We give a proof of an explicit formula for affine coodinates of points in the Sato’s infinite Grassmannian corresponding to tau-functions for the KdV hierarchy.
This paper concerns the exponential attitude-orbit coordinated control problems for gravitational-wave detection formation spacecraft systems.Notably,the large-scale communication delays resulting from oversized inter...This paper concerns the exponential attitude-orbit coordinated control problems for gravitational-wave detection formation spacecraft systems.Notably,the large-scale communication delays resulting from oversized inter-satellite distance of space-based laser interferometers are first modeled.Subject to the delayed communication behaviors,a new delay-dependent attitude-orbit coordinated controller is designed.Moreover,by reconstructing the less conservative Lyapunov-Krasovskii functional and free-weight matrices,sufficient criteria are derived to ensure the exponential stability of the closed-loop relative translation and attitude error system.Finally,a simulation example is employed to illustrate the numerical validity of the proposed controller for in-orbit detection missions.展开更多
Aim To study the Lie symmetries and the consered quantities of the holonomic systems with remainder coordinates. Methods Using the invariance of the ordinary differential equations under the infinitesimal transformati...Aim To study the Lie symmetries and the consered quantities of the holonomic systems with remainder coordinates. Methods Using the invariance of the ordinary differential equations under the infinitesimal transformations to establish the determining equations and the restriction equations of the Lie symmetries of the systems. Results and Conclusion the structure equation and the form of conserved quantities were obtained. An example was given to illustrate the application of the result.展开更多
A direct method to find the first integral for two-dimensional autonomous system in polar coordinates is suggested. It is shown that if the equation of motion expressed by differential 1-forms for a given autonomous H...A direct method to find the first integral for two-dimensional autonomous system in polar coordinates is suggested. It is shown that if the equation of motion expressed by differential 1-forms for a given autonomous Hamiltonian system is multiplied by a set of multiplicative functions, then the general expression of the first integral can be obtained, An example is given to illustrate the application of the results.展开更多
Based on FDTD difference expressions and eigenfunctions of Maxwell functions in cylindrical coordinates, mesh wave impedances (MWIs) in 2D and 3D cylindrical coordinates were introduced. Combined with the concept of p...Based on FDTD difference expressions and eigenfunctions of Maxwell functions in cylindrical coordinates, mesh wave impedances (MWIs) in 2D and 3D cylindrical coordinates were introduced. Combined with the concept of perfectly matched layer (PML), MWI PML absorbing boundary condition (ABC) algorithm was deduced in 2D cylindrical coordinates. Numerical experiments were done to investigate the validity of MWI and its application in cylindrical coordinates FDTD algorithm. The results showed that MWI in cylindrical coordinates can be used to accurately calculate the numerical reflection error caused by different mesh increments in non uniform FDTD. MWI can also provide theoretical criterion to define the permitted variable range of mesh dimension. MWI PML ABC is easy to be applied and reduces low numerical reflection, which only causes a little higher reflection error compared with Teixeira's PML.展开更多
An FDTD system associated with uniaxial perfectly matched layer（UPML） for an electromagnetic scattering problem in two-dimensional space in polar coordinates is considered.Particularly the FDTD system of an initial-...An FDTD system associated with uniaxial perfectly matched layer（UPML） for an electromagnetic scattering problem in two-dimensional space in polar coordinates is considered.Particularly the FDTD system of an initial-boundary value problems of the transverse magnetic（TM） mode to Maxwell＇s equations is obtained by Yee＇s algorithm,and the open domain of the scattering problem is truncated by a circle with a UPML.Besides,an artificial boundary condition is imposed on the outer boundary of the UPML.Afterwards,stability of the FDTD system on the truncated domain is established through energy estimates by the Gronwall inequality.Numerical experiments are designed to approve the theoretical analysis.展开更多
For classical Hamiltonian with general form H = 1/2∑ijMijpipj＋1/2∑ijLijqiqj we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator （...For classical Hamiltonian with general form H = 1/2∑ijMijpipj＋1/2∑ijLijqiqj we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator （IEO） method （Fan et al. 2004 Phys. Lett. A 321 75） to derive them. The general matrix equation, which relies on M and L, for obtaining the normal coordinates of H is derived.展开更多
Simplify the proof on the domain of convergence of multiple power series and consider the case where some of z1, …, zn are contained only in a finite number of terms of the series. Obtain some results on holomorphic ...Simplify the proof on the domain of convergence of multiple power series and consider the case where some of z1, …, zn are contained only in a finite number of terms of the series. Obtain some results on holomorphic functions in Cn.展开更多
