Islamic calligraphy has an important role in the artistic, spiritual, and cultural heritage of the Islamic world. It is not just beautiful but also serves as a way to express religious beliefs, provide moral lessons, and represent cultural identity. This study looks at how calligraphy is placed in various contexts throughout Islamic civilization, including large structures like mosques, madrasas, shrines, palaces, and civic buildings. It also examines smaller items such as coins, manuscripts, legal documents, weapons, household objects, textiles, jewellery, and luxury arts. The relationship between script, decoration, and space is highlighted, with examples such as the Patio de la Acequia in the Alhambra in Granada where Naskh and Kufic inscriptions combine with geometric and plant designs, changing architectural spaces into areas filled with text and spirituality. This analysis shows that Islamic calligraphy acts not just as decoration but also as a way to express religious feelings, political power, and cultural values, showing its lasting impact in both past and present times.

Numerical simulation of catalytic enhancement in wall-coated enzyme-catalyzed micro-channel via geometric design

Abstract This study presents the design, fabrication, and evaluation of Kresling origami-inspired non-pneumatic tires (NPTs) manufactured via fused deposition modeling (FDM) using thermoplastic polyurethane (TPU). The research focuses on understanding how key geometric parameters-twist angle, layering strategy, and fold direction-govern the structural and dynamic performance of Kresling-based tire architectures. Nine design variants were systematically developed and experimentally tested under controlled impact conditions to assess load-bearing capacity, shock attenuation, and vibrational damping. Finite element simulations were first conducted to identify configurations with superior stress distribution and axial stiffness, followed by experimental validation using peak acceleration, RMS acceleration, and frequency-domain analysis. Results show that a twist angle of 30°, particularly in two-layer configurations with alternating folds, consistently delivers the best balance between stiffness and damping. Layering was found to improve vibrational stability, while fold direction influenced strain distribution and symmetry under loading. The findings highlight the potential of origami-inspired geometries as tunable, manufacturable alternatives to conventional lattice structures in NPTs and offer a geometric design framework for future adaptive and high-performance tire systems.

Geometric design optimization for thermal-mechanical performance of non-structural concrete honeycomb wall panels

ABSTRACT Bird’s nest fungi (Nidula candida) growing along ~18-year-old cedar fences in Pacific Spirit Regional Park, Vancouver, British Columbia, Canada, produce abundant, persistent peridia containing basidiospore-bearing, egg-like peridioles. To reconstruct the initial mode of reproduction of the populations, 37 peridia were collected following a geometric sampling design, with 8–10 peridia collected 6–222 cm apart from each of four fence segments. We cultured dikaryotic mycelium from one whole peridiole from each peridium and 105 monokaryons from basidiospores from 8 peridioles. We then tested mycelial compatibility by confronting pairs of dikaryons and sexual compatibility by mating the monokaryons from basidiospores. The resulting genetic patterns allowed us to map genetic individuals back to their fence segments. The dikaryotic mycelia that grew from whole peridioles fell into six mycelial compatibility groups, with one or two groups per 3–7 m fence segment. Consistent with an outcrossing origin, four different mycelial compatibility groups had different mating types. The largest compatibility group covered over 6 m of fence, producing 114 peridia and ~4.2 billion spores. One compatibility group was present at two fence sites ~40 m apart, suggesting asexual dispersal. This can potentially be explained by somatic growth from the walls of dispersed peridioles. Dikaryons generated by mating sibling monokaryons isolated from basidiospores from the same peridiole showed mycelial incompatibility in 86% of pairings. Thus, the compatible dikaryotic mycelia emerging from whole peridioles likely represent clones of parental mycelium rather than recombinant meiotic hyphae from basidiospores. Asexual reproduction from dispersed fruit body tissue is unusual in Agaricales, but in N. candida fence-hopping of peridioles splashed from peridia and germinating as clonal, parental-type dikaryotic mycelia may have contributed to expansion of a genet along the fence.

