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PatU3 plays a central role in coordinating cell division and differentiation in pattern formation of filamentous cyanobacterium Nostoc sp.PCC 7120

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Science China(Life Sciences) 2023年第12期66卷 2896-2909页

作者： Lei Yin Zhenggao Zheng Yilin Li Xiying Li Dan Cheng Chunxia Dong Yixuan Liu Jindong Zhao State Key Laboratory of Protein and Plant Genetic Engineering School of Life SciencesPeking UniversityBeijing 100871China National Teaching Center for Experimental Biology School of Life SciencesPeking UniversityBeijing 100871China Institute of Hydrobiology Chinese Academy of SciencesWuhan 430072China

Spatial periodic signal for cell differentiation in some multicellular organisms is generated according to Turing's principle for pattern formation.How a dividing cell responds to the signal of differentiation is addressed with the filamentous cyanobacterium Nostoc sp.PCC 7120,which forms the patterned distribution of heterocysts.We show that differentiation of a dividing cell was delayed until its division was completed and only one daughter cell became heterocyst.A mutant of patU3,which encodes an inhibitor of heterocyst formation,showed no such delay and formed heterocyst pairs from the daughter cells of cell division or dumbbell-shaped heterocysts from the cells undergoing cytokinesis.The patA mutant,which forms heterocysts only at the filament ends,restored intercalary heterocysts by a single nucleotide mutation of patU3,and double mutants of patU3/patA and patU3/hetF had the phenotypes of the patU3 mutant.We provide evidence that HetF,which can degrade PatU3,is recruited to cell divisome through its C-terminal domain.A HetF mutant with its N-terminal peptidase domain but lacking the C-terminal domain could not prevent the formation of heterocyst pairs,suggesting that the divisome recruitment of HetF is needed to sequester HetF for the delay of differentiation in dividing cells.Our study demonstrates that PatU3 plays a key role in celldivision coupled control of differentiation.

关键词： cyanobacteria heterocyst differentiation cell division pattern formation PatU3

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Global Solvability,pattern formation and Stability to a Chemotaxis-haptotaxis Model with Porous Medium Diffusion

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Acta Mathematica Sinica,English Series 2023年第8期39卷 1597-1623页

作者： Chun Hua JIN School of Mathematical Sciences South China Normal UniversityGuangzhou 510631P.R.China

In this paper,we deal with the following chemotaxis-haptotaxis system modeling cancer invasion with nonlinear diffusion,ut=Δum−χ∇·(u∇v)−ξ∇·(u∇ω)+μu(1−u−ω),inΩ×R^(+),vt−Δv+v=u,inΩ×R+,ωt=−vω,inΩ×R+,whereΩ⊂R^(N)is a bounded domain.We first supplement the results of global existence and uniform boundedness of solutions for the case m=2N N+2.Then for any m>0 and any spatial dimension,we consider the stability of equilibrium,and find that the chemotaxis has a destabilizing effect,that is for the ODEs,or the diffusion-ODE system without chemotaxis,the solutions tend to a linearly stable uniform steady state(1,1,0).When the chemotactic coefficientχis large,the equilibrium(1,1,0)become unstable.Then we study the existence of nontrivial stationary solutions via bifurcation techniques withχbeing the bifurcation parameter,and obtain nonhomogeneous patterns.At last,we also investigate the stability of these bifurcation solutions.

关键词： Chemotaxis-haptotaxis porous medium diffusion pattern formation stability

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A local discontinuous Galerkin method for the pattern formation dynamical model in polymerizing action flocks

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Science China Mathematics 2022年第4期65卷 849-868页

作者： Lulu Tian Xiuhui Guo Hui Guo Maosheng Jiang Yang Yang Jiansong Zhang College of Science China University of PetroleumQingdao266580China Beijing Computational Science Research Center Beijing100193China Department of Mathematics Michigan Technological UniversityHoughtonMI49931USA

In this paper,we apply local discontinuous Galerkin methods to the pattern formation dynamical model in polymerizing action flocks.Optimal error estimates for the density and filament polarization in different norms are established.We use a semi-implicit spectral deferred correction time method for time discretization,which allows a relative large time step and avoids computation of a Jacobian matrix.Numerical experiments are presented to verify the theoretical analysis and to show the capability for simulations of action wave formation.

关键词： local discontinuous Galerkin method error estimate pattern formation spectral deferred correction time method

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pattern formation in a Dusty Plasma System

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Plasma Science and Technology 2004年第6期6卷 2571-2575页

作者：黄峰叶茂福王龙江南 Institute of Physics Chinese Academy of Sciences Beijing 100080 China

A rich variety of dust patterns have been observed in a capacitively coupled rf discharge dusty plasma system. Dust particles are synthesized through chemical reaction of the filled gas mixture during discharge. Different patterns are formed in different stages of particle growth. In the early stage of particle growth, dust cloud can be formed by a large number of small particles, and its behavior appears to be fluid-like. Such interesting nonlinear phenomena as dust void and complex dust cloud patterns are observed in this stage. As dust particles grow, the particle size and structure can be controlled to follow two different routes. In one of the routes, the particles grow up in a ball-like shape and can be formed into regular lattice and cluster patterns. In the other, the particles grow up in a fractal shape.