To objectively obtain the three-dimensional coordinates of the projectile fuze proximity explosion when projectile intersects the head of missile target, we propose a dynamic seven photoelectric detection screen test ...To objectively obtain the three-dimensional coordinates of the projectile fuze proximity explosion when projectile intersects the head of missile target, we propose a dynamic seven photoelectric detection screen test method, which is made up of six plane detection screens and a flash photoelectric dynamic detection screen. The three-dimensional coordinates calculation model of the projectile proximity explosion position based on seven plane detection screens with dynamic characteristics is established.According to the relation of the dynamic seven photoelectric detection screen planes and the time values,the analytical function of the projectile proximity explosion position parameters under non-linear motion is derived. The projectile signal filtering method based on discrete wavelet transform is explored in this work. Additionally, the projectile signal recognition algorithm using an improved particle swarm is proposed. Based on the characteristics of the time duration and the signal peak error for the projectile passing through the detection screen, the signals attribution of the same projectile passing through six detection screens are analyzed for obtaining precise time values of the same projectile passing through the detection screens. On the basis of the projectile fuze proximity explosion test, the linear motion model and the proposed non-linear motion model are used to calculate and compare the same group of projectiles proximity explosion position parameters. The comparison of test results verifies that the proposed test method and calculation model in this work accurately obtain the actual projectile proximity explosion position parameters.展开更多
This paper studies the finite statistical-mechanical entropy of the Schwarzschild anti-de Sitter （ADS） spacetime arising from quantum massless scalar field by using the ＇brick wall＇ approach in the Painlev; and Le...This paper studies the finite statistical-mechanical entropy of the Schwarzschild anti-de Sitter （ADS） spacetime arising from quantum massless scalar field by using the ＇brick wall＇ approach in the Painlev; and Lemaaitre coordinates. At first glance, it seems that the results would be different from that in the Schwarzschild-like coordinate since both the Painlev; and the Lemaitre spacetimes do not possess the event horizon obviously. However, this paper proves that the entropies in these coordinates are exactly equivalent to that in the Schwarzschild-like coordinate.展开更多
In this paper,various aberrations have been analyzed.Not only the effects of aberration on geometrical center position are taken into account,but also the deviation of displayed star position energy center caused by a...In this paper,various aberrations have been analyzed.Not only the effects of aberration on geometrical center position are taken into account,but also the deviation of displayed star position energy center caused by aberration is analyzed.These two aspects have been taken into comprehensive evaluation and star position correction.The correction method based on polar coordinates is proposed,and cumbersome partition correction and calculated quantity based on two-dimensional coordinates can be simplified.The experimental results show that the correction processing based on polar coordinates is simpler and easier compared with any other correction methods.In addition,the correction results are significantly more accurate.展开更多
We give a brief discussion of some of the contributions of Peter Lax to Com- putational Fluid Dynamics. These include the Lax-Friedrichs and Lax-Wendroff numerical schemes. We also mention his collaboration in the 198...We give a brief discussion of some of the contributions of Peter Lax to Com- putational Fluid Dynamics. These include the Lax-Friedrichs and Lax-Wendroff numerical schemes. We also mention his collaboration in the 1983 HLL Riemann solver. We de- velop two-dimensional Lax-Friedrichs and Lax-Wendroff schemes for the Lagrangian form of the Euler equations on triangular grids. We apply a composite scheme that uses a Lax- Friedrichs time step as a dissipative filter after several Lax-Wendroff time steps. Numerical results for Noh＇s infinite strength shock problem, the Sedov blast wave problem, and the Saltzman piston problem are presented.展开更多
Bond valence method illustrates the relation between valence and length of a particular bond type. This theory has been used to predict structure information, but the effect is very limited. In this paper, two indexes...Bond valence method illustrates the relation between valence and length of a particular bond type. This theory has been used to predict structure information, but the effect is very limited. In this paper, two indexes, i.e., global instability index（GII） and bond strain index（BSI）, are adopted as a judgment of a search-match program for prediction. The results show that with GII and BSI combined as judgment, the predicted atom positions are very close to real ones. The mechanism and validity of this searching program are also discussed. The GII ＆ BSI distribution contour map reveals that the predicted function is a reflection of exponential feature of bond valence formula. This combined searching method may be integrated with other structure-determination method, and may be helpful in refining and testifying light atom positions.展开更多
