The theory of if-E curve in cyclic derivative chronopotentiometry is presented. Theoretical equations of if-E curves in the case of quasi-reversible and irreversible electrode reactions are deduced respectively.
A simple model of chromatographic mechanical mechanism is present, and then a scrics of theoretical chromatographic equations and fundamental Formulae are derived. These theoretical equations and formulae not only res...A simple model of chromatographic mechanical mechanism is present, and then a scrics of theoretical chromatographic equations and fundamental Formulae are derived. These theoretical equations and formulae not only reserve thermodynamic characteristics in the current fundamental chromatographic formulae, but also introduce one or more kinetic parameter, so it is possible to make the macroscopic-control on the effect of kinetic characteristics on chromatographic system.展开更多
The manuscript introduces an “ab initio” quantum model to deduce the Maxwell equations. After general considerations and laying out the model’s theoretical framework, these equations can be derived alongside a broa...The manuscript introduces an “ab initio” quantum model to deduce the Maxwell equations. After general considerations and laying out the model’s theoretical framework, these equations can be derived alongside a broad variety of other results. Specifically, a corollary of the present model proposes a possible mechanism underlying the formation of magnetic monopoles and allows estimating their formation energy in order of magnitude.展开更多
In this paper, the Martin-Hou equation of state is derived by using a power series representation of radial distribution function and an analytic representation of multi-section potential based on the Barker-Henderso...In this paper, the Martin-Hou equation of state is derived by using a power series representation of radial distribution function and an analytic representation of multi-section potential based on the Barker-Henderson hard-particle perturbation theory including high-order terms. In the derivation, a theoretical form of Martin-Hou equation was obtained. It had a similar form and the same capability to predict P-V-T properties as the Martin-Hou equation and no additional data were required for evaluating the constants. The characteristic constants of the theoretical expression have certain relationships with the molecular parameters.展开更多
The settlement of particles is of great importance in many areas. The accurate determination of drag coefficient and settling velocity in wide Reynolds number （Re） range remains a problem. In this paper, a series of...The settlement of particles is of great importance in many areas. The accurate determination of drag coefficient and settling velocity in wide Reynolds number （Re） range remains a problem. In this paper, a series of new formulas for drag coefficient of spherical particles based on theoretical laws, such as the Stokes law, the Oseen law, and the Goldstein law, were developed and fitted using 480 groups of experimental data （Re 〈 2 × 10^5）. The results show that the 2nd approximation of a rational function containing only one parameter can describe Co-Re relationship accurately over the whole Re range of 0-2× 10^5. The new developed formulas containing five parameters show higher goodness over wide Re range than presently existing equations. The introduction of the Oseen law is helpful for improving the fitting goodness of the empirical formulas. On the basis of one of the Oseen-based Co-Re formulas giving the lowest sum of squared relative errors Qover the whole Re range （Re 〈 2 × 10^5）, a general formula for settling velocity ut based on dimensionless parameters was proposed showing high goodness.展开更多
Different factors affecting the efficiency of the orifice energy dissipator were investigated based on a series of theoretical analyses and numerical simulations. The main factors investigated by dimension analysis we...Different factors affecting the efficiency of the orifice energy dissipator were investigated based on a series of theoretical analyses and numerical simulations. The main factors investigated by dimension analysis were identified, including the Reynolds number （Re）, the ratio of the orifice diameter to the inner diameter of the pipe （ did ）, and the ratio of distances between orifices to the inner diameter of the pipe （ LID ）. Then, numerical simulations were conducted with a k-ε two-equation turbulence model. The calculation results show the following： Hydraulic characteristics change dramatically as flow passes through the orifice, with abruptly increasing velocity and turbulent energy, and decreasing pressure. The turbulent energy appears to be low in the middle and high near the pipe wall. For the energy dissipation setup with only one orifice, when Re is smaller than 105, the orifice energy dissipation coefficient K increases rapidly with the increase of Re. When Re is larger than l05, K gradually stabilizes. As diD increases, K and the length of the recirculation region L1 show similar variation patterns, which inversely vary with diD. The function curves can be approximated as straight lines. For the energy dissipation model with two orifices, because of different incoming flows at different orifices, the energy dissipation coefficient of the second orifice （K2） is smaller than that of the first. If LID is less than 5, the K value of the LID model, depending on the variation of/（2, increases with the spacing between two orifices L, and an orifice cannot fulfill its energy dissipation function. If LID is greater than 5, K2 tends to be steady; thus, the K value of the LID model gradually stabilizes. Then, the flow fully develops, and L has almost no impact on the value of K.展开更多
