Pattern Formation Process Research Articles

Procedure to reveal the mechanism of pattern formation process by topological data analysis

Topological data analysis (TDA) is a versatile tool that can be used to extract scientific knowledge from complex pattern formation processes. However, the physics correspondence between the features obtained from TDA and pattern dynamics does not agree one-to-one, and the physical interpretation of the TDA features needs to be set appropriately according to the phenomenon to be analyzed. In this study, we propose an analytical procedure to physically interpret pattern dynamics through TDA and machine learning techniques. The proposed procedure was applied to the process of magnetic domain pattern formation to quantify non-trivial domain pattern classifications and reveal the nature of the underlying dynamics. On the basis of these findings, we also propose a candidate reduction model to understand the nature of magnetic domain formation.

Proportional relations between the wave number and amplitude of spiral waves near Neimark-Sacker bifurcations

The spatiotemporal distribution patterns of interacting populations are broadly accepted as a pivotal factor in sustaining species diversity. Spiral waves represent common spatiotemporal patterns observed in ecosystems and biological systems, encompassing both continuous-time and discrete-time systems. The study of the dynamics and regulation of spiral waves in continuous-time systems, often observed in the vicinity of Hopf bifurcations, has been comprehensively examined. However, the dynamical characteristics and rules governing spiral waves near Hopf bifurcations in discrete-time systems, also named Neimark-Sacker bifurcations, are still not fully understood. Here, we investigate spiral waves in a discrete-time predator-pest model caused by a Neimark-Sacker bifurcation. Our results suggest a linear relationship between the amplitude and wave number of spiral waves near the Neimark-Sacker bifurcation. At last, we propose a model that can describe the behaviors of spiral waves in discrete-time systems near Neimark-Sacker bifurcations. Our findings illuminate the process of pattern formation in discrete-time systems, offering potential insights for forecasting and managing pest distribution.

Горячее деформирование корпусных заготовок в изотермических условиях

Core operations with hollow products, having a periodically changing internal profile, consists in the final machining of press forgings. However, at the same time, metal rejects are high, and despite the high quality of the products obtained, their mechanical characteristics do not always meet the requirements of functioning. For the equipment units, when subjected to heavy loads, the parts are usually made of high-strength materials. Due to the complexity of the work on a workpieces made of high-strength alloys, operations are carried out with heating of the deformed zone of the in-process part or with a total heating. The use of slow deformation in the hot state under certain speed conditions is promising. The process of the internal pattern formation for hollow shells made of titanium alloy VT6 is viewed. These products are mainly used as various airframes and are made using special methods of mechanical engineering. Due to the use of high-strength billet materials, there are difficulties with the mechanization of the production methods. The article evaluates force conditions for generation of geometry on the shells based on CAE modeling. The simulation was performed in the deform complex. The focus of the research was on the assessment of deformation forces and stress intensities. The influence of deformation ratio, strain rates, punch geometry on the strength of the process and stress intensity has been revealed. A regression equation to estimate the forces of the process is deduced. Recommendations on the design of fillets forming operations have been obtained. Deformation modes aimed at achieving rational power modes, respectively, loads on the tool, which indirectly affects its durability, as well as the stress condition in the product, have been found.

Pattern formation in dense populations studied by inference of nonlinear diffusion‐reaction mechanisms

SummaryReaction‐diffusion systems have been proposed as a model for pattern formation and morphogenesis. The Fickian diffusion typically employed in these constructions model the Brownian motion of particles. The biological and chemical elements that form the basis of this process, like cells and proteins, occupy finite mass and volume and interact during migration. We propose a Reaction‐Diffusion system with Maxwell‐Stefan formulation to construct the diffusive flux. This formulation relies on inter‐species force balance and provides a more realistic model for interacting elements. We also present a variational system inference‐based technique to extract these models from spatiotemporal data for these processes. We show that the inferred models can capture the characteristics of local Turing instability that instigates the pattern formation process. Moreover, the equilibrium solutions of the inferred models form similar patterns to the observed data.

