Pattern Formation Research Articles

Periodic Stratification of Colloids in a Liquid Phase Produced by a Precipitation Reaction and Gel Swelling.

Pattern formation is a frequent phenomenon occurring in animate and inanimate systems. The interplay between the mass transport of the chemical species and the underlying chemical reaction networks generates most patterns in chemical systems. Periodic precipitation is an emblematic example of reaction-diffusion patterns, in which the process generates a spatial periodic structure in porous media. Here, we use the dormant reagent method to produce colloidal particles of Prussian blue (PB) and PB analogues at the liquid-gel interface. The generated particles produced a stable periodic stratification pattern in time in the liquid phase placed on top of the solid hydrogel. The phenomenon is governed by periodic swelling of the gel driven by the osmotic stress and stability of the formed particles. To illustrate the phenomenon, we developed an extended reaction-diffusion model, which incorporated the gel swelling and sedimentation effect of the formed colloids and could qualitatively reproduce the pattern formation in the liquid phase.

Coupling of Changing Trends in Population and Construction Land in Traditional Rural Areas and Spatial Patterns in Urban–Rural Development, 2016–2021: A Case Study of Heilongjiang Province, China

Achieving the goal of integrated urban–rural development is to achieve a spatially balanced development of the constituent elements of urban–rural relations in China. Rural populations and land dedicated to construction are the main components of the countryside in traditional agricultural areas; they play an important role in the development of the countryside itself in terms of urban and rural land use and in the formation of urban and rural development patterns. This study analyzes the spatial and temporal changes in rural populations and construction land at the township level, alongside assessing various forms and the extent of coupled development. Herein, we consider the role of urban–rural attractiveness and propose a framework for relationships between urban and rural development based on different forms of coupled development; a model of urban–rural forces is constructed to determine spatial patterns of urban–rural development at the township level that may transpire in the future. Our study shows that the rural population and construction land in the study area are characterized by significant spatial and temporal dynamics, indicating that traditional rural areas are in a process of rapid development and change. The results of our measurements of township-level coupling indicate that there exist four development patterns within urban–rural development: the A-type is most likely to produce new cities or satellite towns in the future and form new urban areas; the B-type is the area most likely to cease and be annexed to other villages or cities to meet building targets; the C-type comprises areas to be focused on in the future to attract populations and strictly control the growth of rural construction land areas (to avoid land transforming into the B-type); and the D-type refers to lands upon which regional township centers may develop in the future, becoming an area devoted to rural revitalization. The A-type and D-type are prioritized for the allocation of construction land, which can be contracted from types B and C. The results of this study have provided important reference for the formulation of population and construction land control policies in accordance with local conditions and the realization of integrated urban and rural development strategies.

Novel techniques to analyze dynamical properties of quantum chaos with peculiar evidence of hybrid systems confinement

Recent results demonstrate the dynamical peculiarities of the quantum chaos within the hybrid systems by chaotic parameters and probe the pattern formation under the influence of condensation. The complex dynamic behavior of the considered systems was determined with numerical simulation and presented an efficient technique that studied fractional systems comprising chaos-coherence fractions. The findings divulge the peculiar association between the coherence structure and the correlations at finite relative momenta. Thus the present study helps to explore the partially chaos hybrid systems in order to stimulate the experimental applications of nonlinear phenomena. The coherent-chaotic parameters can be measured by examining the chaos peculiarities that possess explicit relations with the condensations to demonstrate the environs of the physical systems. We investigate the influence of the multiplicities, chaos, momentum and temperature of the nonlinear system on the coherent-chaotic normalized correlations. The chaotic parameters are suppressed considerably with the coherence fraction and it appears numerically zero at maximum condensation and one at ideal chaos emissions. We procure that the meaningful parameters decrease significantly with the multiplicity of the nonlinear systems and increase with the momentum in the specified regimes. The identical multiplicity leads to contemplating the coherence and thus the normalized chaotic parameters within its spectacular influences exhibit significance worth contemplating in earnest. The findings underscore the significance of cogitating correlations in deciphering the nonlinear system characteristics and bestowing extraordinary perceptiveness into the convoluted essence of complex systems. The contemplated methodology can be applied to evaluating and analyzing the nonlinear systems and such an innovative approach computes the problems of celestial mechanics, heartbeats and chemical reactions in engineering and medical fields.

