Periodic Structures Research Articles

Modeling ground vibration excited by a high-speed train running along a viaduct railway using a new structure-soil interaction method

Ground vibrations generated by high-speed trains running along railways either at grade or on viaduct bridges, are greatly concerned by the railway industry. Considering the train-track-bridge-abutment-pile-soil interactions involved, modeling the problem in an analytical manner is almost impossible, while conventional numerical methods struggle to accurately simulate the dynamic properties of infinitely large soils. Therefore, this study introduces a new substructure methodology for train-track-bridge-abutment-pile-soil interactions that leverages an ingenious combination of the 2.5-dimensional finite element-boundary element method (2.5D FE-BE) for dynamics of infinitely long periodic structures, and a local 3-dimensional finite element model for pile-soil interaction. This innovative method allows for the consideration of detailed pile-soil coupling using a local finite element model, all while retaining the ability to account for the infinite size of the soil structure using the 2.5-dimensional finite element-boundary elements. After a comparison between model prediction and field measurement, the model is employed to explore the environmental vibration characteristics of on-viaduct high-speed railways and analyze the vibration reduction effects of various measures, including rail fasteners, track slab pads, and bridge bearings.

Optothermal‐Enabled Reconfigurable Colloidal Photonic Crystals for Color and Spectrum Manipulation

AbstractColloidal photonic crystals (CPCs) are extensively utilized in nanoscale light manipulation due to their periodic dielectric structure. However, achieving spatial reconfigurability in CPCs remains a significant challenge, despite its importance for broader photonic applications in colloidal science. In this study, an optically induced thermoelectric field is generated by adding ionic surfactants to the solution, leading to the efficient formation of tightly assembled nanoparticles that exhibit the characteristics of CPC, which is termed optothermo‐CPC. Specifically, this CPC exhibits excellent spatial reconfigurability through the tuning of the optically induced thermoelectric field. This allows for the remote control of its position and shape, in a real‐time and high‐precision manner. Additionally, by changing the particle size, it is possible to tune the transmission spectrum and color. Additionally, optothermo‐CPC can navigate obstacles and possess a robust self‐healing ability. These highly adaptable and reconfigurable properties endow CPCs with significant potential for various photonic applications within complex fluidic environments.

Various Grids in Moiré Measurements

The moiré effect is typically observed in regular periodic structures and sometimes in random (aperiodic) structures. However, currently, only regular graphical objects are used in measurements. We propose using graphical objects that are not regular but not entirely random and that resemble rows, such as grids of dotted lines or matrixes of dots. The moiré effect in such objects may become similar to the moiré effect in regular graphical objects if a relatively simple modification of the image processing algorithm is applied. We demonstrated that the results of measurements with five different graphical objects arranged in rows (including text) are similar. Using such objects can be helpful for practical moiré measurements.

Three-channel demultiplexer based on one-dimensional magnonic crystal waveguides using defect modes

Abstract In this work, the transfer matrix method is used to study magnetostatic spin waves (SWs) in magnonic crystal (MC) waveguide. By eliminating structural symmetry and creating a defect in a completely periodic structure, the localization of SWs with frequencies corresponding to the defect mode in the band gap has been realized. The proposed structure consists of three yttrium-iron-garnet films with the same thickness, 5 μm, with an array of etched grooves with different defects. The designed demultiplexer filters specific frequencies with high precision and directs them to designated outputs. The quality factor for the MC waveguides is 20901, 20903 and 20904 at central frequency of 6.2704 GHz, 6.2709 GHz and 6.2714 GHz, respectively. The results demonstrate that the proposed structure leads to the realization of the three-channel GHz-ranged demultiplexer in magnonic circuits.

Association analysis of Talbot positive self-image and negative self-image for spherical wave illuminating on planar grating

Based on planar grating Fresnel diffraction theory, the correlation between Talbot positive self-image and negative self-image for spherical wave illuminating on planar grating is analyzed by theoretical and experimental methods. The results indicate that Talbot positive and negative self-images of orders 0 and ±1 show a checkerboard shape with periodic structure, with opposite phases when the period magnification factor M is the same. However, the detail of Talbot positive self-image is more detailed than the negative self-image, due to phase reversal and changes in Talbot distance, which imply a relationship of mutual constraints between the two images. Additionally, the peak light intensity of positive and negative self-image increases with the increase of M. Talbot positive and negative self-image are observed at corresponding Talbot distance by theoretical and experimental results, and Talbot distance of the two Talbot images is obviously divided into rapidly decreasing and slowly changing as z 0 increases.