Fractal-Based Pattern Quantification of Mineral Grains: A Case Study of Yichun Rare-Metal Granite

The quantification of the irregular morphology and distribution pattern of mineral grains is an essential but challenging task in ore-related mineralogical research, allowing for tracing the footprints of pattern-forming geological processes that are crucial to understanding mineralization and/or diagenetic systems. In this study, a large model, namely, the Segmenting Anything Model (SAM), was employed to automatically segment and annotate quartz, lepidolite and albite grains derived from Yichun rare-metal granite (YCRMG), based on which a series of fractal and multifractal methods, including box-counting calculation, perimeter–area analysis and multifractal spectra, were implemented. The results indicate that the mineral grains from YCRMG show great scaling invariance within the range of 1.04~52,300 μm. The automatic annotation of mineral grains from photomicrographs yields accurate fractal dimensions with an error of only 0.6% and thus can be utilized for efficient fractal-based grain quantification. The resultant fractal dimensions display a distinct distribution pattern in the diagram of box-counting fractal dimension (Db) versus perimeter–area fractal dimension (DPA), in which lepidolites are sandwiched between greater-valued quartz and lower-valued albites. Snowball-textured albites, i.e., concentrically arranged albite laths in quartz and K-feldspar, exhibit characteristic Db values ranging from 1.6 to 1.7, which coincide with the fractal indices derived from the fractal growth model. The zonal albites exhibit a strictly increasing trend regarding the values of fractal and multifractal exponents from core to rim, forming a featured “fractal-index banding” in the radar diagram. This pattern suggests that the snowball texture gradually evolved from rim to core, thus leading to greater fractal indices of outer zones, which represent higher complexity and maturity of the evolving system, which supports a metasomatic origin of the snowball texture. Our study demonstrates that fractal analyses with the aid of a large model are effective and efficient in characterizing and understanding complex patterns of mineral grains.

The primacy of temporal dynamics in driving spatial self-organization of soil iron redox patterns.

This study investigates mechanisms that generate regularly spaced iron-rich bands in upland soils. These striking features appear in soils worldwide, but beyond a generalized association with changing redox, their genesis is yet to be explained. Upland soils exhibit significant redox fluctuations driven by rainfall, groundwater changes, or irrigation. Pattern formation in such systems provides an opportunity to investigate the temporal aspects of spatial self-organization, which have been heretofore understudied. By comparing multiple alternative mechanisms, we found that regular iron banding in upland soils is explained by coupling two sets of scale-dependent feedbacks, the general principle of Turing morphogenesis. First, clay dispersion and coagulation in iron redox fluctuations amplify soil Fe(III) aggregation and crystal growth to a level that negatively affects root growth. Second, the activation of this negative root response to highly crystalline Fe(III) leads to the formation of rhythmic iron bands. In forming iron bands, environmental variability plays a critical role. It creates alternating anoxic and oxic conditions for required pattern-forming processes to occur in distinctly separated times and determines durations of anoxic and oxic episodes, thereby controlling relative rates of processes accompanying oxidation and reduction reactions. As Turing morphogenesis requires ratios of certain process rates to be within a specific range, environmental variability thus modifies the likelihood that pattern formation will occur. Projected changes of climatic regime could significantly alter many spatially self-organized systems, as well as the ecological functioning associated with the striking patterns they present. This temporal dimension of pattern formation merits close attention in the future.

