Ricerc@Sapienza

Fractal structures or geometries have nowadays a key role in all those

> models for natural and industrial processes which exhibit the

> formation of rough surfaces and interfaces. Computer simulations,

> analytical theories and experiments have led to significant advances in

> modeling these phenomena across wild media. Many problems coming from

> engineering, physics or biology are characterized by both the presence

> of different temporal and spatial scales and the presence of contacts

In many applications it is important to sensitivity of eigenvalues of a matrix polynomial polynomial. The sensitivity commonly is described pseudospectra. However, the determination of pseudospectra of matrix polynomials is very demanding computationally. This paper describes a new approach to computing approximations of pseudospectra of matrix polynomials by using rank-one or projected rank-one perturbations. These perturbations are inspired by Wilkinson's analysis of eigenvalue sensitivity. This approach allows the approximation of both structured and unstructured pseudospectra.

The exact regularised point particle (ERPP) method is extended to treat the inter-phase momentum coupling between particles and fluid in the presence of walls by accounting for vorticity generation due to particles close to solid boundaries. The ERPP method overcomes the limitations of other methods by allowing the simulation of an extensive parameter space (Stokes number, mass loading, particle-to-fluid density ratio and Reynolds number) and of particle spatial distributions that are uneven (few particles per computational cell).