This paper investigates the spatial behavior of the solutions of the Stokes equations in a semi-infinite cylinder.We consider four kinds of semi-infinite cylinders with boundary conditions of Dirichlet type.For each t...This paper investigates the spatial behavior of the solutions of the Stokes equations in a semi-infinite cylinder.We consider four kinds of semi-infinite cylinders with boundary conditions of Dirichlet type.For each type of cylinder we obtain the spatial decay estimates for the solutions.To make the attenuation meaningful,we derive the explicit bound for the total energy in terms of the initial boundary data.展开更多
This paper investigates spatial decay bounds and a decay rate for the time- dependent Stokes flow of a viscous fluid in a semi-infinite channel. We show how to obtain a near optimal decay rate that is independent of t...This paper investigates spatial decay bounds and a decay rate for the time- dependent Stokes flow of a viscous fluid in a semi-infinite channel. We show how to obtain a near optimal decay rate that is independent of the Reynolds number. We also show that a modification to an analysis given in the literature and a better choice of arbitrary constants yield a decay rate 1.328, which is clearly an improvement compared to 0.91 obtained in the referenced work.展开更多
A previous study is continued by investigating the Boltzmann equation for particles with quantum effects (BQE). First, the corresponding entropy identity is proved, then if the initial data f(x,v,0) satisfies 0...A previous study is continued by investigating the Boltzmann equation for particles with quantum effects (BQE). First, the corresponding entropy identity is proved, then if the initial data f(x,v,0) satisfies 0≤f(x,v,0)≤CΦ(x,v,0) for a constant 0<C<∞ and function Φ(x,v,t), we prove the existence and uniqueness of spatial decay solutions of the BQE within a given function space B(Φ) using fixed point theory. Moreover, if there is a continuous function F(x,v) which belongs to a function set, then there exists a mild solution f(x,v,t) of the BQE such that f ∞(x,v)= limt→∞f(x+vt,v,t)=F(x,v).展开更多
The Boltzmann equations for Fermi-Dirac particles and Bose-Einstein particles, both in the absence of external force fields, are combined into a more general form called the Boltzmann equation with quantum effects (BQ...The Boltzmann equations for Fermi-Dirac particles and Bose-Einstein particles, both in the absence of external force fields, are combined into a more general form called the Boltzmann equation with quantum effects (BQE). It is assumed that the initial data f(x,v,0) satisfies 0≤f(x,v,0)≤cΦ(x,v,0) for a positive constant c and certain types of control functions Φ(x,v,t). Then within a given function space B(Φ), we prove that f(x+tv,v,t) uniformly converges to f ∞(x,v) in a certain norm where f ∞(x,v)= limt→∞f(x+tv,v,t) and different initial data determines different long time limits.展开更多
The spatial decay of solutions to initial-boundary value problems for a semilinear parabolic equation in a semi-infinite cylinder of variable cross-section subject to zero condition on the lateral boundaries is invest...The spatial decay of solutions to initial-boundary value problems for a semilinear parabolic equation in a semi-infinite cylinder of variable cross-section subject to zero condition on the lateral boundaries is investigated. A second-order differential inequality that shows the spatial decay O（exp（-z2/（4（t ＋ t0）））） for an L2p cross-sectional measure of the solution is obtained. A first-order differential inequality leading to growth or decay is also derived. In the case of growth, an upper bound for blow-up in space is obtained, while in the case of decay an upper bound for the total energy in terms of data is obtained.展开更多
Vitality transfer patterns are essential for creating vibrant,sustainable cities,yet their dynamic changes over time remain underexplored.Taking Nanjing as a case study,this study employed 24 h of location-based servi...Vitality transfer patterns are essential for creating vibrant,sustainable cities,yet their dynamic changes over time remain underexplored.Taking Nanjing as a case study,this study employed 24 h of location-based service data as a time series to explore the vitality transfer pattern within a day from both distribution and aggregation perspectives.Spatial dependence decay patterns were detected using residual clustering relationships,and the LightGBM model was used to explore the relationship between vitality transfer and 50 factors in five categories:transportation,function,economy,morphology,and geography.The results show that the urban vitality distribution has a polycentric agglomeration pattern,which goes through four periods in a day.Vitality transfer is the cyclical process of transformation from one aggregated state to another.The spatial dependence was maximized at 0.75 km^(2).The magnitude of vitality fluctuation is strongly influenced by factors such as morphology,transportation,and function.Spatial differences in factors combine to drive vitality transfer in distribution and aggregation,with factors such as accessibility and building age diversity influencing distribution,and factors such as accessibility and POI diversity altering aggregation.This study supports the rational design of vibrant urban spaces and promotes effective vitality transfer and sustainable urban development.展开更多
A position-sensitive detector is designed for neutron detection. It uses a single continuous screen of a self-made lithium glass scintillator, rather than discrete crystal implementations, coupling with a multi-anode ...A position-sensitive detector is designed for neutron detection. It uses a single continuous screen of a self-made lithium glass scintillator, rather than discrete crystal implementations, coupling with a multi-anode PMT （MaPMT）. The scintillator is fast and efficient; with a decay time of 34 ns and thermal neutron detection efficiency of around 95.8% for the 3 mm thick screen, and its light yield is around 5670 photons per neutron and 3768 photons per MeV γ rays deposition. The spatial resolution is around 1.6 mm （FWHM） with the energy resolution around 34.7% by using α （5.2 MeV） rays test.展开更多
基金Supported by the Key Projects of Universities in Guangdong Province(NATURAL SCIENCE)(Grant No.2019KZDXM042)Research Team Project of Guangzhou Huashang College(Grant No.2021HSKT01).
