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 deepl...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 .展开更多
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 c...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.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
Guastello’s polynomial regression method for solving cusp catastrophe model has been widely applied to analyze nonlinear behavior outcomes. However, no statistical power analysis for this modeling approach has been r...Guastello’s polynomial regression method for solving cusp catastrophe model has been widely applied to analyze nonlinear behavior outcomes. However, no statistical power analysis for this modeling approach has been reported probably due to the complex nature of the cusp catastrophe model. Since statistical power analysis is essential for research design, we propose a novel method in this paper to fill in the gap. The method is simulation-based and can be used to calculate statistical power and sample size when Guastello’s polynomial regression method is used to do cusp catastrophe modeling analysis. With this novel approach, a power curve is produced first to depict the relationship between statistical power and samples size under different model specifications. This power curve is then used to determine sample size required for specified statistical power. We verify the method first through four scenarios generated through Monte Carlo simulations, and followed by an application of the method with real published data in modeling early sexual initiation among young adolescents. Findings of our study suggest that this simulation-based power analysis method can be used to estimate sample size and statistical power for Guastello’s polynomial regression method in cusp catastrophe modeling.展开更多
Current methods that utilize simple data or models to evaluate soil restoration under ecological restoration are not sufficiently rigorous.Soil restoration under ecological restoration measures was evaluated in the re...Current methods that utilize simple data or models to evaluate soil restoration under ecological restoration are not sufficiently rigorous.Soil restoration under ecological restoration measures was evaluated in the red soil hilly region of China by applying the catastrophe model.Among 89 soil sites selected,26(29.21%) were in the middle lobe,10(11.24%) in the upper lobe,and 53(70.79%)in the lower lobe of the process surface in the Cusp catastrophe model.The catastrophic direction of the 26 unstable soil sites was to the upper lobe of the process surface according to vegetation cover change and fieldwork.There was a significant negative correlation of the variation in bifurcation set(? value) with vegetation cover increase,and a higher vegetation cover increase was related to higher unstable probability.The four ecological restoration measures were listed in the order:low-quality forest improvement(LQFI)>arbor-bush-herb mixed plantation(ABHMP)>orchard improvement(OI)>closing measures(CM) according to the proportions of unstable soil sites,which were all higher than no restoration measure,while they were in the order:LQFI<ABHMP<OI<CM according to their ? values,which were all lower than those of no restoration measure.Farmers' assessment of soil restoration under the four ecological restoration measures was in accordance with the proportions of unstable soil sites and inversely proportional to the? value.Therefore,farmers' assessment can prove the evaluation of soil restoration under ecological restoration measures based on catastrophe model.展开更多
The Graz Ionospheric Flux Tube Simulations （GIFTS） has been improved. The improved GIFTS model was used to numerically investigate the energy particle precipitation on the distribution of electron density in the ion...The Graz Ionospheric Flux Tube Simulations （GIFTS） has been improved. The improved GIFTS model was used to numerically investigate the energy particle precipitation on the distribution of electron density in the ionospheric cusp foot-point region under conditions of large plasma convection during magnetic storm. After including the effects of low energy incident particles, the ionospheric electron densities increase remarkably above altitude of -250 km, showing a peak at about 350 km. The percent enhancements of electron densities increase gradually with altitude, exceed- ing 60% near the upper boundary of the calculation. The calculated ionospheric F2-peak was remarkably enhanced and lifted up by the incident low energy electrons.展开更多
文摘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 .
文摘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.
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.
文摘Guastello’s polynomial regression method for solving cusp catastrophe model has been widely applied to analyze nonlinear behavior outcomes. However, no statistical power analysis for this modeling approach has been reported probably due to the complex nature of the cusp catastrophe model. Since statistical power analysis is essential for research design, we propose a novel method in this paper to fill in the gap. The method is simulation-based and can be used to calculate statistical power and sample size when Guastello’s polynomial regression method is used to do cusp catastrophe modeling analysis. With this novel approach, a power curve is produced first to depict the relationship between statistical power and samples size under different model specifications. This power curve is then used to determine sample size required for specified statistical power. We verify the method first through four scenarios generated through Monte Carlo simulations, and followed by an application of the method with real published data in modeling early sexual initiation among young adolescents. Findings of our study suggest that this simulation-based power analysis method can be used to estimate sample size and statistical power for Guastello’s polynomial regression method in cusp catastrophe modeling.
基金supported by the National Natural Science Foundation of China(Nos.41371512 and 41171232)the Natural Science Foundation of Fujian Province,China(No.2017J01462)
文摘Current methods that utilize simple data or models to evaluate soil restoration under ecological restoration are not sufficiently rigorous.Soil restoration under ecological restoration measures was evaluated in the red soil hilly region of China by applying the catastrophe model.Among 89 soil sites selected,26(29.21%) were in the middle lobe,10(11.24%) in the upper lobe,and 53(70.79%)in the lower lobe of the process surface in the Cusp catastrophe model.The catastrophic direction of the 26 unstable soil sites was to the upper lobe of the process surface according to vegetation cover change and fieldwork.There was a significant negative correlation of the variation in bifurcation set(? value) with vegetation cover increase,and a higher vegetation cover increase was related to higher unstable probability.The four ecological restoration measures were listed in the order:low-quality forest improvement(LQFI)>arbor-bush-herb mixed plantation(ABHMP)>orchard improvement(OI)>closing measures(CM) according to the proportions of unstable soil sites,which were all higher than no restoration measure,while they were in the order:LQFI<ABHMP<OI<CM according to their ? values,which were all lower than those of no restoration measure.Farmers' assessment of soil restoration under the four ecological restoration measures was in accordance with the proportions of unstable soil sites and inversely proportional to the? value.Therefore,farmers' assessment can prove the evaluation of soil restoration under ecological restoration measures based on catastrophe model.
基金the National Natural Science Foundation o China(40404015, 40390150)the Open Foundation of the Key Laboratory o Geospace Environment and Geodesy of Ministry of Education
文摘The Graz Ionospheric Flux Tube Simulations （GIFTS） has been improved. The improved GIFTS model was used to numerically investigate the energy particle precipitation on the distribution of electron density in the ionospheric cusp foot-point region under conditions of large plasma convection during magnetic storm. After including the effects of low energy incident particles, the ionospheric electron densities increase remarkably above altitude of -250 km, showing a peak at about 350 km. The percent enhancements of electron densities increase gradually with altitude, exceed- ing 60% near the upper boundary of the calculation. The calculated ionospheric F2-peak was remarkably enhanced and lifted up by the incident low energy electrons.
