European Journal of Emerging Engineering and Mathematics
type: channel
description: ISSN: 3087-4572 Publication Frequency: Halfyearly Open Access | International Journal | Double Blinded Peer Reviewed Journal
publisher: The Parthenon Frontiers
language: en
publication name: European Journal of Emerging Engineering and Mathematics
issn: 3087-4572
copyright: All articles published by The Parthenon Frontiers and its associated journals are distributed under the terms of the Creative Commons Attribution (CC BY 4.0) International License unless otherwise stated. Authors retain full copyright of their published work. By submitting their manuscript, authors agree to grant The Parthenon Frontiers a non-exclusive license to publish, archive, and distribute the article worldwide. Authors are free to: Share their article on personal websites, institutional repositories, or social media platforms. Reuse their content in future works, presentations, or educational materials, provided proper citation of the original publication.
items: Data‑Centric Governance And Ethical Frameworks For Trustworthy AI And Big Data Systems
items: Digital Financial Transformation In Islamic And Gulf Banking: Innovators, Enablers, And Customer Perceptions
items: Critical Success Factors And Strategic Frameworks For ERP Implementation In Smes: A Comprehensive Analytical Study
items: Artificial Intelligence–Driven Transformation Of Insurance Enterprises: Strategic, Architectural, And Governance Implications Toward 2030
items: AI-Enhanced Event-Driven Architectures In Digital Finance: Transforming Risk, Decision-Making, And Real-Time Enterprise Systems
items: Adversarial Robustness In Time Series And Computer Vision Models: A Unified Theoretical And Empirical Examination Of Attacks, Defenses, And Methodological Frontiers
items: Advancing The Cloud-Edge Continuum: Architectures, Orchestration, And Future Directions In Edge-Native And Serverless Computing
items: Advancements In Post-Silicon Debugging And Verification For System-On-Chip Architectures
items: A COMPARATIVE ANALYSIS OF POTENTIAL-BASED AND NON-POTENTIAL-BASED COHESIVE MODELS FOR SIMULATING LOADING AND UNLOADING IN SLIDING ELASTIC LAMINATES
items: Learning Physically Consistent Dynamics: A Human-Centric Approach to Entropy-Stable Neural Networks
items: Extremum Seeking for the First Derivative of Nonlinear Maps with Constant Delays via a Time-Delay Approach
items: Asymptotic Behaviour of Nonlinear Viscoelastic Wave Equations with Boundary Feedback
items: A β-Factor for Stability: Provably Stable, High-Order Splitting Schemes for Incompressible Flows
items: A Unified Nonlocal and Memory-Dependent Moore-Gibson-Thompson Framework for Laser-Induced Magneto-Thermo-Mechanical Waves
items: A Foundational Criterion in Boundary Value Problems for Pseudo-Differential Operators

Data‑Centric Governance And Ethical Frameworks For Trustworthy AI And Big Data Systems
type: item
description: The rapid proliferation of artificial intelligence (AI), big data analytics, and cloud‑based data governance frameworks has catalyzed transformative changes across sectors including health, commerce, urban infrastructure, and scientific inquiry. Despite immense potential, such data‑driven technologies present complex ethical, regulatory, and governance challenges that require systematic theoretical and practical frameworks. This article critically explores the intersection of data governance, ethics, compliance, and trustworthiness in AI and big data ecosystems. Drawing on multidisciplinary scholarship and empirical insights, it synthesizes scholarly debate on responsible AI, scalable governance mechanisms, ethical data practices, and compliance strategies, while articulating novel theoretical linkages across these dimensions. Findings illustrate the need for robust data governance frameworks to address redundancy, quality, and ethical risks, while advocating for transparency, accountability, and alignment with societal values. Implications underscore how integrated governance approaches can enable trustworthy and socially beneficial AI systems. The article concludes with recommendations for future research and policy priorities in the ethical governance of AI and big data.
subject: Articles
  topic: section
subject: Data governance
  topic: keywords
subject: ethical AI
  topic: keywords
subject: cloud analytics
  topic: keywords
subject: compliance
  topic: keywords
subject: transparency
  topic: keywords
subject: trustworthy systems
  topic: keywords
subject: big data ethics
  topic: keywords
creator: Dr. Markus Keller
creator: Prof. Amina Hassan
rights: Copyright (c) 2026 https://creativecommons.org/licenses/by/4.0
date: 2026-01-08
publication date: 2026-01-08
starting page: 05
ending page: 10

