Free spans or suspended spans normally occur in subsea pipelines due to the irregularity of seabed and byscouring phenomena around the installed non-buried pipeline. The hydrodynamic around the pipeline canlead to a vibration of the pipeline.This kind of vibration may cause fatigue damage to the pipeline. In orderto study the hydrodynamic around the pipeline, calculating the natural frequency o...

We study the regularity of the free boundary in the obstacle for the p-Laplacian, min { −∆pu, u − φ } = 0 in Ω ⊂ R. Here, ∆pu = div ( |∇u|p−2∇u ) , and p ∈ (1, 2) ∪ (2,∞). Near those free boundary points where ∇φ 6= 0, the operator ∆p is uniformly elliptic and smooth, and hence the free boundary is well understood. However, when ∇φ = 0 then ∆p is singular or degenerate, and nothing was known ab...

Existence and regularity of minimizers in elliptic free boundary problems have been extensively studied in the literature. We initiate the corresponding study of higher critical points by considering a superlinear free boundary problem related to plasma confinement. The associated energy functional is nondifferentiable, and therefore standard variational methods cannot be used directly to prove...

In this paper, the sloshing response of liquid in a two dimensional rigid rectangular tank with rigid baffles is investigated using boundary element technique. A baffle is a supplementary structural element which supplies a kind of passive control on the effects of ground shaking. The complicated liquid domain is divided into two simple sub-domains so that the liquid velocity potential in each ...

This study concentrates on the free pure radial vibrations of hollow spheres made of hypothetically functionally simple power rule graded materials having identical inhomogeneity indexes for both Young’s modulus and the density in an analytical manner. After offering the exact elements of the free vibration coefficient matrices for free-free, free-fixed, and fixed-fixed restraints, a parametric...

We study an optimal control problem for a semilinear elliptic boundary value problem giving rise to a free boundary. Here, the free boundary is generated due to the fact that the nonlinear term of the state equation is not differentiable. The new aspect considered in this paper, with respect to other control problems involving free boundaries, is that here the cost functional explicitly depends...

We study the critical stochastic q-state Potts model on the square lattice. Unlike the expected behavior when the phase transition is continuous (q = 2, 3, 4)—a universal power-law for the mixing time independently of the boundary conditions— the mixing time at a discontinuous phase transition, tmix, is highly sensitive to those. It was recently shown by the authors that tmix ≥ exp(cn) on an n×...

this work reports the effect of nanotube aspect ratio and waviness index on stress and displacement distributions of functionally graded nanocomposite cylinders reinforced by wavy single walled carbon nanotubes based on a mesh-free method. the mechanical properties of these composites are assumed to be graded along radial direction and estimate by a micro mechanical model. in the mesh-free anal...

An equivalent continuum model based on the Eshelby-Mori-Tanaka approach was employed to estimate the effective constitutive law for an elastic isotropic medium (i.e., the matrix) with oriented straight carbon nanotubes (CNTs). The two-dimensional generalized differential quadrature method was an efficient and accurate numerical tool for discretizing equations of motion and for implementing vari...