Quasiperiodic Structures Research Articles

Shear layers in two-stage compound channels investigated with LS-PIV

Flow experiments are conducted in a two-stage compound open-channel, with varying intensity of the velocity difference between the main channel (deep part) and the floodplain (shallower part), using a large-scale free surface PIV technique (LS-PIV). For all investigated flows, a shear layer develops at the interface between main channel and floodplain, characterised by a peak of turbulent shear stress. Yet, two different kinds of shear layer could be identified. The first kind is characterised by the presence of large-scale quasi-periodic structures of Kelvin-Helmholtz type which are growing in downstream direction, whereas the second kind is characterised by smaller-scale vortical structures without quasi-periodicity and which do not grow in downstream direction. The shear parameter lambda =(U_2-U_1)/(U_2+U_1), where U_1 and U_2 are defined as the velocities outside the shear layer, is identified as a key parameter to distinguish between these two types of shear layers, supporting a result from Proust et al. (Water Resour Res 53: 3387–3406, 2017). A physical interpretation of the lambda-criterion is proposed, based on the inhibiting effect of ambient turbulence (the turbulence level outside the shear layer) on the emergence of Kelvin-Helmholtz structures. Accordingly, the threshold value of lambda, above which large-scale structures can develop, is dependent on the level of the ambient turbulence. Despite their very different behaviours, the two types of shear layer have the same efficiency to generate turbulent shear stress for a given velocity difference across the shear layer, except for lambda-values close to the threshold value.

Comparative Analysis of Magnetic Polaritons in Periodic and Quasi-periodic Structures

Comparative Analysis of Magnetic Polaritons in Periodic and Quasi-periodic Structures

Periodic and quasi-periodic one-dimensional phononic crystal biosensor: a comprehensive study for optimum sensor design.

The resonant acoustic band gap materials have introduced an innovative generation of sensing technology. Based on the local resonant transmitted peaks, this study aims to comprehensively investigate the use of periodic and quasi-periodic one-dimension (1D) layered phononic crystals (PnCs) as a highly sensitive biosensor for the detection and monitoring of sodium iodide (NaI) solution. Meanwhile, a defect layer is introduced defect layer inside the phononic crystal designs to be filled with NaI solution. The proposed biosensor is developed based on the periodic PnCs structure and quasi-periodic PnCs structure. The numerical findings demonstrated that the quasi-periodic PnCs structure provided a wide phononic band gap and a large sensitivity compared to the periodic one. Moreover, many resonance peaks through the transmission spectra are introduced for the quasi-periodic design. The results also show that the resonant peak frequency changes effectively with varying NaI solution concentrations in the third sequence of the quasi-periodic PnCs structure. The sensor can differentiate between concentrations ranging from 0 to 35% with a 5% step, which is extremely satisfying for precise detection and can contribute to a variety of issues in medical applications. Additionally, the sensor provided excellent performance for all the concentrations of the NaI solution. For instance, the sensor has a sensitivity of 959 MHz, a quality factor of 6947, a very low damping factor of 7.19 × 10-5, and a figure of merit of 323.529.

New quasiperiodic structures in nematic liquid crystals.

Liquid crystal molecules tend to align with each other, often forming regions of opposite alignment that meet at a boundary-topological defects. These often offer information on configuration of the liquid crystal molecules with competing constraints on their order. Here, we experimentally demonstrate a mechanism to generate topological defects in the form of spatially oscillatory domain walls in nematic liquid crystals. We initially orient the molecules perpendicular to the substrate (i.e. homeotropic alignment) and when a horizontal electric field is applied, domain walls that change their shape with time emerge. These walls form at low frequencies of the applied electric field and remain stable as the frequency increases. If the initial biasing field is at larger frequencies (kHz regime), the domain walls still form, but are not oscillatory. We develop a general theory to predict the three-dimensional liquid crystal director evolution in any two-dimensional varying field. This theory gives the time dependence for the domain walls and confirms that both the oscillatory and straight walls are stable.

