Stripe Pattern Formation Research Articles

Formation of periodic size-segregated stripe pattern via directed self-assembly of binary colloids and its mechanism

Convective self-assembly, well known for producing highly ordered monolayer structures, has been used in this study to create novel surface patterns using the binary mixture of colloids. We demonstrate that different patterns form, based on the size ratio (Small/Large) of the particles, and particles volume ratio. Surprisingly, certain binary particle mixtures resulted in spontaneous size based segregation. In some cases, the particle separation occurred along the direction of the meniscus contact line, and by the mere design of the process, we created periodic stripe patterns with controlled width. The particle volume fraction, size differences, surface tension, and the curvature of the meniscus played a crucial factor in the segregation process as well as in determining the width of each of the stripes. Furthermore, based on both empirical and numerical analysis, a mechanism for size-based segregation of particles via directed self-assembly is proposed.

Developmental mechanisms of longitudinal stripes in the Japanese four‐lined snake

The developmental mechanisms of color patterns formation and its evolution remain unclear in reptilian sauropsids. We, therefore, studied the pigment cell mechanisms of stripe pattern formation during embryonic development of the snake Elaphe quadrivirgata. We identified 10 post-ovipositional embryonic developmental stages based on external morphological characteristics. Examination for the temporal changes in differentiation, distribution, and density of pigment cells during embryonic development revealed that melanophores first appeared in myotome and body cavity but not in skin surface at Stage 5. Epidermal melanophores were first recognized at Stage 7, and dermal melanophores and iridophores appeared in Stage 9. Stripe pattern first appeared to establish at Stage 8 as a spatial density gradient of epidermal melanophores between the regions of future dark brown longitudinal stripes and light colored background. Our study, thus, provides a comprehensive pigment-cell-based understanding of stripe pattern formation during embryonic development. We briefly discuss the importance of the gene expression studies by considering the biologically relevant theoretical models with standard developmental staging for understanding reptilian color pattern evolution.

Toll ligand Spätzle3 controls melanization in the stripe pattern formation in caterpillars

A stripe pattern is an aposematic or camouflage coloration often observed among various caterpillars. However, how this ecologically important pattern is formed is largely unknown. The silkworm dominant mutant Zebra (Ze) has a black stripe in the anterior margin of each dorsal segment. Here, fine linkage mapping of 3,135 larvae revealed a 63-kbp region responsible for the Ze locus, which contained three candidate genes, including the Toll ligand gene spätzle3 (spz-3). Both electroporation-mediated ectopic expression and RNAi analyses showed that, among candidate genes, only processed spz-3 induced melanin pigmentation and that Toll-8 was the candidate receptor gene of spz-3 This Toll ligand/receptor set is also involved in melanization of other mutant Striped (pS ), which has broader stripes. Additional knockdown of 5 other spz family and 10 Toll-related genes caused no drastic change in the pigmentation of either mutant, suggesting that only spz-3/Toll-8 is mainly involved in the melanization process rather than pattern formation. The downstream pigmentation gene yellow was specifically up-regulated in the striped region of the Ze mutant, but spz-3 showed no such region-specific expression. Toll signaling pathways are known to be involved in innate immunity, dorsoventral axis formation, and neurotrophic functions. This study provides direct evidence that a Toll signaling pathway is co-opted to control the melanization process and adaptive striped pattern formation in caterpillars.

Effects of signal-dependent motilities in a Keller–Segel-type reaction–diffusion system

This work considers the Keller–Segel-type parabolic system [Formula: see text] in a smoothly bounded convex domain [Formula: see text], [Formula: see text], under no-flux boundary conditions, which has recently been proposed as a model for processes of stripe pattern formation via so-called “self-trapping” mechanisms. In the two-dimensional case, in stark contrast to the classical Keller–Segel model in which large-data solutions may blow up in finite time, for all suitably regular initial data the associated initial value problem is seen to possess a globally-defined bounded classical solution, provided that the motility function [Formula: see text] is uniformly positive. In the corresponding higher-dimensional setting, it is shown that certain weak solutions exist globally, where in the particular three-dimensional case this solution actually is bounded and classical if the initial data are suitably small in the norm of [Formula: see text]. Finally, if still [Formula: see text] but merely the physically interpretable quantity [Formula: see text] is appropriately small, then the above-weak solutions are proved to become eventually smooth and bounded.

