free surface modeling plays an important role in some ocean structures design, especially in oscillating water column (owc) devices. boundary element method (bem) is a suitable method for free surface modeling due to its simplicity, quick solving, and low data storage requirement. in this paper, bem was used for free surface modeling in owc chamber and out of it. linear kinematic and dynamic bo...

In this section we will consider the general properties of the solution p(r, t) of the Smoluchowski equation in the case that the force field is derived from a potential, i.e., F (r) = −∇U(r) and that the potential is finite everywhere in the diffusion doamain Ω. We will demonstrate first that the solutions, in case of reaction-free boundary conditions, obey an extremum principle, namely, that ...

We consider the van der Waals’ free energy functional, with scaling parameter ε, in the plane domain R+ × R+, with inhomogeneous Dirichlet boundary conditions. We impose the two stable phases on the horizontal boundaries R+×{0} and R+×{∞}, and free boundary conditions on {∞}×R+. Finally, the datum on {0} ×R+ is chosen in such a way that the interface between the pure phases is pinned at some po...

This paper considers a class of one-dimensional solidification problem in which kinetic undercooling is incorporated into the temperature condition at the interface. A model problem with nonlinear kinetic law is considered. The main result is an existence theorem. The mathematical effects of the kinetic term are discussed

Let f , U and C represent, respectively, the free energy, the internal energy and the specific heat of the critical Ising model on the square M×N lattice with periodic boundary conditions, and f∞ represents f as M,N → ∞. We find that f , U and C can be written as: N(f −f∞) = ∑ ∞ i=1 fi/N 2i−1, U = − √ 2+ ∑ ∞ i=1 ui/N 2i−1 and C = 8 π lnN+ ∑ ∞ i=0 ci/N i andNf and U are well-defined odd function...

Controllability properties of a partial differential equation (PDE) model describing a thermoelastic plate are studied. The PDE is composed of a Kirchoff plate equation coupled to a heat equation on a bounded domain, with the coupling taking place on the interior and boundary of the domain. The coupling in this PDE is parameterized by α > 0. Boundary control is exerted through the (two) free bo...

Distributed sensing of structural states is essential to vibration control, health monitoring and shape control of precision structronic systems. Paraboloidal shells of revolution are widely used in aerospace, telecommunication, etc. structures. However, distributed sensing of paraboloidal shell structures is rarely investigated over the years. Micro-sensing characteristics, sensor segmentation...

2014 We derive a model of convection appropriate for containers with large width to height ratios. It couples a real rapidly varying convective variable to a slowly varying « drift » velocity field given by its stream-function. The derivation assumes stress-free boundary conditions at the top and the bottom. We discuss its extension to the more realistic no-slip case and the analogies/differenc...

Using a weak convergence approach, we prove a LPD for the solution of 2D stochastic Navier Stokes equations when the viscosity converges to 0 and the noise intensity is multiplied by the square root of the viscosity. Unlike previous results on LDP for hydrodynamical models, the weak convergence is proven by tightness properties of the distribution of the solution in appropriate functional spaces.

In this work we deduce an explicit Sommerfeld-type radiation condition able to prove uniqueness for the problem of outgoing wave propagation in isotropic elastic half-spaces with free boundary condition. The expression is obtained by a rigorous asymptotic analysis of the Green’s function associated with this problem. Observe that this is an exterior problem with unbounded frontier. The main dif...