Tuning the diffusion constant to optimize the readout of positional information of spatial concentration patterns

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.

Simulation of Crack Pattern Formation Due to Shrinkage in a Drying Material

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&#730 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.

A perspective on regression and Bayesian approaches for system identification of pattern formation dynamics

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.

The roles of R2R3-MYBs in regulating complex pigmentation patterns in flowers

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.

Laser-induced pattern formation from homogeneous polyisoprene solutions

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.

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

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.

Pattern formation in superdiffusion Oregonator model

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.

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

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.

Pattern Formation in a Dusty Plasma System

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.

The Application of Pattern Recognition to the Formability of Quasicrystal Formation in Al-alloys

Four parameters of chemical bond havebeen used to span a feature space to classifyquasicrystal-forming Al-alloys from thatalloys without quasicrystal formationwith good result. Since the first quasicrystal-formingsystem, Al-Mn system, discovered by She-chtman in 1984[1], a series of quasicrystal-forming binary alloy systems have beenfound. Most of these systems are Al-contain-ing systems. Bancel has indicated thatthere are three factors affecting theformability of quasicrystals [2]: (1) ele-ctrochemical factor (this factor can be

Turing/Turing-like patterns:Products of random aggregation of spatial components

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.

Formation Dynamics and Quantitative Prediction of Hydrocarbons of the Superpressure System in the Dongying Sag

Based on the theory of formation dynamics of oil/gas pools, the Dongying sag can be divided into three dynamic systems regarding the accumulation of oil and gas： the superpressure closed system, the semi-closed system and the normal pressure open system. Based on the analysis of genesis of superpressure in the superpressure closed system and the rule of hydrocarbon expulsion, it is found that hydrocarbon generation is related to superpressure, which is the main driving factor of hydrocarbon migration. Micro fractures formed by superpressure are the main channels for hydrocarbon migration. There are three dynamic patterns for hydrocarbon expulsion： free water drainage, hydrocarbon accumulation and drainage through micro fissures. In the superpressure closed system, the oil-driving-water process and oil/gas accumulation were completed in lithologic traps by way of such two dynamic patterns as episodic evolution of superpressure systems and episodic pressure release of faults. The oil-bearing capacity of lithologic traps is intimately related to reservoir-forming dynamic force. Quantitative evaluation of dynamic conditions for pool formation can effectively predict the oil-bearing capability of traps.

Filling Pattern of Volcanostratigraphy of Cenozoic Volcanic Rocks in the Changbaishan Area and Possible Future Eruptions

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.

Controlling the transition between Turing and antispiral patterns by using time-delayed-feedback

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.

Various concentric-ring patterns formed in a water-anode glow discharge operated at atmospheric pressure

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.

Sedimentary characteristics and processes of the Paleogene Dainan Formation in the Gaoyou Depression, North Jiangsu Basin, eastern China

In this paper,the type,vertical evolution,and distribution pattern of sedimentary facies of the Paleogene Dainan Formation in the Gaoyou Depression of the North Jiangsu Basin are studied in detail.Results show that fan delta,delta,nearshore subaqueous fan,and lacustrine facies developed during the Dainan Formation period and their distribution pattern was mainly controlled by tectonics and paleogeography.The fan delta and nearshore subaqueous fan facies predominantly occur in the southern steep slope region where fault-induced subsidence is thought to have created substantial accommodation,whereas the delta facies are distributed on the northern gentle slope which is thought to have experienced less subsidence.Finally,the lacustrine facies is shown to have developed in the center of the depression,as well as on the flanks of the fan delta,delta,and nearshore subaqueous fan facies.Vertically,the Dainan Formation represents an integrated transgressiveregressive cycle,with the E2d1being the transgressive sequence and the E2d2being the regressive sequence.This distribution model of sedimentary facies plays an important role in predicting favorable reservoir belts for the Dainan Formation in the Gaoyou Depression and similar areas.In the Gaoyou Depression,sandstones of the subaqueous distributary channels in the fan delta and the subaqueous branch channels in the delta are characterized by physical properties favorable for reservoir formation.

Numerical Simulation of a Domain-Tessellation Pattern on a Spherical Surface Using a Phase Field Model

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.

Numerical simulation and analysis of complex patterns in a two-layer coupled reaction diffusion system

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.

Turing Instability and Pattern Induced by Cross-Diffusion for a Nonlinear Reaction-Diffusion System of Turbulence-Shear Flow Interaction

The Turing instability and the phenomena of pattern formation for a nonlinear reaction-diffusion(RD) system of turbulence-shear flowinteraction are investigated.By the linear stability analysis,the essential conditions for Turing instability are obtained.It indicates that the emergence of cross-diffusion terms leads to the destabilizing mechanism.Then the amplitude equations and the asymptotic solutions of the model closed to the onset of instability are derived by using the weakly nonlinear analysis.

Control of the patterns by using time-delayed feedback near the codimension-three Turing-Hopf-Wave bifurcations

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.