Field-aligned coordinates have been implemented in the gyrokinetic semi-Lagrangian code NLT, Ye et al （2016 J. Comput. Phys. 316 180）, to improve the computational efficiency for the numerical simulations of tokamak...Field-aligned coordinates have been implemented in the gyrokinetic semi-Lagrangian code NLT, Ye et al （2016 J. Comput. Phys. 316 180）, to improve the computational efficiency for the numerical simulations of tokamak turbulence and transport. 4D B-spline interpolation in field- aligned coordinates is applied to solve the gyrokinetic Vlasov equation. A fast iterative algorithm is proposed for efficiently solving the quasi-neutrality equation. A pseudo transform method is used for the numerical integration of the gyro-average operator for perturbations with a high toroidal mode number. The new method is shown to result in an improved code performance for reaching a given accuracy. Some numerical tests are presented to illustrate the new methods.展开更多
This paper discusses the symmetry of Lagrangians of holonomic systems in terms of quasi-coordinates. Firstly, the definition and the criterion of the symmetry are given. Secondly, the condition under which there exist...This paper discusses the symmetry of Lagrangians of holonomic systems in terms of quasi-coordinates. Firstly, the definition and the criterion of the symmetry are given. Secondly, the condition under which there exists a conserved quantity and the form of the conserved quantity are obtained. Finally, an example is shown to illustrate the application of the results.展开更多
The selection and coordinated application of government innovation policies are crucial for guiding the direction of enterprise innovation and unleashing their innovation potential.However,due to the lengthy,voluminou...The selection and coordinated application of government innovation policies are crucial for guiding the direction of enterprise innovation and unleashing their innovation potential.However,due to the lengthy,voluminous,complex,and unstructured nature of regional innovation policy texts,traditional policy classification methods often overlook the reality that these texts cover multiple policy topics,leading to lack of objectivity.In contrast,topic mining technology can handle large-scale textual data,overcoming challenges such as the abundance of policy content and difficulty in classification.Although topic models can partition numerous policy texts into topics,they cannot analyze the interplay among policy topics and the impact of policy topic coordination on enterprise innovation in detail.Therefore,we propose a big data analysis scheme for policy coordination paths based on the latent Dirichlet allocation(LDA)model and the fuzzyset qualitative comparative analysis(fsQCA)method by combining topic models with qualitative comparative analysis.The LDA model was employed to derive the topic distribution of each document and the word distribution of each topic and enable automatic classi-fication through algorithms,providing reliable and objective textual classification results.Subsequently,the fsQCA method was used to analyze the coordination paths and dynamic characteristics.Finally,experimental analysis was conducted using innovation policy text data from 31 provincial-level administrative regions in China from 2012 to 2021 as research samples.The results suggest that the proposed method effectively partitions innovation policy topics and analyzes the policy configuration,driving enterprise innovation in different regions.展开更多
Electrocatalytic nitrate reduction reaction has attracted increasing attention due to its goal of low carbon emission and environmental protection.Here,we report an efficient NitRR catalyst composed of single Mn sites...Electrocatalytic nitrate reduction reaction has attracted increasing attention due to its goal of low carbon emission and environmental protection.Here,we report an efficient NitRR catalyst composed of single Mn sites with atomically dispersed oxygen(O)coordination on bacterial cellulose-converted graphitic carbon(Mn-O-C).Evidence of the atomically dispersed Mn-(O-C_(2))_(4)moieties embedding in the exposed basal plane of carbon surface is confirmed by X-ray absorption spectroscopy.As a result,the as-synthesized Mn-O-C catalyst exhibits superior NitRR activity with an NH_(3)yield rate(RNH_(3))of 1476.9±62.6μg h^(−1)cm^(−2)at−0.7 V(vs.reversible hydrogen electrode,RHE)and a faradaic efficiency(FE)of 89.0±3.8%at−0.5 V(vs.RHE)under ambient conditions.Further,when evaluated with a practical flow cell,Mn-O-C shows a high RNH_(3)of 3706.7±552.0μg h^(−1)cm^(−2)at a current density of 100 mA cm−2,2.5 times of that in the H cell.The in situ FT-IR and Raman spectroscopic studies combined with theoretical calculations indicate that the Mn-(O-C_(2))_(4)sites not only effectively inhibit the competitive hydrogen evolution reaction,but also greatly promote the adsorption and activation of nitrate(NO_(3)^(−)),thus boosting both the FE and selectivity of NH_(3)over Mn-(O-C_(2))_(4)sites.展开更多
