By using the mean-field Jordan-Wigner transformation analysis,this paper studies the one-dimensionalspin-1/2 XYZ antiferromagnetic chain in the transverse field with uniform long-range interactions among the z-compone...By using the mean-field Jordan-Wigner transformation analysis,this paper studies the one-dimensionalspin-1/2 XYZ antiferromagnetic chain in the transverse field with uniform long-range interactions among the z-components of the spins.The thermodynamic quantities,such as Helmholtz free energy,the internal energy,the specificheat,and the isothermal susceptibility,are obtained.Under degenerating condition,our results agree with numericalresults of the other literatures.展开更多
We study the Drude weight D and optical conductivity of the two-dimensional (2D) Hubbard model at half filling with staggered magnetic flux (SMF). When SMF being introduced, the hopping integrals are modulated by ...We study the Drude weight D and optical conductivity of the two-dimensional (2D) Hubbard model at half filling with staggered magnetic flux (SMF). When SMF being introduced, the hopping integrals are modulated by the magnetic flux. The optical sum rule, which is related to the mean kinetic energy of band electrons, is evaluated for this 2D Hubbard Hamiltonian. Our present result gives the dependence of the kinetic energy, D and the optical conductivity on SMF and U. At half filling D vanishes exponentially with system size. We also find in the frequency dependence of the optical conductivity, there is δ-function peak at ω ≈ 2|m|U and the incoherent excitations begin to present themselves extended to a higher energy region.展开更多
With suitable assumptions a hydrodynamic model for the magnetic fluid motion in an axial variable gap seal was con- structed, and the solution to the equations of the model was deduced. The characteristics of a magnet...With suitable assumptions a hydrodynamic model for the magnetic fluid motion in an axial variable gap seal was con- structed, and the solution to the equations of the model was deduced. The characteristics of a magnetic fluid seal and its motion, including the speed and pressure distribution, and the seal capacity of a magnetic fluid rotating seal were systematically described. The factors affecting seal capacity and ways to improve seal capacity based on the hydrodynamic model are discussed. The basic condition for dynamic seal availability is presented. The rotating speed and radius of the shafts should be decreased. The work can provide proof of a seal design or suggest ways to improve the seal capacity of magnetic fluid seals.展开更多
An experimental method is introduced in this paper to build the dynamics of AMSS (the active magnetic suspension system), which doesn’t depend on system’s physical parameters. The rotor can be reliably suspended und...An experimental method is introduced in this paper to build the dynamics of AMSS (the active magnetic suspension system), which doesn’t depend on system’s physical parameters. The rotor can be reliably suspended under the unit feedback control system designed with the primary dynamic model obtained. Online identification in frequency domain is processed to give the precise model. Comparisons show that the experimental method is much closer to the precise model than the theoretic method based on magnetic circuit law. So this experimental method is a good choice to build the primary dynamic model of AMSS.展开更多
The linear and non-linear math models of the switched reluctance generator (SRG) in generator mode were established in this work. The phase current and energy conversion process during generator operation were simulat...The linear and non-linear math models of the switched reluctance generator (SRG) in generator mode were established in this work. The phase current and energy conversion process during generator operation were simulated by the linear math model. The non-linear math model was used to analyze the characteristics of the SRG operation in self-excitation mode and in separately-excitation mode. Some important findings on how the SRG is operated and controlled were obtained in this study, which provides theoretical basis for further design and experimental study.展开更多
A good mechanical model of magnetorheological damper (MRD) is essential to predict the shock isolation performance of MRD in numerical simulation. But at present, the mechanical models of MRD were all derived from the...A good mechanical model of magnetorheological damper (MRD) is essential to predict the shock isolation performance of MRD in numerical simulation. But at present, the mechanical models of MRD were all derived from the experiment subjected to harmonic vibration loads. In this paper, a commercial MRD (type RD-1005-3) manufactured by Lord Corporation was studied ex-perimentally in order to investigate its isolation performance under the impact loads. A new me-chanical model of MRD was proposed according to the data obtained by impact test. A good agreement between the numerical results and test data was observed, which showed that the model was good to simulate the dynamic properties of MRD under impact loads. It is also demon-strated that MRD can improve the acceleration and displacement response of the structure obvi-ously under impact loads.展开更多
With a perfect mathematical method by us, we obtain some expressions of the orbital effect for a test particle and some meaningful results in the gravitational field of the center mass with electric charge and magneti...With a perfect mathematical method by us, we obtain some expressions of the orbital effect for a test particle and some meaningful results in the gravitational field of the center mass with electric charge and magnetic moment.展开更多