Digital Financial Transformation In Islamic And Gulf Banking: Innovators, Enablers, And Customer Perceptions
type: item
description: The rapid emergence of financial technologies (FinTech) has transformed traditional banking paradigms across global markets, particularly within emerging and Islamic financial landscapes. This study synthesizes interdisciplinary scholarship to investigate the dynamics of FinTech adoption, the technological enablers shaping innovation ecosystems, and the customer perceptual frameworks that influence adaptability in Islamic and Gulf banking sectors. Drawing on seminal work situating FinTech within broader financial and InsurTech innovation (Yan et al. 2018), the article explores both structural and behavioral dimensions that facilitate or constrain technology-mediated financial intermediation. The research engages complex theoretical discourses on digital innovation diffusion, encompassing socio-technical system theory, institutional adaptation, and customer experience paradigms. It reviews empirical insights into service quality effects on satisfaction (Paul et al. 2016), longitudinal impacts of digital protocols like SWIFT on bank performance (Scott et al. 2017), and region-specific investigations of Saudi and Malaysian Islamic banking perceptions (Oladapo et al. 2022; Zouari & Abdelhedi 2021). Using a comprehensive literature integrative framework, the analysis scrutinizes the enabling conditions in the Saudi context (Makki & Alqahtani 2022) and contrasts FinTech’s role across Gulf Cooperation Council (GCC) economies (Khan & Saad 2022), ultimately delineating implications for strategic digital governance and future research trajectories. The discussion addresses limitations in current empirical modalities and proposes a nuanced research agenda that foregrounds customer-centric evaluation metrics and systemic innovation assessments.
subject: Articles
  topic: section
subject: FinTech adoption
  topic: keywords
subject: Islamic banking
  topic: keywords
subject: digital innovation
  topic: keywords
subject: customer perception
  topic: keywords
subject: financial intermediation
  topic: keywords
subject: banking technology
  topic: keywords
subject: Saudi Arabia
  topic: keywords
creator: Dr. François Lambert
creator: Prof. Chinedu Okafor
creator: Dr. Irina Smirnova
rights: Copyright (c) 2026 https://creativecommons.org/licenses/by/4.0
date: 2026-01-01
publication date: 2026-01-01
starting page: 01
ending page: 04

Critical Success Factors And Strategic Frameworks For ERP Implementation In Smes: A Comprehensive Analytical Study
type: item
description: Enterprise Resource Planning (ERP) systems have emerged as pivotal technological infrastructures for modern organizational management, enabling the integration of diverse business processes, optimizing resource allocation, and facilitating real-time decision-making. Despite the proven potential of ERP systems, small and medium-sized enterprises (SMEs) frequently encounter implementation challenges, leading to project delays, cost overruns, or outright failure. The literature identifies critical success factors (CSFs) as determinants that significantly influence the likelihood of successful ERP deployment. This research comprehensively examines ERP implementation within SMEs, emphasizing the multidimensional factors—organizational, technological, strategic, and human-centric—that drive successful adoption. Grounded in established theoretical frameworks and contemporary empirical studies, this article synthesizes findings from a wide array of scholarly sources, including Achanga, Shehab, Roy, and Nelder (2006), who highlight the importance of lean management principles and process alignment in driving ERP success. Methodologically, this study employs an integrative literature review complemented by analytical discourse, critically evaluating the convergence of theoretical constructs with practical implementation experiences across global SME contexts. The investigation reveals that top management commitment, effective change management, rigorous process reengineering, user training, and continuous post-implementation evaluation are indispensable for ERP success. Moreover, the transition toward cloud-based ERP solutions introduces additional layers of complexity, necessitating robust IT infrastructure, data governance, and strategic alignment with business objectives (Alsharari, Al-Shboul, & Alteneiji, 2020). Cross-national studies further indicate that contextual factors, such as regulatory environments, cultural perceptions of technology, and organizational maturity,…
subject: Articles
  topic: section
subject: Enterprise Resource Planning
  topic: keywords
subject: SMEs
  topic: keywords
subject: Critical Success Factors
  topic: keywords
subject: ERP Implementation
  topic: keywords
subject: Organizational Change
  topic: keywords
subject: Cloud ERP
  topic: keywords
subject: Digital Transformation
  topic: keywords
creator: Dr. Ethan Parker
creator: Prof. Sun-Young Lee
rights: Copyright (c) 2026 https://creativecommons.org/licenses/by/4.0
date: 2025-12-05
publication date: 2025-12-05
starting page: 21
ending page: 25

