We derived the properties of the terrestrial magnetopause(MP)from two modeling approaches,one global–fluid,the other local–kinetic,and compared the results with data collected in situ by the Magnetospheric Multiscal...We derived the properties of the terrestrial magnetopause(MP)from two modeling approaches,one global–fluid,the other local–kinetic,and compared the results with data collected in situ by the Magnetospheric Multiscale 2(MMS2)spacecraft.We used global magnetohydrodynamic(MHD)simulations of the Earth’s magnetosphere(publicly available from the NASA-CCMC[National Aeronautics and Space Administration–Community Coordinated Modeling Center])and local Vlasov equilibrium models(based on kinetic models for tangential discontinuities)to extract spatial profiles of the plasma and field variables at the Earth’s MP.The global MHD simulations used initial solar wind conditions extracted from the OMNI database at the time epoch when the MMS2 observes the MP.The kinetic Vlasov model used asymptotic boundary conditions derived from the same in situ MMS measurements upstream or downstream of the MP.The global MHD simulations provide a three-dimensional image of the magnetosphere at the time when the MMS2 crosses the MP.The Vlasov model provides a one-dimensional local view of the MP derived from first principles of kinetic theory.The MMS2 experimental data also serve as a reference for comparing and validating the numerical simulations and modeling.We found that the MP transition layer formed in global MHD simulations was generally localized closer to the Earth(roughly by one Earth radius)from the position of the real MP observed by the MMS.We also found that the global MHD simulations overestimated the thickness of the MP transition by one order of magnitude for three analyzed variables:magnetic field,density,and tangential speed.The MP thickness derived from the local Vlasov equilibrium was consistent with observations for all three of these variables.The overestimation of density in the Vlasov equilibrium was reduced compared with the global MHD solutions.We discuss our results in the context of future SMILE(Solar wind Magnetosphere Ionosphere Link Explorer)campaigns for observing the Earth’s MP.展开更多
The reverse magnetohydrodynamic(MHD)energy bypass technology is a promising energy redis⁃tribution technology in the scramjet system,in augmented with a power generation equipment to supply the neces⁃sary long-distanc...The reverse magnetohydrodynamic(MHD)energy bypass technology is a promising energy redis⁃tribution technology in the scramjet system,in augmented with a power generation equipment to supply the neces⁃sary long-distance flight airframe power.In this paper,a computational model of the scramjet magnetohydrody⁃namic channel is developed and verified by using the commercial software Fluent.It is found that when the mag⁃netic induction intensity is 1,2,3,4 T,the power generation efficiency is 22.5%,22.3%,22.0%,21.5%,and decreases with the increase of the magnetic induction intensity,and the enthalpy extraction rate is 0.026%,0.1%,0.21%,0.34%,and increases with the increase of the magnetic induction intensity.The deceleration ef⁃fect of electromagnetic action on the airflow in the power channel increases with the increase of magnetic induc⁃tion intensity.The stronger the magnetic field intensity,the more obvious the decreasing effect of fluid Mach num⁃ber in the channel.The power generation efficiency decreases as the magnetic induction intensity increases and the enthalpy extraction rate is reversed.As the local currents gathering at inlet and outlet of the power generation area,total temperature and enthalpy along the flow direction do not vary linearly,and there are maximum and minimum values at inlet and outlet.Increasing the number of electrodes can effectively regulate the percentage of Joule heat dissipation,which can improve the power generation efficiency.展开更多
Various busbar configurations were built and modeled by the custom code based on the commercial package ANSYS for the 500 kA aluminum electrolysis cell.The configuration parameters,such as side riser entry ratio,numbe...Various busbar configurations were built and modeled by the custom code based on the commercial package ANSYS for the 500 kA aluminum electrolysis cell.The configuration parameters,such as side riser entry ratio,number of cathode bars connected to each riser,vertical location of side cathode busbar and short side cathode busbar,distance between rows of cells in potline,the number of neighboring cells,ratio of compensation busbar carried passing under cell and its horizontal location under cell along with large magnetohydrodynamic(MHD) computation based on the custom evaluation function were simulated and discussed.The results show that a cell with riser entry ratio of 11:9:8:9:11 and cathode busbar located at the level of aluminum solution,50% upstream cathode current passing under cell for magnetic field compensation,the distance between rows of 50 m is more stable.展开更多
