Complex Pattern Formation Research Articles

Multi-target trapping in constrained environments using gene regulatory network-based pattern formation

Inspired by the morphogenesis of biological organisms, gene regulatory network-based methods have been used in complex pattern formation of swarm robotic systems. In this article, obstacle information was embedded into the gene regulatory network model to make the robots trap targets with an expected pattern while avoiding obstacles in a distributed manner. Based on the modified gene regulatory network model, an implicit function method was adopted to represent the expected pattern which is easily adjusted by adding extra feature points. Considering environmental constraints (e.g. tunnels or gaps in which robots must adjust their pattern to conduct trapping task), a pattern adaptation strategy was proposed for the pattern modeler to adaptively adjust the expected pattern. Also to trap multiple targets, a splitting pattern adaptation strategy was proposed for diffusively moving targets so that the robots can trap each target separately with split sub-patterns. The proposed model and strategies were verified through a set of simulation with complex environmental constraints and non-consensus movements of targets.

Competition of tolerant strategies in the spatial public goods game

Tolerance implies enduring trying circumstances with a fair and objective attitude. To determine whether evolutionary advantages might be stemming from diverse levels of tolerance in a population, we study a spatial public goods game, where in addition to cooperators, defectors, and loners, tolerant players are also present. Depending on the number of defectors within a group, a tolerant player can either cooperate in or abstain from a particular instance of the game. We show that the diversity of tolerance can give rise to synergistic effects, wherein players with a different threshold in terms of the tolerated number of defectors in a group compete most effectively against defection and default abstinence. Such synergistic associations can stabilise states of full cooperation where otherwise defection would dominate. We observe complex pattern formation that gives rise to an intricate phase diagram, where invisible yet stable strategy alliances require outmost care lest they are overlooked. Our results highlight the delicate importance of diversity and tolerance for the provisioning of public goods, and they reveal fascinating subtleties of the spatiotemporal dynamics that is due to the competition of subsystem solutions in structured populations.

Bifurcation, chaos and pattern formation in a space- and time-discrete predator–prey system

The spatiotemporal dynamics of a space- and time-discrete predator–prey system is investigated in this research. The conditions for stable homogeneous stationary state of the system are derived via stability analysis. By using center manifold theorem and bifurcation theory, critical parameter values for flip bifurcation, Hopf bifurcation and Turing bifurcation are determined, respectively. Based on the bifurcation analysis, pattern formation conditions are also provided. Numerical simulations are performed not only to illustrate the theoretical results, but also to exhibit new and complex dynamical behaviors, including period-doubling cascade, invariant circles, periodic windows, chaotic dynamics, and pattern formation. Maximum Lyapunov exponents are calculated to distinguish chaos from regular behaviors. In the routes from bifurcation to chaos, flip-Turing instability and Hopf-Turing instability emerge, capturing the formation of diverse complex patterns, such as mosaic, circle, spiral, spatiotemporal chaotic patterns, and so on. The analysis and results in this research contribute to a new understanding on the relationship among bifurcation, chaos and pattern formation.

Coherence loss of partially mode-locked fibre laser.

Stochastically driven nonlinear processes limit the number of amplified modes in a natural system due to competitive mode interaction, which is accompanied by loss of coherence when increasing the complexity of the system. Specifically, we find that modulation instability, which exhibits great fluctuations when it spontaneously grows from noise in conservative systems, may possess a high degree of coherence in dissipative laser system with gain. Nonlinear mode interactions can be competitive or cooperative: adjusting the intracavity polarization state controls the process of loss of coherence. Single-shot spectra reveal that, first, the fibre laser redistributes its energy from the center wavelength mode into sidebands through parametric instabilities. Subsequently, longitudinal modes are populated via cascaded four-wave-mixing. Parametric frequency conversion populates longitudinal modes with a random distribution of position, intensity and polarization, resulting in partially (rather than highly) coherent pulses. These dynamics unveil a new route towards complex pattern formation in nonlinear laser systems, and they may be also beneficial for the understanding of supercontinuum, Kerr-combs phenomena, and optical rogue waves.

