Stable Periodic Structures Research Articles

Single-atom platinum with asymmetric coordination environment on fully conjugated covalent organic framework for efficient electrocatalysis

Two-dimensional (2D) covalent organic frameworks (COFs) and their derivatives have been widely applied as electrocatalysts owing to their unique nanoscale pore configurations, stable periodic structures, abundant coordination sites and high surface area. This work aims to construct a non-thermodynamically stable Pt-N2 coordination active site by electrochemically modifying platinum (Pt) single atoms into a fully conjugated 2D COF as conductive agent-free and pyrolysis-free electrocatalyst for the hydrogen evolution reaction (HER). In addition to maximizing atomic utilization, single-atom catalysts with definite structures can be used to investigate catalytic mechanisms and structure-activity relationships. In this work, in-situ characterizations and theoretical calculations reveal that a nitrogen-rich graphene analogue COF not only exhibits a favorable metal-support effect for Pt, adjusting the binding energy between Pt sites to H* intermediates by forming unique Pt-N2 instead of the typical Pt-N4 coordination environment, but also enhances electron transport ability and structural stability, showing both conductivity and stability in acidic environments.

Arnold Tongue-Like Structures and Coexisting Attractors in the Memristive Muthuswamy–Chua–Ginoux Circuit Model

The three-dimensional Muthuswamy–Chua–Ginoux (MCG) circuit model is a generalization of the paradigmatic canonical Muthuswamy–Chua circuit, where a physical memristor assumes the role of a thermistor, and it is connected in series with a linear passive capacitor, a linear passive inductor, and a nonlinear resistor. The physical memristor presents an electrical resistance which is a function of temperature. Nowadays, the MCG circuit model has gained considerable attention due to the lack of extensive numerical explorations and their distinct dynamical properties, exemplified by phenomena such as the transition from torus breakdown to chaos, giving rise to a double spiral attractor associated to independent period-doubling cascades. In this contribution, the complex dynamics of the MCG circuit model is studied in terms of the Lyapunov exponents spectra, Kaplan–Yorke (KY) dimension, and the number of local maxima (LM) computed in one period of oscillation, as two parameters are simultaneously varied. Using the Lyapunov spectra to distinguish different dynamical regimes, KY dimension to estimate the attractors’ dimension, and the number of LM to characterize different periodic attractors, we construct high-resolution two-dimensional stability diagrams considering specific ranges of the parameter pairs [Formula: see text]. These parameters are associated with the inverse of the capacitance in the passive capacitor, and the heat capacitance and dissipation constant of the thermistor, respectively. Unexpectedly, we identify sequences of infinite self-organized generic stable periodic structures (SPSs) and Arnold tongues-like structures (ATSs) merged into chaotic dynamics domains, and the coexistence of different attracting sets (attractors) for the same parameter combinations and different initial conditions (multistability). We explore the multistable dynamics using the stability analysis and computation of Lyapunov coefficients, the inspection of the coexisting attractors, bifurcations diagrams, and basins of attraction. The periods of the ATSs and a particular sequence of shrimp-shaped SPSs obey specific generating and recurrence rules responsible for the bifurcation cascades. As the MCG circuit model has the crucial properties presented by the usual Muthuswamy–Chua circuit model, specific properties explored in our study should be helpful in real problems involving circuits with the presence of physical memristor playing the role of thermistors.

Quint points lattice and multistability in a damped-driven curved carbon nanotube oscillator model.

Single-walled carbon nanotubes (SWCNTs) can undergo arbitrarily large nonlinear deformations without permanent damage to the atomic structure and mechanical properties. The dynamic response observed in curved SWCNTs under externally driven forces has fundamental implications in science and technology. Therefore, it is interesting to study the nonlinear dynamics of a damped-driven curved SWCNT oscillator model if two control parameters are varied simultaneously, e.g., the external driven strength and damping parameters. For this purpose, we construct high-resolution two-dimensional stability diagrams and, unexpectedly, we identify (i) the existence of a quint points lattice merged in a domain of periodic dynamics, (ii) the coexistence of different stable states for the same parameter combinations and different initial conditions (multistability), and (iii) the existence of infinite self-organized generic stable periodic structures (SPSs) merged into chaotic dynamics domains. The quint points lattice found here is composed of five distinct stability domains that coalesce and are associated with five different periodic attractors. The multistability is characterized by the coexistence of three different multi-attractors combinations for three exemplary parameter sets: two periodic attractors, two chaotic attractors, or one periodic and one chaotic attractor. This study demonstrates how complex the dynamics of a damped-driven curved SWCNT oscillator model can be when parameters and initial conditions are varied. For this reason, it may have a relevant impact on new theoretical and experimental applications of damped-driven curved SWCNTs.

