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In order to investigate the impact of an external electric field on the sensitivity of β-HMX explosives, we employ first-principles calculations to determine the molecular structure, dipole moment, and electronic properties of both β-HMX crystals and individual β-HMX molecules under varying electric fields. When the external electric field is increasing along the [100], [010], and [001] crystallographic directions of β-HMX, the calculation results indicate that an increase in the bond length (N1–N3/N1′–N3′) of the triggering bond, an increase in the main Qnitro(N3, N3′) value, an increase in the minimum surface electrostatic potential, and a decrease in band gap all contribute to a reduction in its stability. Among these directions, the [010] direction exhibits the highest sensitivity, which can be attributed to the significantly smaller effective mass along the [010] direction compared with the [001] and [100] directions. Moreover, the application of an external electric field along the Ydirection of the coordinate system on individual β-HMX molecules reveals that the strong polarization effect induced by the electric field enhances the decomposition of the N1–N3 bonds. In addition, due to the periodic potential energy of β-HXM crystal, the polarization effect of β-HMX crystal caused by an external electric field is much smaller than that of a single β-HXM molecule.

The aim of this paper is to utilize special skills and potential well method to deal with questions of local and global well-posedness to a nonlinear diffusion equation driven by the p-Laplace operator, which reveals a subtle relationship between singular potential and nonlinear operator, and further generalizes some previous early results about local existence of the weak solution from a class of evolution equations involved the linear dissipative term and singular potential. Specifically, the results of stability and blow-up of solutions are established for the first time to this initial boundary value problem with singular potential.

We are interested in the existence and multiplicity of ground state solutions for a class of p(x)-Laplacian Dirichlet problem in bounded domains. Firstly, combining constraint variational method and quantitative deformation lemma, we prove that the equation possesses at least one least energy sign-changing solution with exactly two nodal domains. Finally, using a strong maximum principle, we obtain three ground state solutions (one positive, one negative, and one sign-changing) for this problem.