Crack patterns observed in nature have attracted the interest of researchers in various fields, and the mechanism of the pattern formation has been investigated. However, the phenomenon is very complicated, and many f...Crack patterns observed in nature have attracted the interest of researchers in various fields, and the mechanism of the pattern formation has been investigated. However, the phenomenon is very complicated, and many factors affect the process. Therefore, we are motivated to construct a general simulation code with a simple algorithm. In this study, crack pattern formation due to shrinkage caused by the drying of a wet material was simulated. The process was simplified as follows: tensile force is generated in the model, and a crack is generated when the tension exceeds a critical value. The tensile forces in the x and y directions are independently evaluated. A crack propagates perpendicular to the tension until it reaches another crack or a boundary. Based on this modeling, simulations with a two-dimensional square domain were performed. Consequently, a cross-divided pattern was generated. Assuming zigzag crack propagation, more realistic patterns were obtained. The effects of the boundary and domain size were also considered, and various characteristic patterns were obtained. Furthermore, the orientation dependency was simulated, and 45˚ declined patterns and rectangularly divided patterns were generated. The model presented in this study is very simplified and is expected to be applicable to various objects.展开更多
The article presents multi-pattern formation exchange of mobile robots according to the image signals, programs motion paths using A＊ searching algorithm, and avoids the collision points of motion paths. The system c...The article presents multi-pattern formation exchange of mobile robots according to the image signals, programs motion paths using A＊ searching algorithm, and avoids the collision points of motion paths. The system contains an image system, a grid based motion platform, some wireless Radio Frequency （RF） modules and five mobile robots. We use image recognition algorithm to classify variety pattern formation according to variety Quick Response （QR） code symbols on the user interface of the supervised computer. The supervised computer controls five mobile robots to execute formation exchange and presents the movement scenario on the grid based motion platform. We have been developed some pattern formations according to game applications, such as long snake pattern formation, phalanx pattern formation, crane wing pattern formation, sword pattern formation, cone pattern formation, sward pattern tbrmation, T pattern formation, rectangle pattern formation and so on. We develop the user interface of the multi-robot system to program motion paths for variety pattern formation exchange according to the minimum displacement. In the experimental results, the supervised computer recognizes the various QR-code symbols using image system and decides which pattern formation to be selected on real-time. Mobile robots can receive the pattern formation command from the supervised computer, present the movement scenario from the original pattern formation to the assigned pattern formation on the motion platform, and avoid other mobile robots on real-time.展开更多
We conducted experiments on specially designed microfluidic chips that generate droplets through a microfluidic ow-focusing approach. The fluid flow in the microfluidic channel produced a shear flow field at low Reyno...We conducted experiments on specially designed microfluidic chips that generate droplets through a microfluidic ow-focusing approach. The fluid flow in the microfluidic channel produced a shear flow field at low Reynolds numbers. The droplets in the microfluidic system exhibited special droplet pattern formations similar to periodic crystal-like lattices because of the competition between shear forces and surface tension. By adjusting the flow rate ratio of the water （droplet phase） to oil （continuous phase） phases and changing the outlet channel widths, the droplets formed monolayer dispersion to double-layer formation to monolayer squeezing when the outlet channel widths were 250 or 300 μm. We also obtained droplets with monolayer dispersion, three-layer arrangements, double-layer squeezing, and monolayer squeezing when the outlet channel width was 350 μm. The outlet channel width was increased to 400 μm, and four-layer arrangements were observed. We also studied the translation of droplet formation, which resulted in a detailed strategy to control drop size and droplet pattern formation for emulsi cation in microfluidic devices. We expect that our strategy can provide theoretical guidance to synthesize dispersion or polydisperse colloid particles.展开更多
We present two approaches to system identification, i.e. the identification of partial differentialequations (PDEs) from measurement data. The first is a regression-based variational systemidentification procedure tha...We present two approaches to system identification, i.e. the identification of partial differentialequations (PDEs) from measurement data. The first is a regression-based variational systemidentification procedure that is advantageous in not requiring repeated forward model solves andhas good scalability to large number of differential operators. However it has strict data typerequirements needing the ability to directly represent the operators through the available data.The second is a Bayesian inference framework highly valuable for providing uncertaintyquantification, and flexible for accommodating sparse and noisy data that may also be indirectquantities of interest. However, it also requires repeated forward solutions of the PDE modelswhich is expensive and hinders scalability. We provide illustrations of results on a model problemfor pattern formation dynamics, and discuss merits of the presented methods.展开更多