The phenomenon of hysteresis of contact angle is an important topic subject to a long time of argument.A simple hydrostatic model of sessile drops under the gravity in combination with an ideal surface roughness model...The phenomenon of hysteresis of contact angle is an important topic subject to a long time of argument.A simple hydrostatic model of sessile drops under the gravity in combination with an ideal surface roughness model is used to interpret the process of drop volume increase or decrease of a planar sessile drop and to shed light on the contact angle hysteresis and its relationship with the solid surface roughness. With this model, the advancing and receding contact angles are conceptually explained in terms of equilibrium contact angle and surface roughness only,without invoking the thermodynamic multiplicity. The model is found to be qualitatively consistent to experimental observations on contact angle hysteresis and it suggests a possible way to approach the hysteresis of three-dimensional sessile drops.展开更多
A novel magnetic adsorbent was synthesized by magnetizing bentonite by APTES-Fe_3O_4 via a functional groupbridged interaction. The characterization of APTES-Fe_3O_4/bentonite was conducted via transmission electron m...A novel magnetic adsorbent was synthesized by magnetizing bentonite by APTES-Fe_3O_4 via a functional groupbridged interaction. The characterization of APTES-Fe_3O_4/bentonite was conducted via transmission electron microscope(TEM), X-ray diffraction(XRD), Fourier transform infrared spectrophotometer(FT-IR), thermal gravimetric analysis(TGA), vibrating sample magnetometer(VSM), zeta potential analysis and Brunner–Emmet–Teller(BET). The APTES-Fe_3O_4/bentonite was assessed as adsorbents for methylene blue(MB) with a high adsorption capacity(91.83 mg·g^(-1)). Factors affecting the adsorption of MB(such as p H, equilibrium time, temperature and initial concentration) were investigated. The adsorption process completely reaches equilibrium after 120 min and the maximum sorption is achieved at p H 8.0. The adsorption trend follows the pseudosecond order kinetics model. The adsorption data gives good fits with Langmuir isotherm model. The parameter factor RLfalls between 0 and 1, indicating the adsorption of MB is favorable. The adsorption process is endothermic with positive ΔH^0 values. The positive values of ΔG^0 confirm the affinity of the adsorbent towards MB, and suggest an increased randomness at the solid–liquid interface during the adsorption process. Regeneration of the saturated adsorbent was easily carried out via gamma-irradiation.展开更多
A transverse Ising spin system, in the presence of time-dependent longitudinal field, is studied by the effective-field theory (EFT). The effective-field equations of motion of the average magnetization are given fo...A transverse Ising spin system, in the presence of time-dependent longitudinal field, is studied by the effective-field theory (EFT). The effective-field equations of motion of the average magnetization are given for the simple cubic lattice (Z ---- 6) and the honeycomb lattice (Z = 3). The Liapunov exponent A is calculated for discussing the stability of the magnetization and it is used to determine the phase boundary. The dynamic phase transition diagrams in ho/ZJ - F/ZJ plane and in ho/ZJ - T/ZJ plane have been drawn, and there is no dynamical tricritical point on the dynamic phase transition boundary. The effect of the thermal fluctuations upon the dynamic phase boundary has been discussed.展开更多
Lattice Boltzmann Method is recently developed within numerical schemes for simulating a variety of physical systems. In this paper a new lattice Bhatnagar-Gross-Krook (LBGK) model for two-dimensional incompressible m...Lattice Boltzmann Method is recently developed within numerical schemes for simulating a variety of physical systems. In this paper a new lattice Bhatnagar-Gross-Krook (LBGK) model for two-dimensional incompressible magnetohydrodynamics (IMHD) is presented. The model is an extension of a hydrodynamics lattice BGK model with 9 velocities on a square lattice, resulting in a model with 17 velocities. Most of the existing LBGK models for MHD can be viewed as compressible schemes to simulate incompressible flows. The compressible effect might lead to some undesirable errors in numerical simulations. In our model the compressible effect has been overcome successfully. The model is then applied to the Hartmann flow, giving reasonable results.展开更多
A novel magnetic integrated controllable reactor of transformer type(CRT)has the advantages of simple structure,flexible assembly,convenient maintenance and practicability.To analyze its operation characteristics accu...A novel magnetic integrated controllable reactor of transformer type(CRT)has the advantages of simple structure,flexible assembly,convenient maintenance and practicability.To analyze its operation characteristics accurately,we establish corresponding equivalent mathematical model considering magnetic leakage based on magnetic circuit and circuit dualistic transformation method.The distribution of magnetic leakage field of each winding is analyzed qualitatively,and the analytical calculation formulas of magnetizing inductance and leakage inductance of each winding are derived.Based on this,the analytical calculation formulas of short-circuit impedance and winding current of CRT under different working conditions are derived.The field-circuit coupling finite element model of the magnetic integrated CRT is established to simulate the current of each winding under different working conditions.The results show that the analytical calculation results of each winding current have good consistency with the finite element calculation results,indicating the validity of CRT equivalent mathematical model and correctness of the analytical formulas of leakage inductance,short-circuit impedance and winding current of CRT.The working winding current of CRT is increasing gradually with the operation of control winding in turn to realise the transition of CRT compensation capacity from zero to a rated value.展开更多
