The distribution of the sediment material storage quantity along the debris flow channels(SMSQ_DFC)can provide a foundation for runoffgenerated debris flow prediction or susceptibility assessment.Current models for es...The distribution of the sediment material storage quantity along the debris flow channels(SMSQ_DFC)can provide a foundation for runoffgenerated debris flow prediction or susceptibility assessment.Current models for estimating SMSQ_DFC do not consider the capacity of the channel cross-section to accommodate sediment materials.This accommodation condition serves as a limiting factor in determining whether the expected surplus of sediment materials can ultimately be stored.To address this issue,a mass-conservative index was used to represent the balance of deposit materials at any cross-section,considering the influx from upstream,outflux to downstream,and accommodation capacity.Based on this index,a new model for estimating SMSQ_DFC was developed and subsequently evaluated.The evaluation results show that the model meets the accuracy requirements with average error rates of 14.06%for self-validation and 14.81%for generalization ability validation.To assess its practical applications,the model was applied to the Yeniu Gully in Wenchuan County,Sichuan Province,an area with detailed field survey data.The results show that the model exhibits a commendable performance.Compared to traditional theoretical and semi-theoretical statistical models,our model is easier to use(input parameters can be obtained using Geographic Information Systems(GIS)).The modeling parameters chosen in this study have more theoretical significance than those used in existing purely statistical models,offering more effective technical support for estimating SMSQ_DFC.展开更多
In this paper, we derive W^(1,∞) and piecewise C^(1,α) estimates for solutions, and their t-derivatives, of divergence form parabolic systems with coefficients piecewise H¨older continuous in space variables x ...In this paper, we derive W^(1,∞) and piecewise C^(1,α) estimates for solutions, and their t-derivatives, of divergence form parabolic systems with coefficients piecewise H¨older continuous in space variables x and smooth in t. This is an extension to parabolic systems of results of Li and Nirenberg [Comm Pure Appl Math, 2003, 56:892–925] on elliptic systems. These estimates depend on the shape and the size of the surfaces of discontinuity of the coefficients, but are independent of the distance between these surfaces.展开更多
基金supported by Geological Disaster Patterns and Mitigation Strategies Under River-Reservoir Hydrodynamics in the Three Gorges Reservoir Fluctuation Zone(5000002024CC20004)the National Key Research and Development Program of China(2023YFC3007205)+1 种基金the National Natural Science Foundation of China(No.42271013)the West Light Foundation of the Chinese Academy of Sciences.
文摘The distribution of the sediment material storage quantity along the debris flow channels(SMSQ_DFC)can provide a foundation for runoffgenerated debris flow prediction or susceptibility assessment.Current models for estimating SMSQ_DFC do not consider the capacity of the channel cross-section to accommodate sediment materials.This accommodation condition serves as a limiting factor in determining whether the expected surplus of sediment materials can ultimately be stored.To address this issue,a mass-conservative index was used to represent the balance of deposit materials at any cross-section,considering the influx from upstream,outflux to downstream,and accommodation capacity.Based on this index,a new model for estimating SMSQ_DFC was developed and subsequently evaluated.The evaluation results show that the model meets the accuracy requirements with average error rates of 14.06%for self-validation and 14.81%for generalization ability validation.To assess its practical applications,the model was applied to the Yeniu Gully in Wenchuan County,Sichuan Province,an area with detailed field survey data.The results show that the model exhibits a commendable performance.Compared to traditional theoretical and semi-theoretical statistical models,our model is easier to use(input parameters can be obtained using Geographic Information Systems(GIS)).The modeling parameters chosen in this study have more theoretical significance than those used in existing purely statistical models,offering more effective technical support for estimating SMSQ_DFC.
基金supported by National Natural Science Foundation of China (Grant Nos. 11571042, 11371060 and 11631002)Fok Ying Tung Education Foundation (Grant No. 151003)National Science Foundation of USA (Grant No. DMS-0701545)
文摘In this paper, we derive W^(1,∞) and piecewise C^(1,α) estimates for solutions, and their t-derivatives, of divergence form parabolic systems with coefficients piecewise H¨older continuous in space variables x and smooth in t. This is an extension to parabolic systems of results of Li and Nirenberg [Comm Pure Appl Math, 2003, 56:892–925] on elliptic systems. These estimates depend on the shape and the size of the surfaces of discontinuity of the coefficients, but are independent of the distance between these surfaces.
