With the rapid development of solar power generation technology, the hotspot effect of photovoltaic (PV) arrays poses a key challenge to the efficiency and stability of the system. Conventional PV array models have significant limitations in dealing with complex shadow shading and multi-peak output characteristics, especially when confronted with complex topologies such as the complex-total-cross-tied (CTCT) structures. To address this issue, this paper proposed a mathematical model for PV arrays based on multipoint parabolic motion, which could accurately simulate the output characteristics of PV arrays under localized shading conditions. The model decomposed the current-voltage ($I-V$) characteristic curve of the PV arrays into multiple parabolic trajectories. A shadow shading model for complex structures was successfully constructed by combining with a kinematic model. MATLAB/Simulink simulations and experimental validation showed that the proposed model guaranteed computational accuracy with error less than 5%, while computational efficiency was greatly improved. The proposed model could accurately capture the multi-peak characteristics when compared with the traditional engineering model. Results from the experiment further verified the robustness of the model in dynamic shading scenarios, hence providing an efficient and reliable tool for maximum power tracking and hotspot localization in the PV system.

Efficient management of airflow and heat dissipation in data centers is becoming increasingly critical as computing densities increase and thermal loads grow. To address these challenges, this study numerically examines the thermo-fluid behavior of a medium-sized data center containing twelve heat-generating server racks under multiple ventilation strategies. A three-dimensional CFD model was developed using the RANS equations with the SST $k$–$\omega$ turbulence formulation and the Boussinesq approximation to account for buoyancy-driven flow. Eight ventilated configurations were evaluated by combining two louver orientations (20$^{\circ}$ and 50$^{\circ}$), two inlet heights (top or bottom), and two inlet velocity modes (constant or pulsatile), in addition to a no-ventilation control scenario. Both steady and transient simulations were performed to capture the interactions between inlet momentum, recirculation patterns, and thermal stratification over a one-hour operational period. The control case exhibited strong thermal stratification and a stable hot layer beneath the ceiling, demonstrating the inadequacy of natural convection alone. Introducing ventilation significantly modified the airflow topology and improved cooling performance, though with considerable sensitivity to inlet design. Shallower-angle louvers (20$^{\circ}$) enhanced horizontal jet penetration and reduced recirculation pockets, whereas steeper louvers (50$^{\circ}$) generated stronger impingement and more localized hot spots. Inlet height further shaped vertical temperature distribution: bottom inlets effectively cooled lower and mid-rack levels, while top inlets reduced ceiling-layer temperatures by disrupting buoyant plumes. Pulsatile ventilation outperformed constant inflow by periodically increasing momentum, enhancing mixing, and weakening plume formation during peak phases. Mass-flow analysis similarly showed that extraction capacity strongly correlated with inlet velocity amplitude. Overall, the results highlight the importance of coordinated selection of inlet position, louver angle, and temporal forcing. The combined use of shallow-angle louvers and pulsatile ventilation presents a promising pathway for improving cooling uniformity and thermal management in high-density data centers.