The characteristics of the novel switched reluctance motor with auxiliary winding and four big swallow-tailed-slots in the internal surface of stator is analysed with the stator cross section and winding photo given, ...The characteristics of the novel switched reluctance motor with auxiliary winding and four big swallow-tailed-slots in the internal surface of stator is analysed with the stator cross section and winding photo given, and the nlathematical model of the novel switched reluctance motor presented. To show that the auxiliary winding causes the electromotive force to improve current waveform and increase output power. The different effects of auxiliary winding on system performance under different speeds are analyzed and experimented. Simulation analyzing and experiments studying of the novel switched reluctance motor demonstrate validity of auxiliary winding improving current waveforms, increasing output power.展开更多
We study the effect of potential and thermal gradient induced non-equilibrium magnetization in quasi1-d itinerant magnets.A semi-phenomenological theory is employed in conjunction with the drift-diffusion model forthi...We study the effect of potential and thermal gradient induced non-equilibrium magnetization in quasi1-d itinerant magnets.A semi-phenomenological theory is employed in conjunction with the drift-diffusion model forthis study.Using the methods of non-equilibrium thermodynamics,we derive the transport currents correspondingto charge,heat,and magnetization flows in the presence of non-equilibrium magnetization textures.It is shown howtime-dependent magnetic textures give rise to charge and thermal currents even in the absence of external potential andthermal gradients through spin pumping.The presence of dynamical textures also affect the thermodynamic parametersof the system.As an application,we consider the case of a helimagnet.展开更多
A mathematical model based on mixed integer programming is presented in this paper for the passive shimming of magnet in magnetic resonance imaging(MRI) scanner.In this model,the magnetic field inhomogeneity tolerance...A mathematical model based on mixed integer programming is presented in this paper for the passive shimming of magnet in magnetic resonance imaging(MRI) scanner.In this model,the magnetic field inhomogeneity tolerance and the central value of the magnetic field after shimming are programmed together with the volume of each shim piece as the variables,which increases the degree of freedom and guarantees a better solution.The magnetic field inhomogeneity tolerance after shimming with a weighting coefficient and the total volume of shim pieces are both contained in the objective function of the model.By assigning different values to the weighting coefficient in the objective function,different shimming plans with different emphases can be obtained.A simulation test has been carried out on a small permanent magnet with frame structure.Several solutions are given and compared in this paper,which indicates that a practical shimming plan can be obtained quickly by solving this model.展开更多
The topology and dynamics of the three-dimensional magnetic field in the solar atmosphere govern various solar eruptive phenomena and activities, such as flares, coronal mass ejections, and filaments/prominences. We h...The topology and dynamics of the three-dimensional magnetic field in the solar atmosphere govern various solar eruptive phenomena and activities, such as flares, coronal mass ejections, and filaments/prominences. We have to observe and model the vector magnetic field to understand the structures and physical mechanisms of these solar activities. Vector magnetic fields on the photosphere are routinely observed via the polarized light, and inferred with the inversion of Stokes profiles. To analyze these vector magnetic fields, we need first to remove the 180° ambiguity of the transverse components and correct the projection effect. Then, the vector magnetic field can be served as the boundary conditions for a force-free field modeling after a proper preprocessing. The photospheric velocity field can also be derived from a time sequence of vector magnetic fields.Three-dimensional magnetic field could be derived and studied with theoretical force-free field models, numerical nonlinear force-free field models, magnetohydrostatic models, and magnetohydrodynamic models. Magnetic energy can be computed with three-dimensional magnetic field models or a time series of vector magnetic field. The magnetic topology is analyzed by pinpointing the positions of magnetic null points, bald patches, and quasi-separatrix layers. As a well conserved physical quantity,magnetic helicity can be computed with various methods, such as the finite volume method, discrete flux tube method, and helicity flux integration method. This quantity serves as a promising parameter characterizing the activity level of solar active regions.展开更多
基金the Open Fund of Jiangsu Laboratory of Advanced Functional Materials under Grant No.06KFJJ004
文摘By using the mean-field Jordan-Wigner transformation analysis,this paper studies the one-dimensionalspin-1/2 XYZ antiferromagnetic chain in the transverse field with uniform long-range interactions among the z-components of the spins.The thermodynamic quantities,such as Helmholtz free energy,the internal energy,the specificheat,and the isothermal susceptibility,are obtained.Under degenerating condition,our results agree with numericalresults of the other literatures.