Seismic properties of lawsonite eclogites from the southern Motagua fault zone, Guatemala

We present new data on the crystal preferred orientation (CPO) and seismic properties of omphacite and lawsonite in extremely fresh eclogite from the southern Motagua fault zone, Guatemala, to discuss the seismic anisotropy of subducting oceanic crust. The CPO of omphacite is characterized by (010)[001], and it shows P-wave seismic anisotropies (AVP) of 1.4%–3.2% and S-wave seismic anisotropies (AVS) of 1.4%–2.7%. Lawsonite exhibits (001) planes parallel to the foliation and [010] axes parallel to the lineation, and seismic anisotropies of 1.7%–6.6% AVP and 3.4%–14.7% AVS. The seismic anisotropy of a rock mass consisting solely of omphacite and lawsonite is 1.2%–4.1% AVP and 1.8%–6.8% AVS. For events that propagate more or less parallel to the maximum extension direction, X, the fast S-wave velocity (VS) polarization is parallel to the Z in the Y–Z section (rotated from the X–Z section), causing trench-normal seismic anisotropy for orthogonal subduction. Based on the high modal abundance and strong fabric of lawsonite, the AVS of eclogites is estimated as ~11.7% in the case that lawsonite makes up ~75% of the rock mass. On this basis, we suggest that lawsonite in both blueschist and eclogite may play important roles in the formation of complex pattern of seismic anisotropy observed in NE Japan: weak trench-parallel anisotropy in the forearc basin domains and trench-normal anisotropy in the backarc region.

Occurrence of Unusual Quartz Xenocryst-Laden Dykes in the Chhota Udaipur Alkaline-Carbonatite Sub-province, Deccan Igneous Province, India

Occurrence of unusual basaltic dykes laden with a dense population of quartz xenocrysts within the Chhota Udaipur alkaline-carbonatitic sub-province of the Deccan Igneous Province is reported here. These dykes occur near Rorda (22°07.890 ' N; 74°04.267 ' E) and Samalavat (22°05.586 ' N; 74°07.261 ' E). The xenocrysts vary in size and shape and show effects of corrosion and partial assimilation by the host magma. These dykes have been affected by the carbonatitic fluids which commonly attack quartz xenocrysts, resulting in the formation of a complex growth pattern between quartz and carbonates. Mineralogical study confirms the presence of plagioclase, magnetite, ilmenite, rutile, chlorite, apatite, barytes and hydrated Fe-oxides. Original basaltic texture (sub-ophitic) and mineralogy (plagioclase, magnetite, ilmenite) is preserved, though pyroxenes are converted to chlorite; hematite, ilmenite, calcite and altered glassy material occur profusely in the groundmass. Basaltic dykes of such description have not so far been reported from the Deccan Igneous Province, although there are few references to the occurrence of quartz xenocrysts within basaltic dykes. It appears prima facie that quartzite xenoliths were selectively escalated by the basaltic magma at depth at the time of crustal extension leading to formation of Narmada rift; roughly coinciding with the emplacement of alkaline-carbonatite magma.

Oscillatory Turing Pattern Formation from the Interactions between Hopf and Turing Bifurcations

Coupled positive and negative feedback loops are not only a fundamental building block of more complex networks but also an object of engineered gene regulatory networks in synthetic biology. Here, we analyze a two-component reaction-diffusion system of coupled positive and negative feedback loops. By Hopf and Turing bifurcation analyses both identifying system parameter regions where spatial patterns emerge, we find that the interactions between the two kinds of bifurcation modes can lead to oscillatory Turing patterns, such as holes and stripes as well as their coexisting modes, whereas the pure Turing instability only can lead to paralleling stripes or hexagons. Our analysis indicates that the formation of complex patterns depends on the bifurcation types as well as the interactions among bifurcation modes.

APERIODIC TILING USING P SYSTEM

Tile Pasting P System is a computational model, based on the P System model, to generate two-dimensional tiling patterns using pasting rules at the edges of the regular polygons. Computational mechanism plays an important role in understanding the various complexities involved in the formation of complex patterns. In this paper we study the construction of non-periodic tiling patterns using corner tiles and aperiodic Wang tiles using the computational model Tile Pasting P System. We show that the Tile Pasting P System requires a minimum of four membranes to generate the non-periodic Wang tiling.