Synergy of electromagnetic effects and thermophysical properties of metals in the formation of laser-induced periodic surface structures

Femtosecond (fs) pulsed lasers have been widely used over the past few decades for precise materials structuring at the micro- and nano-scales. However, in order to realize efficient material processing and account for the formation of laser-induced periodic surface structures (LIPSS), it is very important to understand the fundamental laser–matter interaction processes. A significant contribution to the LIPSS profile appears to originate from the electromagnetic fingerprint of the laser source. In this work, we follow a systematic approach to predict the pulse-by-pulse formation of LIPSS on metals due to the development of a spatially periodic energy deposition that results from the interference of electromagnetic far fields on a non-flat surface profile. On the other hand, we demonstrate that the induced electromagnetic effects alone are not sufficient to allow the formation of LIPSS, therefore we emphasize the crucial role of electron diffusion and electron–phonon coupling on the formation of stable periodic structures. Gold (Au) and stainless steel (SS) are considered as two materials to test the theoretical model while simulation results appear to confirm the experimental results that, unlike with Au, fabrication of pronounced LIPSS on SS is feasible.

Noise-induced stabilization of the FitzHugh-Nagumo neuron dynamics: Multistability and transient chaos.

The nonlinear dynamics of a FitzHugh-Nagumo (FHN) neuron driven by an oscillating current and perturbed by a Gaussian noise signal with different intensities D is investigated. In the noiseless case, stable periodic structures [Arnold tongues (ATS), cuspidal and shrimp-shaped] are identified in the parameter space. The periods of the ATSs obey specific generating and recurrence rules and are organized according to linear Diophantine equations responsible for bifurcation cascades. While for small values of D, noise starts to destroy elongations ("antennas") of the cuspidals, for larger values of D, the periodic motion expands into chaotic regimes in the parameter space, stabilizing the chaotic motion, and a transient chaotic motion is observed at the periodic-chaotic borderline. Besides giving a detailed description of the neuronal dynamics, the intriguing novel effect observed for larger D values is the generation of a regular dynamics for the driven FHN neuron. This result has a fundamental importance if the complex local dynamics is considered to study the global behavior of the neural networks when parameters are simultaneously varied, and there is the necessity to deal the intrinsic stochastic signal merged into the time series obtained from real experiments. As the FHN model has crucial properties presented by usual neuron models, our results should be helpful in large-scale simulations using complex neuron networks and for applications.

Asymptotic Behavior of 3D Unstable Structures Made of Beams

In our previous papers (Griso et al. in J. Elast. 141:181–225, 2020; J. Elast., 2021, https://doi.org/10.1007/s10659-021-09816-w), we considered thick periodic structures (first paper) and thin stable periodic structures (second paper) made of small cylinders (length of order varepsilon and cross-sections of radius r). In the first paper r=kappa varepsilon with kappa a fixed constant, varepsilon to 0, while in the second varepsilon to 0 and {r/ varepsilon }to 0. In this paper, our aim is to give the asymptotic behavior of thin periodic unstable structures, when varepsilon to 0, {r/ varepsilon }to 0 and varepsilon ^{2}/ rto 0.Our analysis is again based on decompositions of displacements. As for stable periodic structures, Korn type inequalities are proved. Several classes of unstable and auxetic structures are introduced. The unfolding and limit homogenized problems are really different of those obtained for the thin stable periodic structures. The limit homogenized operators are anisotropic, the spaces containing the macroscopic limit displacements depend on the periodicity cells. It was not the case in the two previous studies. Some examples are given.

