Formation Of Regular Patterns Research Articles

Wave propagation in a light-temperature neural network under adaptive local energy balance.

External electric and mechanical stimuli can induce shape deformation in excitable media because of its intrinsic flexible property. When the signals propagation in the media is described by a neural network, creation of heterogeneity or defect is considered as the effect of shape deformation due to accumulation or release of energy in the media. In this paper, a temperature-light sensitive neuron model is developed from a nonlinear circuit composed of a phototube and a thermistor, and the physical energy is kept in capacitive and inductive terms. Furthermore, the Hamilton energy for this function neuron is obtained in theoretical way. A regular neural network is built on a square array by activating electric synapse between adjacent neurons, and a few of neurons in local area is excited by noisy disturbance, which induces local energy diversity, and continuous coupling enables energy propagation and diffusion. Initially, the Hamilton energy function for a temperature-light sensitive neuron can be obtained. Then, the finite neurons are applied noise to obtain energy diversity to explore the energy spread between neurons in the network. For keeping local energy balance, one intrinsic parameter is regulated adaptively until energy diversity in this local area is decreased greatly. Regular pattern formation indicates that local energy balance creates heterogeneity or defects and a few of neurons show continuous parameter shift for keeping energy balance in a local area, which supports gradient energy distribution for propagating waves in the network.

Electric-field-induced patterns in a hockey-stick nematic

The response to applied electric field of a newly synthesized hockey-stick nematic 8-F-OH has been studied. Unusual pattern forming scenarios were found, which show rich variety as a function of frequency, temperature and initial director alignment. The behavior has been compared with those, observed in calamitic and bent-core nematics. Experiments show that contrary to calamitic nematics, here the elastically strongly deformed layers due to Fréedericksz transition play a decisive role in the formation of regular patterns. This is attributed to the cybotactic nematic phase with polar smectic clusters, where flexoelectricity might also have influence. Static and dynamic behaviors of the patterns have been characterized and an application idea is formulated.

Xylan adsorption on cellulose: Preferred alignment and local surface immobilizing effect

Interaction between xylan and cellulose microfibrils is required to maintain the integrity of secondary cell walls. However, the mechanisms governing their assembly and the effects on cellulose surface polymers are not fully clear. Here, molecular dynamics simulations are used to study xylan adsorption onto hydrated cellulose fibrils. Based on multiple spontaneous adsorption simulations it is shown that an antiparallel orientation is thermodynamically preferred over a parallel one, and that adsorption is accompanied by the formation of regular but orientation-dependent hydrogen bond patterns. Furthermore, xylan adsorption restricts the local dynamics of the adjacent glucose residues in the surface layer to a level of the crystalline core, which is manifested as a three-fold increase in their 13C NMR T1 relaxation time. These results suggest that xylan forms a rigid and ordered layer around the cellulose fibril that functions as a transition phase to more flexible and disordered polysaccharide and lignin domains.

A Comparison of the \u201cReduced Losses\u201d and \u201cIncreased Production\u201d Models for Mussel Bed Dynamics

Self-organised regular pattern formation is one of the foremost examples of the development of complexity in ecosystems. Despite the wide array of mechanistic models that have been proposed to understand pattern formation, there is limited general understanding of the feedback processes causing pattern formation in ecosystems, and how these affect ecosystem patterning and functioning. Here we propose a generalised model for pattern formation that integrates two types of within-patch feedback: amplification of growth and reduction of losses. Both of these mechanisms have been proposed as causing pattern formation in mussel beds in intertidal regions, where dense clusters of mussels form, separated by regions of bare sediment. We investigate how a relative change from one feedback to the other affects the stability of uniform steady states and the existence of spatial patterns. We conclude that there are important differences between the patterns generated by the two mechanisms, concerning both biomass distribution in the patterns and the resilience of the ecosystems to disturbances.

Strain localization regularization and patterns formation in rate-dependent plastic materials with multiphysics coupling

Strain localization is an instability phenomenon occurring in deformable solid materials which undergo dissipative deformation mechanisms. Such instability is characterized by the localization of the displacement or velocity fields in a zone of finite thickness and is generally associated with the failure of materials. In several fields of material engineering and natural sciences, estimating the thickness of localized deformation is required to make accurate predictions of the evolution of the physical properties within localized strain regions and of the material strength. In this context, scientists and engineers often rely on numerical modeling techniques to study strain localization in solid materials. However, classical continuum theory for elasto-plastic materials fails at estimating strain localization thicknesses due to the lack of an internal length in the model constitutive laws. In this study, we investigate at which conditions multiphysics coupling enables to regularize the problem of strain localization using rate-dependent plasticity. We show that coupling the constitutive laws for deformation to a single generic diffusion–reaction equation representing a dissipative state variable can be sufficient to regularize the ill-posed problem under some conditions on the softening parameters in the plastic potential. We demonstrate in these cases how rate-dependent plasticity and multiphysics coupling can lead to material instabilities depicting one or several internal length scales controlled by the physical parameters resulting in the formation of regular or erratic patterns. As we consider a general form of the equations, the results presented in this study can be applied to a large panel of examples in the material engineering and geosciences communities.

