Ali Tozar

Decarbonising isolated energy hubs through green hydrogen hinges on managing electrolysis, fuel-cell reconversion, and grid supply as competing energy-conversion pathways under the financial risk that volatile renewable generation imposes on investors. This study examines how investor risk aversion reshapes the optimal capacity portfolio, conversion-pathway choice, and dispatch of a multi-vector energy hub on the Orkney Islands (UK), integrating wind power, electrolysis, fuel cells, heat pumps, and thermal storage. A two-stage stochastic mixed-integer linear programme with a mean–Conditional-Value-at-Risk objective is solved for eleven risk-aversion levels, using ten representative days derived from k-medoids clustering of a full-year hourly dataset. As risk aversion increases, the optimal portfolio pivots from surplus-driven electrolysis toward grid-dependent thermal supply, reducing the green hydrogen fraction from 77% to 42% and increasing annual carbon emissions more than tenfold. System conversion efficiency paradoxically rises under high risk aversion, not from improved conversion but from abandoning the electrolyser–fuel-cell round-trip pathway (η≈33%)—a phenomenon we term "passive efficiency." Monte Carlo propagation of renewable-forecast uncertainty (400 scenarios, ±5–20%) shows that a balanced risk posture keeps green hydrogen above 70% even under severe forecast errors, while a highly risk-averse posture locks the system into grid-and-boiler operation regardless of wind availability. A carbon-price × risk-aversion factorial analysis (56 scenarios) shows that carbon pricing is most effective precisely where risk aversion is highest, recovering up to 25 percentage points of green hydrogen fraction. These findings give island energy-system operators and regulators quantitative guidance for managing the conversion-technology portfolio under financial risk.

The characterization of topological phases in disordered non-Hermitian systems remains a formidable challenge, as the non-Hermitian skin effect (NHSE) disrupts the conventional bulk-boundary correspondence and renders spectral invariants unreliable. In this Letter, we propose the real part of the biorthogonal entanglement entropy as a precise, basis-independent diagnostic that cuts through this complexity. Investigating a disordered non-reciprocal Kitaev chain, we demonstrate that this entropic probe provides a robust, boundary-sensitive diagnostic that faithfully tracks the topological phase transition even in regimes where traditional winding numbers fluctuate wildly. Crucially, we uncover an anomalous critical scaling of the entanglement entropy: while the Hermitian limit follows standard conformal scaling (c_eff ≈ 1.69), the non-Hermitian critical point exhibits a super-critical effective central charge of c_eff ≈ 2.81. Within the system sizes studied (L ≤ 600), this enhancement is consistent with skin-effect-driven non-unitary behavior at the critical point. Our findings establish biorthogonal entanglement not only as a robust order parameter for the Topological Anderson Insulator but also as an experimentally accessible signature in topo-electric circuits.

Decarbonising isolated energy hubs through green hydrogen is a strategic priority, yet the financial risk associated with volatile renewable generation can deter investment. This study examines how investor risk aversion reshapes the optimal design and operation of a multi-vector energy hub on the Orkney Islands (UK), integrating wind power, electrolysis, fuel cells, heat pumps, and thermal storage. A two-stage stochastic mixedinteger linear programme with a mean–Conditional-Value-at-Risk objective is solved for eleven risk-aversion levels (from risk-neutral to worst-case-minimising, in steps of 0.1), using ten statistically representative days derived from k-medoids clustering of a full-year hourly dataset. A paradoxical outcome emerges: as risk aversion increases, the system pivots from surplus-driven electrolysis to grid-dependent thermal supply, reducing the green hydrogen fraction from approximately 77% at the risk-neutral optimum to 42% at the highest risk-aversion level and increasing annual carbon emissions more than tenfold. System efficiency paradoxically rises under high risk aversion, not from improved conversion but from the elimination of hydrogen pathways—a phenomenon we term “passive efficiency.” Monte Carlo uncertainty propagation (400 scenarios, ±5–20% forecast errors) demonstrates that a balanced risk posture (intermediate level of risk aversion) maintains green hydrogen above 70% even under severe renewable forecast errors, whereas a highly risk-averse posture locks the system into grey hydrogen dependency. A carbon–risk interaction analysis (56 scenarios: 8 carbon prices × 7 risk levels) reveals that carbon pricing is most effective precisely where risk aversion is highest, narrowing the green hydrogen penalty by up to 25 percentage points. These findings provide quantitative guidance for island energy regulators seeking to reconcile financial prudence with decarbonisation ambitions.

Discovering differential equations from noisy data faces the derivative–noise dilemma: numerical differentiation amplifies noise, requiring a smoothing window (w) whose optimal value depends on unknown noise levels and dynamical timescales. Existing methods decouple smoothing from the equation search, making them fragile to misspecification. We introduce PyPhysDisc, a genetic-programming framework where each individual carries a candidate expression tree and a window gene encoding w. Consequently, signal processing and symbolic regression are jointly optimised under a single selection pressure. We provide quantitative evidence of this co-evolutionary coupling through Shannon entropy analysis: window-gene entropy drops by 82% over 40 generations, with elite-population dominance reaching 1.0, confirming directed selection rather than drift. Benchmark experiments on chaotic (Lorenz), limit-cycle (Van der Pol), stiff (Duffing), and predator–prey (Lotka–Volterra) systems at up to 20% additive noise show that PyPhysDisc maintains high accuracy (R² > 0.89 for three systems) without manual tuning. On the Lorenz system, the co-evolutionary strategy achieves R² = 0.961, within 2.2 percentage points of an oracle holding the true optimal window, while a naïve fixed-window baseline collapses to R² = 0.279 and exhibits 22× higher variance. Furthermore, the framework discovers non-polynomial laws (-sinθ) without predefined basis libraries. By internalising the choice of w as a co-adapting trait, PyPhysDisc establishes a self-sufficient mechanism for robust physical law discovery.

Natural science and mathematics play a fundamental role in humanity's scientific and technological advancement. These fields hold a critical place in the process of understanding the universe, explaining natural phenomena, and providing solutions to social problems. Natural science and mathematics are fundamental fields that form the building blocks of our modern world and contribute to human development. Research and findings in these fields are vital not only for scientific progress but also for solving social, economic, and environmental problems. Therefore, supporting studies in s natural cience and mathematics is a critical step towards the sustainable development of societies and leaving a more livable world for future generations. In this book, we have discussed the importance of natural studies in science and mathematics under various headings. We aim to provide resources for undergraduate and graduate students studying these fields and to provide valuable data for educators in the field.