Perbandingan Algoritma Klasifikasi Data Mining Pada Prediksi Penyakit Diabetes

Diabetes is a chronic disease that attacks humans. One of the causes of diabetes in humans is that sugar intake is too high which the body cannot balance due to absorption or activities carried out. Diabetes is often considered a common disease among people, but the impacts caused by this disease are very detrimental to humans. Based on this, it is necessary for everyone to know whether they suffer from diabetes or not. Therefore, this problem must be resolved appropriately, where it is necessary to predict whether someone will have diabetes or not. The prediction process is carried out to determine whether someone has diabetes or not by knowing the patterns or possible symptoms that cause someone to suffer from diabetes. In this research, the pattern formation process is based on data stored in the past collected in a dataset. A dataset is a collection of past data that occurred in fact and was then collected over a certain period of time on a large scale. Data mining is a method used to process data based on collections of past data, whether in datasets or others. In data mining, the data processing process is carried out using various techniques, one of which is the solution technique in data mining is classification. In this research, the Naïve Bayes algorithm, the K-Nearest Neighbor (K-NN) algorithm and the C4.5 algorithm will be used. In the data mining classification process, there are 3 (three) algorithms used, namely Naïve Bayes, K-Nearest Neighbor and C4.5. From the results of the tests that have been carried out, the accuracy performance results for the Naïve Bayes algorithm are 75%, accuracy for the K-Nearest Neighbor algorithm by 80.60% and the C4.5 algorithm by 91.80%. In this case, it indicates that the C4.5 algorithm has better performance compared to other algorithms. Therefore, the pattern results produced by the C4.5 algorithm are used to make predictions about diabetes.

High‐Resolution Intaglio Transfer Printing of Silver Nanowires for Wearable Electrophysiological Sensors

Silver nanowires (NWs) are promising materials for flexible electronics, such as electronic skins due to their excellent electrical, thermal, and mechanical properties. Achieving precise patterning of Ag NWs is essential for the successful integration and miniaturization of the electronic device system, but the high aspect ratio (AR) of NWs and the high porosity of NW networks pose challenges in forming high‐resolution patterns. Herein, the intaglio transfer printing technique to create high‐resolution patterning of ultralong Ag NWs (AR≈1000) is presented. During the pattern formation process, the external force becomes concentrated specifically at the edge of the intaglio trench, resulting in the breaking of the entangled Ag NW network in the corresponding region. This simple yet effective technique enables precise high‐resolution (minimum line width: 7 µm) and complicated Ag NW patterns on flexible substrates. The patterned Ag NWs are conformally attached to the various curvilinear surfaces and show high mechanical stability under continuous bending conditions. Wearable electrophysiological sensors are demonstrated to monitor electromyography and electrocardiogram signals in real‐time for continuous healthcare monitoring. This patterning strategy offers an effective approach for achieving high‐resolution patterns of highly anisotropic nanomaterials and highlights the potential of patterned Ag NWs in wearable electronics.

Event pattern analysis: the point density around the appearance and disappearance of points

ABSTRACT Point pattern analysis is a fundamental analytical tool in various academic fields related to spatial information science. Basic but important patterns discussed in existing studies are spatially clustered and dispersed points. Analysis of these static patterns aims to reveal their underlying structure, i.e. why and how they are formed. However, to answer this research question, the direct tracking of the pattern formation process is more effective, though we have not yet fully conducted such analysis along the temporal axis. To fill the research gap, this paper develops a new method of spatiotemporal analysis. We focus on the point density around the appearance and disappearance of points. A research question is whether points appear/disappear in dense or sparse space. Extending Ripley’s K-function, we develop four measures statistically evaluating the point density. We applied the proposed method to the analysis of the competition among convenience store chains in Shibuya-ku, Tokyo.

Turing patterns in hyperbolic reaction-transport vegetation models with cross-diffusion

In this paper, the pattern formation process in arid environments on flat terrains is investigated. In particular, a class of one-dimensional hyperbolic reaction-transport vegetation model with a cross-diffusion term accounting for plant roots’ suction in the soil water diffusion feedback is considered. To characterize the emerging Turing patterns, linear stability analysis on the uniform steady states is first addressed. Then, multiple-scale weakly nonlinear analysis is performed to describe the time evolution of the pattern amplitude close to the stability threshold. Finally, to validate analytical predictions, a modified Klausmeier model which takes also into account the internal competition rate is studied. The effects of the inertial times as well as the cross-diffusion and the internal competition rate are illustrated both analytically and numerically.

