China’s economic transformation.The main results are that,how to measure the warning,critical and mutation area of employee turnover;the real relationship between the complex economic environment and the demission of employees;the control policy from the macroscopic governmental measures and microscopic enterprise ways.

Catastrophe Theory and Semiophysics:With an Application to "Movie Physics"

In the humanities the applications of catastrophe theory and other models stemming from "dynamic systems theory",a field of applied mathematics based on topology and differential calculus,was the first theoretical innovation since the computer/mind-boom which began in the sixties and brought many research fields to public recognition and institutional success which exploited the metaphor of the computer as mind or artificial intelligence;cf.AI and the Chomsky paradigm.The rise of dynamic model designs began in the late sixties with the publications of Rene Thom,a Fields Medal winner in mathematics,and Christopher Zeeman,a renowned researcher in applied mathematics(mostly in biology and psychology/neurology).The French and English endeavor received much support after 1974-1977 culminating in a joint conference in Cerisy-la-Salle in 1982.The first sections review this development,the catastrophe controversy 1978-1980 and later developments mainly in the work of Rene Thom and his major followers(Petitot,Wildgen,& Brandt).Thorn's new impulse,his "semiophysics"(Thom,1988),and the research which followed are summarized and the notions of "saillance" — "pregnance"(perceptual salience and biological relevance) including its evolutionary aspects are sketched.A specific application to the concept of sign applying the hyper-cycles proposed by Eigen and Schuster(1979) is put forward.Eventually,a new application by the author called "movie physics" is described,which gives a hint to further evolutions of this new field of semiotic theorizing,mainly in the media.

The Theory of Relativity on the Finsler Spacetime

According to some local properties of Lorentz transformation, Einstein stated: 'Vetheitiss greater than that of light have no possibility of existence.' He neglected to point out the applicable range of the special theory of relativity. In fact, it could only be applied to the subluminal-speeds. This paper shows that if ones think of the possibility of the existence of the superluminal-speeds and redescribe the special theory of relativity following Einstein's way, it could be supposed that the physical spacetime is a Finsler spacetime, characterized by the metric ds4=gijkldxidxidxkdxl. If so, a new spactime transformation could be found by invariant ds4 and the theory of relativity is discussed on this transformation it is possible that the Finsler spacetime F(x,y) may be endowed with a catastrophic nature. Based on the different properties between the ds2 and ds4, it is discussed that the flat spacetime will also have the catastrophic nature on the Finsler metric ds4. The spacetime transformations and the Physical quantities will suddenly change at the catastrophe set of the spacetime, the light cone. It will be supposed that only the dual velocity of the superluminal-speeds could be observed. If so, a particle with the superluminal-speed v> c could be regarded as its anti-particle with the dual velocity v1=c2/ v< c. On the other hand, it could be assumed that the horizon of the field of the general relativity is also a catastrophic set. If so, a particle with the superluminal-speeds could be projected near the horizon of these fields, and the particle will move on the sauce-like curves. It is very interesting that, in the Schwarzschild fields, the theoretical calculation for the sauce-like curves should be in agreement with tie data of the superluminal expansion of extragalactic radio sources observed year after year. (see Gao, 1992b).The ca- tastrophe of spacetime has some deep cosmological means. According to the some interested subjects in the Process of evolution of the universe the catastrophe nature of the Finsler spacetime and its cosmological impli= cations are discussed. It is shown that the nature of the universal evolution could be attributed to the geometric features of the Finsler spacetime. (see Cao, 1993)

Catastrophic mechanism of coal and gas outbursts and their prevention and control

Based on the engineering observations of coal and gas outbursts during mining processes and the experimental results,we built a thin plate mechanical model for layered and spalled coal bodies.We studied the mechanical mechanism of outbursts,due to instability,of thin plates of coal rocks under the action of in-plane load and normal load,by using the catastrophe theory.The total potential function is derived for the layered rock system,the cusp catastrophe model for the system is established,the bifurcation set that makes the system unstable is given,the process in which gradual change of action forces leads to catastrophic change of state is analyzed,and the effect of movement path of point(P,q) in the control space on the stability of rock plate is analyzed.The study results show that during the process of coal mining,the stability of the layered coal bodies depends not only on its physical properties and dimensions but also on the magnitudes and changing paths of the in-plane load and the normal load.When the gas in the coal bodies ahead of the mining face is pre-drained,the gas pressure can be reduced and the normal load q can be lowered.Consequently,disasters such as coal and gas outbursts can be effectively prevented.

Effect of turbulent atmosphere on the on-axis average intensity of Pearcey–Gaussian beam

The propagation characteristics of the Pearcey–Gaussian（PG） beam in turbulent atmosphere are investigated in this paper.The Pearcey beam is a new kind of paraxial beam,based on the Pearcey function of catastrophe theory,which describes diffraction about a cusp caustic.By using the extended Huygens–Fresnel integral formula in the paraxial approximation and the Rytov theory,an analytical expression of axial intensity for the considered beam family is derived.Some numerical results for PG beam propagating in atmospheric turbulence are given by studying the influences of some factors,including incident beam parameters and turbulence strengths.

