This paper investigates the dynamic interactions between biosurfactant-producing bacteria and their environment through pattern formations in diffusive predator-prey models.By analyzing the model’s equilibrium points...This paper investigates the dynamic interactions between biosurfactant-producing bacteria and their environment through pattern formations in diffusive predator-prey models.By analyzing the model’s equilibrium points and applying the Routh-Hurwitz criteria with bifurcation analysis,we determine the conditions for the existence of Turing patterns.Numerical simulations confirm these analytical findings and reveal diverse pattern formations influenced by diffusion and concentration zones,including both Turing and non-Turing patterns.We observe a correlation between the distribution of the two species through pattern formations and the effectiveness of biosurfactant-mediated oil recovery.More interestingly,our model focuses on the dynamics of bacterial and biosurfactant concentrations by showing that areas of high biosurfactant concentration are associated with the release of trapped oil from pores,thereby contributing to successful oil recovery.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
Pattern formations by Gierer-Meinhardt(GM)activator-inhibitor model are considered in this paper.By linear analysis,critical value of bifurcation parameter can be evaluated to ensure Turing instability.Numerical simul...Pattern formations by Gierer-Meinhardt(GM)activator-inhibitor model are considered in this paper.By linear analysis,critical value of bifurcation parameter can be evaluated to ensure Turing instability.Numerical simulations are tested by using second order semi-implicit backward difference methods for time discretization and the meshless Kansa method for spatially discretization.We numerically show the convergence of our algorithm.Pattern transitions in irregular domains are shown.We also provide various parameter settings on some irregular domains for different patterns appeared in nature.To further simulate patterns in reality,we construct different kinds of animal type domains and obtain desired patterns by applying proposed parameter settings.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
The dynamics of fluid and non-buoyant particles in a librating horizontal annulus is studied experimentally.In the absence of librations,the granular material forms a cylindrical layer near the outer boundary of the a...The dynamics of fluid and non-buoyant particles in a librating horizontal annulus is studied experimentally.In the absence of librations,the granular material forms a cylindrical layer near the outer boundary of the annulus and undergoes rigid-body rotation with the fluid and the annulus.It is demonstrated that the librational liquefaction of the granular material results in pattern formation.This self-organization process stems from the excitation of inertial modes induced by the oscillatory motion of liquefied granular material under the influence of the gravitational force.The inertial wave induces vortical fluid flow which entrains particles from rest and forms eroded areas that are equidistant from each other along the axis of rotation.Theoretical analysis and experiments demonstrate that a liquefied layer of granular material oscillates with a radian frequency equal to the angular velocity of the annulus and interacts with the inertial wave it excites.The new phenomenon of libration-induced pattern formation is of practical interest as it can be used to control multiphase flows and mass transfer in rotating containers in a variety of industrial processes.展开更多
This review paper provides a comprehensive introduction to various numerical methods for the phase-field model used to simulate the phase separation dynamics of diblock copolymer melts.Diblock copolymer systems form c...This review paper provides a comprehensive introduction to various numerical methods for the phase-field model used to simulate the phase separation dynamics of diblock copolymer melts.Diblock copolymer systems form complex structures at the nanometer scale and play a significant role in various applications.The phase-field model,in particular,is essential for describing the formation and evolution of these structures and is widely used as a tool to effectively predict the movement of phase boundaries and the distribution of phases over time.In this paper,we discuss the principles and implementations of various numerical methodologies for this model and analyze the strengths,limitations,stability,accuracy,and computational efficiency of each method.Traditional approaches such as Fourier spectral methods,finite difference methods and alternating direction explicit methods are reviewed,as well as recent advancements such as the invariant energy quadratization method and the scalar auxiliary variable scheme are also presented.In addition,we introduce examples of the phase-field model,which are fingerprint image restoration and 3D printing.These examples demonstrate the extensive applicability of the reviewed methods and models.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