A new exact solution for nonlinear interaction of two pulsatory waves of the Korteweg-de Vries (KdV) equation is computed by decomposition in an invariant zigzag hyperbolic tangent (ZHT) structure. A computational alg...A new exact solution for nonlinear interaction of two pulsatory waves of the Korteweg-de Vries (KdV) equation is computed by decomposition in an invariant zigzag hyperbolic tangent (ZHT) structure. A computational algorithm is developed by experimental programming with lists of equations and expressions. The structural solution is proved by theoretical programming with symbolic general terms. Convergence, tolerance, and summation of the ZHT structural approximation are discussed. When a reference level vanishes, the two-wave solution is reduced to the two-soliton solution of the KdV equation.展开更多
Although several theoretical calculation methods for high-pressure jet are available,there is currently no theoretical model for the high-pressure CO_(2)jet based on the high-precision equation of state(EOS).To invest...Although several theoretical calculation methods for high-pressure jet are available,there is currently no theoretical model for the high-pressure CO_(2)jet based on the high-precision equation of state(EOS).To investigate the flow field of the high-pressure CO_(2)jet in cases of the composite rock-breaking under the high-pressure CO_(2)Jet and PDC cutter,a semi-analytical approach of the high-pressure CO_(2)jet is developed based on the Span-Wagner EOS and CO_(2)jet theory.The semi-analytical calculations and the physical property calculations under the action of the high-pressure CO_(2)jet are conducted with consideration of the jet pressure,the jet distance,the nozzle diameter and the jet angle.The results indicate that the distribution of the physical properties calculated by the semi-analytical approaches is similar to that obtained by experimental monitoring and numerical simulation,which indicates that the calculation method of the high-pressure CO_(2)jet presented in this paper is effective and reliable.The properties of the CO_(2)jet obtained by the theoretical calculation see a significant difference between the initial region and the jet impact region.At the temperature of 300 K,the increase of the initial pressure can effectively increase the impact force and the cooling ability of the jet.The proportion of the jet core lengths in the jet on the axis increases with the increase of the ratio of the nozzle diameter to the jet length,accompanied with the increase of the impact force of the jet.The increase of the jet angle can effectively increase the impacting force of the jet,but hampers the fluid diffusion.The study combines the theoretical calculation of the jet with the calculation of the physical properties of the high-pressure CO_(2),for comprehensively understanding the CO_(2)jet field in the composite rock-breaking under the action of the high-pressure CO_(2)jet and PDC cutter.This theoretical calculation of the CO_(2)jet based on the high-precision EOS provides an option for the convenient calculation of the CO_(2)drilling in practical engineering.展开更多
Silicate melts are very active in the interior of the Earth and other terrestrial planets, and are important carriers for the transport of material and energy. The determination of the equation of state(EOS) for silic...Silicate melts are very active in the interior of the Earth and other terrestrial planets, and are important carriers for the transport of material and energy. The determination of the equation of state(EOS) for silicate melts and the acquisition of a precise quantitative relationship between molar volume(or density) and temperature, pressure, and composition is essential for simulating the generation, migration, and eruption processes of magmas and the evolution of the magma ocean stage during the early formation of the Earth and other terrestrial planets, for calculating and modeling the phase equilibria involving silicate melts, and for revealing the variation of the microstructure of silicate melts with pressure. However, it is experimentally challenging to determine the volumetric properties of silicate melts and the accumulated density data at high pressure are still very limited due to a series of problems such as: the high liquidus temperature of silicate rocks; proneness for silicate melts to react with sample capsules