A new hybrid method, Monte-Carlo-Heat-Flux (MCHF) method, was presented to analyze the radiative heat transfer of participating medium in a three-dimensional rectangular enclosure using combined the Monte-Carlo meth...A new hybrid method, Monte-Carlo-Heat-Flux (MCHF) method, was presented to analyze the radiative heat transfer of participating medium in a three-dimensional rectangular enclosure using combined the Monte-Carlo method with the heat flux method. Its accuracy and reliability was proved by comparing the computational results with exact results from classical "Zone Method".展开更多
The output power of a photovoltaic system largely depends on the amount of solar radiation that can be received by the photovoltaic panel, and the solar radiation energy reaching the ground is affected by the radiatio...The output power of a photovoltaic system largely depends on the amount of solar radiation that can be received by the photovoltaic panel, and the solar radiation energy reaching the ground is affected by the radiation transmission process. However, in engineering practice, numerical simulation prediction schemes tend to adopt a kind of radiation scheme, and the prediction of solar radiation and photovoltaic power cannot always meet the prediction accuracy. In this paper, NCEP-NCAR reanalysis data are used as the initial field, and a variety of radiation parameterization schemes are used to produce simulations for the Xinjiang area. Through analysis of examples, it is found that the simulation results differ greatly depending on the radiation parameterization scheme employed, with the maximum absolute error of the total radiation and the predicted power being 106.67 W m-2 and 3.5 MW, respectively. Meanwhile, the mean absolute percentage error of the total radiation ranges from 8.6% to 17.3%, and that of the predicted power from 11.3% to 20.2%. Having analyzed the simulation results of the different radiation parameterization schemes, we conclude that the RRTM/Dudhia and CAM (Community Atmospheric Model) schemes are the most appropriate when under clear-weather conditions.展开更多
Based on the thermodynamics theory and physical micro-properties of solid materials subjected to external loading at room temperature,a formula of calculating temperature difference of infrared radiation in terms of t...Based on the thermodynamics theory and physical micro-properties of solid materials subjected to external loading at room temperature,a formula of calculating temperature difference of infrared radiation in terms of the sum of three principal strains was deduced to quantitatively investigate the infrared radiation characteristics in test. Two typical specimens,the three-point bending beam and the disc pressed in diameter,were tested and their principal strains were calculated by finite element method in order to obtain the temperature differences of infrared radiation. Numerical results are in a good agreement with test results,which verifies the validity of the formula of calculating temperature differences of infrared radiation and the model of quantitatively describing the infrared radiation characteristics of solid materials,and reveals the corresponding inner physical mechanism.展开更多
In this study, the clear sky hourly global and net solar irradiances at the surface determined using SUNFLUX, a simple parameterization scheme, for three stations (Gaize, Naqu, and Lhasa) on the Tibetan Plateau were...In this study, the clear sky hourly global and net solar irradiances at the surface determined using SUNFLUX, a simple parameterization scheme, for three stations (Gaize, Naqu, and Lhasa) on the Tibetan Plateau were evaluated against observation data. Our modeled results agree well with observations. The correlation coefficients between modeled and observed values were 〉 0.99 for all three stations. The relative error of modeled results, in average was 〈 7%, and the root-mean-square variance was 〈 27 W m-2. The solar irradiances in the radiation model were slightly overestimated compared with observation data; there were at least two likely causes. First, the radiative effects of aerosols were not included in the radiation model. Second, solar irradiances determined by thermopile pyranometers include a thermal offset error that causes solar radiation to be slightly underestimated. The solar radiation absorbed by the ozone and water vapor was estimated. The results show that monthly mean solar radiation absorbed by the ozone is 〈 2% of the global solar radiation (〈 14 W m-2). Solar radiation absorbed by water vapor is stronger in summer than in winter. The maximum amount of monthly mean solar radiation absorbed by water vapor can be up to 13% of the global solar radiation (95 W m-2). This indicates that water vapor measurements with high precision are very important for precise determination of solar radiation.展开更多
Different SiGe processes and device designs are the critical influences of ionizing radiation damage. Based on the different ionizing radiation damage in SiGe HBTs fabricated by Huajie and an IBM SiGe process, quantit...Different SiGe processes and device designs are the critical influences of ionizing radiation damage. Based on the different ionizing radiation damage in SiGe HBTs fabricated by Huajie and an IBM SiGe process, quantitatively numerical simulation of ionizing radiation damage was carried out to explicate the distribution of radiation-induced charges buildup in KT9041 and IBM SiGe HBTs. The sensitive areas of the EB-spacer and isolation oxide of KT9041 are much larger than those of the IBM SiGe HBT, and the distribution of charge buildup in KT9041 is several orders of magnitude greater than that of the IBM SiGe HBT. The result suggests that the simulations are consistent with the experiment, and indicates that the geometry of the EB-spacer, the area of the Si/SiO2 interface and the isolation structure could be contributing to the different ionizing radiation damage.展开更多