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. Diffe...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.展开更多
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...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 selection criterion of pattern formation.展开更多
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 predato...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.展开更多
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...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.展开更多
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 fraction...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.展开更多
Positional information encoded in spatial concentration patterns is crucial for the development of multicellular organisms.However,it is still unclear how such information is affected by the physically dissipative dif...Positional information encoded in spatial concentration patterns is crucial for the development of multicellular organisms.However,it is still unclear how such information is affected by the physically dissipative diffusion process.Here we study one-dimensional patterning systems with analytical derivation and numerical simulations.We find that the diffusion constant of the patterning molecules exhibits a nonmonotonic effect on the readout of the positional information from the concentration patterns.Specifically,there exists an optimal diffusion constant that maximizes the positional information.Moreover,we find that the energy dissipation due to the physical diffusion imposes a fundamental upper limit on the positional information.展开更多
In this paper,two fully-discrete local discontinuous Galerkin(LDG)methods are applied to the growth-mediated autochemotactic pattern formation model in self-propelling bacteria.The numerical methods are linear and dec...In this paper,two fully-discrete local discontinuous Galerkin(LDG)methods are applied to the growth-mediated autochemotactic pattern formation model in self-propelling bacteria.The numerical methods are linear and decoupled,which greatly improve the computational efficiency.In order to resolve the time level mismatch of the discretization process,a special time marching method with high-order accuracy is constructed.Under the condition of slight time step constraints,the optimal error estimates of this method are given.Moreover,the theoretical results are verified by numerical experiments.Real simulations show the patterns of spots,rings,stripes as well as inverted spots because of the interplay of chemotactic drift and growth rate of the cells.展开更多
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 ...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.展开更多
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=−v...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.展开更多
In this paper,we apply local discontinuous Galerkin(LDG)methods for pattern formation dynamical model in polymerizing actin focks.There are two main dificulties in designing effective numerical solvers.First of all,th...In this paper,we apply local discontinuous Galerkin(LDG)methods for pattern formation dynamical model in polymerizing actin focks.There are two main dificulties in designing effective numerical solvers.First of all,the density function is non-negative,and zero is an unstable equilibrium solution.Therefore,negative density values may yield blow-up solutions.To obtain positive numerical approximations,we apply the positivitypreserving(PP)techniques.Secondly,the model may contain stif source.The most commonly used time integration for the PP technique is the strong-stability-preserving Runge-Kutta method.However,for problems with stiff source,such time discretizations may require strictly limited time step sizes,leading to large computational cost.Moreover,the stiff source any trigger spurious filament polarization,leading to wrong numerical approximations on coarse meshes.In this paper,we combine the PP LDG methods with the semi-implicit Runge-Kutta methods.Numerical experiments demonstrate that the proposed method can yield accurate numerical approximations with relatively large time steps.展开更多
Background： Developmental patterning is highly reproducible and accurate at the single-cell level during fly embryogenesis despite the gene expression noise and external perturbations such as the variation of the emb...Background： Developmental patterning is highly reproducible and accurate at the single-cell level during fly embryogenesis despite the gene expression noise and external perturbations such as the variation of the embryo length, temperature and genes. To reveal the underlying mechanism, it is very important to characterize the noise transmission during the dynamic pattern formation. Two hypotheses have been proposed. The ＂channel＂ scenario requires a highly reproducible input and an accurate interpretation by downstream genes. In contrast, the ＂filter＂ scenario proposes a noisy input and a noise filter via the cross-regulation of the downstream network. It has been under great debates which scenario the fly embryogenesis follows. Results： The first 3-h developmental patterning of fly embryos is orchestrated by a hierarchical segmentation gene network, which rewires upon the maternal to zygotic transition. Starting from the highly reproducible maternal gradients, the positional information is refined to the single-cell precision through the highly dynamical evolved zygotic gene expression profiles. Thus the fly embryo development might strictly fit into neither the originally proposed ＂filter＂ nor ＂channel＂ scenario. The controversy that which scenario the fly embryogenesis follows could be further clarified by combining quantitative measurements and modeling. Conclusions： Fly embryos have become one of the perfect model systems for quantitative systems biology studies. The underlying mechanism discovered from fly embryogenesis will deepen our understanding of the noise control of the gene network, facilitate searching for more efficient and safer methods for cell programming and reprogramming, and have the great potential for tissue engineering and regenerative medicine.展开更多