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
The controllable transition between Turing and antispiral patterns is studied by using a time-delayed-feedback strategy in a FitzHugh-Nagumo model. We treat the time delay as a perturbation and analyse the effect of t...The controllable transition between Turing and antispiral patterns is studied by using a time-delayed-feedback strategy in a FitzHugh-Nagumo model. We treat the time delay as a perturbation and analyse the effect of the time delay on the Turing and Hopf instabilities near the Turing Hopf codimension-two phase space. Numerical simulations show that the transition between the Turing patterns （hexagon, stripe, and honeycomb）, the dual-mode antispiral, and the antispiral by applying appropriate feedback parameters. The dual-mode antispiral pattern originates from the competition between the Turing and Hopf instabilities. Our results have shown the flexibility of the time delay on controlling the pattern formations near the Turing-Hopf codimension-two phase space.展开更多
The Cenozoic volcanostratigraphy in the Changbaishan area had complex building processes.Twenty-two eruption periods have been determined from the Wangtian＇e, Touxi, and Changbaishan volcanoes. The complex volcanostr...The Cenozoic volcanostratigraphy in the Changbaishan area had complex building processes.Twenty-two eruption periods have been determined from the Wangtian＇e, Touxi, and Changbaishan volcanoes. The complex volcanostratigraphy of the Changbaishan area can be divided into four types of filling patterns from bottom to top. They are lava flows filling in valleys（LFFV）, lava flows filling in platform（LFFP）, lava flows formed the cone（LFFC）, and pyroclastic Flow filling in crater or valleys（PFFC/V）. LFFV has been divided into four layers and terminates as a lateral overlap. The topography of LFFV, which is controlled by the landform, is lens shaped with a wide flat top and narrow bottom.LFFP has been divided into three layers and terminates as a lateral downlap. The topography of LFFP is sheet and tabular shaped with a narrow top and wide bottom. It has large width to thickness ratio. It was built by multiple eruptive centers distributed along the fissure. The topography of LFFC, which is located above the LFFP, has a hummocky shape with a narrow sloping top and a wide flat bottom. It terminates as a later downlap or backstepping. It has large width to thickness ratio. It was built by a single eruptive center. The topography of PFFC/V, which located above the LFFC, LFFP, or valley, has the shape of fan and terminates as a lateral downlap or overlap. It has a small width to thickness ratio and was built by a single eruptive center. The filling pattern is controlled by temperature, SiO_2 content,volatile content, magma volume, and the paleolandform. In the short term, the eruptive production of the Changbaishan area is comenditic ash or pumice of a Plinian type eruption. The eruptive volume in future should be smaller than that of the Baguamiao period, and the filling pattern should be PFFC/V,which may cause huge damage to adjacent areas.展开更多
Crystal patterns in ultrathin films of six poly（ethylene oxide） fractions with molecular weights from 25000 to 932000 g/mol were characterized within crystallization temperature range from 20 ℃to 60℃. Labyrinthine...Crystal patterns in ultrathin films of six poly（ethylene oxide） fractions with molecular weights from 25000 to 932000 g/mol were characterized within crystallization temperature range from 20 ℃to 60℃. Labyrinthine, dendritic and faceted crystal patterns were observed in different temperature ranges, and then labyrinthine-to-dendritic and dendritic-to- faceted transition temperatures T_L-D and T_D-F were quantitatively identified. Their molecular weight dependences are T_L-D（M_w） = T_L-D（∞） -K_L-D/M_w, where T_L-D（∞） = 38.2 ℃ and K_L-D = 253000 ℃.g/mol and T_D-F（M_w） = T_D-F（∞） -K_D-F/M_w, where T_D-F（∞） = 54.7 ℃ and K_D-F= 27000 ℃.g/mol. Quasi two-dimensional blob models were proposed to provide empirical explanations of the molecular weight dependences. The labyrinthine-to-dendritic transition is attributed to a molecular diffusion process change from a local-diffusion to diffusion-limited-aggregation （DLA） and a polymer chain with M_w ≈253000 g/mol within a blob can join crystals independently. The dendritic-to-faceted transition is attributed to a turnover of the pattern formation mechanism from DLA to crystallization control, and a polymer chain with a M_w ≈27000 g/tool as an independent blob crosses to a depletion zone to join crystals. These molecular weight dependences reveal a macromolecular effect on the crystal pattern formation and selection of crystalline polymers.展开更多