Vegetation pattern formation of a water-biomass model

In this paper, a mathematical model with diffusion and cross-diffusion is proposed to describe the interaction between the vegetation and the soil water. Based on the view of Turing pattern, we discuss the conditions of the diffusion-induced instability and the cross-diffusion-induced instability of a homogenous uniform steady state. We find that either a fast diffusion speed of water or a great hydraulic diffusivity due to the suction of roots may drive the instability of the homogenous steady state. Furthermore, we find that both the rain-fall rate and the infiltration feedback parameter can induce the transitions among the vegetation state, pattern formation and bare soil state. It is also found that the “terrain slope” may cause the instability of the homogenous steady state and drive the formation of periodic stripe pattern. Consequently, the diversity of dryland vegetation in reality can be explained as a result of pattern solutions of the model.

Pigment cell mechanism of postembryonic stripe pattern formation in the Japanese four-lined snake.

Postembryonic changes in the dermal and epidermal pigment cell architecture of the striped and nonstriped morph of the Japanese four-lined snake Elaphe quadrivirgata were examined to reveal stripe pattern formation after hatching. The striped and nonstriped morphs were distinguishable at the hatching, suggesting that the basis of stripe pattern was formed during embryonic development. In the striped morph, the color of stripes changed from red-brown in juveniles to vivid dark-brown in adults, and density of dermal melanophore increased much more in the stripe than background dorsal scales with growth. This increase in density of dermal melanophore was accompanied not only by the increased epidermal melanophore density but also by the change in vertical structures of dermal melanophore. By contrast, the density of epidermal and dermal melanophore evenly increased over the dorsal scales in the nonstriped morph. Thus, the increased vividness of the stripe pattern after hatching is achieved through localized increase of melanophore density particularly in the stripe region but not over the whole dorsal scales.

Modelling stripe formation in zebrafish: an agent-based approach.

Zebrafish have distinctive black stripes and yellow interstripes that form owing to the interaction of different pigment cells. We present a two-population agent-based model for the development and regeneration of these stripes and interstripes informed by recent experimental results. Our model describes stripe pattern formation, laser ablation and mutations. We find that fish growth shortens the necessary scale for long-range interactions and that iridophores, a third type of pigment cell, help align stripes and interstripes.

In situ observation of meniscus shape deformation with colloidal stripe pattern formation in convective self-assembly.

Vertical convective self-assembly is capable of fabricating stripe-patterned structures of colloidal particles with well-ordered periodicity. To unveil the mechanism of the stripe pattern formation, in the present study, we focus on the meniscus shape and conduct in situ observations of shape deformation associated with particulate line evolution. The results reveal that the meniscus is elongated downward in a concave fashion toward the substrate in accordance with solvent evaporation, while the concave deformation is accelerated by solvent flow, resulting in the rupture of the liquid film at the thinnest point of the meniscus. The meniscus rupture triggers the meniscus to slide off from the particulate line, followed by the propagation of the sliding motion of the three-phase contact line, resulting in the formation of stripe spacing.

A method to evaluate explosive crystallization velocity of amorphous silicon films during flash lamp annealing

Flash lamp annealing (FLA) of micrometre-order thick amorphous silicon (a-Si) films can induce explosive crystallization (EC), high-speed lateral crystallization driven by the release of latent heat. We develop multipulse FLA system, which emits a quasi-millisecond pulse consisting of a number of subpulses. The emission frequency of the subpulses can be systematically controlled, and the emission of subpulses leads to the periodic modulation of the temperature of a Si film and the resulting formation of macroscopic stripe patterns. The relationship between a subpulse emission frequency and the width of the macroscopic stripe patterns yields EC velocity. Two kinds of EC modes can be observed, depending on the methods of precursor a-Si deposition and (or) a-Si film thickness.

Endothelin signalling in iridophore development and stripe pattern formation of zebrafish.

ABSTRACTColour patterns of adult fish are composed of several different types of pigment cells distributing in the skin during juvenile development. The zebrafish, Danio rerio, displays a striking pattern of dark stripes of melanophores interspersed with light stripes of xanthophores. A third cell type, silvery iridophores, contributes to both stripes and plays a crucial role in adult pigment pattern formation. Several mutants deficient in iridophore development display similar adult phenotypes with reduced numbers of melanophores and defects in stripe formation. This indicates a supporting role of iridophores for melanophore development and maintenance. One of these mutants, rose (rse), encodes the Endothelin receptor b1a. Here we describe a new mutant in zebrafish, karneol (kar), which has a phenotype similar to weak alleles of rse with a reduction in iridophore numbers and defects of adult pigment patterning. We show that, unlike rse, kar is not required in iridophores. The gene defective in the kar mutant codes for an endothelin-converting enzyme, Ece2, which activates endothelin ligands by proteolytic cleavage. By morpholino-mediated knockdown, we identify Endothelin 3b (Edn3b) as the ligand for endothelin receptor signalling in larval iridophores. Thus, Endothelin signalling is involved in iridophore development, proliferation and stripe morphogenesis in larvae as well as adult zebrafish. In mammals the pathway is required for melanocyte development; therefore, our results indicate a previously unrecognized close evolutionary relationship between iridophores in zebrafish and melanocytes in mammals.