Gap junctions in Turing-type periodic feather pattern formation.

Periodic patterning requires coordinated cell-cell interactions at the tissue level. Turing showed, using mathematical modeling, how spatial patterns could arise from the reactions of a diffusive activator-inhibitor pair in an initially homogenous 2D field. Most activators and inhibitors studied in biological systems are proteins, and the roles of cell-cell interaction, ions, bioelectricity, etc. are only now being identified. Gap junctions (GJs) mediate direct exchanges of ions or small molecules between cells, enabling rapid long-distance communications in a cell collective. They are therefore good candidates for propagating nonprotein-based patterning signals that may act according to the Turing principles. Here, we explore the possible roles of GJs in Turing-type patterning using feather pattern formation as a model. We found 7 of the 12 investigated GJ isoforms are highly dynamically expressed in the developing chicken skin. In ovo functional perturbations of the GJ isoform, connexin 30, by siRNA and the dominant-negative mutant applied before placode development led to disrupted primary feather bud formation. Interestingly, inhibition of gap junctional intercellular communication (GJIC) in the ex vivo skin explant culture allowed the sequential emergence of new feather buds at specific spatial locations relative to the existing primary buds. The results suggest that GJIC may facilitate the propagation of long-distance inhibitory signals. Thus, inhibition of GJs may stimulate Turing-type periodic feather pattern formation during chick skin development, and the removal of GJ activity would enable the emergence of new feather buds if the local environment were competent and the threshold to form buds was reached. We further propose Turing-based computational simulations that can predict the sequential appearance of these ectopic buds. Our models demonstrate how a Turing activator-inhibitor system can continue to generate patterns in the competent morphogenetic field when the level of intercellular communication at the tissue scale is modulated.

Pattern Formation in Evaporating Polymer Solutions─Interplay between Dewetting and Decomposition

Pattern Formation in Evaporating Polymer Solutions─Interplay between Dewetting and Decomposition

Formation of convective roll patterns over a longitudinal throughflow in an active inhomogeneous porous medium with weak clogging

The convective stability of a plane-parallel longitudinal throughflow in a system consisting of two porous sublayers with distinct permeability is studied taking into account the weak pore clogging effect and given a finite difference in concentration between the upper and lower boundaries of the system. A system of differential equations for convection is derived within the framework of the continuum approach and the nonlinear MIM model. A linear stability analysis of the basic longitudinal flow is carried out. The boundary value problem is solved using the numerical technique for constructing a fundamental system of solutions. The neutral stability curves of the basic flow with respect to the disturbances in the form of rolls with different wavelength are obtained. For the absence of pore clogging, the convective stability maps of the critical solutal Rayleigh-Darcy number versus the permeability ratio for the initial uncontaminated sublayers, as well as the plots of the critical disturbance frequency and wave number versus the permeability ratio for some values of the Peclet number, are constructed. It is shown that these results have symmetry with respect to the solution for equal initial permeability of sublayers. The clogging effect associated with the solute adsorption and desorption in a porous medium is studied in the two-layered systems with the values 0.1 and 10 of the ratio of initial permeabilities of the sublayers; convection localization occurs in distinct sublayers. It was found that clogging increases the stability of the longitudinal basic flow relative to solutal inhomogeneity and breaks the symmetry of solutions with respect to the case when the two-layered system is reduced to a single layer with the same filtration properties of the porous medium throughout its volume. The influence of sorption effects on the critical parameters of oscillatory convection is investigated by plotting the critical solutal Rayleigh-Darcy number, disturbance frequency and wave number against the adsorption coefficient at fixed values of the desorption coefficient. The isolines of the stream function are constructed to analyze convective flow patterns. It was established that there is a weak relationship between the typical size of local convective roll patterns and the clogging parameters. It is shown that the sorption processes, which can lead to clogging, have a significant impact on the velocity of convective rolls moving along the two-layered system at a slight variation in their sizes.

