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Simulation of maize drought degree in Xi'an City based on cusp catastrophe model

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Water Science and Engineering 2021年第1期14卷 28-35页

作者： Hai-tao Chen Ji He Wen-chuan Wang Xiao-nan Chen School of Water Resources North China University of Water Resources and Electric PowerZhengzhou 450045China Construction and Administration Bureau of South-to-North Water Diversion Middle Route Project Beijing 100038China

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%.

关键词： cusp catastrophe Drought degree Crop growth period Soil moisture content Maize

A Nonlinear Coupled Soil Moisture-Vegetation Model

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Advances in Atmospheric Sciences 2005年第3期22卷 337-342页

作者：刘式适刘式达付遵涛孙岚 School of Physics & Laboratory for Severe Storm and Flood DisasterPeking University Beijing 100871 School of Physics & Laboratory for Severe Storm and Flood DisasterPeking University Beijing 100871 State Key Laboratory for Turbulence and Complex Systems Peking University Beijing 100871 School of Physics & Laboratory for Severe Storm and Flood Disaster Peking University Beijing 100871 State Key Laboratory for Turbulence and Complex Systems Peking University Beijing 100871 Chinese Academy of Meteorological Sciences Beijing 100081

Based on the physical analysis that the soil moisture and vegetation depend mainly on the precipitation and evaporation as well as the growth, decay and consumption of vegetation a nonlinear dynamic coupled system of soil moisture-vegetation is established. Using this model, the stabilities of the steady states of vegetation are analyzed. This paper focuses on the research of the vegetation catastrophe point which represents the transition between aridness and wetness to a great extent. It is shown that the catastrophe point of steady states of vegetation depends mainly on the rainfall P and saturation value υ0, which is selected to balance the growth and decay of vegetation. In addition, when the consumption of vegetation remains constant, the analytic solution of the vegetation equation is obtained.

关键词： vegetation steady states equilibrium points catastrophe point cusp catastrophe

catastrophe FRACTURE OF THIN-WALL PRESSURE TUBES

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Applied Mathematics and Mechanics(English Edition) 2002年第2期23卷 146-149页

作者： WEI De-min(魏德敏) YANG Gui-tong(杨桂通) Department of Civil Engineering South China University of TechnologyGuangzhou510640 P R China Applied Mechanical Institute Taiyuan University of TechnologyTaiyuan030024 P R China

catastrophe theory was used to investigate the fracture behavior of thin-wall cylindrical tubes subjected to internal explosive pressure. Based on the energy theory and catastrophe theory, a cusp catastrophe model for... 详细信息

关键词： pressure tube brittle fracture cusp catastrophe bifurcation set

A catastrophe ANALYSIS ON THE STABILITY OF THE CRACK GROWTH IN THREE-POINT BENDING SPECIMENS

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Acta Mechanica Solida Sinica 1996年第2期9卷 179-183页

作者： Wei Demin Fan Xuejun, Taiyuan Unversity of Technology, Taiyuan 030024 Taiyuan University of Technology Taiyuan 030024

This paper presents an attempt at the application of catastrophe theory to the stability analysis of J-controlled crack growth in three-point bending specimens. By introducing the solutions of J-integral in the completely yielding state for the ideal plastic material, the critical condition of losing stability for the crack propagation in the specimen is obtained, based on the cusp catastrophe theory. The process of the crack growth from geometrical sense is described.

关键词： crack growth stability cusp catastrophe J-integral three-point bending specimen

AN EXAMPLE OF APPLICATIONS OF THE ELEMENTARY catastrophe THEORY IN HAMILTONIAN SYSTEMS

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Acta Mechanica Sinica 1985年第2期1卷 185-192页

作者： Ling Fuhua Wei Huanmin Shanghai Jiaotong University Shanghai Jiaotong University Shanghai China

The convection in atmosphere discussed in ref. [1] is rigorously treated by consider-ing the variation of environmental temperature T(z) with the height. This represents an example ofapplications of the elementary cat... 详细信息

关键词： elementary catastrophe theory Hamiltonian system cusp catastrophe convection in atmosphere nonlinear convection current model.