基金National Natural Science Foundation of China under Grant No.10247010the Foundation for Key Program of Ministry of Education of China under Grant No.205181
文摘We study the Drude weight D and optical conductivity of the two-dimensional (2D) Hubbard model at half filling with staggered magnetic flux (SMF). When SMF being introduced, the hopping integrals are modulated by the magnetic flux. The optical sum rule, which is related to the mean kinetic energy of band electrons, is evaluated for this 2D Hubbard Hamiltonian. Our present result gives the dependence of the kinetic energy, D and the optical conductivity on SMF and U. At half filling D vanishes exponentially with system size. We also find in the frequency dependence of the optical conductivity, there is δ-function peak at ω ≈ 2|m|U and the incoherent excitations begin to present themselves extended to a higher energy region.
基金Project 59975083 supported by the National Natural Science Foundation of China
文摘With suitable assumptions a hydrodynamic model for the magnetic fluid motion in an axial variable gap seal was con- structed, and the solution to the equations of the model was deduced. The characteristics of a magnetic fluid seal and its motion, including the speed and pressure distribution, and the seal capacity of a magnetic fluid rotating seal were systematically described. The factors affecting seal capacity and ways to improve seal capacity based on the hydrodynamic model are discussed. The basic condition for dynamic seal availability is presented. The rotating speed and radius of the shafts should be decreased. The work can provide proof of a seal design or suggest ways to improve the seal capacity of magnetic fluid seals.
基金Supported by the National Nature Foundation of China (No.59975073)
文摘An experimental method is introduced in this paper to build the dynamics of AMSS (the active magnetic suspension system), which doesn’t depend on system’s physical parameters. The rotor can be reliably suspended under the unit feedback control system designed with the primary dynamic model obtained. Online identification in frequency domain is processed to give the precise model. Comparisons show that the experimental method is much closer to the precise model than the theoretic method based on magnetic circuit law. So this experimental method is a good choice to build the primary dynamic model of AMSS.
文摘The linear and non-linear math models of the switched reluctance generator (SRG) in generator mode were established in this work. The phase current and energy conversion process during generator operation were simulated by the linear math model. The non-linear math model was used to analyze the characteristics of the SRG operation in self-excitation mode and in separately-excitation mode. Some important findings on how the SRG is operated and controlled were obtained in this study, which provides theoretical basis for further design and experimental study.
基金Supported by National Natural Science Foundation of China (No.50638030,50525825)the National Science and Technology SupportProgram (No.2006BAJ13B02)
文摘A good mechanical model of magnetorheological damper (MRD) is essential to predict the shock isolation performance of MRD in numerical simulation. But at present, the mechanical models of MRD were all derived from the experiment subjected to harmonic vibration loads. In this paper, a commercial MRD (type RD-1005-3) manufactured by Lord Corporation was studied ex-perimentally in order to investigate its isolation performance under the impact loads. A new me-chanical model of MRD was proposed according to the data obtained by impact test. A good agreement between the numerical results and test data was observed, which showed that the model was good to simulate the dynamic properties of MRD under impact loads. It is also demon-strated that MRD can improve the acceleration and displacement response of the structure obvi-ously under impact loads.