A new type of AC PDP(alternating current plasma display panel) cell with a five-electrode structure is developed to improve the luminous efficiency of AC PDP.The discharge efficiency of this new cell structure is inve...A new type of AC PDP(alternating current plasma display panel) cell with a five-electrode structure is developed to improve the luminous efficiency of AC PDP.The discharge efficiency of this new cell structure is investigated by a 2D fluid simulation. Continuity equations and flux density equations for charged particles and excited atoms, energy balance equation for electrons are included in the model. The discharge gas is He+5%Xe. The reactions of ionization, excitation, recombination, and radiation are taken into account. The vacuum ultraviolet radiation efficiency of the five-electrode cell structure is about 20% higher than that of a conventional three-electrode cell structure.展开更多
For the sake of a more accurate shell boundary and calculation of radiation heat transfer in the Directional Solidification(DS) process, a radiation heat transfer model based on the Finite Element Method(FEM)is develo...For the sake of a more accurate shell boundary and calculation of radiation heat transfer in the Directional Solidification(DS) process, a radiation heat transfer model based on the Finite Element Method(FEM)is developed in this study. Key technologies, such as distinguishing boundaries automatically, local matrix and lumped heat capacity matrix, are also stated. In order to analyze the effect of withdrawing rate on DS process,the solidification processes of a complex superalloy turbine blade in the High Rate Solidification(HRS) process with different withdrawing rates are simulated; and by comparing the simulation results, it is found that the most suitable withdrawing rate is determined to be 5.0 mm·min^(-1). Finally, the accuracy and reliability of the radiation heat transfer model are verified, because of the accordance of simulation results with practical process.展开更多
By coupling the three-dimensional hydrodynamic model with the wave model, numerical simulations of the three- dimensional wave-induced current are carried out in this study. The wave model is based on the numerical so...By coupling the three-dimensional hydrodynamic model with the wave model, numerical simulations of the three- dimensional wave-induced current are carried out in this study. The wave model is based on the numerical solution of the modified wave action equation and eikonal equation, which can describe the wave refraction and diffraction. The hydrodynamic model is driven by the wave-induced radiation stresses and affected by the wave turbulence. The numerical implementation of the module has used the finite-volume schemes on unstructured grid, which provides great flexibility for modeling the waves and currents in the complex actual nearshore, and ensures the conservation of energy propagation. The applicability of the proposed model is evaluated in calculating the cases of wave set-up, longshore currents, undertow on a sloping beach, rip currents and meandering longshore currents on a tri-cuspate beach. The results indicate that it is necessary to introduce the depth-dependent radiation stresses into the numerical simulation of wave-induced currents, and comparisons show that the present model makes better prediction on the wave procedure as well as both horizontal and vertical structures in the wave-induced current field.展开更多
With the development of molecular imaging,Cherenkov optical imaging technology has been widely concerned.Most studies regard the partial boundary flux as a stochastic variable and reconstruct images based on the stead...With the development of molecular imaging,Cherenkov optical imaging technology has been widely concerned.Most studies regard the partial boundary flux as a stochastic variable and reconstruct images based on the steadystate diffusion equation.In this paper,time-variable will be considered and the Cherenkov radiation emission process will be regarded as a stochastic process.Based on the original steady-state diffusion equation,we first propose a stochastic partial differential equationmodel.The numerical solution to the stochastic partial differential model is carried out by using the finite element method.When the time resolution is high enough,the numerical solution of the stochastic diffusion equation is better than the numerical solution of the steady-state diffusion equation,which may provide a new way to alleviate the problem of Cherenkov luminescent imaging quality.In addition,the process of generating Cerenkov and penetrating in vitro imaging of 18 F radionuclide inmuscle tissue are also first proposed by GEANT4Monte Carlomethod.The result of the GEANT4 simulation is compared with the numerical solution of the corresponding stochastic partial differential equations,which shows that the stochastic partial differential equation can simulate the corresponding process.展开更多