Accurate tokamak plasma equilibrium solution in flux coordinates is crucial for many stability and transport studies.Different approaches for dealing with singularities in solving the nonlinear Grad-Shafranov(GS)equat...Accurate tokamak plasma equilibrium solution in flux coordinates is crucial for many stability and transport studies.Different approaches for dealing with singularities in solving the nonlinear Grad-Shafranov(GS)equation in flux coordinates or also known as straight field line coordinates are proposed in this paper.The GS equation is solved by iterating the position of grids directly in flux coordinates,and hence,no additional errors are introduced due to mapping process for a convergent solution.The singularity at magnetic axis in flux coordinates is removed by using a novel coordinate transform technique.Different from other techniques previously developed,no assumption in boundary condition at magnetic axis is used.This is consistent with the fact that there is no physical boundary at the magnetic axis.A flux coordinate system with poloidal coordinate chosen as the geometric poloidal angle is proposed.It conquers the difficulty in no definition of poloidal coordinate in flux coordinates at separatrix because of the singularity at x-point(s)in a divertor configuration.It also simplifies the process for computing poloidal flux coordinate during the iteration for solving the nonlinear GS equation.Non-uniform grids can be applied in both radial and poloidal coordinates,which allows it to increase the spacial resolution near x-point(s)in a divertor configuration.Based on the model proposed in this paper,a new Flux coordinates based EQuilibrium solver(FEQ)in tokamaks is developed.The numerical solutions from this code agree well with both the analytic Solov’ev solution and the numerical one from the EFIT code for a divertor configuration in the EAST tokamak.This code can be applied for simulating different equilibria with prescribed shape,pressure and current profiles,i.e.including both limiter and divertor configurations,positive triangularity and negative triangularity,differentβ,arbitrary magnetic shear profile etc.It provides a powerful and convenient fixed-boundary inverse equilibrium solver including both magnetic axis and separatrix in the solution for tokamak researches.展开更多
Atom-level modulation of the coordination environment for single-atom catalysts(SACs)is considered as an effective strategy for elevating the catalytic performance.For the MNxsite,breaking the symmetrical geometry and...Atom-level modulation of the coordination environment for single-atom catalysts(SACs)is considered as an effective strategy for elevating the catalytic performance.For the MNxsite,breaking the symmetrical geometry and charge distribution by introducing relatively weak electronegative atoms into the first/second shell is an efficient way,but it remains challenging for elucidating the underlying mechanism of interaction.Herein,a practical strategy was reported to rationally design single cobalt atoms coordinated with both phosphorus and nitrogen atoms in a hierarchically porous carbon derived from metal-organic frameworks.X-ray absorption spectrum reveals that atomically dispersed Co sites are coordinated with four N atoms in the first shell and varying numbers of P atoms in the second shell(denoted as Co-N/P-C).The prepared catalyst exhibits excellent oxygen reduction reaction(ORR)activity as well as zinc-air battery performance.The introduction of P atoms in the Co-SACs weakens the interaction between Co and N,significantly promoting the adsorption process of ^(*)OOH,resulting in the acceleration of reaction kinetics and reduction of thermodynamic barrier,responsible for the increased intrinsic activity.Our discovery provides insights into an ultimate design of single-atom catalysts with adjustable electrocatalytic activities for efficient electrochemical energy conversion.展开更多
We propose a new concept of the conformal invariance and the conserved quantities for holonomic systems with quasi-coordinates. A one-parameter infinitesimal transformation group and its infinitesimal transformation v...We propose a new concept of the conformal invariance and the conserved quantities for holonomic systems with quasi-coordinates. A one-parameter infinitesimal transformation group and its infinitesimal transformation vector of generators for holonomic systems with quasi-coordinates are described in detail. The conformal factor in the determining equations of the Lie symmetry is found. The necessary and sufficient conditions of conformal invariance, which are simultaneously of Lie symmetry, are given. The conformal invariance may lead to corresponding Hojman conserved quantities when the conformal invariance satisfies some conditions. Finally, an illustration example is introduced to demonstrate the application of the result.展开更多
文摘We give a proof of an explicit formula for affine coodinates of points in the Sato’s infinite Grassmannian corresponding to tau-functions for the KdV hierarchy.