Optical soliton solutions in a distinctive class of nonlinear Schrödinger’s equation with cubic, quintic, septic, and nonic nonlinearities

The Biswas–Mollivic equation is a special type of nonlinear Schrödinger equation, which explains the spatio-temporal behaviour of excitable media. In this paper, we investigate the optical soliton solutions of the Biswas–Mollivic equation with cubic–quintic–septic–nonic nonlinearities using the generalized Riccati equation mapping method. This method is efficient and provides new perspectives. It also provides novel insights into the dynamics of excitable media. Our findings add to a better understanding of the complex spatio-temporal patterns that develop in excitable media and have potential applications in the design of new technologies for controlling and manipulating pattern formation. To depict optical soliton solutions graphically, we use the MATLAB software.

Pattern formation in charge density wave states after a quantum quench

Pattern formation in charge density wave states after a quantum quench

Nonstandard Nearly Exact Analysis of the FitzHugh–Nagumo Model

The FitzHugh–Nagumo model has been used empirically to model certain types of neuronal activities. It is also a non-linear dynamical system applicable to chemical kinetics, population dynamics, epidemiology and pattern formation. In the literature, many approaches have been proposed to study its dynamics. In this paper, initially, we have employed cutting-edge tools from discrete dynamics for discretization and fixed points. It has been proven that an exact discrete scheme exists for this paradigm. This project also considers the phase space and integral surfaces of these evolutionary equations. In addition, it carries out a thorough symmetry analysis of this reaction diffusion system to find equivalent systems. Moreover, steady-state solutions are obtained using ansatzes for traveling wave solutions. The existence of infinite traveling wave solutions has also been proven. Yet again, this investigation establishes the potential of symmetry methods to unravel non-linearity. Finally, singular perturbation theory has been employed to obtain analytical approximations and to study stability in different parameter regimes.

Gradient elasticity in Swift–Hohenberg and phase-field crystal models

The Swift–Hohenberg (SH) and phase-field crystal (PFC) models are minimal yet powerful approaches for studying phenomena such as pattern formation, collective order, and defects via smooth order parameters. They are based on a free-energy functional that inherently includes elasticity effects. This study addresses how gradient elasticity (GE), a theory that accounts for elasticity effects at microscopic scales by introducing additional characteristic lengths, is incorporated into SH and PFC models. After presenting the fundamentals of these theories and models, we first calculate the characteristic lengths for various lattice symmetries in an approximated setting. We then discuss numerical simulations of stress fields at dislocations and comparisons with analytic solutions within first and second strain-gradient elasticity. Effective GE characteristic lengths for the elastic fields induced by dislocations are found to depend on the free-energy parameters in the same manner as the phase correlation length, thus unveiling how they change with the quenching depth. The findings presented in this study enable a thorough discussion and analysis of small-scale elasticity effects in pattern formation and crystalline systems using SH and PFC models and, importantly, complete the elasticity analysis therein. Additionally, we provide a microscopic foundation for GE in the context of order-disorder phase transitions.

Nonequilibrium dynamics of two-component Bose gas with tunable Rydberg interactions: From ring dark soliton to self-structured pattern formation

We explore the nonequilibrium dynamics of ring dark solitons in a two-dimensional binary Bose–Einstein condensate with tunable Rydberg interactions by numerical simulation of the time-dependent Gross–Pitaevskii equation. Our results show that both the vortex dynamics and self-structured pattern formation show strong dependence on the periodic modulation of Rydberg interactions. For the cases without periodic modulation of the interactions, or the periodic modulation part is almost equal to the fixed part, the system exhibits exotic vortex dynamics without self-structured pattern formation. Finally, the effect of periodically varying Rydberg interactions on the lifetime of ring dark soliton is also considered.

Lane formation in an active particle model with chirality for pedestrian traffic

We analyze the pattern formation in systems of active particles with chiral forces in the context of pedestrian dynamics. To describe the interparticle interactions, we use the standard social force model and supplement it with a new type of force that reflects chirality. We perform numerical simulations of two pedestrian flows moving in opposite directions along a corridor. We observe two dynamic phase transitions that occur for varying number densities of particles and strengths of the chirality force: one from disordered motion to multi-lane motion and another from multi-lane to two-lane motion. We develop a qualitative theory that describes the demarcation lines for these phase transitions in the phase diagram chirality-density. The results of our analysis agree fairly well with the simulation data. A comparison with previously reported experimental data has been provided. Our findings may find applications in urban and transportation-planning problems.

