Periodic Configurations Research Articles

Band gap generation in cantilever beams through periodic material removal

Traditional methods for generating band gaps in beams usually involve adding periodic elements like tuned mass dampers or masses, or applying complex geometrical changes. This research suggests a subtraction-based method achieved by removing material in the thickness direction through straightforward machining operations, thus forming periodic cells. The numerical studies start with band gap analysis, using periodic theory to assess different periodic cell configurations. This is followed by numerical and experimental studies on cantilever beams, each containing a set number of these periodic cells. Non-contact vibration measurements are conducted on one plain and six machined aluminum beams using a multipoint laser vibrometer and an automated impact hammer. The experimental findings corroborate the band gaps predicted by the numerical model, confirming the effectiveness of this approach. The study notes that the optimal periodicity of the cells and the contrast in thickness vary with the beam’s dimensions, and that the thickness contrast markedly affects the quantity, width, and intensity of the resulting band gaps. These results indicate that (1) periodic material removal in beam-like structures allows improved vibration reduction while mass is reduced, and (2) manufacturing can play a key role in vibration control in simple structures.

The role of non-uniform magnetization texture for magnon–magnon coupling in an antidot lattice

We numerically study the spin-wave dynamics in an antidot lattice based on a Co/Pd multilayer structure with reduced perpendicular magnetic anisotropy at the edges of the antidots. This structure forms a magnonic crystal with a periodic antidot pattern and a periodic magnetization configuration consisting of out-of-plane magnetized bulk and in-plane magnetized rims. Our results show a different behavior of spin waves in the bulk and in the rims under varying out-of-plane external magnetic field strength, revealing complex spin-wave spectra and hybridizations between the modes of these two subsystems. A particularly strong magnon–magnon coupling, due to exchange interactions, is found between the fundamental bulk spin-wave mode and the second-order radial rim modes. However, the dynamical coupling between the spin-wave modes at low frequencies, involving the first-order radial rim modes, is masked by the changes in the static magnetization at the bulk–rim interface with magnetic field changes. The study expands the horizons of magnonic-crystal research by combining periodic structural patterning and non-collinear magnetization texture to achieve strong magnon–magnon coupling, highlighting the significant role of exchange interactions in the hybridization.

Geometrical uncertainties influence on the failure load estimation of lattice structures

Lattice structures can provide high strength with modest weight. For this reason, they are found in many natural systems at the microscopic level and have also been adopted in engineering at many scales. Assessment of the load-bearing capacity of such structures is crucial and cannot ignore considerations of imperfections, whether due to natural factors if the material exists naturally or to manufacturing defects if it is created artificially. Defects can affect many geometrical aspects of the lattice such as the shape of cells and the thickness and the waviness of trusses. In this paper, we will focus on the first aspect, investigating the effect of variation of the shape of the cells by applying a perturbation to the periodic configuration for common geometries. The failure load of these systems is evaluated by means of an upper bound limit analysis through linear programming, varying the relative density of the lattice and the intensity of imperfections. The failure load is addressed by statistical moments and probability density functions.

DUGKS-GPU: An efficient parallel GPU code for 3D turbulent flow simulations using Discrete Unified Gas Kinetic Scheme

