Search Results (435)

Air-penetrating and noise-canceling constructions are required for numerous noise control issues. High ventilation performance conflicts with effective sound insulation, and vice versa. For this reason, ventilated noise barriers are currently being intensively researched and developed. One of the most popular solutions is the louvered-type barrier, whose acoustic efficiency depends on its geometric parameters as well as the acoustic properties of the louvers. One of the main challenges is optimizing the acoustic impedance of louver surfaces in order to achieve maximum reflection, absorption, or minimum transmission of sound waves. This paper proposes an analytical solution to the diffraction problem of a plane sound wave incident on a periodic array of similar thin screens with arbitrary impedance surfaces. An infinite system of linear equations is derived, and its numerical solution allows us to find the reflection and transmission coefficients. It has been shown that screens with reactive impedance are necessary to achieve maximum sound reflection. On the other hand, dissipative screens are required for minimal sound transmission. Additionally, the absorption properties of the array have been studied. It has been found that there is an optimal impedance value that provides the maximum absorption coefficient. Full article

Periodically supported beams are widely employed in engineering structures, where effective control of low-frequency vibration and noise is often required. To achieve broadband elastic wave manipulation, an inertial amplification (IA) mechanism was introduced to generate low-frequency and ultra-wide bandgaps. Based on the Timoshenko beam theory, analytical models for flexural wave propagation in periodically supported beams with IA structures were established using the generalized state transfer matrix method and the Floquet transform method, respectively. The validity of the analytical models was verified by vibration transmission analysis using a finite element model. The results demonstrate that the Floquet transform method enables rapid and accurate solution of the wave model. The introduction of the IA mechanism can generate low-frequency bandgaps, which are most sensitive to the amplification angle and amplification mass. The bandgap formation mechanism arises from the modulation of Bragg scattering in the periodically supported beam by the IA structure. This modulation causes the standing wave mode frequencies to shift to lower frequencies, thereby widening the bandgaps. Furthermore, hybrid IA structure configuration can achieve broader bandgaps, facilitating elastic wave control in the ultra-wide low-frequency range. These findings provide valuable insights for low-frequency vibration and noise attenuation in engineering structures. Full article

This work explores the qualitative dynamics of the modified unstable time-fractional nonlinear Schrödinger equation (mUNLSE), a model applicable to nonlinear wave propagation in plasma and optical fiber media. By transforming the governing equation into a planar conservative Hamiltonian system, a detailed bifurcation study is carried out, and the associated equilibrium points are classified using Lagrange’s theorem and phase-plane analysis. A family of exact wave solutions is then constructed in terms of both trigonometric and Jacobi elliptic functions, with solitary, kink/anti-kink, periodic, and super-periodic profiles emerging under suitable parameter regimes and linked directly to the type of the phase plane orbits. The validity of the solutions is discussed through the degeneracy property which is equivalent to the transmission between the phase orbits. The influence of the fractional derivative order on amplitude, localization, and dispersion is illustrated through graphical simulations, exploring the memory impacts in the wave evolution. In addition, an externally periodic force is allowed to act on the mUNLSE model, which is reduced to a perturbed non-autonomous dynamical system. The response to periodic driving is examined, showing transitions from periodic motion to quasi-periodic and chaotic regimes, which are further confirmed by Lyapunov exponent calculations. These findings deepen the theoretical understanding of fractional Schrödinger-type models and offer new insight into complex nonlinear wave phenomena in plasma physics and optical fiber systems. Full article

This paper proposes a grating Moiré fringe signal compensation method based on Variational Mode Decomposition (VMD) to address signal errors in grating encoders. VMD decomposes Moiré fringe signals into multiple amplitude-modulated and frequency-modulated components, and realizes noise compensation through parameter optimization and signal reconstruction. The Multi-Strategy Particle Swarm Optimization (MSPSO) enhances optimization performance via adaptive inertia weight adjustment and chaotic perturbation, solving the problems of mode mixing or over-decomposition caused by blind parameter selection in traditional VMD. A hardware-software co-design test system based on ZYNQ FPGA is developed, which optimally allocates tasks between the Processing System and Programmable Logic, resolving issues of large data volume and long computation time in traditional systems. The compensation scheme provides excellent signal processing performance. The experimental tests on random periodic signals, triangular waves and square waves with different duty cycles have demonstrated the robustness of this scheme. After compensation, the output signal exhibits excellent sinuosity and orthogonality, with harmonic components and noise in the frequency domain almost negligible. It provides a practical solution for high-precision measurement in ultra-precision machining, semiconductor manufacturing, and automated control. Full article

