Pattern Formation Process Research Articles

On the field-aligned currents pattern formation in the magnetosphere

Assuming an assembly of field-aligned current (FAC) elements, the interaction of FAC elements irrespective from their wave/static nature is examined. Considering that the FAC assembly elements are governed by the Gibbs distribution module Θ we arrive to a macroscopic/fluid description of the FAC systems. Solutions of the derived nonlinear differential equation yield periodic spatial structures of the FAC systems in the magnetosphere. The FAC structures are a consequence of the pattern formation process that appears owing to the FAC intensity increase down the magnetic field lines. It is shown that critical values (threshold values) for an initiation of FAC structure formation exist. A coexistence of large-scale and intermediate-scale FAC structures is possible above threshold values. The threshold values depend on the ambient plasma temperature and the spatial scales of the newly formed FAC structures. Generally, the critical values are easily attainable for low β plasma conditions realizable for the magnetosphere regions just above the ionosphere.

Maximum norms of random sums and transient pattern formation

Many interesting and complicated patterns in the applied sciences are formed through transient pattern formation processes. In this paper we concentrate on the phenomenon of spinodal decomposition in metal alloys as described by the Cahn-Hilliard equation. This model depends on a small parameter, and one is generally interested in establishing sharp lower bounds on the amplitudes of the patterns as the parameter approaches zero. Recent results on spinodal decomposition have produced such lower bounds. Unfortunately, for higher-dimensional base domains these bounds are orders of magnitude smaller than what one would expect from simulations and experiments. The bounds exhibit a dependence on the dimension of the domain, which from a theoretical point of view seemed unavoidable, but which could not be observed in practice. In this paper we resolve this apparent paradox. By employing probabilistic methods, we can improve the lower bounds for certain domains and remove the dimension dependence. We thereby obtain optimal results which close the gap between analytical methods and numerical observations, and provide more insight into the nature of the decomposition process. We also indicate how our results can be adapted to other situations.

Wave nucleation rate in excitable systems in the low noise limit.

Motivated by recent experiments on intracellular calcium dynamics, we study the general issue of fluctuation-induced nucleation of waves in excitable media. We utilize a stochastic Fitzhugh-Nagumo model for this study, a spatially extended nonpotential pair of equations driven by thermal (i.e., white) noise. The nucleation rate is determined by finding the most probable escape path via minimization of an action related to the deviation of the fields from their deterministic trajectories. Our results pave the way both for studies of more realistic models of calcium dynamics as well as of nucleation phenomena in other nonequilibrium pattern-forming processes.

Cell behavior and cell–cell communication during fruiting body morphogenesis in Myxococcus xanthus

Formation of spatial patterns of cells from a mass of initially identical cells is a recurring theme in developmental biology. The dynamics that direct pattern formation in biological systems often involve morphogenetic cell movements. An example is fruiting body formation in the gliding bacterium Myxococcus xanthus in which an unstructured population of identical cells rearranges into an asymmetric, stable pattern of multicellular fruiting bodies in response to starvation. Fruiting body formation depends on changes in organized cell movements from swarming to aggregation. The aggregation process is induced and orchestrated by the cell-surface associated 17 kDa C-signal protein. C-signal transmission depends on direct contact between cells. Evidence suggests that C-signal transmission is geometrically constrained to cell ends and that productive C-signal transmission only occurs when cells engage in end-to-end contacts. Here, we review recent progress in the understanding of the pattern formation process that leads to fruiting body formation. Gliding motility in M. xanthus involves two polarly localized gliding machines, the S-machine depends on type IV pili and the A-machine seems to involve a slime extrusion mechanism. Using time-lapse video microscopy the gliding motility parameters controlled by the C-signal have been identified. The C-signal induces cells to move with increased gliding speeds, in longer gliding intervals and with decreased stop and reversal frequencies. The combined effect of the C-signal dependent changes in gliding motility behaviour is an increase in the net-distance travelled by a cell per minute. The identification of the motility parameters controlled by the C-signal in combination with the contact-dependent C-signal transmission mechanism have allowed the generation of a qualitative model for C-signal induced aggregation. In this model, the directive properties of the C-signal are a direct consequence of the contact-dependent signal-transmission mechanism, which is a local event involving direct contact between cells that results in a global organization of cells. This pattern formation process does not depend on a diffusible substance. Rather it depends on a cell-surface associated signal to direct the cells appropriately.

