Effective mechanical properties of multilayer nano-heterostructures

Two-dimensional and quasi-two-dimensional materials are important nanostructures because of their exciting electronic, optical, thermal, chemical and mechanical properties. However, a single-layer nanomaterial may not possess a particular property adequately, or multiple desired properties simultaneously. Recently a new trend has emerged to develop nano-heterostructures by assembling multiple monolayers of different nanostructures to achieve various tunable desired properties simultaneously. For example, transition metal dichalcogenides such as MoS2 show promising electronic and piezoelectric properties, but their low mechanical strength is a constraint for practical applications. This barrier can be mitigated by considering graphene-MoS2 heterostructure, as graphene possesses strong mechanical properties. We have developed efficient closed-form expressions for the equivalent elastic properties of such multi-layer hexagonal nano-hetrostructures. Based on these physics-based analytical formulae, mechanical properties are investigated for different heterostructures such as graphene-MoS2, graphene-hBN, graphene-stanene and stanene-MoS2. The proposed formulae will enable efficient characterization of mechanical properties in developing a wide range of application-specific nano-heterostructures

Quasilinear degenerate elliptic unilateral problems

We will be concerned with the existence result of a degenerate elliptic unilateral problem of the form Au+H(x,u,∇u)=f, where A is a Leray-Lions operator from W1,p(Ω,w) into its dual. On the nonlinear lower-order term H(x,u,∇u), we assume that it is a Carathéodory function having natural growth with respect to |∇u|, but without assuming the sign condition. The right-hand side f belongs to L1(Ω)

Existence of solutions for quasilinear degenerate elliptic equations

In this paper, we study the existence of solutions for quasilinear degenerate elliptic equations of the form $A(u)+g(x,u,abla u)=h$, where $A$ is a Leray-Lions operator from $W_0^{1,p}(Omega,w)$ to its dual. On the nonlinear term $g(x,s,xi)$, we assume growth conditions on $xi$, not on $s$, and a sign condition on $s$