Self-organized Periodic Structures Research Articles

Cardiac behaviors and chaotic arrhythmias in the Hindmarsh–Rose model

The Hindmarsh–Rose is one of the best-known models of computational neuroscience. Despite its popularity as a neuron model, we demonstrate that it is also a complete cardiac model. We employ a method based on bifurcations of the interspike interval to redraw its phase diagram and reveal a cardiac region. This diagram bears great resemblance to that of the map-based model for neurons and cardiac cells, the KTz model. Both phase diagrams are compared, showing a very similar placement of behaviors in the parameter space. Adjusting the Hindmarsh–Rose parameters allows us to obtain behaviors similar to atrial, ventricular and pacemaker cells. We also report the neuronal behavior of sustained subthreshold oscillations in the diagram, also unknown in the model. We demonstrate the existence of periodic and chaotic early afterdepolarizations, a behavior linked to life-threatening arrhythmias. In a second phase diagram, we find a chaotic region with early afterdepolarizations and self-organized periodic structures known as shrimps. We also propose a new and simple method to calculate the electrocardiogram using the membrane potential of a point cell and demonstrate its use for the study of QT syndromes using the Hindmarsh–Rose model. Given the smaller number of equations and parameters than detailed conductance models and richer dynamics than other general models, this work presents the Hindmarsh–Rose as a promising alternative for computational cardiology studies.

Tunability of Self-Organized Structures Based on Thermodynamic Flux.

Nature establishes structures and functions via self-organization of constituents, including ions, molecules, and particles. Understanding the selection rule that determines the self-organized structure formed from many possible alternatives is fundamentally and technologically important. In this study, the selection rule for the self-organization associated with a reaction-diffusion system was explored using the Liesegang phenomenon, by which a periodic precipitation pattern is formed as a model system. Experiments were conducted by systematically changing the mass flux. At low mass fluxes, a vertically periodic pattern was formed, whereas at high mass fluxes, a horizontally periodic pattern was formed. The results inferred that a structural vertical-to-horizontal periodicity transition occurred in the self-organized periodic structure at the crossover flux at which the entropy production rate reversed. Numerical analyses attributed the as-observed flux-dependent structural transition to the selection of the self-organized pattern with a higher entropy production rate. These findings contribute to our understanding of how nature controls self-organized structures and geometry, potentially facilitating the development of novel designs, syntheses, and fabrication processes for well-controlled organized functional structures.

Laser-Driven One- and Two-Dimensional Subwavelength Periodic Patterning of Thin Films Made of a Metal–Organic MoS2 Precursor

Laser-based surface processing is an established way for the maskless generation of surface structures and functionalities on a large variety of materials. Laser-driven periodic surface texturing and structuring of thin films is reported for metallic-, semiconductive-, and polymeric films. Here, we introduce subwavelength surface patterning of metal-organic thin films of [Mo2S4(S2CNnBu2)2], a MoS2 precursor. Accurate control of one- and two-dimensional (1D and 2D) periodic patterns is achieved on silicon wafers with a pulsed 532 nm ns laser. With suitable combinations of laser polarization, laser pulse energy, the thickness of the SiO2 passivation layer, and the MoS2 precursor's thin film thickness, high-quality 1D and 2D self-organized periodic structures are obtained in virtually unlimited areas. The material redistribution related to the pattern formation is thermally driven at low laser energies. Increasing pulse energies beyond a threshold level, in our experiments a factor of 2, fully converts the precursor to MoS2.

Morphology and waveguiding properties of ultrafast-laser-inscribed type-II waveguides in IG2

Ultrafast-laser-inscribed type-II waveguides inside the chalcogenide glass IG2 and the morphology of the inscribed tracks are presented for the first time to our knowledge. Self-organized periodic structures induced by the ultrafast laser in the tracks are characterized. The near-infrared waveguiding properties are studied for various pulse energies, durations, repetition rates, and polarization states, as well as different separations between the two written tracks. A propagation loss of ∼ 2.3 dB/cm is demonstrated in a type-II waveguide formed in IG2.

Simultaneous nanopatterning and reduction of graphene oxide by femtosecond laser pulses

This paper presents a novel one-step method for the periodical nanopatterning and reduction of graphene oxide (GO). Self-organized periodic structures of reduced graphene oxide (rGO) appear on GO surfaces upon processing with a femtosecond laser at fluences slightly higher than the fluence needed for reduction of the GO. This indicates that the periodic pattern is formed either simultaneously with or due to the reduction of the GO. The laser-induced reduction of GO was identified by sheet resistance measurements, Raman and X-ray photoelectron spectroscopy. This fast and simple method to both reduce and periodically structure GO offers a variety of possible applications in printed and flexible electronics.

