Protection motivation theory and cigarette smoking among vocational high school students in China:a cusp catastrophe modeling analysis

Background:Tobacco use is one of the greatest public health problems worldwide and the hazards of cigarette smoking to public health call for better recognition of cigarette smoking behaviors to guide evidence-based policy.Protection motivation theory(PMT)provides a conceptual framework to investigate tobacco use.Evidence from diverse sources implies that the dynamics of smoking behavior may be quantum in nature,consisting of an intuition and an analytical process,challenging the traditional linear continuous analytical approach.In this study,we used cusp catastrophe,a nonlinear analytical approach to test the dual-process hypothesis of cigarette smoking.Methods:Data were collected from a random sample of vocational high school students in China(n=528).The multivariate stochastic cusp modeling was used and executed with the Cusp Package in R.The PMT-based Threat Appraisal and Coping Appraisal were used as the two control variables and the frequency of cigarette smoking(daily,weekly,occasional,and never)in the past month was used as the outcome variable.Results:Consistent with PMT,the Threat Appraisal(asymmetry,α1=0.1987,p<0.001)and Coping Appraisal(bifurcation,β2=0.1760,p<0.05)significantly predicted the smoking behavior after controlling for covariates.Furthermore,the cusp model performed better than the alternative linear and logistic regression models with regard to higher R2(0.82 for cusp,but 0.21 for linear and 0.25 for logistic)and smaller AIC and BIC.Conclusion:Study findings support the conclusion that cigarette smoking in adolescents is a quantum process and PMT is relevant to guide studies to understand smoking behavior for smoking prevention and cessation.

A Complementary Engineering-Based Building Damage Estimation for Earthquakes in Catastrophe Modeling

Catastrophe modeling for earthquakes is conventionally designed as a probabilistic model to estimate the losses based on risk and vulnerability of a portfolio of exposures for a foreseeable set of events. This approach lacks a physical science of building damage that is linked to ground-shaking characteristics. A proposed engineeringbased building damage estimation model based on established theories of seismic wave propagation and structural resonance is presented to address some of these shortcomings. A damage factor is introduced to provide an indication of the relative extent of damage to buildings.Analysis based on the proposed methodology is carried out using data derived from four case studies: the 2011 Tohoku earthquake; the 2007 Bengkulu earthquake; the 2011 Christchurch earthquake; and the 1999 Chi-Chi earthquake.Results show that the computed damage factors reasonably reflect the extent of actual damage to buildings that was observed in post-earthquake reconnaissance surveys. This indicates that the proposed damage simulation model has a promising future as a complementary assessment tool in building damage estimation in catastrophe modeling.

DESCRIPTION AND PREDICTION OF CATASTROPHE OF VIBRATION STATE FOR FAULTY ROTORS

A sudden increase of vibration amplitude with no foreboding often results in an abrupt breakdown of a mechanical system.The catastrophe of vibration state of a faulty rotor is a typical nonlinear phenomenon,and very difficult to be described and predicted with linear vibration theory.On the basis of nonlinear vibration and catastrophe theory,fhe eatastrophe of the vibration amplitude of the faulty rotor is described;a way to predict its emergence is developed.

Catastrophe model and its experimental verification ofstatic loading rock system under impact load

According to the catastrophe model for impact buckling of static loading structures, a new catastrophe model for impact loading failure of a static loading rock system was established, and one dimension (1D) catastrophe model was analyzed. The analysis results indicate that the furcation collection where catastrophe may take place is not only decided by mechanical system itself but also relates to exterior loading, which is different from the results obtained under mono-static loading where the bifurcation collection is only determined by mechanics of the system itself and has nothing to do with exterior loading. In addition, the corresponding 1D coupled static-dynamic loading experiment is designed to verify the analysis results of catastrophe model. The test is done with Instron 1342 electro-servo controlled testing system, in which medium strain rate is caused by monotony rising dynamic load. The parameters are obtained combining theoretical model with experiment. The experimental and theoretical curves of critical dynamic load vs static load are rather coincided, thus the new model is proved to be correct.

