Viscous gravity currents over flat inclined surfaces

Previous analyses of the flow of low-Reynolds-number, viscous gravity currents down inclined planes are investigated further and extended. Particular emphasis is on the motion of the fluid front and tail, which previous analyses treated somewhat cavalierly. We obtain reliable, approximate, analytic solutions in these regions, the accuracies of which are satisfactorily tested against our numerical evaluations. The solutions show that the flow has several time scales determined by the inclination angle, $\alpha$ . At short times, the influence of initial and boundary conditions is important and the flow is governed by both the pressure gradient and the direct action of gravity due to inclination. Later on, the areas where the boundary conditions are important shrink. This fact explains why previous solutions, being inaccurate near the front and the tail, described experimental data with high accuracy. At larger times, of the order of $\alpha ^{-5/2}$ , the influence of the pressure gradient may be neglected and the fluid profile converges to the square-root shape predicted in previous works. Important extensions of our approach are also outlined.

Retraction: Modeling and development of a fundamentally new way of landing a quadcopter on inclined surfaces (J. Phys.: Conf. Ser 2061 012109)

This article has been retracted by IOP Publishing following an allegation that this article substantially overlaps with [1]. IOP Publishing has investigated in line with the COPE guidelines, and agree that while the reference is listed in the article, the overlap is substantial and is unethical. Consequently, this paper has been retracted by IOP Publishing. Citations to this work should be redirected to [1]. The authors agree to this retraction. [1]. John Bass and Alexis Lussier Desbiens, (2020), 'Improving Multirotor Landing Performance on Inclined Surfaces Using Reverse Thrust', IEEE Robotics and Automation Letters, Volume: 5, Issue: 4, https://ieeexplore.ieee.org/abstract/document/9143402 Retraction published: 23 December 2021

Generalized IBL models for gravity-driven flow over inclined surfaces

In this investigation we propose several generalized first-order integral-boundary-layer (IBL) models to simulate the two-dimensional gravity-driven flow of a thin fluid layer down an incline. Various cases are considered and include: isothermal and non-isothermal flows, flat and wavy bottoms, porous and non-porous surfaces, constant and variable fluid properties, and Newtonian and non-Newtonian fluids. A numerical solution procedure is also proposed to solve the various model equations. Presented here are some results from our numerical experiments. To validate the generalized IBL models comparisons were made with existing results and the agreement was found to be reasonable.

Balancing inverted pendulum cart on inclines using accelerometers

The balance of inverted pendulum on inclined surfaces is the precursor to their control in unstructured environments. Researchers have devised control algorithms with feedback from contact (encoders - placed at the pendulum joint) and non-contact (gyroscopes, tilt) sensors. We present feedback control of Inverted Pendulum Cart (IPC) on variable inclines using non-contact sensors and a modified error function. The system is in the state of equilibrium when it is not accelerating and not falling over (rotational equilibrium). This is achieved when the pendulum is aligned along the gravity vector. The control feedback is obtained from non-contact sensors comprising of a pair of accelerometers placed on the inverted pendulum and one on the cart. The proposed modified error function is composed of the dynamic (non-gravity) acceleration of the pendulum and the velocity of the cart. We prove that the system is in equilibrium when the modified error is zero. We present algorithm to calculate the dynamic acceleration and angle of the pendulum, and incline angle using accelerometer readings. Here, the cart velocity and acceleration are assumed to be proportional to the motor angular velocity and acceleration. Thereafter, we perform simulation using noisy sensors to illustrate the balance of IPC on surfaces with unknown inclination angles using PID feedback controller with saturated motor torque, including valley profile that resembles a downhill, flat and uphill combination. The successful control of the system using the proposed modified error function and accelerometer feedback argues for future design of controllers for unstructured and unknown environments using all-accelerometer feedback.

Modeling and development of a fundamentally new way of landing a quadcopter on inclined surfaces

Methods and software and hardware for modeling and developing a fundamentally new way of landing a quadrocopter on inclined surfaces are discussed in the paper. The current state of the project under elaboration is conditioned and described. Various approaches to the solution are feasible due to the complexity of the considered issue. Solutions can differ both in the distribution of control functions between the ground control station and the quadcopter itself, and in the choice of principles that can be used as the basis for the control system and determine its design and dynamic characteristics. Simulation and testing processes demonstrate that reverse thrust alone can increase the landing zone of an average mass quadcopter, almost doubling the maximum tilt angle at which a landing maneuver is made, thus, allowing for a high vertical speed landing. It is clearly shown that low-power adhesion mechanisms such as electrical adhesion, switchable magnets, grippers or dry glue are activated after landing, allowing it to stay on the surface after the back thrust has ceased. This can be useful in situations where sudden interference is likely to occur. Such a result is achieved using a classic quadrocopter as DJI F450 without adding any equipment.

Evaluation of Electrophysical Properties of Soils in the Slope Zones of the Foundation During GPR Survey

The article describes a new method for conducting a ground penetrating radar survey of slope zones of soil objects of transport infrastructure. In the lithological section of these objects, there are sub-horizontal and inclined soil boundaries, as well as slope zones. Traditional survey methods (drilling, pitting), as well as the standard GPR method, make it possible to reliably survey at these objects, as a rule, only the zones under the horizontal main ground of the subgrade and sub-horizontal sections of the ground outside its boundaries. Survey under inclined surfaces is often difficult or technically impossible; geophysical methods, just like traditional ones, provide initial information that is exceedingly difficult for further decoding. The sections are filled with re-reflections and noises, and the process of decoding them is associated with great methodological problems.This paper presents a new method for determining speed of propagation of radio waves in the slope zones of the foundation. The initial information is the data obtained during the survey using the common depth point (CDP) method, using a well-known survey technique and a standard set of hardware. The novelty of the article results is determined by the algorithm for processing the measurement results developed by the authors. The software implementation made on its basis makes it possible to obtain the hodograph equation considering the slope of the layers. Defining geometric characteristics of embankments associated with the presence of slopes of variable steepness have been considered. A technique for calculating propagation speed of radio waves for a two-layer medium with a boundary inclined to the scanning surface has been proposed. The validity of the developed method was verified using finite-difference time-domain modelling.The article provides examples of practical application of the developed method in the GPR survey of real track foundation objects (transport infrastructure objects). The method proposed in the article makes it possible to increase the informative area of the surveyed diameters. At the same time, the accuracy of the GPR method is preserved, the area of its application for obtaining reliable information is increased to 60 % of the cross-sectional area of the foundation.