The Navier-Stokes system for one-dimensional compressible fluids with density-dependent viscosities when the initial density connects to vacuum continuously is considered in the present paper. When the viscosity coeff...The Navier-Stokes system for one-dimensional compressible fluids with density-dependent viscosities when the initial density connects to vacuum continuously is considered in the present paper. When the viscosity coefficient u is proportional to pθ with 0 〈 θ 〈 1, the global existence and the uniqueness of weak solutions are proved which improves the previous results in [Vong, S. W., Yang, T., Zhu, C. J.： Compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuum II. J. Differential Equations, 192（2）, 475-501 （2003）]. Here p is the density. Moreover, a stabilization rate estimate for the density as t → ＋∞ for any θ 〉 0 is also given.展开更多
This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depen...This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/4.Furthermore,we obtain the global C^(∞)-solutions if the initial data is smooth.展开更多
In this study,we investigate the cluster radioactivity(CR)of new superheavy elements with Z=119 and 120 based on two successful theoretical methods with modified parameters:the density-dependent cluster model(DDCM)and...In this study,we investigate the cluster radioactivity(CR)of new superheavy elements with Z=119 and 120 based on two successful theoretical methods with modified parameters:the density-dependent cluster model(DDCM)and unified decay formula(UDF).First,we employ the DDCM and UDF to accurately reproduce the experimental half-lives of cluster emissions,which demonstrates the high reliability of our theoretical methods.Then,we systematically predict the probable cluster modes of ^(293-311)119 and ^(293-302)120 as well as their corresponding decay energies and half-lives.The half-lives of cluster decay derived from the DDCM are consistent with those from the UDF.Therefore,our results reveal that the cluster emission of ^(8)Be,emitted from the Z=119 and 120 isotopic chains,exhibits the minimum half-life for cluster emission,and hence,^(8)Be emission is considered the most probable cluster decay mode.Moreover,we explore the competition betweenαdecay and CR and find thatαdecay may be the dominant decay mode against CR.Furthermore,the good linear relationship between the decay energy and the number ofαparticles within the emitted cluster is extended to the range of superheavy nuclei(SHN).We anticipate that our theoretical predictions for CR will provide valuable references for the experimental synthesis of new SHN.展开更多
We study the large-time behavior toward viscous shock waves to the Cauchy problem of the one-dimensional compressible isentropic Navier-Stokes equations with density- dependent viscosity. The nonlinear stability of th...We study the large-time behavior toward viscous shock waves to the Cauchy problem of the one-dimensional compressible isentropic Navier-Stokes equations with density- dependent viscosity. The nonlinear stability of the viscous shock waves is shown for certain class of large initial perturbation with integral zero which can allow the initial density to have large oscillation. Our analysis relies upon the technique developed by Kanel~ and the continuation argument.展开更多
In this paper, we consider the global existence of classical solution to the 3-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient λ(ρ)provided that the initial energy is small in s...In this paper, we consider the global existence of classical solution to the 3-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient λ(ρ)provided that the initial energy is small in some sense. In our result, we give a relation between the initial energy and the viscosity coefficient μ, and it shows that the initial energy can be large if the coefficient of the viscosity μ is taken to be large, which implies that large viscosity μ means large solution.展开更多
This paper studies the existence and uniqueness of local strong solutions to an Oldroyd-B model with density-dependent viscosity in a bounded domain Ω ⊂ R<sup>d</sup>, d = 2 or 3 via incompressible limit,...This paper studies the existence and uniqueness of local strong solutions to an Oldroyd-B model with density-dependent viscosity in a bounded domain Ω ⊂ R<sup>d</sup>, d = 2 or 3 via incompressible limit, in which the initial data is “well-prepared” and the velocity field enjoys the slip boundary conditions. The main idea is to derive the uniform energy estimates for nonlinear systems and corresponding incompressible limit.展开更多
In this paper,a class of brucellosis transmission model with seasonal alternation,density-dependent growth,stage-structure,maturation delay,time-varying incubation is established.The basic reproduction number Ro is de...In this paper,a class of brucellosis transmission model with seasonal alternation,density-dependent growth,stage-structure,maturation delay,time-varying incubation is established.The basic reproduction number Ro is derived,by which we find that the brucellosis is uniformly persistent if R_(0)>1,while the disease-free periodic solution is globally attractive if R_(0)<1.The theoretical results are illustrated by numerical simulation,from which we find that the brucellosis transmission would be overestimated(or underestimated)if we ignore the influence of time-varying incubation or maturation delay.If density-dependent growth of animals is ignored,the risk of brucellosis may be far underestimated,the extinction of brucellosis can be obtained by numerical simulation under the same conditions.Seasonality significantly affects the long-term dynamic behavior of brucellosis,and the inconsistency of parameter periods results in complex dynamic behavior.展开更多