文摘This paper investigates the spatial behavior of the solutions of the Stokes equations in a semi-infinite cylinder.We consider four kinds of semi-infinite cylinders with boundary conditions of Dirichlet type.For each type of cylinder we obtain the spatial decay estimates for the solutions.To make the attenuation meaningful,we derive the explicit bound for the total energy in terms of the initial boundary data.
基金supported by the Korea Research Foundation Grant of the Korean Government (No.KRF-2008-521-C00021)
文摘This paper investigates spatial decay bounds and a decay rate for the time- dependent Stokes flow of a viscous fluid in a semi-infinite channel. We show how to obtain a near optimal decay rate that is independent of the Reynolds number. We also show that a modification to an analysis given in the literature and a better choice of arbitrary constants yield a decay rate 1.328, which is clearly an improvement compared to 0.91 obtained in the referenced work.
基金Supported by the Tsinghua U niversity Science Fund
文摘A previous study is continued by investigating the Boltzmann equation for particles with quantum effects (BQE). First, the corresponding entropy identity is proved, then if the initial data f(x,v,0) satisfies 0≤f(x,v,0)≤CΦ(x,v,0) for a constant 0<C<∞ and function Φ(x,v,t), we prove the existence and uniqueness of spatial decay solutions of the BQE within a given function space B(Φ) using fixed point theory. Moreover, if there is a continuous function F(x,v) which belongs to a function set, then there exists a mild solution f(x,v,t) of the BQE such that f ∞(x,v)= limt→∞f(x+vt,v,t)=F(x,v).
基金Supported by the Tsinghua U niversity Science Fund
文摘The Boltzmann equations for Fermi-Dirac particles and Bose-Einstein particles, both in the absence of external force fields, are combined into a more general form called the Boltzmann equation with quantum effects (BQE). It is assumed that the initial data f(x,v,0) satisfies 0≤f(x,v,0)≤cΦ(x,v,0) for a positive constant c and certain types of control functions Φ(x,v,t). Then within a given function space B(Φ), we prove that f(x+tv,v,t) uniformly converges to f ∞(x,v) in a certain norm where f ∞(x,v)= limt→∞f(x+tv,v,t) and different initial data determines different long time limits.
基金supported by the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education,Science,and Technology(No.NRF 2010-0012215)
文摘The spatial decay of solutions to initial-boundary value problems for a semilinear parabolic equation in a semi-infinite cylinder of variable cross-section subject to zero condition on the lateral boundaries is investigated. A second-order differential inequality that shows the spatial decay O（exp（-z2/（4（t ＋ t0）））） for an L2p cross-sectional measure of the solution is obtained. A first-order differential inequality leading to growth or decay is also derived. In the case of growth, an upper bound for blow-up in space is obtained, while in the case of decay an upper bound for the total energy in terms of data is obtained.
基金supported by the National Natural Science Foundation of China(Grant No.52078307).
文摘Vitality transfer patterns are essential for creating vibrant,sustainable cities,yet their dynamic changes over time remain underexplored.Taking Nanjing as a case study,this study employed 24 h of location-based service data as a time series to explore the vitality transfer pattern within a day from both distribution and aggregation perspectives.Spatial dependence decay patterns were detected using residual clustering relationships,and the LightGBM model was used to explore the relationship between vitality transfer and 50 factors in five categories:transportation,function,economy,morphology,and geography.The results show that the urban vitality distribution has a polycentric agglomeration pattern,which goes through four periods in a day.Vitality transfer is the cyclical process of transformation from one aggregated state to another.The spatial dependence was maximized at 0.75 km^(2).The magnitude of vitality fluctuation is strongly influenced by factors such as morphology,transportation,and function.Spatial differences in factors combine to drive vitality transfer in distribution and aggregation,with factors such as accessibility and building age diversity influencing distribution,and factors such as accessibility and POI diversity altering aggregation.This study supports the rational design of vibrant urban spaces and promotes effective vitality transfer and sustainable urban development.
基金Supported by the National Natural Science Foundation of China(10875140,10890092)
文摘A position-sensitive detector is designed for neutron detection. It uses a single continuous screen of a self-made lithium glass scintillator, rather than discrete crystal implementations, coupling with a multi-anode PMT （MaPMT）. The scintillator is fast and efficient; with a decay time of 34 ns and thermal neutron detection efficiency of around 95.8% for the 3 mm thick screen, and its light yield is around 5670 photons per neutron and 3768 photons per MeV γ rays deposition. The spatial resolution is around 1.6 mm （FWHM） with the energy resolution around 34.7% by using α （5.2 MeV） rays test.