This paper presents a parallel implementation of the Discrete Unified Gas Kinetic Scheme (DUGKS) on the GPU system using the CUDA Fortran and CUDA C++ programming languages. Firstly, we conducted an extensive revision of our original CPU-based code, resulting in a threefold decrease in memory usage. This new implementation is also paired with a novel approach to compute cell face flux using trilinear interpolation. It is shown analytically that the interpolation-based approach to flux calculation is more accurate compared to the one used in the original DUGKS. The initial simulation results using this new approach suggest that trilinear interpolation can reduce numerical errors on a coarse mesh. For example, in the case of the decaying Taylor-Green vortex flow at a 1283 mesh resolution, the relative numerical error in the energy dissipation rate at t⁎=2, using the spectral simulation result as the benchmark, is approximately 30% lower than that of the original implementation. The improved GPU DUGKS method is applied to laminar and turbulent flows in periodic and wall-bounded boundary configurations. A performance comparison of the GPU implementation is also presented and compared to the previous CPU implementation. A maximum speedup of 7.64x was achieved on a desktop-level GPU compared to a 32-core CPU. The strong scaling test, conducted on an eight-GPU node, demonstrated the efficient utilization of available multiple GPU resources by the code. Program summaryProgram Title: DUGKS-GPUCPC Library link to program files:https://doi.org/10.17632/yykv5s9g2n.1Developer's repository link:https://github.com/kairzhan/DUGKS-GPUCode Ocean capsule:https://codeocean.com/capsule/3b1e4f74-cdd3-4781-8923-8514d5923dfb/Licensing provisions: GNU General Public License 3Programming language: CUDA C++, CUDA FortranSupplementary material:Nature of problem: DUGKS-GPU is an advanced numerical code designed to accelerate the simulation of turbulent fluid flows through the application of the kinetic method known as the Discrete Unified Gas Kinetic Scheme (DUGKS). This computational tool comprises a CUDA Fortran version, tailored for a single GPU, as well as a CUDA C++ version developed for multi-GPU platforms.Solution method: The code employs a second-order finite-volume discretization of the discrete velocity Boltzmann equation with the BGK collision model. It can be used to simulate small to medium-scale problems on modern multi-GPU platforms with CUDA architecture.

Collective Spin-Wave Dynamics in Gyroid Ferromagnetic Nanostructures.

Expanding upon the burgeoning discipline of magnonics, this research elucidates the intricate dynamics of spin waves (SWs) within three-dimensional nanoenvironments. It marks a shift from traditionally used planar systems to exploration of magnetization configurations and the resulting dynamics within 3D nanostructures. This study deploys micromagnetic simulations alongside ferromagnetic resonance measurements to scrutinize magnetic gyroids, periodic chiral configurations composed of chiral triple junctions with a period in nanoscale. Our findings uncover distinctive attributes intrinsic to the gyroid network, most notably the localization of collective SW excitations and the sensitivity of the gyroid's ferromagnetic response to the orientation of the static magnetic field, a correlation closely tied to the crystallographic alignment of the structure. Furthermore, we show that for the ferromagnetic resonance, multidomain gyroid films can be treated as a magnonic material with effective magnetization scaled by its filling factor. The implications of our research carry the potential for practical uses such as an effective, metamaterial-like substitute for ferromagnetic parts and lay the groundwork for radio frequency filters. The growing areas of 3D magnonics and spintronics present exciting opportunities to investigate and utilize gyroid nanostructures for signal processing purposes.

Development of Interactive Multimedia on Electron Configuration Concept

Interactive multimedia has an important role in the learning process. The interactive multimedia presented the learning material in various forms and supported students’ understanding of those who have different learning styles. To help students understand the topic and to facilitate students’ learning style the PeT-EFig is developed. PeT-EFig (periodic table and electron configuration) as interactive multimedia which supported students’ understanding of electron configuration concepts. The objectives of this study were a) to determine the feasibility of PeT-EFig, and b) to determine the response of chemistry teachers and students of PeT-EFig as interactive multimedia. The research method used is research and development (RD) using the ADDIE model with five stages: analysis, design, and development stages. However, the research was only conducted up to the development stage due to time constraints. Based on the result, PeT-EFig is considered very suitable by the experts with 96 and 95% respectively. Likewise, teachers at SMA Muhammadiyah 1 Pontianak who teach chemistry subjects, stated that they strongly approved PeT-EFig as interactive multimedia on electron configuration 96%. Additionally, students also provided very positive feedback on the PeT-EFig through a small-scale trial involving 15 students with an average percentage of 87% for each aspect. Similarly, when a large-scale trial with 40 students, the final percentage score for each aspect was found to be 87%. The result indicated that the PeT-EFig could assist teachers in delivering the concepts and help students understand the electron configuration and atomic structure

