Drought generally has significant impacts on crops.It is essential to quantitatively evaluate the relationship between crop production and drought degree to provide technical support for drought disaster prevention.In...Drought generally has significant impacts on crops.It is essential to quantitatively evaluate the relationship between crop production and drought degree to provide technical support for drought disaster prevention.In this study,a drought degree index that can reflect the changes in precipitation,evapotranspiration,and soil moisture was developed on the basis of crop yield reduction rate.Four drought scenarios were set up to simulate the effects of meteorological drought on drought degree of crops at different growth stages.A cusp catastrophe model was constructed to analyze the mutation characteristics of the drought degree of maize at different growth stages under different meteorological drought conditions.Xi'an City in China was selected as the study area,and summer maize was selected as the research crop.Precipitation and crop yield data from 1951 to 2010 were used as the fundamental data to investigate drought degree mutation of summer maize.The results show that,under the meteorological drought conditions at the emergence-jointing stage,drought degree may change abruptly,and soil moisture content at the sowingemergence,jointing-tasseling,and tasseling-mature stages should be kept higher than 39%.展开更多
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 ...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.展开更多
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,fi...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.展开更多
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 d...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.展开更多
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 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.展开更多
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 drawi...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.展开更多
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 calcula...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.展开更多
基金This work was supported by the Key Scientific and Technological Research Project in Henan Province(Grant No.192102110199).
文摘Drought generally has significant impacts on crops.It is essential to quantitatively evaluate the relationship between crop production and drought degree to provide technical support for drought disaster prevention.In this study,a drought degree index that can reflect the changes in precipitation,evapotranspiration,and soil moisture was developed on the basis of crop yield reduction rate.Four drought scenarios were set up to simulate the effects of meteorological drought on drought degree of crops at different growth stages.A cusp catastrophe model was constructed to analyze the mutation characteristics of the drought degree of maize at different growth stages under different meteorological drought conditions.Xi'an City in China was selected as the study area,and summer maize was selected as the research crop.Precipitation and crop yield data from 1951 to 2010 were used as the fundamental data to investigate drought degree mutation of summer maize.The results show that,under the meteorological drought conditions at the emergence-jointing stage,drought degree may change abruptly,and soil moisture content at the sowingemergence,jointing-tasseling,and tasseling-mature stages should be kept higher than 39%.
文摘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.
基金This research was funded by the National Key Research and Development Program of China(2018YFD0200402)Ph.D.Programs of the Foundation of Ministry of Education of China(20130204110004).
文摘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.
文摘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.
基金financial support from the Czech Science Foundation under the 20-17295S“Cryptoassets:Pricing,Interconnectedness,Mining,and their Interactions”project and from the Charles University PRIMUS program(project PRIMUS/19/HUM/17)Jiri Kukacka gratefully acknowledges financial support from the Charles University UNCE program(project UNCE/HUM/035)supported by the Cooperatio Program at Charles University,research area Economics.
文摘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.
文摘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.
基金the National Natural Science Foundation of China(Grant No.51675203).
文摘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.
