This paper focuses on the analysis of a free energy functional, that models dilute suspension magnetic nanoparticles in two-dimensional nematic well. The first part article is devoted to asymptotic global minimizers limit vanishing elastic constant, ℓ→0 where re-scaled constant ℓ inversely proportional domain area. results concern strong H1-convergence and ℓ-independent H2-bound for smooth boun...

In this paper we consider a semiclassical version of the wave equations with singular Hölder time-dependent propagation speeds on lattice ħZn. We allow speed to vanish leading weakly hyperbolic nature equations. Curiously, very much contrary Euclidean case considered by Colombini, de Giorgi and Spagnolo [2] other authors, Cauchy problem in is well-posed ℓ2(ħZn). However, also recover well-posed...

In this paper, free vibration analysis and forced vibration analysis of FG doubly clamped micro-beams is studied based on the third order shear deformation and modified couple stress theories. The size dependent dynamic equilibrium equations and both the classical and non-classical boundary conditions are derived using a variational approach. It is assumed that all properties of the FG micro-be...