铌酸锂微纳波导中的二阶非线性光学效应研究进展

<p indent="0mm">Lithium niobate (LiNbO₃, LN) crystal has a large second-order nonlinear coefficient (<italic>d</italic>₃₃=25.2 pm/V@1064 nm), wide transparent window (0.35–5 μm), and stable periodic microdomain structure preparation, which is a good platform for the study and application of second-order nonlinear optical effects. Lithium niobate thin film (LNTF) is regarded as a promising integrated photonics platform due to its excellent linear and nonlinear optical properties. As the basic unit of an integrated optical system, lithium niobate micro/nano waveguide has been studied as a transmission and control device, and it shows excellent second-order nonlinear optical characteristics. The second-order nonlinearity plays an important role in modern optics, including second-harmonic generation (SHG), sum- and difference-frequency generation, parametric down conversion, and parametric oscillation. Efficient and compact wavelength converters based on second-order nonlinearity are key components for a wide range of applications, including entangled photon sources, optical parametric oscillators, and optical parametric amplifiers. The second-order nonlinear polarization intensity is proportional to the square of the electric field intensity. Micro/nano optical waveguides can improve the light intensity in the device through the local characteristics of the spatial light field, to improve the conversion efficiency of the nonlinear processes. And significantly enhanced electric field strength makes the normalized nonlinear conversion efficiency of LNTF waveguides exceed that of the reverse proton<bold> </bold>exchange lithium niobate waveguides (frequency conversion efficiency 150% W^–1 cm^–2@1550 nm) by one order of magnitude. The nonlinear conversion efficiency of LNTF micro/nano waveguides can be further improved through mode phase matching (MPM) or quasi-phase matching (QPM) to optimize the spatial overlap between the eigenmodes involved in the nonlinear process. The detailed theory, fabrication and application were demonstrated in the manuscript as follows: (1) The theory of second harmonic generation. As an example of second-order nonlinear process, the factors affecting the conversion efficiency of second harmonic generation were analyzed, and can be summarized as nonlinear coefficient, mode special overlap, mode area and phase-matching condition. (2) The fabrication of periodically poled lithium niobate waveguides and periodically poled technics. Based on the micro fabrication processes such as electron beam lithography, dry etching and chemico-mechanical polishing, the propagation loss could be reduced to <sc>0.027 dB/cm.</sc> With the combination of low loss waveguides and the electrode polarization process, periodically poled lithium niobate microstructures and the detailed fabrication processes were discussed in the manuscript. (3) Efficient second harmonic generation based on MPM and QPM. It was reported that the normalized efficiency can reach 1000% W^–1 cm^–2, and we described broadband and tunable SHG in detail. (4) Spontaneous parametric down conversion. With the development of quantum information technology and its application in the fields of secure communication and precision measurement, quantum photon sources with high speed, high brightness and high purity have attracted more and more attention. Due to the strong optical confinement, the micro/nano waveguides reduce the pump power and improve the quality of generated photon pairs, which is helpful to realize the integrated optical path of quantum information processing. In summary, this paper reviews the recent development of second-order nonlinear optical effects in LNTF micro/nano waveguides. Firstly, the theory of second harmonic conversion is introduced, and then the fabrication and periodically poled techniques of LNTF micro/nano waveguides are discussed. As an example, the efficient SHG and parametric down conversion of LNTF waveguides were detailedly demonstrated. The processes of mode phase matching and quasi-phase matching technics, tunable SHG and wideband frequency doubling effect were emphatically investigated.

Chemical structure characteristics and multidimensional model construction of Fushun oil shale kerogen: An experimental and simulation study

