A ctitious domain method based on boundary Lagrange multipliers is proposed for linear elasticity problems in two dimensional domains. The solution of arising saddle-point problem is obtained iteratively using MINRES method with a positive deenite block diagonal preconditioner which is based on a fast direct solver for diiusion problems. Numerical experiments demonstrate the behavior of conside...

We study deterministic and stochastic perturbations of incompressible flows on a two-dimensional torus. Even in the case of purely deterministic perturbations, the long-time behavior of such flows can be stochastic. The stochasticity is caused by the instabilities near the saddle points as well as by the ergodic component of the locally Hamiltonian system on the torus.

Nilsson et al. have recently shown how a velocity field in geostrophic and hydrostatic balance in an f -plane may be diagnosed from prescribed distributions of buoyancy and wind stress, in a basin with closed isobaths. I extend their analysis to cover basins with more complex depth contours, treating in particular the behavior of the flow in the presence of a saddle point.

General thermo-mechanical behavior of composites reinforced by shape memory alloy fibers is predicted using a three-dimensional analytical micromechanical method to consider the effect of fibers activation. Composite due to the micromechanical method can be exposed to general normal and shear mechanical and thermal loading which cause to activate the shape memory alloy fibers within polymeric m...

For certain singularly perturbed two-component reaction-diffusion (RD) systems, the bifurcation diagram of steady-state spike solutions is characterized by a saddle-node behavior in terms of some parameter β in the system. For some such systems, such as the Gray-Scott model, a spike self-replication behavior is observed as a parameter varies across the saddle-node point. We demonstrate and anal...

The classical surface curvature measures, such as the Gaussian and the mean curvature at a point of a surface, are not very indicative of local shape. The two principal curvatures (taken as a pair) are more informative, but one would prefer a single shape indicator rather than a pair of numbers. Moreover, the shape indicator should preferably be independent of the size i.e. the amount of curvat...