基金supported by the Na⁃tional Key R&D Program of China(No.2022YFC2204800)the Graduate Student Independent Exploration and Innovation Program of Central South University(No.2024ZZTS 0767).
文摘This paper concerns the exponential attitude-orbit coordinated control problems for gravitational-wave detection formation spacecraft systems.Notably,the large-scale communication delays resulting from oversized inter-satellite distance of space-based laser interferometers are first modeled.Subject to the delayed communication behaviors,a new delay-dependent attitude-orbit coordinated controller is designed.Moreover,by reconstructing the less conservative Lyapunov-Krasovskii functional and free-weight matrices,sufficient criteria are derived to ensure the exponential stability of the closed-loop relative translation and attitude error system.Finally,a simulation example is employed to illustrate the numerical validity of the proposed controller for in-orbit detection missions.
文摘Aim To study the Lie symmetries and the consered quantities of the holonomic systems with remainder coordinates. Methods Using the invariance of the ordinary differential equations under the infinitesimal transformations to establish the determining equations and the restriction equations of the Lie symmetries of the systems. Results and Conclusion the structure equation and the form of conserved quantities were obtained. An example was given to illustrate the application of the result.
文摘A direct method to find the first integral for two-dimensional autonomous system in polar coordinates is suggested. It is shown that if the equation of motion expressed by differential 1-forms for a given autonomous Hamiltonian system is multiplied by a set of multiplicative functions, then the general expression of the first integral can be obtained, An example is given to illustrate the application of the results.
文摘Based on FDTD difference expressions and eigenfunctions of Maxwell functions in cylindrical coordinates, mesh wave impedances (MWIs) in 2D and 3D cylindrical coordinates were introduced. Combined with the concept of perfectly matched layer (PML), MWI PML absorbing boundary condition (ABC) algorithm was deduced in 2D cylindrical coordinates. Numerical experiments were done to investigate the validity of MWI and its application in cylindrical coordinates FDTD algorithm. The results showed that MWI in cylindrical coordinates can be used to accurately calculate the numerical reflection error caused by different mesh increments in non uniform FDTD. MWI can also provide theoretical criterion to define the permitted variable range of mesh dimension. MWI PML ABC is easy to be applied and reduces low numerical reflection, which only causes a little higher reflection error compared with Teixeira's PML.
文摘An FDTD system associated with uniaxial perfectly matched layer（UPML） for an electromagnetic scattering problem in two-dimensional space in polar coordinates is considered.Particularly the FDTD system of an initial-boundary value problems of the transverse magnetic（TM） mode to Maxwell＇s equations is obtained by Yee＇s algorithm,and the open domain of the scattering problem is truncated by a circle with a UPML.Besides,an artificial boundary condition is imposed on the outer boundary of the UPML.Afterwards,stability of the FDTD system on the truncated domain is established through energy estimates by the Gronwall inequality.Numerical experiments are designed to approve the theoretical analysis.
基金supported by the National Natural Science Foundation of China (Grant No.10874174)the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.20070358009)
文摘For classical Hamiltonian with general form H = 1/2∑ijMijpipj＋1/2∑ijLijqiqj we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator （IEO） method （Fan et al. 2004 Phys. Lett. A 321 75） to derive them. The general matrix equation, which relies on M and L, for obtaining the normal coordinates of H is derived.
文摘Simplify the proof on the domain of convergence of multiple power series and consider the case where some of z1, …, zn are contained only in a finite number of terms of the series. Obtain some results on holomorphic functions in Cn.
