First order perturbation approach for the free surface flow over a step with large Weber number

The problem of two-dimensional free surface flow of inviscid and incompressible fluid over a step is considered. The flow is assumed to be as steady and irrotational, the effect of the surface tension is considered, but the gravity force is neglected. This problem is characterized by the nonlinear condition given by Bernoulli's equation on the unknown free surface, which can be considered as part of the solution. The main purpose of this work is to give an approximate solution of this problem, by using the Hilbert transformation and the perturbation technique; the results are calculated for a large values of the Weber number and small inclination angle of the step values. These results demonstrate that the used method is easily implemented, and provides approximate solutions to these kinds of problems.

Eigenstates of quasi-Keplerian self-gravitating particle discs

ABSTRACT Although quasi-Keplerian discs are among the most common astrophysical structures, computation of secular angular momentum transport within them routinely presents a considerable practical challenge. In this work, we investigate the secular small-inclination dynamics of a razor-thin particle disc as the continuum limit of a discrete Lagrange–Laplace secular perturbative theory and explore the analogy between the ensuing secular evolution – including non-local couplings of self-gravitating discs – and quantum mechanics. We find the ‘quantum’ Hamiltonian that describes the time evolution of the system and demonstrate the existence of a conserved inner product. The lowest-frequency normal modes are numerically approximated by performing a Wick rotation on the equations of motion. These modes are used to quantify the accuracy of a much simpler local-coupling model, revealing that it predicts the shape of the normal modes to a high degree of accuracy, especially in narrow annuli, even though it fails to predict their eigenfrequencies.

Averaging technique in the problem of satellite attitude stabilization in indirect position in the orbital reference frame with the use of Lorentz torque

A dynamically symmetric satellite in a circular orbit of small inclination is considered. The problem of the Lorentzian stabilization of the satellite in the orbital coordinate system in the indirect equilibrium position is solved under the conditions of the perturbing effect of the gravitational torque. To solve this problem, which is characterized by incomplete control, a method of averaging differential equations is developed. Using the original construction of the unsteady Lyapunov function, we obtain sufficient conditions for the asymptotic stability of the programmed satellite motion mode in the form of constructive inequalities with respect to the control parameters.

Numerical simulation of the effect of fault inclination on the sudden water of the fault bottom plate

The main reason for the frequent occurrence of water accidents on the bottom plate of the working surface near the mine fault in China is that the excavation activities cause the fault to activate and direct the pressure water of the aquifer. The distribution of ground stress fields and plastic regions under the influence of extraction disturbance spree is analyzed by using the flaC3D simulation software FLAC3D simulation software. The results show that the greater the inclination of the fault, the greater the shear stress and the normal stress at the fault level, and the deeper the activation range of the mining fault is larger than that of the shallow one ,and the small inclination positive fault is more likely to produce the fissure between the working surface base plate and the aquifer, and the small inclination positive fault should be left with a wider water-bearing coal column in the actual safety design. Using this software, the evolution of the stress field and plastic zone in the adjacent mining area is a preview, which is of great application value to prevent the surface plate burst water and determine the retention width of the fault waterproof coal column.

Well-flow behavior of reorientation fracture considering permeability anisotropy

Purpose In petroleum industry, hydraulic fracturing is essential to enhance oil productivity. The hydraulic fractures are usually generated in the process of hydraulic fracturing. Although some mathematical models were proposed to analyze the well-flow behavior of conventional fracture, there are few models to depict unconventional fracture like reorientation fracture. To figure out the effect of reorientation fracture on production enhancement and guide the further on-site operating, this paper aims to investigate the well-flow behavior of vertical reorientation fracture in horizontal permeability anisotropic reservoir. Design/methodology/approach Based on the governing equation considering horizontal permeability anisotropy, the mathematical models for reorientation fractures in infinite reservoir are developed by using the principle of superposition. Furthermore, a rectangular closed drainage area is also considered to investigate the well-flow behavior of reorientation fracture, and the mathematical models are developed by using Green’s and source functions. Findings Computational results indicate that the flux distribution of infinite conductivity fracture is uniform at very early times. After a period, it will stabilize eventually. High permeability anisotropy and small inclination angle of reorientation will cause significant end point effect in the infinite conductivity fracture. The reorientation fractures with small inclination angle in high anisotropic reservoir are capable of improving 1-1.5 times more oil productivity in total. Originality/value This paper develops the mathematical methods to study the well-flow behavior for unconventional fracture, especially for reorientation fracture. The results validate the production enhancement effect of reorientation fracture and identify the sensitive parameters of productivity.

Strategies of traversing obstacles and the simulation for a forestry chassis

As to the complicated terrain in forest, forestry chassis with an articulated body with three degrees of freedom and installed luffing wheel-legs (FC-3DOF&LW) is a novel chassis that can surmount obstacles. In addition, the rear frame of FC-3DOF&LW is regarded as the platform to carry equipment. Small inclination angle for rear frame contributes to stability and ride comfort. This article describes the strategy of traversing obstacles and simulation for FC-3DOF&LW that drives in forest terrain. First, key structures of FC-3DOF&LW are briefly introduced, which include articulated structure with three degrees of freedom and luffing wheel-leg. Based on the sketch of luffing wheel-leg, the movement range of luffing wheel-leg is obtained by hydraulic cylinder operation. Second, the strategy of crossing obstacles that are simplified three models of terrain is presented, and the simulation for surmounting obstacles is constructed in multibody dynamics software. The simulation results demonstrate that the inclination angle of rear frame is 18° when slope is 30°. A maximum 12° decrease of inclination angle for rear frame can be acquired when luffing wheel-legs are applied. For traversing obstacles with both sides, the maximum inclination angle of rear frame is about 1.2° and is only 3° for traversing obstacles with single side.