Solid state 13C nuclear magnetic resonance (13C NMR), Fourier transform infrared (FT-IR), X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS) were carried out to characterize the chemical structure characteristics and to establish the average molecular structure of kerogen extracted from Fushun oil shale. NMR predictor was used to calculate the chemical shift of carbon atoms to verify the rationality of the constructed model. And the stability of 3D model was studied by molecular dynamics (MD) simulations. 13C NMR results demonstrate that Fushun kerogen consists of 76.98% of aliphatic structure dominated by long linear methylene and 21.6% of aromatic structure (mainly protonated aromatic carbon). Functional groups observed in 13C NMR spectra were also detected in FT-IR spectra at wavenumber range of 1800-1000 cm−1. XPS analysis indicates that nitrogen-containing groups were pyrrole, pyridine and primary amines, and sulfur existed as sulfoxides, thiophenes and mercaptans. By comparing the calculated 13C NMR and experimental 13C NMR, it was found that the aromatic structure condensed in two aromatic rings and the aliphatic structure without alicyclic and epoxy ether were more rational for the chemical structure model of Fushun kerogen. A new method to evaluate the average methylene chain length was proposed. Finally, a relatively rational 2D molecular structure with a molecular formula of C228H350O10N6S3 was constructed. The most stable 3D periodic structure (20 optimized molecules, 48.44 × 49.63 × 50.28 Å3) with the lowest total potential energy was obtained by MD simulation and density of it was 0.943 g/cm3.

Transient dynamics and multistability in two electrically interacting FitzHugh-Nagumo neurons.

We analyze the existence of chaotic and regular dynamics, transient chaos phenomenon, and multistability in the parameter space of two electrically interacting FitzHugh-Nagumo (FHN) neurons. By using extensive numerical experiments to investigate the particular organization between periodic and chaotic domains in the parameter space, we obtained three important findings: (i) there are self-organized generic stable periodic structures along specific directions immersed in a chaotic portion of the parameter space; (ii) the existence of transient chaos phenomenon is responsible for long chaotic temporal evolution preceding the asymptotic (periodic) dynamics for particular parametric combinations in the parameter space; and (iii) the existence of various multistable domains in the parameter space with an arbitrary number of attractors. Additionally, we also prove through numerical simulations that chaos, transient chaos, and multistability prevail even for different coupling strengths between identical FHN neurons. It is possible to find multistable attractors in the phase and parameter spaces and to steer them apart by increasing the asymmetry in the coupling force between neurons. Such a strategy can be essential to experimental matters, as setting the right parameter ranges. As the FHN model shares the crucial properties presented by the more realistic Hodgkin-Huxley-like neurons, our results can be extended to high-dimensional coupled neuron models.

Bifurcations and organized structures in a predator-prey model with hunting cooperation

Abstract We report new organized structures in bi-parameter space for a nonlinear discrete predator-prey model with hunting cooperation. The intrinsic hunting cooperation among predator populations alters the dynamical behaviors of the model significantly. Especially, the stable periodic organized structures, viz. the Arnold tongues and shrimp-shaped structures in quasi-periodic and chaotic regimes exist near the boundary of Neimark-Sacker bifurcation for moderate values of the hunting cooperation parameter. Interestingly, these regular structures lead to different period-adding sequences. The transition to chaos via period-bubbling cascade near the inner boundaries of the shrimp-shaped structures is obtained. Shrimp structures maintain the universality of period 3-times self-similarity. Also, the coexistence of multiple periodic cycles and chaotic attractors with fractal basin boundaries are found owing to the hunting cooperation among the predators.

The emergence of sequence-dependent structural motifs in stretched, torsionally constrained DNA.

The double-helical structure of DNA results from canonical base pairing and stacking interactions. However, variations from steady-state conformations resulting from mechanical perturbations in cells have physiological relevance but their dependence on sequence remains unclear. Here, we use molecular dynamics simulations showing sequence differences result in markedly different structural motifs upon physiological twisting and stretching. We simulate overextension on different sequences of DNA ((AA)12, (AT)12, (CC)12 and (CG)12) with supercoiling densities at 200 and 50 mM salt concentrations. We find that DNA denatures in the majority of stretching simulations, surprisingly including those with over-twisted DNA. GC-rich sequences are observed to be more stable than AT-rich ones, with the specific response dependent on the base pair order. Furthermore, we find that (AT)12 forms stable periodic structures with non-canonical hydrogen bonds in some regions and non-canonical stacking in others, whereas (CG)12 forms a stacking motif of four base pairs independent of supercoiling density. Our results demonstrate that 20–30% DNA extension is sufficient for breaking B-DNA around and significantly above cellular supercoiling, and that the DNA sequence is crucial for understanding structural changes under mechanical stress. Our findings have important implications for the activities of protein machinery interacting with DNA in all cells.

