Mechanism Of Pattern Formation Research Articles

Self-assembled micro-patterns in uphill-diffusion solution system.

In this work we present self-organized regular patterns in a solution system through uphill-diffusion. Micrometer thick organic semiconductor solution is sandwiched between a substrate and cover-plate. Self-assembled regular patterns can be observed on the substrate after solvent evaporation. Different micro-patterns and pattern defects were displayed and analyzed. Mechanisms of defect formation, mode selection process during patten generation, and pattern sedimentation onto substrate from solution were proposed. Organic thin film transistors were fabricated with the assembled line patterns which demonstrate a promising way to produce patterned micro/nano materials.

Controlled Protein-Membrane Interactions Modulate Self-Organization of Min Protein Patterns.

Self-organizing protein patterns are crucial for living systems, governing important cellular processes such as polarization and division. While the field of protein self-organization has reached a point where basic pattern-forming mechanisms can be reconstituted in vitro using purified proteins, understanding how cells can dynamically switch and modulate these patterns, especially when transiently needed, remains an interesting frontier. Here, we demonstrate the efficient regulation of self-organizing protein patterns through the modulation of simple biophysical membrane parameters. Our investigation focuses on the impact of membrane affinity changes on Min protein patterns at lipid membranes composed of Escherichia coli lipids or minimal lipid compositions, and we present three major results. First, we observed the emergence of a diverse array of pattern phenotypes, ranging from waves over flower-shaped patterns to snowflake-like structures. Second, we demonstrated the dependency of these patterns on the density of protein-membrane linkers. Finally, we demonstrate thatthe shape of snowflake-like patterns isfine-tuned by membrane charge. Our results demonstrate the significant influence of membrane linkage as a straightforward biophysical parameter governing protein pattern formation. Our research points towards a simple yet intriguing mechanism by which cells can adeptly tune and switch protein patterns on the mesoscale.

Spatial patterns of the Brusselator model with asymmetric Lévy diffusion

Abstract The formation of spatial patterns is an important issue in reaction–diffusion systems. Previous studies have mainly focused on the spatial patterns in reaction–diffusion models equipped with symmetric diffusion (such as normal or fractional Laplace diffusion), namely, assuming that spatial environments of the systems are homogeneous. However, the complexity and heterogeneity of spatial environments of biochemical reactions in vivo can lead to asymmetric diffusion of reactants. Naturally, there arises an open question of how the asymmetric diffusion affects dynamical behaviors of biochemical reaction systems. To answer this, we build a general asymmetric Lévy diffusion model based on the theory of a continuous time random walk. In addition, we investigate the two-species Brusselator model with asymmetric Lévy diffusion, and obtain a general condition for the formation of Turing and wave patterns. More interestingly, we find that even though the Brusselator model with symmetric diffusion cannot produce steady spatial patterns for some parameters, the asymmetry of Lévy diffusion for this model can produce wave patterns. This is different from the previous result that wave instability requires at least a three-species model. In addition, the asymmetry of Lévy diffusion can significantly affect the amplitude and frequency of the spatial patterns. Our results enrich our knowledge of the mechanisms of pattern formation.

Self-organization in spatial ecology

Biologists have long known that populations of organisms - microbes, plants, animals - can self-organize into emergent patterns. Yet, the fact that such patterns can arise with remarkable symmetry at the scale of entire ecosystems remains astonishing, even as aerial imagery has documented their existence across all continents. As the enormous scale of landscape patterns makes them experimentally intractable, ecologists have relied on theoretical modelling - typically rooted in physics - to investigate the underlying pattern-forming mechanisms. Such models have succeeded in generating mechanistic hypotheses and indicate that self-organized spatial patterns can reflect the health of an ecosystem. However, most of these hypotheses remain untested. This essay reflects on our current understanding of the causes and consequences of ecosystem-scale pattern formation.

The effect of diffusion on multistability and stochastic sensitivity in spatially extended systems

A spatially-extended reaction-diffusion model is considered. The work is focused on self-organization mechanisms of diffusion instability and Turing pattern formation. Pattern generation and multistability of the system is demonstrated for varying diffusion intensity. In the stochastic variant of the model, the sensitivity of coexisting patterns to noise is studied. The stochastic sensitivity function technique is used for the analysis of noise-induced transitions between patterns. Application of stochastic sensitivity functions is discussed on examples.