Periodic, quasi-periodic, chaotic waves and solitonic structures of coupled Benjamin-Bona-Mahony-KdV system

Abstract In this paper, we mainly focus on studying the dynamical behaviour and soliton solution of the coupled Benjamin-Bona-Mahony-Korteweg–de Vries (BBM-KdV) system, which characterizes the propagation of long waves in weakly nonlinear dispersive media. The paper utilizes different tools to detect chaos, such as time series analysis, bifurcation diagrams, power spectra, phase portraits, Poincare maps, and Lyapunov exponents. This analysis helps in more accurate predictive modeling of the systems. This understanding can aid in the design of control strategies, resulting in enhancements in prediction, control, optimization, and design. Additionally, we construct the system’s solitary wave structures using the Jacobi elliptic function (JEF) method. We identify periodic wave solutions expressed in terms of rational, hyperbolic, and trigonometric functions. Certain parameter values can lead to periodic wave solutions, solitary waves (bell-shaped solitons), shock wave solutions (kink-shaped soliton solutions), and double periodic wave solutions.

Improving the functionality of biosensors through the use of periodic and quasi-periodic one-dimensional phononic crystals

Abstract Resonant acoustic band gap materials have steered a new sensing technology era. This study is presented to investigate of the one-dimensional (1D) phononic crystals (PnCs), involving periodic, as well as quasi-periodic 1D layered PnCs represented as a highly sensitive biosensor to detect and monitor the quality of milk. In this regard, the numerical findings show that the examined periodic PnCs structure outperformed the quasi-periodic structure. In particular, it provides a wider phononic band gap and greater sensitivity as well. In addition, the quasi-periodic design (especially Fibonacci sequence S4) introduces multiple resonance peaks via transmission spectra, which may lead to some conflicts during the detection process. The findings reveal that the frequency of the resonant peak can effectively change with varied milk solution concentrations and temperatures. The optimized sensor is capable of differentiating between concentrations ranging between 0 and 50 % with a 10 % step, and it can also differentiate between temperatures, which range between 5 °C and 50 °C. This makes it ideal for precise detection of other liquids and solutions. The sensor performs efficiently for all milk solution concentrations. Here, the findings demonstrated that the examined defective PnC structure exhibited the most favorable sensitivity of the value of 94.34 MHz, so it showed the highest sensitivity when varying milk concentrations. In addition, the configurated sensor provided high QF and FOM values of 3,853.645161 and 157.42, respectively. On the other hand, the sensor performs very well for all temperatures of the milk solution. As such, the S 4 quasi-periodic structure is characterized as the optimal sensor structure when varying temperatures, introducing a sensitivity of 4.78 MHz/°C, QF of 4,278.521, and FOM of 7.48 °C−1.

Can one hear the shape of a crystal?

Isospectrality is a general fundamental concept often involving whether various operators can have identical spectra, i.e., the same set of eigenvalues. In the context of the Laplacian operator, the famous question “Can one hear the shape of a drum?” concerns whether different shaped drums can have the same vibrational modes. The isospectrality of a lattice in d-dimensional Euclidean space Rd is a tantamount to whether it is uniquely determined by its theta series, i.e., the radial distribution function g2(r). While much is known about the isospectrality of Bravais lattices across dimensions, little is known about this question of more general crystal (periodic) structures with an n-particle basis (n≥2). Here, we ask what is nmin(d), the minimum value of n for inequivalent (i.e., unrelated by isometric symmetries) crystals with the same theta function in space dimension d? To answer these questions, we use rigorous methods as well as a precise numerical algorithm that enables us to determine the minimum multiparticle basis of inequivalent isospectral crystals. Our algorithm identifies isospectral four-, three- and two-particle bases in one, two, and three spatial dimensions, respectively. For many of these isospectral crystals, we rigorously show that they indeed possess identically the same g2(r)'s for all values of r. Based on our analyses, we conjecture that nmin(d)=4, 3, 2 for d=1, 2, 3, respectively. The identification of isospectral crystals enables one to study the degeneracy of the ground-state under the action of isotropic pair potentials. Indeed, using inverse statistical-mechanical techniques, we find an isotropic pair potential whose low-temperature configurations in two dimensions obtained via simulated annealing can lead to both of two isospectral crystal structures with n=3, the proportion of which can be controlled by the cooling rate. Our findings provide general insights into the structural and ground-state degeneracies of crystal structures as determined by radial pair information. Published by the American Physical Society 2024