基金support from the European Space Agency(ESA)PRODEX(PROgramme de Développement d’Expériences scientifiques)Project mission(No.PEA4000134960)Partial funding was provided by the Romanian Ministry of Research,Innovation and Digitalization under Romanian National Core Program LAPLAS VII(Contract No.30N/2023)+2 种基金the Belgian Solar-Terrestrial Centre of Excellencesupported by the project Belgian Research Action through Interdisciplinary Networks(BRAIN-BE)2.0(Grant No.B2/223/P1/PLATINUM)funded by the Belgian Office for Research(BELSPO)partially supported by a grant from the Romanian Ministry of Education and Research(CNCS-UEFISCDI,Project No.PN-III-P1-1.1TE-2021-0102)。
文摘We derived the properties of the terrestrial magnetopause(MP)from two modeling approaches,one global–fluid,the other local–kinetic,and compared the results with data collected in situ by the Magnetospheric Multiscale 2(MMS2)spacecraft.We used global magnetohydrodynamic(MHD)simulations of the Earth’s magnetosphere(publicly available from the NASA-CCMC[National Aeronautics and Space Administration–Community Coordinated Modeling Center])and local Vlasov equilibrium models(based on kinetic models for tangential discontinuities)to extract spatial profiles of the plasma and field variables at the Earth’s MP.The global MHD simulations used initial solar wind conditions extracted from the OMNI database at the time epoch when the MMS2 observes the MP.The kinetic Vlasov model used asymptotic boundary conditions derived from the same in situ MMS measurements upstream or downstream of the MP.The global MHD simulations provide a three-dimensional image of the magnetosphere at the time when the MMS2 crosses the MP.The Vlasov model provides a one-dimensional local view of the MP derived from first principles of kinetic theory.The MMS2 experimental data also serve as a reference for comparing and validating the numerical simulations and modeling.We found that the MP transition layer formed in global MHD simulations was generally localized closer to the Earth(roughly by one Earth radius)from the position of the real MP observed by the MMS.We also found that the global MHD simulations overestimated the thickness of the MP transition by one order of magnitude for three analyzed variables:magnetic field,density,and tangential speed.The MP thickness derived from the local Vlasov equilibrium was consistent with observations for all three of these variables.The overestimation of density in the Vlasov equilibrium was reduced compared with the global MHD solutions.We discuss our results in the context of future SMILE(Solar wind Magnetosphere Ionosphere Link Explorer)campaigns for observing the Earth’s MP.
文摘The reverse magnetohydrodynamic(MHD)energy bypass technology is a promising energy redis⁃tribution technology in the scramjet system,in augmented with a power generation equipment to supply the neces⁃sary long-distance flight airframe power.In this paper,a computational model of the scramjet magnetohydrody⁃namic channel is developed and verified by using the commercial software Fluent.It is found that when the mag⁃netic induction intensity is 1,2,3,4 T,the power generation efficiency is 22.5%,22.3%,22.0%,21.5%,and decreases with the increase of the magnetic induction intensity,and the enthalpy extraction rate is 0.026%,0.1%,0.21%,0.34%,and increases with the increase of the magnetic induction intensity.The deceleration ef⁃fect of electromagnetic action on the airflow in the power channel increases with the increase of magnetic induc⁃tion intensity.The stronger the magnetic field intensity,the more obvious the decreasing effect of fluid Mach num⁃ber in the channel.The power generation efficiency decreases as the magnetic induction intensity increases and the enthalpy extraction rate is reversed.As the local currents gathering at inlet and outlet of the power generation area,total temperature and enthalpy along the flow direction do not vary linearly,and there are maximum and minimum values at inlet and outlet.Increasing the number of electrodes can effectively regulate the percentage of Joule heat dissipation,which can improve the power generation efficiency.
基金Project(20010533009) supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China
文摘Various busbar configurations were built and modeled by the custom code based on the commercial package ANSYS for the 500 kA aluminum electrolysis cell.The configuration parameters,such as side riser entry ratio,number of cathode bars connected to each riser,vertical location of side cathode busbar and short side cathode busbar,distance between rows of cells in potline,the number of neighboring cells,ratio of compensation busbar carried passing under cell and its horizontal location under cell along with large magnetohydrodynamic(MHD) computation based on the custom evaluation function were simulated and discussed.The results show that a cell with riser entry ratio of 11:9:8:9:11 and cathode busbar located at the level of aluminum solution,50% upstream cathode current passing under cell for magnetic field compensation,the distance between rows of 50 m is more stable.
