Single-layer 1T′1T'-MoS2_2 under electron irradiation from abab initioinitio molecular dynamics

Irradiation with high-energy particles has recently emerged as an effective tool for tailoring the properties of two-dimensional transition metal dichalcogenides. In order to carry out an atomically-precise manipulation of the lattice, a detailed understanding of the beam-induced events occurring at the atomic scale is necessary. Here, we investigate the response of $1T'$-MoS$_2$ to the electron irradiation by $ab$ $initio$ molecular dynamics means. Our simulations suggest that an electron beam with energy smaller than 75 keV does not result in any knock-on damage. The displacement threshold energies are different for the two nonequivalent sulfur atoms in $1T'$-MoS$_2$ and strongly depend on whether the top or bottom chalcogen layer is considered. As a result, a careful tuning of the beam energy can promote the formation of ordered defects in the sample. We further discuss the effect of the electron irradiation in the neighborhood of a defective site, the mobility of the sulfur vacancies created and their tendency to aggregate. Overall, our work provides useful guidelines for the imaging and the defect engineering of $1T'$-MoS$_2$ using electron microscopy.Comment: 8 pages, 5 figure

Propagation and filtering of elastic and electromagnetic waves in piezoelectric composite structures

In this article we discuss the modelling of elastic and electromagnetic wave propagation through one- and two-dimensional structured piezoelectric solids. Dispersion and the effect of piezoelectricity on the group velocity and positions of stop bands are studied in detail. We will also analyze the reflection and transmission associated with the problem of scattering of an elastic wave by a heterogeneous piezoelectric stack. Special attention is given to the occurrence of transmission resonances in finite stacks and their dependence on a piezoelectric effect. A 2D doubly-periodic piezoelectric checkerboard structure is subsequently introduced, for which the dispersion surfaces for Bloch waves have been constructed and analysed, with the emphasis on the dynamic anisotropy and special features of standing waves within the piezoelectric structure.Comment: 24 pages, 18 figures, 3 tables. Preprint version of a research article, accepted for publication in "Mathematical Methods in the Applied Science (2016)

Generalized Hamilton-Jacobi equations for nonholonomic dynamics

Employing a suitable nonlinear Lagrange functional, we derive generalized Hamilton-Jacobi equations for dynamical systems subject to linear velocity constraints. As long as a solution of the generalized Hamilton-Jacobi equation exists, the action is actually minimized (not just extremized)