Research on the Model of Household Credit Risk Evaluation of Rural Microfinance

Since rural microfinance is a credit which grants loans without collateral and guarantees to farmers,it is considerably important to evaluate and control the household credit risk.Through establishing the evaluation index system and then using catastrophe progression theory,three common types of catastrophe system and the normalization formula,we get the comprehensive evaluation.Finally,we take the empirical test and the result shows that this method is simpler and more objective which can be used by the credit cooperatives to decide whether to authorize the loans.

NONLINEAR DYNAMIC STABILITY OF COMPOSITE LAMINATED PLATES

Catastrophe theory was applied to the investigation of nonlinear dynamic stability of composite laminated plates. The influence of large deflection, initial imperfection, support conditions and ply_angle of the fibers were considered. The catastrophic models and the critical conditions of dynamic buckling of composite laminated plates are obtained.

Hydrostratigraphy and Its Relation to Ground-Water Potentiality of an Area of the Ganges River Delta in Bangladesh

To identify the potential groundwater bearing zones for future groundwater resources development of the study area, an investigation has been made using lithology, groundwater monitoring and elevation data. The stratigraphic cross-sections of the area reveal six distinct hydrostratigraphic features viz. clay-silt-sand, fine sand, fine to medium sand, medium sand, medium to coarse sand and coarse sand. On the basis of lithological information, the groundwater bearing zone of the area has been divided into two main hydrostratigraphic units viz. aquitard and aquifer, which consist of clay-silt-sand and sands of different grain sizes respectively. The aquifer zone is further divided into two categories: “small scale aquifer” made dominantly of fine and “main aquifer” comprising of fine-medium to coarse sand. The annual fluctuation of water table in the study area is observed from 4.9 m to 5.6 m. The area is demarcated as three different groundwater bearing zones based on Catastrophe theory using GIS.

Regularization of mathematical model for chip flow angle catastrophe

The chip flow angle(CFA)catastrophe in double-edged cutting results in a significant reduction in the cutting force,which can benefit the applications.However,established potential functions(i.e.,cutting power calculation functions)of mathematical models for the CFA catastrophe are presented in the form of transcendental functions with two control parameters and one state parameter,which are extremely complex.A method is proposed herein to realize the regularization of the potential functions and establish mathematical models in a standard form and with complete content for the CFA catastrophe.Using this method,the potential function of the CFA catastrophe is expanded into a k-order Taylor polynomial at each midpoint of N end-to-end equally partitioned intervals of the state parameter using the Taylor function provided in MATLAB.The potential function after piecewise Taylor expansion is transformed into the same form as the potential function of the standard cusp catastrophe model by truncating the first five terms of the Taylor polynomial and eliminating the third-order term of the state parameter with elementary transformation.Hence,the regularization of potential function is realized.Subsequently,the regularization of equilibrium surface and bifurcation set can be realized based on the conclusions of the catastrophe theory.Regularization errors of the potential function,equilibrium surface,and bifurcation set are defined to evaluate the effectiveness of this regularization method.The problem of calculating regularization errors is regarded as an optimization problem.The‘‘simulannealbnd’’function provided in MATLAB is used to solve the problem.Applying the proposed method,the regularization of a mathematical model for the CFA catastrophe established by the predecessor is completed;a mathematical model(i.e.,standard cusp catastrophe model)in a standard form and with complete content for the CFA catastrophe is established;and the corresponding regularization errors are analyzed.The regularization errors of the potential function,equilibrium surface,and bifurcation set curves are 5.4855910-4%,0.3206%,and 4.6539%,respectively.Based on the equilibrium surface and the bifurcation set curves constructed using the regularized mathematical model for the CFA catastrophe,the mechanism of the CFA catastrophe and the specific approach to render the cutting system operable in a low-energy consumption state by controlling the historical change path of the control point are analyzed.This study will promote the rational use of the CFA catastrophe.

THE NONLINEAR CUSP-CATASTROPHE MODEL OF THE SEDIMENT TRANSPORT RATE

In the catastrophe theory of nonlinear science, the intensity of water flow Θ and the coefficient of non uniform sediment m are regarded as two bound variables, and the intensity of bed load transport Φ as the state variable in the motion of non uniform sediment in cusp catastrophe model. Based on the standard equation of the cusp catastrophe theory, the relation equation between the intensity of bed load transport Φ and the intensity of water flow Θ has been derived by used coordinate transform and topology transform. The equation of bed load transport rate was built on the cusp catastrophe theory of nonlinear science. The others are applied to verify this equation, that the results calculated by the cusp catastrophe equation agree well with the other equations. This indicates that the cusp catastrophe equation is reasonable, and the results fully reflect the characteristics of threshold motion and transport of non uniform sediment. The purpose of this paper is to explore the incipient motion and transport laws of non uniform sediment from the viewpoint of nonlinear science.