Magnetic control of flexoelectric domains in a nematic fluid.

The formation of flexoelectric stripe patterns (flexodomains) was studied under the influence of external electric and magnetic fields in a nematic liquid crystal. The critical voltage and wavevector of flexodomains were investigated in different geometries by both experiments and simulations. It is demonstrated that upon altering the orientation of the magnetic field with respect to the director, the critical voltage and wavenumber behave substantially differently. In the geometry of the twist Freedericksz transition, a non-monotonic behavior as a function of the magnetic field was found.

Scaling law and mechanism for the formation of stripe patterns in a binary mixture of granular materials under horizontal vibration

In this study, we performed experimental studies on the formation of stripe patterns in a granular mixture under horizontal vibration. The granular mixture was prepared by mixing brass and glass beads of 1 mm in diameter in the ratio of 1:2 by volume and immersing them in a liquid. The mixture becomes separated into glass-only and brass-only bands of random sizes. The number of bands is an increasing function of \(\Gamma \times \sqrt {\operatorname{Re} } \) only (Γ: acceleration relative to gravity; Re: Reynolds number based on the particle diameter). As the mechanism of stripe formation, the formation of clusters in the mixture due to local fluctuations and strong hydrodynamic interactions between particles is proposed. The initial-condition dependency also supports the cluster formation mechanism rather than the Kelvin-Helmholtz-like hydrodynamic instability.

Synthetic biology: a new approach to study biological pattern formation

The principles and molecular mechanisms underlying biological pattern formation are difficult to elucidate in most cases due to the overwhelming physiologic complexity associated with the natural context. The understanding of a particular mechanism, not to speak of underlying universal principles, is difficult due to the diversity and uncertainty of the biological systems. Although current genetic and biochemical approaches have greatly advanced our understanding of pattern formation, the progress mainly relies on experimental phenotypes obtained from time‐consuming studies of gain or loss of function mutants. It is prevailingly considered that synthetic biology will come to the application age, but more importantly synthetic biology can be used to understand the life. Using periodic stripe pattern formation as a paradigm, we discuss how to apply synthetic biology in understanding biological pattern formation and hereafter foster the applications like tissue engineering.

Pigment cell mechanisms underlying dorsal color-pattern polymorphism in the japanese four-lined snake

To provide histological foundation for studying the genetic mechanisms of color-pattern polymorphisms, we examined light reflectance profiles and cellular architectures of pigment cells that produced striped, nonstriped, and melanistic color patterns in the snake Elaphe quadrivirgata. Both, striped and nonstriped morphs, possessed the same set of epidermal melanophores and three types of dermal pigment cells (yellow xanthophores, iridescent iridophores, and black melanophores), but spatial variations in the densities of epidermal and dermal melanophores produced individual variations in stripe vividness. The densities of epidermal and dermal melanophores were two or three times higher in the dark-brown-stripe region than in the yellow background in the striped morph. However, the densities of epidermal and dermal melanophores between the striped and background regions were similar in the nonstriped morph. The melanistic morph had only epidermal and dermal melanophores and neither xanthophores nor iridophores were detected. Ghost stripes in the shed skin of some melanistic morphs suggested that stripe pattern formation and melanism were controlled independently. We proposed complete- and incomplete-dominance heredity models for the stripe-melanistic variation and striped, pale-striped, and nonstriped polymorphisms, respectively, according to the differences in pigment-cell composition and its spatial architecture.