Diffractive optical elements with a double identical microstructure for determination of statistical parameters of random phase objects

Physical processes of interference pattern formation in partially coherent and coherent optical systems containing special diffractive optical elements with a double identical microstructure are studied in the case when a thin scattering object is present in the optical system. Methods for determining the spatial coherence function of the light field, the autocorrelation function of transmission of random phase screens, and the statistical parameters of the screens are considered.

Cavity pattern formation with incoherent light.

We study the propagation dynamics of an incoherent light beam circulating in a passive cavity containing noninstantaneous nonlinear media. It is shown that patterns form in this cavity in spite of spatial incoherence of the light. We show that the pattern formation process is always associated with two consecutive thresholds. The first (instability) threshold is unaffected by the cavity boundary conditions, whereas the second threshold is induced by the feedback through the interplay of nonlinear gain and cavity loss.

Stencil Mask Technology for Electron-Beam Projection Lithography

The development of silicon stencil masks for cell projection lithography (CPL), electron projection lithography (EPL), low-energy electron-beam-proximity-projection lithography (LEEPL), and low-energy electron-beam lithography (LEB) is described. To satisfy the required pattern accuracy of the stencil masks, such as critical dimension and image placement, we developed a high-aspect stencil pattern formation technique to achieve a side-wall angle of over 90 deg and a membrane stress control technique using a stress-correction layer. In addition, for fabricating low-magnification stencil masks, we developed a new mask substrate with a sputtered scattering silicon membrane and a sputtered intermediate stopper layer as an etching stopper. We selected CrNx as the intermediate layer material, which demonstrated high performance in stencil mask fabrication. By improving the CrNx film qualities, its durability to dry and wet etching of backside silicon was improved. In order to improve the pattern image placement accuracy caused by membrane stress changes during stencil pattern formation, we developed a new and simple technique using a stress correction layer, which also functions as a silicon deep-etching mask. By using this functional layer, the total stress change in the pattern field in a mask pattern formation process was reduced to within 5 N/m, which corresponds to less than a 10 nm pattern image placement (IP) error.

Role of calcineurin in activity-dependent pattern formation in the dorsal lateral geniculate nucleus of the ferret.

In the retinogeniculate pathway of the ferret, in addition to the separation of the inputs from the two eyes to form eye-specific layers, there is also an anatomical segregation of the terminal arbors of on-center retinal ganglion cells from the terminal arbors of off-center retinal ganglion cell axons to form on/off sublaminae. Sublamination normally occurs during postnatal weeks 3-4 and requires the activity of retinal afferents, N-methyl-D-aspartate receptors, nitric oxide synthase, and a target of nitric oxide, cyclic guanosine monophosphate. Calcineurin is a calcium/calmodulin dependent serine, threonine protein phosphatase suggested to mediate NMDA-receptor dependent synaptic plasticity in the hippocampus. We have examined whether calcineurin plays a role during on/off sublamination in the dorsal lateral geniculate nucleus (dLGN) of the ferret. Immunohistochemistry showed that calcineurin expression is transiently up-regulated in dLGN cells and neuropil during the period of on/off sublamination. A functional role for calcineurin during sublamination was investigated by blocking the enzyme locally via intracranial infusion of FK506. Treatment with FK506 during postnatal weeks 3-4 disrupted the appearance of sublaminae. These results suggest that calcineurin may play a role during this process of activity-dependent pattern formation in the visual pathway.

Utilizing nonlinear optical pattern formation for a simple image-processing task

A novel scheme for all-optical image processing is suggested, which is based on spontaneous pattern-formation processes. The spatiotemporal instabilities, connected with these self-organization effects, appear in many nonlinear optical systems and mostly obstruct the intended application. We propose to utilize the particular features of pattern formation for parallel image processing, namely the sensitivity to external influences, the selection of well-defined final states, and the rotational and translational invariance. We report here on a single-feedback experiment with a liquid crystal light valve as the optical nonlinearity. In this experiment, the recognition of hexagonal structures is realized. We characterize the response dynamics and study associative properties of this scheme. The extension to square patterns is discussed, and first steps towards a practical implementation are undertaken in providing a simple post-processing scheme and testing the concept on realistic input images.

