In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,t...In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.展开更多
In this work,we construct two efficient fully decoupled,linear,unconditionally stable numerical algorithms for the thermally coupled incompressible magnetohydrodynamic equations.Firstly,in order to obtain the desired ...In this work,we construct two efficient fully decoupled,linear,unconditionally stable numerical algorithms for the thermally coupled incompressible magnetohydrodynamic equations.Firstly,in order to obtain the desired algorithm,we introduce a scalar auxiliary variable(SAV)to get a new equivalent system.Secondly,by combining the pressure-correction method and the explicit-implicit method,we perform semi-discrete numerical algorithms of first and second order,respectively.Then,we prove that the obtained algorithms follow an unconditionally stable law in energy,and we provide a detailed implementation process,which we only need to solve a series of linear differential equations with constant coefficients at each time step.More importantly,with some powerful analysis,we give the order of convergence of the errors.Finally,to illustrate theoretical results,some numerical experiments are given.展开更多
In this paper,we construct a new class of efficient and high-order schemes for the Cahn-Hilliard-Navier-Stokes equations with periodic boundary conditions.These schemes are based on two types of scalar auxiliary varia...In this paper,we construct a new class of efficient and high-order schemes for the Cahn-Hilliard-Navier-Stokes equations with periodic boundary conditions.These schemes are based on two types of scalar auxiliary variable approaches.By using a new pressure correction method,the accuracy of the pressure has been greatly improved.Furthermore,one only needs to solve a series of fully decoupled linear equations with constant coefficients at each time step.In addition,we prove the unconditional energy stability of the schemes,rigorously.Finally,plenty of numerical simulations are carried out to verify the convergence rates,stability,and effectiveness of the proposed schemes numerically.展开更多
From[J.Differential Geom.,1990,31(1):285-299],one can obtain that compact self-shrinking hypersufaces in R^(n+1) with constant scalar curvature must be the standard sphere S^(n)(√n)(cf.[Front.Math.,2023,18(2):417-430...From[J.Differential Geom.,1990,31(1):285-299],one can obtain that compact self-shrinking hypersufaces in R^(n+1) with constant scalar curvature must be the standard sphere S^(n)(√n)(cf.[Front.Math.,2023,18(2):417-430]).This result was generalized by Guo[J.Math.Soc.Japan,2018,70(3):1103-1110]with assumption of a lower or upper scalar curvature bound.In this paper,we will generalize the scalar curvature rigidity theorem of Guo to the case of λ-hypersurfaces.We will also give an alternative proof of the theorem(cf.[2014,arXiv:1410.5302]and[Proc.Amer.Math.Soc.,2018,146(10):4459-4471])that λ-hypersurfaces which are entire graphs must be hyperplanes.展开更多
QED(quantum electrodynamics)is the QFT(quantum field theory)describing the interaction between light and matter.While conventional QED is based on TEM(transverse electromagnetic)waves,there has been increasing interes...QED(quantum electrodynamics)is the QFT(quantum field theory)describing the interaction between light and matter.While conventional QED is based on TEM(transverse electromagnetic)waves,there has been increasing interest in the theoretical and experimental exploration of LSW(longitudinal scalar waves)solutions that are often omitted in CED(classical electrodynamics)but may have physical significance in nontrivial vacuum conditions.This paper delves into the theoretical foundation of LSW,their role in QED,and the associated mathematical equations governing their dynamics.展开更多
Air quality is a critical factor in maintaining health and well-being, influencing both current conditions and future outcomes. Hospitals are one of the sensitive areas of our society, for they are built as sanctuarie...Air quality is a critical factor in maintaining health and well-being, influencing both current conditions and future outcomes. Hospitals are one of the sensitive areas of our society, for they are built as sanctuaries for treatment and recovery, making the quality of paramount importance. This study investigates the impact of traffic-related emissions on indoor air quality within a Level 5 Hospital outpatient ward. Measurements were taken over five consecutive days, revealing that while CO2 levels generally remained within safe limits, there were instances where concentrations exceeded 3000 ppm, categorizing them as “Hazardous.” Notably, particulate matter (PM2.5 and PM10) levels fluctuated significantly, with peak concentrations observed during working hours correlating with increased vehicle activity. The data indicated that PM2.5 levels reached as high as 75 µg/m3, with 91.68% of recorded values exceeding the World Health Organization’s (WHO) and Environmental Protection Agency 24-hour mean threshold of 25 µg/m3. Similarly, PM10 concentrations peaked at 120 µg/m3, with 61.19% of values surpassing the WHO threshold of 50 µg/m3, both of which pose serious health risks, particularly to vulnerable populations such as pregnant women, infants, and the elderly. Additionally, the study highlighted the critical role of wind direction in pollutant dispersion, with specific patterns contributing to elevated indoor concentrations. These findings underscore the urgent need for targeted interventions and proactive air quality management strategies in healthcare facilities, including the strategic design of hospital wards away from primary emission sources and the promotion of electric vehicle use to mitigate traffic-related emissions.展开更多
In this paper,we prove that for certain fiber bundles there is a k-Futaki-Ono conformally Kahler metric related to a metric in any given Kahler class for any k≥2.