Characterizing the Dynamics of the Watt Governor System Under Harmonic Perturbation and Gaussian Noise

We investigate the disturbance on the dynamics of a Watt governor system model due to the addition of a harmonic perturbation and a Gaussian noise, by analyzing the numerical results using two distinct methods for the nonlinear dynamics characterization: (i) the well-known Lyapunov spectrum, and (ii) the 0-1 test for chaos. The results clearly show that for tiny harmonic perturbations only the smallest stable periodic structures (SPSs) immersed in chaotic domains are destroyed, whereas for intermediate harmonic perturbation amplitudes there is the emergence of quasiperiodic motion, with the existence of typical Arnold tongues and, the consequent distortion of the SPSs embedded in the chaotic region. For large enough harmonic perturbations, the SPSs immersed in chaotic domains are suppressed and the dynamics becomes essentially chaotic. Regarding the noise perturbations, it is able to suppress periodic motion even if tiny noise intensities are considered, as analyzed by a periodic attractor subject to different noise intensities. The threshold of noise amplitude for chaos generation in periodic structures is reported by both methods. Additionally, we investigate the robustness of the 0-1 test for chaos characterization in both noiseless and noise cases, and for the first time, we compare the Lyapunov exponents and 0-1 test methods in the parameter-planes. Our findings are generic due to their remarkable agreement with results previously reported for dynamical systems in other contexts.

Tracking multistability in the parameter space of a Chua’s circuit model

The effect of applying an asymmetric periodic continuous-feedback signal F(x), which is a function of voltage x, across one of the capacitors in the classical Chua’s circuit model is examined. We have performed a numerical investigation on the dynamics of the Chua’s circuit model to discuss a procedure of distorting, suppressing and moving attractors and stable periodic structures (SPSs) in phase and parameter spaces, respectively, by accordingly choosing the control parameters in the function F(x). Increasing the asymmetry strength in F(x), we are able to track and to move overlapped SPSs related to multistability phenomenon in phase space, and to suppress SPSs related to one single attractor. Our results indicate that the methodology used here will have a wide spectrum of applications in generic nonlinear complex dynamical systems presenting multistability, related to both theoretical and experimental issues.

Exploring the Dynamics of a Third-Order Phase-Locked Loop Model

We study the dynamics and characterize the bifurcation structure of a phase-locked loop (PLL) device modeled by a third-order autonomous differential equation with sinusoidal phase detector. The development of this work was performed using rigorous analysis and numerical experiments. Through theoretical analysis the bifurcation structures related to two fundamental equilibrium points of the system are described. By using extensive numerical experiments we investigate the intricate organization between periodic and chaotic domains in parameter space (named here parameter plane as the PLL model has only two control parameters) and obtain two following remarkable findings: (i) there are self-organized generic stable periodic structures along specific directions in parameter plane, whose periods are defined by a mathematical rule and, (ii) the existence of transient chaos phenomenon responsible for long chaotic temporal evolution preceding the asymptotic (periodic) dynamics for some particular control parameter pairs is characterized. Our theoretical and numerical results present an astonishing concordance. We believe that the present study, specially the parameter plane analysis, may have a great importance to experimental studies and general applications involving PLL devices when, for example, one would like to avoid the chaotic regimes.

Nanometric pitch in modulated structures of twist-bend nematic liquid crystals

The extended Frank elastic energy density is used to investigate the existence of a stable periodically modulated structure that appears as a ground state exhibiting a twist-bend molecular arrangement. For an unbounded sample, we show that the twist-bend nematic phase NTB is characterized by a heliconical structure with a pitch in the nanometric range, in agreement with experimental results. For a sample of finite thickness, we show that the wavevector of the stable periodic structure depends not only on the elastic parameters, but also on the anchoring energy, easy axis direction, and the thickness of the sample.

