Improved local smoothing estimate for the wave equation in higher dimensions

In this paper, we establish the sharp $k$-broad estimate for a class of phase functions satisfying the homogeneous convex conditions. As an application, we obtain improved local smoothing estimates for the half-wave operator in dimensions $n\ge3$. As a byproduct, we also generalize the restriction estimates of Ou--Wang to a broader class of phase functions.Comment: 32 pages, 3 figures, Referees' suggestions incorporated. To appear in J. Func. Ana

Square function estimates and Local smoothing for Fourier Integral Operators

We prove a variable coefficient version of the square function estimate of Guth--Wang--Zhang. By a classical argument of Mockenhaupt--Seeger--Sogge, it implies the full range of sharp local smoothing estimates for $2+1$ dimensional Fourier integral operators satisfying the cinematic curvature condition. In particular, the local smoothing conjecture for wave equations on compact Riemannian surfaces is completely settled.Comment: 39 pages, 3 figures, Referees' suggestions incorporated. To appear in Proc. Lond. Math. So

Study on Dynamic Loading Characteristics of Rock Containing Holes

Accurately characterizing the mechanical behavior and fracture mechanisms of rock containing holes under dynamic loads is essential for ensuring the stability of underground rock structures. In this study, to enhance the understanding of the fracture processes in rock specimens with cavities subjected to dynamic impacts, experimental and numerical studies focusing on the influence of borehole geometry and strain rate are conducted. The results reveal that the strain rate affects the specimens’ dynamic mechanical strength and peak strain. However, the degree of such influence diminishes as the borehole diameter increases in specimens containing two holes. Fractures that lead to failure are primarily initiated at the axial and radial edges of the holes, the specimen extremities, and around the rock bridges in specimens with dual cavities, indicating significant stress concentration zones within the stress field distribution for specimens with a single hole. Further analysis using displacement field diagrams confirms that shear-induced fractures are the predominant cause of failure across all specimens. These findings provide critical insights for developing borehole pressure relief technology to protect against the risks of deep dynamic impacts

Numerical and in-situ investigation on the ground behavior of the end roof in fully mechanized caving face

Fully mechanized top coal caving is a major high-yield and high-efficiency coal mining method for thick seam mining. At present, it is affected by the further popularization and application of fully mechanized caving mining because the recovery rate is limited. The research on the technology of fully mechanized top coal caving and transitional coal mining is crucial. This paper aims at the top coal recovery with the top coal of the fully mechanized caving face and the transitional frame at both ends of the working face. With the top roof structure model of the fully mechanized caving face, the numerical simulation and field measurement is used to compare the end coal caving. With caving coal or not, the destruction and migration rules of the top coal in the fully mechanized caving face are obtained. The study found that at the end of the transport trough, the maximum concentration factor of the support pressure in the coal is 2.35, and the maximum vertical displacement is 9.2cm. And at the end of the return air trough, the support pressure concentration factor is 3.53, and the maximum vertical displacement of the roof is 102cm. The above research reveals the law of the occurrence of the pressure and the movement of the top coal when caving the coal at the end, while ensuring the safe production and efficient mining of the coal mine