Geometrical incompatibility regulated pattern selection and morphological evolution in growing spherical soft tissues

Surface morphological patterns are widely observed in natural systems, which are closely correlated to vital biological functions and inspire surface morphology designs in soft matter systems. Geometrical incompatibility widely exists in biological tissues across different length scales and plays an important role in growth-induced pattern selection and morphological evolution of soft tissues. However, the underlying physical mechanism of growth-induced pattern formation and post-buckling evolution in geometrically incompatible spherical soft tissues remain elusive. Here, the effect of geometrical incompatibility on the growth-induced pattern selection and post-buckling evolution are investigated through swelling experiment, theoretical analysis and numerical simulation. The results show that not only the instability pattern but also the instability threshold can be regulated by manipulating geometric incompatibility. Notably, when the geometrical incompatibility parameter exceeds a critical value, spontaneous instability is observed before growth. With continuous growth, the core–shell soft sphere buckles into a periodic buckyball pattern and evolves toward a bean-shaped pattern, and then undergoes a wrinkle-to-fold transition into a labyrinth topography. Our results demonstrate, both experimentally and theoretically, that geometrical incompatibility can guide the growth-induced pattern formation and morphological evolution effectively. This study not only enhances our understanding of the growth-induced pattern selection and morphological evolution in spherical soft tissues, but also provides an inspiring insight for the fabrication of morphological patterns on curved surfaces.

Formation mechanism of radial and circular cracks promoted by delamination in drying silica colloidal deposits.

Cracks with radial and circular patterns are appealing in nature and industry. Although morphologies and propagation conditions of cracks are extensively studied, the formation mechanism of crack pattern by the interaction of channel fracture and interfacial delamination remains elusive. Here, we present the transition of radial to coexisting radial and circular crack patterns when the thickness of colloidal deposits on both hard and soft substrates exceeds a critical value, through the colloidal volume fraction dependence. In addition, a thickness-dependent phase diagram from radial crack to coexistence of radial and circular cracks was constructed with respect to the radius and the volume fractions of silica colloidal deposits. A phase-field fracture model is developed to elucidate how the formation of radial cracks is facilitated by simultaneous delamination. The warping-induced radial tensile stress at the bottom surface of the striped deposit is proportional to the thickness. It leads to subsequent nucleation and growth of circular cracks in thick deposits. This work provides insight into the formation mechanism of complex crack patterns in drying colloidal deposits and revolutionizes the design space of crack-based micro-nano structures.

Acoustofluidic Diversity Achieved by Multiple Modes of Acoustic Waves Generated on Piezoelectric-Film-Coated Aluminum Sheets.

Excitation of multiple acoustic wave modes on a single chip is beneficial to implement diversified acoustofluidic functions. Conventional acoustic wave devices made of bulk LiNbO3 substrates generally generate few acoustic wave modes once the crystal-cut and electrode pattern are defined, limiting the realization of acoustofluidic diversity. In this paper, we demonstrated diversity of acoustofluidic behaviors using multiple modes of acoustic waves generated on piezoelectric-thin-film-coated aluminum sheets. Multiple acoustic wave modes were excited by varying the ratios between IDT pitch/wavelength and substrate thickness. Through systematic investigation of fluidic actuation behaviors and performances using these acoustic wave modes, we demonstrated fluidic actuation diversities using various acoustic wave modes and showed that the Rayleigh mode, pseudo-Rayleigh mode, and A0 mode of Lamb wave generally have better fluidic actuation performance than those of Sezawa mode and higher-order modes of Lamb wave, providing guidance for high-performance acoustofluidic actuation platform design. Additionally, we demonstrated diversified particle patterning functions, either on two sides of acoustic wave device or on a glass sheet by coupling acoustic waves into the glass using the gel. The pattern formation mechanisms were investigated through finite element simulations of acoustic pressure fields under different experimental configurations.

Spatial patterning and species coexistence: A case study using concentric circular vegetation patches in saline land

