This paper is ttie continuation of part （Ⅰ）, which completes the derivations of the 3D global wave modes solutions, yields the stability criterion and, on the basis of the results obtained, demonstrates the selecti...This paper is ttie continuation of part （Ⅰ）, which completes the derivations of the 3D global wave modes solutions, yields the stability criterion and, on the basis of the results obtained, demonstrates the selection criterion of pattern formation.展开更多
The performance of six statistical approaches,which can be used for selection of the best model to describe the growth of individual fish,was analyzed using simulated and real length-at-age data.The six approaches inc...The performance of six statistical approaches,which can be used for selection of the best model to describe the growth of individual fish,was analyzed using simulated and real length-at-age data.The six approaches include coefficient of determination(R2),adjusted coefficient of determination(adj.-R2),root mean squared error(RMSE),Akaike's information criterion(AIC),bias correction of AIC(AICc) and Bayesian information criterion(BIC).The simulation data were generated by five growth models with different numbers of parameters.Four sets of real data were taken from the literature.The parameters in each of the five growth models were estimated using the maximum likelihood method under the assumption of the additive error structure for the data.The best supported model by the data was identified using each of the six approaches.The results show that R2 and RMSE have the same properties and perform worst.The sample size has an effect on the performance of adj.-R2,AIC,AICc and BIC.Adj.-R2 does better in small samples than in large samples.AIC is not suitable to use in small samples and tends to select more complex model when the sample size becomes large.AICc and BIC have best performance in small and large sample cases,respectively.Use of AICc or BIC is recommended for selection of fish growth model according to the size of the length-at-age data.展开更多
A method of continuous-discontinuous cellular automaton for modeling the growth and coalescence of multiple cracks in brittle material is presented. The method uses the level set to track arbitrary discontinuities, an...A method of continuous-discontinuous cellular automaton for modeling the growth and coalescence of multiple cracks in brittle material is presented. The method uses the level set to track arbitrary discontinuities, and calculation grids are independent of the discontinuities and no remeshing are required with the crack growing. Based on Grif- fith fracture theory and Mohr-Coulumb criterion, a mixed fracture criterion for multiple cracks growth in brittle mate- rial is proposed. The method treats the junction and coales- cence of multiple cracks, and junction criterion and coales- cence criterion for brittle material are given, too. Besides, in order to overcome the tracking error in the level set ap- proximation for crack junction and coalescence, a dichotomy searching algorithm is proposed. Introduced the above the- ories into continuous-discontinuous cellular automaton, the present method can be applied to solving multiple crack growth in brittle material, and only cell stiffness is needed and no assembled global stiffness is needed. Some numerical examples are given to shown that the present method is efficient and accurate for crack junction, coalescence and percolation problems.展开更多
Dendritic pattern formation at the interface between liquid and solid is a commonly observed phenomenon in crystal growth and solidification process. The theoretical investigation of dendritic growth is one of the mos...Dendritic pattern formation at the interface between liquid and solid is a commonly observed phenomenon in crystal growth and solidification process. The theoretical investigation of dendritic growth is one of the most profound and highly challenging subjects in the broad areas of interfacial pattern formation, condensed matter physics and materials science, preoccupying many researchers from various areas. Some longstanding key issues on this subject finally gained a breakthrough in the late of last century, via the ＇Interracial Wave （IFW） Theory＇ on the ground of systematical global stability analysis of the basic state of dendritic growth. The original form of the IFW theory mainly focus on the investigation of various axi-symmetric unsteady perturbed modes solutions around the axi-symmetrie basic state of system of dendritic growth. In reality, the system may allow various non-axi-symmetric, unsteady perturbed states. Whether or not the system of dendritic growth allows some growing non-axi-symmetric modes？ Will the stationary dendritic pattern be destroyed by some of such non-axi- symmetric modes？ Or, in one word, what is the stability property of the system, once the non-axi-symmetric modes can be evoked？ The answers for these questions are important for the solid foundation of IFW theory. The present work attempts to settle down these issues and develop a three-dimensional （3D） interfacial wave theory of dendritic growth. Our investigations verify that dendritic growth indeed allows a discrete set of non-axi-symmetric unstable global wave modes, which gives rise to a set of multiple arms spiral waves propagating along the Ivantsov＇s paraboloid.展开更多
传统断裂判据在分析岩石裂纹尖端起裂特性时忽略了非奇异项参数的影响,从而导致理论结果与试验结果产生较大的偏差。比例边界有限元法(Scaled boundary finite element method-SBFEM)是一种半解析的数值计算方法,可以较精确的计算实数...传统断裂判据在分析岩石裂纹尖端起裂特性时忽略了非奇异项参数的影响,从而导致理论结果与试验结果产生较大的偏差。比例边界有限元法(Scaled boundary finite element method-SBFEM)是一种半解析的数值计算方法,可以较精确的计算实数、复数以及幂-对数奇异性问题同时不需要对裂纹尖端进行特殊处理,应力强度因子等裂尖奇异参数都可以根据定义直接进行提取。基于此方法对复合型岩石裂纹尖端奇异参数I、II型应力强度因子和T应力进行了提取,并建立了考虑T应力的断裂准则,对不同裂纹形式下岩石的起裂特性进行研究,并与现有试验结果进行对比。结果表明,T应力为正值时会加剧裂纹扩展,T应力为负值时会抑制裂纹扩展,可见裂纹尖端的非奇异参数即T应力的影响不容忽视。展开更多
基金supported by the Nankai University, China and in part by NSERC Grant of Canada
文摘This paper is ttie continuation of part （Ⅰ）, which completes the derivations of the 3D global wave modes solutions, yields the stability criterion and, on the basis of the results obtained, demonstrates the selection criterion of pattern formation.