Role of axonal fibers in the cortical folding patterns: A tale of variability and regularity

Cortical folding is one of the most complex processes that occur during the normal development of the human brain. Despite variability in folding patterns of different individuals, there are a few specific types of preserved folding patterns within individuals or across species. The origin and formation mechanism of variable or regular folding patterns in the human brain yet remains to be thoroughly explored. This study aims to delineate how the interplay between the differential tangential growth of cerebral cortex and axonal fiber tension induces and regulates the folding patterns in a developing human brain. To achieve this aim, an image-based multiscale mechanical model on the basis of the embedded nonlinear finite element method is employed to investigate a set of growth and folding scenarios. Our results show that the differential growth between cortical and subcortical layers is the main inducer of cortical folding. In addition, the gyrification of the cortex pulls the areas with a high density of stiff axonal fiber bundles towards gyri rather than sulci; therefore, axonal fiber bundles induce symmetry breaking, and regulate the folding patterns. In particular, spatial distribution of axonal fiber bundles is the determinant factor to control the locations of gyri and sulci. In conclusion, we propose that neural wiring might be the main regulator of folding patterns responsible for the formation of regular cortical folding patterns. This study provides a deeper understanding of cortical folding and its morphogenesis which are the key to interpreting normal brain development and growth. Statement of SignificanceThere is a vital need to discover the role of axonal fibers of the brain’s connectivity on the formation and modulation of folding patterns in the developing human brain. The lack of knowledge of the physical interplay between cortical folding and neural wiring is a critical barrier to the fundamental understanding of the relationship between cortical folding, brain connectivity, and brain function in different neurodevelopmental stages. This study by using image-based multiscale mechanical models investigates the role of the differential tangential growth of cerebral cortex and axonal fibers in the formation and regulation of the folding patterns in the developing human brain. This is the first study to explain why despite variation in folding patterns, there are some specific types of regular shapes within individuals or across species and why axonal fibers connected to gyri in the human brain are typically denser than those connected to sulci. The study has a positive impact on the deeper understanding of cortical folding and its morphogenesis that is the key to interpreting the normal development of the human brain during the early stages of growth.

Pyric tree spatial patterning interactions in historical and contemporary mixed conifer forests, California, USA.

Tree spatial patterns in dry coniferous forests of the western United States, and analogous ecosystems globally, were historically aggregated, comprising a mixture of single trees and groups of trees. Modern forests, in contrast, are generally more homogeneous and overstocked than their historical counterparts. As these modern forests lack regular fire, pattern formation and maintenance is generally attributed to fire. Accordingly, fires in modern forests may not yield historically analogous patterns. However, direct observations on how selective tree mortality among pre‐existing forest structure shapes tree spatial patterns is limited. In this study, we (a) simulated fires in historical and contemporary counterpart plots in a Sierra Nevadan mixed‐conifer forest, (b) estimated tree mortality, and (c) examined tree spatial patterns of live trees before and after fire, and of fire‐killed trees. Tree mortality in the historical period was clustered and density‐dependent, because trees were aggregated and segregated by tree size before fire. Thus, fires maintained an aggregated distribution of tree groups. Tree mortality in the contemporary period was widespread, except for dispersed large trees, because most trees were a part of large, interconnected tree groups. Thus, postfire tree patterns were more uniform and devoid of moderately sized tree groups. Postfire tree patterns in the historical period, unlike the contemporary period, were within the historical range of variability identified for the western United States. This divergence suggests that decades of forest dynamics without significant disturbances have altered the historical means of pyric pattern formation. Our results suggest that ecological silvicultural treatments, such as forest restoration thinnings, which emulate qualities of historical forests may facilitate the reintroduction of fire as a means to reinforce forest structural heterogeneity.

Defect patterns on the curved surface of fish retinae suggest a mechanism of cone mosaic formation.

