Dynamics Of Pattern Formation Research Articles

Size of a steady disturbance source affects the frequency of a target wave

Controlling the frequency of a target wave is an important issue in the dynamics of pattern formation. A common method for controlling is to apply a local disturbance to the media, such as a periodic disturbance source which is not always valid in practice. In the present study, we proposed a method to control the frequency of a target wave by the application of a steady disturbance. We found that the size of a steady disturbance source affects the frequency of the chemical wave by the numerical simulations of three mathematical models. The simulation results are confirmed by theoretical analysis. Our theory and method shed light in the controlling frequency of the oscillatory media.

Third Order Dispersion in Time-Delayed Systems.

Time-delayed dynamical systems materialize in situations where distant, pointwise, nonlinear nodes exchange information that propagates at a finite speed. However, they are considered devoid of dispersive effects, which are known to play a leading role in pattern formation and wave dynamics. We show how dispersion may appear naturally in delayed systems and we exemplify our result by studying theoretically and experimentally the influence of third order dispersion in a system composed of coupled optical microcavities. Dispersion-induced pulse satellites emerge asymmetrically and destabilize the mode-locking regime.

Improved Prediction of Periodicity Using Quartet Approximation in a Lattice Model of Intracellular Calcium Release

This study uses a probabilistic cellular automata (PCA) to model the spatial lattice arrangement of calcium release units (CRUs) within cardiac myocytes. The CRUs are subject to random activation, nearest-neighbor recruitment, and temporal refractoriness, and their interactions produce a physiologically-important condition called calcium alternans, a beat-to-beat oscillation in the amount of calcium released. In the PCA this manifests as a transition to period-2 behavior in the fraction of activated lattice sites. We investigate this phenomenon using PCA simulations and moment-closure approximation methods of zero order (mean-field), first order (pair), and second order (quartet). We show that only the quartet approximation (QA) accurately predicts the thresholds of the activation and recruitment probabilities for the onset of periodic behavior (alternans), as the lower-order approximations do not sufficiently account for important spatial correlations. The QA also accurately predicts the emergence of spatio-temporal clustering in the PCA, providing an analytical framework for investigating pattern formation dynamics in such models. Our analysis demonstrates a systematic approach to efficiently handling the increased combinatorial complexity of the QA, whose required computation time is nontrivially larger compared to the mean-field approximation but remains an order of magnitude lower than the numerical PCA simulations.

Pattern Formation With Locally Active S-Type NbOx Memristors

The main focus of this paper is the evolution of complex behavior in a system of coupled nonlinear memristor circuits depending on the applied coupling conditions. Thereby, the parameter space for the local activity and the edge-of-chaos domain will be determined to enable the emergence of the pattern formation in locally coupled cells according to Chua’s principle. Each cell includes a Niobium oxide-based memristor, which may feature a locally active behavior once it is suitably biased on the negative differential resistance region of its DC current-voltage characteristic. It will be shown that there exists a domain of parameters under which each uncoupled cell may become locally active around a stable bias state. More specifically, under these conditions, the coupled cells are on the edge-of-chaos, and can support the static and dynamic pattern formation. The emergence of such complex spatio-temporal behavior in homogeneous structures is a prerequisite for information processing. The theoretical results are confirmed by measurements as well as by the numerical simulations of the accurate device and circuit models.

Pattern phase diagram of spiking neurons on spatial networks.

We study an abstracted model of neuronal activity via numerical simulation and report spatiotemporal pattern formation and criticallike dynamics. A population of pulse coupled, discretized, relaxation oscillators is simulated over networks with varying edge density and spatial embeddedness. For intermediate edge density and sufficiently strong spatial embeddedness, we observe a spatiotemporal pattern in the field of oscillator phases, visually resembling the surface of a frothing liquid. Increasing the edge density results in a distribution of neuronal avalanche sizes which follows a power law with exponent one (Zipf's law). Further increasing edge density yields metastability between pattern formation and synchronization, before transitioning entirely into synchrony.