Extensive Numerical Study and Circuitry Implementation of the Watt Governor Model

In this work we carry out extensive numerical study of a Watt centrifugal governor system model, and we also implement an electronic circuit by analog computation to experimentally solve the model. Our numerical results show the existence of self-organized stable periodic structures (SPSs) on parameter-space of the largest Lyapunov exponent and isospikes of time series of the Watt governor system model. A peculiar hierarchical organization and period-adding bifurcation cascade of the SPSs are observed, and this self-organized cascade accumulates on a periodic boundary. It is also shown that the periods of these structures organize themselves obeying the solutions of Diophantine equations. In addition, an experimental setup is implemented by a circuitry analogy of mechanical systems using analog computing technique to characterize the robustness of our numerical results. After applying an active control of chaos in the experiment, the effect of intrinsic experimental noise was minimized such that, the experimental results are astonishingly well in agreement with our numerical findings. We can also mention as another remarkable result, the application of analog computing technique to perform an experimental circuitry analysis in real mechanical problems.

The effect of temperature on generic stable periodic structures in the parameter space of dissipative relativistic standard map

In this work, we have characterized changes in the dynamics of a two-dimensional relativistic standard map in the presence of dissipation and specially when it is submitted to thermal effects modeled by a Gaussian noise reservoir. By the addition of thermal noise in the dissipative relativistic standard map (DRSM) it is possible to suppress typical stable periodic structures (SPSs) embedded in the chaotic domains of parameter space for large enough temperature strengths. Smaller SPSs are first affected by thermal effects, starting from their borders, as a function of temperature. To estimate the necessary temperature strength capable to destroy those SPSs we use the largest Lyapunov exponent to obtain the critical temperature ($T_C$) diagrams. For critical temperatures the chaotic behavior takes place with the suppression of periodic motion, although, the temperature strengths considered in this work are not so large to convert the deterministic features of the underlying system into a stochastic ones.

Dynamic control of spin wave spectra using spin-polarized currents

We describe a method of controlling the spin wave spectra dynamically in a uniform nanostripe waveguide through spin-polarized currents. A stable periodic magnetization structure is observed when the current flows vertically through the center of nanostripe waveguide. After being excited, the spin wave is transmitted at the sides of the waveguide. Numerical simulations of spin-wave transmission and dispersion curves reveal a single, pronounced band gap. Moreover, the periodic magnetization structure can be turned on and off by the spin-polarized current. The switching process from full rejection to full transmission takes place within less than 3ns. Thus, this type magnonic waveguide can be utilized for low-dissipation spin wave based filters.

In Situ Live Observation of Nucleation and Dissolution of Sodium Chlorate Nanoparticles by Transmission Electron Microscopy

The formation of crystals from solution requires the initial self-assembly of units of matter into stable periodic structures reaching a critical size. The early stages of this process , called nucleation, are very difficult to visualize. Here we describe a novel method that allows real time observation of the dynamics of nucleation and dissolution of sodium chlorate clusters in an ionic liquid solution using in situ transmission electron microscopy. Using ionic liquids as solvent circumvents the problem of evaporation and charging, while the nucleation frequency was reduced by using saturated solutions. We observe simultaneous formation and dissolution of prenucleation clusters, suggesting that high-density fluctuations leading to solid cluster formation exist even under equilibrium conditions. In situ electron diffraction patterns reveal the simultaneous formation of crystalline nuclei of two polymorphic structures, the stable cubic phase and the metastable monoclinic phase, during the earliest stages of nucleation. These results demonstrate that molecules in solution can form clusters of different polymorphic phases independently of their respective solubility.

Periodic magnetic structures generated by spin–polarized currents in nanostripes

The influence of a spin-polarized current on long ferromagnetic nanostripes is studied numerically. The current flows perpendicularly to the stripe. The study is based on the Landau-Lifshitz phenomenological equation with the Slonczewski-Berger spin-torque term. The magnetization behavior is analyzed for all range of the applied currents, up to the saturation. It is shown that the saturation current is a nonmonotonic function of the stripe width. For a stripe width increasing it approaches the saturation value for an infinite film. A number of stable periodic magnetization structures are observed below the saturation. Type of the periodical structure depends on the stripe width. Besides the one-dimensional domain structure, typical for narrow wires, and the two-dimensional vortex-antivortex lattice, typical for wide films, a number of intermediate structures are observed, e.g. cross-tie and diamond state. For narrow stripes an analytical analysis is provided.