Dissolution Behavior of Fluoroalkylated Diazonaphthoquinone and Its Blends with Fluorinated Copolymers under UV Irradiation.

This article reports on the synthesis of materials containing both a fluoroalkyl group and a diazonaphthoquinone (DNQ) moiety as well as the fabrication of negative- and positive-tone stencil patterns. Additionally, the photoreaction mechanism that contributes to the pattern formation process is discussed, and the application of these materials is explored in the pixel-formation process in organic light-emitting diode (OLED) displays. Fluoroalkylated diazonaphthoquinone (RF2D1) was synthesized using chemically binding a DNQ unit, which can be converted into carboxylic acid derivatives having stronger polarity, with two fluorinated alkyl chains. The purified compound is found to be soluble in a nonpolar fluorous solvent and can be uniformly coated as a thin film. When the thin film of RF2D1 is exposed to 365 nm UV light, its solubility in a fluorous solvent decreases due to the Wolff rearrangement and subsequent hydrolysis of a ketene moiety. In contrast, when a mixture of RF2D1 and a hydrophobic, fluorinated copolymer is tested for the patterning process, the copolymer delays the conversion of the ketene intermediate to carboxylic acid, resulting in the dissolution of the exposed areas in the fluorous solvent. Finally, the applicability of these materials in micropatterning is demonstrated by adopting them in the orthogonal photolithography process to create pixels of OLEDs.

Quantitative Analysis of the Coordinated Movement of Cells in a Freely Moving Cell Population

Coordinated movement of self-propelled agents has been well studied in collectives or swarms that display directional movement. Self-propelled agents also develop stable spatial patterns in which the agents do not necessarily exhibit directional collective movement. However, quantitative measures that are required to analyze the local and temporal coordinated movements during pattern formation processes have not been well established. Here, we study the coordinated movement of individual pairs of two different types of cells in a freely moving cell population. We introduced three criteria to evaluate coordinated movement in live imaging data obtained from the abdomen of the fruit fly, Drosophila melanogaster, at the pupal stage. All three criteria were able to reasonably identify coordinated movement. Our analysis indicates that the combined usage of these criteria can improve the evaluation of whether a pair of cells exhibits coordinated movement or not by excluding false positives. Quantitative approaches to identifying coordinated movement in a population of freely moving agents constitute a key foundational methodology to study pattern formations by self-propelled agents.

Self-organized submicron structures in photoresist films by UV-laser irradiation at water-confined conditions

A new kind of self-organized pattern formation process has been found during laser irradiation of polymer films in water confinement just below the laser ablation threshold, resulting in a randomly oriented pattern with a period of about 475 nm. The morphology, orientation, period, and amplitude of these patterns are inconsistent with both laser-induced periodic surface structures that typically consist of linear grooves with periods smaller the laser wavelength and wrinkling patterns that feature a much larger period and appear at layered systems. Excimer laser (λ = 248 nm, tp = 25 ns) exposure of 650 nm thick photoresist films on silicon wafers cause the growth of irregular submicron patterns. The pattern morphology that is examined with imaging techniques is correlated to processing parameters. The amplitude of these laser-induced self-organized (LISE) submicron structures are strengthened with pulse number and laser fluence. The experimental results are discussed together with simulations of laser heating the photoresist film in water confinement. The proposed pattern formation mechanism of such laser-induced self-organized submicron structures at temporal excitation of a confined polymer surface comprises the formation of an oriented roughness based on LIPSS that are developed to wrinkled structures due to the transient formation of a soft subsurface area that provides conditions for wrinkling of the water cooled, stiff polymer surface by laser-induced stress fields. Size, amplitude, and morphology of the LISE pattern provide good properties for applications in such fields as wetting, friction, optics, and bioactivity.

