In this paper,we consider the fully parabolic Chemotaxis system with the general logistic source{ut=Δ(γ(v)u)+λu-μu^(k),x∈Ω,t>0,vt=△v+wz,x∈Ω,t>0,wt=-wz,x∈Ω,t>0,zt=△z-z+u,x∈Ω,t>0 whereΩ⊂ℝn(n≥...In this paper,we consider the fully parabolic Chemotaxis system with the general logistic source{ut=Δ(γ(v)u)+λu-μu^(k),x∈Ω,t>0,vt=△v+wz,x∈Ω,t>0,wt=-wz,x∈Ω,t>0,zt=△z-z+u,x∈Ω,t>0 whereΩ⊂ℝn(n≥1)is a smooth and bounded domain,λ≥0,μ≥0,κ>1,and the motility function satisfies thatγ(v)∈C3([0,∞)),γ(v)>0,γ′(v)≤0 for all v≥0.Considering the Neumann boundary condition,we obtain the global boundedness of solutions if one of the following conditions holds:(i)λ=μ=0,1≤nλ3;(ii)λ>0,μ>0,combined withκ>1,1≤n≤3 or k>n+2/4,,n>3.Moreover,we prove that the solution (u, v, w, z) exponentially converges to the constant steady state ((λ/μ)1/k-1,∫Ωv0dx+∫Ωw0dx/|Ω|,0,(λ/μ)1/k-1).展开更多
In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-depe...In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-dependent problems.We use the convex splitting method,the variant energy quadratization method,and the scalar auxiliary variable method coupled with the LDG method to construct first-order temporal accurate schemes based on the gradient flow structure of the models.These semi-implicit schemes are decoupled,energy stable,and can be extended to high accuracy schemes using the semi-implicit spectral deferred correction method.Many bound preserving DG discretizations are only worked on explicit time integration methods and are difficult to get high-order accuracy.To overcome these difficulties,we use the Lagrange multipliers to enforce the implicit or semi-implicit LDG schemes to satisfy the bound constraints at each time step.This bound preserving limiter results in the Karush-Kuhn-Tucker condition,which can be solved by an efficient active set semi-smooth Newton method.Various numerical experiments illustrate the high-order accuracy and the effect of bound preserving.展开更多
该文在有界光滑域Ω■R^(n)(n≥3)上研究了一个带奇异灵敏度的两组分非局部模型,该模型是三组分的Jones-Brantingham-Chayes趋向性模型的一个简化模型,后者被用于模拟在警察威慑下犯罪活动的时空动态.该文在较大趋化敏感系数范围内证明...该文在有界光滑域Ω■R^(n)(n≥3)上研究了一个带奇异灵敏度的两组分非局部模型,该模型是三组分的Jones-Brantingham-Chayes趋向性模型的一个简化模型,后者被用于模拟在警察威慑下犯罪活动的时空动态.该文在较大趋化敏感系数范围内证明了相应初边值问题拥有全局经典解.值得指出的是,相较于无警察威慑效应的Short et al趋向性犯罪模型的相关结果,警察威慑扩大了确保解全局存在的趋化敏感系数范围,在某种意义下这也表明了警察威慑效应对模型解性质具有正则化效应.注意,先前数值结果(Jones,Brantingham and Chayes.Math Models Methods Appl Sci,2010)表明警察威慑有益于镇压犯罪热点的形成,因此该文的研究结果也是相应数值结果的一个理论支持.展开更多
To promote growth,terrestrial plants release photosynthetic products into the rhizosphere in the form of root exudates through their root systems.Under the attraction of root exudates,plant growth-promoting rhizobacte...To promote growth,terrestrial plants release photosynthetic products into the rhizosphere in the form of root exudates through their root systems.Under the attraction of root exudates,plant growth-promoting rhizobacteria(PGPR)colonize the rhizosphere to stimulate plant growth and/or suppress the growth of pathogenic microorganisms.The rhizospheric recruitment of PGPR,as well as the establishment of root-microbe interactions,is initiated by chemotaxis towards root exudates.Over the past several decades,scientists have made notable strides in identifying representative chemoeffectors in root exudates,as well as the corresponding chemoreceptors.We review here the most recent developments in rhizospheric chemotaxis,particularly the chemoeffectors in root exudates,the structural and functional characterization of methyl-accepting chemotaxis proteins of PGPR,and the impacts of rhizospheric chemotaxis on root colonization,biofilm formation,and other root-microbe interactions during recruitment.Finally,we propose several perspectives that aim to fully unlock the potential of PGPR as bioinoculants in sustainable agriculture.展开更多
In this paper, we use contraction mapping principle, operator-theoretic approach and some uniform estimates to establish local solvability of the parabolic-hyperbolic type chemotaxis system with fixed boundary in 1-di...In this paper, we use contraction mapping principle, operator-theoretic approach and some uniform estimates to establish local solvability of the parabolic-hyperbolic type chemotaxis system with fixed boundary in 1-dimensional domain. In addition, local solvability of the free boundary problem is considered by straightening the free boundary.展开更多