The outer epithelial layer of zebrafish retinae contains a crystalline array of cone photoreceptors, called the cone mosaic. As this mosaic grows by mitotic addition of new photoreceptors at the rim of the hemispheric retina, topological defects, called “Y-Junctions”, form to maintain approximately constant cell spacing. The generation of topological defects due to growth on a curved surface is a distinct feature of the cone mosaic not seen in other well-studied biological patterns like the R8 photoreceptor array in the Drosophila compound eye. Since defects can provide insight into cell-cell interactions responsible for pattern formation, here we characterize the arrangement of cones in individual Y-Junction cores as well as the spatial distribution of Y-junctions across entire retinae. We find that for individual Y-junctions, the distribution of cones near the core corresponds closely to structures observed in physical crystals. In addition, Y-Junctions are organized into lines, called grain boundaries, from the retinal center to the periphery. In physical crystals, regardless of the initial distribution of defects, defects can coalesce into grain boundaries via the mobility of individual particles. By imaging in live fish, we demonstrate that grain boundaries in the cone mosaic instead appear during initial mosaic formation, without requiring defect motion. Motivated by this observation, we show that a computational model of repulsive cell-cell interactions generates a mosaic with grain boundaries. In contrast to paradigmatic models of fate specification in mostly motionless cell packings, this finding emphasizes the role of cell motion, guided by cell-cell interactions during differentiation, in forming biological crystals. Such a route to the formation of regular patterns may be especially valuable in situations, like growth on a curved surface, where the resulting long-ranged, elastic, effective interactions between defects can help to group them into grain boundaries.

Generation of regular optical patterns and photonic structures by a single Gaussian beam in a photorefractive LiNbO3:Fe crystal

We report 2D micrometric scale regular optical patterns formation induced by a laser beam propagating through a Fe doped lithium niobate (LN:Fe) crystal. A single mode CW laser radiation at 632.8 nm wavelength and beam powers from 0.5 to 10 mW and LN:Fe samples with 0.03 wt% Fe concentration and thicknesses of 4 mm and 10 mm were used in the experiments. The observed phenomenon of optical patterns formation in photorefractive crystal is explained with the light-induced complex refractive index variation with a central minimum (negative lens) and symmetric maxima (positive lenses) on each side due to photovoltaic effect in the crystal. Light-induced complex lenses produce beam defocusing from the beam center and focusing on the periphery. Mutual interference of the beams leads to a regular optical pattern formation. Regular optical pattern, in its turn, leads to the formation of quasi-crystalline photonic structure in LN:Fe crystal. Experimental results are supported by numerical simulations.

Nonlinear compositional and morphological evolution of ion irradiated GaSb prior to nanostructure formation

Low-energy ion irradiation of III-V semiconductor surfaces can lead to the formation of regular hexagonal dot patterns at the surface. We present experimental and computational results for ion irradiation of GaSb surfaces which elucidate the nature of the coupled compositional and morphological pattern-formation mechanisms. We demonstrate by in-situ grazing-incidence small-angle x-ray scattering (GISAXS) and angle-resolved Auger electron spectroscopy (ARAES) that the emergence of an altered compositional depth profile is essential to induce morphological changes at the surface. This morphological evolution of the surface follows nucleation-and-growth kinetics. Furthermore, we show from massive-scale molecular dynamics (MD) simulations that the compositional depth profile evolution leads to thermodynamic phase separation, providing a lateral compositional instability that drives pattern formation. Additionally, high-fluence simulations elucidate the irradiation-induced mechanisms of compositional depth profile formation. Prompt ion effects drive formation of single-element “protoclusters”, predominantly of Sb. Structural and energetic characterization of the simulation results indicate that Sb may be more mobile than Ga, providing a diffusional pathway for long-temporal-scale compositional evolution of the irradiated surface. Our findings motivate the development of new, comprehensive models which consider the total spatial and temporal complexity of multicomponent systems evolving under ion irradiation.

Spike-induced ordering: Stochastic neural spikes provide immediate adaptability to the sensorimotor system

Most biological neurons exhibit stochastic and spiking action potentials. However, the benefits of stochastic spikes versus continuous signals other than noise tolerance and energy efficiency remain largely unknown. In this study, we provide an insight into the potential roles of stochastic spikes, which may be beneficial for producing on-site adaptability in biological sensorimotor agents. We developed a platform that enables parametric modulation of the stochastic and discontinuous output of a stochastically spiking neural network (sSNN) to the rate-coded smooth output. This platform was applied to a complex musculoskeletal-neural system of a bipedal walker, and we demonstrated how stochastic spikes may help improve on-site adaptability of a bipedal walker to slippery surfaces or perturbation of random external forces. We further applied our sSNN platform to more general and simple sensorimotor agents and demonstrated four basic functions provided by an sSNN: 1) synchronization to a natural frequency, 2) amplification of the resonant motion in a natural frequency, 3) basin enlargement of the behavioral goal state, and 4) rapid complexity reduction and regular motion pattern formation. We propose that the benefits of sSNNs are not limited to musculoskeletal dynamics. Indeed, a wide range of the stability and adaptability of biological systems may arise from stochastic spiking dynamics.

