In machine learning, interest in neural fractional differential equations has surged due to their capabilities in modeling memory-dependent system dynamics. While most existing approaches concentrate on constant-order fractional derivatives, employing variable-order fractional operators provides a more adaptable and descriptive means of capturing intricate memory effects. Also, fractal–fractional derivatives extend classical fractional calculus by combining memory effects with fractal geometry, yielding more accurate models of complex real-world phenomena. In this study, we introduce the Physics-informed Neural Variable-Order Fractal–Fractional Differential Equation (PiNVoFFDE) network, a novel architecture that integrates variable-order fractal–fractional derivative in the Caputo sense with a trainable neural network guided by prior physical knowledge for solving variable-order fractal–fractional differential equations. By allowing the derivative order to adjust dynamically based on time, we obtain a more general model that captures richer update dynamics and delivers greater modeling flexibility. The Adams–Bashforth–Moulton predictor–corrector scheme is employed to provide the numerical solution to the PiNVoFFDE model, utilizing the recently introduced average-and-subtraction-based optimizer (ASBO) for model training. Using our proposed framework, we obtain the numerical solution of the system of fractal–fractional Bloch equations, which are a fundamental system of differential equations widely used in physics, chemistry, magnetic resonance imaging (MRI), and nuclear magnetic resonance (NMR) to describe how magnetization evolves under external magnetic fields and internal relaxation processes. The results reveal that PiNVoFFDE consistently outperforms constant-order fractional models and exceeds alternative approaches, demonstrating its superior adaptability and overall performance.
Carbon fibre reinforced polymers (CFRPs) are increasingly used in biomedical and safety-critical applications, where embedded and real-time non-destructive testing (NDT) is essential to ensure structural integrity. This paper presents a cost-effective, AI-assisted thermographic inspection system designed from an embedded electronics and circuit-level perspective. The proposed platform integrates a long-wave infrared (LWIR) sensor, dedicated signal conditioning and power management circuits, and a Raspberry Pi-based processing unit within a unified hardware-software co-design approach. Infrared data acquired under surface heating conditions are processed on-board using a convolutional neural network based on a U-Net architecture, enabling automatic localisation and classification of subsurface defects in CFRP samples. Particular attention is devoted to embedded design constraints, including sensor interfacing, acquisition timing, end-to-end latency, and real-time processing scalability. Experimental results confirm the feasibility of real-time surface heat assessment and the robustness of the proposed architecture in detecting delaminations and voids. The presented system contributes to the development of intelligent embedded inspection electronics and provides a reference design for edge AI-enabled NDT systems in industrial and biomedical applications.
The dynamics of compressible fluids with viscosity and capillarity remain only partially understood, particularly in relation to phase transitions and nonlinear wave propagation. Due to the difficulties posed by its mixed-type nature, where eigenvalue variations result in hyperbolic-elliptic transitions and shock formation, thorough symmetry-based and bifurcation analyses of the one-dimensional viscous-capillarity compressible van der Waals system (the p-system) remain limited despite prior research. This paper examines the model using soliton solutions, bifurcation theory, and Lie symmetry techniques. Symmetry analysis identifies invariant structures, making analytical and numerical treatment easier. Soliton solutions reveal robust nonlinear waveforms that accurately model shock structures and capillary-driven interfacial phenomena, while bifurcation analysis reveals critical stability thresholds controlled by viscosity and surface tension. In the natural sciences and engineering, where phase transitions and interfacial effects are crucial, the results offer practical significance and a deeper theoretical understanding of nonlinear compressible flows.
Wood modification is a process that alters the properties of wood through chemical, thermal, or physical treatments, thereby improving its performance, including durability and dimensional stability. Steaming is a hygrothermal treatment that can modify physical properties and may affect mechanical performance depending on process severity. This study investigated the effects of low-temperature steaming on olive wood (Olea europaea L.) by applying a constant temperature (80 °C) and varying treatment duration (12, 18, and 36 h) compared with natural seasoning (control). Color and dynamic modulus of elasticity (MOEd) were measured on boards before and after treatment; after, specimens were tested for dimensional stability, bending properties (MOR and MOEs), compression strength, Janka hardness, and abrasion resistance. Steaming produced significant color changes in both heartwood and sapwood, with stronger responses in sapwood. Bending properties showed non-significant increasing trends, with mean MOR increasing from 50.21 MPa (control) to 62.24–64.71 MPa and the highest mean MOEs observed in the 12 h group (+ 13.45
Electrical Impedance Tomography (EIT) represents a promising and non-invasive technique for the characterisation of biological tissues, but its diagnostic performance strongly depends on the electrode configuration, system geometry, and electronic acquisition strategies. In this work, a three-dimensional model based on the Finite Element Method (FEM) is developed to investigate the detectability of epithelial neoplasms through optimised electrode excitation schemes. The adjacent and opposite configurations are systematically compared in terms of impedance contrast, spatial sensitivity, and neoplastic inclusion localisation capability. The simulations were implemented using an open-source finite element solver with heterogeneous multilayer tissue models. The results show that the configuration with opposite electrodes significantly improves impedance contrast and sensitivity in three-dimensional models, allowing for better detection of localised conductivity anomalies. The proposed approach contributes to the design of optimised EIT electronic systems for early and non-invasive screening applications of epithelial cancer.