Development of Micro/Nano Pattern Arrays with Grating-Based Periodic Structures using the Direct Laser Lithography System

Introduction: This research delves into utilizing the Direct Laser Lithography System to produce micro/nanopattern arrays with grating-based periodic structures. Initially, refining the variation in periodic structures within these arrays becomes a pivotal pursuit. This demands a deep comprehension of how structural variation aligns with specific applications, particularly in photonics and material science. Method: Advancements in hardware, software, or process optimization techniques hold potential for reaching this objective. Using an optical beam, this system enables the engraving of moderate periodic and quasi-periodic structures, enhancing pattern formation in a three-dimensional environment. Through cost-effective direct-beam interferometry systems utilizing 405 nm GaN and 290 to 780 nm AlInGaN semiconductor laser diodes, patterns ranging from in period were created, employing 300 nm gratings. Result: The system's cost-efficiency and ability to achieve high-resolution permit the creation of both regular and irregular grating designs. By employing an optical head assembly from a bluray disc recorder, housing a semiconductor laser diode and an objective lens with an NA of 0.85, this system displays promising potential in progressing the fabrication of micro/nanopattern arrays. Conclusion: Assessing their optical, mechanical, and electrical properties and exploring potential applications across varied fields like optoelectronics, photovoltaics, sensors, and biomedical devices represent critical strides for further exploration and advancement.

INFLUENCE OF SILK ROAD CULTURE ON MODERN DESIGN: ARTISTIC FEATURES OF CHINESE BROCADE PATTERNS

Goal: this study aims to analyze the influence of Silk Road culture on the style of brocade patterns in the Tang and Ming Dynasties of China, as well as to consider the practices of using brocade motifs of ancient dynasties in modern design. Methodology: based on the research of scientific literature, this article compares and analyses the stylistic characteristics of brocade patterns: connected beads, curly grass, treasure and cloud; the analysis makes it possible to trace the process of formation and evolution of brocade patterns in the Tang Dynasty. The methods of figurative and stylistic, formal analysis, methods of systematisation, and processing of results are also involved. Results. The study pointed out that the opening of the Silk Road promoted cultural exchanges between East and West, and the prosperity of politics, economy, and culture in the Tang Dynasty promoted the diversity and development of patterns. The above-mentioned motives, through integration with foreign cultures, formed symmetrical beauty, curvilinear beauty, and symbolic characteristics of Tang Dynasty patterns. In the example of the creativity of the modern Chinese designer Chen Liwen, the transformation of the motif «Tiger Sniffs the Rose» and the image of the Chinese tiger of the Ming Dynasty period in the development of modern design products is shown. Scientific novelty. This article reveals the historical evolution of the popular brocade patterns in the Tang and Ming Dynasties of China, summarizes his unique artistic style, and provides inspiration for contemporary clothing innovation design. Practical significance. The significance of this study lies in providing historical data for the integration of ethnic cultures and demonstrating the overall characteristics and evolution process of the Tang and Ming Dynasties patterns.

Trend and interannual variability of summer marine heatwaves in the tropical Indian ocean: Patterns, mixed layer heat budget, and seasonal prediction

Marine heatwaves (MHWs) are extreme sea surface temperature (SST) events in all ocean basins, with far-reaching impacts on marine ecosystems and socio-economy. The leading patterns, trend, and interannual variability of summer MHWs in the tropical Indian Ocean (TIO) are investigated in this study. The first empirical orthogonal function (EOF) mode of frequency of MHWs exhibits a monopole pattern over the entire basin. This mode is highly associated with the concurrent Indian Ocean Basin warming, indicating a remarkable trend over the past four decades. The linear trend in MHW properties largely relates to increased summer Indian Ocean mean SST. The second EOF mode exhibits a zonal dipole with the MHW numbers increasing in the west and decreasing in the east. On the interannual timescale, the first two EOF modes are remotely affected by antecedent and concurrent El Niño events, respectively. The ocean mixed layer budget is utilized for examining the formation of different summer MHW patterns. During the preceding spring, the surface heat flux is important for the development of MHWs, while the ocean advections play a secondary role in the South Indian Ocean for the MHW monopole. Once the SST anomaly rises in summer, the ocean advections play a dominant role in maintaining the SST. Last, we assess the prediction skill of summer TIO MHWs by performing a bilinear seasonal statistical prediction model. Our results suggest the frequency of summer MHWs in the TIO could be predicted one season in advance. This study has great implications for understanding and predicting ocean extreme events in the TIO.

