In this paper, a unified analytical approach is proposed to investigate vibrational behavior of functionally graded shells. Theoretical formulation is established based on Sanders’ thin shell theory. The modal forms are assumed to have the axial dependency in the form of Fourier series whose derivatives are legitimized using Stokes transformation. Material properties are assumed to be graded in...

Multiphase ow simulation with various nonhomogeneous boundary conditions in ground water hydrology and petroleum engineering is considered The phase ow equations are given in a fractional ow formulation i e in terms of a saturation and a global pressure It is shown that most commonly used boundary conditions for groundwater hydrology and petroleum engineering problems can be incorporated into t...

the isogeometric analysis is increasingly used in various engineering problems. it is based on non-uniform rational b-splines (nurbs) basis function applied for the solution field approximation and the geometry description. one of the major concerns with this method is finding an efficient approach to impose essential boundary conditions, especially for inhomogeneous boundaries. the main contri...

An analytic solution is presented describing ̄ow to a drain in a semi-in®nite domain bounded by a leaky layer of constant thickness. The solution is developed by applying the method of images to two parallel boundaries: an inhomogeneity boundary and an equipotential boundary. It is then demonstrated that the solution for the problem with the leaky layer approximated by a leaky boundary (a mixed...

For one-dimensional p-Laplacian with weights in Lγ : L 0, 1 ,R 1 ≤ γ ≤ ∞ balls, we are interested in the extremal values of the mth positive half-eigenvalues associated with Dirichlet, Neumann, and generalized periodic boundary conditions, respectively. It will be shown that the extremal value problems for half-eigenvalues are equivalent to those for eigenvalues, and all these extremal values a...

Immersing a physical system in a heat bath results in the fields acquiring different properties according to their statistics. E.g., finite-temperature bosonic fields obey periodic boundary conditions, while fermionic fields satisfy antiperiodic b.c.’s. Such a distinction can be seen also at the level of the Green’s functions. Depending on the field’s statistics, thermal propagators obey either...

The Cauchy problem for the 2D Boussinesq system with periodic boundary conditions is studied. The global existence and uniqueness of a solution with initial data (u(0), θ(0)) ∈ Φ(α) is established, where Φ(α) is the space of functions the kth Fourier coefficients of which decay at infinity as 1 |k|α , α > 2. It is proved that the solution becomes analytic at any positive time. Bibliography: 10 ...

We consider the one-dimensional Willmore equation subject to Navier boundary conditions, i.e. the position and the curvature are prescribed on the boundary. In a previous work, explicit symmetric solutions to symmetric data have been constructed. Within a certain range of boundary curvatures one has precisely two symmetric solutions while for boundary curvatures outside the closure of this rang...

We have simulated a system of classical particles confined on the surface of a sphere interacting with a repulsive r potential. The same system simulated on a plane with periodic boundary conditions has van der Waals loops in pressure-density plots which are usually interpreted as evidence for a first order melting transition, but on the sphere such loops are absent. We also investigated the st...