Chemotaxis to water-soluble attractants is mainly controlled by ASE sensory neuron whose specification is regulated by che-1 in Caenorhabditis elegans. Our data suggested that exposure to high concentrations of metals...Chemotaxis to water-soluble attractants is mainly controlled by ASE sensory neuron whose specification is regulated by che-1 in Caenorhabditis elegans. Our data suggested that exposure to high concentrations of metals, such as Pb, Cu, Ag, and Cr, would result in severe defects of chemotaxis to water-soluble attractants of NaCl, cAMP, and biotin. Moreover, the morphology of ASE neuron structures as observed by relative fluorescent intensities and relative size of fluorescent puncta of cell bodies, relative lengths of sensory endings in ASE neurons, and the expression patterns of che-1 were obviously altered in metal exposed animals when they meanwhile exhibited obvious chemotaxis defects to water-soluble attractants. In addition, the dendrite morphology could be noticeably changed in animals exposed to 150 μmol/L of Pb, Cu, and Ag. Furthermore, we observed significant decreases of chemotaxis to water-soluble attractants in Pb exposed che-1 mutant at concentrations more than 2.5 μmol/L, and in Cu, Ag, and Cr exposed che-1 mutant at concentrations more than 50 μmol/L. Therefore, impairment of the ASE neuron structures and functions may largely contribute to the appearance of chemotaxis defects to water-soluble attractants in metal exposed nematodes.展开更多
基金supported by the NSFC(12301260)the Hong Kong Scholars Program(XJ2023002,2023-078)+14 种基金the Double First-Class Construction-Talent Introduction of Southwest University(SWU-KR22037)the Chongqing Post-Doctoral Fund for Staying in Chongqing(2022)partially supported by the NSFC(12271064,11971082)the Chongqing Talent Support Program(cstc2022ycjh-bgzxm0169)the Natural Science Foundation of Chongqing(cstc2021jcyj-msxmX1051)the Fundamental Research Funds for the Central Universities(2020CDJQY-Z001,2019CDJCYJ001)the Key Laboratory of Nonlinear Analysis and its Applications(Chongqing University)Ministry of EducationChongqing Key Laboratory of Analytic Mathematics and Applicationssupported by the NSFC(12301261)the Scientific Research Starting Project of SWPU(2021QHZ016)the Sichuan Science and Technology Program(2023NSFSC1365)the Nanchong Municipal Government-Universities Scientific Cooperation Project(SXHZ045)supported by the China Scholarship Council(202206050060)the Graduate Research and Innovation Foundation of Chongqing(CYB22044)。
文摘In this paper,we consider the fully parabolic Chemotaxis system with the general logistic source{ut=Δ(γ(v)u)+λu-μu^(k),x∈Ω,t>0,vt=△v+wz,x∈Ω,t>0,wt=-wz,x∈Ω,t>0,zt=△z-z+u,x∈Ω,t>0 whereΩ⊂ℝn(n≥1)is a smooth and bounded domain,λ≥0,μ≥0,κ>1,and the motility function satisfies thatγ(v)∈C3([0,∞)),γ(v)>0,γ′(v)≤0 for all v≥0.Considering the Neumann boundary condition,we obtain the global boundedness of solutions if one of the following conditions holds:(i)λ=μ=0,1≤nλ3;(ii)λ>0,μ>0,combined withκ>1,1≤n≤3 or k>n+2/4,,n>3.Moreover,we prove that the solution (u, v, w, z) exponentially converges to the constant steady state ((λ/μ)1/k-1,∫Ωv0dx+∫Ωw0dx/|Ω|,0,(λ/μ)1/k-1).
文摘In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-dependent problems.We use the convex splitting method,the variant energy quadratization method,and the scalar auxiliary variable method coupled with the LDG method to construct first-order temporal accurate schemes based on the gradient flow structure of the models.These semi-implicit schemes are decoupled,energy stable,and can be extended to high accuracy schemes using the semi-implicit spectral deferred correction method.Many bound preserving DG discretizations are only worked on explicit time integration methods and are difficult to get high-order accuracy.To overcome these difficulties,we use the Lagrange multipliers to enforce the implicit or semi-implicit LDG schemes to satisfy the bound constraints at each time step.This bound preserving limiter results in the Karush-Kuhn-Tucker condition,which can be solved by an efficient active set semi-smooth Newton method.Various numerical experiments illustrate the high-order accuracy and the effect of bound preserving.