Hysteresis behaviors of compressor rotating stall with cusp catastrophic model

Rotating stall is a complex nonlinear dynamic phenomenon which is always characterized by catastrophe and hysteresis in high aerodynamic-loading compressor. Exploring the key contributing factors and characteristic rules of hysteresis is very important for compressor design and flow instability control. In this paper, a novel model method is proposed to analyze the hysteresis behaviors to extend the understanding of compressor rotating stall. The equilibrium states of compressor system under different conditions are first described based on Moore-Greitzer model. Then,through assessing the stability of the equilibrium points by Liapunov＇s theorem, the ratio of shutoff head to compressor characteristic semi-height is found to affect the stall hysteresis： the size of hysteresis loop will gradually decrease, even disappear with the increase of the ratio. Combing the effects of both the ratio and throttle coefficient, the hysteresis behaviors of compressor stall under multi-parameters can be found to be consistent with the topological properties of cusp catastrophic model by Thom＇s catastrophe theory. Finally, according to topological invariant rules, from the perspective of potential function, the equilibrium surface equation of compressor system is developed by standard cusp catastrophic model to describe the various hysteresis behaviors of compressor rotating stall along different control routes.

Study on effects of thickness on airfoil-stall at low Reynolds numbers by cusp-catastrophic model based on GA(W)-1 airfoil

The phenomena of an airfoil stall present the behaviors of catastrophe and hysteresis at low Reynolds numbers.Numerical simulation results of two-dimensional airfoil GA(W)-1 show that the width of the hysteresis loop of airfoil stall will gradually decrease and even disappear with the decrease of thickness ratio.These nonlinear characteristics are in accordance with the topological features of the cusp catastrophic model.According to the topological invariant principle,a novel topological mapping method is developed to establish the mapping relationship between cusp catastrophic model and stall characteristics of the airfoil,then the effect of thickness ratio on airfoil stall is successfully described quantitatively by cusp catastrophic model.Further,based on the established topological mapping relationship,combined with the mean flow field of the airfoil stall,potential function approach of cusp catastrophic model is first introduced to interpret the catastrophe and hysteresis of the airfoil stall,and it is found that as the thickness ratio decreases,the system’s maximal potential energy gradually disappears,and the short separation bubble at the leading edge of the airfoil changes to long separation bubble,so the airfoil stall changes from a bistable system to a monostable system.

Assessment of recharge capacity potential of groundwater using comparative multi-criteria decision analysis approaches

Groundwater resources have always been some of the most valuable resources of human settlements.Climate changes and ever-increasing water demands registered in the last century have led to diminishing levels of groundwater reserves,as well as reduced recharging potential.Therefore,in order to use groundwater aquifers in a sustainable manner,it is required to identify areas with higher replenishing potential.The current study addresses the issue of generating a map for identifying differently ranked groundwater recharging potential values,in the aquifers of the Moldavian Plain region,Romania.For the purpose of conducting the analysis,maps were created through GIS based multi-criteria Analytic Hierarchy Process(AHP)and Catastrophe Theory(CT),with seven relevant,thematic,spatial layers:precipitation distribution,lithological strata,soil texture,declivity,drainage density,land use and the distribution of groundwater level tendencies.The results of the two methods of analysis are similar.Prediction differences are of maximum 3%,in the case of extreme classes(very bad and very good)and in the case of middle classes the deviation is not greater than 0.4%.Following the validation of the results generated by the two methods that were applied,it was observed that the predictions offered by CT are more accurate.This aspect can be based on the fact that the main factors that contribute to the prediction are different.This type of workflow emphasizes the necessity of implementing appropriate groundwater management plans for mitigating reservoir scarcity/depletion,and recommending sustainable solutions for future groundwater exploitation practices.

Cross-fault Newton force measurement for Earthquake prediction

Earthquake prediction is a common scientific challenge for academics worldwide.This dilemma originates from the lack of precursory indicators that meet the sufficient and necessary conditions of earthquake occurrence,which may be the root cause of the failure of earthquake prediction.In light of this,a double-block catastrophic mechanics theory for earthquakes based on cross-fault Newton force measurement is proposed herein.Based on this theory and laboratory physical model tests of seismic Newton force monitoring,a new academic thought is envisioned“the sufficient and necessary condition for earthquake occurrence is the change of Newton force,and the sudden drop of Newton force on the fault surface can be used as a predictor of earthquake disaster.”Several equipment systems have been independently developed,and the technology has been successfully applied to engineering practice.This concept has currently been proven in small-scale double-block catastrophic events such as landslides.Based on the double-block catastrophic mechanics theory,landslides and earthquakes have the similar nature but different scales.According to the on-site monitoring of landslides,it is verified that the sudden drop of Newton force can be used as a predictor of landslide disaster which successfully solves the problem of short-term landslide prediction.The introduction of cross-fault Newton force measurement technology and idea has laid a foundation for improving the method and level of international earthquake monitoring and solving the world-class scientific problem of short-term earthquake prediction.