Phase Pattern Formation in Grain Boundaries.

In this Letter we derive conditions that predict the existence of two-phase periodic-pattern grain boundary structures that are stable against coarsening. While previous research has established that elastic effects can lead to phase pattern formation on crystal surfaces, the possibility of stable grain boundary structures composed of alternating grain boundary phases has not been previously analyzed. Our theory identifies the specific combination of grain boundary and materials properties that enable the emergence of patterned grain boundary states and shows that the dislocation content of grain boundary phase junctions, absent in surface phenomena, weakens the stability of the patterned structures. The predictions of the theory are tested using a model copper grain boundary that exhibits multiple phases and two-phase pattern formation. We discuss how, similarly to surfaces, elastic effects associated with grain boundary phase junctions have profound implications for how grain boundary phases transform.

Underlying catastrophes: umbilics and pattern formation

AbstractBifurcation theory provides a very general means to classify the local changes in numbers of zeros of vector fields, but not a general means to find where a given bifurcation occurs, at least at higher codimensions. Instead, it turns out, these bifurcations can be found by looking for their underlying catastrophes. Here I show that the concept of underlying catastrophes can be extended to the umbilics. The umbilics are important in opening up qualitatively different forms of bifurcations beyond the ‘corank 1’ catastrophes of folds, cusps, swallowtails, etc. An example is given showing how four zeros of a vector field bifurcating from a single point, may do so either via a 3-parameter swallowtail catastrophe involving equilibria of similar stabilities, or via a 4-parameter umbilic catastrophe involving equilibria of opposing stabilities. This opens an avenue to studying spatiotemporal pattern formation around high codimension bifurcation points, and I conclude with some illustrative examples.

A Sharp Interface Limit of a Nonlocal Variational Model for Pattern Formation in Biomembranes

A Sharp Interface Limit of a Nonlocal Variational Model for Pattern Formation in Biomembranes

Pattern formation and delay-induced instability in a Leslie–Gower type prey–predator system with Smith growth function

In this article, we have investigated the spatiotemporal dynamics and delay-induced instability of a Leslie–Gower type prey–predator model under the influence of environmental toxicants with Smith growth function. This growth function is more realistic than logistic growth as it better describes the growth of the biological population. It has been used where the growth limitations are based on the proportion of available resources not utilized. A few works of Smith’s growth models are reported in the literature. Therefore, spatiotemporal dynamics and pattern formation with delay effect remain an exciting area of research, which motivates the present work. This work has studied two types of dynamical systems: (i) an ordinary differential temporal system with time delay and (ii) a reaction–diffusion system with time delay. The existence of equilibrium points and their stability conditions are discussed. Hopf bifurcation emerges in both proposed systems with respect to delay parameter. The stability and direction of Hopf bifurcation and delay-diffusion-driven instability have been investigated for the reaction–diffusion system. Numerical simulation is performed to support the analytical results and theorems. Moreover, the existence of Hopf and delay-induced instability are proved numerically. Interesting one-dimensional regular and irregular stripe patterns are obtained for increased values of the time delay parameter. Also, the presence of natural toxicants has a negative impact on the growth of prey–predator species.

Interview with Surendra Ghaskadbi – President of the Indian Society of Cell Biology

ABSTRACT Surendra Ghaskadbi is a cell and developmental biologist who held the positions of Senior and Emeritus Scientist at the MACS–Agharkar Research Institute in Pune, India. His lab has been particularly interested in cell signalling and pattern formation during early development, focusing on using Hydra as a research organism. More recently, Surendra has played a role in teaching and outreach in India, and he is also the current President of the Indian Society of Cell Biology. We chatted to him to find out more about his career, his advice for junior researchers and his role as society President.