Abnormal Domain Growth during Polarization Reversal in Lithium Niobate Crystal Modified by Proton Exchange

The results of an experimental study of the abnormal domain structure kinetics in lithium niobate single crystals with a surface layer modified by soft proton exchange are presented. Domain switching in a wide field range allowed two qualitatively different types of domain structure evolution to be revealed: (1) the traditional growth of hexagonal domains in fields higher than 21.5 kV/mm and (2) the abnormal growth of stripe domains oriented along the Y crystallographic directions in the field range from 3.8 to 21.5 kV/mm. The stripe domains had a width up to 4 µm and depth up to 30 µm. It was shown that the time dependence of the total length of stripe domains could be analyzed in terms of the modified Kolmogorov–Avrami approach, taking into account the transition from the one-dimensional β-model to the one-dimensional α-model. The possibility of the controllable creation of a quasi-periodic structure of stripe domains with an average period of 5 µm by a two-stage polarization switching process was demonstrated. The formation and growth of stripe domains were considered in terms of the kinetic approach to the evolution of the domain structure as a result of the domain walls’ motion under inefficient screening conditions caused by the presence of a modified surface layer. The abnormally low threshold fields were attributed to a presence of a “built-in” field facilitating switching, created by a composition gradient induced by soft proton exchange.

Multiband topological states in the Penrose-triangle photonic crystals.

The topological edge state (TES) and topological corner state (TCS) in photonic crystals (PCs) provide effective ways to manipulate the propagation of light. To improve the performance and integration of topological photonic devices, the realization of multiband topological states by PCs combined with quasi-periodic structure needs to be urgently explored. In this Letter, a Penrose-triangle (P-T) PC, which arranges the basic structural unit of a 12-fold Penrose-type photonic quasi-crystal (PQC) in a triangular lattice, is proposed. The TES and TCS at low- and high-frequency bands can be generated in the same structure, accompanied by the realization of three groups of TCSs. This will provide a new structure for the generation of TESs and TCSs in PCs, and will provide a new way to improve the performance and integration of topological photonic devices.

ELECTROMAGNETIC COUPLING OF PIEZOELECTRIC/FERRITE COMPOSITE WITH INITIAL STRESS STATE

A mathematical model of electromagnetic thermoelasticity for an initial-stressed transversal-isotropic composite with piezoelectric magnetostrictive phases has been developed. To solve the related boundary value problem of electromagnetic thermoe-lasticity, the Green function method was used as part of a generalized singular approximation of the statistical mechanics of composites, taking into account the initial stress state of the representative domain of the composite at micro- and macro-levels. The solution of the problem of "effective module" for tensors of effective elastic, piezomechanical, magnetostrictive properties, dielectric permittivity and magnetic permit-tivity, temperature, pyroelectric, pyromagnetic coefficients and (which appeared only at the macro level) electromagnetic and magnetoelectric couplings of a quasi-periodic composite with an initial electromagnetic elastic state was obtained. The solutions for the desired tensors of effective properties of the quasi-periodic composite are presented in the form of analytical formulas of simple linear decompositions by solutions for tensors of effective properties of the periodic structure and statistical mixture, decomposition coefficients are the coefficient of "periodicity" (correlation of quasi-periodic and periodic structures) p and "disordering" 1-p, respectively. Results of calculation of all independent components of tensors of effective coefficients of electromagnetic and magnetoelectric couplings of different structures (periodic, quasi-periodic and statistical mixture) are presented in unidirectional direction of fibrous composite "PZT-4/ferrite" with axisymmet-ric tensor of initial macrostrain of composite. For a quasi-periodic composite (with initial macrostrain), the significantly non-monotonic nature of the dependencies of relative (to values in the absence of an initial stress state) values of effective coefficients of electromagnetic and magnetoelectric couplings from the volume fraction of ferrite fibers was revealed. It was revealed that we have an increase in the absolute values of the electromagnetic and magnetoelectric coupling coefficients of composite at negative values of its initial axisymmetric axial macrostrains. The most significant effect is the initial comprehensive macrostrain in the transversal plane on the coefficients of the transversal magnetoelectric coupling of the composite.