Pattern formation is a very interesting phenomenon formed above a water anode in atmospheric pressure glow discharge.Up to now,concentric-ring patterns only less than four rings have been observed in experiments.In th...Pattern formation is a very interesting phenomenon formed above a water anode in atmospheric pressure glow discharge.Up to now,concentric-ring patterns only less than four rings have been observed in experiments.In this work,atmospheric pressure glow discharge above a water anode is conducted to produce diversified concentric-ring patterns.Results indicate that as time elapses,the number of concentric rings increases continuously and up to five rings have been found in the concentric-ring patterns.Moreover,the ring number increases continuously with increasing discharge current.The electrical conductivity of the anode plays an important role in the transition of the concentric patterns due to its positive relation with ionic strength.Hence,the electrical conductivity of the water anode is investigated as a function of time and discharge current.From optical emission spectrum,gas temperature and intensity ratio related with density and temperature of electron have been calculated.The various concentric-ring patterns mentioned above have been simulated at last with an autocatalytic reaction model.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
Control of the spatiotemporal patterns near the codimension-three Turing–Hopf–Wave bifurcations is studied by using time-delayed feedback in a three-variable Brusselator model. Linear stability analysis of the syste...Control of the spatiotemporal patterns near the codimension-three Turing–Hopf–Wave bifurcations is studied by using time-delayed feedback in a three-variable Brusselator model. Linear stability analysis of the system shows that the competition among the Turing-, Hopf- and Wave-modes, the wavenumber, and the oscillation frequency of patterns can be controlled by changing the feedback parameters. The role of the feedback intensity Pu played on controlling the pattern competition is equivalent to that of Pw, but opposite to that of Pv. The role of the feedback intensity Pu played on controlling the wavenumber and oscillation frequency of patterns is equivalent to that of Pv, but opposite to that of Pw. When the intensities of feedback are applied equally, changing the delayed time could not alter the competition among these modes, however, it can control the oscillation frequency of patterns. The analytical results are verified by two-dimensional （2D） numerical simulations.展开更多
A numerical simulation scheme is proposed to analyze domain tessellation and pattern formation on a spherical surface using the phase-field method. A multi-phase-field model is adopted to represent domain growth, and ...A numerical simulation scheme is proposed to analyze domain tessellation and pattern formation on a spherical surface using the phase-field method. A multi-phase-field model is adopted to represent domain growth, and the finite-difference method (FDM) is used for numerical integration. The lattice points for the FDM are distributed regularly on a spherical surface so that a mostly regular triangular domain division is realized. First, a conventional diffusion process is simulated using this lattice to confirm its validity. The multi-phase-field equation is then applied, and pattern formation processes under various initial conditions are simulated. Unlike pattern formation on a flat plane, where the regular hexagonal domains are always stable, certain different patterns are generated. Specifically, characteristic stable patterns are obtained when the number of domains, n, is 6, 8, or 12;for instance, a regular pentagonal domain division pattern is generated for n = 12, which corresponds to a regular dodecahedron.展开更多
Turing patterns are typical spatiotemporal ordered structures in various systems driven far from thermodynamic equilibrium.Turing’s reaction-diffusion theory,containing a long-range inhibiting agent and a local catal...Turing patterns are typical spatiotemporal ordered structures in various systems driven far from thermodynamic equilibrium.Turing’s reaction-diffusion theory,containing a long-range inhibiting agent and a local catalytic agent,has provided an explanation for the formation of some patterns in nature.Numerical,experimental and theoretical studies about Turing/Turing-like patterns have been generally focused on systems driven far from thermodynamic equilibrium.The local dynamics of these systems are commonly very complex,which brings great difficulties to