Topological Defect Arrays in Nematic Liquid Crystals Assisted by Polymeric Pillar Arrays: Effect of the Geometry of Pillars

Topological defects that spontaneously occur in condensed matter and structured fluids such as liquid crystals are useful for their elastic and optical properties, but often the applicability of defect arrays to optics and photonic devices relies on the regularity and tunability of the system. In our recent work [Adv. Opt. Mater. 8, 1900991 (2020)], we showed the formation of regular, reconfigurable, and scalable patterns by exploiting the elastic response of a defect array in liquid crystals in the presence of a polymeric pillar array. In this work, we experimentally investigate the role of size and shape of the pillars on the defect array. We find that the pillar size and geometry provide additional means to regulate the response time, the threshold voltage for the defects’ formation, and the spatial arrangement of the defects.

Formation of Regular Wormlike Patterns by Dewetting Aqueous Dispersions of Halloysite Nanotubes

The worm-like micropatterns were elaborated by drying halloysite clay nanotube dispersions placed between two horizontal glass slides. This 0.1-0.2 mm thick confined space induces the fractal self-...

Regular pattern formation regulates population dynamics: Logistic growth in cellular automata

Regular pattern formation is common in nature, but its ecological role in population dynamics is not well understood. In this article, we present a logistic probabilistic cellular automata (LPCA) model that combines a basic logistic growth model with two-dimensional spatial dynamics to simulate regular pattern formation. For model generality, only propagation and competition were assumed to occur in LPCA, and their dynamics follow local logistic growth. Simulation outcomes show that the resource scarcity and shape of the neighborhood are the main causes of different regular patterns. We use reference data from an arid ecosystem in Shapotou to parameterize the LPCA model and find that the pattern shifts form spots, labyrinths, to gaps with decreasing resource scarcity and that anisotropic neighborhoods generate banded patterns. The influences of regular patterns on population dynamics were studied by comparing the LPCA model and its mean field approximation (MFA), which discards particular spatial configurations and makes global predictions of population dynamics. The outcomes show that regular patterns can regulate population dynamics and alter equilibrium population size. Furthermore, regular patterns work as optimized spatial configuration to balance space and resource competition.

Regular and Irregular Vegetation Pattern Formation in Semiarid Regions: A Study on Discrete Klausmeier Model

The research on regular and irregular vegetation pattern formation in semiarid regions is an important field in ecology. Applying the framework of coupled map lattice, a novel nonlinear space- and time-discrete model is developed based on discretizing the classical Klausmeier model and the vegetation pattern formation in semiarid regions is restudied in this research. Through analysis of Turing-type instability for the discrete model, the conditions for vegetation pattern formation are determined. The discrete model is verified by Klausmeier’s results with the same parametric data, and shows advantages in quantitatively describing diverse vegetation patterns in semiarid regions, such as the patterns of regular mosaicirregular patches, stripes, fractured stripesspots, and stripes-spots, in comparing with former theoretical models. Moreover, the discrete model predicts variations of rainfall and vegetation types can cause transitions of vegetation patterns. This research demonstrates that the nonlinear mechanism of the discrete model better captures the diversity and complexity of vegetation pattern formation in semiarid regions.

Spatiotemporal pattern formation in E. coli biofilms explained by a simple physical energy balance.

While the biofilm growth mode conveys notable thriving advantages to bacterial populations, the mechanisms of biofilm formation are still strongly debated. Here, we investigate the remarkable spontaneous formation of regular spatial patterns during the growth of an Escherichia coli biofilm. These patterns reported here appear with non-motile bacteria, which excludes both chemotactic origins and other motility-based ones. We demonstrate that a minimal physical model based on phase separation describes them well. To confirm the predictive capacity of our model, we tune the cell-cell and cell-surface interactions using cells expressing different surface appendages. We further explain how F pilus-bearing cells enroll their wild type kindred, poorly piliated, into their typical pattern when mixed together. This work supports the hypothesis that purely physicochemical processes, such as the interplay of cell-cell and cell-surface interactions, can drive the emergence of a highly organized spatial structure that is potentially decisive for community fate and for biological functions.