In this paper, we study the time-space truncated M-fractional model of shallow water waves in a weakly nonlinear dispersive media that characterizes the nano-solitons of ionic wave propagation along microtubules in living cells. A fractional wave transformation is applied, reducing the model to a third-order differential equation formulated as a conservative Hamiltonian system. The stability of the equilibrium points is analyzed, and the corresponding phase portraits are constructed, providing valuable insights into the expected types of solutions. Utilizing the dynamical systems approach, a variety of predicted exact fractional solutions are successfully derived, including solitary, periodic and unbounded singular solutions. One of the most notable features of this approach is its ability to identify the real propagation regions of the desired waves from both physical and mathematical perspectives. The impacts of the fractional order and gravitational force variations on the solution profiles are systematically analyzed and graphically illustrated. Moreover, the quasi-periodic dynamics and chaotic behavior of the model are explored. Full article

Urban heat waves are intensifying under climate change, posing growing public health risks, particularly in rapidly urbanizing cities. Green infrastructure is widely promoted as a nature-based solution for heat mitigation, yet its health benefits may vary across urban contexts. This study examines how neighborhood-level green infrastructure modifies heat-related health risks in Tabriz, Iran—a historically cold city experiencing increasing heat stress. The Normalized Difference Vegetation Index (NDVI) was derived from Landsat 8 imagery for 190 neighborhoods and classified into quartiles. Heat waves were defined as two or more consecutive days with mean temperatures at or above the 95th percentile. Emergency department visits for cardiovascular, respiratory, and all-cause conditions (2018–2020) were analyzed using Distributed Lag Non-linear Models with quasi-Poisson regression. Neighborhoods with low-to-moderate greenness (second and third NDVI quartiles) consistently exhibited lower relative risks of heat-related cardiovascular and all-cause visits, while both the lowest and highest NDVI quartiles showed elevated risk estimates. Risk patterns varied by lag period and demographic subgroup, with higher vulnerability observed among males and younger adults in highly vegetated areas, though estimates were imprecise. These findings suggest a non-linear relationship between urban greenness and heat-related health risks. Moderate green infrastructure appears most protective, underscoring the importance of context-sensitive and equitable greening strategies for climate adaptation in heat-vulnerable cities. Full article

This paper explores the integrability of the Akbota equation with various types of solitary wave solutions. This equation belongs to a class of Heisenberg ferromagnet-type models. The model captures the dynamics of interactions between atomic magnetic moments, as governed by Heisenberg ferromagnetism. To reveal its further physical importance, we calculate more solutions with the applications of the logarithmic transformation, the M-shaped rational solution method, the periodic cross-rational solution technique, and the periodic cross-kink wave solution approach. These methods allow us to derive new analytical families of soliton solutions, highlighting the interplay of discrete and continuous symmetries that govern soliton formation and stability in Heisenberg-type systems. In contrast to earlier studies, our findings present notable advancements. These results hold potential significance for further exploration of similar frameworks in addressing nonlinear problems across applied sciences. The results highlight the intrinsic role of symmetry in the underlying nonlinear structure of the Akbota equation, where integrability and soliton formation are governed by continuous and discrete symmetry transformations. The derived solutions provide original insights into how symmetry-breaking parameters control soliton dynamics, and their novelty is verified through analytical and computational checks. The interplay between these symmetries and the magnetic spin dynamics of the Heisenberg ferromagnet demonstrates how symmetry-breaking parameters control the diversity and stability of optical solitons. Additionally, the outcomes contribute to a deeper understanding of fluid propagation and incompressible fluid behavior. The solutions obtained for the Akbota equation are original and, to the best of our knowledge, have not been previously reported. Several of these solutions are illustrated through 3-D, contour, and 2-D plots by using Mathematica software. The validity and accuracy of all solutions we present here are thoroughly verified. Full article