Elastocapillary coalescence of plates and pillars.

When a fluid-immersed array of supported plates or pillars is dried, evaporation leads to the formation of menisci on the tips of the plates or pillars that bring them together to form complex patterns. Building on prior experimental observations, we use a combination of theory and computation to understand the nature of this instability and its evolution in both the two- and three-dimensional setting of the problem. For the case of plates, we explicitly derive the interaction torques based on the relevant physical parameters associated with pillar deformation, contact-line pinning/depinning and fluid volume changes. A Bloch-wave analysis for our periodic mechanical system captures the window of volumes where the two-plate eigenvalue characterizes the onset of the coalescence instability. We then study the evolution of these binary clusters and their eventual elastic arrest using numerical simulations that account for evaporative dynamics coupled to capillary coalescence. This explains both the formation of hierarchical clusters and the sensitive dependence of the final structures on initial perturbations, as seen in our experiments. We then generalize our analysis to treat the problem of pillar collapse in three dimensions, where the fluid domain is completely connected and the interface is a minimal surface with the uniform mean curvature. Our theory and simulations capture the salient features of experimental observations in a range of different situations and may thus be useful in controlling the ensuing patterns.

G114 Phase Field法を用いた界面凝固不安定性における異方性の影響(OS-14:凝固・融解伝熱および結晶成長の新展開(1))

Phase field model is known to be very powerful in describing the complex pattern formation of the interface in non-equilibrium state, such as growth of dendritic crystals. In this study, the effects of anisotropy of the crystals on Mullins-Sekerka instability in growth of solid-liquid interface were investigated numerically. Given the sign curves at the solid-liquid interface in supercooled state, the growth of the interface was simulated using phase field model. The direction of the anisotropy of the crystals, the intensity of the anisotropy and the surface tension were varied as the parameters, and the conditions at which the amplitude of the curves increases were picked up.

Block Copolymer Assembly on Nanoscale Patterns of Polymer Brushes Formed by Electrohydrodynamic Jet Printing

Fundamental understanding of the self-assembly of domains in block copolymers (BCPs) and capabilities in control of these processes are important for their use as nanoscale templates in various applications. This paper focuses on the self-assembly of spin-cast and printed poly(styrene-block-methyl methacrylate) BCPs on patterned surface wetting layers formed by electrohydrodynamic jet printing of random copolymer brushes. Here, end-grafted brushes that present groups of styrene and methyl methacrylate in geometries with nanoscale resolution deterministically define the morphologies of BCP nanostructures. The materials and methods can also be integrated with lithographically defined templates for directed self-assembly of BCPs at multiple length scales. The results provide not only engineering routes to controlled formation of complex patterns but also vehicles for experimental and simulation studies of the effects of chemical transitions on the processes of self-assembly. In particular, we show that the methodology developed here provides the means to explore exotic phenomena displayed by the wetting behavior of BCPs, where 3-D soft confinement, chain elasticity, interfacial energies, and substrate's surface energy cooperate to yield nonclassical wetting behavior.

Two-Dimensional Pattern Formation Using Graphoepitaxy of PS-b-PMMA Block Copolymers for Advanced FinFET Device and Circuit Fabrication

Directed self-assembly (DSA) of lamellar phase block-co-polymers (BCPs) can be used to form nanoscale line-space patterns. However, exploiting the potential of this process for circuit relevant patterning continues to be a major challenge. In this work, we propose a way to impart two-dimensional pattern information in graphoepitaxy-based lamellar phase DSA processes by utilizing the interactions of the BCP with the template pattern. The image formation mechanism is explained through the use of Monte Carlo simulations. Circuit patterns consisting of the active region of Si FinFET transistors, referred to as Si "fins", were fabricated to demonstrate the applicability of this technique to the formation of complex patterns. The quality of the Si fin features produced by this process was validated by demonstrating the first functional DSA-patterned FinFET devices with 29 nm-pitch fins.