Spatially Resolved XPS Characterization of Electrochemical Surfaces

Synchrotron-based scanning photoelectron microscopy (SPEM) has opened unique opportunities for exploiting processes occurring at surfaces and interfaces, which control the properties of materials for electrochemical devices, where issues of chemical and morphological complexity at microscopic length scales should be faced and understood. The present article aims to demonstrate the present capabilities of SPEM to explore the surface composition of micro- and nano-structured materials, focusing on cases relevant to electrochemical technologies. We report and discuss a selection of recent results about three different systems, targeting hot topics in the fields of electrochemical energy storage and electrochemical fabrication: (i) an in-depth analysis of Ag-In electrodeposited alloys exhibiting dynamic pattern formation, (ii) the analysis of electrochemical processes at the electrodes of a self-driven solid oxide fuel cell and (iii) an operando characterization of a single-chamber solid oxide fuel cell. The last example has been performed at near-ambient pressure conditions using a unique specially designed setup which extends the traditional capabilities of scanning photoemission microscopes in the ultra-high and high-vacuum regimes to operating conditions that are closer to realistic ones, contributing to overcome the so-called “pressure gap”.

Electronic Structure Mosaicity of Monolayer Transition Metal Dichalcogenides by Spontaneous Pattern Formation of Donor Molecules.

Modulating the electronic structure of semiconducting materials is critical to developing high-performance electronic and optical devices. Transition metal dichalcogenides (TMDCs) are atomically thin semiconducting materials. However, before they can be used successfully in electronic and optical devices, modulation of their carrier concentration at the nanometer scale must be achieved. Molecular doping has been successful in modulating the carrier concentration; however, the scientific approach for selective and local carrier doping at the nanometer scale is still missing. Here, we demonstrate a proof-of-concept of modulating the carrier concentration of TMDCs laterally on a scale of around 100 nm using spontaneous pattern formation of an ultrathin film consisting of molecular electron dopants. When the water made contact with the molecular film (∼10 nm), a spontaneous pattern formation was observed on both the monolayer and bulk TMDCs. We revealed that the pattern-formation dynamics and nanoscopic flow rate of the molecules were highly dependent on the thickness of the TMDCs, since the band gap varies based on the number of layers. Analyses of topographic images of the molecular patterns and photoluminescence spectra of the TMDCs indicated that the spontaneously patterned molecular films induced a local carrier doping. Our results demonstrate a spontaneous formation of a mosaic electronic structure. This work is useful for making tiny-scale electronic junctions on TMDCs and semiconducting materials to make numerous p/n junctions simultaneously for optoelectronic devices.

Dynamic phases, stratification, laning, and pattern formation for driven bidisperse disk systems in the presence of quenched disorder

Using numerical simulations, we examine the dynamics of driven two-dimensional bidisperse disks flowing over quenched disorder. The system exhibits a series of distinct dynamical phases as a function of applied driving force and packing fraction, including a phase-separated state as well as a smectic state with liquid-like or polycrystalline features. At low driving forces, we find a clogged phase with an isotropic density distribution, while at intermediate driving forces the disks separate into bands of high and low densities with either liquid-like or polycrystalline structure in the high-density bands. In addition to the density phase separation, we find that in some cases there is a fractionation of the disk species, particularly when the disk size ratio is large. The species phase-separated regimes form a variety of patterns such as large disks separated by chains of smaller disks. Our results show that the formation of laning states can be enhanced by tuning the ratio of disk radius of the two species, due to the clumping of small disks in the interstitial regions between the large disks. This system could be experimentally realized using sterically interacting colloidal particles suspended in a viscous fluid driven over random pinning arrays or granular matter suspended in fluid moving over a random landscape.

Nano-structured thin films growth in stochastic plasma-condensate systems

We derive the stochastic model of plasma-condensate systems by taking into account anisotropy in transference of adatoms between neighbor layers and by introducing fluctuations of adsorbate flux. We show, that by varying the fluctuation's intensity on can govern dynamics of pattern formation on intermediate layer of multi-layer plasma-condensate system. It is shown that the morphology of the growing surface, type of surface structures and their linear size can be controlled by the intensity of the adsorbate flux fluctuations.

