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The sandy environment is one of the typical environments in which helicopters operate. Air-sand two-phase flow in sandy environments may be an important factor affecting flight safety. Taking a typical example, this paper aims to investigate the aerodynamic and rotor trim characteristics of the UH-60 helicopter in sandy environments.

A computational study is conducted to simulate the air-sand flow over airfoils based on the Euler–Lagrange framework. The simulation uses the S-A turbulence model and the two-way momentum coupling methodology. Additionally, the trim characteristics of the UH-60 rotor are calculated based on the isolated rotor trim algorithm.

The simulation results show that air-sand flow significantly affects the aerodynamic characteristics of the SC1095 airfoil and the SC1094R8 airfoil. The presence of sand particles leads to a decrease in lift and an increase in drag. The calculation results of the UH-60 helicopter rotor indicate that the thrust decreases and the torque increases in the sandy environment. To maintain a steady forward flight in sandy environments, it is necessary to increase the collective pitch and the longitudinal cyclic pitch.

In this paper, the aerodynamic characteristics of airfoils and the trim characteristics in the air-sand flow of the UH-60 helicopter are discussed, which might be a new view to analyse the impact of sandy environments on helicopter safety and manoeuvring.

In the process of conveying the solid–liquid two-phase medium of the centrifugal slurry pump, the wear of the flow-passing parts is an important problem affecting its life and safe operation. Therefore, a numerical investigation on the wear characteristics of the centrifugal slurry pump under different particle conditions was conducted.

A solid-liquid two-phase model based on CFD-DEM coupling is established and used to analyze the flow field and the wear characteristics of the flow-passing parts with different particle densities, volume fractions and sizes.

Particle conditions will affect the pump flow field. To analyze the pump wear characteristics, the wear distribution, wear value and cumulative force laws of flow-passing parts under different particle conditions are obtained. In each flow-passing part, with the increase of particle density, volume fraction and size, the wear area is concentrated and the wear depth increases. Under different particle conditions, the wear is mainly on the volute chamber and the blade pressure surface, and the tangential cumulative force of flow-passing parts is much larger than the normal cumulative force.

An accurate model and a coupled simulation method for predicting the wear of the slurry pump are obtained, and the wear characteristic law can provide a reference for the design of the slurry pump to reduce friction.

This paper focuses on the application of a robotic technique for modeling a three-wheeled mobile robot (WMR), considering it as a multibody polyarticulated system. Then the dynamic behavior of the developed model is verified using a physical model obtained by Simscape Multibody.

Firstly, a geometric model is developed using the modified Denavit–Hartenberg method. Then the dynamic model is derived using the algorithm of Newton–Euler. The developed model is performed for a three-wheeled differentially driven robot, which incorporates the slippage of wheels by including the Kiencke tire model to take into account the interaction of wheels with the ground. For the physical model, the mobile robot is designed using Solidworks. Then it is exported to Matlab using Simscape Multibody. The control of the WMR for both models is realized using Matlab/Simulink and aims to ensure efficient tracking of the desired trajectory.

Simulation results show a good similarity between the two models and verify both longitudinal and lateral behaviors of the WMR. This demonstrates the effectiveness of the developed model using the robotic approach and proves that it is sufficiently precise for the design of control schemes.

The motivation to adopt this robotic approach compared to conventional methods is the fact that it makes it possible to obtain models with a reduced number of operations. Furthermore, it allows the facility of implementation by numerical or symbolical programming. This work serves as a reference link for extending this methodology to other types of mobile robots.

The purpose of this study is to find the suitable trajectory path of the Numerical model of the Quadcopter. Quadcopters are widely used in various applications due to their compact size and ease of assembly. Because they are quite unstable, autonomous control systems would be used to overcome this problem. Modelling autonomous control is predominant as the research scope faces challenges because of its highly non-linear, multivariable system with 6 degree of freedom.

Quadcopters with antonym systems can operate in an unknown environment by overcoming unexpected disturbances. The first objective when designing such a system is to design an accurate mathematical model to describe the dynamics of the system. Newton’s law of motion was used to build the mathematical model of the system.

Establishment of the mathematical model and the physics behind a four propeller drone for the frame TAROT 650 carbon was done. Simulink model was developed based on the mathematical model for simulating the complete dynamics of the drone as well as location and gusts were included to check the stability.