to change the melt composition; and proneness for melts to flow and leak during the high pressure and high temperature experiments. In recent years, there is rapid progress in the high pressure and high temperature experimental techniques, in terms of not only the extension of temperature and pressure ranges but also the improvement on the accuracy of measurements, and the emergence of new methods for in-situ measurements. Here, we review the widely-used theoretical models of ambient-pressure and high-pressure EOS for silicate melts, and illustrate some problems that need to be solved urgently:(1) the room pressure EOS for iron-and titanium-bearing silicate melts needs to be improved;(2) the partial molar properties of the H2 O and CO2 components in silicate melts containing volatile components may vary markedly with the melt composition, which need to be addressed in high-pressure EOS;(3) how the formulation and applicable range of EOS correspond to changes in melt structure and compression mechanism requires further study. We highlight the basic principle and applicable range of various methods for determining the EOS for silicate melts, and compare the advantages and disadvantages of doublebob Archimedes method, fusion curve analysis, shock compression experiments, sink-float method, X-ray absorption, X-ray diffraction and ultrasonic interferometry. Future trends in this field are to develop experimental techniques for in situ measurements on melt density or sound velocity at high temperature and high pressure and to accumulate more experimental data,and on the other hand, to improve the theoretical models of the EOS for silicate melts by a combination of research on the microstructure and compression mechanisms of silicate melts.展开更多
由于现有协议的安全性为基于某种安全假设的计算安全,依赖于敌手的计算能力,因此,本文针对恶意敌手模型,使用矩阵伪装技术对方程的系数矩阵进行隐藏,结合矩阵的LU分解(lower-upper decomposition)算法,提出一种新的信息论安全外包求解...由于现有协议的安全性为基于某种安全假设的计算安全,依赖于敌手的计算能力,因此,本文针对恶意敌手模型,使用矩阵伪装技术对方程的系数矩阵进行隐藏,结合矩阵的LU分解(lower-upper decomposition)算法,提出一种新的信息论安全外包求解线性代数方程组(information-theoretically secure outsourcing of linear algebraic equations,ITS-OutsLAE)方法 .与之前的研究相比,在保持计算和通信复杂度与现有最优方案保持一致的同时,首次将方程组唯一解的安全性提升至信息论安全(完美保密).给出了形式化的安全性证明,并通过理论分析和实验证明了所提方法的实用性.展开更多
Cycle sets were introduced to reduce non-degenerate unitary Yang-Baxter maps to an algebraic system with a single binary operation. Every finite cycle set extends uniquely to a finite cycle set with a compatible abeli...Cycle sets were introduced to reduce non-degenerate unitary Yang-Baxter maps to an algebraic system with a single binary operation. Every finite cycle set extends uniquely to a finite cycle set with a compatible abelian group structure. Etingof et al. introduced affine Yang-Baxter maps. These are equivalent to cycle sets with a specific abelian group structure. Abelian group structures have also been essential to get partial results for the still unsolved retraction problem. We introduce two new classes of cycle sets with an underlying abelian group structure and show that they can be transformed into each other while keeping the group structure fixed. This leads to a proper extension of the retractibility conjecture and new evidence for its truth.展开更多
基金Supported by the National Natural Science Foundation of China
文摘The theory of if-E curve in cyclic derivative chronopotentiometry is presented. Theoretical equations of if-E curves in the case of quasi-reversible and irreversible electrode reactions are deduced respectively.
文摘A simple model of chromatographic mechanical mechanism is present, and then a scrics of theoretical chromatographic equations and fundamental Formulae are derived. These theoretical equations and formulae not only reserve thermodynamic characteristics in the current fundamental chromatographic formulae, but also introduce one or more kinetic parameter, so it is possible to make the macroscopic-control on the effect of kinetic characteristics on chromatographic system.
文摘The manuscript introduces an “ab initio” quantum model to deduce the Maxwell equations. After general considerations and laying out the model’s theoretical framework, these equations can be derived alongside a broad variety of other results. Specifically, a corollary of the present model proposes a possible mechanism underlying the formation of magnetic monopoles and allows estimating their formation energy in order of magnitude.
基金Zhejiang Provincial Natural Science Foundation of China!(No. 298013)
文摘In this paper, the Martin-Hou equation of state is derived by using a power series representation of radial distribution function and an analytic representation of multi-section potential based on the Barker-Henderson hard-particle perturbation theory including high-order terms. In the derivation, a theoretical form of Martin-Hou equation was obtained. It had a similar form and the same capability to predict P-V-T properties as the Martin-Hou equation and no additional data were required for evaluating the constants. The characteristic constants of the theoretical expression have certain relationships with the molecular parameters.