Based on the newest experimentally extracted nuclear density distributions for double-magic nucleus208Pb(Tarbert et al. in Phys Rev Lett 112:242502, 2014),the sensitivity of α-decay half-life to nuclear skin thicknes...Based on the newest experimentally extracted nuclear density distributions for double-magic nucleus208Pb(Tarbert et al. in Phys Rev Lett 112:242502, 2014),the sensitivity of α-decay half-life to nuclear skin thickness is explored in the vicinity of the shell closure region around208 Pb, i.e., isotopes of Z ? 82 and isotones of N ? 126.With the two-parameter Fermi(2PF) density distributions and an analytically derived formula, the α-decay half-life is found to be closely related to the magnitude of nuclear skin thickness. For a decays to the Z ? 82 isotopes, the α-decay half-life is found to decrease with the increasing neutron skin thickness, while the opposite behavior is found for a decays to the N ? 126 isotones. Therefore, it could be a possible way to extract the nuclear skin thickness from measured α-decay half-lives.展开更多
In order to test whether density dependence influences community diversity, a combination of manipulative experimentation and plot surveys were done using Cryptocarya concinna, a dominant species in subtropical evergr...In order to test whether density dependence influences community diversity, a combination of manipulative experimentation and plot surveys were done using Cryptocarya concinna, a dominant species in subtropical evergreen forest. Twelve pairs of 1 m^2 seedling plots were built around 12 adults, and plots were treated monthly with either a fungicide or a control. The surviving proportion of C. concinna seedlings at different stages was calculated, and an analysis was conducted on the impact of fungicide on seedling survival and species richness. Correlation between relative abundance and community evenness at different ages was analyzed using plot surveys. The results showed that fungicide treatment decreased species richness of the seedling community by pro- moting the recruitment of common species. Furthermore, census of a 25 m radius around adult C. concinna trees confirmed that the density of saplings increased with distance from adults. Relative abundance of C. concinna decreased with increasing age, and decreasing C. concinna dominance resulted in an increase in community even- ness. To avoid the appearance of a single optimum population, the dominance of C. concinna decreased with age via density dependence, and subsequently improved community species diversity.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 10401012, 10771170)supported by (#10625105)the Key Laboratory of Mathematical Physics of Hubei Province
文摘The Navier-Stokes system for one-dimensional compressible fluids with density-dependent viscosities when the initial density connects to vacuum continuously is considered in the present paper. When the viscosity coefficient u is proportional to pθ with 0 〈 θ 〈 1, the global existence and the uniqueness of weak solutions are proved which improves the previous results in [Vong, S. W., Yang, T., Zhu, C. J.： Compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuum II. J. Differential Equations, 192（2）, 475-501 （2003）]. Here p is the density. Moreover, a stabilization rate estimate for the density as t → ＋∞ for any θ 〉 0 is also given.
基金supported by the Key Project of the NSFC(12131010)the NSFC(11771155,12271032)+1 种基金the NSF of Guangdong Province(2021A1515010249,2021A1515010303)supported by the NSFC(11971179,12371205)。
文摘This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/4.Furthermore,we obtain the global C^(∞)-solutions if the initial data is smooth.
基金Supported by the National Natural Science Foundation of China(12035011,11975167,11947211,11905103,11881240623,11961141003)the National Key R&D Program of China(2018YFA0404403)。
文摘In this study,we investigate the cluster radioactivity(CR)of new superheavy elements with Z=119 and 120 based on two successful theoretical methods with modified parameters:the density-dependent cluster model(DDCM)and unified decay formula(UDF).First,we employ the DDCM and UDF to accurately reproduce the experimental half-lives of cluster emissions,which demonstrates the high reliability of our theoretical methods.Then,we systematically predict the probable cluster modes of ^(293-311)119 and ^(293-302)120 as well as their corresponding decay energies and half-lives.The half-lives of cluster decay derived from the DDCM are consistent with those from the UDF.Therefore,our results reveal that the cluster emission of ^(8)Be,emitted from the Z=119 and 120 isotopic chains,exhibits the minimum half-life for cluster emission,and hence,^(8)Be emission is considered the most probable cluster decay mode.Moreover,we explore the competition betweenαdecay and CR and find thatαdecay may be the dominant decay mode against CR.Furthermore,the good linear relationship between the decay energy and the number ofαparticles within the emitted cluster is extended to the range of superheavy nuclei(SHN).We anticipate that our theoretical predictions for CR will provide valuable references for the experimental synthesis of new SHN.