Artificial Intelligence–Driven Transformation Of Insurance Enterprises: Strategic, Architectural, And Governance Implications Toward 2030
type: item
description: The insurance industry is undergoing a structural transformation driven by the rapid diffusion of artificial intelligence across underwriting, claims management, pricing, fraud detection, customer engagement, and enterprise architecture. Unlike prior waves of digitization that focused primarily on process automation and front-end digitization, contemporary AI adoption reconfigures the epistemic foundations of insurance decision-making by shifting actuarial judgment, risk classification, and operational governance toward data-intensive, adaptive, and algorithmically mediated systems. This article develops an extensive, publication-ready analysis of how artificial intelligence is reshaping insurance enterprises as they progress toward the year 2030. Grounded strictly in the provided scholarly and industry references, the study integrates strategic foresight literature, technical analyses of AI-enabled underwriting, regulatory perspectives, and microservices-based architectural paradigms to construct a comprehensive interpretive framework for AI-led insurance transformation. The article advances three core arguments. First, AI adoption in insurance is not merely a technological upgrade but a systemic reconstitution of value creation logic, wherein predictive analytics, computer vision, and machine learning models redefine how insurers perceive, price, and pool risk. Second, this transformation is inseparable from architectural modernization, particularly the transition from monolithic systems to microservices-based ecosystems that enable scalable, resilient, and governable AI deployment. Third, the expansion of algorithmic decision-making introduces profound governance, ethical, and regulatory challenges that require new institutional arrangements, transparency mechanisms, and human–AI collaboration models. Methodologically, the study employs a qualitative, integrative research design that synthesizes conceptual analysis, interpretive comparison, and cross-source trian…
subject: Articles
  topic: section
subject: Artificial intelligence in insurance
  topic: keywords
subject: AI underwriting
  topic: keywords
subject: insurance microservices architecture
  topic: keywords
subject: algorithmic governance
  topic: keywords
subject: insurance digital transformation
  topic: keywords
subject: AI regulation
  topic: keywords
subject: insurance strategy
  topic: keywords
creator: Prof. Pierre Dubois
creator: Dr. Samuel Okoye
creator: Prof. Elena Petrova
rights: Copyright (c) 2026 https://creativecommons.org/licenses/by/4.0
date: 2025-10-11
publication date: 2025-10-11
starting page: 17
ending page: 20

AI-Enhanced Event-Driven Architectures In Digital Finance: Transforming Risk, Decision-Making, And Real-Time Enterprise Systems
type: item
description: The convergence of artificial intelligence, event-driven architectures, and digital financial systems represents a paradigm shift in contemporary enterprise decision-making frameworks. This paper investigates the theoretical foundations, technological constructs, and applied implications of AI-powered risk modeling and real-time data processing in financial systems, emphasizing the transformative potential of intelligent, event-driven architectures. The research situates these developments within historical and contemporary technological trajectories, highlighting the evolution from monolithic computing systems to microservices-based event-driven infrastructures, particularly in high-concurrency environments. Through an extensive review of existing literature, the study identifies critical challenges, including latency management, system resilience, and human–machine interaction complexities, while underscoring the potential for enhanced predictive capabilities and strategic enterprise decision support. Integrating principles from stream processing, complex event processing, and intelligent service systems, this study examines the interrelationship between technological sophistication and organizational agility in dynamic financial markets. Moreover, the discourse critically evaluates the role of AI in redefining risk assessment, portfolio management, and operational forecasting, exploring both the theoretical underpinnings and practical applications of such frameworks. By synthesizing findings across finance, computational intelligence, and information systems research, this work contributes a comprehensive, multi-dimensional understanding of next-generation enterprise architectures, providing a blueprint for future digital transformation strategies and robust analytical systems. The study also elucidates key design principles, performance considerations, and governance mechanisms, ensuring that AI-driven, event-oriented infrastructures are aligned with organizatio…
subject: Articles
  topic: section
subject: AI
  topic: keywords
subject: event-driven architecture
  topic: keywords
subject: digital finance
  topic: keywords
subject: real-time data processing
  topic: keywords
subject: microservices
  topic: keywords
subject: risk modeling
  topic: keywords
subject: enterprise systems
  topic: keywords
creator: Prof. Miguel Alvarez
creator: Dr. Hannah Fischer
rights: Copyright (c) 2026 https://creativecommons.org/licenses/by/4.0
date: 2025-09-07
publication date: 2025-09-07
starting page: 12
ending page: 16