Universality in visual cortical pattern formation

During ontogenetic development, the visual cortical circuitry is remodeled by activity-dependent mechanisms of synaptic plasticity. From a dynamical systems perspective this is a process of dynamic pattern formation. The emerging cortical network supports functional activity patterns that are used to guide the further improvement of the network’s structure. In this picture, spontaneous symmetry breaking in the developmental dynamics of the cortical network underlies the emergence of cortical selectivities such as orientation preference. Here universal properties of this process depending only on basic biological symmetries of the cortical network are analyzed. In particular, we discuss the description of the development of orientation preference columns in terms of a dynamics of abstract order parameter fields, connect this description to the theory of Gaussian random fields, and show how the theory of Gaussian random fields can be used to obtain quantitative information on the generation and motion of pinwheels, in the two dimensional pattern of visual cortical orientation columns.

Pattern formation in a nonlinear model for animal coats

Several models have been proposed for describing the formation of animal coat patterns. We consider reaction–diffusion models due to Murray, which rely on a Turing instability for the pattern selection. In this paper, we describe the early stages of the pattern formation process for large domain sizes. This includes the selection mechanism and the geometry of the patterns generated by the nonlinear system on one-, two-, and three-dimensional base domains. These results are obtained by an adaptation of results explaining the occurrence of spinodal decomposition in materials science as modeled by the Cahn–Hilliard equation. We use techniques of dynamical systems, viewing solutions of the reaction–diffusion model in terms of nonlinear semiflows. Our results are applicable to any parabolic system exhibiting a Turing instability.

Guided Formation of Nanostructures in Thin Films

ABSTRACTA thin two-component epilayer grown on a solid surface may separate into distinct phases. Sometimes the phases select sizes about 10 nm, and order into an array of stripes or disks. However, the pattern types are limited and the location of the features is not controlled. This paper develops a dynamic model to simulate guided self-assembly. In particular, we look at the effect of surface chemistry on the pattern formation process. The simulations suggest that diverse patterns may be produced by tuning the surface chemistry of a substrate. In addition, the self-assembled features may be anchored at specific locations.

Occurrence of articulins and epiplasmins in protists.

The cortex of ciliates. dinoflagellates, and euglenoids comprises a unique structure called the epiplasm, implicated in pattern-forming processes of the cell cortex and in maintaining cell shape. Articulins, a novel class of cytoskeletal proteins, are major constituents of the epiplasm in the flagellate Euglena gracilis and the ciliate Pseudomicrothorax dubius. The hallmark of articulins is a core domain of repetitive motifs of alternating valine and proline residues, the VPV-motif. The VPV-motif repeats are 12 residues long. Positively and negatively charged residues segregate in register with valine and proline positions. The VPV-motif is unique to articulins. The terminal domains flanking the core are generally hydrophobic and contain a series of hexa- or heptapeptide repeats rich in glycine and hydrophobic residues. Using molecular and immunological tools we show that articulins are also present in the dinoflagellate Amphidinium carterae and the ciliates Paramecium tetraurelia and Paramecium caudatum, Tetrahymena pyriformis, and Euplotes aediculatus. Our analysis further shows that epiplasmins, a group of epiplasmic proteins first characterized in Paramecium, are also present in all these species. Moreover, we present evidence that epiplasmins and articulins represent two distinct classes of cytoskeletal proteins.

Liesegang patterns: Estimation of diffusion coefficient and a plausible justification for colloid explanation

The Liesegang phenomenon is interpreted as a moving boundary problem. The existing time law, spacing law, and width law are revisited and reformulated on the basis of the new scenario. A better understanding of the basic facts associated with pattern formation is made possible with the new concept. The phenomenon is explained on the basis of colloidal kinetics. Diffusion coefficients of the outer electrolyte in the gel for various experiments in the literature are calculated. The diffusion coefficients so calculated range from 1.792–5.996×10–10 m2 s–1. It is suggested that such values confirm the fast colloidal dynamics during the process of periodic precipitation pattern formation.

Broken symmetries and pattern formation in two-frequency forced faraday waves.

We exploit the approximate (broken) symmetries of time translation, time reversal, and Hamiltonian structure to obtain general scaling laws governing the process of pattern formation in weakly damped Faraday waves. Using explicit parameter symmetries we determine, for the case of two-frequency forcing, how the strength of observed three-wave interactions depends on the frequency ratio and on the relative phase of the two driving terms. These symmetry-based predictions are verified for numerically calculated coefficients, and help explain the results of recent experiments.