Abstract Curved and topologically nontrivial magnetic structures offer new pathways to control spin-wave behavior beyond planar geometries. Here, we study spin-wave dynamics in Möbius-shaped soft-magnetic nanostrips using micromagnetic simulations. By comparing single-, double-, and triple-twisted Möbius strips to a topologically trivial bent ring, we isolate the roles of helical twist and non-orientable topology. Möbius geometries exhibit non-degenerate mode doublets associated with counterpropagating spin waves, in contrast to the standing-wave doublets in the trivial case. This splitting arises from a twist-induced geometric (Berry) phase that breaks propagation symmetry, producing non-reciprocal dispersion relations. The Möbius topology further imposes antisymmetric boundary conditions, resulting in half-integer wavelength quantization. Local RF excitation allows for the selective generation of spin waves with defined frequency and propagation direction. An analytical model reproduces the dispersion behavior with excellent agreement. These results highlight how geometric and topological design can be leveraged to engineer spin-wave transport in three-dimensional magnonic systems.

Background: Perforator flaps improved the reconstruction paradigm in the lower extremity, increasing coverage possibilities. This study aims to quantify how added perforators could enhance standard geometrical patterns (compared to random flaps). Methods: A total of 29 cases of lower limb soft tissue reconstruction (STR)—52% trauma, 21% osteomyelitis with skin fistulas, 21% healing disorders with unstable scarring and 6% cancer-related surgery—were performed in our institution between 2012 to 2023 with geometric random (GR) local flaps (34%), geometric perforator-enhanced (GP) flaps (32%) or pure propeller perforator (PP) flaps (34%), were retrospectively analysed. Patients with proximal thigh defects, a follow up of less than 3 months and those who received an axial, muscle or free flap were excluded. Geometric patterns (as length:width ratio (L:W)) were compared among groups, analysing healing outcomes and complications. Results: Leg defects were categorized into 62% distal, 14% middle, 14% proximal third and 10% distal thigh. No significant difference in defect size was detected among groups. Mean flap size was significantly larger for GP (70.5 cm2, (p < 0.05)) and PP (74.4 cm2, (p < 0.01)) than GR (53.7 cm2). The L:W ratio was significantly higher in GP (L:W 2.2:1, (p < 0.05)) and PP (L:W 2.8:1, (p < 0.01)) than in GR (1.5:1), but no significant difference was found between GP and PP. A reduced complications rate (partial flap loss, infection, healing, revision surgery, etc.) was observed in the GP group, when compared to GR. Conclusions: Flap geometric design can be significantly improved by the inclusion of perforators, maintaining spatial advantages with larger ductility and improved vascular solidity.

This study proposes an alternative formwork system using recycled plastic to reduce the use of wood in the construction of tie columns and tie beams in San Pedro Sula, Honduras. The main objective is to develop a more sustainable and efficient solution to reduce wood consumption and the high costs that these formworks represent in projects. A geometric design was developed using reinforced recycled plastic boards, tailored to meet the structural needs of secondary concrete elements. The study applied a comparative methodology, evaluating the proposed system against traditional wooden formwork based on parameters such as assembly time, reuse potential, resistance, and material reduction. Results showed a 20% to 30% decrease in formwork assembly and disassembly time, along with an over 80% reduction in wood consumption. The recycled plastic formwork demonstrated greater durability and resistance to moisture compared to wood, offering improved performance in terms of lifespan and reusability. In conclusion, the proposed system proved to be a functional, cost-effective, and environmentally friendly alternative for the construction sector in Honduras. It also promotes the reuse of plastic waste in the development of modern, sustainable construction technologies.