文摘该文在有界光滑域Ω■R^(n)(n≥3)上研究了一个带奇异灵敏度的两组分非局部模型,该模型是三组分的Jones-Brantingham-Chayes趋向性模型的一个简化模型,后者被用于模拟在警察威慑下犯罪活动的时空动态.该文在较大趋化敏感系数范围内证明了相应初边值问题拥有全局经典解.值得指出的是,相较于无警察威慑效应的Short et al趋向性犯罪模型的相关结果,警察威慑扩大了确保解全局存在的趋化敏感系数范围,在某种意义下这也表明了警察威慑效应对模型解性质具有正则化效应.注意,先前数值结果(Jones,Brantingham and Chayes.Math Models Methods Appl Sci,2010)表明警察威慑有益于镇压犯罪热点的形成,因此该文的研究结果也是相应数值结果的一个理论支持.
基金sponsored by the National Science Foundation of China(Nos.52200189,52230006,and 32271700)the Guangxi Science and Technology Project,China(Nos.2021GXNSFBA220055,2020GXNSFAA297256,and Guike AB21220049)+2 种基金the Guangxi Key Laboratory of Environmental Pollution Control Theory and TechnologyGuangxi Engineering Research Center of Comprehensive Treatment for Agricultural Non-Point Source PollutionModern Industry College of Ecology and Environmental Protection from Guilin University of Technology,China for support。
文摘To promote growth,terrestrial plants release photosynthetic products into the rhizosphere in the form of root exudates through their root systems.Under the attraction of root exudates,plant growth-promoting rhizobacteria(PGPR)colonize the rhizosphere to stimulate plant growth and/or suppress the growth of pathogenic microorganisms.The rhizospheric recruitment of PGPR,as well as the establishment of root-microbe interactions,is initiated by chemotaxis towards root exudates.Over the past several decades,scientists have made notable strides in identifying representative chemoeffectors in root exudates,as well as the corresponding chemoreceptors.We review here the most recent developments in rhizospheric chemotaxis,particularly the chemoeffectors in root exudates,the structural and functional characterization of methyl-accepting chemotaxis proteins of PGPR,and the impacts of rhizospheric chemotaxis on root colonization,biofilm formation,and other root-microbe interactions during recruitment.Finally,we propose several perspectives that aim to fully unlock the potential of PGPR as bioinoculants in sustainable agriculture.
基金Supported by the National Natural Science Foundation of China(11131005)the Fundamental Research Funds for the Central Universities(2014201020202)
文摘In this paper, we use contraction mapping principle, operator-theoretic approach and some uniform estimates to establish local solvability of the parabolic-hyperbolic type chemotaxis system with fixed boundary in 1-dimensional domain. In addition, local solvability of the free boundary problem is considered by straightening the free boundary.
基金supported by the National Natural Science Foundation of China (No. 30771113, 30870810)the Program for New Century Excellent Talents in Universityprovided by the Caenorhabdits Genetics Center (funded by the NIH National Center for Research Resource, USA).
文摘Chemotaxis to water-soluble attractants is mainly controlled by ASE sensory neuron whose specification is regulated by che-1 in Caenorhabditis elegans. Our data suggested that exposure to high concentrations of metals, such as Pb, Cu, Ag, and Cr, would result in severe defects of chemotaxis to water-soluble attractants of NaCl, cAMP, and biotin. Moreover, the morphology of ASE neuron structures as observed by relative fluorescent intensities and relative size of fluorescent puncta of cell bodies, relative lengths of sensory endings in ASE neurons, and the expression patterns of che-1 were obviously altered in metal exposed animals when they meanwhile exhibited obvious chemotaxis defects to water-soluble attractants. In addition, the dendrite morphology could be noticeably changed in animals exposed to 150 μmol/L of Pb, Cu, and Ag. Furthermore, we observed significant decreases of chemotaxis to water-soluble attractants in Pb exposed che-1 mutant at concentrations more than 2.5 μmol/L, and in Cu, Ag, and Cr exposed che-1 mutant at concentrations more than 50 μmol/L. Therefore, impairment of the ASE neuron structures and functions may largely contribute to the appearance of chemotaxis defects to water-soluble attractants in metal exposed nematodes.
