Pattern Formation Research Articles

Drone direction estimation: phase method with two-channel direction finder

This scientific article presents a block diagram of a two-channel radio direction finder that effectively uses the phase method to determine the direction of the signal source. The main attention is paid to the mathematical model of the formation of the cardioid radiation pattern of biconical antennas, which have unique directivity characteristics. These features significantly affect the accuracy and reliability of the bearing determination process. The developed algorithm aims to accurately determine the direction of motion of an unmanned aerial vehicle, especially in the context of a two-channel radio receiver and a five-element antenna system. This antenna system provides unique capabilities for increased resolution and directional accuracy. The article also touches on the issue of software implementation of the developed algorithm, which is aimed at increasing the number of generated bearing estimates in conditions of limited time for observing an unmanned aerial vehicle. Thus, the proposed method is of interest in the field of precision direction finding in the context of small unmanned vehicles.

Balanced clustering for student admission school zoning by parameter tuning of constrained k-means

The Indonesian government issued a regulation through the Ministry of Education and Culture, number 51 of 2018, which contains zoning rules to improve the quality of education in school educational institutions. This research aims to compare the performance of the k-means algorithm with the constrained k-means algorithm to model the zoning of each school area based on the shortest distance parameter between the school location and the domicile of prospective students. The study used data from 2248 prospective students and 22 public school locations. The results of testing the k-means algorithm in grouping showed the formation of non-circular patterns in the cluster membership with different numbers of centroid cluster members. In contrast, testing the constrained k-means algorithm showed balanced outcomes in cluster membership with a membership value of 103 for each school as the cluster center. The research findings state that the developed constrained k-means algorithm solves the problem of unbalanced data clustering and overlapping issues in the process of new student admissions. In other words, the constrained k-means algorithm can be a reference for the government in making decisions on new student admissions

Local Discontinuous Galerkin Methods with Decoupled Implicit-Explicit Time Marching for the Growth-Mediated Autochemotactic Pattern Formation Model

Local Discontinuous Galerkin Methods with Decoupled Implicit-Explicit Time Marching for the Growth-Mediated Autochemotactic Pattern Formation Model

Emergence of Diverse Epidermal Patterns via the Integration of the Turing Pattern Model with the Majority Voting Model

Animal skin patterns are increasingly explained using the Turing pattern model proposed by Alan Turing. The Turing model, a self-organizing model, can produce spotted or striped patterns. However, several animal patterns exist that do not correspond to these patterns. For example, the body patterns of the ornamental carp Nishiki goi produced in Japan vary randomly among individuals. Therefore, predicting the pattern of offspring is difficult based on the parent fish. Such a randomly formed pattern could be explained using a majority voting model. This model is a type of cellular automaton model that counts the surrounding states and transitions to high-number states. Nevertheless, the utility of these two models in explaining fish patterns remains unclear. Interestingly, the patterns generated by these two models can be detected among very closely related species. It is difficult to think that completely different epidermal formation mechanisms are used among species of the same family. Therefore, there may be a basic model that can produce both patterns. Herein, the Turing pattern and majority voting method are represented using cellular automata, and the possibility of integrating these two methods is examined. This integrated model is equivalent to both models when the parameters are adjusted. Although this integrated model is extremely simple, it can produce more varied patterns than either one of the individual models. However, further research is warranted to determine whether this model is consistent with the mechanisms involved in the formation of animal fish patterns from a biological perspective.

Anti-Vasculogenic, Antioxidant, and Anti-Inflammatory Activities of Sulfated Polysaccharide Derived from Codium tomentosum: Pharmacokinetic Assay

The purpose of this paper was to investigate the anti-inflammatory and anti-angiogenic activities of sulfated polysaccharide from C. tomentosum (PCT) using carrageenan (CARR)-induced paw edema in a rat model and anti-vasculogenic activity on a chorioallantoic membrane assay (CAM) model. Based on in vitro tests of anti-radical, total antioxidant, and reducing power activities, PCT presents a real interest via its antioxidant activity and ability to scavenge radical species. The in vivo pharmacological tests suggest that PCT possesses anti-inflammatory action by reducing paw edema and leukocyte migration, maintaining the redox equilibrium, and stabilizing the cellular level of several pro-/antioxidant system markers. It could significantly decrease the malondialdehyde levels and increase superoxide dismutase, glutathione peroxidase, and glutathione activities in local paw edema and erythrocytes during the acute inflammatory reaction of CARR. PCT pretreatment was effective against DNA alterations in the blood lymphocytes of inflamed rats and reduced the hematological alteration by restoring blood parameters to normal levels. The anti-angiogenic activity results revealed that CAM neovascularization, defined as the formation of new vessel numbers and branching patterns, was decreased by PCT in a dose-dependent manner, which supported the in silico bioavailability and pharmacokinetic findings. These results indicated the therapeutic effects of polysaccharides from C. tomentosum and their possible use as anti-proliferative molecules based on their antioxidant, anti-inflammatory, and anti-angiogenic activities.