Complex dynamics of a three-dimensional continuous-time autonomous system

Results in a recent paper, concerning a novel three-dimensional chaotic system consisting of a particular set of three autonomous first-order nonlinear ordinary differential equations, are quite extended. We report on numerically computed parameter plane plots for a six-parameter system. The dynamical behavior of each point is characterized by using Lyapunov exponents, or by counting the number of maxima of one of the variables, in one complete trajectory in the phase-space. Each of these diagrams indicates parameter values for which chaos or periodicity may be found, i.e., each one of them shows delimited regions of both chaos and periodicity. Moreover, we show that several of these parameter planes display self-organized periodic structures, embedded in a chaotic region.

Formation of Ultrathin Liesegang Patterns.

For many years, it has been believed that self-organized periodic ring structures known by the name of Liesegang patterns (LPs) are formed only in quite thick media, typically thicker than at least several micrometers. Actually growing LPs in ultrathin films is extremely difficult because of the drying of film and susceptibility to rapid capillary wetting. The present work reports how we obtain successful LPs in ultrathin films of 65 nm thick. The key parameters are temperature control and the introduction of equilibrium water vapor in the sample environment. Atomic force microscope images clearly showed that the LPs are composed of 300-600 nm laterally coagulated particles. We have also evaluated the densities and thicknesses of the ultrathin films by X-ray reflectivity. During the present research, new patterns, which are different from ordinary LPs, have been discovered for the first time in the outermost part of the whole pattern. Studying LPs in ultrathin films may help to forge a better understanding of the mechanism underlying the intriguing phenomenon. Because of nanoscale scale thicknesses, self-organized periodic structures including so-called LPs will open up new opportunities in nanotechnologies.

High Resolution Parameter-Space from a Two-Level Model on Semi-Insulating GaAs

Semi-insulating Gallium Arsenide ( SI-GaAs ) samples experimentally show, under high electric fields and even at room temperature, negative differential conductivity in N-shaped form (NNDC). Since the most consolidated model for n-GaAs , namely, "the model", proposed by E. Schöll was not capable to generate the NNDC curve for SI-GaAs , in this work we have proposed an alternative model. The model proposed, "the two-valley model" is based on the minimal set of generation-recombination equations for two valleys inside of the conduction band, and an equation for the drift velocity as a function of the applied electric field, that covers the physical properties of the nonlinear electrical conduction of the SI-GaAs system. The "two-valley model" was capable to generate theoretically the NNDC region for the first time, and with that, we were able to build a high resolution parameter-space of the periodicity (PSP) using a Periodicity-Detection (PD) routine. In the parameter-space were observed self-organized periodic structures immersed in chaotic regions. The complex regions are presented in a "shrimp" shape rotated around a focal point, which forms in large-scale a "snail shell" shape, with intricate connections between different "shrimps". The knowledge of detailed information on parameter spaces is crucial to localize wide regions of smooth and continuous chaos.

Investigation on the spectrum of complex self-organized plasma photonic crystal

A complex plasma photonic crystal (PPC) was obtained by self-organization of filaments in air dielectric barrier discharge using two planar water electrodes. The PPC structure consists of many square sublattices, and each sublattice is composed of large spots, two kinds of small spots and lines, corresponding to thick plasma columns, two kinds of thin plasma columns, and plasma slices, respectively. By using the optical emission spectrum method, the electron densities and molecular vibration temperatures at different positions of the PPC were studied. The electron densities were compared by comparing the broadenings of Ar I (2P2-->1S5) spectrum line, and the molecular vibration temperatures were calculated by the spectrum line of nitrogen band of second positive system (C3Πu-->B3Πg) . It was found that the electron densities and molecular vibration temperatures at different positions are both different, showing that the plasma states at different positions are different. The descending order of the electron density is: thin plasma columns around the thick plasma columns, thick plasma columns, plasma slices, and thin plasma columns at junction of plasma slices. The descending order of the molecular vibration temperature is: thin plasma columns at junction of plasma slices, plasma slices, thick plasma columns, and thin plasma columns around the thick plasma columns, which is opposite to that of the electron density. So, the electron densities and the molecular vibration temperatures in different positions of the PPC show the opposite changing trend. As the refractive index of plasma is dependent upon the electron density, the thick plasma columns, two kinds of thin plasma columns and plasma slices in this PPC have different refractive indexes. Together with the surrounding area where no discharges occur, in which the refractive index is also different from the discharging areas, the complex PPC can be seen as a self-organized periodic structure with five different refractive indexes. The PPC has the advantages of being obtained easily, having structural diversity, and being analyzed simply, which may lead to wide applications in many scientific and technical areas.