基金financially supported by the National Natural Science Foundation of China (No.50464004)
文摘A new hybrid method, Monte-Carlo-Heat-Flux (MCHF) method, was presented to analyze the radiative heat transfer of participating medium in a three-dimensional rectangular enclosure using combined the Monte-Carlo method with the heat flux method. Its accuracy and reliability was proved by comparing the computational results with exact results from classical "Zone Method".
基金funded by the National Natural Science Foundation of ChinaNational Research Council of Thailand Joint Research Project[grant number 51561145011]a State Grid Corporation of Science and Technology Project[grant number NY71-15-056]
文摘The output power of a photovoltaic system largely depends on the amount of solar radiation that can be received by the photovoltaic panel, and the solar radiation energy reaching the ground is affected by the radiation transmission process. However, in engineering practice, numerical simulation prediction schemes tend to adopt a kind of radiation scheme, and the prediction of solar radiation and photovoltaic power cannot always meet the prediction accuracy. In this paper, NCEP-NCAR reanalysis data are used as the initial field, and a variety of radiation parameterization schemes are used to produce simulations for the Xinjiang area. Through analysis of examples, it is found that the simulation results differ greatly depending on the radiation parameterization scheme employed, with the maximum absolute error of the total radiation and the predicted power being 106.67 W m-2 and 3.5 MW, respectively. Meanwhile, the mean absolute percentage error of the total radiation ranges from 8.6% to 17.3%, and that of the predicted power from 11.3% to 20.2%. Having analyzed the simulation results of the different radiation parameterization schemes, we conclude that the RRTM/Dudhia and CAM (Community Atmospheric Model) schemes are the most appropriate when under clear-weather conditions.
基金Projects (10775018, 10702010, 50374073) supported by the National Natural Science Foundation of ChinaProject(2002CB412701) supported by the National Basic Research Program of China
文摘Based on the thermodynamics theory and physical micro-properties of solid materials subjected to external loading at room temperature,a formula of calculating temperature difference of infrared radiation in terms of the sum of three principal strains was deduced to quantitatively investigate the infrared radiation characteristics in test. Two typical specimens,the three-point bending beam and the disc pressed in diameter,were tested and their principal strains were calculated by finite element method in order to obtain the temperature differences of infrared radiation. Numerical results are in a good agreement with test results,which verifies the validity of the formula of calculating temperature differences of infrared radiation and the model of quantitatively describing the infrared radiation characteristics of solid materials,and reveals the corresponding inner physical mechanism.
基金supported by the National Natural Science Foundation of China(GrantNos.40905038,40921003,40775020,and40905071)
文摘In this study, the clear sky hourly global and net solar irradiances at the surface determined using SUNFLUX, a simple parameterization scheme, for three stations (Gaize, Naqu, and Lhasa) on the Tibetan Plateau were evaluated against observation data. Our modeled results agree well with observations. The correlation coefficients between modeled and observed values were 〉 0.99 for all three stations. The relative error of modeled results, in average was 〈 7%, and the root-mean-square variance was 〈 27 W m-2. The solar irradiances in the radiation model were slightly overestimated compared with observation data; there were at least two likely causes. First, the radiative effects of aerosols were not included in the radiation model. Second, solar irradiances determined by thermopile pyranometers include a thermal offset error that causes solar radiation to be slightly underestimated. The solar radiation absorbed by the ozone and water vapor was estimated. The results show that monthly mean solar radiation absorbed by the ozone is 〈 2% of the global solar radiation (〈 14 W m-2). Solar radiation absorbed by water vapor is stronger in summer than in winter. The maximum amount of monthly mean solar radiation absorbed by water vapor can be up to 13% of the global solar radiation (95 W m-2). This indicates that water vapor measurements with high precision are very important for precise determination of solar radiation.