understanding of formation of patterns.Here,we investigate a type of Turing-like patterns in a near-equilibrium thermodynamic system experimentally and theoretically,and put forward a new formation mechanism and a quantitative method for Turing/Turing-like patterns.Specifically,we observe a type of Turing-like patterns in starch solutions,and study the effect of concentration on the structure of patterns.The experimental results show that,with the increase of concentration,patterns change from spots to inverse spots,and labyrinthine stripe patterns appear in the region of intermediate concentration.We analyze and model the formation mechanism of these patterns observed in experiments,and the simulation results agree with the experimental results.Our conclusion indicates that the random aggregation of spatial components leads to formation of these patterns,and the proportion of spatial components determines the structures.Our findings shed light on the formation mechanism for Turing/Turing-like patterns.展开更多
The resonance interaction between two modes is investigated using a two-layer coupled Brusselator model. When two different wavelength modes satisfy resonance conditions, new modes will appear, and a variety of superl...The resonance interaction between two modes is investigated using a two-layer coupled Brusselator model. When two different wavelength modes satisfy resonance conditions, new modes will appear, and a variety of superlattice patterns can be obtained in a short wavelength mode subsystem. We find that even though the wavenumbers of two Turing modes are fixed, the parameter changes have influences on wave intensity and pattern selection. When a hexagon pattern occurs in the short wavelength mode layer and a stripe pattern appears in the long wavelength mode layer, the Hopf instability may happen in a nonlinearly coupled model, and twinkling-eye hexagon and travelling hexagon patterns will be obtained. The symmetries of patterns resulting from the coupled modes may be different from those of their parents, such as the cluster hexagon pattern and square pattern. With the increase of perturbation and coupling intensity, the nonlinear system will con- vert between a static pattern and a dynamic pattern when the Turing instability and Hopf instability happen in the nonlinear system. Besides the wavenumber ratio and intensity ratio of the two different wavelength Turing modes, perturbation and coupling intensity play an important role in the pattern formation and selection. According to the simulation results, we find that two modes with different symmetries can also be in the spatial resonance under certain conditions, and complex patterns appear in the two-layer coupled reaction diffusion systems.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
文摘This paper investigates the dynamic interactions between biosurfactant-producing bacteria and their environment through pattern formations in diffusive predator-prey models.By analyzing the model’s equilibrium points and applying the Routh-Hurwitz criteria with bifurcation analysis,we determine the conditions for the existence of Turing patterns.Numerical simulations confirm these analytical findings and reveal diverse pattern formations influenced by diffusion and concentration zones,including both Turing and non-Turing patterns.We observe a correlation between the distribution of the two species through pattern formations and the effectiveness of biosurfactant-mediated oil recovery.More interestingly,our model focuses on the dynamics of bacterial and biosurfactant concentrations by showing that areas of high biosurfactant concentration are associated with the release of trapped oil from pores,thereby contributing to successful oil recovery.
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 a Hong Kong Research Grant Council GRF Grant,and a Hong Kong Baptist University FRG Grant.
文摘Pattern formations by Gierer-Meinhardt(GM)activator-inhibitor model are considered in this paper.By linear analysis,critical value of bifurcation parameter can be evaluated to ensure Turing instability.Numerical simulations are tested by using second order semi-implicit backward difference methods for time discretization and the meshless Kansa method for spatially discretization.We numerically show the convergence of our algorithm.Pattern transitions in irregular domains are shown.We also provide various parameter settings on some irregular domains for different patterns appeared in nature.To further simulate patterns in reality,we construct different kinds of animal type domains and obtain desired patterns by applying proposed parameter settings.
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funded by the Ministry of Education of the Russian Federation within the framework of a state assignment,number 1023032300071-6-2.3.1.
