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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Uncertainty Reduction Through Data Management in the Development, Validation, Calibration, and Operation of a Hurricane Vulnerability Model

Catastrophe models estimate risk at the intersection of hazard,exposure,and vulnerability.Each of these areas requires diverse sources of data,which are very often incomplete,inconsistent,or missing altogether.The poor quality of the data is a source of epistemic uncertainty,which affects the vulnerability models as well as the output of the catastrophe models.This article identifies the different sources of epistemic uncertainty in the data,and elaborates on strategies to reduce this uncertainty,in particular through identification,augmentation,and integration of the different types of data.The challenges are illustrated through the Florida Public Hurricane Loss Model(FPHLM),which estimates insured losses on residential buildings caused by hurricane events in Florida.To define the input exposure,and for model development,calibration,and validation purposes,the FPHLM teams accessed three main sources of data:county tax appraiser databases,National Flood Insurance Protection(NFIP)portfolios,and wind insurance portfolios.The data from these different sources were reformatted and processed,and the insurance databases were separately cross-referenced at the county level with tax appraiser databases.The FPHLM hazard teams assigned estimates of natural hazard intensity measure to each insurance claim.These efforts produced an integrated and more complete set of building descriptors for each policy in the NFIP and wind portfolios.The article describes the impact of these uncertainty reductions on the development and validation of the vulnerability models,and suggests avenues for data improvement.Lessons learned should be of interest to professionals involved in disaster risk assessment and management.

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.