The control response of the system was simulated numerically results are discussed. The trajectory path was found. The phases with their own parameters can be used to implement the mathematical model for another type of quadcopter model and achieve quick development.

The purpose of this paper is to obtain values that stabilize the lateral and longitudinal flight of the quadrotor for which the morphing amount and the best Proportional-Integral-Derivative (PID) coefficients are determined by using the simultaneous perturbation stochastic approximation (SPSA) optimization algorithm.

Quadrotor consists of body and arms; there are propellers at the ends of the arms to take off and rotors that rotate them. By reducing the angle between mechanism 1 and the rotors with the horizontal plane, the angle between mechanism 2 and the arms, the rotors rise and different configurations are obtained. Conventional multi-rotor aircraft has a fixed fuselage and does not need a tail rotor to change course as helicopters do. The translational and rotational movements are provided by the rotation of the rotors of the aircraft at different speeds by creating moments about the geometric center in 6-degree-of-freedom (DOF) space. These commands sent from the ground are provided by the flight control board in the aircraft. The longitudinal and lateral flight stability and properties of different configurations evaluated by dynamic analysis and simulations in 6 DOF spaces are investigated. An algorithm and PID controller are being developed using SPSA to achieve in-flight position and attitude control of an active deformable aircraft. The results are compared with the results of the literature review and the results of the previous article.

With SPSA, the best PID coefficients were obtained in case of morphing.

The effects of quadrotor arm height and hub angle changes affect flight stability. With the SPSA optimization method presented in this study, the attitude is quickly stabilized.

With the optimization method, the most suitable PID coefficients and angle values for the lateral and longitudinal flight stability of the quadrotor are obtained.

The transition rate and PID coefficients are determined by using the optimization method, which is advantageous in terms of cost and practicality.

With the proposed method, the aircraft can change shape to adapt to different environments, and the parameters required for more stable flight for each situation will be calculated, and this will be obtained more quickly and safely with the SPSA optimization method.

The purpose of this study is to classify harmonic homomorphisms ϕ : (G, g) → (H, h), where G, H are connected and simply connected three-dimensional unimodular Lie groups and g, h are left-invariant Riemannian metrics.

This study aims the classification up to conjugation by automorphism of Lie groups of harmonic homomorphism, between twodifferent non-abelian connected and simply connected three-dimensional unimodular Lie groups (G, g) and (H, h), where g and h are two left-invariant Riemannian metrics on G and H, respectively.

This study managed to classify some homomorphisms between two different non-abelian connected and simply connected three-dimensional uni-modular Lie groups.

The theory of harmonic maps into Lie groups has been extensively studied related homomorphism in compact Lie groups by many mathematicians, harmonic maps into Lie group and harmonics inner automorphisms of compact connected semi-simple Lie groups and intensively study harmonic and biharmonic homomorphisms between Riemannian Lie groups equipped with a left-invariant Riemannian metric.

This paper applies a volume-price probability wave differential equation to propose a conceptual theory and has innovative behavioral interpretations of intraday dynamic market equilibrium price, in which traders' momentum, reversal and interactive behaviors play roles.

The authors select intraday cumulative trading volume distribution over price as revealed preferences. An equilibrium price is a price at which the corresponding cumulative trading volume achieves the maximum value. Based on the existence of the equilibrium in social finance, the authors propose a testable interacting traders' preference hypothesis without imposing the invariance criterion of rational choices. Interactively coherent preferences signify the choices subject to interactive invariance over price.

The authors find that interactive trading choices generate a constant frequency over price and intraday dynamic market equilibrium in a tug-of-war between momentum and reversal traders. The authors explain the market equilibrium through interactive, momentum and reversal traders. The intelligent interactive trading preferences are coherent and account for local dynamic market equilibrium, holistic dynamic market disequilibrium and the nonlinear and non-monotone V-shaped probability of selling over profit (BH curves).

The authors will understand investors' behaviors and dynamic markets through more empirical execution in the future, suggesting a unified theory available in social finance.

The authors can apply the subjects' intelligent behaviors to artificial intelligence (AI), deep learning and financial technology.

Understanding the behavior of interacting individuals or units will help social risk management beyond the frontiers of the financial market, such as governance in an organization, social violence in a country and COVID-19 pandemics worldwide.

It uncovers subjects' intelligent interactively trading behaviors.