A new magnetic field configuration is proposed by introducing a cusped field to the helicon plasma thruster(HPT),and the effects of the cusped field on the discharge characteristics of the HPT are investigated.The exp...A new magnetic field configuration is proposed by introducing a cusped field to the helicon plasma thruster(HPT),and the effects of the cusped field on the discharge characteristics of the HPT are investigated.The experimental results show that the thruster can still achieve a stable W mode discharge with the additional cusped field,while the discharge conditions have been changed so that a higher RF power is required to achieve the W mode under the same experimental conditions.However,the ion density in the plume region is increased by at least one order of magnitude and the ion flux density is increased by a factor of 4 to 5.The ionization enhancement is attributed to the change in magnetic field configuration,which improves the energy coupling efficiency and the ability to confine charged particles(particularly electrons).This magnetic confinement could employ more electrons to ionize the working medium atoms,and the ionization rate is enhanced.The increase in ion density leads to a reduction in the energy available for ion acceleration,resulting in a slight decrease in ion energy.展开更多
Previous studies have shown that leak electro ns in cusped field thrusters can move along the channel axis to the anode after crossing the magnetic cusp on the exit.In this paper,a onedimensional fluid model is built ...Previous studies have shown that leak electro ns in cusped field thrusters can move along the channel axis to the anode after crossing the magnetic cusp on the exit.In this paper,a onedimensional fluid model is built along two typical electron paths to study the influence of leak electrons on the discharge characteristics of a cusped field thruster,considering the electron temperature equation.It is found that the frequencies of low-frequency oscillations increase with a decrease in the proportion of leak electrons,which is related to an increase in the ion speed in the channel.Simulation results show that the position of the peak electron temperature is near the magnetic cusp on the exit and the position of the peak electron density is located downstream from the middle magnetic tip.With a decrease in the proportion of the leak electrons,the peak electron temperature and peak electron density decrease and the position of the peak electron density moves away from the exit,which is related to a decrease in the potential fall on the exit and an increase in confinement of electrons to the middle magnetic cusp.展开更多
Magnetic mirror used as an efficient tool to confine plasma has been widely adopted in many different areas especially in recent cusped field thrusters. In order to check the influence of magnetic mirror effect on the...Magnetic mirror used as an efficient tool to confine plasma has been widely adopted in many different areas especially in recent cusped field thrusters. In order to check the influence of magnetic mirror effect on the plasma distribution in a cusped field thruster, three different radii of the discharge channel(6 mm, 4 mm, and 2 mm) in a cusped field thruster are investigated by using Particle-in-Cell Plus Monte Carlo(PIC-MCC) simulated method, under the condition of a fixed axial length of the discharge channel and the same operating parameters. It is found that magnetic cusps inside the small radius discharge channel cannot confine electrons very well. Thus, the electric field is hard to establish. With the reduction of the discharge channel’s diameter, more electrons will escape from cusps to the centerline area near the anode due to a lower magnetic mirror ratio. Meanwhile, the leak width of the cusped magnetic field will increase at the cusp. By increasing the magnetic field strength in a small radius model of a cusped field thruster, the negative effect caused by the weak magnetic mirror effect can be partially compensated. Therefore, according to engineering design, the increase of magnetic field strength can contribute to obtaining a good performance, when the radial distance between the magnets and the inner surface of the discharge channel is relatively big.展开更多
The qualitative theory of differential equations is applied to the Ostrovsky equation. The cusped soliton and loop-soliton solutions of the Ostrovsky equation are obtained. Asymptotic behavior of eusped soliton soluti...The qualitative theory of differential equations is applied to the Ostrovsky equation. The cusped soliton and loop-soliton solutions of the Ostrovsky equation are obtained. Asymptotic behavior of eusped soliton solutions is given. Numerical simulations are provided for cusped solitons and so-called loop-solitons of the Ostrovsky equation.展开更多
The microwave discharge cusped field thruster is a novel concept of electric micropropulsion device,which operatesμN level thrust in low mass flow rate conditions,making use of a coaxial transmission line resonator.W...The microwave discharge cusped field thruster is a novel concept of electric micropropulsion device,which operatesμN level thrust in low mass flow rate conditions,making use of a coaxial transmission line resonator.With its advantages of low thrust noise and high thrust resolution over a wide range of thrust,the thruster has emerged as a candidate thruster for the space-borne gravitational wave detection mission.The cathode effects commonly exist in many kinds of electric propulsion,and they are typically significant in micropropulsions.In order to find out the cathode position effects on a microwave discharge cusped field thruster,a thermionic cathode is mounted on a cross-slider for coupling.Under different cathode positions,the plume is analyzed by a Faraday probe and a retarding potential analyzer to analyze the performance and discharge characteristics.The results show that the magnetic mirror effect leads to significant degradation of anode current and an increase in low-energy ion ratio as the cathode moves away from the thruster exit.The electron conduction route also significantly impacts anode current efficiency,related to the cathode-exit distance and the thruster magnetic topology.展开更多