Multicomponent induced localized coupling in Penrose tiling for electromagnetic wave absorption and multiband compatibility

• Design quasiperiodic absorbers with long-range order but no periodicity. • Explored the relationship between electromagnetic parameters and frequency by structural design and component selection in depth. • The effective absorption bandwidth of Penrose absorber can realize 9.32 GHz in 2 mm thickness. • The multilayer metamaterials perfectly unify radar-infrared compatible capability. In the electronic information and intelligent era, microwave absorption materials have been focused on the issue of electromagnetic (EM) pollution, but high-performance absorbers with thin thickness are highly desirable. The positive action between structural design and component selection can be regarded as a function to optimize the microwave loss capacity, which contributes to understanding the response mechanisms from the micro and macro. Therefore, we designed the absorber with quasiperiodic structures of Penrose tiling that has finely engineered the location of maximum absorption peak, the spherical carbonyl iron in thin rhombus, and flakey carbonyl iron in fat rhombus, the effective absorption bandwidth (Reflection Loss ≤ –10 dB) was realized from 6.46 GHz to 15.78 GHz in the 2 mm thickness. The unique arrangement of Penrose tiling can respond alternatingly to EM waves at large scales, and multicomponent coupling is distinctly in the neighboring unit cells. In addition, spraying aluminum pigment as the upper layer, the infrared emissivity is less than 0.35 to meet the complex application environment. This work opens up novel ideas on quasiperiodic structure combined multicomponent and injects infinite vitality to provide prospects for broadband responsive and high-efficiency EM absorbers.

Quasi-periodic and chaotic structure of Alfvén waves in a plasma containing double spectral distributed electrons

The nonlinear characteristics of Alfvén waves in a plasma medium composed of double spectral electron distribution and positive and negative ions are investigated. A Korteweg–de Vries (KdV-type) equation is derived using the reductive perturbation technique. The periodic and soliton structures are investigated. The effects of the two spectral indices r and q on the produced periodic structures are studied. It is found that the amplitude of the rarefactive periodic wave increases by increasing the values of r and q. Some external perturbation intruders on the system are considered, and the quasi periodic and chaotic structures of Alfvén waves are discussed. It is found that by decreasing the values of β− (knowing that β known as the ratio of kinetic to magnetic pressures), the periodic structure is converted gradually into chaotic structure passing through the quasi-periodic one. The results of this study are helpful in describing the behavior of the Alfvénic structure of periodic waves and other related events in the ionosphere region.

Application of the laws to compose fractal computation algorithms when modeling and analyzing their growth

Generalized analysis of the methods to construct fractals let to find algebraic patterns of fractal algorithm, fractal operators fi formalizing basic operations to construct the fractal structures of a specific type being the major concept. The fi are introduced with multiplication and addition operations together with the concepts of singular, zero and inverse operator that allow defining periodic and quasi-periodic fractal structures. An endless fractal length - basic operator which can give a possibility to obtain a limit fractal synthesis idea as a structure without self-similarity but with a regularly decreasing scale. The connection between fractal growth computations and widely examples of application in the nature is considered. Methods to analyze growth processes are offered, their basic characteristics are shown. The mathematical description of the fractal growth characteristics and their dependence on specifically defined parameters of algorithm are given. The analysis of fractal point growth trajectory is made. The algorithms applied and the methods to analyze growth processes are shown to be modernized and adapted for wide spectrum of tasks.

A WISER way for simulating the performance of gratings.

Soft X-ray monochromators for synchrotron radiation sources have been continuously developed over the years, improving energy resolution and stability. Great effort has been made in improving the surface quality of the optics involved, reaching values permitting diffraction-limited images. Still, one problem has not been solved, nor fully understood, yet: groove placing errors. Nowadays, these are one of the major factors responsible for resolving the power reduction of diffraction-gratings-based X-ray monochromators. Despite decades of use of gratings, there is not yet a universally established method for predicting and simulating the effect of groove placing errors on monochromator performance. This is especially important in the new scenario of high-coherent X-ray sources, i.e. diffraction-limited storage rings and free-electron lasers. To address this problem, in this article an approach based on WISER (Wavefront propagatIon Simulation codE libRary) is presented. WISER is a physical optics simulation package, also available in the user-friendly Orange Synchrotron Radiation Suite - OASYS. Even though it was originally conceived to assess the focusing performance of X-ray mirrors in the presence of height defects, it perfectly simulates the performance of a periodic (or quasi-periodic) structure like a diffraction grating. In this article, the way to use WISER and its application to a specific case, e.g. the design of a monochromator for the upgrade of a beamline at the Advanced Light Source, are shown. A simple rule for estimating how well the grooves are placed on a grating, based on calculation of the Strehl ratio, is also presented.

