Liutex is a mathematical definition of vortex,which is called the third generation of vortex definition and identification.This paper introduces the mathematical foundation of the Liutex theoretical system including d...Liutex is a mathematical definition of vortex,which is called the third generation of vortex definition and identification.This paper introduces the mathematical foundation of the Liutex theoretical system including differences in definition and operations between tensor/vector and matrix.The right version of velocity gradient tensor matrix is given to correct the old version which has been widely distributed by many mathematics and fluid dynamics textbooks.A unique velocity gradient principal matrix is provided.The mathematical foundation for Liutex definition is given.The coordinate rotation(Q-and P-rotation)for principal coordinate system and principal matrix is derived,which is the key issue of the new fluid kinematics.The divergence of velocity gradient tensor is given in different forms which may be beneficial in developing new governing equations for fluid dynamics.展开更多
Objective:To establish a scientific,objective and applicable index system for evaluating out- standing biomedical scientists for science foundation of Shanghai.Methods:According to the principal in- dices that have be...Objective:To establish a scientific,objective and applicable index system for evaluating out- standing biomedical scientists for science foundation of Shanghai.Methods:According to the principal in- dices that have been used in the developed countries for evaluating their talented personnel and the reality of our country,an index system was set up to evaluate the outstanding biomedical scientists for Shanghai science foundation.The following parameters were used to simplify the indices.,correlation coefficient, multiple correlation coefficient,partial correlation coefficient,creditability,and discriminatory power. And analytic hierarchy process was used to determine the weights of each index.Results and Conclusions: The established index system is scientific and applicable;it is helpful for cultivating and evaluating out- standing biomedical scientists.展开更多
Considering the level distribution of soil layers, the soils surrounding pile are simulated with level finite layer elements. Supposing that the vertical deformation of the soil elements surrounding pile varies in the...Considering the level distribution of soil layers, the soils surrounding pile are simulated with level finite layer elements. Supposing that the vertical deformation of the soil elements surrounding pile varies in the form of exponent function with radial distance, and considering the nonlinear constitutive relation of stress and strain, the stiffness matrix is established. The mechanics behavior of the pile—soil interface is simulated with a nonlinear interface element. This method can truly express the behavior of the pile-soil system. The load-settlement relation Q-S curves of two big diameter prototype piles on bearing test are analyzed, and satisfying results are obtained. This method is reasonable in theory and feasible in engineering.展开更多
基金The current development of Liutex theory and application is under support by US National Science Foundation(Grant No.2300052)the University of Texas at Arlington for providing financial support.
文摘Liutex is a mathematical definition of vortex,which is called the third generation of vortex definition and identification.This paper introduces the mathematical foundation of the Liutex theoretical system including differences in definition and operations between tensor/vector and matrix.The right version of velocity gradient tensor matrix is given to correct the old version which has been widely distributed by many mathematics and fluid dynamics textbooks.A unique velocity gradient principal matrix is provided.The mathematical foundation for Liutex definition is given.The coordinate rotation(Q-and P-rotation)for principal coordinate system and principal matrix is derived,which is the key issue of the new fluid kinematics.The divergence of velocity gradient tensor is given in different forms which may be beneficial in developing new governing equations for fluid dynamics.
文摘Objective:To establish a scientific,objective and applicable index system for evaluating out- standing biomedical scientists for science foundation of Shanghai.Methods:According to the principal in- dices that have been used in the developed countries for evaluating their talented personnel and the reality of our country,an index system was set up to evaluate the outstanding biomedical scientists for Shanghai science foundation.The following parameters were used to simplify the indices.,correlation coefficient, multiple correlation coefficient,partial correlation coefficient,creditability,and discriminatory power. And analytic hierarchy process was used to determine the weights of each index.Results and Conclusions: The established index system is scientific and applicable;it is helpful for cultivating and evaluating out- standing biomedical scientists.
文摘Considering the level distribution of soil layers, the soils surrounding pile are simulated with level finite layer elements. Supposing that the vertical deformation of the soil elements surrounding pile varies in the form of exponent function with radial distance, and considering the nonlinear constitutive relation of stress and strain, the stiffness matrix is established. The mechanics behavior of the pile—soil interface is simulated with a nonlinear interface element. This method can truly express the behavior of the pile-soil system. The load-settlement relation Q-S curves of two big diameter prototype piles on bearing test are analyzed, and satisfying results are obtained. This method is reasonable in theory and feasible in engineering.