Aperiodic Two-Dimensional Acoustic Black Holes for Broadband Vibration Attenuation in a Strip

Abstract Purpose Acoustic black holes (ABHs) are promising for vibration control in lightweight structures as proven for one- or two-dimensional periodic arrangements. Here, we explored the effects of spatial disorder and heterogeneous designs of ABHs to broaden an intrinsically limited attenuation bandwidth of periodic counterparts. Method We proposed several strategies to introduce non-periodic arrangements and/or different ABH profiles by solving a maximization problem for the attenuation bandwidth of a plate strip decorated by five ABHs. These strategies allow for finding appropriate dimensions and positions of the ABHs by analyzing a small design subset and are verified experimentally. Results The identified periodic heterogeneous ABHs enable greatly extending the attenuation bandwidth, while disordered identical ABHs allow for increasing the attenuation intensity as compared to the corresponding periodic configurations. The mechanisms underlying the wave attenuation enhancement were clarified by tracing the evolution of the wave transmission and structural vibration modes at each design step. We have found that the broadened wave attenuation attributes to the activation of strongly localized modes at broadband frequencies in aperiodic scenarios. These abundant modes are multi-frequency local resonances in ABHs that are sensitive to both the ABH profile and their spatial arrangement. Conclusion We prove that relaxing the periodicity requirement on multiple two-dimensional ABHs can extend the vibration attenuation to broadband regimes below the ABH characteristic frequency, numerically and experimentally. Aperiodic designs of ABHs thus enlarge the design space by enabling a broadband wave mitigation with attenuation intensity comparable to that of periodic counterparts without increasing the structural mass.

Formation of Polar Crown Filament Magnetic Fields by Supergranular Helicity Injection

To understand the magnetic fields of the polar crown filaments (PCFs) at high latitudes near polar regions of the Sun, we perform magnetofrictional numerical simulations on the long-term magnetic evolution of bipolar fields with roughly east–west polarity inversion lines (PILs) in a 3D spherical wedge domain near polar regions. The Coriolis-effect-induced vortical motions at the boundaries of several supergranular cells inject magnetic helicity from the photospheric boundary into the solar atmosphere. Supergranular-scale helicity injection, transfer, and condensation produce strongly sheared magnetic fields. Magnetic reconnections at footpoints of the sheared fields produce magnetic flux ropes (MFRs) with helicity signs consistent with the observed hemispheric helicity rule. The cross-sectional area of MFRs exhibits an uneven distribution, resembling a “foot-node-foot” periodic configuration. Experiments with different tilt directions of PILs indicate that the PCFs preferably form along PILs with the western end close to the polar region. The bending of PILs caused by supergranular flows, forming S-shape (Z-shape) PIL segments, promotes the formation of dextral (sinistral) MFRs. The realistic magnetic models we obtained can serve as starting points for the study of the plasma formation and eruption of PCFs.

Equivalent Circuits for Microwave Metamaterial Planar Components.

Metamaterial components and antennas are based on the general understanding that an artificial structure composed of adequately designed and manufactured elementary cells or arrays has unusual resonance and propagation properties. Metamaterials exhibit equivalent values of the dielectric constant and magnetic permeability that are both negative simultaneously, in contrast with ordinary materials. Single elements, periodic, or quasi-periodic configurations can be suitable for a metamaterial response. In this paper, equivalent circuits for microwave propagation and resonance are compared, deriving a lumped element modeling complementary to those already available in the literature, with a particular focus on planar resonating devices and calculating the effective value for the dielectric constant and the magnetic permeability directly from experimental findings using the impedance (Z-parameters) notation.

