Heriot-Watt University

This research aims to explore the response of sea surface wave fields across mesoscale eddies under the influence of tropical cyclones (TCs) in the South China Sea, utilizing numerical simulations from the Finite-Volume Community Ocean Model (FVCOM) one-way coupling with the Simulating WAves Nearshore (SWAN) model. Four types of vertical coordinates were tested in FVCOM to improve the representation of upper-ocean variability under rapidly changing depths. The high-resolution hindcast sea surface temperature data was used for validation, revealing that the general vertical coordinate in FVCOM exhibited the most accurate results, showing a correlation (COR) of 0.90 and a root mean square error (RMSE) reaching 0.29 °C. Wave simulations were conducted using the SWAN model, which incorporated wave breaking influenced by depth and complex nonlinear interactions between waves. Based on 51 mesoscale eddies detected during five TCs from 2022 to 2024, the results reveal distinct modulation patterns. Regression analysis indicates a significant coupling among wind, waves, currents, and Eddy Kinetic Energy (EKE) within the eddies. While significant wave height (SWH) increases with prolonged TC forcing duration, TC translation speed shows no significant impact on SWH or EKE, suggesting that internal geostrophic adjustment plays a dominant role in eddy dynamics. Structurally, intense TC forcing was observed to disrupt pre-existing eddies and trigger the ageostrophic cold eddies characterized by high Rossby numbers (> 0.5) and low Richardson numbers (< 0.25). Furthermore, the modulation of TC-induced waves is identified as a spatial process involving steepening-induced dissipation at the periphery and refraction-induced redistribution at the edge. The warm eddy periphery acts as a low-pass filter, dissipating high-frequency energy early due to opposing currents. Combined with refractive effects, this mechanism leads to wave energy convergence in cold eddies versus divergence in warm eddies.

We give the solution to the complete noncommutative Kadomtsev-Petviashvili (KP) hierarchy. We achieve this via direct linearisation which involves the Gelfand-Levitan-Marchenko (GLM) equation. This is a linear integral equation in which the scattering data satisfies the linearised KP hierarchy. The solution to the GLM equation is then shown to coincide with the solution to the noncommutative KP hierarchy. We achieve this via the approach pioneered by P & ouml;ppe, Inverse Problems 5(1989), 613-630. We assume the scattering data is semi-additive and by direct substitution, we show that the solution to the GLM equation satisfies the infinite set of field equations representing the noncommutative KP hierarchy. This approach relies on the augmented pre-P & ouml;ppe algebra. This is a representative algebra that underlies the field equations representing the hierarchy. It is nonassociative, and isomorphic to a descent algebra equipped with a grafting product. Indeed, it is an example of a weakly nonassociative algebra. While we perform computations in the nonassociative descent algebra, the final result which establishes the solution to the complete hierarchy, resides in the natural associative subalgebra. The advantages of this approach are that it is constructive, explicit, highlights the underlying combinatorial structures within the hierarchy, and reveals the mechanisms underlying the solution procedure.

The growing reliance on digital financial services necessitates a secure, efficient, and privacy-centric approach to identity verification and Know Your Customer (KYC) compliance. Traditional identity management systems rely on centralized databases, making them susceptible to data breaches, inefficiencies, and regulatory constraints. Over 10 billion identity records have been exposed in centralized KYC breaches, leading to a 60% increase in financial fraud cases. The rise of Decentralized Finance (DeFi) has further complicated KYC compliance, requiring innovative solutions that balance privacy and regulatory requirements. This paper proposes a Web3-powered decentralized identity framework that leverages blockchain technology, self-sovereign identity (SSI), verifiable credentials (VCs), and zero-knowledge proofs (ZKPs). By eliminating reliance on centralized authorities, our system enhances data privacy, reducing personally identifiable information (PII) disclosure by 80% while ensuring compliance with AML and GDPR regulations. The integration of zk-SNARKs enables trustless identity verification with an average proof generation time of 12.5 seconds, significantly reducing the 3-5 day verification period required by traditional systems. Smart contract-based KYC automation eliminates intermediaries, cutting compliance costs by 40% and reducing fraud risk by 60%. Through comparative analysis, we highlight that decentralized KYC improves security, cost-effectiveness, and scalability compared to traditional models. Performance evaluation confirms that transaction throughput remains within acceptable blockchain limits, with gas costs stabilized at 35,000-55,000 Gwei per verification request. Despite challenges in regulatory adaptation and zk-SNARK scalability, the proposed model demonstrates the feasibility of Web3-driven identity management for trustless, privacy-preserving, and compliant financial ecosystems.

Common whelk is a neo-gastropod that is intensively fished on the west and east temperate Atlantic with baited pots. The UK hosts the largest Whelk fishery contributing 10–15

This article surveys the manifestations, in a variety of dispersive settings, of the phenomenon of revivals. Some are classical, observed since the 1850’s and known as the Talbot effect, but have been studied only in the last 30 years. Other, unexpected manifestations have been discovered only very recently.