Adversarial Robustness In Time Series And Computer Vision Models: A Unified Theoretical And Empirical Examination Of Attacks, Defenses, And Methodological Frontiers
type: item
description: The accelerating integration of deep learning models into safety-critical, economic, and societal decision-making systems has foregrounded the urgent challenge of adversarial robustness. While early adversarial machine learning research was predominantly anchored in computer vision, recent advances demonstrate that time series models—widely deployed in finance, healthcare, cybersecurity, climate forecasting, and industrial monitoring—are equally vulnerable to carefully crafted perturbations. This article presents a comprehensive, theory-driven, and empirically grounded examination of adversarial attacks and defenses across both computer vision and time series learning paradigms, with a particular emphasis on neural architectures, evaluation protocols, and ensemble-based strategies. Drawing upon an extensive and diversified body of literature, the study synthesizes foundational adversarial concepts, modern attack mechanisms, and contemporary defense methodologies, including adversarial training, distillation, ensemble learning, and robustness-oriented architectural design. The analysis is guided by the recognition that adversarial vulnerability is not an incidental artifact of specific models, but rather an emergent property of high-dimensional statistical learning systems optimized under conventional empirical risk minimization. By integrating insights from seminal theoretical works and recent empirical contributions, including comprehensive surveys and domain-specific studies, this article articulates a unified conceptual framework that bridges computer vision and time series classification. The methodological section outlines a rigorous literature-driven analytical approach that emphasizes interpretive synthesis over numerical benchmarking, enabling cross-domain comparison without reliance on visual or mathematical formalism. The results section presents an in-depth descriptive analysis of adversarial behaviors, highlighting recurring patterns of susceptibility, t…
subject: Articles
  topic: section
subject: Adversarial machine learning
  topic: keywords
subject: Time series classification
  topic: keywords
subject: Neural network robustness
  topic: keywords
subject: Ensemble defenses
  topic: keywords
subject: Computer vision security
  topic: keywords
subject: Deep learning reliability
  topic: keywords
creator: Prof. Oliver Schmidt
creator: Prof. James
rights: Copyright (c) 2026 https://creativecommons.org/licenses/by/4.0
date: 2025-08-07
publication date: 2025-08-07
starting page: 06
ending page: 11

Advancing The Cloud-Edge Continuum: Architectures, Orchestration, And Future Directions In Edge-Native And Serverless Computing
type: item
description: The evolution of computing paradigms has witnessed a paradigmatic shift from centralized cloud infrastructures toward distributed, edge-centric architectures that enable low-latency, context-aware, and resource-efficient services. Edge computing, a pivotal component of this continuum, promises transformative capabilities in the domains of the Internet of Things (IoT), real-time analytics, and pervasive artificial intelligence applications. This paper provides a comprehensive, scholarly exploration of edge-native computing paradigms, serverless function deployment across the edge-cloud continuum, and the orchestration mechanisms underpinning these environments. Leveraging an extensive corpus of contemporary research, the study delineates theoretical foundations, architectural frameworks, and methodological approaches to optimize service placement, mobility-aware computing, and energy efficiency within distributed ecosystems. Furthermore, critical discussion is provided on the security, reliability, and scalability challenges inherent in edge-native deployments. By synthesizing perspectives from seminal research (Shi et al., 2016; Khan et al., 2019; Cao et al., 2020) and recent technological initiatives, this work highlights opportunities for the convergence of cloud-native principles with edge computing strategies. The paper emphasizes the role of predictive orchestration, function-as-a-service (FaaS) paradigms, and AI-driven resource allocation in facilitating a responsive, resilient, and context-sensitive computing continuum. The theoretical insights presented aim to inform the design of next-generation platforms that integrate cognitive, autonomous, and human-centric capabilities while addressing the practical constraints imposed by latency, bandwidth, and mobility. Finally, the study identifies gaps in current literature, proposing avenues for rigorous experimental validation and cross-disciplinary collaboration to advance the frontiers of edge computing research…
subject: Articles
  topic: section
subject: Edge computing
  topic: keywords
subject: serverless computing
  topic: keywords
subject: cloud-edge continuum
  topic: keywords
subject: edge-native applications
  topic: keywords
subject: orchestration
  topic: keywords
subject: mobility-aware computing
  topic: keywords
subject: IoT platforms
  topic: keywords
creator: Prof. Chloe Martin
creator: Dr. Hiroshi Sato
rights: Copyright (c) 2025 Prof. Chloe Martin, Dr. Hiroshi Sato (Author) https://creativecommons.org/licenses/by/4.0
date: 2025-07-07
publication date: 2025-07-07
starting page: 01
ending page: 05