In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system w...In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system with three singular straight lines,and derive all possible phase portraits under corresponding parameter conditions.Then we show the existence and dynamics of two types of peaked traveling wave solutions including peakons and periodic cusp wave solutions.The exact explicit expressions of two peakons are given.Besides,we also derive smooth solitary wave solutions,periodic wave solutions,compacton solutions,and kink-like(antikink-like)solutions.Numerical simulations are further performed to verify the correctness of the results.Most importantly,peakons and periodic cusp wave solutions are newly found for the equation,which extends the previous results.展开更多
Letλ_(f×f)(n)be the nth Fourier coeficient of Rankin-Selberg L-function L(f×f,s).In this paper,we are interested in the average behavior of coeficients of Rankin-Selberg L-functions over sparse sequences,an...Letλ_(f×f)(n)be the nth Fourier coeficient of Rankin-Selberg L-function L(f×f,s).In this paper,we are interested in the average behavior of coeficients of Rankin-Selberg L-functions over sparse sequences,and establish the asymptotic formula ofΣ_(n≤xλ_(f×f)n^(m)).展开更多
Let f be a primitive holomorphic cusp form with even integral weight k≥2 for the full modular groupΓ=SL(2,Z)andλ_(sym^(j)f)(n)be the n-th coefficient of Dirichlet series of j-th symmetric L-function L(s,sym^(j)f)at...Let f be a primitive holomorphic cusp form with even integral weight k≥2 for the full modular groupΓ=SL(2,Z)andλ_(sym^(j)f)(n)be the n-th coefficient of Dirichlet series of j-th symmetric L-function L(s,sym^(j)f)attached to f.In this paper,we study the mean value distribution over a specific sparse sequence of positive integers of the following sum∑(a^(2)+b^(2)+c^(2)+d^(2)≤x(a,b,c,d)∈Z^(4))λ_(sym^(j))^(i)f(a^(2)+b^(2)+c^(2)+d^(2))where j≥2 is a given positive integer,i=2,3,4 andαis sufficiently large.We utilize Python programming to design algorithms for higher power conditions,combining Perron's formula,latest results of representations of natural integers as sums of squares,as well as analytic properties and subconvexity and convexity bounds of automorphic L-functions,to ensure the accuracy and verifiability of asymptotic formulas.The conclusion we obtained improves previous results and extends them to a more general settings.展开更多
Let f be a Hecke eigenform of even integral weight k for the full modular group SL_(2)(Z).Denote byλ_(f)(n)the n th normalized coefficient of f.The sum of Fourier coefficients of cusp form over the quadratic polynomi...Let f be a Hecke eigenform of even integral weight k for the full modular group SL_(2)(Z).Denote byλ_(f)(n)the n th normalized coefficient of f.The sum of Fourier coefficients of cusp form over the quadratic polynomial m^(2)+n^(2) is considered,i.e.,∑_( m^( 2)+n^( 2))≤λ^(2)_( f)(m^(2)+n^(2))=CX+O(X ^(337/491+ϵ)),here X large enough and C is a constant.展开更多
运用EMBOSS(The european molecular biology open software suite)软件包中的CHIPS(Condonheterozygosity in a protein coding sequence)和CUSP(Create a condon usage table)程序对红豆杉属的52个基因的密码子偏性进行综合分析,并与...运用EMBOSS(The european molecular biology open software suite)软件包中的CHIPS(Condonheterozygosity in a protein coding sequence)和CUSP(Create a condon usage table)程序对红豆杉属的52个基因的密码子偏性进行综合分析,并与大肠杆菌、酵母、拟南芥和水稻的密码子偏性进行比较。结果表明,红豆杉属基因的Nc(有效密码子数)为45～58,大部分密码子使用频率较为一致。部分氨基酸密码子使用频率存在较大差异,如Ala、Asp、Phe、Gly、His、Asn、Arg、Thr、Tyr等。红豆杉属基因密码子偏性与拟南芥等双子叶植物较接近,与原核生物和单子叶植物相差较远。展开更多
A rational parametric planar cubic H spline curve is defined by a set of control vertices in a plane and percentage factors of line segments between every two control vertices. Movement of any control vertex affects ...A rational parametric planar cubic H spline curve is defined by a set of control vertices in a plane and percentage factors of line segments between every two control vertices. Movement of any control vertex affects three curve segments. This paper is the succession and development of reference of Tang Yuehong. We analyze the geometric features like cusps and inflection points in the curve and calculate the cusps and inflection points, then give a necessary and sufficient condition to the inflection points in the curve when it is non degenerative, and finally show that the curves have no cusps in the interval (0,1). In many applications, it is desirable to analyze the parametric curves for undesirable features like cusps and inflection points展开更多
基金sponsored by the National Key Research and Development Program of China(Nos.2020YFC2201100 and 2021YFE0116000)National Natural Science Foundation of China(Nos.12175032,12102082,12275044,52372373 and 12211530449)+4 种基金the Fundamental Research Funds for the Central Universities(Nos.DUT22GF305 and DUT22QN232)S&T Program of Hebei Province(Nos.YCYZ202201 and 216Z1901G)S&T Innovation Program of Hebei Province(Nos.SJMYF2022X18 and SJMYF2022X 06)Beijing Nova Program(No.20240484718)Langfang Science and Technology Program(No.2022011039).