基金financial support of the Natural Science Foundation of China (NSFC,No.50974094)
文摘The settlement of particles is of great importance in many areas. The accurate determination of drag coefficient and settling velocity in wide Reynolds number （Re） range remains a problem. In this paper, a series of new formulas for drag coefficient of spherical particles based on theoretical laws, such as the Stokes law, the Oseen law, and the Goldstein law, were developed and fitted using 480 groups of experimental data （Re 〈 2 × 10^5）. The results show that the 2nd approximation of a rational function containing only one parameter can describe Co-Re relationship accurately over the whole Re range of 0-2× 10^5. The new developed formulas containing five parameters show higher goodness over wide Re range than presently existing equations. The introduction of the Oseen law is helpful for improving the fitting goodness of the empirical formulas. On the basis of one of the Oseen-based Co-Re formulas giving the lowest sum of squared relative errors Qover the whole Re range （Re 〈 2 × 10^5）, a general formula for settling velocity ut based on dimensionless parameters was proposed showing high goodness.
文摘Different factors affecting the efficiency of the orifice energy dissipator were investigated based on a series of theoretical analyses and numerical simulations. The main factors investigated by dimension analysis were identified, including the Reynolds number （Re）, the ratio of the orifice diameter to the inner diameter of the pipe （ did ）, and the ratio of distances between orifices to the inner diameter of the pipe （ LID ）. Then, numerical simulations were conducted with a k-ε two-equation turbulence model. The calculation results show the following： Hydraulic characteristics change dramatically as flow passes through the orifice, with abruptly increasing velocity and turbulent energy, and decreasing pressure. The turbulent energy appears to be low in the middle and high near the pipe wall. For the energy dissipation setup with only one orifice, when Re is smaller than 105, the orifice energy dissipation coefficient K increases rapidly with the increase of Re. When Re is larger than l05, K gradually stabilizes. As diD increases, K and the length of the recirculation region L1 show similar variation patterns, which inversely vary with diD. The function curves can be approximated as straight lines. For the energy dissipation model with two orifices, because of different incoming flows at different orifices, the energy dissipation coefficient of the second orifice （K2） is smaller than that of the first. If LID is less than 5, the K value of the LID model, depending on the variation of/（2, increases with the spacing between two orifices L, and an orifice cannot fulfill its energy dissipation function. If LID is greater than 5, K2 tends to be steady; thus, the K value of the LID model gradually stabilizes. Then, the flow fully develops, and L has almost no impact on the value of K.
文摘A new exact solution for nonlinear interaction of two pulsatory waves of the Korteweg-de Vries (KdV) equation is computed by decomposition in an invariant zigzag hyperbolic tangent (ZHT) structure. A computational algorithm is developed by experimental programming with lists of equations and expressions. The structural solution is proved by theoretical programming with symbolic general terms. Convergence, tolerance, and summation of the ZHT structural approximation are discussed. When a reference level vanishes, the two-wave solution is reduced to the two-soliton solution of the KdV equation.
基金This work was supported by the Sichuan Science and Technology Program(Grant No.2021JDRC0114)the Starting Project of Southwest Petroleum University(Grant No.2019QHZ009)+2 种基金the China Postdoctoral Science Foundation(Grant No.2020M673285)the Open Project Program of Key Laboratory of Groundwater Resources and Environment,Ministry of Education,Jilin University(Grant No.202005009KF)the Chinese Scholarship Council funding(Grant No.202008515107).
文摘Although several theoretical calculation methods for high-pressure jet are available,there is currently no theoretical model for the high-pressure CO_(2)jet based on the high-precision equation of state(EOS).To investigate the flow field of the high-pressure CO_(2)jet in cases of the composite rock-breaking under the high-pressure CO_(2)Jet and PDC cutter,a semi-analytical approach of the high-pressure CO_(2)jet is developed based on the Span-Wagner EOS and CO_(2)jet theory.The semi-analytical calculations and the physical property calculations under the action of the high-pressure CO_(2)jet are conducted with consideration of the jet pressure,the jet distance,the nozzle diameter and the jet angle.The results indicate that the distribution of the physical properties calculated by the semi-analytical approaches is similar to that obtained by experimental monitoring and numerical simulation,which indicates that the calculation method of the high-pressure CO_(2)jet presented in this paper is effective and reliable.The properties of the CO_(2)jet obtained by the theoretical calculation see a significant difference between the initial region and the jet impact region.At the temperature of 300 K,the increase of the initial pressure can effectively increase the impact force and the cooling ability of the jet.The proportion of the jet core lengths in the jet on the axis increases with the increase of the ratio of the nozzle diameter to the jet length,accompanied with the increase of the impact force of the jet.The increase of the jet angle can effectively increase the impacting force of the jet,but hampers the fluid diffusion.The study combines the theoretical calculation of the jet with the calculation of the physical properties of the high-pressure CO_(2),for comprehensively understanding the CO_(2)jet field in the composite rock-breaking under the action of the high-pressure CO_(2)jet and PDC cutter.This theoretical calculation of the CO_(2)jet based on the high-precision EOS provides an option for the convenient calculation of the CO_(2)drilling in practical engineering.