Structure and phase transitions of two-dimensional core-softened colloidal dumbbells: a molecular dynamics study

Formation of two-dimensional (2D) quasi-crystalline structure by colloidal dumbbells interacting via a core-softened potential is studied using molecular dynamics simulations. Owing to the presence of two length scales associated with the rigid bond length of the dumbbell and the minimum of the core-softened repulsive force well, the dumbbell system exhibits rich complex 2D patterns ranging from low-density triangular ordered lattice, coupled stripe-ordered triangular lattice structure, hexagonal lattice, Kagome patterns, to high density clusters as density increases. At very high density, the 2D dumbbells form compact triangular ordered lattice. We have also identified the order-to-disorder transition temperature at which the ordered phase transitions to disordered structure by examining the potential energy, heat capacity and radial distribution functions of the system. In addition to 2D dimeric dumbbells, we studied the structures formed by 2D monomeric spheres that interact through the same core-softened potential. We found that although the monomeric spheres can produce most of the quasi crystalline patterns found for the dumbbell system, there are notable differences. The interplay of the two spatial length scales present in the dumbbells can produce a unique coupled stripe-triangular lattice structure at intermediate densities that is not observed for monomeric particles. The disparity between the two spatial lengths also has the effect of disrupting the formation of regular patterns leading to irregular and defective hexagons and Kagome lattices. This study shows that the two spatial length scales, present in the dumbbells, can be utilized to generate unique structures and demonstrates the potential for using dumbbells as building blocks for creating 2D structures.

Dynamics of DNA Origami Lattice Formation at Solid-Liquid Interfaces.

The self-organized formation of regular patterns is not only a fascinating topic encountered in a multitude of natural and artificial systems, but also presents a versatile and powerful route toward large-scale nanostructure assembly and materials synthesis. The hierarchical, interface-assisted assembly of DNA origami nanostructures into regular, 2D lattices represents a particularly promising example, as the resulting lattices may exhibit an astonishing degree of order and can be further utilized as masks in molecular lithography. Here, we thus investigate the development of order in such 2D DNA origami lattices assembled on mica surfaces by employing in situ high-speed atomic force microscopy imaging. DNA origami lattice formation is found to resemble thin-film growth in several aspects. In particular, the Na+/Mg2+ ratio controls DNA origami adsorption, surface diffusion, and desorption, and is thus equivalent in its effects to substrate temperature which controls adatom dynamics in thin-film deposition. Consequently, we observe a pronounced dependence of lattice order on Na+ concentration. At low Na+ concentrations, lattice formation resembles random deposition and results in unordered monolayers, whereas very high Na+ concentrations are accompanied by rapid diffusion and especially DNA origami desorption, which prevent lattice formation. At intermediate Na+ concentrations, highly ordered DNA origami lattices are obtained that display an intricate symmetry, stemming from the complex shape of the employed Rothemund triangle. Nevertheless, even under such optimized conditions, the lattices display a considerable number of defects, including grain boundaries, point and line defects, and screw-like dislocations. By monitoring the dynamics of selected lattice defects, we identify mechanisms that limit the obtainable degree of lattice order. Possible routes toward further increasing lattice order by postassembly annealing are discussed.

Patterns in ash-covered melting snow

The formation of regular patterns in snow covered by a layer of dark material is investigated as an instability phenomenon. A detailed analysis of the energy balance of the system highlights the prevalent role of solar radiation in such phenomena, and puts the base for further investigations.

FEM-bifurcation analysis for 3D crack patterns

During the shrinkage of volcanic rock, columnar joints evolve with an almost regular hexagonal pattern formation and a very distinct column diameter defining the crack spacing. This phenomenon is caused by an inhomogeneous, constantly moving temperature field. The constant column growth is presumably always close to a bifurcation point at which the ideal regular pattern of hexagons could branch off to a pattern with a different symmetry due to slightly changing cooling conditions. This paper presents an energy-based fracture mechanical bifurcation analysis to determine this point and its stability by evaluating first and second order derivatives of the free Helmholtz energy with respect to a limited number of coefficients of a truncated Fourier series expansion of the three-dimensional crack front contour. The energy is obtained by linear elastic simulations on three-dimensional Finite Element models of the periodically repeatable patterns before and after bifurcation. While providing an understanding of the column growth procedure of volcanic rock, the characteristics of the approach suggest applications for various complex three-dimensional crack growth systems in engineering.