The Role of Cellular Replicative Lifespan and Stem Cell Dynamics on Corneal Epithelium Homeostasis and Pattern Formation

The anterior outer transparent part of the eye, the cornea, acts as a lens that focuses light into the eye. In addition, it serves as a barrier that protects the eye against external hazards and injury and thus maintaining its integrity and its continuous regeneration is crucial for proper vision in vertebrates. Stem cells reside in niches at the circumference of the cornea, the limbus, which separates the cornea from the conjunctiva replenish and maintain corneal homeostasis. Recent lineage tracing experiments resulted in spike-like patterns that extended from the limbus to the center of the cornea over time. The mechanism that underlies these centripetal dynamics is not fully understood. We developed a novel mathematical model that capture the stochastic dynamics of epithelial cells and pattern formation in the cornea. Our model capture both short and long interaction range between cells. Moreover, we take into account two opposing models of stem cell dynamics that have been proposed: The Hierarchical model where stem-cells are rare long-lived, slow-dividing cells and the Stochastic model where stem-cells are abundant equipotent cells that divide frequently and their loss is dictated by neutral drift. We show that the replicative life-span of the cells and the spatial correlation between replication and removal from the cornea play a major role in whether homeostasis can be maintained without symmetry breaking signals. We derive the conditions that allow homeostasis that is consistent with biological timescales and mutants dynamics. We show how the conditions for self-organizing homeostasis depend on the stem cell dynamics and provide an experimental prediction to discriminate between the models. The result of this study can be extended to any cellular system in which spatial homeostasis is maintained through cell division.

Modulation instability associated nonlinear dynamics of spin–orbit coupled Bose–Einstein condensates**T Mithun dedicates this article to the memory of beloved guide Professor K Porsezian, who passedaway on 11 August, 2018.

We study pattern-forming nonlinear dynamics starting from a continuous wave state of quasi-one-dimensional two-component Bose–Einstein condensates with synthetic spin–orbit coupling induced by Raman lasers. Modulation instability (MI) can occur even when the miscibility condition due to the interatomic interactions is satisfied. We find that the initial stage of the nonlinear development is consistent with the prediction of MI, where the two primary and secondary instability bands lead to the spontaneous growth of the modulation and the subsequent complicated dynamics of pattern formation. At later stages of the evolution, the wave functions undergo clear separation in the momentum space, reflected in the dispersion of the single particle Hamiltonian.

Super Multi-Armed and Segmented Spiral Pattern in a Reaction-Diffusion Model

The super multi-armed and segmented (SMAS) spiral pattern has been observed in nature, such as sunflower inflorescence, spiral aloe, pine cone, ball cactus and Roman broccoli, which is characterized by several segmented spiral arms sharing the same spiral tip. The mechanism for the emergency of the SMAS spiral pattern has not been found. In this article, we observed the emergence of the SMAS spiral pattern by the simulations of a reaction-diffusion model. Additionally, our theoretical analysis found that the instability of concentrations in spiral arms leads to the emergence of this pattern. This study provides an alternative explanation for the formation of this type of pattern in nature and sheds light on the dynamics of pattern formation.

Quantitative Characteristic of ncRNA Regulation in Gene Regulatory Networks.

RNA is mostly known for its role in protein synthesis, where it encodes information for protein sequence in its messenger RNA (mRNA) form (translation). Yet, RNA molecules regulate several cellular processes other than translation. Here, we present an overview of several mathematical models that help understanding and characterizing the role of noncoding RNA molecules (ncRNAs) in regulating gene expression and protein synthesis. First, we discuss relatively simple models where ncRNAs can modulate protein synthesis via targeting a mRNA. Then, we consider the case of feedback interactions between ncRNAs and their target proteins, and discuss several biological applications where these feedback architectures modulate a cellular phenotype and control the levels of intrinsic and extrinsic noise. Building from these simple circuit motifs, we examine feed-forward circuit motifs involving ncRNAs that generate precise spatial and temporal patterns of protein expression. Further, we investigate the competition between ncRNAs and other endogenous RNA molecules and show that the cross talk between coding and noncoding RNAs can form large genetic circuits that involve up to hundreds of chemical species. Finally, we discuss the role of ncRNAs in modulating cell-cell signaling pathways and therefore the dynamics of spatiotemporal pattern formation in a tissue.