Pigmentation patterns are ubiquitous in nature.Visually striking pigmentation patterns are not only aesthetically appealing,but also crucial to pollinator interaction and plant fitness.The formation of complex floral ...Pigmentation patterns are ubiquitous in nature.Visually striking pigmentation patterns are not only aesthetically appealing,but also crucial to pollinator interaction and plant fitness.The formation of complex floral pigmentation patterns mainly relies on the spatiotemporal expression of R2R3-MYB transcription factors and is often associated with certain floral development programs,such as floral organ identity,symmetry,which likely provide key information to initiate the patterning.For a complex pigmentation pattern to form,at least a pair of activator and inhibitor is required,despite their interaction might vary depending on the system being investigated.The regulation of pigmentation pattern involves multiple molecular mechanisms,such as transcriptional regulation,small RNA,transposon-mediated gene silencing,and methylation of gene body.Identifying these regulators can be facilitated by using single-cell and spatial transcriptomics as well as innovative plant transformation technologies.Moreover,plant organ development and pigmentation patterns are often interdependent,but current methods of describing patterns are static.Therefore,more precise and quantitative measurements are needed to elucidate the developmental mechanisms underlying complex pigmentation patterns in flowers.展开更多
In the paper, we investigate an elliptic system well-known as the Gray-Scott model and present some further results for positive solutions of this model. More precisely, we give the refined a priori estimates of posit...In the paper, we investigate an elliptic system well-known as the Gray-Scott model and present some further results for positive solutions of this model. More precisely, we give the refined a priori estimates of positive solutions, and improve some previous results for the non-existence and existence of positive non-constant solutions as the parameters are varied, which imply some certain conditions where the pattern formation occurs or not.展开更多
The interaction of bodies like spheres and disks in rotating fluids leads to novel flow structures. The primary swirling flow in circumferential direction is superimposed by a secondary motion in the meridional plane....The interaction of bodies like spheres and disks in rotating fluids leads to novel flow structures. The primary swirling flow in circumferential direction is superimposed by a secondary motion in the meridional plane. The flow is visualized by introducing ink through a hole in the center of the axes and distributed radially in the central plane between the interacting bodies. The flow structure depends on the shape of the bodies, their geometrical arrangement and the Reynolds number given by the rotational speed. The observed flow structures gave rise to further investigations with PIV-measurcments and numerical simulations.展开更多
After Bénard＇s experiment in 1900, Rayleigh formulated heat convection problems by the Oberbeck-Boussinesq approximation in the horizontal strip domain in 1916. The pattern formations have been investigated by t...After Bénard＇s experiment in 1900, Rayleigh formulated heat convection problems by the Oberbeck-Boussinesq approximation in the horizontal strip domain in 1916. The pattern formations have been investigated by the bifurcation theory, weakly nonlinear theories and computational approaches. The boundary conditions for the velocity on the upper and lower boundaries are usually assumed as stress-free or no-slip. In the first part of this paper, some bifurcation pictures for the case of the stress-free on the upper boundary and the no-slip on the lower boundary are obtained. In the second part of this paper, the bifurcation pictures for the case of the stress-free on both boundaries by a computer assisted proof are verified. At last., Bénard-Marangoni heat convections for the ease of the free surface of the upper boundary are considered.展开更多
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 a...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.展开更多
文摘Crack patterns observed in nature have attracted the interest of researchers in various fields, and the mechanism of the pattern formation has been investigated. However, the phenomenon is very complicated, and many factors affect the process. Therefore, we are motivated to construct a general simulation code with a simple algorithm. In this study, crack pattern formation due to shrinkage caused by the drying of a wet material was simulated. The process was simplified as follows: tensile force is generated in the model, and a crack is generated when the tension exceeds a critical value. The tensile forces in the x and y directions are independently evaluated. A crack propagates perpendicular to the tension until it reaches another crack or a boundary. Based on this modeling, simulations with a two-dimensional square domain were performed. Consequently, a cross-divided pattern was generated. Assuming zigzag crack propagation, more realistic patterns were obtained. The effects of the boundary and domain size were also considered, and various characteristic patterns were obtained. Furthermore, the orientation dependency was simulated, and 45˚ declined patterns and rectangularly divided patterns were generated. The model presented in this study is very simplified and is expected to be applicable to various objects.