Spatial patterns in plant community structures within stressed ecosystems have drawn much attention in the field of ecology. However, the mechanisms underlying spatial formation and its impact on species coexistence and diversity remain controversial. In this study, we investigated concentric circular vegetation patches in coastal saline land, and analysed the spatial patterning of plant communities and associated soil physicochemical properties. Thereafter, we tested how the soil conditioned by plant communities from different locations within the vegetation patches influence the species growth and inter-specific competition. Our results show soil salinity enlarges in a centrifugal manner in horizontal direction in all patches. Soil salinity decreased and species diversity increased along with the increase of patch size. In addition, we found significant shifts in both the composition of plant communities and in soil physicochemical properties from outer to center. The results indicate that the pioneer species Suaeda salsa facilitated the subsequent species. However Suaeda salsa was inhibited and became inferior competitor in the soil conditioned by the subsequent species. We infer that the less-visible spatial patterns of soil physicochemical properties at small scales create ecological niches for specialized species, allowing them to coexist but not mix. We suggest that a trade-off between tolerance to salt stress and competitive ability under ameliorated conditions may underlie mechanisms of pattern formation in small scale. Our findings lend support to the idea that soil stress constraints community assembly and triggers spatial patterns, which, in turn, buffer the stress on plant communities and enhance species diversity.

Spatial distribution of self-seeded air lasers induced by the femtosecond laser filament plasma

The femtosecond laser filament-induced air laser plays a significant role for the remote sensing of air pollutants. The spatial distributions of air laser intensity were investigated experimentally in previous studies. However, the mechanism of the air laser propagation properties inside the filament plasma has not been quite clear yet. Moreover, few studies have been dedicated to the reproduction of the air laser profile from nitrogen molecules propagating in the filament plasma based on the numerical simulation method. In this study, the lasing action of the air laser from the transition of the first negative (0,0) band of nitrogen ions at 391 nm was simulated during the femtosecond laser filamentation. The beam profile of the air laser changes from a Gaussian or super-Gaussian shape to an outer ring structure by increasing the filament length or nitrogen ion density, which is in accord with the previous experimental result. A multiple-diffraction effect has been proposed to clarify the mechanism of the outer rings beam pattern formation, which is induced by the dynamical interaction between the lasing effect and diffraction effect of the air laser propagating inside the filament plasma. In addition, the amplified air laser power as a function of both the filament length and nitrogen ion density was investigated. Our study would pave the way to improve the energy conversion efficiency and directivity of remote air lasers, which would be significant for remote sensing applications.

Formation mechanism of bright and dark concentric-ring pattern in dielectric barrier discharge

In this work, a bright and dark concentric-ring pattern is reported in a dielectric barrier discharge for the first time. The spatiotemporal dynamics of the bright and dark concentric-ring pattern are investigated with an intensified charge-coupled device and photomultiplier tubes. The results indicate that the bright and dark concentric-ring pattern is composed of three concentric-ring sublattices. These are bright concentric-ring structures, dark concentric-ring structures and wider concentric-ring structures, respectively. The bright concentric-ring structures and dark concentric-ring structures are alternately distributed. The bright concentric-ring structures are located at the centre of the wider concentric-ring structures. The wider concentric-ring structures first form from the outer edge and gradually develop to the centre. The essence of all three concentric-ring structures is the individual discharge filaments. The optical emission spectra of different sublattices are acquired and analysed. It is found that the plasma parameters of the three concentric-ring sublattices are different. Finally, the formation mechanism of the bright and dark concentric-ring pattern is discussed.

Nature of instability in flow-driven porous anodic oxide.

Self-organized porous anodic oxide films are formed by the electrochemical oxidation of reactive metal aluminum in acidic solutions in which the oxide is soluble. Recently, viscous flow models have shown using linear stability analysis that the instability results from a trade-off between the destabilizing effect of viscous flow of oxide and the stabilizing effect of oxide formation, which provides the wavelength selection mechanism for pattern formation. Anion adsorption on surface growth sites causes nonuniform compressive stress at the oxide-solution interface, which drives the flow. This anodic instability is analogous to the classical Marangoni instability induced by surface tension gradients. In this work, nature of the instability beyond the stability threshold is determined using a weakly nonlinear analysis. For the growth of well-developed pores beyond the threshold, a subcritical nature of the instability is essential. However, our weakly nonlinear analysis shows that the solutions emerging from neutral stability are supercritical in nature at all wavenumbers for the practical range of anodizing control parameters investigated. We also determine the region where the model is Hadamard stable, a necessary condition for well-posedness.

