Band 81, Heft 3

The translational motion of bubbles is closely related to the formations of bubble clouds of varying structures and sizes, which is crucial for the distribution of cavitation energy in ultrasonic fields. This paper investigates the time-varying characteristics and influencing factors of the translational motion of bubbles with different initial radii. Our findings indicate that bubbles with identical initial radii exhibit mutual repulsion during their expansion phase and attraction during their contraction phase. For bubbles with different initial radii, they exhibit mutual repulsion during the expansion stage of the larger bubble and mutual attraction during its contraction stage. This behavior indicates that the translational motion of the bubbles ultimately aligns with the radial oscillation of the larger bubble. Furthermore, when one bubble’s initial radius equals the linear resonance radius and the other bubble’s initial radius is larger, the bubbles initially exhibit mutual attraction before transitioning into a uniform translational motion with a constant inter-bubble distance. The two bubbles transition from attraction to repulsion due to the 3rd harmonic resonance effect caused by the increased ultrasonic pressure amplitude. The translational motion of the bubbles can be reversed as the driven frequency approaches the main resonance, the 2nd order harmonic, and the 1/2 order subharmonic resonance frequencies.

The nonlinear phenomena of waves in ferromagnetic systems have complex interactions with each other, which are not properly modeled by the classical theory. To overcome this shortcoming, in the present study the conformable nonlinear fractional Schrödinger equation (CNFSE) is used, whose conformable derivative retains the essential properties of classical calculus and that allows unambiguous travelling wave reductions. Using the method of ϕ expansion, dark, bright and singular soliton solutions in the exact form are constructed and the effect of fractional order κ ∈ (0, 2] on localization and dispersion is analyzed. Three-dimensional surface plots as well as contour plots show the influence of variations of parameters on wave stability and propagation. Meanwhile, bifurcation and sensitivity analyses construct features of stable and unstable equilibria, and responses to perturbations in initial conditions. The resulting analytical-computational framework provides new insights into fractional wave dynamics in corridors and ferromagnetic media, with potential applications in power transmission systems.

This study aims to analyze the linear and nonlinear dynamic responses of variable cross-section microbeams. To represent microscale structural behavior, Hamilton’s principle is applied to obtain the governing equations, while the Modified Couple Stress Theory was incorporated into the formulation. To solve the nonlinear differential equations, the Generalized Differential Quadrature Method and the Multi-Time Scale Perturbation Method are employed in conjunction. While spatial discretization is performed with high numerical accuracy using GDQM, the MTS method ensured that the nonlinear behavior developing over time is captured analytically. The analysis reveals that small-scale effects in the microstructure play a significant role in determining natural frequencies and that, when MCST is considered, the stiffness of the system increases, thereby raising the natural frequencies. Additionally, it is determined that a decrease in the radius ratio leads to a reduction in natural frequencies, while the mode shapes become more complex due to microscale effects. The findings emphasize the importance of considering nonlinear dynamics in the design and analysis of applications such as micro-electromechanical systems.

In this paper, we explore optical solitons in a generalized third-order nonlinear Schrödinger equation (GNLSE) for ultrashort pulse propagation in nonlinear optical fibers. Using the collective variable (CV) method, we derive a system of ordinary differential equations that describes key soliton parameters, such as amplitude, width, chirp, and frequency. The numerical solutions obtained using the fourth-order Runge–Kutta algorithm show periodic oscillations of the aforementioned parameters. Another key result of the study is the discovery of bright soliton solutions using the semi-inverse method with fractal derivatives. We also demonstrate the effects of fractal parameters on the soliton solution with graphical simulations. Fractal dimensions (Ψ < 1) generate pulse irregularities that match experimental observations. The results clarify the interaction of higher-order effects, nonlinearity, and dispersion. In addition, the study’s findings highlight the importance of two methods used to improve data transmission in optical fibers and relate the theoretical analysis to potential real-world applications.