Programmable mechanical metamaterials enable precise regulation of mechanical responses through geometric design, ushering in transformative paradigms for transformable structures. To systematically map the knowledge landscape and development trends in this field, this study employs knowledge mapping methods to analyze the current research status, core hotspots, and future directions of programmable mechanical metamaterials. During the research process, we expanded keywords using the litsearchr tool to optimize the retrieval strategy. Bibliometric tools, including CiteSpace 6.3.R3 and bibliometrix, were utilized to conduct multidimensional analyses on 2017 original papers related to mechanical metamaterials in transformable architecture from 2015 to 2025. These analyses encompass co-word analysis, co-citation clustering, and structural variation analysis. Key aspects include (1) identifying core journals and their attributes to clarify interdisciplinary dynamics, (2) mapping research themes and evolutionary trends through keyword analysis and clustering, and (3) pinpointing research hotspots and future directions based on citation networks and clustering results. The results reveal significant interdisciplinary characteristics, with core knowledge emerging from the intersection of materials science, mechanics, and civil engineering. Mathematical system theory provides a cross-scale modeling foundation for metamaterial microstructure design. The field is evolving from static structural design toward environment-adaptive intelligent systems. Future efforts should prioritize multi-physics collaborative regulation, engineering integration, and technical chain refinement. These findings offer a theoretical reference for the innovative development of transformable architecture.

In this study, a W-polyethylene terephthalate glycol (PETG)-based 3D-printed composite was designed for medical radiation shielding, and syringe shielding components were fabricated to evaluate shielding performance and particle dispersion characteristics. Up to 70 wt% of tungsten powder was incorporated into the PETG polymer matrix to produce W-PETG filaments suitable for 3D printing. Using the fused deposition modeling (FDM) method, a 3.0 mm-thick radiation shielding cover for a 10 mL syringe was fabricated. Radiation shielding performance was assessed using a 99mTc (200 µCi) source at distances of 30, 50, and 100 cm. While a conventional 1.0 mm Pb shield exhibited shielding efficiencies of 92.24%, 94.26%, and 95.13% at each distance, the 3.0 mm W-PETG shield demonstrated efficiencies of 70.67%, 75.64%, and 77.57%, respectively. Higher temperatures improved shielding efficiency by approximately 5.48 percentage points. When processed above 160 °C, tungsten particle clustering decreased and a more uniform dispersion was achieved, enhancing shielding performance. The interrelationship among filament fabrication parameters, particle dispersion behavior, and shielding performance of W-PETG composites was quantitatively demonstrated. The lightweight, geometric design flexibility, and compatibility with 3D-printing processes of W-PETG composites suggest strong potential as alternative materials for custom medical radiation shielding devices.

Recent studies have examined the elastocaloric response of graphene kirigami (GK) and shown how it may be tailored through geometric design. This tunability makes GK a promising platform for applications in nanoscale solid-state thermal devices. In this work, we combine molecular dynamics (MD) simulations and machine learning (ML) to explore how GK geometries affect the elastocaloric coefficient (ECC), defined as the adiabatic ratio between temperature change and applied tensile stress. A data set of 16,807 GK configurations was generated through systematic cut patterns and evaluated via MD at room temperature. Using this data, both classical and deep-learning models were trained, with a convolutional neural network (CNN) achieving the best performance (RMSE = 0.064 K GPa-1; R2 = 0.96). Model-guided optimization identified high-ECC designs 10 times faster than random search, demonstrating the power of ML-assisted strategies for the accelerated discovery of advanced elastocaloric materials.

This study presents an optimal design combined with comprehensive multiphysics validation to enhance the torque density of a coaxial magnetic gear (CMG) incorporating an overhang structure. Four high non-integer gear-ratio CMG configurations exceeding 1:10 were designed using different pole-pair combinations, and three-dimensional finite element method (3D FEM) was employed to accurately capture axial leakage flux and overhang-induced three-dimensional effects. Eight key geometric design variables were selected within non-saturating limits, and 150 sampling points were generated using an Optimal Latin Hypercube Design (OLHD). Multiple surrogate models were constructed and evaluated using the root-mean-square error (RMSE), and the Kriging model was selected for multi-objective optimization using a genetic algorithm. The optimized CMG with a 1:10.66 gear ratio achieved a 130.76% increase in average torque (65.75 Nm) and a 162.51% improvement in torque density (117.14 Nm/L) compared with the initial design. Harmonic analysis revealed a strengthened fundamental component and a reduction in total harmonic distortion, indicating improved waveform quality. To ensure the feasibility of the optimized design, comprehensive multiphysics analyses—including electromagnetic–thermal coupled simulation, high-temperature demagnetization analysis, and structural stress evaluation—were conducted. The results confirm that the proposed CMG design maintains adequate thermal stability, magnetic integrity, and mechanical robustness under rated operating conditions. These findings demonstrate that the proposed optimal design approach provides a reliable and effective means of enhancing the torque density of high gear-ratio CMGs, offering practical design guidance for electric mobility, robotics, and renewable energy applications.