Selective Ablation and Laser-Induced Periodical Surface Structures (LIPSS) Produced on (Ni/Ti) Nano Layer Thin Film with Ultra-Short Laser Pulses

The interaction of ultra-short laser pulses (USLP) with Nickel/Titanium (Ni/Ti) thin film has been presented. The nano layer thin film (NLTF), composed of ten alternating Ni and Ti layers, was deposited on silicon (Si) substrate by ion-sputtering. A single and multi-pulse irradiation was performed in air with focused and linearly polarized laser pulses. For achieving selective ablation of one or more surface layers, without reaching the Si substrate, single pulse energy was gradually increased from near the ablation threshold value to an energy value that caused the complete removal of the NLTF. In addition to single-pulse selective ablation, the multi-pulse USLP irradiation and production of laser-induced periodic surface structures (LIPSSs) were also studied. In the presented experiment, we found the optimal combination of accumulated pulse number and pulse energy to achieve the LIPSS formation on the thin film. The laser-induced morphology was examined with optical microscopy, scanning electron microscopy, and optical profilometry. To interpret the experimental observations, a theoretical simulation has been performed to explore the thermal response of the NLTFs after irradiation with single laser pulses.

Progress and Perspective of High‐Entropy Strategy Applied in Layered Transition Metal Oxide Cathode Materials for High‐Energy and Long Cycle Life Sodium‐Ion Batteries

AbstractLayered transition metal oxide (LTMO) cathode materials of sodium‐ion batteries (SIBs) have shown great potential in large‐scale energy storage applications owing to their distinctive periodic layered structure and 2D ion diffusion channels. However, several challenges have hindered their widespread application, including phase transition complexities, interface instability, and susceptibility to air exposure. Fortunately, an impactful solution has emerged in the form of a high‐entropy doping strategy employed in energy storage research. Through the implementation of high‐entropy doping, LTMOs can overcome the aforementioned limitations, thereby elevating LTMO materials to a highly competitive and attractive option for next‐generation cathodes of SIBs. Thus, a comprehensive overview of the origins, definition, and characteristics of high‐entropy doping is provided. Additionally, the challenges associated with LTMOs in SIBs are explored, and discussed various modification methods to address these challenges. This review places significant emphasis on conducting a thorough analysis of the research advancements about high‐entropy LTMOs utilized in SIBs. Furthermore, a meticulous assessment of the future development trajectory is undertaken, heralding valuable research insights for the design and synthesis of advanced energy storage materials.

A homogenization model for multiple buckling response of axially compressed cellular cylindrical shells

Pattern transformation in periodic cellular structures induces significant property changes under specific external stimuli, resulting in unusual mechanical behavior. This paper proposes an efficient homogenization method for predicting multiple buckling responses of cellular cylindrical shells composed of such pattern-transformation metamaterial. FEM simulations reveal four distinct buckling modes and three kinds of post-buckling processes, achieved through controlled adjustments in the ratio of cylindrical shell thickness to the radius and structural porosity. An efficient homogenization method with the local buckling in the cellular cylindrical shell modeled as an equivalent plasticity in the homogenized shell enables us to predict the critical buckling stress and the post-buckling morphology in good agreement with FEM simulations, analytical analysis, and experiments. The derived solution for the critical buckling load of the cellular cylindrical shells provides practical insights for designing and applying such cylindrical cellular structures.

Detection of Nonlinearity in Photonic Lattices

AbstractAlthough periodic photonic structures, especially associated with nonlinearity, play a prominent role in optics nowadays, effective detection of their nonlinearity still remains a critical challenge. Here, an approach is proposed to detect the nonlinearity of photonic lattices in a direct way. By properly launching structured beams, namely Airy beams, into the lattices, the nonlinear response function of the discrete system can be directly obtained in the nonlinearly‐shaped beam profiles. To be specific, a single Airy beam is utilized to map self‐defocusing nonlinearity, while self‐focusing nonlinearity, which is hard to visualize in the bulk case, is readily discerned by employing double Airy beams in photonic structures. The proposed method is validated numerically and experimentally by detecting different types of nonlinearities of photonic lattices fabricated in a nonlinear crystal. These findings introduce a promising route for characterizing the nonlinear response of optical structures, thereby broadening the scope of nonlinear measurement and is expected to be extended into other periodic photonic structures.

