Given the definition of the reference Knudsen number for micro gas journal bearings,the range in the number is related to the viscosity of air at different temperatures. A modified Reynolds equation for micro gas jour...Given the definition of the reference Knudsen number for micro gas journal bearings,the range in the number is related to the viscosity of air at different temperatures. A modified Reynolds equation for micro gas journal bearings based on Burgdorfer's first-order slip boundary condition is proposed that takes into account the gas rarefaction effect. The finite difference method (FDM) is adopted to solve the modified Reynolds equation to obtain the pressure profiles,load capacities and attitude angles for micro gas journal bearings at different reference Knudsen numbers,bearing numbers and journal eccentricity ratios. Numerical analysis shows that pressure profiles and non-dimensional load capacities decrease markedly as gas rarefaction in-creases. Attitude angles change conversely,and when the eccentricity ratio is less than 0.6,the attitude angles rise slightly and the influence of the reference Knudsen number is not marked. In addition,the effect of gas rarefaction on the non-dimensional load capacity and attitude angle decreases with smaller bearing numbers.展开更多
The performance of rechargeable batteries and other electrochemical systems depends on the rate at which the working ion(often a cation)is transported from one electrode to the other.The cation transference number is ...The performance of rechargeable batteries and other electrochemical systems depends on the rate at which the working ion(often a cation)is transported from one electrode to the other.The cation transference number is an important transport parameter that affects this rate.The purpose of this perspective is to distinguish between approximate and rigorous methods used in the literature to measure the transference number.We emphasize the fact that this parameter is dependent on the reference frame used in the analysis;care must be taken when comparing values obtained from different sources to account for differences in reference frames.We present data obtained from a well-characterized electrolyte.We compare rigorously determined transference numbers in two reference frames with values obtained by an approximate method.We conclude with a qualitative discussion of the relationship between the transference number and salt concentration gradients that are obtained when current is drawn through a battery。展开更多
The paper summarizes the contributions of the three philosophies of mathematics—logicism, intuitionism-constructivism (constructivism for short) and formalism and their rectification—which constitute the new foundat...The paper summarizes the contributions of the three philosophies of mathematics—logicism, intuitionism-constructivism (constructivism for short) and formalism and their rectification—which constitute the new foundations of mathematics. The critique of the traditional foundations of mathematics reveals a number of errors including inconsistency (contradiction or paradox) and undefined and vacuous concepts which fall under ambiguity. Critique of the real and complex number systems reveals similar defects all of which are responsible not only for the unsolved long standing problems of foundations but also of traditional mathematics such as the 379-year-old Fermat’s last theorem (FLT) and 274-year-old Goldbach’s conjecture. These two problems require rectification of these defects before they can be resolved. One of the major defects is the inconsistency of the field axioms of the real number system with the construction of a counterexample to the trichotomy axiom that proved it and the real number system false and at the same time not linearly ordered. Indeed, the rectification yields the new foundations of mathematics, constructivist real number system and complex vector plane the last mathematical space being the rectification of the complex real number system. FLT is resolved by a counterexample that proves it false and the Goldbach’s conjecture has been proved both in the constructivist real number system and the new real number system. The latter gives to two mathematical structures or tools—generalized integral and generalized physical fractal. The rectification of foundations yields the resolution of problem 1 and the solution of problem 6 of Hilbert’s 23 problems.展开更多
This paper expounds the effect of"Qi"on human body by constructing the model of Qi,classifies the parts according to the category of Yin and Yang on the coordinate frame of 5 models of Yin and Yang,and compa...This paper expounds the effect of"Qi"on human body by constructing the model of Qi,classifies the parts according to the category of Yin and Yang on the coordinate frame of 5 models of Yin and Yang,and compares each kind of parts according to the normal image state of human body.with the running direction of integer instead of Qi,the number of Qi in each part is calculated by the method of modern number theory,and the development and changes of human physiology and diseases are explained by"Qi".To explore the Trasitional Chinese Medicine treatment method of"the morbid Qi state of the human body adjusts the qi mode,the direction of qi operation and the intensity of Qi by means of medicinal taste and acupuncture,and returns to the normal state of qi balance mode in the direction of operation".展开更多
In order to quantitatively evaluate the spurious dianeutral mixing in a global ocean model MPAS-Ocean （Model for Prediction Across Scales） using a spherical centroidal voronoi tessellations developed jointly by the ...In order to quantitatively evaluate the spurious dianeutral mixing in a global ocean model MPAS-Ocean （Model for Prediction Across Scales） using a spherical centroidal voronoi tessellations developed jointly by the National Center for Atmospheric Research and the Los Alamos National Laboratory in the United States, we choose z＊ vertical coordinate system in MPAS-Ocean, in which all physical mixing processes, such as convection adjustment and explicit diffusion parameter schemes, are omitted, using a linear equation of state. By calculating the Reference Potential Energy （RPE）, front revolution position, time rate of RPE change, probability density function distribution and dimensionless parameter 2＂, from the perspectives of resolution, viscosity, Horizontal Grid Reynolds Number （HGRN）, Rea, and momentum transmission scheme, using two ideal cases, overflow and baroclinic eddy channel, we qualitatively analyze the simulation results by comparison with the three non-isopycnal models in Ilicak et al. （2012）, i.e., MITocM, MOM, and ROMS. The results show that the spurious dianeutral mixing in the MPAS-Ocean increases over time. The spurious dianeutral transport is proportional to the HGRN directly and is reduced by increasing the lateral viscosity or using a finer resolution to control HGRN. When the HGRN is less than 10, spurious transport is reduced significantly. When using the proper viscosity closure, MPAS-Ocean performs better than MIT6c and MOM, closely to ROMS, in the 2D case without rotation, and much better than the above-mentioned three ocean models under the condition of 3D space with rotation due to the cell area difference between the hexa- gon cell and the quadrilateral cell with the same resolution. Both the Zalesak （1979） flux corrected transport scheme and Leith closure in MPAS-Ocean play an excellent role in reducing spurious dianeutral mixing. The performance of Leith scheme is preferable to the condition of three-dimensional baroclinic eddy.展开更多
基金supported by the National Natural Science Foundation of China (No. 10472101)the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20070335184)
文摘Given the definition of the reference Knudsen number for micro gas journal bearings,the range in the number is related to the viscosity of air at different temperatures. A modified Reynolds equation for micro gas journal bearings based on Burgdorfer's first-order slip boundary condition is proposed that takes into account the gas rarefaction effect. The finite difference method (FDM) is adopted to solve the modified Reynolds equation to obtain the pressure profiles,load capacities and attitude angles for micro gas journal bearings at different reference Knudsen numbers,bearing numbers and journal eccentricity ratios. Numerical analysis shows that pressure profiles and non-dimensional load capacities decrease markedly as gas rarefaction in-creases. Attitude angles change conversely,and when the eccentricity ratio is less than 0.6,the attitude angles rise slightly and the influence of the reference Knudsen number is not marked. In addition,the effect of gas rarefaction on the non-dimensional load capacity and attitude angle decreases with smaller bearing numbers.
