Formation Of Two-dimensional Patterns Research Articles

Turing Instabilities and Rotating Spiral Waves in Glycolytic Processes.

We study single-frequency oscillations and pattern formation in the glycolytic process modeled by a reduction in the well-known Sel'kov's equations (Sel'kov in Eur J Biochem 4:79, 1968), which describe, in the whole cell, the phosphofructokinase enzyme reaction. By using averaging theory, we establish the existence conditions for limit cycles and their limiting average radius in the kinetic reaction equations. We analytically establish conditions on the model parameters for the appearance of unstable nonlinear modes seeding the formation of two-dimensional patterns in the form of classical spots and stripes. We also establish the existence of a Hopf bifurcation, which characterizes the reaction dynamics, producing glycolytic rotating spiral waves. We numerically establish parameter regions for the existence of these spiral waves and address their linear stability. We show that as the model tends toward a suppression of the relative source rate, the spiral wave solution loses stability. All our findings are validated by full numerical simulations of the model equations. Finally, we discuss in vitro evidence of spatiotemporal activity patterns found in glycolytic experiments, and propose plausible biological implications of our model results.

Brush-painted superhydrophobic silica coating layers for self-cleaning solar panels

Superhydrophobic coatings have potential applications in fouling resistance, self-cleaning, waterproofing, and drag reduction. In this work, using a facile brush-painting method for outdoor application, superhydrophobic silica coating layers were developed with high contact angle above 150°, high light-transmittance above 90 %, and strong weather resistance via three strategies: (i) hexadecyltrimethoxysilane-modified SiO2 (H-SiO2) particle agglomeration in colloidal coating solutions, and the formation of (ii) two-dimensional (2D) mud-crack patterns and (iii) three-dimensional (3D) micro-bumps. First, particle agglomeration was optimized in a mixed solution of water and ethanol with a relative permittivity of ε = 48.0. Second, high transmittance and full-covered hydrophobic properties were achieved from the silica coating layers with 2D mud-crack patterns. Third, maximal contact angle of 152.6° was obtained from the superhydrophobic silica coating layers consisting of heterogeneous 3D micro-bumps on the 2D mud-crack patterns. The superhydrophobic coating layers exhibited high light-transmittance of 90.2 % and near-zero sliding angle, making them suitable for use as self-cleaning solar panels. These brush-painted superhydrophobic silica layers have potential uses in industrial coating applications by providing self-cleaning capability, weather resistance, flexibility, and transparency.

Polarized holographic lithography system for high-uniformity microscale patterning with periodic tunability

Periodic microscale array structures play an important role in diverse applications involving photonic crystals and diffraction gratings. A polarized holographic lithography system is proposed for patterning high-uniformity microscale two-dimensional crossed-grating structures with periodic tunability. Orthogonal two-axis Lloyd’s mirror interference and polarization modulation produce three sub-beams, enabling the formation of two-dimensional crossed-grating patterns with wavelength-comparable periods by a single exposure. The two-dimensional-pattern period can also be flexibly tuned by adjusting the interferometer spatial positioning. Polarization states of three sub-beams, defining the uniformity of the interference fringes, are modulated at their initial-polarization states based on a strict full polarization tracing model in a three-dimensional space. A polarization modulation model is established considering two conditions of eliminating the unexpected interference and providing the desired identical interference intensities. The proposed system is a promising approach for fabricating high-uniformity two-dimensional crossed gratings with a relatively large grating period range of 500–1500 nm. Moreover, our rapid and stable approach for patterning period-tunable two-dimensional-array microstructures with high uniformity could be applicable to other multibeam interference lithography techniques.

A “metaphorical” nonlinear multimode fiber laser approach to weakly dissipative Bose-Einstein condensates a aContribution to the Focus Issue Turbulent Regimes in Bose-Einstein Condensates edited by Alessandra Lanotte, Iacopo Carusotto and Alberto Bramati.

We demonstrate the stabilization of two-dimensional nonlinear wave patterns by means of a dissipative confinement potential. Our analytical and numerical analysis, based on the generalized dissipative Gross-Pitaevskii equation, makes use of the close analogy between the dynamics of a Bose-Einstein condensate and that of mode-locked fiber laser, operating in the anomalous dispersion regime. In the last case, the formation of stable two-dimensional patterns corresponds to spatiotemporal mode locking, using dissipation-enhanced mode cleaning. We analyze the main scenarios of pattern destabilization, varying from soliton dissolution to its splitting and spatiotemporal turbulence, and their dependence on graded dissipation.

Two-dimensional patterns in dip coating - first steps on the continuation path

We present a brief comparative investigation of the bifurcation structure related to the formation of two-dimensional deposition patterns as described by continuum models of Cahn–Hilliard type. These are, on the one hand a driven Cahn–Hilliard model for Langmuir–Blodgett transfer of a surfactant layer from the surface of a bath onto a moving plate and on the other hand a driven thin-film equation modelling the surface acoustic wave-driven coating of a plate by a simple liquid. In both cases, we present selected two-dimensional steady states corresponding to deposition patterns and discuss the main structure of the corresponding bifurcation diagrams.

Water stability of self-assembled peptide nanostructures for sequential formation of two-dimensional interstitial patterns on layered materials

Sequential-assembly of LEY and GrBP5 peptides on a graphite surface.