基金supported by the National Natural Science Foundation of China(Grant Nos.61274106 and 61574171)
文摘Different SiGe processes and device designs are the critical influences of ionizing radiation damage. Based on the different ionizing radiation damage in SiGe HBTs fabricated by Huajie and an IBM SiGe process, quantitatively numerical simulation of ionizing radiation damage was carried out to explicate the distribution of radiation-induced charges buildup in KT9041 and IBM SiGe HBTs. The sensitive areas of the EB-spacer and isolation oxide of KT9041 are much larger than those of the IBM SiGe HBT, and the distribution of charge buildup in KT9041 is several orders of magnitude greater than that of the IBM SiGe HBT. The result suggests that the simulations are consistent with the experiment, and indicates that the geometry of the EB-spacer, the area of the Si/SiO2 interface and the isolation structure could be contributing to the different ionizing radiation damage.
基金The project supported by 2002 project for Science and Technology of Ministry of Education
文摘A new type of AC PDP(alternating current plasma display panel) cell with a five-electrode structure is developed to improve the luminous efficiency of AC PDP.The discharge efficiency of this new cell structure is investigated by a 2D fluid simulation. Continuity equations and flux density equations for charged particles and excited atoms, energy balance equation for electrons are included in the model. The discharge gas is He+5%Xe. The reactions of ionization, excitation, recombination, and radiation are taken into account. The vacuum ultraviolet radiation efficiency of the five-electrode cell structure is about 20% higher than that of a conventional three-electrode cell structure.
基金financially supported by the Program for New Century Excellent Talents in University(No.NCET-13-0229,NCET-09-0396)the National Science & Technology Key Projects of Numerical Control(No.2012ZX04010-031,2012ZX0412-011)the National High Technology Research and Development Program("863"Program)of China(No.2013031003)
文摘For the sake of a more accurate shell boundary and calculation of radiation heat transfer in the Directional Solidification(DS) process, a radiation heat transfer model based on the Finite Element Method(FEM)is developed in this study. Key technologies, such as distinguishing boundaries automatically, local matrix and lumped heat capacity matrix, are also stated. In order to analyze the effect of withdrawing rate on DS process,the solidification processes of a complex superalloy turbine blade in the High Rate Solidification(HRS) process with different withdrawing rates are simulated; and by comparing the simulation results, it is found that the most suitable withdrawing rate is determined to be 5.0 mm·min^(-1). Finally, the accuracy and reliability of the radiation heat transfer model are verified, because of the accordance of simulation results with practical process.
基金financially supported by the the National Natural Science Foundation of China(Grant No.51709054)the Public Science and Technology Research Funds Projects of Ocean(Grant Nos.201405025 and 201505019)
文摘By coupling the three-dimensional hydrodynamic model with the wave model, numerical simulations of the three- dimensional wave-induced current are carried out in this study. The wave model is based on the numerical solution of the modified wave action equation and eikonal equation, which can describe the wave refraction and diffraction. The hydrodynamic model is driven by the wave-induced radiation stresses and affected by the wave turbulence. The numerical implementation of the module has used the finite-volume schemes on unstructured grid, which provides great flexibility for modeling the waves and currents in the complex actual nearshore, and ensures the conservation of energy propagation. The applicability of the proposed model is evaluated in calculating the cases of wave set-up, longshore currents, undertow on a sloping beach, rip currents and meandering longshore currents on a tri-cuspate beach. The results indicate that it is necessary to introduce the depth-dependent radiation stresses into the numerical simulation of wave-induced currents, and comparisons show that the present model makes better prediction on the wave procedure as well as both horizontal and vertical structures in the wave-induced current field.
基金National Science Foundation of China(NSFC)(61671009,12171178).
文摘With the development of molecular imaging,Cherenkov optical imaging technology has been widely concerned.Most studies regard the partial boundary flux as a stochastic variable and reconstruct images based on the steadystate diffusion equation.In this paper,time-variable will be considered and the Cherenkov radiation emission process will be regarded as a stochastic process.Based on the original steady-state diffusion equation,we first propose a stochastic partial differential equationmodel.The numerical solution to the stochastic partial differential model is carried out by using the finite element method.When the time resolution is high enough,the numerical solution of the stochastic diffusion equation is better than the numerical solution of the steady-state diffusion equation,which may provide a new way to alleviate the problem of Cherenkov luminescent imaging quality.In addition,the process of generating Cerenkov and penetrating in vitro imaging of 18 F radionuclide inmuscle tissue are also first proposed by GEANT4Monte Carlomethod.The result of the GEANT4 simulation is compared with the numerical solution of the corresponding stochastic partial differential equations,which shows that the stochastic partial differential equation can simulate the corresponding process.