Extracting high-quality surface wave dispersion curves from crosscorrelation functions (CCFs) of ambient noise data is critical for seismic velocity inversion and subsurface structure interpretation. However, the non-uniform spatial distribution of noise sources may introduce spurious noise into CCFs, significantly reducing the signal-to-noise ratio (SNR) of empirical Green’s functions (EGFs) and degrading the accuracy of dispersion measurement and velocity inversion. To mitigate this issue, this study aims to develop an effective denoising approach that enhances the quality of CCFs and facilitates more reliable surface wave extraction. We propose a fractional Laplacian-based adaptive progressive denoising (FLAPD) method that leverages local gradient information and a fractional Laplacian mask to estimate noise variance and construct a fractional bilateral kernel for iterative noise removal. We applied the proposed method to the CCFs from 79 long-period seismic stations in Shandong, China. The results demonstrate that the denoising method enhanced the data quality substantially, increasing the number of reliable dispersion curves from 1094 to 2196, and allowing an increased number of temporal sampling points to be retrieved from previously low-SNR curves. This helps to expand the spatial coverage and results in a more accurate velocity inversion result than that without denoising. This study provides a robust denoising solution for ambient noise tomography in regions with complex noise source distributions. Full article

In this article, we investigate the dynamical analysis and soliton solutions of the microtubule equation. First, the Lie symmetry method is applied to the considered model to reduce the governing partial differential equation into an ordinary differential equation. Next, the multivariate generalized exponential rational integral function method is employed to derive exact soliton solutions. Finally, the bifurcation analysis of the corresponding dynamical system is discussed to explore the qualitative behavior of the obtained solutions. When an external force influences the system, its behavior exhibits chaotic and quasi-periodic phenomena, which are detected using chaos detection tools. We detect the chaotic and quasi-periodic phenomena using 2D phase portrait, time analysis, fractal dimension, return map, chaotic attractor, power spectrum, and multistability. Phase portraits illustrating bifurcation and chaotic patterns are generated using the RK4 algorithm in Matlab version 24.2. These results offer a powerful mathematical framework for addressing various nonlinear wave phenomena. Finally, conservation laws are explored. Full article

Yamamoto’s theoretical solution for a two-dimensional wave-induced response of an elastic seabed with finite permeability needs a simultaneous equation to be solved. Analysis of the dimensionless simultaneous equation demonstrated that it becomes unsolvable due to the singularity of its matrix when the permeability coefficient of the seabed approaches infinity and zero, representing (elementwise) fully drained and undrained conditions, respectively. To address this limitation and thus expand the verifiable drainage condition for a finite element analysis code, theoretical solutions for seabed responses under the fully drained and undrained conditions were derived. The feasibility of these solutions was discussed through comparison of the forms of these solutions with the one of Yamamoto. Furthermore, characteristics of seabed behaviors explained by these solutions were obtained. Finally, these theoretical solutions and Yamamoto’s solution were utilized to verify a finite element analysis code by considering horizontally periodic seabed behavior in the numerical analysis. It turned out that the numerical code was capable of expressing seabed behavior in any drainage condition without any approximation to a governing equation as made in the derivation of the fully drained and undrained solutions. Therefore, the numerical analysis code is now reliably used for further studies on wave-induced seabed behaviors even out of the verifiable range of drainage conditions by Yamamoto’s solution. Full article

Global data consumption is experiencing exponential growth, driving the demand for wireless links with higher transmission speeds, lower latency, and support for emerging applications such as 6G. A promising approach to address these requirements is the use of higher-frequency bands, which in turn necessitates the development of advanced antenna systems. This work presents the design and experimental validation of a reconfigurable, low-cost leaky-wave antenna capable of controlling the propagation direction of single-, dual-, and triple-beam configurations in the FR3 frequency band. The antenna employs slotted periodic patterns to enable directional electromagnetic field leakage, and it is based on a cost-effective and simple 3D-printing fabrication process. Laboratory testing confirms the theoretical and simulated predictions, demonstrating the feasibility of the proposed antenna solution. Full article

This study investigates the convective–diffusive Cahn–Hilliard equation, a nonlinear model which is used in real-world applications to phase separation and material pattern formation. Using the modified Sardar sub-problem technique, which is an extension of the Sardar sub-equation approach, we derive multiple classes of exact soliton solutions, including bright, dark, kink, and periodic forms. The parametric behaviors of these solutions are examined and visualized through analytical plots generated in Mathematica and Maple. Furthermore, UV–Vis spectrophotometry is employed to examine the optical response of copper oxide (CuO) thin films. The films exhibited a sharp absorption edge around 380–410 nm and an optical band gap of approximately 2.3 eV, confirming their semiconducting nature. The experimentally observed periodic transmission characteristics are linked with the theoretical soliton profiles predicted by the model. Overall, the proposed analytical and experimental framework establishes a clear connection between nonlinear wave theory and thin-film optical characterization, providing new insights into soliton transformation phenomena in complex material systems. Full article

