The Buckling of Single-Layer MoS2 Under Uniaxial Compression

Molecular dynamics simulations are performed to investigate the buckling of single-layer MoS2 under uniaxial compression. The strain rate is found to play an important role on the critical buckling strain, where higher strain rate leads to larger critical strain. The critical strain is almost temperature-independent for T<50 K, and it increases with increasing temperature for T>50 K owning to the thermal vibration assisted healing mechanism on the buckling deformation. The length-dependence of the critical strain from our simulations is in good agreement with the prediction of the Euler buckling theory.Comment: Nanotechnology, accepte

Graphene Versus MoS2: a Short Review

Graphene and MoS2 are two well-known quasi two-dimensional materials. This review is a comparative survey of the complementary lattice dynamical and mechanical properties of graphene and MoS2. This comparison facilitates the study of graphene/MoS2 heterostructures, which is expected to mitigate the negative properties of each individual constituent.Comment: Frontiers of Physics, published, Focus Revie

Monomial ideals under ideal operations

In this paper, we show for a monomial ideal $I$ of $K[x_1,x_2,\ldots,x_n]$ that the integral closure \ol{I} is a monomial ideal of Borel type (Borel-fixed, strongly stable, lexsegment, or universal lexsegment respectively), if $I$ has the same property. We also show that the $k^{th}$ symbolic power $I^{(k)}$ of $I$ preserves the properties of Borel type, Borel-fixed and strongly stable, and $I^{(k)}$ is lexsegment if $I$ is stably lexsegment. For a monomial ideal $I$ and a monomial prime ideal $P$, a new ideal $J(I, P)$ is studied, which also gives a clear description of the primary decomposition of $I^{(k)}$. Then a new simplicial complex $_J\bigtriangleup$ of a monomial ideal $J$ is defined, and it is shown that $I_{_J\bigtriangleup^{\vee}} = \sqrt{J}$. Finally, we show under an additional weak assumption that a monomial ideal is universal lexsegment if and only if its polarization is a squarefree strongly stable ideal.Comment: 18 page