Ordering dynamics of striped patterns in vertically vibrated granular layers

We experimentally studied the process of pattern formation in granular layers. Ten layers of granular materials inside a vacuum container were placed under a vertical vibration of A sin 2πft . Control parameters were the dimensionless acceleration Γ= A(2 πf) 2/ g and vibration frequency f. When the system was quenched from a flat pattern state to a striped pattern state by instantly increasing Γ, there were more than 10 4 periods before a full steady striped pattern appeared. This non-equilibrium and non-steady process showed dynamic scaling behavior, where the growth exponent of the ordered domain was 0.25, which agrees with that of the Swift–Hohenberg system. Furthermore, dependency of the ordering process on Γ was studied.

Coarsening dynamics of striped patterns in thin granular layers under vertical vibration.

The process of pattern formation in granular layers was experimentally studied. Ten layers of granular materials inside a vacuum container were placed under a vertical vibration of A sin2pi f t. Control parameters were the dimensionless acceleration Gamma = A(2pi f)(2)/g and vibration frequency f. When the system was quenched from a flat pattern state to a striped pattern state by instantly increasing Gamma, there were more than 10(4) periods before a full steady striped pattern appeared. This nonequilibrium and nonsteady process showed dynamic scaling behavior. The growth exponent of the characteristic length scale of the ordered domain was 0.25, which agrees with that of the Swift-Hohenberg system.

Nonlinear Dynamics as a Tool for Modelling in Plant Physiology

Abstract: We show that recent methods from nonlinear dynamics and complexity theory developed in theoretical physics can and should be applied to the description and analysis of systems in plant physiology, in particular to interpret data series in time and space, i.e., rhythms and pattern formation processes. We start with a brief introduction into the key ideas of nonlinear dynamics, including a short outline of topics which are currently the focus of theoretical interest, in particular the concept, origin and possible function of noise in biological systems. The theoretical concepts are applied to a model system of circadian rhythmicity in plant physiology, crassulacean acid metabolism. With this application, we illustrate the main idea of our article: nonlinear dynamics serves as a remarkable tool for unveiling the internal mechanisms at work in a system's process of self‐organization.

Pattern formation by a cell surface-associated morphogen in Myxococcus xanthus.

In response to starvation, an unstructured population of identical Myxococcus xanthus cells rearranges into an asymmetric, stable pattern of multicellular fruiting bodies. Central to this pattern formation process are changes in organized cell movements from swarming to aggregation. Aggregation is induced by the cell surface-associated C-signal. To understand how aggregation is accomplished, we have analyzed how C-signal modulates cell behavior. We show that C-signal induces a motility response that includes increases in transient gliding speeds and in the duration of gliding intervals and decreases in stop and reversal frequencies. This response results in a switch in cell behavior from an oscillatory to a unidirectional type of behavior in which the net-distance traveled by a cell per minute is increased. We propose that the C-signal-dependent regulation of the reversal frequency is essential for aggregation and that the remaining C-signal-dependent changes in motility parameters contribute to aggregation by increasing the net-distance traveled by starving cells per minute. In our model for symmetry-breaking and aggregation, C-signal transmission is a local event involving direct contacts between cells that results in a global organization of cells. This pattern formation mechanism does not require a diffusible substance or other actions at a distance. Rather it depends on contact-induced changes in motility behavior to direct cells appropriately

Straight river: its formation and speciality

Straight river is generally regarded as one of the typical river patterns in conventional classifications in terms of their channel plain landforms. However, very few straight patterns were found to be distributed in wider spatial and temporal spans in the self-adjusted fluvial rivers. Thus, the questions occur such as that is it possible for a channel takes on a stable straight pattern? What are the main factors controlling the processes of the river pattern formation and transformation from a straight to other patterns? Various theories and hypotheses including geomorphic threshold hypothesis, the extreme hypothesis on energy dissipation rate, the stability theory, etc. have been developed to explain the aforementioned questions, but none of them is sound for the explanation to the straight-river formation. From the modern fluvial plain patterns, the straight patterns are not as stable as other typical patterns which occurred in nature; from the historic records of the river sedimentation, no apparent evidence was found to support the stable straight river evolution. Based on the analysis of existing theories, observations, evolvement processes of the channel patterns in the experimental results, this paper concluded that the straight pattern should not be included as one of the typical patterns that are self-formed and developed. This study is of importance to understanding of the river pattern formation and transformation.