基金Supported by Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)+2 种基金Basic Research Plan of Shanxi Province(202203021211129)Shanxi Province Natural Science Research(202203021212249)Special/Youth Foundation of Taiyuan University of Technology(2022QN101)。
文摘In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.
基金Supported by Research Project Supported by Shanxi Scholarship Council of China(2021-029)Shanxi Provincial International Cooperation Base and Platform Project(202104041101019)Shanxi Province Natural Science Foundation(202203021211129)。
文摘In this work,we construct two efficient fully decoupled,linear,unconditionally stable numerical algorithms for the thermally coupled incompressible magnetohydrodynamic equations.Firstly,in order to obtain the desired algorithm,we introduce a scalar auxiliary variable(SAV)to get a new equivalent system.Secondly,by combining the pressure-correction method and the explicit-implicit method,we perform semi-discrete numerical algorithms of first and second order,respectively.Then,we prove that the obtained algorithms follow an unconditionally stable law in energy,and we provide a detailed implementation process,which we only need to solve a series of linear differential equations with constant coefficients at each time step.More importantly,with some powerful analysis,we give the order of convergence of the errors.Finally,to illustrate theoretical results,some numerical experiments are given.
基金Supported by the Research Project Supported of Shanxi Scholarship Council of China(No.2021-029)Shanxi Provincial International Cooperation Base and Platform Project(202104041101019)Shanxi Province Natural Science Research(202203021211129)。
文摘In this paper,we construct a new class of efficient and high-order schemes for the Cahn-Hilliard-Navier-Stokes equations with periodic boundary conditions.These schemes are based on two types of scalar auxiliary variable approaches.By using a new pressure correction method,the accuracy of the pressure has been greatly improved.Furthermore,one only needs to solve a series of fully decoupled linear equations with constant coefficients at each time step.In addition,we prove the unconditional energy stability of the schemes,rigorously.Finally,plenty of numerical simulations are carried out to verify the convergence rates,stability,and effectiveness of the proposed schemes numerically.
文摘From[J.Differential Geom.,1990,31(1):285-299],one can obtain that compact self-shrinking hypersufaces in R^(n+1) with constant scalar curvature must be the standard sphere S^(n)(√n)(cf.[Front.Math.,2023,18(2):417-430]).This result was generalized by Guo[J.Math.Soc.Japan,2018,70(3):1103-1110]with assumption of a lower or upper scalar curvature bound.In this paper,we will generalize the scalar curvature rigidity theorem of Guo to the case of λ-hypersurfaces.We will also give an alternative proof of the theorem(cf.[2014,arXiv:1410.5302]and[Proc.Amer.Math.Soc.,2018,146(10):4459-4471])that λ-hypersurfaces which are entire graphs must be hyperplanes.
文摘QED(quantum electrodynamics)is the QFT(quantum field theory)describing the interaction between light and matter.While conventional QED is based on TEM(transverse electromagnetic)waves,there has been increasing interest in the theoretical and experimental exploration of LSW(longitudinal scalar waves)solutions that are often omitted in CED(classical electrodynamics)but may have physical significance in nontrivial vacuum conditions.This paper delves into the theoretical foundation of LSW,their role in QED,and the associated mathematical equations governing their dynamics.
文摘Air quality is a critical factor in maintaining health and well-being, influencing both current conditions and future outcomes. Hospitals are one of the sensitive areas of our society, for they are built as sanctuaries for treatment and recovery, making the quality of paramount importance. This study investigates the impact of traffic-related emissions on indoor air quality within a Level 5 Hospital outpatient ward. Measurements were taken over five consecutive days, revealing that while CO2 levels generally remained within safe limits, there were instances where concentrations exceeded 3000 ppm, categorizing them as “Hazardous.” Notably, particulate matter (PM2.5 and PM10) levels fluctuated significantly, with peak concentrations observed during working hours correlating with increased vehicle activity. The data indicated that PM2.5 levels reached as high as 75 µg/m3, with 91.68% of recorded values exceeding the World Health Organization’s (WHO) and Environmental Protection Agency 24-hour mean threshold of 25 µg/m3. Similarly, PM10 concentrations peaked at 120 µg/m3, with 61.19% of values surpassing the WHO threshold of 50 µg/m3, both of which pose serious health risks, particularly to vulnerable populations such as pregnant women, infants, and the elderly. Additionally, the study highlighted the critical role of wind direction in pollutant dispersion, with specific patterns contributing to elevated indoor concentrations. These findings underscore the urgent need for targeted interventions and proactive air quality management strategies in healthcare facilities, including the strategic design of hospital wards away from primary emission sources and the promotion of electric vehicle use to mitigate traffic-related emissions.
基金supported by the Nature Science Foundation of China(12171140).
文摘In this paper,we prove that for certain fiber bundles there is a k-Futaki-Ono conformally Kahler metric related to a metric in any given Kahler class for any k≥2.