On the bandgap mechanism of periodic acoustic black holes

Acoustic black holes (ABHs) are primarily intended to eliminate the propagation of bending waves in structures although the same physical principles have been used to reduce the propagation of acoustic waves in ducts. The latter are usually referred to as sonic black holes (SBHs). ABHs (and also SBHs) only work well above a certain cut-on frequency which depends on their size compared to the incident wavelength. This limits their effectiveness to the high frequency range. To overcome this problem, several works have proposed the design of periodic ABHs to generate stopbands for low frequencies and improve their operating range. The purpose of this communication is to shed some light on the nature of such bandgaps. The k(ω) method is used to calculate the complex dispersion curves of various periodic ABH configurations and it is shown that, contrary to what is suggested in many works, the generation of bandgaps is essentially due to Bragg scattering and not to local resonances for embedded ABHs, although the latter play a role in some cases. The opposite occurs for additive ABHs. It is also observed that the complex dispersion curves of periodic ABHs present an intriguing behaviour compared to those usually found in metamaterials, since they tend to disappear at high frequencies, where the local wave intensity is stronger. An explanation of all these facts is given in the case of a periodic SBH, single-leaf and double-leaf embedded ABHs, and pillar and single-leaf additive ABHs.

Evaporation of sessile droplets on nanoscale periodic cubic-pillar surface: Experimental investigation

To enhance liquid–vapor phase-change heat transfer, the evaporation of droplets on nanostructured surfaces has been experimentally and numerically investigated. Nevertheless, understanding of how the nanostructured surfaces influence evaporation remains insufficient. In particular, physical models have been unable to predict evaporation characteristics. The present study employs periodic nanostructured surfaces. Electron beam lithography is used to fabricate nanoscale cubic pillars in a periodic configuration on silicon specimens. The pillars are nominally 100 nm in width, height, and gap opening. Water droplets can spread on the nanostructured surface, which shows better wettability than the silicon flat surface. In addition, the contact line of the droplet is effectively pinned on the nanostructured surface. We confirm that the nanostructured surfaces can reduce the lifetime of an evaporating droplet by approximately one-half at maximum. In addition, the nanostructured surfaces induce a unique intermediate evaporation mode between the constant contact radius (CCR) and constant contact angle (CCA) modes, herein referred to as the transition mode. In the transition mode, the contact line slowly recedes, together with the transient change in contact angle, during the evaporation process and the dynamics differ from those in the CCR and CCA modes. A novel phenomenological predictive model is proposed for the nanostructured surface.

Statistical assessment of the concentration fluctuations in street canyons via time-resolved wind tunnel experiments

Time-resolved wind tunnel experiments are performed for three periodic street canyon configurations: one of uniform (H/W = 1) and two of variable building height (consisting of 0.5H and 1.5H tall towers in aligned and staggered arrangements) for perpendicular wind direction. The velocity field is mapped using Laser Doppler Anemometry (LDA), and the tracer gas concentration is sampled using Fast Flame Ionization Detection (FFID). The concentration field is characterized by the mean concentration and the characteristic percentiles of the concentration-time series, such as the median and the peak, represented by the 99th percentile, in a total of 1138 sampling points. The probability distribution of the concentration in each point is modeled using the gamma distribution, which is fitted based on the mean and the variance of the measured time series. The results show that the mean pedestrian exposure to air pollutants is significantly lower in the case of heterogeneous roof height, although the mean concentration at the leeward corner of the source canyon can locally exceed those of the uniform street canyons for both tower arrangements of variable building height. Moreover, it is shown that the concentration peaks for both tower configurations can significantly exceed those of the uniform canyons case, especially near the sources.

Invariant sets and nilpotency of endomorphisms of algebraic sofic shifts

Abstract Let G be a group and let V be an algebraic variety over an algebraically closed field K. Let A denote the set of K-points of V. We introduce algebraic sofic subshifts ${\Sigma \subset A^G}$ and study endomorphisms $\tau \colon \Sigma \to \Sigma $ . We generalize several results for dynamical invariant sets and nilpotency of $\tau $ that are well known for finite alphabet cellular automata. Under mild assumptions, we prove that $\tau $ is nilpotent if and only if its limit set, that is, the intersection of the images of its iterates, is a singleton. If moreover G is infinite, finitely generated and $\Sigma $ is topologically mixing, we show that $\tau $ is nilpotent if and only if its limit set consists of periodic configurations and has a finite set of alphabet values.

