Computation

This study proposes a non-uniform meshing strategy for finite element (FE) discretization aimed at improving mechanical accuracy under controlled nodal budgets in structural analyses with localized field gradients. Unlike quasi-uniform meshing, the proposed approach uses a priori node placement based on the zeros of Chebyshev polynomials. Their natural clustering near the endpoints of [−1, 1] is mapped onto the physical domain to generate a non-uniform distribution by construction, without adaptive refinement or iterative remeshing. The main contribution therefore lies not in the Chebyshev points themselves, but in their use as a deterministic, solution-independent rule for placing the vertices of low-order FE meshes. Three meshing strategies are compared: quasi-uniform, graded, and Chebyshev-based meshes. The graded mesh deliberately concentrates nodes in predefined critical regions, whereas the Chebyshev-based mesh follows a predefined analytical placement rule. Performance is assessed against converged fine-mesh FE reference solutions using relative errors in displacement and von Mises stress, local and peak-stress errors, mesh-quality indicators, stiffness-matrix conditioning, and computational cost. For the two-hole plate at $N_{tot}=2200$ the relative displacement error decreases from $1.28\times {10}^{-2}$ for the quasi-uniform mesh to $8.48\times {10}^{-3}$ for the Chebyshev-based mesh, while the graded mesh reaches $7.75\times {10}^{-3}.$ Overall, the Chebyshev-based strategy improves displacement accuracy relative to quasi-uniform meshing in the investigated configurations, although the geometrically graded mesh generally achieves lower errors and improvements in stress accuracy are not systematic.

So far, synchronization tasks designed in complex systems are working at the level of their constituting elements. The proposed pilot study explores synchronization at the level of emergents. The main objective of this research is threefold: (i) to demonstrate that synchronizing emergent structures rise from a continuous interaction of micro-processes that are operating above a constituting matrix (medium) using a simple microevolution rule and a special type of extended neighborhood; (ii) to provide a specific example of a long-range emergent coordination that is generated within a short-range communicating medium; and (iii) to demonstrate a possibility of synchronization at the level of emergents. Those goals are achieved by the utilization of emergent information processing that uses uniform changes of all updated elements of the matrix, a fixed microevolution rule, and a fixed neighborhood. A fast solution to a computational problem of solving long-range synchronization within massively parallel and short-range communicating environments is presented. It is named the semi-two-dimensional synchronization problem (S2D-SP). The proposed emergent solution of S2D-SP differs from all previous manually designed solutions to other synchronization tasks. The number of steps t, which is necessary to synchronize an emergent array, is substantially lower than the width w of the synchronized emergent array. In addition to the pure theoretical importance, the solution demonstrates the usefulness of the concept of extended neighborhoods in search of not only biologically relevant computational models of self-organization and emergence. The presented solution of the S2D-SP problem uncovers a novel approach to the design of artificial, self-organizing emergent systems and possibly paves a path towards understanding natural computation. The software GoL-N24 v1.4 used to generate all results is publicly available.

This study addresses a limitation in classical models of nanofluid flow, namely, their inability to adequately capture microscale effects associated with fluid-element microrotation and local microstructural dynamics. Specifically, the effects of nanoparticle geometry and microrotation on the hydrodynamic and thermal behavior of copper (Cu)–water nanofluids flowing over a stretching surface under a transverse magnetic field are investigated. Four nanoparticle morphologies: bricks, cylinders, platelets, and blades, are considered, with water (Pr = 6.2) as the base fluid. Appropriate similarity transformations are employed to reduce the governing nonlinear partial differential equations (PDEs) to a system of ordinary differential equations (ODEs), which is solved numerically using the Runge–Kutta–Fehlberg (RKF) integration scheme. A comprehensive parametric analysis is conducted to examine the effects of the governing physical parameters on the velocity, microrotation, and temperature distributions. The results reveal that increasing the thermal radiation parameter enhances the temperature distribution for all four nanoparticle morphologies. Furthermore, comparative analysis indicates that water-based nanofluids exhibit a more pronounced temperature gradient than kerosene-based fluids under identical physical conditions. These findings highlight the importance of nanoparticle morphology and microscale rotational effects in modeling the flow and heat transfer characteristics of nanofluids.