基金supported by Project of the National Natural Science Foundation of China (No.62073256, 61773305)the Key Science and Technology Program of Shaanxi Province (No.2020GY-125)Xi’an Science and Technology Innovation talent service enterprise project (No.2020KJRC0041)。
文摘To objectively obtain the three-dimensional coordinates of the projectile fuze proximity explosion when projectile intersects the head of missile target, we propose a dynamic seven photoelectric detection screen test method, which is made up of six plane detection screens and a flash photoelectric dynamic detection screen. The three-dimensional coordinates calculation model of the projectile proximity explosion position based on seven plane detection screens with dynamic characteristics is established.According to the relation of the dynamic seven photoelectric detection screen planes and the time values,the analytical function of the projectile proximity explosion position parameters under non-linear motion is derived. The projectile signal filtering method based on discrete wavelet transform is explored in this work. Additionally, the projectile signal recognition algorithm using an improved particle swarm is proposed. Based on the characteristics of the time duration and the signal peak error for the projectile passing through the detection screen, the signals attribution of the same projectile passing through six detection screens are analyzed for obtaining precise time values of the same projectile passing through the detection screens. On the basis of the projectile fuze proximity explosion test, the linear motion model and the proposed non-linear motion model are used to calculate and compare the same group of projectiles proximity explosion position parameters. The comparison of test results verifies that the proposed test method and calculation model in this work accurately obtain the actual projectile proximity explosion position parameters.
基金Project supported by the National Natural Science Foundation of China （Grant No 10675045） and the Foundation for the Author of National Excellent Doctoral Dissertation of China （Grant No 200317） and the SRFDP （Grant No 20040542003）.
文摘This paper studies the finite statistical-mechanical entropy of the Schwarzschild anti-de Sitter （ADS） spacetime arising from quantum massless scalar field by using the ＇brick wall＇ approach in the Painlev; and Lemaaitre coordinates. At first glance, it seems that the results would be different from that in the Schwarzschild-like coordinate since both the Painlev; and the Lemaitre spacetimes do not possess the event horizon obviously. However, this paper proves that the entropies in these coordinates are exactly equivalent to that in the Schwarzschild-like coordinate.
文摘In this paper,various aberrations have been analyzed.Not only the effects of aberration on geometrical center position are taken into account,but also the deviation of displayed star position energy center caused by aberration is analyzed.These two aspects have been taken into comprehensive evaluation and star position correction.The correction method based on polar coordinates is proposed,and cumbersome partition correction and calculated quantity based on two-dimensional coordinates can be simplified.The experimental results show that the correction processing based on polar coordinates is simpler and easier compared with any other correction methods.In addition,the correction results are significantly more accurate.
基金performed under the auspices of the National Nuclear Security Administration of the US Department of Energy at Los Alamos National Laboratory under Contract No.DE-AC52-06NA25396supported in part by the Czech Science Foundation GrantP205/10/0814the Czech Ministry of Education grants MSM 6840770022 and LC528
文摘We give a brief discussion of some of the contributions of Peter Lax to Com- putational Fluid Dynamics. These include the Lax-Friedrichs and Lax-Wendroff numerical schemes. We also mention his collaboration in the 1983 HLL Riemann solver. We de- velop two-dimensional Lax-Friedrichs and Lax-Wendroff schemes for the Lagrangian form of the Euler equations on triangular grids. We apply a composite scheme that uses a Lax- Friedrichs time step as a dissipative filter after several Lax-Wendroff time steps. Numerical results for Noh＇s infinite strength shock problem, the Sedov blast wave problem, and the Saltzman piston problem are presented.
基金Project supported by the National Natural Science Foundation of China(Grant No.51272027)
文摘Bond valence method illustrates the relation between valence and length of a particular bond type. This theory has been used to predict structure information, but the effect is very limited. In this paper, two indexes, i.e., global instability index（GII） and bond strain index（BSI）, are adopted as a judgment of a search-match program for prediction. The results show that with GII and BSI combined as judgment, the predicted atom positions are very close to real ones. The mechanism and validity of this searching program are also discussed. The GII ＆ BSI distribution contour map reveals that the predicted function is a reflection of exponential feature of bond valence formula. This combined searching method may be integrated with other structure-determination method, and may be helpful in refining and testifying light atom positions.