文摘The performance of rechargeable batteries and other electrochemical systems depends on the rate at which the working ion(often a cation)is transported from one electrode to the other.The cation transference number is an important transport parameter that affects this rate.The purpose of this perspective is to distinguish between approximate and rigorous methods used in the literature to measure the transference number.We emphasize the fact that this parameter is dependent on the reference frame used in the analysis;care must be taken when comparing values obtained from different sources to account for differences in reference frames.We present data obtained from a well-characterized electrolyte.We compare rigorously determined transference numbers in two reference frames with values obtained by an approximate method.We conclude with a qualitative discussion of the relationship between the transference number and salt concentration gradients that are obtained when current is drawn through a battery。
文摘The paper summarizes the contributions of the three philosophies of mathematics—logicism, intuitionism-constructivism (constructivism for short) and formalism and their rectification—which constitute the new foundations of mathematics. The critique of the traditional foundations of mathematics reveals a number of errors including inconsistency (contradiction or paradox) and undefined and vacuous concepts which fall under ambiguity. Critique of the real and complex number systems reveals similar defects all of which are responsible not only for the unsolved long standing problems of foundations but also of traditional mathematics such as the 379-year-old Fermat’s last theorem (FLT) and 274-year-old Goldbach’s conjecture. These two problems require rectification of these defects before they can be resolved. One of the major defects is the inconsistency of the field axioms of the real number system with the construction of a counterexample to the trichotomy axiom that proved it and the real number system false and at the same time not linearly ordered. Indeed, the rectification yields the new foundations of mathematics, constructivist real number system and complex vector plane the last mathematical space being the rectification of the complex real number system. FLT is resolved by a counterexample that proves it false and the Goldbach’s conjecture has been proved both in the constructivist real number system and the new real number system. The latter gives to two mathematical structures or tools—generalized integral and generalized physical fractal. The rectification of foundations yields the resolution of problem 1 and the solution of problem 6 of Hilbert’s 23 problems.
文摘This paper expounds the effect of"Qi"on human body by constructing the model of Qi,classifies the parts according to the category of Yin and Yang on the coordinate frame of 5 models of Yin and Yang,and compares each kind of parts according to the normal image state of human body.with the running direction of integer instead of Qi,the number of Qi in each part is calculated by the method of modern number theory,and the development and changes of human physiology and diseases are explained by"Qi".To explore the Trasitional Chinese Medicine treatment method of"the morbid Qi state of the human body adjusts the qi mode,the direction of qi operation and the intensity of Qi by means of medicinal taste and acupuncture,and returns to the normal state of qi balance mode in the direction of operation".
基金supported by the National Natural Science Foundation of China (Grant No.41175089)
文摘In order to quantitatively evaluate the spurious dianeutral mixing in a global ocean model MPAS-Ocean （Model for Prediction Across Scales） using a spherical centroidal voronoi tessellations developed jointly by the National Center for Atmospheric Research and the Los Alamos National Laboratory in the United States, we choose z＊ vertical coordinate system in MPAS-Ocean, in which all physical mixing processes, such as convection adjustment and explicit diffusion parameter schemes, are omitted, using a linear equation of state. By calculating the Reference Potential Energy （RPE）, front revolution position, time rate of RPE change, probability density function distribution and dimensionless parameter 2＂, from the perspectives of resolution, viscosity, Horizontal Grid Reynolds Number （HGRN）, Rea, and momentum transmission scheme, using two ideal cases, overflow and baroclinic eddy channel, we qualitatively analyze the simulation results by comparison with the three non-isopycnal models in Ilicak et al. （2012）, i.e., MITocM, MOM, and ROMS. The results show that the spurious dianeutral mixing in the MPAS-Ocean increases over time. The spurious dianeutral transport is proportional to the HGRN directly and is reduced by increasing the lateral viscosity or using a finer resolution to control HGRN. When the HGRN is less than 10, spurious transport is reduced significantly. When using the proper viscosity closure, MPAS-Ocean performs better than MIT6c and MOM, closely to ROMS, in the 2D case without rotation, and much better than the above-mentioned three ocean models under the condition of 3D space with rotation due to the cell area difference between the hexa- gon cell and the quadrilateral cell with the same resolution. Both the Zalesak （1979） flux corrected transport scheme and Leith closure in MPAS-Ocean play an excellent role in reducing spurious dianeutral mixing. The performance of Leith scheme is preferable to the condition of three-dimensional baroclinic eddy.