Pattern Formation and Oscillatory Dynamics in a Two-Dimensional Coupled Bulk-Surface Reaction-Diffusion System

On a two-dimensional circular domain, we analyze the formation of spatio-temporal patterns for a class of coupled bulk-surface reaction-diffusion models for which a passive diffusion process occurring in the interior bulk domain is linearly coupled to a nonlinear reaction-diffusion process on the domain boundary. For this coupled PDE system we construct a radially symmetric steady state solution and from a linearized stability analysis formulate criteria for which this base state can undergo either a Hopf bifurcation, a symmetry-breaking pitchfork (or Turing) bifurcation, or a codimension-two pitchfork-Hopf bifurcation. For each of these three types of bifurcations, a multiple time-scale asymptotic analysis is used to derive normal form amplitude equations characterizing the local branching behavior of spatio-temporal patterns in the weakly nonlinear regime. Among the novel aspects of this weakly nonlinear analysis are the two-dimensionality of the bulk domain, the systematic treatment of arbitrary reaction kinetics restricted to the boundary, the bifurcation parameters which arise in the boundary conditions, and the underlying spectral problem where both the differential operator and the boundary conditions involve the eigenvalue parameter. The normal form theory is illustrated for both Schnakenberg and Brusselator reaction kinetics, and the weakly nonlinear results are favorably compared with numerical bifurcation results and results from time-dependent PDE simulations of the coupled bulk-surface system. Overall, the results show the existence of either subcritical or supercritical Hopf and symmetry-breaking bifurcations, and mixed-mode oscillations characteristic of codimension-two bifurcations. Finally, the formation of global structures such as large amplitude rotating waves is briefly explored through PDE numerical simulations.

Method for disarranging the pigment pattern of zebrafish by optogenetics

To investigate the spatiotemporal dynamics of skin pattern formation, we developed a simple method for artificially disarranging the placement of all three pigment cell types in the body trunk of zebrafish (Danio rerio). We generated transgenic fish with melanophores that ectopically expressed a variant of channelrhodopsin-2 (ChR2). Blue light (BL) irradiation induced melanophore depolarization and random migration; the latter resulted in the disarrangement of the two other pigment cell types (xanthophores and iridophores). This BL disarrangement (BLD) method was effective in both young and adult fish, but it did not affect the initial placement of pigment cells in juvenile fish (approximately 5 weeks post-fertilization). Irradiation with BL was not harmful to cells, and the patterning process immediately resumed when BL was switched off. Using the BLD method, we demonstrated that interactions between pigment cells determined stripe width in the absence of any pre-set positional cues, while the initial horizontal alignment of iridophores determined their directionality. The BLD method can be adapted to any zebrafish skin-pattern mutant, providing a novel tool for analyzing pattern formation mechanisms under a variety of conditions and facilitating further study in this field.

The dynamics of interactional and intentional pattern formation in children's language socialization

The paradigm of Language Socialization draws upon the theoretical and analytical concepts used in linguistic anthropology, poststructuralist approaches to the study of discourse and practice, and the phenomenology of Edmund Husserl. This blending of different philosophical positions leaves Language Socialization with an incoherent concept of subjectivity. The purpose of this article is to demonstrate, first, how a coherent concept may be reached. The article argues for a phenomenological approach to the concept of habitus that brings the intentionality of consciousness back into focus as the true object of socialization processes. Second, the article demonstrates how an integrational approach to language, invested in the first-person perspective, can further an understanding of socialization as a dynamics of interactional and intentional pattern formation in children's development.

Reaction-induced porosity fingering: Replacement dynamic and porosity evolution in the KBr-KCl system