Complex Processing of Lidar Survey Data of Marine Areas

The complex processing of data from the shipborne lidar survey of the Black Sea coastal areas was carried out. In this area, internal waves are often observed according to contact and satellite observations. The source of probing linearly polarized laser pulses in the lidar is a solid-state laser with diode pumping of the YAG: Nd active element with a pulse power of 20 mJ at a wavelength of 532 nm and a duration of 7 ns. The co- and cross-polarized components of the echo signal were recorded during the lidar survey. The cross-polarized component of the echo signal was mainly used due to its greater sensitivity to various kinds of inhomogeneities in the vertical distribution of hydrooptical characteristics. The purpose of processing is to identify quasi-periodic structures in the spatial distribution of the characteristics of lidar echo signals caused the propagation of short-period internal waves. Three processing methods were applied: the approximation method, the wavelet analysis method, and the Hilbert-Huang transform method. A large array of data obtained during 50 hours of lidar survey has been processed. Three 60-minute tracks containing quasi-periodic structures have been identified. The three processing methods results are in good agreement with each other and make it possible to obtain the most complete information about the parameters of the studied processes. The parameters of the recorded quasi-periodic processes are typical for internal waves observed in the coastal areas of the Black Sea. In the future, when processing a large amount of lidar sounding data, it is advisable to carry out fast processing by automated spectral methods at the first stage, and to carry out detailed processing by the approximation method only for those survey areas where quasi-periodic processes have been identified.

Two-scale cut-and-projection convergence for quasiperiodic monotone operators

Averaging a certain class of quasiperiodic monotone operators can be simplified to the periodic homogenization setting by mapping the original quasiperiodic structure onto a periodic structure in a higher dimensional space using the cut-and projection method. We characterize the cut-and-projection convergence limit of the nonlinear monotone partial differential operator −divσx,Rxη,∇uη for a bounded sequence uη in W01,p(Ω), where 1<p<∞, and Ω is a bounded open subset in Rn with Lipschitz boundary. We identify the homogenized problem with a local equation defined on a hyperplane, or a lower dimensional plane in the higher-dimensional space. A new corrector result is established.

ITO-based metamaterials for polarization-independent wide-angle mid-infrared thermal radiation

The realization of mid-infrared thermal radiation based on metamaterials insensitive to angle and polarization plays an important role in various thermal photonic applications. However, the challenges include the following: most previously designed thermal emitters usually contain metal components with unsatisfied physicochemical stability, accompanied with complex manufacturing technology. The present study proposes a mid-infrared thermal emitter at 3–6 μm wavelength range based on Fibonacci quasi-periodic structure, and a flat one-dimensional structure based on Fibonacci geometry resorting to ITO is designed. The proposed thermal emitter is, theoretically and experimentally, proven to possess good angular and polarization-independent selective thermal emission performance in a relatively wide infrared wavelength range. Furthermore, the good optical and high-temperature thermal stability of the designed thermal emitter is verified in the present experimental research. The thermal emitters proposed have advantages in polarization-independence without scale restraint and low cost but with wide vision. In summary, the present study provides a new tactics for obtaining non-metal spectral selective thermal emitters in a relatively wide wavelength range and thermal photonic applications under harsh conditions.

Additional Cover

The cover image is based on the Research Article Topology optimization design of multi-material quasi-periodic cellular structures for thermoelastic responses by Guowei Liang et al., https://doi.org/10.1002/nme.7012.