基金the National Basic Research Program of China under,湖南省教育厅自然科学基金
文摘With a perfect mathematical method by us, we obtain some expressions of the orbital effect for a test particle and some meaningful results in the gravitational field of the center mass with electric charge and magnetic moment.
文摘The phenomenon of hysteresis of contact angle is an important topic subject to a long time of argument.A simple hydrostatic model of sessile drops under the gravity in combination with an ideal surface roughness model is used to interpret the process of drop volume increase or decrease of a planar sessile drop and to shed light on the contact angle hysteresis and its relationship with the solid surface roughness. With this model, the advancing and receding contact angles are conceptually explained in terms of equilibrium contact angle and surface roughness only,without invoking the thermodynamic multiplicity. The model is found to be qualitatively consistent to experimental observations on contact angle hysteresis and it suggests a possible way to approach the hysteresis of three-dimensional sessile drops.
基金Supported by the National Natural Science Foundation of China(61601227)the Natural Science Foundation of Jiangsu Province(BK20160939)+1 种基金the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(16KJB180010)the Qing Lan Project and Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)
文摘A novel magnetic adsorbent was synthesized by magnetizing bentonite by APTES-Fe_3O_4 via a functional groupbridged interaction. The characterization of APTES-Fe_3O_4/bentonite was conducted via transmission electron microscope(TEM), X-ray diffraction(XRD), Fourier transform infrared spectrophotometer(FT-IR), thermal gravimetric analysis(TGA), vibrating sample magnetometer(VSM), zeta potential analysis and Brunner–Emmet–Teller(BET). The APTES-Fe_3O_4/bentonite was assessed as adsorbents for methylene blue(MB) with a high adsorption capacity(91.83 mg·g^(-1)). Factors affecting the adsorption of MB(such as p H, equilibrium time, temperature and initial concentration) were investigated. The adsorption process completely reaches equilibrium after 120 min and the maximum sorption is achieved at p H 8.0. The adsorption trend follows the pseudosecond order kinetics model. The adsorption data gives good fits with Langmuir isotherm model. The parameter factor RLfalls between 0 and 1, indicating the adsorption of MB is favorable. The adsorption process is endothermic with positive ΔH^0 values. The positive values of ΔG^0 confirm the affinity of the adsorbent towards MB, and suggest an increased randomness at the solid–liquid interface during the adsorption process. Regeneration of the saturated adsorbent was easily carried out via gamma-irradiation.
文摘A transverse Ising spin system, in the presence of time-dependent longitudinal field, is studied by the effective-field theory (EFT). The effective-field equations of motion of the average magnetization are given for the simple cubic lattice (Z ---- 6) and the honeycomb lattice (Z = 3). The Liapunov exponent A is calculated for discussing the stability of the magnetization and it is used to determine the phase boundary. The dynamic phase transition diagrams in ho/ZJ - F/ZJ plane and in ho/ZJ - T/ZJ plane have been drawn, and there is no dynamical tricritical point on the dynamic phase transition boundary. The effect of the thermal fluctuations upon the dynamic phase boundary has been discussed.
文摘Lattice Boltzmann Method is recently developed within numerical schemes for simulating a variety of physical systems. In this paper a new lattice Bhatnagar-Gross-Krook (LBGK) model for two-dimensional incompressible magnetohydrodynamics (IMHD) is presented. The model is an extension of a hydrodynamics lattice BGK model with 9 velocities on a square lattice, resulting in a model with 17 velocities. Most of the existing LBGK models for MHD can be viewed as compressible schemes to simulate incompressible flows. The compressible effect might lead to some undesirable errors in numerical simulations. In our model the compressible effect has been overcome successfully. The model is then applied to the Hartmann flow, giving reasonable results.