关键词： dusty plasma pattern formation

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pattern formation in superdiffusion Oregonator model

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Chinese Physics B 2016年第10期25卷 197-201页

作者：冯帆闫佳刘富成贺亚峰 Hebei Key Laboratory of Optic-electronic Information Materials College of Physics Science and TechnologyHebei University

pattern formations in an Oregonator model with superdiffusion are studied in two-dimensional(2D) numerical simulations. Stability analyses are performed by applying Fourier and Laplace transforms to the space fractional reaction–diffusion systems. Antispiral, stable turing patterns, and travelling patterns are observed by changing the diffusion index of the activator. Analyses of Floquet multipliers show that the limit cycle solution loses stability at the wave number of the primitive vector of the travelling hexagonal pattern. We also observed a transition between antispiral and spiral by changing the diffusion index of the inhibitor.

关键词： pattern formation reaction diffusion system anomalous diffusion

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Three-dimensional interfacial wave theory of dendritic growth: (Ⅱ). non-axi-symmetric global wave modes and selection criterion of pattern formation

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Chinese Physics B 2009年第2期18卷 686-698页

作者：陈永强唐熊忻徐鉴君 School of Mathematical Science Nankai University Department of Fundamental Subject Tianjin Institute of Urban Construction School of materials Science and Engineering University of Science and Technology Beijing Department of Mathematics and Statistics McGill University

This paper is ttie continuation of part （Ⅰ）, which completes the derivations of the 3D global wave modes solutions, yields the stability criterion and, on the basis of the results obtained, demonstrates the selecti... 详细信息

关键词： dendritic growth pattern formation interracial waves selection criterion

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Spatial pattern formation of a ratio-dependent predator-prey model

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Chinese Physics B 2010年第9期19卷 78-85页

作者：林望 College of Mathematics and Information Science Wenzhou University

This paper presents a theoretical analysis of evolutionary process that involves organisms distribution and their interaction of spatially distributed population with diffusion in a Holling-III ratio-dependent predator-prey model, the sufficient conditions for diffusion-driven instability with Neumann boundary conditions are obtained. Furthermore, it presents novel numerical evidence of time evolution of patterns controlled by diffusion in the model, and finds that the model dynamics exhibits complex pattern replication, and the pattern formation depends on the choice of the initial conditions. The ideas in this paper may provide a better understanding of the pattern formation in ecosystems.

关键词： ratio-dependent predator-prey model Holling III functional response diffusion-driven instability pattern formation

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Laser-induced pattern formation from homogeneous polyisoprene solutions

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Chinese Physics B 2008年第6期17卷 2156-2159页

作者：林殿阳黎明王淑杰吕志伟 Institute of Opto-Electronics Harbin Institute of Technology College of Science Inner Mongolia University of Technology School of Management Harbin Institute of Technology

This paper reports that the pattern formation in homogeneous solutions of polyisoprene in toluene saturated with C60 induced by a continuous-wave visible laser is observed experimentally. The transmitted beam patterns change with the increase of the laser irradiation time. In the initial phase, the patterns with concentric ring-shaped structure are formed. In the end, the patterns become speckle-shaped. The incubation time of the transmitted beam widening is inversely proportional to the laser power density and solution concentration. The pattern formation results from the optical-field-induced refractive index changes in the solutions, but the mechanism of optical-field-induced refractive index changes in the polymer solutions needs to be further studied.

关键词： laser-induced pattern formation polyisoprene

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Enslaved Phase-Separation Fronts and Liesegang pattern formation

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Communications in Computational Physics 2011年第5期9卷 1081-1093页

作者： E.M.Foard A.J.Wagner Department of Physics North Dakota State UniversityFargoND 58105USA

We show that an enslaved phase-separation front moving with diffusive speeds U=C/√T can leave alternating domains of increasing size in their wake.We find the size and spacing of these domains is identical to Liesegang patterns.For equal composition of the components we are able to predict the exact form of the pattern analytically.To our knowledge this is the first fully analytical derivation of the Liesegang laws.We also show that there is a critical value for C below which only two domains are formed.Our analytical predictions are verified by numerical simulations using a lattice Boltzmann method.

关键词： Liesegang phase separation front reaction diffusion pattern formation lattice Boltzmann Matalon-Packter

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CDS Simulation and pattern formation of Phase Separation

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Communications in Nonlinear Science and Numerical Simulation 1998年第4期3卷 233-236页

作者： Zhanaji LIU Men CHENG Jiong RUAN and Shouji CHENG (Department of Mechanics and Engineering Science, Fudan University, Shanghai 200433,China)(Department of Mathematics, Fudan University, Shanghai 200433, China) Dept. of Mechanics and Eng. Science Fudan University Shanghai 200433 China Department of Mathematics Fudan University Shanghai 200433 China

Several properties of the generation and evolution of phase separating patterns for binary material studied by CDS model are proposed. The main conclusions are (1) for alloys spinodal decomposition, the conceptions of "macro-pattern" and "micropattern" are posed by "black-and- white graph" and "gray-scale graph" respectively.We find that though the four forms of map f that represent the self-evolution of order parameter in a cell(lattice) are similar to each other in "macro-pattern" , there are evident differences in their micro-pattern, e.g., some different fine netted structures in the blackdomain and the white domain are found by the micro-pattern, so that distinct mechanical and physical behaviors shall be obtained. (2) If the two constitutions of block copolymers are not symmetric (i.e. r ≠ 0.5), a pattern called "grain-strip cross pattern"is discovered,in the 0.43 < r < 0.45.

关键词： lattice gas automata CDS phase separation pattern formation

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