Coarse-to-fine Disentangling Demoiréing Framework for Recaptured Screen Images.

Removing the undesired moiré patterns from images capturing the contents displayed on screens is of increasing research interest, as the need for recording and sharing the instant information conveyed by the screens is growing. Previous demoiréing methods provide limited investigations into the formation process of moiré patterns to exploit moiré-specific priors for guiding the learning of demoiréing models. In this paper, we investigate the moiré pattern formation process from the perspective of signal aliasing, and correspondingly propose a coarse-to-fine disentangling demoiréeing framework. In this framework, we first disentangle the moiré pattern layer and the clean image with alleviated ill-posedness based on the derivation of our moiré image formation model. Then we refine the demoiréing results exploiting both the frequency domain features and edge attention, considering moiré patterns' property on spectrum distribution and edge intensity revealed in our aliasing based analysis. Experiments on several datasets show that the proposed method performs favorably against state-of-the-art methods. Besides, the proposed method is validated to adapt well to different data sources and scales, especially on the high-resolution moiré images.

Insights into Permanent Encodings of Macroscopic Spike Patterns by Magnetic-Field-Directed Evaporative Self-Assembly from Ferrofluids.

Field-directed assembly has the potential to make large hierarchically ordered structures from nanoscale objects. Shear forces and optical, electric, and magnetic fields have been used for this purpose. Ferrofluids consist of magnetic nanoparticles hosted in mobile liquids. Though they exhibit rich structures and lattice patterns in response to an applied magnetic field, the patterns collapse when the field is removed. Recently, we adapted evaporation-induced self-assembly to obtain permanent encodings of the complex field response of magnetite nanoparticles in alkane media. The encodings are characterized by order that culminates in macrostructures comprising kinetically trapped spike patterns. The present work examines a number of variables that control pattern formation associated with this encoding. Control variables include applied magnetic field strength, magnetic field gradient, nanoparticle concentration, solvent evaporation conditions, and alkane solvent chain length. The pattern formation process is captured in six stages of evolution until the solvent host has evaporated and the pattern is permanently fixed. The macropatterns consist of hexagonal arrays that coexist with different pentagonal and heptagonal defects. The Voronoi entropy is calculated for different patterns that arise due to changes in the control parameters. Insight into order in the lattice patterns is achieved by extracting measurables like peak-to-peak spike wavelength, spike population, spike height, and base diameter from the patterns. The pattern measurables depend nonlinearly on the magnetic field gradient, solvent evaporation rate, and solvent chain length. Nanoparticle concentration does not impact the measurables significantly. Nonetheless, the results agree qualitatively with a linear expression for the critical magnetization and wavelength that explicitly contains the field gradient and surface tension.

How multiple weak species jeopardise biodiversity in spatial rock–paper–scissors models

We study generalised rock–paper–scissors models with an arbitrary odd number N≥5 of species, among which n are weak, with 2≤n≤(N−1)/2. Because of the species’ weakness, the probability of individuals conquering territory in the cyclic spatial game is low. Running stochastic simulations, we study the role of unevenness in the rock–paper–scissors game in spatial patterns and population dynamics, considering diverse models where the weak species are in different positions in the cyclic game order. Studying systems with five and seven species, we discover that the individuals’ spatial organisation arising from the pattern formation process determines the stability of the cyclic game with multiple weak species. Our outcomes show that the presence of species unbalances the spatial distribution of organisms of the same species bringing consequences on territorial dominance, with the predominant species being determined by the position in the cyclic game order. Our simulations elucidate that, in general, the further apart the regions inhabited by different weak species are, the less the coexistence between the species is jeopardised. We show that if multiple weak species occupy adjacent spatial domains, the unevenness in the cyclic game is reinforced, maximising the chances of biodiversity loss. Our discoveries may also be helpful to biologists in comprehending systems where weak species unbalance biodiversity stability.