Role of Japan Sea Throughflow in the spatial variability of the long-term sea surface temperature trend

AbstractThe Japan Sea shows a much stronger warming of long-term sea surface temperature (SST) than surrounding oceans. The warming trend possesses a meridionally alternating zonal band pattern, with weak trends along the paths of the Japan Sea Throughflow and strong trends in the remaining interior region. Using idealized models of the Japan Sea Throughflow and atmospheric heating, this study examines the process behind the formation of such spatial patterns in the SST trend. We find that zonal band structures form in a flat rectangular coastline model, and heat budget analysis shows that horizontal heat transport, due to throughflow, reduces the warming effect created by the surface heat flux. A weak SST trend appears around the jet, while a strong SST trend appears elsewhere. Bathymetric effects are also examined using a model with realistic coastline settings. The location of the western boundary current stabilizes, and the coastal branch begins to disconnect from the Japanese coastline toward the north, allowing a more stable SST warming region to form in the southern interior region. Lagrangian particle tracking experiments confirm that a weak (strong) SST trend corresponds to a short (long) residence time, and eddies in the Japan Sea prolong the residence time in interior regions. The model results suggest that the accumulation time of surface heating is essential to the spatial distribution of the long-term SST warming trend.

TGF-β signaling molecules in Hydra: role of BMP and BMP inhibitors during pattern formation.

Understanding the evolution of body plans has been one of the major areas of investigation in developmental and evolutionary biology. Cnidaria, the sister group to bilaterians, provides an opportunity to elucidate the origin and evolution of body axes. Hydra, a freshwater cnidarian, is a useful model to study signaling pathways governing pattern formation, which are conserved up to vertebrates including humans. The transforming growth factor β (TGF-β) signaling pathway is one of the fundamental pathways that regulate axis formation and organogenesis during embryonic development. In this article, we discuss the TGF-β pathway members identified in Hydra along with other cnidarians with an emphasis on bone morphogenetic proteins (BMPs) and their inhibitors. TGF-β members, especially those involved in BMP signaling pathway, are mainly involved in maintaining the Organizer region and patterning the body axis in Hydra. Identification of other members of this pathway in Hydra and fellow cnidarians would provide insights into the evolution of body axes and pattern formation in more complex metazoans.

More severe surface relief but stronger fatigue resistance at small scales: Vacancy-assisted fatigue damage mechanism

Surface relief in forms of extrusions and intrusions as the substantial feature of early fatigue damage is one of the most important phenomena studied in metal fatigue. The most common surface relief models in bulk metals are agreed to be correlated with the formation of typical dislocation patterns as persistent slip bands (PSBs), while little is known about the fundamental mechanisms at submicron and even nanometer scales where dislocation pattern formation is fully inhibited. Here, as exampled with thin Au films, the underlying fatigue damage mechanism at small scales is investigated through the quantitative characterization of fatigue damages. Continuous generation and migration of vacancies is found to be crucial for the shape of extrusion/intrusions and kinetics of their growth at submicron and even nanometer scales. Due to the degraded dislocation interaction and intensified vacancy diffusion, the delayed vacancy accumulation in the small-scale metal interior suppresses the extrusion and interface void formation in thinner films, which finally leads to the superior ability to support tremendous surface relief and strong fatigue resistance. The finding of the vacancy-dominated fatigue mechanism at small scales extends our understanding of the metal fatigue mechanisms down to the submicron and even nanometer scales and suggests a novel interface engineering strategy by vacancy behavior modulation for fatigue-tolerance material design.

Leveraging Autoencoders for Better Representation Learning

ABSTRACT The effectiveness of a machine learning algorithm depends to a considerable extent on the representation used for the modeling. It is more critical with medical image data like Parkinson’s, where complexity plays a significant role. The paper proposes a methodology that leverages representation learning in Parkinson’s disease data. It uses seven types of autoencoders as learning techniques, identifying the best among them. The method is validated using three additional measures: Firstly, another dataset of Parkinson’s is used to confirm its effectiveness, thereby making the method dataset-agnostic. Secondly, seven machine-learning techniques formulate the problem in a supervised learning setting by taking the representation given by the best autoencoder as the features and the disease stage as the labels. Lastly, it uses three-dimensionality reduction techniques to visualize these latent variables or representations in a lower dimension. The high accuracy demonstrated at the supervised learning level, and the formation of patterns exhibited at the visualization level demonstrate the effectiveness of the proposed methodology.

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.