基金supported by the National Natural Science Foundation of China(Grant Nos.40972028,41520104004,and 41672036)
文摘Silicate melts are very active in the interior of the Earth and other terrestrial planets, and are important carriers for the transport of material and energy. The determination of the equation of state(EOS) for silicate melts and the acquisition of a precise quantitative relationship between molar volume(or density) and temperature, pressure, and composition is essential for simulating the generation, migration, and eruption processes of magmas and the evolution of the magma ocean stage during the early formation of the Earth and other terrestrial planets, for calculating and modeling the phase equilibria involving silicate melts, and for revealing the variation of the microstructure of silicate melts with pressure. However, it is experimentally challenging to determine the volumetric properties of silicate melts and the accumulated density data at high pressure are still very limited due to a series of problems such as: the high liquidus temperature of silicate rocks; proneness for silicate melts to react with sample capsules to change the melt composition; and proneness for melts to flow and leak during the high pressure and high temperature experiments. In recent years, there is rapid progress in the high pressure and high temperature experimental techniques, in terms of not only the extension of temperature and pressure ranges but also the improvement on the accuracy of measurements, and the emergence of new methods for in-situ measurements. Here, we review the widely-used theoretical models of ambient-pressure and high-pressure EOS for silicate melts, and illustrate some problems that need to be solved urgently:(1) the room pressure EOS for iron-and titanium-bearing silicate melts needs to be improved;(2) the partial molar properties of the H2 O and CO2 components in silicate melts containing volatile components may vary markedly with the melt composition, which need to be addressed in high-pressure EOS;(3) how the formulation and applicable range of EOS correspond to changes in melt structure and compression mechanism requires further study. We highlight the basic principle and applicable range of various methods for determining the EOS for silicate melts, and compare the advantages and disadvantages of doublebob Archimedes method, fusion curve analysis, shock compression experiments, sink-float method, X-ray absorption, X-ray diffraction and ultrasonic interferometry. Future trends in this field are to develop experimental techniques for in situ measurements on melt density or sound velocity at high temperature and high pressure and to accumulate more experimental data,and on the other hand, to improve the theoretical models of the EOS for silicate melts by a combination of research on the microstructure and compression mechanisms of silicate melts.
文摘由于现有协议的安全性为基于某种安全假设的计算安全,依赖于敌手的计算能力,因此,本文针对恶意敌手模型,使用矩阵伪装技术对方程的系数矩阵进行隐藏,结合矩阵的LU分解(lower-upper decomposition)算法,提出一种新的信息论安全外包求解线性代数方程组(information-theoretically secure outsourcing of linear algebraic equations,ITS-OutsLAE)方法 .与之前的研究相比,在保持计算和通信复杂度与现有最优方案保持一致的同时,首次将方程组唯一解的安全性提升至信息论安全(完美保密).给出了形式化的安全性证明,并通过理论分析和实验证明了所提方法的实用性.
文摘Cycle sets were introduced to reduce non-degenerate unitary Yang-Baxter maps to an algebraic system with a single binary operation. Every finite cycle set extends uniquely to a finite cycle set with a compatible abelian group structure. Etingof et al. introduced affine Yang-Baxter maps. These are equivalent to cycle sets with a specific abelian group structure. Abelian group structures have also been essential to get partial results for the still unsolved retraction problem. We introduce two new classes of cycle sets with an underlying abelian group structure and show that they can be transformed into each other while keeping the group structure fixed. This leads to a proper extension of the retractibility conjecture and new evidence for its truth.