文摘The article presents multi-pattern formation exchange of mobile robots according to the image signals, programs motion paths using A＊ searching algorithm, and avoids the collision points of motion paths. The system contains an image system, a grid based motion platform, some wireless Radio Frequency （RF） modules and five mobile robots. We use image recognition algorithm to classify variety pattern formation according to variety Quick Response （QR） code symbols on the user interface of the supervised computer. The supervised computer controls five mobile robots to execute formation exchange and presents the movement scenario on the grid based motion platform. We have been developed some pattern formations according to game applications, such as long snake pattern formation, phalanx pattern formation, crane wing pattern formation, sword pattern formation, cone pattern formation, sward pattern tbrmation, T pattern formation, rectangle pattern formation and so on. We develop the user interface of the multi-robot system to program motion paths for variety pattern formation exchange according to the minimum displacement. In the experimental results, the supervised computer recognizes the various QR-code symbols using image system and decides which pattern formation to be selected on real-time. Mobile robots can receive the pattern formation command from the supervised computer, present the movement scenario from the original pattern formation to the assigned pattern formation on the motion platform, and avoid other mobile robots on real-time.
基金This work was supported by the National Natural Science Foundation of China （No.20934004 and No.91127046） and the National Basic Research Program of China （No.2012CB821500 and No.2010CB934500）.
文摘We conducted experiments on specially designed microfluidic chips that generate droplets through a microfluidic ow-focusing approach. The fluid flow in the microfluidic channel produced a shear flow field at low Reynolds numbers. The droplets in the microfluidic system exhibited special droplet pattern formations similar to periodic crystal-like lattices because of the competition between shear forces and surface tension. By adjusting the flow rate ratio of the water （droplet phase） to oil （continuous phase） phases and changing the outlet channel widths, the droplets formed monolayer dispersion to double-layer formation to monolayer squeezing when the outlet channel widths were 250 or 300 μm. We also obtained droplets with monolayer dispersion, three-layer arrangements, double-layer squeezing, and monolayer squeezing when the outlet channel width was 350 μm. The outlet channel width was increased to 400 μm, and four-layer arrangements were observed. We also studied the translation of droplet formation, which resulted in a detailed strategy to control drop size and droplet pattern formation for emulsi cation in microfluidic devices. We expect that our strategy can provide theoretical guidance to synthesize dispersion or polydisperse colloid particles.
基金We acknowledge the support of Defense Advanced Research Projects Agency(Grant HR00111990S2)Toyota Research Institute(Award#849910).
文摘We present two approaches to system identification, i.e. the identification of partial differentialequations (PDEs) from measurement data. The first is a regression-based variational systemidentification procedure that is advantageous in not requiring repeated forward model solves andhas good scalability to large number of differential operators. However it has strict data typerequirements needing the ability to directly represent the operators through the available data.The second is a Bayesian inference framework highly valuable for providing uncertaintyquantification, and flexible for accommodating sparse and noisy data that may also be indirectquantities of interest. However, it also requires repeated forward solutions of the PDE modelswhich is expensive and hinders scalability. We provide illustrations of results on a model problemfor pattern formation dynamics, and discuss merits of the presented methods.
文摘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.
基金supported by the Nankai University, China and in part by NSERC Grant of Canada
文摘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 selection criterion of pattern formation.
基金supported by the Natural Science Foundation of Zhejiang Province of China (Grant No.Y7080041)
文摘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.