Magnetic Domain Wall Networked Films – Configurational Switching for Tunable Magnetization Dynamics by Perforated Thin Films

AbstractSetting the magnetization and its properties in magnetic materials and films is of the utmost fundamental and technological importance for magnetic applications and devices. Magnetic permeabilities in a material are generally defined by the acting magnetic anisotropies together with an applied magnetic field. Here, deterministic switching of the effective dynamic magnetic properties is demonstrated by tunable networks of magnetic domain walls. By perforating magnetic films, a reversible switching between different magnetization states is achieved. Due to the resulting local effective dynamic fields for the changed domain configurations, different zero‐field permeability spectra are attained for the same material structure. Using local configurational magnetic resonances confined by magnetic domain walls, deterministic switchable bimodal dynamic behavior is achieved. Dynamic magnetooptical Kerr microscopy with picosecond temporal resolution proves that the varying periodic magnetic domain configurations are responsible for the dynamic magnetic bistability. In particular, the field‐free precessional magnetic response can be reproducibly switched between 1.3 and 2.3 GHz. The magnetization dynamics can be modified by small interventions in a repeatable manner beyond fixed material and structural properties. The described fundamental mechanism enables to design new energy efficient configurational microwave devices by switching between zero‐field magnetic arrangements.

Maximal Polarization for Periodic Configurations on the Real Line

Abstract We prove that among all 1-periodic configurations $\Gamma $ of points on the real line $\mathbb{R}$ the quantities $\min _{x \in \mathbb{R}} \sum _{\gamma \in \Gamma } e^{- \pi \alpha (x - \gamma )^{2}}$ and $\max _{x \in \mathbb{R}} \sum _{\gamma \in \Gamma } e^{- \pi \alpha (x - \gamma )^{2}}$ are maximized and minimized, respectively, if and only if the points are equispaced and whenever the number of points $n$ per period is sufficiently large (depending on $\alpha $). This solves the polarization problem for periodic configurations with a Gaussian weight on $\mathbb{R}$ for large $n$. The first result is shown using Fourier series. The second result follows from the work of Cohn and Kumar on universal optimality and holds for all $n$ (independent of $\alpha $).

Observation of Plasmonics Talbot effect in graphene nanostructures

We report on the theoretical models of the plasmoincs Talbot effect in graphene nanostructure. The Talbot effect for the plasmonics applications in the IR range is theoretically studied and the respective Talbot effect for the novel advanced plasmonics structures are numerically investigated for the first time. It is shown that the metamaterial structures with periodic grating configuration represents a complex three-dimensional lattice of beamlet-like graphene plasmonics devices. The calculated results agree well with the experimental ones. The results obtained can be used to create and optimize the structures considering diffraction limit for a wide range of application areas. Effective focusing of plasmonic waves with exact focal spots and a subwavelength full width at half maximum can be obtained by using periodic graphene grating.

Flow-induced periodic chiral structures in an achiral nematic liquid crystal

Supramolecular chirality typically originates from either chiral molecular building blocks or external chiral stimuli. Generating chirality in achiral systems in the absence of a chiral input, however, is non-trivial and necessitates spontaneous mirror symmetry breaking. Achiral nematic lyotropic chromonic liquid crystals have been reported to break mirror symmetry under strong surface or geometric constraints. Here we describe a previously unrecognised mechanism for creating chiral structures by subjecting the material to a pressure-driven flow in a microfluidic cell. The chirality arises from a periodic double-twist configuration of the liquid crystal and manifests as a striking stripe pattern. We show that the mirror symmetry breaking is triggered at regions of flow-induced biaxial-splay configurations of the director field, which are unstable to small perturbations and evolve into lower energy structures. The simplicity of this unique pathway to mirror symmetry breaking can shed light on the requirements for forming macroscopic chiral structures.