基金Weinan Science and Technology Plan Project(No.2020ZDYF-JCYJ-177)General Special Scientific Research Projects of Education Department of Shaanxi Provincial Government(No.21JK0582)+2 种基金Young and Middle-aged Scientific and Technological Talents Project of Shaanxi Railway Institute(No.KJRC202001)Scientific Research Fund Project of Shaanxi Railway Institute(No.KY2021-34)Science and Technology Innovation Team of Shaanxi Railway Institute(No.KJTD201901)。
文摘A novel magnetic integrated controllable reactor of transformer type(CRT)has the advantages of simple structure,flexible assembly,convenient maintenance and practicability.To analyze its operation characteristics accurately,we establish corresponding equivalent mathematical model considering magnetic leakage based on magnetic circuit and circuit dualistic transformation method.The distribution of magnetic leakage field of each winding is analyzed qualitatively,and the analytical calculation formulas of magnetizing inductance and leakage inductance of each winding are derived.Based on this,the analytical calculation formulas of short-circuit impedance and winding current of CRT under different working conditions are derived.The field-circuit coupling finite element model of the magnetic integrated CRT is established to simulate the current of each winding under different working conditions.The results show that the analytical calculation results of each winding current have good consistency with the finite element calculation results,indicating the validity of CRT equivalent mathematical model and correctness of the analytical formulas of leakage inductance,short-circuit impedance and winding current of CRT.The working winding current of CRT is increasing gradually with the operation of control winding in turn to realise the transition of CRT compensation capacity from zero to a rated value.
文摘The characteristics of the novel switched reluctance motor with auxiliary winding and four big swallow-tailed-slots in the internal surface of stator is analysed with the stator cross section and winding photo given, and the nlathematical model of the novel switched reluctance motor presented. To show that the auxiliary winding causes the electromotive force to improve current waveform and increase output power. The different effects of auxiliary winding on system performance under different speeds are analyzed and experimented. Simulation analyzing and experiments studying of the novel switched reluctance motor demonstrate validity of auxiliary winding improving current waveforms, increasing output power.
文摘We study the effect of potential and thermal gradient induced non-equilibrium magnetization in quasi1-d itinerant magnets.A semi-phenomenological theory is employed in conjunction with the drift-diffusion model forthis study.Using the methods of non-equilibrium thermodynamics,we derive the transport currents correspondingto charge,heat,and magnetization flows in the presence of non-equilibrium magnetization textures.It is shown howtime-dependent magnetic textures give rise to charge and thermal currents even in the absence of external potential andthermal gradients through spin pumping.The presence of dynamical textures also affect the thermodynamic parametersof the system.As an application,we consider the case of a helimagnet.
基金supported by the National Natural Science Foundation of China(Grant No.50807050)
文摘A mathematical model based on mixed integer programming is presented in this paper for the passive shimming of magnet in magnetic resonance imaging(MRI) scanner.In this model,the magnetic field inhomogeneity tolerance and the central value of the magnetic field after shimming are programmed together with the volume of each shim piece as the variables,which increases the degree of freedom and guarantees a better solution.The magnetic field inhomogeneity tolerance after shimming with a weighting coefficient and the total volume of shim pieces are both contained in the objective function of the model.By assigning different values to the weighting coefficient in the objective function,different shimming plans with different emphases can be obtained.A simulation test has been carried out on a small permanent magnet with frame structure.Several solutions are given and compared in this paper,which indicates that a practical shimming plan can be obtained quickly by solving this model.
基金supported by National Natural Science Foundation of China (Grant Nos. 11533005, 11203014, 11373023, and 11303016)National Key Basic Research Special Foundation (Grant No. 2014CB744203)
文摘The topology and dynamics of the three-dimensional magnetic field in the solar atmosphere govern various solar eruptive phenomena and activities, such as flares, coronal mass ejections, and filaments/prominences. We have to observe and model the vector magnetic field to understand the structures and physical mechanisms of these solar activities. Vector magnetic fields on the photosphere are routinely observed via the polarized light, and inferred with the inversion of Stokes profiles. To analyze these vector magnetic fields, we need first to remove the 180° ambiguity of the transverse components and correct the projection effect. Then, the vector magnetic field can be served as the boundary conditions for a force-free field modeling after a proper preprocessing. The photospheric velocity field can also be derived from a time sequence of vector magnetic fields.Three-dimensional magnetic field could be derived and studied with theoretical force-free field models, numerical nonlinear force-free field models, magnetohydrostatic models, and magnetohydrodynamic models. Magnetic energy can be computed with three-dimensional magnetic field models or a time series of vector magnetic field. The magnetic topology is analyzed by pinpointing the positions of magnetic null points, bald patches, and quasi-separatrix layers. As a well conserved physical quantity,magnetic helicity can be computed with various methods, such as the finite volume method, discrete flux tube method, and helicity flux integration method. This quantity serves as a promising parameter characterizing the activity level of solar active regions.