文摘The dynamics of fluid and non-buoyant particles in a librating horizontal annulus is studied experimentally.In the absence of librations,the granular material forms a cylindrical layer near the outer boundary of the annulus and undergoes rigid-body rotation with the fluid and the annulus.It is demonstrated that the librational liquefaction of the granular material results in pattern formation.This self-organization process stems from the excitation of inertial modes induced by the oscillatory motion of liquefied granular material under the influence of the gravitational force.The inertial wave induces vortical fluid flow which entrains particles from rest and forms eroded areas that are equidistant from each other along the axis of rotation.Theoretical analysis and experiments demonstrate that a liquefied layer of granular material oscillates with a radian frequency equal to the angular velocity of the annulus and interacts with the inertial wave it excites.The new phenomenon of libration-induced pattern formation is of practical interest as it can be used to control multiphase flows and mass transfer in rotating containers in a variety of industrial processes.
文摘This review paper provides a comprehensive introduction to various numerical methods for the phase-field model used to simulate the phase separation dynamics of diblock copolymer melts.Diblock copolymer systems form complex structures at the nanometer scale and play a significant role in various applications.The phase-field model,in particular,is essential for describing the formation and evolution of these structures and is widely used as a tool to effectively predict the movement of phase boundaries and the distribution of phases over time.In this paper,we discuss the principles and implementations of various numerical methodologies for this model and analyze the strengths,limitations,stability,accuracy,and computational efficiency of each method.Traditional approaches such as Fourier spectral methods,finite difference methods and alternating direction explicit methods are reviewed,as well as recent advancements such as the invariant energy quadratization method and the scalar auxiliary variable scheme are also presented.In addition,we introduce examples of the phase-field model,which are fingerprint image restoration and 3D printing.These examples demonstrate the extensive applicability of the reviewed methods and models.
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 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.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10975043 and 10947166)the Natural Science Foundation of Hebei Province,China (Grant Nos. A2011201006 and A2010000185)the Science Foundation of Hebei University
文摘The controllable transition between Turing and antispiral patterns is studied by using a time-delayed-feedback strategy in a FitzHugh-Nagumo model. We treat the time delay as a perturbation and analyse the effect of the time delay on the Turing and Hopf instabilities near the Turing Hopf codimension-two phase space. Numerical simulations show that the transition between the Turing patterns （hexagon, stripe, and honeycomb）, the dual-mode antispiral, and the antispiral by applying appropriate feedback parameters. The dual-mode antispiral pattern originates from the competition between the Turing and Hopf instabilities. Our results have shown the flexibility of the time delay on controlling the pattern formations near the Turing-Hopf codimension-two phase space.
基金supported by the Natural Science Foundation of Jilin Province(20170101001JC)Natural Science Foundation of China(41472304)National Major Fundamental Research and Development Projects(2012CB822002)
文摘The Cenozoic volcanostratigraphy in the Changbaishan area had complex building processes.Twenty-two eruption periods have been determined from the Wangtian＇e, Touxi, and Changbaishan volcanoes. The complex volcanostratigraphy of the Changbaishan area can be divided into four types of filling patterns from bottom to top. They are lava flows filling in valleys（LFFV）, lava flows filling in platform（LFFP）, lava flows formed the cone（LFFC）, and pyroclastic Flow filling in crater or valleys（PFFC/V）. LFFV has been divided into four layers and terminates as a lateral overlap. The topography of LFFV, which is controlled by the landform, is lens shaped with a wide flat top and narrow bottom.LFFP has been divided into three layers and terminates as a lateral downlap. The topography of LFFP is sheet and tabular shaped with a narrow top and wide bottom. It has large width to thickness ratio. It was built by multiple eruptive centers distributed along the fissure. The topography of LFFC, which is located above the LFFP, has a hummocky shape with a narrow sloping top and a wide flat bottom. It terminates as a later downlap or backstepping. It has large width to thickness ratio. It was built by a single eruptive center. The topography of PFFC/V, which located above the LFFC, LFFP, or valley, has the shape of fan and terminates as a lateral downlap or overlap. It has a small width to thickness ratio and was built by a single eruptive center. The filling pattern is controlled by temperature, SiO_2 content,volatile content, magma volume, and the paleolandform. In the short term, the eruptive production of the Changbaishan area is comenditic ash or pumice of a Plinian type eruption. The eruptive volume in future should be smaller than that of the Baguamiao period, and the filling pattern should be PFFC/V,which may cause huge damage to adjacent areas.