Stochastic Resonance in Superconducting Nb Film with Periodic Array of Holes

Stochastic fluxon dynamics and spatial ordering are studied in a superconducting Nb film patterned with a periodic (3×3 micron) square array of holes. First, imaging of the film is performed using Scanning Hall Probe Microscope following application of the random noise magnetic drive. We observe formation of the fluxon stripe patterns oriented preferentially along the principal axes of the array. Next, ac magnetic field is applied as superposition of harmonic and random noise components and the local magnetic response is probed with the micron-sized Hall sensor at a single array site. We find that hopping of the fluxons becomes synchronized with the harmonic driving at certain amplitude of the random noise; the latter is found to be dependent upon the harmonic drive frequency. We attribute our observations to the phenomenon of stochastic resonance that is ubiquitous in non-linear multi-level systems with dynamic threshold and discuss a possibility of flux manipulation using stochastically-resonant periodic driving.

Investigation of Colloidal Stripe Formation Mechanism by In-situ Analysis of Meniscus Shape in Convective Self-assembly Process

Convective self-assembly technique is of growing importance as a robust technique to arrange various colloidal particles without any templates. Here we focus on stripe pattern formation by the convective self-assembly technique. To unveil the mechanism of the stripe formation process, we employed an in-situ observation of the variation of meniscus shape during the particle assembly process. The observation revealed a following new stripe formation mechanism, which is different from the "depinning" model. A meniscus is elongated downward to be concave toward a substrate as the solvent evaporation progresses. The convective flow toward the meniscus tip accelerates the deformation of the meniscus, resulting in the rupture of liquid film at the thinnest point of the meniscus.

Formation of Stripe Patterns in Charged Colloids during Unidirectional Crystallization in the Presence of Impurity Particles

Abstract We examine the spatial distributions of fluorescent-labeled polystyrene (PS) particles added to colloidal silica that resulted after unidirectional crystal growth due to diffusion of pyridine. We find that the PS particles are arranged in a stripe pattern with a submillimeter-sized spacing. The patterning mechanism is attributable to the formation of lamella-shaped crystal grains and exclusion of the PS particles to the crystal grain boundaries.

Substrate-mediated pattern formation in monolayer transfer: a reduced model

The formation of regular stripe patterns during the transfer of surfactant monolayers from water surfaces onto moving solid substrates can be understood as a phase decomposition process under the influence of the effective molecular interaction between the substrate and the monolayer, also called substrate-mediated condensation (SMC). To describe this phenomenon, we propose a reduced model based on an amended Cahn–Hilliard equation. A combination of numerical simulations and continuation methods is employed to investigate stationary and time-periodic solutions of the model and to determine the resulting bifurcation diagram. The onset of spatiotemporal pattern formation is found to result from a homoclinic and a Hopf bifurcation at small and large substrate speeds, respectively. The critical velocity corresponding to the Hopf bifurcation can be calculated by means of the marginal stability criterion for pattern formation behind propagating fronts. In the regime of low transfer velocities, the stationary solutions exhibit snaking behavior.

Experimental investigation on the formation of stripe pattern in flowing argon discharge system

Stable stripe pattern is observed in flowing argon at atmospheric pressure by using a dielectric barrier discharge device with two transparent water electrodes. Based on the photography and the electrical measurement, the formation mechanism of stripe is investigated. Results show that a stripe pattern can be obtained at a lower peak value of the applied voltage in flowing argon, and the discharge turns homogeneous at a higher voltage. Results show that the formation of stripe pattern results from the movement of discharge filament in the direction of gas flow. The moving velocity of filaments almost keeps constant during the voltage varying. However, the moving velocity increases with the increase of gas flow rate. The memory effect of active particles in the discharge space is very important for the formation of stripe pattern. Furthermore, the electric characteristics of discharge are studied in flowing gas in this paper. It is found that both the discharge current and the gas inception voltage decrease with the increase of the gas flow rate. A qualitative explanation is given for this experimental phenomenon. These results are of great importance for the research of pattern formation dynamics and industrial applications of dielectric barrier discharge.

Mean-Field Pairing Theory for the Charge-Stripe Phase of High-Temperature Cuprate Superconductors

Striped high-T(c) superconductors such as La(2-y-x)Nd(y)Sr(x)CuO(4) and La(2-x)Ba(x)CuO(4) near x = 1/8 show a fascinating competition between spin and charge order and superconductivity. A theory for these systems therefore has to capture both the spin correlations of an antiferromagnet and the pair correlations of a superconductor. For this purpose we present here an effective Hartree-Fock theory incorporating both electron pairing with finite center-of-mass momentum and antiferromagnetism. We show that this theory reproduces the key experimental features such as the formation of the antiferromagnetic stripe patterns at 7/8 band filling or the quasi-one-dimensional electronic structure observed by photoemission spectroscopy.