Abnormal arrangement of a collagen/apatite extracellular matrix orthogonal to osteoblast alignment is constructed by a nanoscale periodic surface structure

Morphological and directional alteration of cells is essential for structurally appropriate construction of tissues and organs. In particular, osteoblast alignment is crucial for the realization of anisotropic bone tissue microstructure. In this article, the orientation of a collagen/apatite extracellular matrix (ECM) was established by controlling osteoblast alignment using a surface geometry with nanometer-sized periodicity induced by laser ablation. Laser irradiation induced self-organized periodic structures (laser-induced periodic surface structures; LIPSS) with a spatial period equal to the wavelength of the incident laser on the surface of biomedical alloys of Ti–6Al–4V and Co–Cr–Mo. Osteoblast orientation was successfully induced parallel to the grating structure. Notably, both the fibrous orientation of the secreted collagen matrix and the c-axis of the produced apatite crystals were orientated orthogonal to the cell direction. To the best of our knowledge, this is the first report demonstrating that bone tissue anisotropy is controllable, including the characteristic organization of a collagen/apatite composite orthogonal to the osteoblast orientation, by controlling the cell alignment using periodic surface geometry.

Organization of the Dynamics in a Parameter Plane of a Tumor Growth Mathematical Model

We report results of a numerical investigation on a two-dimensional cross-section of the parameter-space of a set of three autonomous, eight-parameter, first-order ordinary differential equations, which models tumor growth. The model considers interaction between tumor cells, healthy tissue cells, and activated immune system cells. By using Lyapunov exponents to characterize the dynamics of the model in a particular parameter plane, we show that it presents typical self-organized periodic structures embedded in a chaotic region, that were before detected in other models. We show that these structures organize themselves in two independent ways: (i) as spirals that coil up toward a focal point while undergoing period-adding bifurcations and, (ii) as a sequence with a well-defined law of formation, constituted by two mixed period-adding bifurcation cascades.

Self-organized periodic structures on Ge-S based chalcogenide glass induced by femtosecond laser irradiation

Self-organized periodic structures have been observed on the surface of the ablation craters of Ge-S based chalcogenide glass produced after irradiation by a focused beam of a femtosecond Ti:sapphire laser (1 kHz, 34 fs, 806 nm). Scanning electron microscopy and atomic force microscopy images of irradiated spots show a periodic structure of ripples with a spatial period of 720 nm (close to the wavelength of fs laser pulses) and an alignment parallel to the electric field of light. With an increasing number of pulses, from 5 to 50 pulses, a characteristic evolution of ripples was observed from a random structure to a series of generally aligned peaks-and-valleys self-organized periodic structures. Additionally, at the center of the ablated spot, micro-domains appear where the ripples are still regular but are assembled in a more complex fashion. The experimental observations are interpreted in terms of strong temperature gradients combined with interference of the incident laser irradiation and a scattered surface electromagnetic wave.

Nanograting Bragg responses of femtosecond laser written optical waveguides in fused silica glass

Multiple Bragg nanograting stop bands are reported for the first time in single and multi-mode optical waveguides generated by femtosecond laser direct writing in bulk fused silica glass. The stop bands observed in the guided broadband light spectra originated with the orthogonal alignment of volume nanogratings co-generated with the waveguides. Rapid shifting of stop bands across the near UV and visible spectrum was sensitively controlled by laser exposure and sample scanning direction. Bragg periods anticipated from the observed stop bands concurred with the nanograting structural pitches revealed by scanning electron microscopy. The spectroscopic characterization of nanogratings along macroscopic-scale (12.5 mm long) waveguide sections constitutes a non-destructive, convenient and sensitive approach to examine long-range order and uniformity of the self-organized periodic structures that may assist to unravel the laser-glass interaction physics of nanograting formation.

Hopfield neural network: The hyperbolic tangent and the piecewise-linear activation functions

This paper reports two-dimensional parameter-space plots for both, the hyperbolic tangent and the piecewise-linear neuron activation functions of a three-dimensional Hopfield neural network. The plots obtained using both neuron activation functions are compared, and we show that similar features are present on them. The occurrence of self-organized periodic structures embedded in chaotic regions is verified for the two cases.

Dynamics of an erbium-doped fiber dual-ring laser

We report results of a numerical investigation on two-dimensional parameter-spaces of a set of four autonomous, seven-parameter, first-order ordinary differential equations, which models an erbium-doped fiber dual-ring laser. By using Lyapunov exponents to numerically characterize the dynamics of the model in the parameter-space, we show that it presents typical self-organized periodic structures embedded in a chaotic region.