Drivers of β-diversity and its component-dependence along the natural restoration in an extremely heterogeneous forest ecosystem

β-diversity usually refers to species turnover along a gradient or changes in species diversity between communities. It is a key concept in understanding the mechanisms of biodiversity pattern formation. However, the component dependence and the driving factors of β-diversity during natural restoration remain unclear. In this study, a series of forest dynamic plots (FDPs) were established through the natural restoration stages in degraded karst forests, including the shrub-canopy mixed forest stage (SC), the secondary-growth forest stage (SG), and the old-growth forest stage (OG). After comparing species composition during natural restoration and its dependence on species turnover and nestedness, it was found that natural restoration significantly influenced the species composition by altering the species turnover in degraded karst forests rather than the nestedness. The contribution of turnover to β-diversity gradually increased, while the contribution of nestedness decreases gradually. Furthermore, the PER-SIMPER method was used to quantify the first-order assembly process that drives variations in species composition during restoration stages. To identify the factors influencing β-diversity, both variation partitioning analysis and a random forest model were employed. The results suggested that differences in species compositions across restoration stages were mainly driven by stochastic processes, and the deterministic processes were strengthened during the natural restoration. In addition, topographic factors contributed more to β-diversity than soil nutrient factors. This study highlighted changes in component dependence of degraded karst forests during natural restoration and emphasized the importance of a more comprehensive framework in assessing the restoration of degraded forest ecosystems. More attention should be paid to topographic structure in understanding biodiversity patterns, especially in highly heterogeneous forest ecosystems.

Mechanism for axial pattern formation of concentrated suspension in a horizontal rotating cylinder

We have performed numerical simulations to investigate the phenomenon of axial pattern formation exhibited by a non-neutrally buoyant concentrated suspension. Continuum modelling of the concentrated suspension is done using the suspension balance model to identify the underlying mechanism of the phenomenon. We demonstrate that axial concentration variations become amplified to axial bands owing to the influence of the second normal stress difference ( $N_2$ ), and the first normal difference ( $N_1$ ) accentuates the effect of $N_2$ . We demonstrate that the end walls of the rotating cylinder are necessary to prevent the smearing out of axial bands but are not a direct cause of the phenomenon.

Automatic design of gene regulatory mechanisms for spatial pattern formation

Gene regulatory mechanisms (GRMs) control the formation of spatial and temporal expression patterns that can serve as regulatory signals for the development of complex shapes. Synthetic developmental biology aims to engineer such genetic circuits for understanding and producing desired multicellular spatial patterns. However, designing synthetic GRMs for complex, multi-dimensional spatial patterns is a current challenge due to the nonlinear interactions and feedback loops in genetic circuits. Here we present a methodology to automatically design GRMs that can produce any given two-dimensional spatial pattern. The proposed approach uses two orthogonal morphogen gradients acting as positional information signals in a multicellular tissue area or culture, which constitutes a continuous field of engineered cells implementing the same designed GRM. To efficiently design both the circuit network and the interaction mechanisms—including the number of genes necessary for the formation of the target spatial pattern—we developed an automated algorithm based on high-performance evolutionary computation. The tolerance of the algorithm can be configured to design GRMs that are either simple to produce approximate patterns or complex to produce precise patterns. We demonstrate the approach by automatically designing GRMs that can produce a diverse set of synthetic spatial expression patterns by interpreting just two orthogonal morphogen gradients. The proposed framework offers a versatile approach to systematically design and discover complex genetic circuits producing spatial patterns.

Droplet dynamics affecting the shape of patterns formed spontaneously by transforming UV-curable emulsions

Forming large pitch and depth patterns spontaneously based on a bottom–up approach is a challenging task but with great industrial value. It is possible to spontaneously form an uneven (concave–convex) patterns with submillimeter-to-millimeter-scale pitches and depths by the direct pattern exposure of a UV-curable oil-in-water (O/W) emulsion liquid film. UV irradiation generates a latent pattern of a cured particle aggregation in the liquid film, and an uneven structure is spontaneously formed during the subsequent drying process. This process does not require any printing and embossing plates or development process. In this report, we presented an example of unevenness formation with a maximum pattern depth of approximately 0.4 mm and a maximum pitch width of 5 mm. The patterns formed by this method have raised edges in the exposed areas and fogging in unexposed areas. The pattern shapes become conspicuous under overexposure conditions, but the formation mechanism has not yet been understood in detail and needs to be investigated. In this study, we focused on the exposure process and clarified the mechanism of pattern formation by analyzing the dynamics of emulsion droplets in the medium by an in situ microscopy observation method. As a result, we found that the fogging was mainly caused by light leakage from the exposed area, and the raised pattern edges were caused by droplets transported from the unexposed area to the exposed area. Furthermore, the convection caused by the heat generated from polymerization is a determining factor affecting all these phenomena. By controlling the pattern shape related to convection utilizing direct projection exposure, we showed an example of eliminating raised pattern edges with a height difference of approximately 0.1 mm. By devising and selecting exposure methods, we can expand the range of design applications such as interior decorative patterns.