Designing modular reaction-diffusion programs for complex pattern formation

Cells use sophisticated, multiscale spatial patterns of chemical instructions to control cell fate and tissue growth. While some types of synthetic pattern formation have been well studied1-6, it remains unclear how to design chemical processes that can reproducibly create similar spatial patterns. Here we describe a scalable approach for the design of processes that generate such patterns, which can be implemented using synthetic DNA reaction-diffusion networks7,8. In our method, black-box modules are connected together into integrated programs for arbitrarily complex pattern formation. These programs can respond to input stimuli, process information, and ultimately produce stable output patterns that differ in size and concentration from their inputs. To build these programs, we break a target pattern into a set of patterning subtasks, design modules to perform these subtasks independently, and combine the modules into networks. We demonstrate in simulation how programs designed with our methodology can generate complex patterns, including a French flag and a stick figure.

Complex solitary wave dynamics, pattern formation and chaos in the gain–loss nonlinear Schrödinger equation

A numerical exploration of a gain–loss nonlinear Schrödinger equation was carried out utilizing over 180 000 core hours to conduct more than 10 000 unique simulations in an effort to characterize the model's six dimensional parameter space. The study treated the problem in full generality, spanning a minimum of eight orders of magnitude for each of three linear and nonlinear gain terms and five orders of magnitude for higher order nonlinearities. The gain–loss nonlinear Schrödinger equation is of interest as a model for spin wave envelopes in magnetic thin film active feedback rings and analogous driven damped nonlinear physical systems. Bright soliton trains were spontaneously driven out of equilibrium and behaviors stable for tens of thousands of round trip times were numerically identified. Nine distinct complex dynamical behaviors with lifetimes on the order of ms were isolated as part of six identified solution classes. Numerically located dynamical behaviors include: (i) low dimensional chaotic modulations of bright soliton trains; (ii) spatially symmetric/asymmetric interactions of solitary wave peaks; (iii) dynamical pattern formation and recurrence; (iv) steady state solutions; and (v) intermittency. Simulations exhibiting chaotically modulating bright soliton trains were found to qualitatively match previous experimental observations. Ten new dynamical behaviors, eight demonstrating long lifetimes, are predicted to be observable in future experiments.

How the chemotactic characteristics of bacteria can determine their population patterns

Spatial distribution of soil microorganisms is relevant for the functioning and performance of many ecosystem processes such as nutrient cycling or biodegradation of organic matters and contaminants. Beside the multitude of abiotic environmental factors controlling the distribution of microorganisms in soil systems, many microbial species exhibit chemotactic behavior by directing their movement along concentration gradients of nutrients or of chemoattractants produced by cells of their own kind. This chemotactic ability has been shown to promote the formation of complex distribution patterns even in the absence of environmental heterogeneities. Microbial population patterns in heterogeneous soil systems might be, hence, the result of the interplay between the heterogeneous environmental conditions and the microorganisms' intrinsic pattern formation capabilities.In this modeling study, we combined an individual-based modeling approach with a reactive pore-network model to investigate the formation of bacterial patterns in homogeneous and heterogeneous porous media. We investigated the influence of different bacterial chemotactic sensitivities (toward both substrate and bacteria) on bacterial distribution patterns. The emerging population patterns were classified with the support of a geostatistical approach, and the required conditions for the formation of any specific pattern were analyzed.Results showed that the chemotactic behavior of the bacteria leads to non-trivial population patterns even in the absence of environmental heterogeneities. The presence of structural pore scale heterogeneities had also an impact on bacterial distributions. For a range of chemotactic sensitivities, microorganisms tend to migrate preferably from larger pores toward smaller pores and the resulting distribution patterns thus resembled the heterogeneity of the pore space. The results clearly indicated that in a porous medium like soil the distribution of bacteria may not only be related to the external constraints but also to the chemotactic behavior of the bacterial cells.

Active suspensions and their nonlinear models

Abstract Active suspensions, such as suspensions of self-propelled microorganisms and related synthetic microswimmers, are known to undergo complex dynamics and pattern formation as a result of hydrodynamic interactions. In this review, we summarize recent efforts to model these systems using continuum kinetic theories. We first derive a basic kinetic model for a suspension of self-propelled rodlike particles and discuss its stability and nonlinear dynamics. We then present extensions of this model to analyze the effective rheology of active suspensions in external flows, the effect of steric interactions in concentrated systems, and the dynamics of chemotactically responsive suspensions in chemical fields.