Advancements In Post-Silicon Debugging And Verification For System-On-Chip Architectures
type: item
description: Post-silicon validation of complex System-on-Chip (SoC) architectures has become an indispensable phase in modern integrated circuit development, owing to the increasingly sophisticated interaction of digital logic, embedded memory, and heterogeneous processing units. The limitations of pre-silicon verification methodologies, including formal verification and simulation, necessitate robust post-silicon debugging techniques that are capable of isolating, reproducing, and analyzing elusive design flaws in silicon hardware. This research synthesizes contemporary approaches in post-silicon debug infrastructure, with a particular focus on reconfigurable design-for-debug (DfD) methodologies, failure propagation tracing, and the integration of formal methods with embedded logic analysis. Grounded in foundational contributions by Abramovici et al. (2006), who proposed a reconfigurable DfD framework for SoCs, this study critically examines the theoretical underpinnings, practical implementations, and comparative efficacy of various post-silicon debug strategies. Additionally, advanced topics such as lossless compression of debug data (Anis & Nicolici, 2007), runtime assertion checking (Boule & Zilic, 2005), and formal backspace analysis techniques (de Paula et al., 2008) are explored to provide a comprehensive framework for evaluating and improving post-silicon validation pipelines. Through descriptive and analytical synthesis of empirical findings across multiple studies, this article elucidates the inherent trade-offs between resource utilization, observability, and fault localization granularity. The discourse further contextualizes these techniques within the broader landscape of SoC design verification, highlighting emergent opportunities for integrating machine-assisted inference, SMT-based reasoning (Barrett et al., 2009), and runtime model checking (Bayazit & Malik, 2005). By bridging historical methodologies with contemporary advancements, the article offers actiona…
subject: Articles
  topic: section
subject: Post-silicon validation
  topic: keywords
subject: System-on-Chip
  topic: keywords
subject: design-for-debug
  topic: keywords
subject: embedded logic analysis
  topic: keywords
subject: failure propagation
  topic: keywords
subject: runtime assertion
  topic: keywords
subject: formal verification
  topic: keywords
creator: Prof. Jessica Adams
creator: Dr. Matteo Bianchi
rights: Copyright (c) 2026 https://creativecommons.org/licenses/by/4.0
date: 2025-01-01
publication date: 2025-01-01
starting page: 01
ending page: 05

A COMPARATIVE ANALYSIS OF POTENTIAL-BASED AND NON-POTENTIAL-BASED COHESIVE MODELS FOR SIMULATING LOADING AND UNLOADING IN SLIDING ELASTIC LAMINATES
type: item
description: When materials break, the process is incredibly complex. To predict and analyze these failures, engineers and scientists use computational tools called Cohesive Zone Models (CZMs)1. These models fall into two main camps: potential-based models, which use a single energy function to describe the fracture process, and non-potential-based models, which offer more freedom to describe complex behaviors, especially when a material is repeatedly loaded and unloaded2. This study takes a close look at both approaches, comparing them in the context of laminated materials sliding against each other3. We've developed a unified mathematical framework that allows us to build both types of models from the ground up, showing how to incorporate the effects of loading and unloading in a natural way, even when the fracture properties change with direction4. Our analysis, backed by clear numerical examples, reveals major differences in how these models predict stiffness, energy loss, and permanent damage5. We show that potential-based models, while elegant, have serious limitations and can produce unrealistic results under the complex conditions of mixed-mode unloading6. In contrast, the non-potential-based approach proves to be a robust and reliable tool that works well in all situations7. These findings help clarify which model to choose for a given problem and offer critical insights for accurately predicting failure in advanced composite materials.
subject: Articles
  topic: section
subject: Cohesive Zone Model (CZM)
  topic: keywords
subject: Potential-Based Models
  topic: keywords
subject: Non-Potential-Based Models
  topic: keywords
subject: Variational Methods
  topic: keywords
creator: Dr. Keeran V. Alnore
creator: Dr. Mihita R. Solven
rights: Copyright (c) 2024 European Journal of Emerging Engineering and Mathematics
date: 2024-12-30
publication date: 2024-12-30
starting page: 57
ending page: 62