Modeling for silicone foam material extrusion with liquid rope coiling

This research demonstrates a Modeling idea using parametric Modeling and considering the process to predict coiling patterns effectively in open-cell foams material extrusion (MEX) with liquid rope coiling (LRC) effect. The model consists of three sub-models, including pneumatic extrusion model, liquid rope coiling model, and geometric model, considering material properties, material extrusion, falling, LRC, pattern formation process and device structure. The model uses four MEX process parameters (back pressure, moving speed, inner nozzle diameter, and nozzle height) to predict three geometric parameters of the coiling pattern. The capability to predict pattern shape (period length, width, and loop length) accurately is validated by comparing the fit of predicted and experimental values when adjusting the process parameters, with R-squared coefficients up to 0.957. Then, application value is demonstrated by printing silicone open-cell foams under the guidance of the proposed model and studying the compression properties of these foams. The obtained three-region stress-strain curves indicate the feasibility of variable stiffness foam fabrication by adjusting the process parameters according to the proposed model during the printing process. Based on the results, the proposed model demonstrates accuracy in predicting geometric parameters of translational coiling pattern, makes predictable manufacturing of complex cellular structures available, and provides a foundation for design and fabrication of load-based variable stiffness silicone open-cell foam.

Stability and dynamics across magnetic phases of vortex-bright type excitations in spinor Bose-Einstein condensates

The static properties, i.e., existence and stability, as well as the quench-induced dynamics of vortex-bright type excitations in two-dimensional harmonically confined spin-1 Bose-Einstein condensates are investigated. Linearly stable vortex-bright-vortex and bright-vortex-bright solutions arise in both antiferromagnetic and ferromagnetic spinor gases upon quadratic Zeeman energy shift variations. Their deformations across the relevant transitions are exposed and discussed in detail evincing also that emergent instabilities can lead to pattern formation. Spatial elongations, precessional motion and spiraling of the nonlinear excitations when exposed to finite temperatures and upon crossing the distinct phase boundaries, via quenching of the quadratic Zeeman coefficient, are unveiled. Spin-mixing processes triggered by the quench lead, among others, to changes in the waveform of the ensuing configurations. Our findings reveal an interplay between pattern formation and spin-mixing processes being accessible in contemporary cold atom experiments.

Polarity and chirality control of an active fluid by passive nematic defects

Much like passive materials, active systems can be affected by the presence of imperfections in their microscopic order, called defects, that influence macroscopic properties. This suggests the possibility to steer collective patterns by introducing and controlling defects in an active system. Here we show that a self-assembled, passive nematic is ideally suited to control the pattern formation process of an active fluid. To this end, we force microtubules to glide inside a passive nematic material made from actin filaments. The actin nematic features self-assembled half-integer defects that steer the active microtubules and lead to the formation of macroscopic polar patterns. Moreover, by confining the nematic in circular geometries, chiral loops form. We find that the exact positioning of nematic defects in the passive material deterministically controls the formation and the polarity of the active flow, opening the possibility of efficiently shaping an active material using passive defects.

Inferring topological transitions in pattern-forming processes with self-supervised learning

The identification of transitions in pattern-forming processes are critical to understand and fabricate microstructurally precise materials in many application domains. While supervised methods can be useful to identify transition regimes, they need labels, which require prior knowledge of order parameters or relevant microstructures describing these transitions. Instead, we develop a self-supervised, neural-network-based approach that does not require predefined labels about microstructure classes to predict process parameters from observed microstructures. We show that assessing the difficulty of solving this inverse problem can be used to uncover microstructural transitions. We demonstrate our approach by automatically discovering microstructural transitions in two distinct pattern-forming processes: the spinodal decomposition of a two-phase mixture and the formation of binary-alloy microstructures during physical vapor deposition of thin films. This approach opens a path forward for discovering unseen or hard-to-discern transitions and ultimately controlling complex pattern-forming processes.