Suppose that f (x) E 1[8[x1, ... , xn] and g(x) E 1[8[x1, ... , xn] are two real polynomials of degree d in n variables. If the polynomials f and g are the same up to orthogonal symmetry, a natural question is then what element of the orthogonal group induces the orthogonal symmetry; i.e. to find the element R E O(n) such that f (R inverted perpendicular x) = g(x). One may directly solve this problem by constructing a nonlinear system of equations induced by the relation f (R inverted perpendicular x) = g(x) along with the identities of the orthogonal group. However, this approach becomes quite computationally expensive for larger values of nand d. To give an alternative and significantly more scalable solution to this problem, we introduce the concept of Polynomial-Weighted Principal Component Analys is (PW-PCA). We in particular show how PW-PCA can be effectively computed and how these techniques can be used to obtain a certificate of orthogonal equivalence, that is we find the R E O(n) such that f (R inverted perpendicular x) = g(x). (c) 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Visual inspection detects scattered track defects, but static appearance alone offers limited evidence for predicting their development and prioritizing follow-up inspection. Sparse longitudinal labels constrain degradation prediction. This paper presents Causal Diagnosis–Prediction–Ranking (CaDPR), a framework that integrates causal context, degradation prediction, and uncertainty-aware ranking to prioritize follow-up inspection. A gated multi-encoder predictor combines image features with nine-dimensional co-defect context to estimate pad and clip degradation, while predictive uncertainty discounts ranking scores. Evaluation uses 1312 corrugation-exposed pairs from two lines in one metro system, with five seeds and five grouped folds. With annotation-derived inputs, the single-model macro-average area under the receiver operating characteristic curve reaches 0.785 ± 0.029; ensemble ranking achieves a normalized discounted cumulative gain at 20 of 0.724 ± 0.055. Ablations support the predictive value of correct context correspondence and association-weighted training. CaDPR extends visual defect diagnosis to degradation-informed prioritization, helping maintenance staff allocate limited inspection capacity.
The rapid advancement of low-power microelectronic technologies has stimulated growing interest in vibrationbased energy harvesting as a promising alternative to conventional batteries. While batteries are widely used at these scales, their replacement becomes highly challenging for systems deployed within inaccessible or remote locations. The major drawback of linear harvesters is their limited frequency bandwidth. This limitation, together with the wide frequency spectrum of ambient excitations, significantly diminishes the energy conversion efficiency of linear harvesters. To address this challenge and improve the performance of such systems in practical environments, it is essential to broaden their frequency bandwidth. Among the various approaches for broadening the frequency bandwidth, employing nonlinear techniques has proven to be highly effective in enhancing the efficiency of vibration energy harvesters. This study proves the theoretical modeling of frequency bandwidth analysis in a piezoelectric energy harvester for a series of experimental cases considering magnetic nonlinearity and impact-induced nonlinearity. Applying both approaches together increases the system efficiency by about 80 % compared to using either method separately. Furthermore, the influence of key system parameters-including magnetic strength, input acceleration amplitude, electrical resistance, and initial gap-on the system's dynamic behavior is investigated. Finally, an efficiency index is introduced to assess the harvester's efficiency relative to the conventional design.
We present a Lagrangian Heterogeneous Multiscale Method (LHMM) for simulating the non-Newtonian rheology of polymer melts in complex two-dimensional flows. The method couples Dissipative Particle Dynamics (DPD) at the microscale with a GENERIC-compliant Smoothed Particle Hydrodynamics (SPH) at the macroscale, in a concurrent framework, overcoming the limitations of traditional Eulerian-based methods in capturing long-memory and history-dependent effects. At the microscale, DPD serves as a virtual rheometer, employing FENE (Finitely Extensible Nonlinear Elastic) bead-spring polymer chains. This approach provides key rheological properties, including shear-thinning and zero-shear-rate viscosities, relaxation times, and viscoelastic dynamics, which are quantified via Carreau-Yasuda fitting and spectral analysis. The LHMM couples SPH-derived strain rates with microscopic stress responses using the Irving-Kirkwood formalism. This approach enables a concurrent interaction between macroscopic strain rates and microscopic stress tensors, ensuring a consistent viscoelastic response across scales. The method is validated against benchmark flows, including Reverse Poiseuille Flow and flow through a Periodic Array of Cylinders, across Weissenberg numbers 0.5 < Wi < 30 and low Reynolds numbers (Re < 1). A final demonstration of flow in a 2D porous medium highlights LHMM’s capability to handle highly heterogeneous geometries. The LHMM is implemented in LAMMPS, making it suitable for integrating multiple models to describe microscales. In contrast, large-scale simulations efficiently utilize GPU and CPU resources, managing multiple coupling and time-scaling levels to maintain numerical stability and accuracy. The framework offers a predictive, constitutive-free tool that links microscopic polymer dynamics to macroscopic flow behavior, making it suitable for multiscale applications.
This article introduces a coupled aerodynamic and dynamic modelling method for variable RPM (VRPM) multi-rotor simulations, utilising an improved gimballed rotor dynamics model and the free vortex wake (FVW) method. Additional degrees of freedom in the gimballed rotor hub, as well as the shaft rotation and lead-lag motion, are modelled. The influence of VRPM on the rotor wake is incorporated into the FVW method. Thus, this simulation model allows the rotor to begin from a stationary state, accelerate to its operating RPM, and decelerate back to rest, covering a wide range of operating conditions relevant to VTOL vehicles. The simulation model is validated against wind tunnel test data, and multiple case studies are presented and analysed to showcase the VRPM multi-rotor simulation and the flight characteristics of the VRPM multi-rotors.