文摘A new magnetic field configuration is proposed by introducing a cusped field to the helicon plasma thruster(HPT),and the effects of the cusped field on the discharge characteristics of the HPT are investigated.The experimental results show that the thruster can still achieve a stable W mode discharge with the additional cusped field,while the discharge conditions have been changed so that a higher RF power is required to achieve the W mode under the same experimental conditions.However,the ion density in the plume region is increased by at least one order of magnitude and the ion flux density is increased by a factor of 4 to 5.The ionization enhancement is attributed to the change in magnetic field configuration,which improves the energy coupling efficiency and the ability to confine charged particles(particularly electrons).This magnetic confinement could employ more electrons to ionize the working medium atoms,and the ionization rate is enhanced.The increase in ion density leads to a reduction in the energy available for ion acceleration,resulting in a slight decrease in ion energy.
文摘Previous studies have shown that leak electro ns in cusped field thrusters can move along the channel axis to the anode after crossing the magnetic cusp on the exit.In this paper,a onedimensional fluid model is built along two typical electron paths to study the influence of leak electrons on the discharge characteristics of a cusped field thruster,considering the electron temperature equation.It is found that the frequencies of low-frequency oscillations increase with a decrease in the proportion of leak electrons,which is related to an increase in the ion speed in the channel.Simulation results show that the position of the peak electron temperature is near the magnetic cusp on the exit and the position of the peak electron density is located downstream from the middle magnetic tip.With a decrease in the proportion of the leak electrons,the peak electron temperature and peak electron density decrease and the position of the peak electron density moves away from the exit,which is related to a decrease in the potential fall on the exit and an increase in confinement of electrons to the middle magnetic cusp.
基金supported by the National Natural Science Foundation of China(Grant No.51006028)the Foundation for Innovative Research Groups of the National Natural Science Foundation of China(Grant No.51121004)
文摘Magnetic mirror used as an efficient tool to confine plasma has been widely adopted in many different areas especially in recent cusped field thrusters. In order to check the influence of magnetic mirror effect on the plasma distribution in a cusped field thruster, three different radii of the discharge channel(6 mm, 4 mm, and 2 mm) in a cusped field thruster are investigated by using Particle-in-Cell Plus Monte Carlo(PIC-MCC) simulated method, under the condition of a fixed axial length of the discharge channel and the same operating parameters. It is found that magnetic cusps inside the small radius discharge channel cannot confine electrons very well. Thus, the electric field is hard to establish. With the reduction of the discharge channel’s diameter, more electrons will escape from cusps to the centerline area near the anode due to a lower magnetic mirror ratio. Meanwhile, the leak width of the cusped magnetic field will increase at the cusp. By increasing the magnetic field strength in a small radius model of a cusped field thruster, the negative effect caused by the weak magnetic mirror effect can be partially compensated. Therefore, according to engineering design, the increase of magnetic field strength can contribute to obtaining a good performance, when the radial distance between the magnets and the inner surface of the discharge channel is relatively big.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10961011 and 60964006
文摘The qualitative theory of differential equations is applied to the Ostrovsky equation. The cusped soliton and loop-soliton solutions of the Ostrovsky equation are obtained. Asymptotic behavior of eusped soliton solutions is given. Numerical simulations are provided for cusped solitons and so-called loop-solitons of the Ostrovsky equation.