基金supported by National Natural Science Foundation of China under Grant Nos.11505240,11375196 and 11405174the National ITER program of China under Contract No.2014GB113000
文摘Field-aligned coordinates have been implemented in the gyrokinetic semi-Lagrangian code NLT, Ye et al （2016 J. Comput. Phys. 316 180）, to improve the computational efficiency for the numerical simulations of tokamak turbulence and transport. 4D B-spline interpolation in field- aligned coordinates is applied to solve the gyrokinetic Vlasov equation. A fast iterative algorithm is proposed for efficiently solving the quasi-neutrality equation. A pseudo transform method is used for the numerical integration of the gyro-average operator for perturbations with a high toroidal mode number. The new method is shown to result in an improved code performance for reaching a given accuracy. Some numerical tests are presented to illustrate the new methods.
基金supported by the National Natural Science Foundation of China (Grant Nos 10572021 and 10772025)the Doctoral Program Foundation of Institution of Higher Education of China (Grant No 20040007022)the Fund for Fundamental Research of Beijing Institute of Technology (Grant No 20070742005)
文摘This paper discusses the symmetry of Lagrangians of holonomic systems in terms of quasi-coordinates. Firstly, the definition and the criterion of the symmetry are given. Secondly, the condition under which there exists a conserved quantity and the form of the conserved quantity are obtained. Finally, an example is shown to illustrate the application of the results.
文摘The selection and coordinated application of government innovation policies are crucial for guiding the direction of enterprise innovation and unleashing their innovation potential.However,due to the lengthy,voluminous,complex,and unstructured nature of regional innovation policy texts,traditional policy classification methods often overlook the reality that these texts cover multiple policy topics,leading to lack of objectivity.In contrast,topic mining technology can handle large-scale textual data,overcoming challenges such as the abundance of policy content and difficulty in classification.Although topic models can partition numerous policy texts into topics,they cannot analyze the interplay among policy topics and the impact of policy topic coordination on enterprise innovation in detail.Therefore,we propose a big data analysis scheme for policy coordination paths based on the latent Dirichlet allocation(LDA)model and the fuzzyset qualitative comparative analysis(fsQCA)method by combining topic models with qualitative comparative analysis.The LDA model was employed to derive the topic distribution of each document and the word distribution of each topic and enable automatic classi-fication through algorithms,providing reliable and objective textual classification results.Subsequently,the fsQCA method was used to analyze the coordination paths and dynamic characteristics.Finally,experimental analysis was conducted using innovation policy text data from 31 provincial-level administrative regions in China from 2012 to 2021 as research samples.The results suggest that the proposed method effectively partitions innovation policy topics and analyzes the policy configuration,driving enterprise innovation in different regions.
基金the financial support from the Natural Science Foundation of China(Grant No.52172106)Anhui Provincial Natural Science Foundation(Grant Nos.2108085QB60 and 2108085QB61)China Postdoctoral Science Foundation(Grant Nos.2020M682057 and 2023T160651).
文摘Electrocatalytic nitrate reduction reaction has attracted increasing attention due to its goal of low carbon emission and environmental protection.Here,we report an efficient NitRR catalyst composed of single Mn sites with atomically dispersed oxygen(O)coordination on bacterial cellulose-converted graphitic carbon(Mn-O-C).Evidence of the atomically dispersed Mn-(O-C_(2))_(4)moieties embedding in the exposed basal plane of carbon surface is confirmed by X-ray absorption spectroscopy.As a result,the as-synthesized Mn-O-C catalyst exhibits superior NitRR activity with an NH_(3)yield rate(RNH_(3))of 1476.9±62.6μg h^(−1)cm^(−2)at−0.7 V(vs.reversible hydrogen electrode,RHE)and a faradaic efficiency(FE)of 89.0±3.8%at−0.5 V(vs.RHE)under ambient conditions.Further,when evaluated with a practical flow cell,Mn-O-C shows a high RNH_(3)of 3706.7±552.0μg h^(−1)cm^(−2)at a current density of 100 mA cm−2,2.5 times of that in the H cell.The in situ FT-IR and Raman spectroscopic studies combined with theoretical calculations indicate that the Mn-(O-C_(2))_(4)sites not only effectively inhibit the competitive hydrogen evolution reaction,but also greatly promote the adsorption and activation of nitrate(NO_(3)^(−)),thus boosting both the FE and selectivity of NH_(3)over Mn-(O-C_(2))_(4)sites.
