The arranged paths of dominoes have many shapes. The scaling law for the propagation speed of domino toppling has been extensively investigated. However, in all previous investigations, the scaling law for the velocity of domino toppling motion in curved lines was not taken into account. In the present work, the finite-element analysis (FEA) program ABAQUS was used to study the velocity of domino toppling motion in curved lines. It is shown that the domino propagation speed has a rising trend with increasing domino spacing in a straight line. It is also found that domino propagation speed is linearly proportional to the square root of domino separation. This research proved that the scaling law for the speed of domino toppling motion given by Sun (2020) is true [B-H. Sun, 2020. Scaling law for the propagation speed of domino toppling. AIP Advances, 10(9),095124.]. Moreover, the shape of domino arrangement paths has no influence on the scaling law for the propagation speed of dominoes but can affect the coefficient of the scaling law for the velocity. Therefore, the amendatory function for the propagation speed of dominoes in curved lines was formulated by the FEA data. The fitted amendatory function, $\varphi_{revise}$, provides the simple method for a domino player to quickly estimate the propagation speed of dominoes in curved lines.

The shear stress generated by wall turbulence is the main cause of wall friction resistance in turbulent flow through pipes. This paper investigates the impact of inserting rest periods (regions of constant Reynolds number) within the pulsating operating cycle of velocity on the fully turbulent flow at large time-averaged Reynolds numbers, using the Large Eddy Simulation (LES) method. The study aims to explore the effect of increasing rest periods within pulsations on drag resistance. The dimensionless shear stress and drag reduction rates during different time periods of rest were analyzed. Numerical simulation results indicate that the pulsating velocity operation mode does not necessarily lead to drag reduction; it may even result in increased resistance. Inserting rest periods within the pulsation cycle can achieve drag reduction effects, with the maximum drag reduction rate reaching 21.8\%. Comparisons with experimental data and Direct Numerical Simulation (DNS) from the literature validate the feasibility of using the LES method for pipe pulsating operation modes.

People have always hoped to be able to fill an entire plane with ``single unit cells'' without periodicity. This wish was realized after the mathematician discovered a 13-sided ``single unit cell'' named `einstein'. These non-periodic tessellations generally exhibit anisotropic properties, making them superior in terms of mechanical performance compared to periodic structures. From the perspective of information entropy, the reason behind the improved mechanical properties of these structures is the higher entropy associated with non-periodic configurations. To quantify the disorder of non-periodic structures, we propose an entropy expression for the `einstein' metamaterial. To demonstrate the mechanical properties of these high-entropy structures, we fabricate specimens using 3D printing and conducte mechanical experiments. For comparative analysis, we also use ABAQUS to perform finite element analysis of the problem. The research results reveal that the mechanical properties of high-entropy structures created by the non-periodic stacking of cells are significantly improved compared to those of low-entropy structures created by periodic stacking. The conclusions drawn from the study of individual issues are generalizable and may be of assistance in future material and structural design.

In nature and engineering applications, flexible fiber beds covering biological surfaces can play a role in reducing resistance. These fibers deform under the action of fluids, and this deformation affects the fluid flow state, forming a complex fluid-solid interaction phenomenon. To quantitatively analyze such issues, the physical model is simplified to the deformation problem of an soft hair bed caused by Stokes flow, and the deformation problem of a single fiber caused by Stokes flow is further studied. The deformation problem of an elastic single fiber in a channel caused by Stokes flow can be described by a nonlinear integral equation. We have obtained a new series solution, which has been compared with the previous perturbation method to verify the accuracy and effectiveness of the series solution. Meanwhile, we have further provided an extended form of flexible fiber deformation through experimental fitting. This fluid-solid interaction problem involves multiple fields and is very important in many natural and engineering systems. The research in this paper can not only help us better understand complex phenomena in nature but also delve into the interaction mechanism between fluids and solids, providing a theoretical basis for future scientific research and engineering applications.