Research on traffic flow forecasting model based on cusp catastrophe theory

This paper intends to describe the relationship between traffic parameters by using cusp catastrophe theory and to deduce highway capacity and corresponding speed forecasting value through suitable transformation of catastrophe model. The five properties of a catastrophe system are outlined briefly, and then the data collected on freeways of Zhujiang River Delta, Guangdong province, China are examined to ascertain whether they exhibit qualitative properties and attributes of the catastrophe model. The forecasting value of speed and capacity for freeway segments are given based on the catastrophe model. Furthermore, speed-flow curve on freeway is drawn by plotting out congested and uncongested traffic flow and the capacity value for the same freeway segment is also obtained from speed-flow curve to test the feasibility of the application of cusp catastrophe theory in traffic flow analysis. The calculating results of catastrophe model coincide with those of traditional traffic flow models regressed from field observed data, which indicates that the deficiency of traditional analysis of relationship between speed, flow and occupancy in two-dimension can be compensated by analysis of the relationship among speed, flow and occupancy based on catastrophe model in three-dimension. Finally, the prospects and problems of its application in traffic flow research in China are discussed.

MECHANISM AND CATASTROPHE THEORY ANALYSIS OF CIRCULAR TUNNEL ROCKBURST

Mechanism of circular tunnel rockburst is that, when the carrying capacity of the centralized zone of plastic deformation in limiting state reduces, the comparatively intact part in rock mass unloads by way of elasticity; rockburst occurs immediately when the elastic energy released by the comparatively intact part exceeds the energy dissipated by plastic deformation. The equivalent strain was taken as a state variable to establish a catastrophe model of tunnel rockburst, and the computation expression of the earthquake energy released by tunnel rockburst was given. The analysis shows that, the conditions of rockburst occurrence are relative to rock＇s ratio of elastic modulus to descendent modulus and crack growth degree of rocks; to rock mass with specific rockburst tendency, there exists a corresponding critical depth of softened zone, and rockburst occurs when the depth of softened zone reaches.

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 .

Fold catastrophe model of strike-slip fault earthquake

Using a differential form of the potential energy function and taking the effect of work applied by external force in far field into account, the mechanism of strike-slip fault earthquake is analyzed. The research indicates that each characteristic displayed with a fold catastrophe model in the catastrophe theory corresPonds to a specific primary characteristic of the strike-slip fault earthquake. The fold catastrophe can describe the positions of starting and end points of a fault failure and the distance of fault dislocation. These include the description of stability of the surrounding rock-fault system before and after the earthquake. Two different illustrations about elastic energy releasing amount of the surrounding rock with the fault failure are shown with the primary characteristics mutually demonstrated. The intensity of strike-slip fault earthquake is related to the surrounding rock press and the stiffness ratio of surrounding rock and fault. The larger the surrounding rock press, the smaller the stiffness ratio. The larger the included angle between the tangential stress axis and the causative fault surface, the stronger the earthquake.

Analysis of main shock of thrust fault earthquake by catastrophe theory

The relationship between work and energy increment of a thrust fault system with quasi-static deformation can be decomposed into two parts： volume strain energy and deviation stress energy. The relationship between work and energy increment of the deviation stress of a simplified thrust fault system is analyzed based on the catastrophe theory. The research indicates that the characteristics displayed by the fold catastrophe model can appropriately describe the condition of earthquake generation, the evolvement process of main shock of thrust fault earthquake, and some important aftershock proper- ties. The bigger the surrounding press of surrounding rock is, the bigger the maximum principal stress is, the smaller the incidences of the potential thrust fault surface are, and the smaller the ratio between the tangential stiffness of surrounding rock and the slope is, which is at the inflexion point on the softened zone of the fault shearing strength curve. Thus, when earthquake occurrs, the larger the elastic energy releasing amount of sur- rounding rock is, the bigger the earthquake magnitude is, the larger the half distance of fault dislocation is, and the larger the displacement amplitude of end face of surrounding rock is. Fracturing and expanding the fault rock body and releasing the volume strain energy of surrounding rock during the earthquake can enhance the foregoing effects to- gether.

A MODEL OF BUTTERFLY CATASTROPHE FOR ANODE EFFECT IN ALUMINA ELECTROLYSIS

A model of butterfly catastrophe is confirmed based on the matching and fitting the previous experimental data from alumina electrolysis when anode effect occurs.The complicated behaviour of the cryolite-alumina melt system with varying parameters could be generally described by this model.Therefore,the anode effect and its occurrence may be thoroughly understood.

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.