Learning Physically Consistent Dynamics: A Human-Centric Approach to Entropy-Stable Neural Networks
type: item
description: From the flow of galaxies to the waves in our oceans, much of the physical world is governed by a class of equations known as hyperbolic conservation laws. Simulating these laws on computers is a monumental task, especially because they often produce sharp, sudden changes like shockwaves. For decades, scientists have hand-crafted complex numerical methods to tackle this challenge, but these methods require deep, specialized knowledge. More recently, artificial intelligence has shown an incredible ability to learn dynamics from data, but these "black-box" models often fail to respect the fundamental laws of physics, leading to unstable or nonsensical results. In this paper, we introduce a new approach that bridges this gap: the Neural Entropy-Stable Conservative Flux (NES-CF) network. Instead of relying on predefined rules, our framework learns the physics of a system directly from data. Our key innovation is to have the AI learn not only the system's dynamics but also a fundamental physical principle known as entropy—a measure of disorder that must always be respected. By building this principle directly into the learning process, our model guarantees that its predictions are physically consistent and stable. We tested our framework on a range of challenging problems, from the simple formation of a shockwave to the complex dynamics of gas, and found that it accurately captures the physics, even when trained with noisy data. This work represents a significant step toward creating AI models for science that are not only powerful but also trustworthy..
subject: Articles
  topic: section
subject: Hyperbolic Conservation Laws
  topic: keywords
subject: Neural Networks
  topic: keywords
subject: Entropy Stability
  topic: keywords
subject: Physics-Informed Machine Learning
  topic: keywords
creator: Dr. Nirelle V. Aumont
creator: Dr. Kaien R. Luskami
creator: Dr. Lioren J. Kevrand
rights: Copyright (c) 2024 European Journal of Emerging Engineering and Mathematics
date: 2024-12-27
publication date: 2024-12-27
starting page: 50
ending page: 56

Extremum Seeking for the First Derivative of Nonlinear Maps with Constant Delays via a Time-Delay Approach
type: item
description: This paper introduces a novel extremum seeking (ES) scheme specifically designed for identifying the first derivative of an unknown nonlinear map, particularly in systems subject to constant transmission delays. Traditional approaches often rely on predictor-based methods to compensate for delays, which can introduce significant complexity. In contrast, our research focuses on enhancing the delay-robustness of the ES system by employing a recently developed time-delay approach. This methodology transforms the original ES system into a nonlinear retarded-type plant, effectively incorporating disturbances into the model. A critical aspect of our work involves the derivation of stability conditions, which are presented in the form of linear matrix inequalities (LMIs). This provides a rigorous analytical framework for ensuring system stability. Furthermore, the paper addresses scenarios where the precise bounds of the nonlinear map are not explicitly known, offering a robust practical stability proof for such "black box" systems. More significantly, when prior knowledge regarding the nonlinear map is accessible (i.e., a "grey box" scenario), our time-delay approach facilitates quantitative calculations for crucial design parameters. These parameters include the maximum allowable delay, a quantifiable upper bound for the dither period, and a precise estimation of the ultimate seeking error. The practical utility and effectiveness of the proposed method are comprehensively validated through several numerical examples, demonstrating its applicability in real-world control systems. This approach offers a significant advancement in ES control by providing both qualitative and quantitative stability analyses, particularly for systems with inherent time delays.
subject: Articles
  topic: section
subject: extremum seeking
  topic: keywords
subject: time delay
  topic: keywords
subject: nonlinear system
  topic: keywords
subject: first derivative
  topic: keywords
creator: Dr. Jalen T. Rovimar
rights: Copyright (c) 2024 European Journal of Emerging Engineering and Mathematics
date: 2024-12-24
publication date: 2024-12-24
starting page: 34
ending page: 49

