Volume 1, Issue 2 (2025)
Table of contents
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The Role of Symmetry in Topological Insulators and Superconductors
Abstract: Topological insulators and superconductors constitute a class of quantum materials characterized by insulating bulks and symmetry-protected conducting boundaries. Symmetry principles, notably time-reversal (TRS), particle-hole (PHS), and chiral symmetry, play a fundamental role in determining the topological phases and their classification within the Altland-Zirnbauer scheme. TRS protects gapless surface states in topological insulators, while PHS stabilizes Majorana modes in topological superconductors. Symmetry-protected topology extends this framework by considering partial symmetry breaking, …
Published in Emerging Trends in Symmetry · Vol. 1, Issue 2, 2025 · pp. 01–05 Read article
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Symmetry Principles in Digital Twin Systems: Modeling, Integration, and Applications
Abstract: This systematic review comprehensively examines the burgeoning field of Digital Twin (DT) technology, analyzing its current state, diverse applications, and future trajectory. Through a rigorous methodology involving a systematic search of academic databases and relevant industry literature, this review synthesizes findings across a spectrum of disciplines. We identify the core components and underlying principles of DTs, distinguishing them from traditional simulation models by their dynamic, realtime data integration and bi-directional …
Published in Emerging Trends in Symmetry · Vol. 1, Issue 2, 2025 · pp. 06–24 Read article
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Symmetry Breaking in Mathematical Models: Bifurcation, Chaos, and Pattern Formation
Abstract: Symmetry breaking serves as a central organizing principle in the understanding of nonlinear systems across physics, biology, chemistry, and engineering. When a system transitions from a symmetric state to an asymmetric configuration, it often signals the onset of new structures, dynamic behaviors, or even chaotic regimes. This review explores symmetry breaking from the theoretical and mathematical perspectives of bifurcation theory, chaos theory, and pattern formation. We discuss how small parameter …
Published in Emerging Trends in Symmetry · Vol. 1, Issue 2, 2025 · pp. 25–30 Read article
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Entropy, Symmetry, and Data Fusion: Emerging Methods in Multi-Objective Decision- Making and Smart Systems
Abstract: In the era of intelligent technologies and data-driven systems, multi-objective decision-making (MODM) has become an essential aspect of managing complex environments such as smart cities, autonomous systems, and cyber-physical networks. As decision-making scenarios become increasingly dynamic and uncertain, there is a growing need for advanced methodologies that can handle diverse objectives, conflicting constraints, and incomplete information. This review highlights the emerging role of entropy, symmetry, and data fusion as foundational …
Published in Emerging Trends in Symmetry · Vol. 1, Issue 2, 2025 · pp. 44–49 Read article