Instability Analysis of Strike-Slip Fault Based on Cusp Catastrophe Model

The distribution of many active faults in western China is an important reasonfor the frequent earthquakes. With the rapid development of the western region, manymajor projects have been built there and the existence of active faults is bound to have aninfluence on the safety of the engineering structure. Therefore, it is of great significanceto study the mechanism of fault slip instability for evaluating the geological stability ofthe region and for the site selection of major projects. In this paper, cusp catastrophetheory is used to establish a cusp catastrophe model with general softened form ofstrike-slip faults on the basis of strike-slip faults. In this model, the influence of thesoftening property of fault zone on fault instability is considered. Based on this model,the conditions of slip instability of strike-slip faults are derived and further the half-slipdistance, far-field displacement and energy release equation of sliding-slip fault arerevealed. The influences of the system stiffness ratio and the softening property of thefault zone on the half-wave displacement, the far-field displacement and the energyrelease are shown. Which lays a good foundation for further research on activefault-induced earthquake mechanism.

A swallow-tail type catastrophic model of earthquake process

This paper considers the effects of damage softening and hydraulic softening on fault zone media and provides a nonlinear mechanics model of fault earthquake. Taking far field displacement,stiffness ratio and permeation parameter as control variables, we obtain a swallowtail type catastrophic model of earthquakes. Then, by this model, we study the effects of permeation, far field displacement and stiffness ratio on the preparation and the occurrence of earthquakes.

Fundamental and speculative components of the cryptocurrency pricing dynamics

The driving forces behind cryptoassets’price dynamics are often perceived as being dominated by speculative factors and inherent bubble-bust episodes.Fundamental components are believed to have a weak,if any,role in the price-formation process.This study examines five cryptoassets with different backgrounds,namely Bitcoin,Ethereum,Litecoin,XRP,and Dogecoin between 2016 and 2022.It utilizes the cusp catastrophe model to connect the fundamental and speculative drivers with possible price bifurcation characteristics of market collapse events.The findings show that the price and return dynamics of all the studied assets,except for Dogecoin,emerge from complex interactions between fundamental and speculative components,includ-ing episodes of price bifurcations.Bitcoin shows the strongest fundamentals,with on-chain activity and economic factors driving the fundamental part of the dynam-ics.Investor attention and off-chain activity drive the speculative component for all studied assets.Among the fundamental drivers,the analyzed cryptoassets present their coin-specific factors,which can be tracked to their protocol specifics and are economi-cally sound.

Evolution of seismic risk management for insurance over the past 30 years

During the past 30 years, there has been spectacular growth in the use of risk analysis and risk management tools developed by engineers in the financial and insurance sectors. The insurance, the reinsurance, and the investment banking sectors have enthusiastically adopted loss estimation tools developed by engineers in developing their business strategies and for managing their financial risks. As a result, insurance/reinsurance strategy has evolved as a major risk mitigation tool in managing catastrophe risk at the individual, corporate, and government level. This is particularly true in developed countries such as US, Western Europe, and Japan. Unfortunately, it has not received the needed attention in developing countries, where such a strategy for risk management is most needed. Fortunately, in the last five years, there has been excellent focus in developing ＂Insur Tech＂ tools to address the much needed ＂Insurance for the Masses＂, especially for the Asian Markets. In the earlier years of catastrophe model development, risk analysts were mainly concerned with risk reduction options through engineering strategies, and relatively little attention was given to financial and economic strategies. Such state-of-affairs still exists in many developing countries. The new developments in the science and technologies of loss estimation due to natural catastrophes have made it possible for financial sectors to model their business strategies such as peril and geographic diversification, premium calculations, reserve strategies, reinsurance contracts, and other underwriting tools. These developments have not only changed the way in which financial sectors assess and manage their risks, but have also changed the domain of opportunities for engineers and scientists.This paper will address the issues related to developing insurance/reinsurance strategies to mitigate catastrophe risks and describe the role catastrophe risk insurance and reinsurance has played in managing financial risk due to natural catastrophes. Historical losses and the share of those losses covered by insurance will be presented. How such risk sharing can help the nation share the burden of losses between tax paying public, the ＂at risk＂ property owners, the insurers and the reinsurers will be discussed. The paper will summarize the tools that are used by the insurance and reinsurance companies for estimating their future losses due to catastrophic natural events. The paper will also show how the results of loss estimation technologies developed by engineers are communicated to the business flow of insurance/reinsurance companies. Finally, to make it possible to grow ＂Insurance for the Masses - IFM＂, the role played by parametric insurance products and Insur Tech tools will be discussed.