Clinical outcomes of peripheral artery disease (PAD) stenting, particularly in the highly dynamic regions of the femoropopliteal artery at the adductor hiatus and behind the knee, leave significant room for improvement. Despite the availability of various stent designs, few are capable of accommodating the severe deformations induced by limb flexion at these locations without causing adverse stent-artery interactions. This study employed finite element analysis and response surface methodology to optimize the geometric design of nitinol PAD stents, with the objectives of improving stent-artery apposition, reducing arterial wall stress, minimizing stress concentrations, and decreasing arterial pinching under limb flexion-induced deformations. Five geometric parameters - strut width, thickness, amplitude, number, and link amplitude - were analyzed to assess their influence on stent performance. Strut width, thickness, amplitude, and the number of struts significantly impacted arterial stress and apposition, while link amplitude had an insignificant effect. We identified two optimized stent configurations that achieved > 97% stent-artery apposition, < 0.6% of the artery with stress > 100kPa, an average arterial stress of < 29kPa, and pinching of < 1.15. The findings revealed that lower strut amplitude and reduced strut cross-sections improved apposition and stress distribution but required careful balancing to minimize arterial pinching and maintain structural integrity. This study underscores the potential of multi-objective optimization in stent design, paving the way for PAD stents that more effectively accommodate femoropopliteal biomechanics and promote favorable mechanical conditions for healing.

3D cell infiltration into porous scaffolds constitutes a fundamental prerequisite for bone tissue engineering. Though pore size and curvature are known to dictate this process, their mathematical coupling remains elusive. Herein, we identified a size-dependent bone marrow-derived mesenchymal stem cells 3D in-growth pattern in which small pores promoted horizontal bridging, while large pores favored vertical cellular migration into the scaffold core. An analytical framework of Porous-Fisher model was developed using a superposition approach tailored to boundary-specific solutions. This approach not only enabled quantitative prediction of coverage rates through examination of grid dimensions and diffusion coefficients but also mathematically elucidated curvature and strategic geometric design. Furthermore, the prediction of cellular diffusion patterns on porous scaffolds was achieved through the alteration of boundary conditions and diffusion coefficients. Convex topological configurations were shown to accelerate cellular infiltration, whereas concave geometries permitted spatiotemporal modulation of tissue growth. Additionally, lower diffusion environments delayed coverage, suggesting scaffold designs with reduced pore sizes might benefit elderly patients. Consequently, the accuracy of model was in vivo validated by a rat cranial defect model. Overall, the mathematical model provided an effective way for ideal pore structure prediction in advance and propel the application of porous scaffolds in tissue engineering.

The geometric design of structures with optimized physical and chemical properties is one of the core topics in materials science. However, designing new functional materials is challenging due to the vast number of existing and possible unknown structures to be enumerated and difficulties in mining the underlying correlations between structures and their properties. Here, we propose a universal method for periodic structural design and property optimization. The key in our approach is a deep-learning-assisted inverse Fourier transform, which enables the creation of arbitrary geometries within crystallographic space groups. It effectively explores extensive parameter spaces to identify ideal structures with desired properties. Taking the research of three-dimensional (3D) photonic structures as a case study, this method is capable of modelling numerous structures and identifying their photonic bandgaps in just a few hours. We confirmed the established knowledge that the widest photonic bandgaps exist in network morphologies, among which the single diamond (dia net) reigns supreme. Additionally, this method identified a rarely known lcs topology with excellent photonic properties, highlighting the infinitely extensible application boundaries of our approach. This work demonstrates the high efficiency and effectiveness of the Fourier-based method, advancing material design and providing insights for next-generation functional materials.