基金Project supported by the Multidiscipline Scientific Research Foundation of Harbin Institute of Technology (Grand No HIT. MD. 2003. 08) and the Program of Excellence Team in Harbin Institute of Technology
文摘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.
基金supported by the National Natural Science Foundation of China(Grant Nos.11205044 and 11405042)the Research Foundation of Education Bureau of Hebei Province,China(Grant Nos.Y2012009 and ZD2015025)+1 种基金the Program for Young Principal Investigators of Hebei Province,Chinathe Midwest Universities Comprehensive Strength Promotion Project
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.32271293 and 11875076)。
文摘Positional information encoded in spatial concentration patterns is crucial for the development of multicellular organisms.However,it is still unclear how such information is affected by the physically dissipative diffusion process.Here we study one-dimensional patterning systems with analytical derivation and numerical simulations.We find that the diffusion constant of the patterning molecules exhibits a nonmonotonic effect on the readout of the positional information from the concentration patterns.Specifically,there exists an optimal diffusion constant that maximizes the positional information.Moreover,we find that the energy dissipation due to the physical diffusion imposes a fundamental upper limit on the positional information.
基金supported by National Natural Science Foundation of China(Grant No.11801569)Natural Science Foundation of Shandong Province(CN)(Grant No.ZR2021MA001)the Fundamental Research Funds for the Central Universities(Grant Nos.22CX03025A and 22CX03020A).
文摘In this paper,two fully-discrete local discontinuous Galerkin(LDG)methods are applied to the growth-mediated autochemotactic pattern formation model in self-propelling bacteria.The numerical methods are linear and decoupled,which greatly improve the computational efficiency.In order to resolve the time level mismatch of the discretization process,a special time marching method with high-order accuracy is constructed.Under the condition of slight time step constraints,the optimal error estimates of this method are given.Moreover,the theoretical results are verified by numerical experiments.Real simulations show the patterns of spots,rings,stripes as well as inverted spots because of the interplay of chemotactic drift and growth rate of the cells.
基金supported by the National Natural Science Foundation of China (32070203)the National Key Research and Development Program of China (2017YFA0503703),National Key Research and Development Program of China (2019YFA0904700,2021YFA0910700,2021YFA0909700)Qidong-SLS Innovation Fund (202001539)。
文摘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.
基金Supported by Guangdong Basic and Applied Basic Research Foundation(Grant No.2021A1515010336),NSFC(Grant Nos.12271186,12171166)。
文摘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.
基金supported by the Natural Science Foundation of Shandong Province(ZR2021MA001)the Fundamental Research Funds for the Central Universities(20CX05011A)+1 种基金supported by National Natural Science Foundation of China Grant 11801569supported by NSF grant DMS-1818467 and Simons Foundation 961585.
文摘In this paper,we apply local discontinuous Galerkin(LDG)methods for pattern formation dynamical model in polymerizing actin focks.There are two main dificulties in designing effective numerical solvers.First of all,the density function is non-negative,and zero is an unstable equilibrium solution.Therefore,negative density values may yield blow-up solutions.To obtain positive numerical approximations,we apply the positivitypreserving(PP)techniques.Secondly,the model may contain stif source.The most commonly used time integration for the PP technique is the strong-stability-preserving Runge-Kutta method.However,for problems with stiff source,such time discretizations may require strictly limited time step sizes,leading to large computational cost.Moreover,the stiff source any trigger spurious filament polarization,leading to wrong numerical approximations on coarse meshes.In this paper,we combine the PP LDG methods with the semi-implicit Runge-Kutta methods.Numerical experiments demonstrate that the proposed method can yield accurate numerical approximations with relatively large time steps.