Consistent temporal behaviors over a non-Newtonian/Newtonian two-phase flow

The temporal behaviors of non-Newtonian/Newtonian two-phase flows are closely tied to flow pattern formation mechanisms, influenced significantly by the non-Newtonian index, and exhibiting nonlinear rheological characteristics. The nonlinear behavior of fluid flow cannot be directly inferred from the rheological models, making their temporal characteristics difficult to predict. This limitation hinders the development of a unified analytical approach and consistent results, confining researches to case-by-case studies. In this study, sets of digital microfluidics experiments, along with continuous-discrete phase-interchanging schemes, yielded 72 datasets under various non-Newtonian fluid solution configurations, micro-channel structures, and multiple Carreau-related models. Among these datasets, we identified consistent temporal behaviors featuring non-Newtonian flow patterns in digital microfluidics. Generally, selecting the most appropriate model to accurately represent the flow characteristics of non-Newtonian fluids is case-dependent. Nonetheless, there exists a generally applicable description of the flow behavior that is not affected by specific rheological model. This discovery is of significant importance for understanding the common behavioral characteristics of non-Newtonian fluids.

Self-enhanced mobility enables vortex pattern formation in living matter.

Ranging from subcellular organelle biogenesis to embryo development, the formation of self-organized structures is a hallmark of living systems. Whereas the emergence of ordered spatial patterns in biology is often driven by intricate chemical signalling that coordinates cellular behaviour and differentiation1-4, purely physical interactions can drive the formation of regular biological patterns such as crystalline vortex arrays in suspensions of spermatozoa5 and bacteria6. Here we discovered a new route to self-organized pattern formation driven by physical interactions, which creates large-scale regular spatial structures with multiscale ordering. Specifically we found that dense bacterial living matter spontaneously developed a lattice of mesoscale, fast-spinning vortices; these vortices each consisted of around 104-105 motile bacterial cells and were arranged in space at greater than centimetre scale and with apparent hexagonal order, whereas individual cells in the vortices moved in coordinated directions with strong polar and vortical order. Single-cell tracking and numerical simulations suggest that the phenomenon is enabled by self-enhanced mobility in the system-that is, the speed of individual cells increasing with cell-generated collective stresses at a given cell density. Stress-induced mobility enhancement and fluidization is prevalent in dense living matter at various scales of length7-9. Our findings demonstrate that self-enhanced mobility offers a simple physical mechanism for pattern formation in living systems and, more generally, in other active matter systems10 near the boundary of fluid- and solid-like behaviours11-17.

Pattern selection mechanism from the equilibrium point and limit cycle.

The outbreak of infectious diseases often exhibits periodicity, and this periodic behavior can be mathematically represented as a limit cycle. However, the periodic behavior has rarely been considered in demonstrating the cluster phenomenon of infection induced by diffusion (the instability modes) in the SIR model. We investigate the emergence of Turing instability from a stable equilibrium and a limit cycle to illustrate the dynamical and biological mechanisms of pattern formation. We identify the Hopf bifurcation to demonstrate the existence of a stable limit cycle using First Lyapunov coefficient in our spatiotemporal diffusion-driven SIR model. The competition between different instability modes induces different types of patterns and eventually spot patterns emerge as stable patterns. We investigate the impact of susceptible, infected, and recovered individuals on the type of patterns. Interestingly, these instability modes play a vital role in selecting the pattern formations, which is directly related to the number of observed spot patterns. Subsequently, we explain the dynamical and biological mechanisms of spot patterns to develop an effective epidemic prevention strategy.

Minimal reaction schemes for pattern formation.

We link continuum models of reaction-diffusion systems that exhibit diffusion-driven instability to constraints on the particle-scale interactions underpinning this instability. While innumerable biological, chemical and physical patterns have been studied through the lens of Alan Turing's reaction-diffusion pattern-forming mechanism, the connections between models of pattern formation and the nature of the particle interactions generating them have been relatively understudied in comparison with the substantial efforts that have been focused on understanding proposed continuum systems. To derive the necessary reactant combinations for the most parsimonious reaction schemes, we analyse the emergent continuum models in terms of possible generating elementary reaction schemes. This analysis results in the complete list of such schemes containing the fewest reactions; these are the simplest possible hypothetical mass-action models for a pattern-forming system of two interacting species.