基金supported by the National Key R&D Program of China(No.2020YFC2201000)National Natural Science Foundation of China(No.11927812)。
文摘The microwave discharge cusped field thruster is a novel concept of electric micropropulsion device,which operatesμN level thrust in low mass flow rate conditions,making use of a coaxial transmission line resonator.With its advantages of low thrust noise and high thrust resolution over a wide range of thrust,the thruster has emerged as a candidate thruster for the space-borne gravitational wave detection mission.The cathode effects commonly exist in many kinds of electric propulsion,and they are typically significant in micropropulsions.In order to find out the cathode position effects on a microwave discharge cusped field thruster,a thermionic cathode is mounted on a cross-slider for coupling.Under different cathode positions,the plume is analyzed by a Faraday probe and a retarding potential analyzer to analyze the performance and discharge characteristics.The results show that the magnetic mirror effect leads to significant degradation of anode current and an increase in low-energy ion ratio as the cathode moves away from the thruster exit.The electron conduction route also significantly impacts anode current efficiency,related to the cathode-exit distance and the thruster magnetic topology.
基金Supported by the National Natural Science Foundation of China(12071162)the Natural Science Foundation of Fujian Province(2021J01302)the Fundamental Research Funds for the Central Universities(ZQN-802).
文摘In this paper,we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach.We obtain a traveling wave system which is a singular planar dynamical system with three singular straight lines,and derive all possible phase portraits under corresponding parameter conditions.Then we show the existence and dynamics of two types of peaked traveling wave solutions including peakons and periodic cusp wave solutions.The exact explicit expressions of two peakons are given.Besides,we also derive smooth solitary wave solutions,periodic wave solutions,compacton solutions,and kink-like(antikink-like)solutions.Numerical simulations are further performed to verify the correctness of the results.Most importantly,peakons and periodic cusp wave solutions are newly found for the equation,which extends the previous results.
基金Supported by Natural Science Foundation of Shandong Province(No.ZR2024MA053)。
文摘Letλ_(f×f)(n)be the nth Fourier coeficient of Rankin-Selberg L-function L(f×f,s).In this paper,we are interested in the average behavior of coeficients of Rankin-Selberg L-functions over sparse sequences,and establish the asymptotic formula ofΣ_(n≤xλ_(f×f)n^(m)).
文摘Let f be a primitive holomorphic cusp form with even integral weight k≥2 for the full modular groupΓ=SL(2,Z)andλ_(sym^(j)f)(n)be the n-th coefficient of Dirichlet series of j-th symmetric L-function L(s,sym^(j)f)attached to f.In this paper,we study the mean value distribution over a specific sparse sequence of positive integers of the following sum∑(a^(2)+b^(2)+c^(2)+d^(2)≤x(a,b,c,d)∈Z^(4))λ_(sym^(j))^(i)f(a^(2)+b^(2)+c^(2)+d^(2))where j≥2 is a given positive integer,i=2,3,4 andαis sufficiently large.We utilize Python programming to design algorithms for higher power conditions,combining Perron's formula,latest results of representations of natural integers as sums of squares,as well as analytic properties and subconvexity and convexity bounds of automorphic L-functions,to ensure the accuracy and verifiability of asymptotic formulas.The conclusion we obtained improves previous results and extends them to a more general settings.
基金Supported in part by the Natural Science Foundation of Henan Youth Foundation(Grant No.222300420034)National Natural Science Foundation of China(Grant No.11871193).
文摘Let f be a Hecke eigenform of even integral weight k for the full modular group SL_(2)(Z).Denote byλ_(f)(n)the n th normalized coefficient of f.The sum of Fourier coefficients of cusp form over the quadratic polynomial m^(2)+n^(2) is considered,i.e.,∑_( m^( 2)+n^( 2))≤λ^(2)_( f)(m^(2)+n^(2))=CX+O(X ^(337/491+ϵ)),here X large enough and C is a constant.
文摘运用EMBOSS(The european molecular biology open software suite)软件包中的CHIPS(Condonheterozygosity in a protein coding sequence)和CUSP(Create a condon usage table)程序对红豆杉属的52个基因的密码子偏性进行综合分析,并与大肠杆菌、酵母、拟南芥和水稻的密码子偏性进行比较。结果表明,红豆杉属基因的Nc(有效密码子数)为45～58,大部分密码子使用频率较为一致。部分氨基酸密码子使用频率存在较大差异,如Ala、Asp、Phe、Gly、His、Asn、Arg、Thr、Tyr等。红豆杉属基因密码子偏性与拟南芥等双子叶植物较接近,与原核生物和单子叶植物相差较远。
文摘A rational parametric planar cubic H spline curve is defined by a set of control vertices in a plane and percentage factors of line segments between every two control vertices. Movement of any control vertex affects three curve segments. This paper is the succession and development of reference of Tang Yuehong. We analyze the geometric features like cusps and inflection points in the curve and calculate the cusps and inflection points, then give a necessary and sufficient condition to the inflection points in the curve when it is non degenerative, and finally show that the curves have no cusps in the interval (0,1). In many applications, it is desirable to analyze the parametric curves for undesirable features like cusps and inflection points