A nonequilibrium phase transition in immune response

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Chinese Physics B 2004年第7期13卷 1171-1176页

作者：张伟漆安慎 DepartmentofSystemScience BeijingNormalUniversityBeijing100875China DepartmentofPhysics BeijingNormalUniversityBeljing100875China

The dynamics of immune response correlated to signal transduction in immune thymic cells (T cells) is studied.In particular, the problem of the phosphorylation of the immune-receptor tyrosine-based activation motifs (ITAM) is explored. A nonlinear model is established on the basis of experimental observations. The behaviours of the model can be well analysed using the concepts of nonequilibrium phase transitions. In addition, the Riemann-Hugoniot cusp catastrophe is demonstrated by the model. Due to the application of the theory of nonequilibrium phase transitions,the biological phenomena can be clarified more precisely. The results can also be used to further explain the signal transduction and signal discrimination of an important type of immune T cell.

关键词： nonequilibrium phase transitions ITAM cusp catastrophe

Application of catastrophe Theory in 3D Seismic Data Interpretation of Coal Mine

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International Journal of Mining Science and Technology 2005年第4期15卷 339-343页

作者： ZHAO Mu-hua, YANG Wen-qiang, CUI Hui-xia College of Resource and Earth Sciences, China University of Mining & Technology, Xuzhou, Jiangsu 221008, China College of Resource and Earth Sciences China University of Mining & TechnologyXuzhouJiangsu 221008China

In order to detect fault exactly and quickly, cusp catastrophe theory is used to interpret 3D coal seismic data in this paper. By establishing a cusp model, seismic signal is transformed into standard form of cusp catastrophe and catastrophe parameters, including time-domain catastrophe potential, time-domain catastrophe time, frequency-domain catastrophe potential and frequency- domain degree, are calculated. catastrophe theory is used in 3D seismic structural interpretation in coal mine. The results show that the position of abnormality of the catastrophe parameter profile or curve is related to the location of fault, and the cusp catastrophe theory is effective to automatically pick up geology information and improve the interpretation precision in 3D seismic data.

关键词： catastrophe theory cusp catastrophe cusp model seismic data interpretation

Instability Leading to Rockbursts and Nonlinear Evolutionary Mechanisms for Coal-pillar-and-roof System

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Instability Leading to Rockbursts and Nonlinear Evolutionary...

Nonlinear evolutionary mechanisms of instability of planar-slip slope:catastrophe,bifurcation,chaos and physical prediction

中国科学院地质与地球物理研究所2006学术年会

作者： Jiu Jimmy Jiao Department of Earth Sciences The University of Hong KongPokfulam RoadHong KongPeople’s Republic of China

This paper studies the unstable mechanisms of the mechanical system that is composed of the stiff hosts(roof and floor) and the coal pillar using catastrophe theory.It is assumed that the roof is an elastic beam and the coal pillar is a strain-softening medium which can be described by the Weibull’s distribution theory of strength.It is found that the instability leading to rockburst depends mainly on the system’s stiffness ratio k,which is defined as the ratio of the flexural stiffness of the beam to the absolute value of the stiffness at the turning point of the constitutive curve of the coal pillar,and the homogeneity index m or shape parameter of the Weibull’s distribution of the coal pillar.A nonlinear dynamical model,which is derived by considering the time-dependent property of the coal pillar,is used to study the physical prediction of rockbursts. An algorithm of inversion on the nonlinear dynamical model is suggested for seeking the precursory abnormality from the observed series of roof settlement.A case study of the Muchengjian coal mine is conducted and its nonlinear dynamical model is established from the observation series using the algorithm of inversion.An important finding is that the catastrophic characteristic index D(i.***.the bifurcation set of the algorithm of inversion) drastically increases to a high peak value and then quickly drops close to instability.From the viewpoint of damage mechanics of coal pillar,a dynamical model of acoustic emission(AE) is established for modeling the AE activities in the evolutionary process of the system.It is revealed that the values of m and the evolutionary path(D=0 or D≠0) of the system have a great impact on the AE activity patterns and characters.

关键词： cusp catastrophe instability stiffness ratio nonlinear physical prediction acoustic emission

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Nonlinear evolutionary mechanisms of instability of planar-s...