A nonuniform mesh method in the Floquet parameter domain for wave scattering by periodic surfaces

In this paper, we propose a new numerical method to simulate acoustic scattering problems in two‐dimensional periodic structures with non‐periodic incident fields. Applying the Floquet‐Bloch transform to the scattering problem yields a family of quasi‐periodic boundary value problems dependent on the Floquet‐Bloch parameter. Consequently, the solution of the original scattering problem is written as the inverse Floquet‐Bloch transform of the solutions to these boundary value problems. The key step in our method is the numerical approximation of this integral transform by a quadrature rule with a nonuniform choice of quadrature points adapted to the regularity of the family of quasi‐periodic solutions. This achieved by a graded subdivision of the full interval for the Floquet‐Bloch parameter and applying a Gauss‐Legrendre quadrature rule on each subinterval. We prove that the numerical method converges exponentially with respect to both the number of subintervals and the number of Gaussian quadrature points. Some numerical experiments are provided to illustrate the results.

Spin-based Atomic Periodic Model—Beyond the Periodic Table

The present article explores the potential re-arragement of all the periodic elements in terms of the spin of their valence electron, modeling them as up-spin or down-spin pointing triangles that together result in larger triangles precluding subshells, shells and the whole electron cloud (as a spin-balanced whole). Stratification of the elements according to their ratio of principal to azimuthal quantum number creates different angular cones, that not only align the elements into a compliante alternative interpretation to Mandelung’s rule, but ultimately result in a three dimensional periodic structure (that fans out and grows radially from the nucleus), resembling the shape of a flower. The model’s energetic umbrella predicts the elements Ununennium and Unbinilium. Electrical and thermal conductivities are mapped onto the new model, suggesting the existance of an instability (peak in 2D or axis in 3D) that governs the (non-) metal nature of the elements.

Inverse opal TiO2-CdS photonic crystal beads with slow light effect for photocatalytic degradation

Photocatalytic oxidation technology using solar energy is an effective strategy to solve environmental pollution and energy shortage. To avoid angle dependence of traditional photonic crystal photocatalysts and address the limitations of high charge recombination rate and low light utilization of TiO2, this study proposed a novel inverse opal TiO2/CdS photonic crystal beads (IO TiO2/CdS PCBs) photocatalyst. By leveraging the synergistic coupling of PCBs’ slow light effect and TiO2/CdS heterojunction, the photocatalytic activity was significantly enhanced. The results revealed that the PCBs matching the blue edge with TiO2′s electronic band gap (IO TiO2-140 PCBs) exhibited the highest apparent rate constant of 0.01901 min−1. By introducing CdS to form a heterojunction with TiO2, the photocatalytic performance was further improved by effectively inhibiting the recombination of photogenerated carriers. The degradation rate of RhB reached 96.6 % in 60 min, outperforming that of IO TiO2 at 65.1 %, with the rate constant increasing by 3.1 times. Electron spin resonance and trapping experiments indicated that h+ was the main active specie, and the possible reaction mechanism path was proposed. The combination of “extrinsic” modifications by doping CdS and “self-structural” modifications by shaping TiO2 into periodic IO PCBs structure provided a systematic insight on the design of novel photocatalysts.

Frequency Selective Surfaces: Design, Analysis, and Applications

This paper aims to provide a general review of the fundamental ideas, varieties, methods, and experimental research of the most advanced frequency selective surfaces available today. Frequency-selective surfaces are periodic structures engineered to work as spatial filters in interaction with electromagnetic (EM) waves with different frequencies, polarization, and incident angles in a desired and controlled way. They are usually made of periodic elements with dimensions less than the operational wavelength. The primary issue examined is the need for more efficient, compact, and adaptable electromagnetic filtering solutions. The research method involved a comprehensive review of recent advancements in FSS design, focusing on structural diversity, miniaturization, multiband operations, and the integration of active components for tunability and reconfigurability. Key findings include the development of highly selective miniaturized FSSs, innovative applications on flexible and textile substrates, and the exploration of FSSs for liquid and strain sensing. The conclusions emphasize the significant potential of FSS technology to enhance wireless communication, environmental monitoring, and defense applications. This study provides valuable insights into the design and application of FSSs, aiming to guide future research and development in this dynamic field.

Focal volume optics for composite structuring in transparent solids

Abstract Achieving high-level integration of composite micro-nano structures with different structural characteristics through a minimalist and universal process has long been the goal pursued by advanced manufacturing research but is rarely explored due to the absence of instructive mechanisms. Here, we revealed a controllable ultrafast laser-induced focal volume light field and experimentally succeeded in highly efficient one-step composite structuring in multiple transparent solids. A pair of spatially coupled twin periodic structures reflecting light distribution in the focal volume are simultaneously created and independently tuned by engineering ultrafast laser-matter interaction. We demonstrated that the generated composite micro-nano structures are applicable to multi-dimensional information integration, nonlinear diffractive elements, and multi-functional optical modulation. This work presents the experimental verification of highly universal all-optical fabrication of composite micro-nano structures with independent controllability in multiple degrees of freedom, expands the current cognition of ultrafast laser-based material modification in transparent solids, and establishes a new scientific aspect of strong-field optics, namely, focal volume optics for composite structuring transparent solids.