文摘Background： Developmental patterning is highly reproducible and accurate at the single-cell level during fly embryogenesis despite the gene expression noise and external perturbations such as the variation of the embryo length, temperature and genes. To reveal the underlying mechanism, it is very important to characterize the noise transmission during the dynamic pattern formation. Two hypotheses have been proposed. The ＂channel＂ scenario requires a highly reproducible input and an accurate interpretation by downstream genes. In contrast, the ＂filter＂ scenario proposes a noisy input and a noise filter via the cross-regulation of the downstream network. It has been under great debates which scenario the fly embryogenesis follows. Results： The first 3-h developmental patterning of fly embryos is orchestrated by a hierarchical segmentation gene network, which rewires upon the maternal to zygotic transition. Starting from the highly reproducible maternal gradients, the positional information is refined to the single-cell precision through the highly dynamical evolved zygotic gene expression profiles. Thus the fly embryo development might strictly fit into neither the originally proposed ＂filter＂ nor ＂channel＂ scenario. The controversy that which scenario the fly embryogenesis follows could be further clarified by combining quantitative measurements and modeling. Conclusions： Fly embryos have become one of the perfect model systems for quantitative systems biology studies. The underlying mechanism discovered from fly embryogenesis will deepen our understanding of the noise control of the gene network, facilitate searching for more efficient and safer methods for cell programming and reprogramming, and have the great potential for tissue engineering and regenerative medicine.
基金financially supported by grants from the National Natural Science Foundation of China(Grant No.32122078)the Fundamental Research Funds for the Central Universities(Grant No.YDZX2023018+1 种基金Grant No.KJYQ2022002)Nanjing Agricultural University start-up funds。
文摘Pigmentation patterns are ubiquitous in nature.Visually striking pigmentation patterns are not only aesthetically appealing,but also crucial to pollinator interaction and plant fitness.The formation of complex floral pigmentation patterns mainly relies on the spatiotemporal expression of R2R3-MYB transcription factors and is often associated with certain floral development programs,such as floral organ identity,symmetry,which likely provide key information to initiate the patterning.For a complex pigmentation pattern to form,at least a pair of activator and inhibitor is required,despite their interaction might vary depending on the system being investigated.The regulation of pigmentation pattern involves multiple molecular mechanisms,such as transcriptional regulation,small RNA,transposon-mediated gene silencing,and methylation of gene body.Identifying these regulators can be facilitated by using single-cell and spatial transcriptomics as well as innovative plant transformation technologies.Moreover,plant organ development and pigmentation patterns are often interdependent,but current methods of describing patterns are static.Therefore,more precise and quantitative measurements are needed to elucidate the developmental mechanisms underlying complex pigmentation patterns in flowers.
基金This work Was partially supported by the National Natural Science Foundation of China(Grant No.10471022)
文摘In the paper, we investigate an elliptic system well-known as the Gray-Scott model and present some further results for positive solutions of this model. More precisely, we give the refined a priori estimates of positive solutions, and improve some previous results for the non-existence and existence of positive non-constant solutions as the parameters are varied, which imply some certain conditions where the pattern formation occurs or not.
文摘The interaction of bodies like spheres and disks in rotating fluids leads to novel flow structures. The primary swirling flow in circumferential direction is superimposed by a secondary motion in the meridional plane. The flow is visualized by introducing ink through a hole in the center of the axes and distributed radially in the central plane between the interacting bodies. The flow structure depends on the shape of the bodies, their geometrical arrangement and the Reynolds number given by the rotational speed. The observed flow structures gave rise to further investigations with PIV-measurcments and numerical simulations.
文摘After Bénard＇s experiment in 1900, Rayleigh formulated heat convection problems by the Oberbeck-Boussinesq approximation in the horizontal strip domain in 1916. The pattern formations have been investigated by the bifurcation theory, weakly nonlinear theories and computational approaches. The boundary conditions for the velocity on the upper and lower boundaries are usually assumed as stress-free or no-slip. In the first part of this paper, some bifurcation pictures for the case of the stress-free on the upper boundary and the no-slip on the lower boundary are obtained. In the second part of this paper, the bifurcation pictures for the case of the stress-free on both boundaries by a computer assisted proof are verified. At last., Bénard-Marangoni heat convections for the ease of the free surface of the upper boundary are considered.
基金supported by National Natural Science Foundation of China(Grant Nos.11801569 and 11571367)Natural Science Foundation of Shandong Province(CN)(Grant Nos.ZR2018BA011 and ZR2019MA015)+1 种基金the Fundamental Research Funds for the Central Universities(Grant Nos.18CX02021A and 18CX05003A)National Science Foundation of USA(Grant No.DMS-1818467).
文摘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.