基金supported by the National Key R&D Program of China(No.2017YFE0301100)National Natural Science Foundation of China(No.11875292)。
文摘Accurate tokamak plasma equilibrium solution in flux coordinates is crucial for many stability and transport studies.Different approaches for dealing with singularities in solving the nonlinear Grad-Shafranov(GS)equation in flux coordinates or also known as straight field line coordinates are proposed in this paper.The GS equation is solved by iterating the position of grids directly in flux coordinates,and hence,no additional errors are introduced due to mapping process for a convergent solution.The singularity at magnetic axis in flux coordinates is removed by using a novel coordinate transform technique.Different from other techniques previously developed,no assumption in boundary condition at magnetic axis is used.This is consistent with the fact that there is no physical boundary at the magnetic axis.A flux coordinate system with poloidal coordinate chosen as the geometric poloidal angle is proposed.It conquers the difficulty in no definition of poloidal coordinate in flux coordinates at separatrix because of the singularity at x-point(s)in a divertor configuration.It also simplifies the process for computing poloidal flux coordinate during the iteration for solving the nonlinear GS equation.Non-uniform grids can be applied in both radial and poloidal coordinates,which allows it to increase the spacial resolution near x-point(s)in a divertor configuration.Based on the model proposed in this paper,a new Flux coordinates based EQuilibrium solver(FEQ)in tokamaks is developed.The numerical solutions from this code agree well with both the analytic Solov’ev solution and the numerical one from the EFIT code for a divertor configuration in the EAST tokamak.This code can be applied for simulating different equilibria with prescribed shape,pressure and current profiles,i.e.including both limiter and divertor configurations,positive triangularity and negative triangularity,differentβ,arbitrary magnetic shear profile etc.It provides a powerful and convenient fixed-boundary inverse equilibrium solver including both magnetic axis and separatrix in the solution for tokamak researches.
基金supported by the National Natural Science Foundation of China(51872115,12234018 and 52101256)Beijing Synchrotron Radiation Facility(BSRF,4B9A)。
文摘Atom-level modulation of the coordination environment for single-atom catalysts(SACs)is considered as an effective strategy for elevating the catalytic performance.For the MNxsite,breaking the symmetrical geometry and charge distribution by introducing relatively weak electronegative atoms into the first/second shell is an efficient way,but it remains challenging for elucidating the underlying mechanism of interaction.Herein,a practical strategy was reported to rationally design single cobalt atoms coordinated with both phosphorus and nitrogen atoms in a hierarchically porous carbon derived from metal-organic frameworks.X-ray absorption spectrum reveals that atomically dispersed Co sites are coordinated with four N atoms in the first shell and varying numbers of P atoms in the second shell(denoted as Co-N/P-C).The prepared catalyst exhibits excellent oxygen reduction reaction(ORR)activity as well as zinc-air battery performance.The introduction of P atoms in the Co-SACs weakens the interaction between Co and N,significantly promoting the adsorption process of ^(*)OOH,resulting in the acceleration of reaction kinetics and reduction of thermodynamic barrier,responsible for the increased intrinsic activity.Our discovery provides insights into an ultimate design of single-atom catalysts with adjustable electrocatalytic activities for efficient electrochemical energy conversion.
基金supported by the National Natural Science Foundation of China (Grant Nos.10672143 and 60575055)
文摘We propose a new concept of the conformal invariance and the conserved quantities for holonomic systems with quasi-coordinates. A one-parameter infinitesimal transformation group and its infinitesimal transformation vector of generators for holonomic systems with quasi-coordinates are described in detail. The conformal factor in the determining equations of the Lie symmetry is found. The necessary and sufficient conditions of conformal invariance, which are simultaneously of Lie symmetry, are given. The conformal invariance may lead to corresponding Hojman conserved quantities when the conformal invariance satisfies some conditions. Finally, an illustration example is introduced to demonstrate the application of the result.