Another strategy to assess sustainable development

The goal of sustainoble development is to preserve sustainabitity trod simultaneously prevent catastrophe in a man-land .system. However, almost all the existing approaches to assessing sustainable development are to measure the sustainability. namely appraise from the obverse side of the sustainable development. So it seems necessary to attack the same task on the reverse, namely to measure the passibility of eatostrophe. In this paper, with a case study of Tianjin, China. we employ catastrophe theory and models to integrate Tianjin＇s sustainable development indicators, and then deduce the catastrophe risk index （ CRI） to present the level of catastrophic possibility in the city. Applying catastrophe theory, is a new strategy to assess sustainable development and shows great practical significance, especially for those developing regions or countries, who always give more priority to their economy and therefore have more obligation to make sure whether their social economic activities might bring forth any ecological environment catastrophe. Besides, being both qualitative and quantitative, the approach could be employed to explore not only static characteristics bat also dynamic mechanism of man-land system. Although our work is only a maiden attempt and still calls for further effort to improve it, the case study of Tianjin in this paper would assure as the great promising future to apply, catastrophe theory to sustoinable devetopment modeling,

Rheological catastrophic model for soft clays

A brief review of the former studies on the mechanisms of soil rheology and microstructure is presented. Then a microstructure model and a set of rheological constitutive relations for sott clays, which describe how the rheological consolidation settlement develops, are established in the framework of the catastrophe theory. The validity of this model is verified by a series of rheological consolidation experiments with different loading rates. The experimental data show that creep deformation can be clearly observed in these tests, and the consolidation settlement is loading rate dependent. The characteristics of the deformation can be explained and reproduced successfully using the model. It can be concluded that only the biggest set of voids would collapse for one load increment. Parameters in the model, k and η, are gained by curve fitting. With only two free parameters, good fits of the data are achieved.

MECHANISM ANALYSIS AND MATHEMATICAL DESCRIPTION OF MECHANICAL ABRUPT FAULTS

Gradual faults and abrupt faults of mechanical systems are differentiated by variation patterns of state varibles.After the reasons of abrupt faults are analyzed by nonlinear dynamics,two methods establishing the mathematical models for abrupt faults are presented.As an example,a cusp catastrophe model of the vibration amplitudes of a Jeffcott rotor with nonlinear stiffness and its parameter condition of the vibration state catastrophe are obtained.

Modeling and Adaptive Sliding Mode Control of the Catastrophic Course of a High-speed Underwater Vehicle

Abstract： The mathematical model of a high-speed underwater vehicle getting catastrophe in the out-of-water course and a nonlinear sliding mode control with the adaptive backstepping approach for the catastrophic course are proposed. The speed change is large at the moment that the high-speed underwater vehicle launches out of the water to attack an air target. It causes motion parameter uncertainties and affects the precision attack ability. The trajectory angle dynamic characteristic is based on the description of the transformed state-coordinates, the nonlinear sliding mode control is designed to track a linear reference model. Furthermore, the adaptive backstepping control approach is utilized to improve the robustness against the unknown parameter uncertainties. With the proposed control of attitude tracking, the controlled navigational control system possesses the advantages of good transient performance and robustness to parametric uncertainties. These can be predicted and regulated through the design of a linear reference model that has the desired dynamic behavior for the trajectory of the high-speed underwater vehicle to attack its target. Finally, some digital simulation results show that the control system can be applied to a catastrophic course, and that it illustrates great robustness against system parameter uncertainties and external disturbances.

Stability analysis of the pillars between bedded salt cavern gas storages by cusp catastrophe model

The failure of pillars between bedded salt cavern gas storages can be seen as processes that the deformations of pillars convert from continuous gradual change system to catastrophe state,which are typical nonlinear catastrophe problems.In the paper,the cusp catastrophe model is proposed to obtain the stability factors of pillars.It can overcome the shortages of traditional strength reduction finite element method(SR FEM) and greatly improve the accuracy of stability factors obtained by numerical simulations.The influences of cavern depth,gas pressure,pillar width,and time on the stability factors are studied.Y-1 and Y-2 salt cavern gas storages,located at Jiangsu province of China,were simulated as examples.The stability factors of pillars between Y-1 and Y-2 were evaluated,and the running parameters were recommended to ensure the pillars stability.The results showed that the cusp catastrophe model has high practicability and can precisely predict the stability factors.The stability factors are equidirectional with the increase of gas pressure and pillar width,but reverse to the increase of cavern depth and time.The stability factors of pillars between Y-1 and Y-2 are small for narrow widths,which are influenced greatly by gas pressure,time,pressure difference,and gas production rate.In order to ensure the safety of pillars,the lowest gas pressure,safe running time,max.pressure difference and max.gas production rate of Y-1 and Y-2 were recommended as 7 MPa,5 years,3 MPa,and 0.50 MPa/d,respectively.