In electroencephalography (EEG) measurements using dry electrodes, a trade-off between signal stability and user comfort is a critical barrier to long-term, wearable applications. While various approaches have been proposed to address this issue, the mechanical impact of electrode tip geometry has not been adequately quantified, and most existing evaluations predominantly rely on subjective assessments. To address this gap with a quantitative, mechanics-based framework, the current study aimed to identify an optimized electrode tip geometry that minimizes mechanical stress on the scalp even under tilted contact conditions. Finite element analysis was conducted using strain energy density (SED), a mechanical index known to correlate with neural impulse activity, as a quantitative indicator of the mechanical influence of tip geometry on the skin. Six types of electrode tip geometries, ranging from flat to hemispherical, were defined based on the ratio of fillet radius to prong radius. These geometries were analyzed under inclination angles from 0 to 5 degree, and their peak SED values were compared. Additionally, a geometry optimization using an iterative search algorithm was performed to minimize peak SED under the 5 degree tillt. The findings revealed that intermediate fillet geometries with gently rounded edges more effectively reduce peak SED under inclined conditions. Optimization further identified a geometry ratio of Rrate* = 0.61875 as the most effective tip geometry for minimizing mechanical loading under the specified conditions. These results offer a potential geometric design guideline for dry EEG electrodes that can help maintain user comfort across varying inclination angles.

Microbial colonization and biofilm formation drive infection persistence and the spread of antimicrobial resistance, particularly under flow conditions typical of medical and natural environments. Here, we combine spontaneously buckled wrinkled topographies with microfluidic platforms to investigate the adhesion of Pseudomonas aeruginosa and Staphylococcus aureus across shear rates of 0.4-200 s-1. Wrinkled surfaces with tunable wavelengths (0.5-20 μm) are fabricated and characterized using optical, atomic force, and scanning electron microscopy. Sinusoidal wrinkles with a 2 μm wavelength reduce bacterial colonization by over 70% when oriented perpendicular to flow, while folded wrinkles of 5 μm achieve more than 90% reduction across broader shear regimes and suppress biofilm formation by over 85% relative to flat controls. These topographies retain antifouling performance under pulsatile flow. This work demonstrates a scalable, chemical-free strategy for passive biofilm control through geometric surface design, enabling durable antimicrobial materials for biomedical and industrial applications.

Poor acoustics may impede communication and user experience, and yet traditional design approaches often ignore the varying acoustic needs. The present paper systematically reviews pertinent literature to assess how flexible geometric design options (e.g., adjustable surfaces, modular panels, or dynamic surfaces) affect relevant acoustic parameters (reverberation time, clarity, and sound distribution) in comparison with conventional empty auditorium designs. By following PRISMA Protocol (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) applied strictly to ensure transparency and reproducibility of the research process, 25 experimental and simulation studies from Scopus, Science Direct, Journal of The Acoustical Society of America, Sage, MDPI, and others were analyzed. Results indicate that proper geometric design can improve acoustics quality variation, particularly in multipurpose applications; however, implementation must consider cost and technical complexity. Therefore, conclusions and recommendations serve as an evidence-based guideline for architects and acoustical engineers involved in designing adaptive performance spaces in terms of real-time adjustment technologies and smart materials. On the other hand, new standards for acoustic evaluation of dynamic designs should also be created.

Intensifying competition from supermarkets and online retailers has reshaped consumer expectations for floral products, compelling brick-and-mortar florists to compete based on design sophistication rather than price alone. To guide data-driven responses, we administered an online survey that solicited the perceived value and willingness to pay (WTP) for five design styles and four flower forms at two price tiers among US consumers A data analysis revealed that geometric designs had the greatest perceived value, and respondents were willing to pay significant premiums for designs featuring parallel design elements and line flowers. Age, income, and gender segments diverged markedly in WTP, especially at the high price tier. These insights suggest florists can widen profit margins by emphasizing geometric forms, selectively incorporating high-value elements, and aligning product mixes with the demographic profile of their clientele. This evidence-based design approach provides a pathway for sustainable growth, enabling firms to enhance perceived value while optimizing material inputs, thereby ensuring economic resilience against low-cost competitors.

Geometric and thermal design of phase change material-thermoelectric system for building energy harvesting and cooling load shaving