Laser-induced fabrication of randomly distributed nanostructures in fused silica surfaces

The nanostructuring of dielectrics is a big challenge for laser patterning methods. In this study a novel laser structuring method for the fabrication of randomly distributed nanostructures, called laser-induced front side etching using in situ pre-structured metal layers (IPSM-LIFE), is presented. The pulsed laser irradiation of a thin metal film deposited onto a dielectric substrate with fluences below the ablation threshold results in the formation of randomly distributed metal structures by self-assembly processes. Further pulsed laser irradiation of these metal structures with higher or equal laser fluences causes the formation of complex patterns at the surface of the dielectric due to localized ablation and melting processes of the dielectric surface induced by the absorption of the laser energy by the metal structures and the local energy transfer into the dielectric surface.

Local control of protein binding and cell adhesion by patterned organic thin films

Control of the cell adhesion and growth on chemically patterned surfaces is important in an increasing number of applications in biotechnology and medicine, for example implants, in-vitro cellular assays, and biochips. This review covers patterning techniques for organic thin films suitable for site-directed guidance of cell adhesion to surfaces. Available surface patterning techniques are critically evaluated, with special emphasis on surface chemistry that can be switched in time and space during cultivation of cells. Examples from the authors' laboratory include the use of cell-repellent self-assembled monolayers (SAM) terminated by oligoethylene glycol (OEG) units and the lifting of the cell repellent properties by use of electrogenerated Br2/HOBr which can be performed with positionable microelectrodes. Structural changes of the SAM were analyzed by polarization-modulated infrared reflection absorption spectroscopy (PM IRRAS). Use of a soft array system of individually addressable microelectrodes enables formation of flexible and complex patterns in a short time and has the potential for further acceleration of probe-induced local manipulation of cell adhesion.

Structure Formation of Ultrathin PEO Films at Solid Interfaces—Complex Pattern Formation by Dewetting and Crystallization.

The direct contact of ultrathin polymer films with a solid substrate may result in thin film rupture caused by dewetting. With crystallisable polymers such as polyethyleneoxide (PEO), molecular self-assembly into partial ordered lamella structures is studied as an additional source of pattern formation. Morphological features in ultrathin PEO films (thickness < 10 nm) result from an interplay between dewetting patterns and diffusion limited growth pattern of ordered lamella growing within the dewetting areas. Besides structure formation of hydrophilic PEO molecules, n-alkylterminated (hydrophobic) PEO oligomers are investigated with respect to self-organization in ultrathin films. Morphological features characteristic for pure PEO are not changed by the presence of the n-alkylgroups.

Cracking the bioelectric code: Probing endogenous ionic controls of pattern formation

Patterns of resting potential in non-excitable cells of living tissue are now known to be instructive signals for pattern formation during embryogenesis, regeneration and cancer suppression. The development of molecular-level techniques for tracking ion flows and functionally manipulating the activity of ion channels and pumps has begun to reveal the mechanisms by which voltage gradients regulate cell behaviors and the assembly of complex large-scale structures. A recent paper demonstrated that a specific voltage range is necessary for demarcation of eye fields in the frog embryo. Remarkably, artificially setting other somatic cells to the eye-specific voltage range resulted in formation of eyes in aberrant locations, including tissues that are not in the normal anterior ectoderm lineage: eyes could be formed in the gut, on the tail, or in the lateral plate mesoderm. These data challenge the existing models of eye fate restriction and tissue competence maps, and suggest the presence of a bioelectric code—a mapping of physiological properties to anatomical outcomes. This Addendum summarizes the current state of knowledge in developmental bioelectricity, proposes three possible interpretations of the bioelectric code that functionally maps physiological states to anatomical outcomes, and highlights the biggest open questions in this field. We also suggest a speculative hypothesis at the intersection of cognitive science and developmental biology: that bioelectrical signaling among non-excitable cells coupled by gap junctions simulates neural network-like dynamics, and underlies the information processing functions required by complex pattern formation in vivo. Understanding and learning to control the information stored in physiological networks will have transformative implications for developmental biology, regenerative medicine and synthetic bioengineering.