In this contribution, we use X-ray computed micro-tomography (X-CT) to observe and quantify dynamic pattern and porosity formation in a fluid-mediated replacement reaction. The evolution of connected porosity distribution helps to understand how fluid can migrate through a transforming rock, for example during dolomitization, a phenomenon extensively reported in sedimentary basins. Two types of experiment were carried out, in both cases a single crystal of KBr was immersed in a static bath of saturated aqueous KCl at room temperature and atmospheric pressure, and in both cases the replacement process was monitored in 3D using X-CT. In the first type of experiment a crystal of KBr was taken out, scanned, and returned to the solution in cycles (discontinuous replacement). In the second type of experiment, 3 samples of KBr were continuously reacted for 15, 55 min and 5.5 h respectively, with the latter being replaced completely (continuous replacement). X-CT of KBr-KCl replacement offers new insights into dynamic porosity development and transport mechanisms during replacement. As the reaction progresses the sample composition changes from KBr to KCl via a K(Br, Cl) solid solution series which generates porosity in the form of fingers that account for a final molar volume reduction of 13% when pure KCl is formed. These fingers form during an initial and transient advection regime followed by a diffusion dominated system, which is reflected by the reaction propagation, front morphology, and mass evolution. The porosity develops as fingers perpendicular to the sample walls, which allow a faster transport of reactant than in the rest of the crystal, before fingers coarsen and connect laterally. In the continuous experiment, finger coarsening has a dynamic behaviour consistent with fingering processes observed in nature. In the discontinuous experiment, which can be compared to rock weathering or to replacement driven by intermittent fluid contact, the pore structure changes from well-organized parallel fingers to a complex 3D connected network, shedding light on the alteration of reservoir properties during weathering.

Emergence of evolutionary driving forces in pattern-forming microbial populations.

Evolutionary dynamics are controlled by a number of driving forces, such as natural selection, random genetic drift and dispersal. In this perspective article, we aim to emphasize that these forces act at the population level, and that it is a challenge to understand how they emerge from the stochastic and deterministic behaviour of individual cells. Even the most basic steric interactions between neighbouring cells can couple evolutionary outcomes of otherwise unrelated individuals, thereby weakening natural selection and enhancing random genetic drift. Using microbial examples of varying degrees of complexity, we demonstrate how strongly cell-cell interactions influence evolutionary dynamics, especially in pattern-forming systems. As pattern formation itself is subject to evolution, we propose to study the feedback between pattern formation and evolutionary dynamics, which could be key to predicting and potentially steering evolutionary processes. Such an effort requires extending the systems biology approach from the cellular to the population scale.This article is part of the theme issue 'Self-organization in cell biology'.

Active particle condensation by non-reciprocal and time-delayed interactions.

We consider the flocking of self-propelling agents in two dimensions, each of which communicates with its neighbors within a limited vision-cone. Also, the communication occurs with some time-delay. The communication among the agents are modeled by Vicsek rules. In this study we explore the combined effect of non-reciprocal interaction (induced by limited vision-cone) among the agents and the presence of delay in the interactions on the dynamical pattern formation within the flock. We find that under these two influences, without any position-based attractive interactions or confining boundaries, the agents can spontaneously condense into "drops". Though the agents are in motion within the drop, the drop as a whole is pinned in space. We find that this novel state of the flock has a well-defined order and it is stabilized by the noise present in the system.

Noise transmission during the dynamic pattern formation in fly embryos

BackgroundDevelopmental patterning is highly reproducible and accurate at the single‐cell level during fly embryogenesis despite the gene expression noise and external perturbations such as the variation of the embryo length, temperature and genes. To reveal the underlying mechanism, it is very important to characterize the noise transmission during the dynamic pattern formation. Two hypotheses have been proposed. The “channel” scenario requires a highly reproducible input and an accurate interpretation by downstream genes. In contrast, the “filter” scenario proposes a noisy input and a noise filter via the cross‐regulation of the downstream network. It has been under great debates which scenario the fly embryogenesis follows.ResultsThe first 3‐h developmental patterning of fly embryos is orchestrated by a hierarchical segmentation gene network, which rewires upon the maternal to zygotic transition. Starting from the highly reproducible maternal gradients, the positional information is refined to the single‐cell precision through the highly dynamical evolved zygotic gene expression profiles. Thus the fly embryo development might strictly fit into neither the originally proposed “filter” nor “channel” scenario. The controversy that which scenario the fly embryogenesis follows could be further clarified by combining quantitative measurements and modeling.ConclusionsFly embryos have become one of the perfect model systems for quantitative systems biology studies. The underlying mechanism discovered from fly embryogenesis will deepen our understanding of the noise control of the gene network, facilitate searching for more efficient and safer methods for cell programming and reprogramming, and have the great potential for tissue engineering and regenerative medicine.