Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational ge-ometry and other areas like image processing, model identi cation, geographical data systems, and triangu-lar computation of a set of points and so on. Comput-ing the convex hull of a set of point is one of the most fundamental and important problems of computational geometry. In this paper a new ALGORITHM is presented for computing the convex hull of a set of random points in the plane by using a SWEEP-line strategy. The SWEEP-line is a horizontal line that is moved from top to bottom on a map of points. Our ALGORITHM is optimal and has time complexity O(nlogn) where n is the size of input.

This paper presents an optimal design of a SWEEP blade for the axial wind turbine using a hybrid surrogate-assisted optimizer. The design problem is defined to maximize the ratio of the torque coefficient to the thrust coefficient of a turbine blade at a low wind velocity of 10 m/s. Pitch angle and leading-edge blade curve are considered as the design variables. For the aerodynamic analysis of the wind turbine blade, computational fluid dynamics has been used as a high-fidelity simulation. While the surrogate models including, the Kriging model (KG), the radial basis function model (RBF), and the proposed hybrid of KG and RBF (HyKG-RBF) models are applied for function approximation or low-fidelity simulation. In this study, to obtain a set of sampling points and surrogate models development, an optimal Latin Hypercube sampling (OLHS) technique is utilized in the design of the experiment (DOE). A differential evolutionary (DE) ALGORITHM is used to solve the proposed design problem. The performance of the proposed hybrid surrogate assisted optimization method is contrasted with two conventional surrogate assisted optimization techniques. Results demonstrate that the proposed hybrid surrogate model viz. HyKG-RBF is the most efficient surrogate-assisted optimization method for solving the SWEEP blade optimization problem.

In the paper a linear-quadratic optimization problem (LCTOR) with unseparated two-point boundary conditions is considered. To solve this problem is proposed a new SWEEP ALGORITHM which increases doubles the dimension of the original system. In contrast to the well-known methods, here it refuses to solve linear matrix and nonlinear Riccati equations, since the solution of such multi-point optimization problems encounters serious difficulties in passing through nodal points. The results are illustrated with a specific numerical example.

Today, with the expansion of the road network and the increase in construction and maintenance costs of pavements, using additives in bitumen has become a popular method to improve asphalt performance. Various polymeric additives are widely used additives in bitumen and asphalt mixture. This paper investigates the effects of 2, 4, and 6 wt% of Styrene-Ethylene/Propylene-Styrene (SEPS) polymer on the bitumen's behavior. In this regard, linear amplitude SWEEP (LAS) and time SWEEP (TS) tests have been used to evaluate the fatigue characteristics of modified bitumen. In addition to the common method of estimating fatigue life in the LAS test, the pseudo-stress method was also used, and the results of three techniques were compared. As a result, using SEPS in bitumen reduces the fatigue life by 12% in the sample containing 2% of SEPS; however, fatigue life increased to 27.9 times greater than virgin bitumen by increasing the percentage of SEPS. The results of LAS and TS tests show a significant difference compared to each other. The LAS test is a suitable method to check the fatigue characteristics of bitumen due to the shorter test time. According to the pseudo-stress method results, the fatigue life of the samples containing 2, 4, and 6 wt% of SEPS are 0.75, 2.5, and 15.8 times greater than the virgin bitumen sample.

We propose a two-phase ALGORITHM for solving continuous rank-one quadratic knapsack problems (R1QKPs). In particular, we study the solution structure of the problem without the knapsack constraint. In fact, an $O(n\log n)$ ALGORITHM is suggested in this case. We then use the solution structure to propose an $O(n^2\log n)$ ALGORITHM that finds an interval containing the optimal value of the Lagrangian dual of R1QKP. In the second phase, we solve the Lagrangian dual problem using a traditional single-variable optimization method. We perform a computational test on random instances and compare our ALGORITHM with the general solver CPLEX.

This study pertains to the design optimization of a four-blade ceiling fan to enhance air circulation and energy efficiency. The SWEEP angle of the blade profile is nonlinear. The design of experiment (DOE) computational fluid dynamics (CFD) and response surface method (RSM) methods were used in parallel to find the optimal design solution. The design variables considered were inboard angle of attack, outboard angle of attack, blade SWEEP, and tip-chord length. Numerical simulations were conducted using steady state Reynolds-averaged Navier– Stokes (RANS) equations and the Spalart– Allmaras turbulence model. The baseline results were validated through experimental data. Subsequently, the DOE method was employed to generate the blade design which reduce the number of simulations without losing the influence of different geometric parameter interactions. The response variables studied were volume flow rate, mass flow rate, torque, and energy efficiency. The simulations exhibited that flow pattern has a distinct feature and is further classified into three groups. In the end, the optimal blade design was identified using response surface methodology (RSM).

Unmanned Combat Aerial Vehicles (UCAVs) are designed to be lightweight and compact, which can impact their overall lift and aerodynamic capabilities. This study focuses on enhancing the Coefficient of Lift (CL) by optimising the Back SWEEP Angle in the Lambda wing-UCAV. The model's baseline geometry remains unchanged during the experimental and numerical analysis, while different back SWEEP angles ranging from δ=00 to δ=500 are investigated at varied free-stream velocities and angles of attack. This helps to understand the generation of induced lift in the intricate shapes of the Lambda Wing. The results indicate a 5% to 10% increase in the lift for every 100 increments of the Back SWEEP Angle, and the vortices' strength increases and reaches a maximum at δ=400. At greater angles (δ >400), the lift drops gradually with the Reynolds number. The stagnation point shifts from 25% to 35% along the chord towards the pressure surface as the angles of attack increase from α=50 to α=100. The angle of attack α>100.

This study addresses the prediction of the flutter speed for a double-SWEEP folding wing in subsonic airflow, an area less explored in past research. Two types of modeling are employed: structural and aerodynamic. The structural model treats the wing as an Euler-Bernoulli beam. For the aerodynamic model, Theodorsen's unsteady aerodynamic theory is used. This theory is initially in the frequency domain but is converted to the time domain using the Kussner function and a new formulation method. Kinetic energy, strain energy, and the work of aerodynamic forces are then calculated. The differential equations governing the wing structure are derived using Hamilton's principle. The wing's motion equation is obtained using assumed modes and the Galerkin method. The instability flutter speed is determined through the p-method, and graphs of frequency versus airflow velocity are plotted. The results indicate that using the Kussner function for variable airflow improves the accuracy of flutter speed prediction. The analysis of SWEEP angle changes on flutter speed and frequency revealed that SWEEP angle one has the least positive effect, while SWEEP angle two has the most positive effect on flutter speed and frequency, respectively.