Toward the search for new photosensitizers for DSSCs: theoretical study of both substituted Zn(II) and Si(IV) phthalocyanines.

We report a density functional theory (DFT) study performed for a set of 66 compounds based on zinc(II) and silicon(IV) phthalocyanines (Pcs) with potential applications in dye-sensitized solar cells (DSSCs). The effect of the metal center (Zn, Si), periplanar and axial substituents, and anchor groups like anhydrous, carboxyl, and catechol on the electronic, optical, photovoltaics, and adsorption properties is investigated. Using the TD-DFT methodology and M06 and CAM-B3LYP functionals, we calculated the absorption spectra on optimized structures and in the solution phase but not on structures relaxed in the solvent. We obtained a strong Q band and a weak Soret band in the UV-Vis region, which are attributed to the transitions of type π-π* as described by the Gouterman orbitals. Q bands calculated show absorption up to 667 nm for ZnPcs and up to 769 nm for SiPcs, suggesting an essential role of the metal atom. The systems have a bathochromic effect in the order of secondary amine > primary amine > hydroxyl > amide > ester. We also found that the anhydrous and carboxyl groups favor absorption at longer wavelengths than the catechol group. The ZnPc systems show a slightly larger electron injection ΔGinj (∼1.1 eV) than SiPcs (∼0.9 eV), with similar values for the three anchor groups. The interaction energies (Eint) between ZnPcs/SiPcs and TiO2 in molecular and periodic configuration and corrected by the counterpoise method indicate that SiPcs predict more negative values than ZnPcs. The anchor group effect is relevant; the carboxyl moiety leads to stronger interactions than the anhydrous moiety. The strategies used could help to identify new photosensitizers for DSSCs.

Reflective 2D diffraction grating based on short pitch chiral liquid crystal

Thermotropic liquid crystals have recently become popular for use in optical components for augmented and virtual reality. Chiral liquid crystal (CLC), is of particular interest due to the formation of a photonic bandgap that allows for the creation of polarization-sensitive reflective optical components. Previous investigations have studied 2D diffraction gratings based on long-pitch (5 μm) CLC in combination with a 2D periodic alignment configuration. This yielded 2D diffraction patterns in transmission with the ability to switch between high and low voltage states with hysteresis. In the current study, short-pitch CLC (400 nm and 1 μm) is deposited between two substrates with perpendicularly rotating periodic photoalignment patterns, the shorter pitch resulting in a diffraction grating that produces a 2D diffraction pattern in reflection for wavelengths in the visible range. While a relatively high diffraction efficiency is achieved in the first diffraction order, additional diffraction orders with lower efficiency are present due to the complex CLC configuration in the bulk.

Innovative Application of Subwavelength Periodic Polystyrene Microspheres as Saturable Absorbers in Nonlinear Optics

Polystyrene (PS) possesses numerous remarkable properties like high transparency, impressive mechanical strength, and a large specific surface area, making it an excellent mask plate or template for the preparation of anti-opal structures. Moreover, it should be noted that PS also exhibits exceptional nonlinear properties due to the subwavelength periodic configuration. In this paper, a self-assembled PS microsphere photonic crystal saturable absorber (PSM-SA) has been proposed and fabricated. It exhibits impressive properties including high stability, high damage threshold, high refractive index, and large specific surface area. It is suggested that the periodic structure of PS in the film has a significant impact on the photonic band gap, resulting in excellent adjustable optical nonlinear characteristics. By integrating PSM-SA into a self-built ring fiber laser system, a Q-switched laser with a pulse width of approximately 2 μs and a repetition rate of 40 kHz at a wavelength of 1562 nm is obtained. These findings demonstrate its potential for enabling efficient and adjustable nonlinear optical functionalities in various optical devices, contributing to the expanding realm of PS microsphere photonic crystals and their significant impact on advancing nonlinear optics technology.