基金supported by"the Fundamental Research Funds for the Central Universities"
文摘We study the large-time behavior toward viscous shock waves to the Cauchy problem of the one-dimensional compressible isentropic Navier-Stokes equations with density- dependent viscosity. The nonlinear stability of the viscous shock waves is shown for certain class of large initial perturbation with integral zero which can allow the initial density to have large oscillation. Our analysis relies upon the technique developed by Kanel~ and the continuation argument.
文摘In this paper, we consider the global existence of classical solution to the 3-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient λ(ρ)provided that the initial energy is small in some sense. In our result, we give a relation between the initial energy and the viscosity coefficient μ, and it shows that the initial energy can be large if the coefficient of the viscosity μ is taken to be large, which implies that large viscosity μ means large solution.
文摘This paper studies the existence and uniqueness of local strong solutions to an Oldroyd-B model with density-dependent viscosity in a bounded domain Ω ⊂ R<sup>d</sup>, d = 2 or 3 via incompressible limit, in which the initial data is “well-prepared” and the velocity field enjoys the slip boundary conditions. The main idea is to derive the uniform energy estimates for nonlinear systems and corresponding incompressible limit.
文摘In this paper,a class of brucellosis transmission model with seasonal alternation,density-dependent growth,stage-structure,maturation delay,time-varying incubation is established.The basic reproduction number Ro is derived,by which we find that the brucellosis is uniformly persistent if R_(0)>1,while the disease-free periodic solution is globally attractive if R_(0)<1.The theoretical results are illustrated by numerical simulation,from which we find that the brucellosis transmission would be overestimated(or underestimated)if we ignore the influence of time-varying incubation or maturation delay.If density-dependent growth of animals is ignored,the risk of brucellosis may be far underestimated,the extinction of brucellosis can be obtained by numerical simulation under the same conditions.Seasonality significantly affects the long-term dynamic behavior of brucellosis,and the inconsistency of parameter periods results in complex dynamic behavior.
基金supported by the National Natural Science Foundation of China(Nos.11175085,11235001,11375086,and 11120101005)the 973 Program of China(No.2013CB834400)+1 种基金the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)the Open Project Program of the State Key Laboratory of Theoretical Physics,Institute of Theoretical Physics,Chinese Academy of Sciences,China(No.Y5KF141CJ1)
文摘Based on the newest experimentally extracted nuclear density distributions for double-magic nucleus208Pb(Tarbert et al. in Phys Rev Lett 112:242502, 2014),the sensitivity of α-decay half-life to nuclear skin thickness is explored in the vicinity of the shell closure region around208 Pb, i.e., isotopes of Z ? 82 and isotones of N ? 126.With the two-parameter Fermi(2PF) density distributions and an analytically derived formula, the α-decay half-life is found to be closely related to the magnitude of nuclear skin thickness. For a decays to the Z ? 82 isotopes, the α-decay half-life is found to decrease with the increasing neutron skin thickness, while the opposite behavior is found for a decays to the N ? 126 isotones. Therefore, it could be a possible way to extract the nuclear skin thickness from measured α-decay half-lives.
基金The Earmarked Fund for China Agriculture Research SystemScientific Research Foundation of Hainan Tropical Ocean University
文摘In order to test whether density dependence influences community diversity, a combination of manipulative experimentation and plot surveys were done using Cryptocarya concinna, a dominant species in subtropical evergreen forest. Twelve pairs of 1 m^2 seedling plots were built around 12 adults, and plots were treated monthly with either a fungicide or a control. The surviving proportion of C. concinna seedlings at different stages was calculated, and an analysis was conducted on the impact of fungicide on seedling survival and species richness. Correlation between relative abundance and community evenness at different ages was analyzed using plot surveys. The results showed that fungicide treatment decreased species richness of the seedling community by pro- moting the recruitment of common species. Furthermore, census of a 25 m radius around adult C. concinna trees confirmed that the density of saplings increased with distance from adults. Relative abundance of C. concinna decreased with increasing age, and decreasing C. concinna dominance resulted in an increase in community even- ness. To avoid the appearance of a single optimum population, the dominance of C. concinna decreased with age via density dependence, and subsequently improved community species diversity.
