Application of interpolation/approximation techniques (metamodels, for brevity) is commonly adopted in numerical optimization, typically to reduce the overall execution time of the optimization process. A limited number of trial solution are computed, cov- ering the design variable space: those trial points are then used for the determination of an estimate of the objective function in any desired location of the design space.

We present an algorithm to solve Netwon methods for nonlinear hypersingular integral equation of Prandtl's type with the help of GMRES .

We consider Volterra integral equations on time scales and present our study about the long time behavior of their solutions. We provide sufficient conditions for the stability and investigate the convergence properties when the kernel of the equations vanishes at infinity.

In the last two decades, PSO (Particle Swarm Optimization) gained a lot of attention among the different derivative-free algorithms for global optimization. The simplicity of the implementation, compact memory usage and parallel structure represent some key features, largely appreciated. On the other hand, the absence of local information about the objective function slow down the algorithm when one or more constraints are violated, even if a penalty approach is applied.

The rheology and dynamics of suspensions of fluid vesicles is investigated by a combination of molecular dynamics and mesoscale hydrodynamics simulations in two dimensions. The vesicle suspension is confined between two no-slip shearing walls. The flow behavior is studied as a function of the shear rate, the volume fraction of vesicles, and the viscosity ratio between inside and outside fluids. Results are obtained for the interactions of two vesicles, the intrinsic viscosity of the suspension, and the cell-free layer near the walls.

Recurrent focal neuropathy with liability to pressure palsies is a relatively frequent autosomal-dominant demyelinating neuropathy linked to peripheral myelin protein 22 (PMP22) gene deletions. The combination of PMP22 gene mutations with other genetic variants is known to cause a more severe phenotype than expected. We present the case of a patient with severe orthostatic hypotension since 12 years of age, who inherited a PMP22 gene deletion from his father. Genetic double trouble was suspected because of selective sympathetic autonomic disturbances.

Double integrals with algebraic and/or logarithmic singularities are of interest in the application of boundary element method, e.g. linear theory of the aerodynamics of slender bodies of revolution and in many other fields, for example computational electromagnetics. Therefore, the numerical evaluation of such type of integrals deserves attention.

Numerical simulations of vesicle suspensions are performed in two dimensions to study their dynamical and rheological properties. An hybrid method is adopted, which combines a mesoscopic approach for the solvent with a curvature-elasticity model for the membrane. Shear flow is induced by two counter-sliding parallel walls, which generate a linear flow profile. The flow behavior is studied for various vesicle concentrations and viscosity ratios between the internal and the external fluid.

We consider two models which were both designed to describe the movement of eukaryotic cells responding to chemical signals. Besides a common standard parabolic equation for the diffusion of a chemoattractant, like chemokines or growth factors, the two models differ for the equations describing the movement of cells. The first model is based on a quasilinear hyperbolic system with damping, the other one on a degenerate parabolic equation. The two models have the same stationary solutions, which may contain some regions with vacuum.