Laser power modulation between disturbed and undisturbed material removal regime in laser chemical processing

Laser chemical machining (LCM) is a method for removing material by thermally induced chemical dissolution of self-passivating metals. However, the process window is limited by disrupted material removal due to gas bubble formation and metallic salts and oxides deposition at higher energy input. Since the temperature increases, and therefore gas bubble growth takes time, it is hypothesized that the temporal modulation of laser power can remove the metal homogeneously, i.e., without disrupted material removal, while achieving a higher removal rate. Based on this, the dynamic process behavior of material removal is investigated for the LCM of titanium in phosphoric acid, using a rectangular modulation of the laser power with varying irradiation durations. As a result, however, high-speed videos show that gas bubbles are consistently generated, regardless of the applied laser power and power modulation, although the quantity of bubbles varies with different parameters. Even with short power durations (10 ms), the material deposition occurs after multiple irradiations. When the duration is longer, the material deposition increases in height along the laser scan direction. For the studied process parameters, a Fourier analysis in the spatial domain further indicates the correlation between the material removal frequencies and the modulation frequencies. In conclusion, the laser power modulation cannot prevent the disturbed material removal at high laser powers. Nevertheless, the material deposition can be utilized to generate periodic surface structures with a depth below and above the initial surface.

Reverse design and application of phononic crystals based on deep learning

Abstract This paper reverse-design phononic crystals with band gaps within a targeted frequency band using the trained conditional variational autoencoder (CVAE) and further studies the vibro-acoustic characteristics of a composite sandwich plate with a phononic crystal panel as the core layer. Firstly, a matrix composed of 0 s and 1 s, representing scatterers and substrates, is randomly generated by MATLAB to represent two-dimensional phononic crystals. The three-dimensional phononic crystals are obtained by stretching the two-dimensional phononic crystals along the average direction, and COMSOL Multiphysics is used to calculate the band gap. In order to maximize the production of phononic crystals with a band gap distribution, the convolutional neural network is trained to predict whether the generated phononic crystals have band gaps. Finally, using data on the structures of phononic crystals and their band gap distributions, the CVAE is trained to achieve the reverse design of artificial periodic structures based on the target band gap. To verify the effectiveness of the structures obtained through the reverse design method on vibration and noise reduction, the submerged vibro-acoustic characteristics of a composite sandwich plate are studied. The plate consists of a phononic crystal panel and carbon fiber panels. The model of the composite sandwich plate is fabricated, and its submerged vibro-acoustic characteristics are tested and compared with numerical results. Finally, the submerged vibro-acoustic response levels of composite sandwich plates with phononic crystal panels and honeycomb panels as core layers are compared using numerical methods. This comparison assesses the phononic crystal panel’s vibration and noise reduction effects.

Enhanced microwave absorption of sandwich panels with magnetized carbon fiber corrugated array reinforced PMI foam core

AbstractIntegrating periodic array structures made of metal wires or conductive inks into the foam core of electromagnetic (EM) wave absorbing sandwich panels can significantly improve broadband absorption performance. However, the complex fabrication process and poor corrosion resistance of these materials limit their practical applications. This work innovatively introduces magnetized carbon fiber (CF) into PMI foam, simultaneously achieving broadband absorption and lightweight characteristics of the sandwich structure through the design of array structure and fiber bundle geometry. Simulation analysis compared the EM absorption performance of sandwich panels with carbonyl iron powder (CIP)/CF tape and helical twisted CIP/CF rope corrugated arrays, determining the optimal array structure parameters, which were then experimentally validated. The experimental results align with the simulations, showing that CIP/CF rope corrugated arrays with an amplitude of 10 mm, a cycle length of 15 mm, and an array spacing of 15 mm provide optimal absorption performance, with a reflection loss below −10 dB across the 9–18 GHz frequency range and a maximum absorption of −33.9 dB at 17 GHz. Finally, the absorption mechanism of these sandwich structures is discussed, highlighting how the synergistic effects between the electromagnetic properties and structural morphology of CIP/CF enhance the absorption performance of the EM absorbing sandwich panel.