Reliable rainfall–runoff estimation is essential for the hydraulic design and planning of canal systems, particularly in ungauged catchments where streamflow records are unavailable. This study aimed to generate design-storm hydrographs and estimate peak runoff for the Narai Canal catchment in Peshawar, Khyber Pakhtunkhwa, Pakistan, using the Log-Pearson Type III (LP-III) distribution and the WinTR-20 model under ungauged-basin conditions. Rainfall frequency analysis was performed using the LP-III distribution to estimate design rainfall for selected return periods. The Soil Conservation Service (SCS) curve number method implemented in WinTR-20 was then used to simulate runoff hydrographs and peak discharges based on watershed characteristics, including land use, curve number, and time of concentration. The analysis produced design-storm hydrographs and corresponding peak discharge estimates that increased with rainfall intensity and return period. The LP-III distribution adequately characterized design rainfall, while the WinTR-20 model provided physically consistent runoff estimates for evaluating watershed response under different design scenarios. The results demonstrate the influence of watershed characteristics on runoff generation and provide preliminary hydrological estimates for the study area, representing a design-scenario analysis for an ungauged basin rather than a validated rainfall–runoff forecasting model. The generated design hydrographs and peak discharge estimates provide useful information for preliminary canal hydraulic design, drainage planning, and flood-risk assessment. Future studies should incorporate observed streamflow data to calibrate and validate the model before it is applied for operational flood forecasting.
This paper examines how logical structures represent sharp and unsharp propositions in classical and quantum systems. Classical sharp logic is modeled by Boolean algebras, where propositions have bivalent truth values, complements are globally defined, and distributivity holds. Quantum sharp logic is modeled by orthomodular lattices of closed Hilbert-space subspaces or projection operators; it retains definite yes–no outcomes for ideal measurements but rejects the Boolean assumptions of global truth valuation and distributivity. Classical unsharp logic uses fuzzy membership or probabilistic truth values to describe vagueness and incomplete information, whereas quantum unsharp logic is expressed through effects and effect algebras, which capture noisy, inefficient, and generalized measurements. The paper’s central question is which algebraic structure is appropriate for each combination of classical or quantum behavior and sharp or unsharp measurement. The analysis shows that the four cases form a coherent hierarchy: Boolean algebras describe deterministic classical events, orthomodular lattices describe ideal quantum propositions, fuzzy or probabilistic models describe classical partial truth, and effect algebras describe realistic quantum effects. This classification clarifies the mathematical and physical role of unsharpness and explains why effect algebras are needed beyond projection-based quantum logic.
The analysis of the fractional time-derivative model of the Caputo-Fabrizio and Atangana-Baleanu in Caputo sense with the ramped temperature on transient free convection flow in the vertical plates with isothermal boundary conditions has been established. The Laplace transform scheme was adopted in solving the governing equations, and semi-analytical solutions were achieved through the inversion of the solutions from the Laplace purview to the time purview. It found that the temperature and velocity obtained via the CF model are higher than ABC model, and the fractional parameters reduced the temperature and slowed down the movement of the fluid. It is perceived that relaxation time parameters boost the temperature and heighten the fluid’s movement. Also noted that the negative augment in the value of the heat source/sink caused retardation in the movement of the fluid, while the positive increment of the heat source/sink heightened the movement of the fluid. Similarly, it is observable that the temperature produced through a ramped temperature is higher than the constant temperature.
As urbanization intensifies and traffic demand continues to grow, understanding and modelling vehicular dynamics in complex transportation systems has become increasingly important. Second-order macroscopic traffic flow models provide a powerful framework for capturing the evolution of both traffic density and velocity, offering significant advantages over first-order formulations. Despite extensive developments in this field, the literature lacks a unified mathematical synthesis that systematically organizes and compares the wide range of second-order models. This paper addresses this gap by presenting a comprehensive review of second-order macroscopic traffic flow models, tracing their evolution from foundational formulations in the 1970s to recent advancements up to 2024. The review adopts a structured methodology, drawing on major academic databases to identify models based on their mathematical formulation and practical relevance. The models are classified into key families, including relaxation-based, kinetic, viscous, anisotropic, nonlocal, and multi-class formulations, providing a coherent taxonomy of the field. In addition to cataloguing model equations, this study synthesizes their fundamental mathematical properties, including hyperbolicity, stability, well-posedness, and parameter identifiability. The review further examines how successive models address limitations of earlier approaches, such as non-physical wave propagation and insufficient representation of driver behaviour. Finally, emerging trends are discussed, including the integration of connected and autonomous vehicle technologies, nonlocal interactions, and data-driven modelling approaches.
In this paper, we develop an effective gauge-theoretic description of atmospheric electrical breakdown where the transition from weakly conducting air to a lightning channel is described via an order parameter instability. The formulation includes the interaction of the degree of ionization and the collective conducting amplitude with the electromagnetic potential. The key question is whether regularities found in lightning initiation, stepped leader propagation, channel confinement, and branching can be captured using topological invariants or just via threshold values of fields. Our model defines the critical field strength to be the point where the conducting order parameter becomes unstable, derives vortex channel solutions with a finite core and an effective flux increment, and connects branch geometry to symmetrically constrained weight vectors. We also describe the limited role played by instanton-like nucleation, anomalous transport terms, and dual confinement within the framework of an effective description rather than as a microscopically justified one. Predictions derived within our approach are formulated in terms of measurable quantities: vortex core length scales, branch angle clustering, field-temperature scaling, radio signals polarization dependence, and magnetic field increment near developing channels.