基金financially supported by the National Science Foundation of China(No.20874053)
文摘Crystal patterns in ultrathin films of six poly（ethylene oxide） fractions with molecular weights from 25000 to 932000 g/mol were characterized within crystallization temperature range from 20 ℃to 60℃. Labyrinthine, dendritic and faceted crystal patterns were observed in different temperature ranges, and then labyrinthine-to-dendritic and dendritic-to- faceted transition temperatures T_L-D and T_D-F were quantitatively identified. Their molecular weight dependences are T_L-D（M_w） = T_L-D（∞） -K_L-D/M_w, where T_L-D（∞） = 38.2 ℃ and K_L-D = 253000 ℃.g/mol and T_D-F（M_w） = T_D-F（∞） -K_D-F/M_w, where T_D-F（∞） = 54.7 ℃ and K_D-F= 27000 ℃.g/mol. Quasi two-dimensional blob models were proposed to provide empirical explanations of the molecular weight dependences. The labyrinthine-to-dendritic transition is attributed to a molecular diffusion process change from a local-diffusion to diffusion-limited-aggregation （DLA） and a polymer chain with M_w ≈253000 g/mol within a blob can join crystals independently. The dendritic-to-faceted transition is attributed to a turnover of the pattern formation mechanism from DLA to crystallization control, and a polymer chain with a M_w ≈27000 g/tool as an independent blob crosses to a depletion zone to join crystals. These molecular weight dependences reveal a macromolecular effect on the crystal pattern formation and selection of crystalline polymers.
基金financially supported by National Natural Science Foundation of China(Nos.11875121 and 51977057)Natural Science Interdisciplinary Research Program of Hebei University(Nos.DXK201908 and DXK202011)+2 种基金Natural Science Foundation of Hebei Province,China(Nos.A2020201025 and A2019201100)the financial support from Post-Graduate’s Innovation Fund Project of Hebei Province(Nos.CXZZBS2019023 and CXZZBS2019029)Post-Graduate’s Innovation Fund Project of Hebei University(Nos.HBU2021ss063 and HBU2021bs011)。
文摘Pattern formation is a very interesting phenomenon formed above a water anode in atmospheric pressure glow discharge.Up to now,concentric-ring patterns only less than four rings have been observed in experiments.In this work,atmospheric pressure glow discharge above a water anode is conducted to produce diversified concentric-ring patterns.Results indicate that as time elapses,the number of concentric rings increases continuously and up to five rings have been found in the concentric-ring patterns.Moreover,the ring number increases continuously with increasing discharge current.The electrical conductivity of the anode plays an important role in the transition of the concentric patterns due to its positive relation with ionic strength.Hence,the electrical conductivity of the water anode is investigated as a function of time and discharge current.From optical emission spectrum,gas temperature and intensity ratio related with density and temperature of electron have been calculated.The various concentric-ring patterns mentioned above have been simulated at last with an autocatalytic reaction model.
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Project supported by the National Nature Science Foundation of China(Grant No.11205044)the Fundamental Research Funds for the Central Universities(Grant No.10ML40)
文摘Control of the spatiotemporal patterns near the codimension-three Turing–Hopf–Wave bifurcations is studied by using time-delayed feedback in a three-variable Brusselator model. Linear stability analysis of the system shows that the competition among the Turing-, Hopf- and Wave-modes, the wavenumber, and the oscillation frequency of patterns can be controlled by changing the feedback parameters. The role of the feedback intensity Pu played on controlling the pattern competition is equivalent to that of Pw, but opposite to that of Pv. The role of the feedback intensity Pu played on controlling the wavenumber and oscillation frequency of patterns is equivalent to that of Pv, but opposite to that of Pw. When the intensities of feedback are applied equally, changing the delayed time could not alter the competition among these modes, however, it can control the oscillation frequency of patterns. The analytical results are verified by two-dimensional （2D） numerical simulations.