Asymptotic Behaviour of Nonlinear Viscoelastic Wave Equations with Boundary Feedback
type: item
description: This study investigates a nonlinear viscoelastic wave equation subject to acoustic boundary conditions and a nonlinear distributed delay feedback acting on the boundary. The analysis of the asymptotic behavior of such systems is of paramount importance for both theoretical advancements in the field of partial differential equations and for practical applications in science and engineering. Viscoelastic materials, which exhibit both elastic and viscous properties, are modeled by equations that incorporate memory effects, often represented by integral terms. The inclusion of nonlinear distributed delay in the boundary feedback introduces additional complexity, reflecting more realistic physical scenarios where system responses are not instantaneous but occur over a range of times. Furthermore, the consideration of acoustic boundary conditions enhances the model's applicability to problems involving wave interactions at material interfaces. In this work, we establish a framework for analyzing the long-term behavior of solutions to this complex system. By employing the multiplier method and constructing a suitable Lyapunov functional, we derive general decay results for the energy of the system. The analysis is carried out under a general set of assumptions on the memory kernel and the nonlinear functions that characterize the boundary feedback and delay. We demonstrate that the energy of the system decays to zero as time tends to infinity, and we provide explicit decay rates that depend on the properties of the memory kernel and the nonlinearities in the system. Our findings contribute to the fundamental understanding of energy dissipation and stability in viscoelastic systems with time-delayed boundary controls. This research not only advances the mathematical theory but also provides valuable insights for the design and analysis of materials and structures where viscoelasticity, acoustic effects, and delayed feedback are significant factors.
subject: Articles
  topic: section
subject: Mathematical model
  topic: keywords
subject: viscoelastic term
  topic: keywords
subject: wave equation
  topic: keywords
subject: asymptotic behaviour
  topic: keywords
creator: Dr. Sorin D. Veltrax
creator: Dr. Nireen A. Makov
creator: Dr. Kaito L. Fenjara
creator: Dr. Elmera T. Qasrin
rights: Copyright (c) 2024 European Journal of Emerging Engineering and Mathematics
date: 2024-12-22
publication date: 2024-12-22
starting page: 26
ending page: 33

A β-Factor for Stability: Provably Stable, High-Order Splitting Schemes for Incompressible Flows
type: item
description: The numerical simulation of incompressible fluid dynamics, governed by the Navier-Stokes equations (NSEs), presents persistent challenges related to computational efficiency and numerical stability, especially for higher-order accurate methods. This paper introduces and analyzes a new class of fully decoupled, higher-order consistent splitting schemes for the incompressible Navier-Stokes equations. The core of our methodology is the formulation of schemes based on Taylor series expansions at a future time point tn+β, where β≥1 is a selectable free parameter. This approach generalizes the classical Backward Differentiation Formula (BDF) methods. The primary contribution of this work is a rigorous stability and error analysis for these schemes. We demonstrate that by selecting appropriate values for the parameter β—specifically, β=3 for the second-order scheme, β=6 for the third-order scheme, and β=9 for the fourth-order scheme—the resulting numerical solutions are uniformly bounded in a strong norm. This constitutes a proof of unconditional stability. Furthermore, we establish optimal global-in-time convergence rates for these schemes in both two and three-dimensional domains. To the best of our knowledge, these findings represent the first comprehensive stability and convergence results for any fully decoupled scheme for the Navier-Stokes equations with an order of accuracy higher than two. The theoretical analysis is substantiated by numerical experiments, which validate the unconditional stability of the new third- and fourth-order schemes. In contrast, we show that schemes based on the conventional BDF approach (i.e., β=1) are not unconditionally stable. The proposed schemes achieve their theoretically predicted orders of convergence, offering a robust and efficient pathway for high-fidelity simulations of incompressible flows..
subject: Articles
  topic: section
subject: Navier-Stokes Equations
  topic: keywords
subject: Consistent Splitting Schemes
  topic: keywords
subject: Higher-Order Methods
  topic: keywords
subject: Stability Analysis
  topic: keywords
creator: Dr. Elian M. Vortenz
rights: Copyright (c) 2024 European Journal of Emerging Engineering and Mathematics
date: 2024-12-15
publication date: 2024-12-15
starting page: 20
ending page: 25