基金Supported by the High Technology Research and Development Program of China (863 Program,No2006AA100301)
文摘The performance of six statistical approaches,which can be used for selection of the best model to describe the growth of individual fish,was analyzed using simulated and real length-at-age data.The six approaches include coefficient of determination(R2),adjusted coefficient of determination(adj.-R2),root mean squared error(RMSE),Akaike's information criterion(AIC),bias correction of AIC(AICc) and Bayesian information criterion(BIC).The simulation data were generated by five growth models with different numbers of parameters.Four sets of real data were taken from the literature.The parameters in each of the five growth models were estimated using the maximum likelihood method under the assumption of the additive error structure for the data.The best supported model by the data was identified using each of the six approaches.The results show that R2 and RMSE have the same properties and perform worst.The sample size has an effect on the performance of adj.-R2,AIC,AICc and BIC.Adj.-R2 does better in small samples than in large samples.AIC is not suitable to use in small samples and tends to select more complex model when the sample size becomes large.AICc and BIC have best performance in small and large sample cases,respectively.Use of AICc or BIC is recommended for selection of fish growth model according to the size of the length-at-age data.
基金supported by the National Key Basic Research Program of China(2013CB036405)the National Natural Science Foundation of China(11002154,41272349,and 41372315)the CAS/SAFEA International Partnership Program for Creative Research Teams(KZCX2-YW-T12)
文摘A method of continuous-discontinuous cellular automaton for modeling the growth and coalescence of multiple cracks in brittle material is presented. The method uses the level set to track arbitrary discontinuities, and calculation grids are independent of the discontinuities and no remeshing are required with the crack growing. Based on Grif- fith fracture theory and Mohr-Coulumb criterion, a mixed fracture criterion for multiple cracks growth in brittle mate- rial is proposed. The method treats the junction and coales- cence of multiple cracks, and junction criterion and coales- cence criterion for brittle material are given, too. Besides, in order to overcome the tracking error in the level set ap- proximation for crack junction and coalescence, a dichotomy searching algorithm is proposed. Introduced the above the- ories into continuous-discontinuous cellular automaton, the present method can be applied to solving multiple crack growth in brittle material, and only cell stiffness is needed and no assembled global stiffness is needed. Some numerical examples are given to shown that the present method is efficient and accurate for crack junction, coalescence and percolation problems.
基金supported by the Nankai University, China and in part by NSERC Grant of Canada
文摘Dendritic pattern formation at the interface between liquid and solid is a commonly observed phenomenon in crystal growth and solidification process. The theoretical investigation of dendritic growth is one of the most profound and highly challenging subjects in the broad areas of interfacial pattern formation, condensed matter physics and materials science, preoccupying many researchers from various areas. Some longstanding key issues on this subject finally gained a breakthrough in the late of last century, via the ＇Interracial Wave （IFW） Theory＇ on the ground of systematical global stability analysis of the basic state of dendritic growth. The original form of the IFW theory mainly focus on the investigation of various axi-symmetric unsteady perturbed modes solutions around the axi-symmetrie basic state of system of dendritic growth. In reality, the system may allow various non-axi-symmetric, unsteady perturbed states. Whether or not the system of dendritic growth allows some growing non-axi-symmetric modes？ Will the stationary dendritic pattern be destroyed by some of such non-axi- symmetric modes？ Or, in one word, what is the stability property of the system, once the non-axi-symmetric modes can be evoked？ The answers for these questions are important for the solid foundation of IFW theory. The present work attempts to settle down these issues and develop a three-dimensional （3D） interfacial wave theory of dendritic growth. Our investigations verify that dendritic growth indeed allows a discrete set of non-axi-symmetric unstable global wave modes, which gives rise to a set of multiple arms spiral waves propagating along the Ivantsov＇s paraboloid.
文摘传统断裂判据在分析岩石裂纹尖端起裂特性时忽略了非奇异项参数的影响,从而导致理论结果与试验结果产生较大的偏差。比例边界有限元法(Scaled boundary finite element method-SBFEM)是一种半解析的数值计算方法,可以较精确的计算实数、复数以及幂-对数奇异性问题同时不需要对裂纹尖端进行特殊处理,应力强度因子等裂尖奇异参数都可以根据定义直接进行提取。基于此方法对复合型岩石裂纹尖端奇异参数I、II型应力强度因子和T应力进行了提取,并建立了考虑T应力的断裂准则,对不同裂纹形式下岩石的起裂特性进行研究,并与现有试验结果进行对比。结果表明,T应力为正值时会加剧裂纹扩展,T应力为负值时会抑制裂纹扩展,可见裂纹尖端的非奇异参数即T应力的影响不容忽视。