Quasi-periodic one-dimensional photonic crystal as a perspective structures for nanophotonics: Analysis of transmittivity spectra

The characteristic matrix approach is used to evaluate optical transmission spectra for a 1D multilayered photonic system. The characteristics of transmittance are analyzed for different incident angles, layer thicknesses (from a few to hundred nanometers), and electron densities for the light wave propagating through both periodic and quasi-periodic photonic structures. The shifting trend of photonic band gap in the infrared wavelength regimes is observed for different types of quasi-sequence. Increased electron density, on the other hand, makes the band gap more robust, although collision frequency has a minor effect on the band gap. Moreover, the physical entities play a key role in the appearance of multiple band gaps in the greater wavelength regimes. For example, such nanophotonic devices as optical bandpass filters in the infrared regime can be designed by using the concept of the proposed structure. We further show that the suggested quasi-periodic multilayered structures can function as resilient adjustable photonic lattices with the above-mentioned properties that can be tuned.

High-quality resonances in quasi-periodic clusters of scatterers for flexural waves

Multiple scattering theory is applied to the study of clusters of point-like scatterers attached to a thin elastic plate and arranged in quasi-periodic distributions. Two types of structures are specifically considered: the twisted bilayer and the quasi-periodic line. The former consists in a couple of two-dimensional lattices rotated a relative angle, so that the cluster forms a moiré pattern. The latter can be seen as a periodic one-dimensional lattice where an incommensurate modulation is superimposed. Multiple scattering theory allows for the fast and efficient calculation of the resonant modes of these structures as well as for their quality factor, which is thoroughly analyzed in this work. The results show that quasi-periodic structures present a large density of states with high quality factors, being therefore a promising way for the design of high quality wave-localization devices.

Optimal design for vibration energy harvesters based on quasi-periodic structures

In this paper, the design of large-scale quasi-periodic Vibration Energy Harvesters (VEH) is optimized to enhance the harvested power of an electromagnetic mode localized structure. This work aims to optimize the output power by employing the energy localization phenomenon in a large-scale periodic configuration by introducing the minimum number of perturbations. The harvested power, number and location of perturbations are among the objectives that need to be optimized. A genetic-based mixed-integer optimization algorithm is used to meet the objective functions within a constraint on the system kinetic energy. Numerical simulations for quasi-periodic systems with 20 and 100 Degrees of Freedom (DOF) are performed. It is shown that the ratio of harvested power increases as the number of perturbations rises and it exceeds 80% of the total output power by perturbing almost one-third of the total DOFs. The proposed methodology is a decision-making aid to provide an optimal design in a generalized quasi-periodic VEH in order to reduce the number of harvesting transducers while providing a significantly high amount of harvested power.

Optical computing of quantum revivals.

Interference is the mechanism through which waves can be structured into the most fascinating patterns. While for sensing, imaging, trapping, or in fundamental investigations, structured waves play nowadays an important role and are becoming the subject of many interesting studies. Using a coherent optical field as a probe, we show how to structure light into distributions presenting collapse and revival structures in its wavefront. These distributions are obtained from the Fourier spectrum of an arrangement of aperiodic diffracting structures. Interestingly, the resulting interference may present quasiperiodic structures of diffraction peaks on a number of distance scales, even though the diffracting structure is not periodic. We establish an analogy with revival phenomena in the evolution of quantum mechanical systems and illustrate this computation numerically and experimentally, obtaining excellent agreement with the proposed theory.

Hofstadter butterfly and topological edge states in a quasiperiodic photonic crystal cavity array.

Quasiperiodic structures with additional synthetic degrees of freedom have recently been recognized as a promising way for investigating high-dimensional topological phases with lower physical dimensions. Here, we investigated the well-known Harper-Aubry-André model on an integrated photonic platform by proposing a new design of a quasiperiodic photonic crystal (PhC) cavity array. This array is composed of closely coupled H1 PhC cavities with their cavity lengths being periodically modulated in the real space. The frequency spectrum of the structure shows the main features of the Hofstadter butterfly, which is one of the most important phenomena in the Harper-Aubry-André model. By varying the modulation phase, this structure exhibits nontrivial topology, which supports strongly localized topological edge states. These results have shown that quasiperiodic PhC cavity arrays can serve as the testbed for studying topological phases and new topological phenomena on an integrated platform.