A Unified Nonlocal and Memory-Dependent Moore-Gibson-Thompson Framework for Laser-Induced Magneto-Thermo-Mechanical Waves
type: item
description: The coupled interplay of mechanical, thermal, and magnetic fields presents a significant area of scientific inquiry, driven by its extensive applications in diverse fields such as geophysics, structural engineering, and aeronautics. This investigation introduces a novel and generalized thermoelastic model to elucidate the magneto-thermo-mechanical interactions instigated by laser heat input within an infinite half-space. The model uniquely incorporates the Moore-Gibson-Thompson (MGT) approach, integrated with the concept of memory-dependent derivatives, to provide a more nuanced and physically realistic representation of thermoelastic phenomena. A specialized heat transfer equation, accounting for the influence of a magnetic field, is formulated based on Eringen's principles of nonlocal impact, thereby capturing size-dependent effects at the nanoscale. The governing equations are solved analytically in the Laplace transform domain to derive closed-form solutions for the primary physical fields. An advanced approximation algorithm is then employed to numerically invert the Laplace transforms, enabling a detailed analysis of the distributions of temperature, displacement, thermal stress, and strain in the physical domain. Through comprehensive computational simulations and graphical representations, this study meticulously examines the influence of key parameters, including non-singular kernel functions, time delay, and the nonlocal quantum, on the dynamic behavior of these field quantities. Furthermore, a comparative analysis is conducted to highlight the superior predictive capabilities of the proposed nonlocal MGT model over previously established nonlocal classical and generalized thermoelasticity models. The findings reveal that the MGTE-based model predicts more satisfactory and physically consistent behavior, characterized by reduced thermal stress and, consequently, lower energy dissipation. This suggests that the proposed framework offers a more robust and re…
subject: Articles
  topic: section
subject: Kernel Function
  topic: keywords
subject: Laser Pulse
  topic: keywords
subject: MGTE Thermal Conductivity Model
  topic: keywords
subject: Nonlocal Effect
  topic: keywords
creator: Dr. Rinel M. Ostavar
creator: Dr. Velina T. Crovan
creator: Dr. Jashwin E. Maltren
rights: Copyright (c) 2024 European Journal of Emerging Engineering and Mathematics
date: 2024-12-07
publication date: 2024-12-07
starting page: 9
ending page: 19

A Foundational Criterion in Boundary Value Problems for Pseudo-Differential Operators
type: item
description: This article explores the fascinating world of non-local operators and the challenges they pose when confined to domains with boundaries. We focus on a class of operators that, while powerful, lack the convenient symmetries of well-studied examples like the fractional Laplacian. These operators often fail to meet the stringent "transmission condition" required by classical theories. Instead, they satisfy a more forgiving criterion: the principal transmission condition. The central discovery we present is that even with this weaker condition, a robust and elegant analytical framework can be built. We show that these operators act naturally on a special family of function spaces—the µ-transmission spaces—which are tailor-made to handle the singular way solutions behave at a boundary. For the important case of strongly elliptic operators, we find that these spaces are not just convenient, but are the exact solution spaces for the Dirichlet problem, leading to precise predictions about solution regularity. A cornerstone of our work is a new, generalized integration by parts formula, a versatile tool that holds even for non-elliptic operators. This formula unlocks further insights, including a Green's formula for "large" solutions that blow up at the boundary. Our approach marks a departure from standard methods, relying on the classic Wiener-Hopf factorization technique to navigate the complexities introduced by the weaker symbolic properties. The result is a unified theory that extends our understanding of a broad and important class of non-local boundary value problems.
subject: Articles
  topic: section
subject: pseudo-differential operators
  topic: keywords
subject: fractional Laplacian
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subject: transmission condition
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subject: boundary value problems
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creator: Dr. Lenric A. Voswain
creator: Dr. Tharuni M. Kavelin
creator: Dr. Jorvan E. Milbrant
rights: Copyright (c) 2024 European Journal of Emerging Engineering and Mathematics
date: 2024-12-01
publication date: 2024-12-01
starting page: 1
ending page: 8