In the development of quantum mechanics in the 1920s, both matrix mechanics (developed by Born, Heisenberg and Jordon) and wave mechanics (developed by Schrödinger) prevailed. These early attempts corresponded to the quantum mechanics of particles. Matrix mechanics was found to lead directly to the Schrödinger equation, and the Schrödinger equation could be used to derive the alternative problem for matrix mechanics. Later emphasis lay on the development of the dynamics of fields, where the classical field equations were quantized (see, for example, Weinberg). Today, quantum field theory is one of the most successful physical theories ever developed. The symmetry between particle and wave mechanics is exploited herein. One of the important properties of quantum mechanics is that it is linear, leading to some confusion about how to treat the problem of nonlinear classical field equations. In the present paper we address the case of classical nonlinear soliton equations which are exactly integrable in terms of the periodic/quasiperiodic inverse scattering transform. This means that all physical spectral solutions of the soliton equations can be computed exactly for these specific boundary conditions. Unfortunately, such solutions are highly nonlinear, leading to difficulties in solving the associated quantum mechanical problems. Here we find a strategy for developing the quantum mechanical solutions for soliton dynamics. To address this difficulty, we apply a recently derived result for soliton equations, i.e., that all solutions can be written as quasiperiodic Fourier series. This means that soliton equations, in spite of their nonlinear solutions, are perfectly linearizable with quasiperiodic boundary conditions, the topic of finite gap theory, i.e., the inverse scattering transform with periodic/quasiperiodic boundary conditions. We then invoke the result that soliton equations are Hamiltonian, and we are able to show that the generalized coordinates and momenta also have quasiperiodic Fourier series, a generalized linear superposition law, which is valid in the case of nonlinear, integrable classical dynamics and is here extended to quantum mechanics. Hamiltonian dynamics with the quasiperiodicity of inverse scattering theory thus leads to matrix mechanics. This completes the main theme of our paper, i.e., that classical, nonlinear soliton field equations, linearizable with quasiperiodic Fourier series, can always be quantized in terms of matrix mechanics. Thus, the solitons and their nonlinear interactions are given an explicit description in quantum mechanics. Future work will be formulated in terms of the associated Schrödinger equation. Full article

The (3 + 1)-dimensional KdV–Calogero–Bogoyavlenskii–Schiff equation, a model that describes long-wave interactions and has numerous applications in mathematics, engineering, and physics, is examined in this work. First, a wave transformation is used to reduce the equation to lower dimensions. The modified Khater method is then used to derive different types of solitary wave solutions, such as chirped, kink, periodic, and kink-bright types. By allocating suitable constant parameters, 3D, 2D, and contour plots are created to demonstrate the physical behavior of these solutions. Phase portraits are used to qualitatively analyze the undisturbed planar system using bifurcation theory. The system is then perturbed by an external force, resulting in chaotic dynamics. Chaos in the system is confirmed using multiple diagnostic tools, including time series plots, Poincaré sections, chaotic attractors, return maps, bifurcation diagrams, power spectra, and Lyapunov exponents. The stability of the model is further investigated with varying initial conditions. A bidirectional scatter plot technique, which efficiently reveals overlapping regions using data point distributions, is presented for comparing solution behaviors. Overall, this work offers useful tools for advancing applied mathematics research as well as a deeper understanding of nonlinear wave dynamics. Full article

This work investigates the dynamical properties of the Kolmogorov–Petrovskii–Piskunov (KPP) equation. We begin by establishing its non-integrability through the Painlevé test. Using a traveling wave transformation, we reduce the equation to a planar dynamical system, which we identify as non-conservative. A subsequent bifurcation analysis, supported by Bendixson’s criterion, rules out the existence of periodic orbits and, thus, periodic solutions—a finding further validated by phase portraits. Furthermore, we classify the types and co-dimensions of the bifurcations present in the system. We demonstrate that under certain conditions, the system can exhibit saddle-node, transcritical, and pitchfork bifurcations, while Hopf and Bogdanov–Takens bifurcations cannot occur. This study concludes by systematically deriving a power series solution for the reduced equation. Full article