文摘A numerical simulation scheme is proposed to analyze domain tessellation and pattern formation on a spherical surface using the phase-field method. A multi-phase-field model is adopted to represent domain growth, and the finite-difference method (FDM) is used for numerical integration. The lattice points for the FDM are distributed regularly on a spherical surface so that a mostly regular triangular domain division is realized. First, a conventional diffusion process is simulated using this lattice to confirm its validity. The multi-phase-field equation is then applied, and pattern formation processes under various initial conditions are simulated. Unlike pattern formation on a flat plane, where the regular hexagonal domains are always stable, certain different patterns are generated. Specifically, characteristic stable patterns are obtained when the number of domains, n, is 6, 8, or 12;for instance, a regular pentagonal domain division pattern is generated for n = 12, which corresponds to a regular dodecahedron.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12205006 and 11975025)the Excellent Youth Scientific Research Project of Anhui Province(Grant No.2022AH030107)+1 种基金the Natural Science Foundation of Anhui Higher Education Institutions of China(Grant No.KJ2020A0504)the International Joint Research Center of Simulation and Control for Population Ecology of Yangtze River in Anhui(Grant No.12011530158).
文摘Turing patterns are typical spatiotemporal ordered structures in various systems driven far from thermodynamic equilibrium.Turing’s reaction-diffusion theory,containing a long-range inhibiting agent and a local catalytic agent,has provided an explanation for the formation of some patterns in nature.Numerical,experimental and theoretical studies about Turing/Turing-like patterns have been generally focused on systems driven far from thermodynamic equilibrium.The local dynamics of these systems are commonly very complex,which brings great difficulties to understanding of formation of patterns.Here,we investigate a type of Turing-like patterns in a near-equilibrium thermodynamic system experimentally and theoretically,and put forward a new formation mechanism and a quantitative method for Turing/Turing-like patterns.Specifically,we observe a type of Turing-like patterns in starch solutions,and study the effect of concentration on the structure of patterns.The experimental results show that,with the increase of concentration,patterns change from spots to inverse spots,and labyrinthine stripe patterns appear in the region of intermediate concentration.We analyze and model the formation mechanism of these patterns observed in experiments,and the simulation results agree with the experimental results.Our conclusion indicates that the random aggregation of spatial components leads to formation of these patterns,and the proportion of spatial components determines the structures.Our findings shed light on the formation mechanism for Turing/Turing-like patterns.
基金Project supported by the National Natural Science Foundation of China(Grant No.11247242)the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.51201057)the Natural Science Foundation of Hebei Province,China(Grant No.A2014208171)
文摘The resonance interaction between two modes is investigated using a two-layer coupled Brusselator model. When two different wavelength modes satisfy resonance conditions, new modes will appear, and a variety of superlattice patterns can be obtained in a short wavelength mode subsystem. We find that even though the wavenumbers of two Turing modes are fixed, the parameter changes have influences on wave intensity and pattern selection. When a hexagon pattern occurs in the short wavelength mode layer and a stripe pattern appears in the long wavelength mode layer, the Hopf instability may happen in a nonlinearly coupled model, and twinkling-eye hexagon and travelling hexagon patterns will be obtained. The symmetries of patterns resulting from the coupled modes may be different from those of their parents, such as the cluster hexagon pattern and square pattern. With the increase of perturbation and coupling intensity, the nonlinear system will con- vert between a static pattern and a dynamic pattern when the Turing instability and Hopf instability happen in the nonlinear system. Besides the wavenumber ratio and intensity ratio of the two different wavelength Turing modes, perturbation and coupling intensity play an important role in the pattern formation and selection. According to the simulation results, we find that two modes with different symmetries can also be in the spatial resonance under certain conditions, and complex patterns appear in the two-layer coupled reaction diffusion systems.
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.