Abrikosov-like lattices in organic crystals on graphite surface

ABSTRACTThe interest for surface patterning presents a fast increasing in the last few years due to several factors ranging from miniaturization trends and sensor design to worries about the absorption of carcinogenic molecules on inhalable particles. Although the existence of a vast literature regarding the self-assembly and patterning of nanoparticles on different types of surfaces, it remains unclear the dynamics and main mechanisms behind the formation and maintenance of two-dimensional symmetric patterns of small molecules on top of surfaces. In this contribution, we report initial results on an investigation on the similarities between the well-known Abrikosov hexagonal lattices in superconductors, and the spontaneous formation of hexagonal patterns of some small polycyclic aromatic hydrocarbons (PAHs) on top of a graphitic surface. In order to attest our results, some experimental results from literature are compared to the obtained results.

Two-Photon Induced Self-Structuring of Polymeric Films Based on Y-Shape Azobenzene Chromophore

We report on optically induced spontaneous formation of periodic two-dimensional patterns on newly synthesized polymers based on Y-shape azobenzene molecules. Thin films of this polymer are exposed to a single femtosecond laser beam in the near-infrared (wavelength = 800 nm), normally incident on the free surface of the polymer film. The spontaneous formation of periodic structures is observed after few seconds, both perpendicularly and parallel to the incident laser polarization direction, with a periodicity of about 470 and 250 nm, respectively, and amplitude up to 100 nm. The features of height and periodicity are analyzed as a function of the incident pulse energy, evidencing the presence of a threshold of 50 μJ/pulse. The spontaneously formed structures can be partially canceled by illuminating with incoherent UV light. This approach, allowing patterning areas of few mm2 within a few minutes, constitutes a simple and straightforward method for the fabrication of polymer periodic nanostructures.

Topology optimization using non-conforming finite elements: three-dimensional case

As in the case of two-dimensional topology design optimization, numerical instability problems similar to the formation of two-dimensional checkerboard patterns occur if the standard eight-node conforming brick element is used. Motivated by the recent success of the two-dimensional non-conforming elements in completely eliminating checkerboard patterns, we aim at investigating the performance of three-dimensional non-conforming elements in controlling the patterns that are estimated overly stiff by the brick elements. To this end, we will investigate how accurately the non-conforming elements estimate the stiffness of the patterns. The stiffness estimation is based on the homogenization method by assuming the periodicity of the patterns. To verify the superior performance of the elements, we consider three-dimensional compliance minimization and compliant mechanism design problems and compare the results by the non-conforming element and the standard 8-node conforming brick element. Copyright © 2005 John Wiley & Sons, Ltd.

Fabrication of photonic structures by means of interference lithography and reactive ion etching

In this study, the fabrication of two-dimensional photonic structures by means of interference lithography is discussed. The proposed method provides flexible formation of various configuration two-dimensional interference patterns depending on the number of beams and their interorientation. Mainly, triangular and square lattice configurations are modeled. It is shown that the dimensions of substructure increase with the number of beams superpositioning. Mask fabrication by SF 6/N 2 reactive ion etching, while transferring the pattern onto silicon substrate is presented.

Localized excitations in a vertically vibrated granular layer

THE formation of two-dimensional patterns in biological, chemical and physical systems is often described by the nonlinear interaction of plane waves1. An alternative approach views patterns as ensembles of interacting localized objects, analogous to the assembly of crystals from atoms. For macroscopic pattern-forming systems, one objection to the latter approach is that no 'atoms' exist; however spatially localized excitations can play an analogous role. One-dimensional localized states are observed in many systems—for example, solitary waves in water2–4 and optical fibres5—and can organize into simple patterns6,7. But few examples of two-dimensional localized states are known, and these tend to be unstable and/or do not show simple pattern-forming interactions8–11. Here we report the observation of stable, two-dimensional localized excitations zin a vibrating layer of sand. These excitations, which we term 'oscillons', have a propensity to assemble into 'molecular' and 'crystalline' structures. Our experimental results, together with the observation of similar localized excitations in model differential equations12–14, indicate a crucial, cooperative role for hysteresis and dissipation in the formation of oscillons, and suggest that similar behaviour may occur in continuous media.

Conventional and unconventional Turing patterns

The formation of two-dimensional Turing patterns in nonequilibrium chemical systems is studied by numerical simulations with an activator-substrate depletion model. The relative stabilities of the different hexagonal patterns and the striped patterns are discussed, in particular in the vicinity of the transition, and compared with the present state theory. The generic instabilities of the striped patterns are evidenced. In particular, we report the formation of stable zigzag patterns which share features both of one-dimensional and two-dimensional patterns. We also provide examples of temporal evolution in a weakly confined system.

Kinetic oscillations in the catalytic CO oxidation on Pt(100): Computer simulations

The previously observed phenomena of temporal and spatial self-organization during the catalytic oxidation of CO on a Pt(100) surface were computer simulated by use of the cellular automaton technique. The underlying model is footed on the knowledge about the individual reaction steps (adsorption, desorption, surface structural transformation, etc.), which in turn formed the basis of a previous theoretical treatment in terms of the formulation and solution of a set of coupled differential equations. The present result nicely show the formation and propagation of two-dimensional patterns, and they reproduce qualitatively well all the experimental observations. The development of macroscopic patterns even with an a priori perfectly homogeneous surface is a particularly interesting effect.