Riccardo Scala

A Rigorous Sharp Interface Limit of a Diffuse Interface Model Related to Tumor Growth

In this paper, we study the rigorous sharp interface limit of a diffuse interface model related to the dynamics of tumor growth, when a parameter

Currents and dislocations at the continuum scale

\varepsilon

A contact problem for viscoelastic bodies with inertial effects and unilateral boundary constraints

ε, representing the interface thickness between the tumorous and non-tumorous cells, tends to zero. More in particular, we analyze here a gradient-flow-type model arising from a modification of the recently introduced model for tumor growth dynamics in Hawkins-Daruud et al. (Int J Numer Math Biomed Eng 28:3–24, 2011) (cf. also Hilhorst et al. Math Models Methods Appl Sci 25:1011–1043, 2015). Exploiting the techniques related to both gradient flows and gamma convergence, we recover a condition on the interface

On the strongly damped wave equation with constraint

\Gamma

Constraint reaction and the Peach–Koehler force for dislocation networks

Γ relating the chemical and double-well potentials, the mean curvature, and the normal velocity.

GRAPHS OF TORUS-VALUED HARMONIC MAPS, WITH APPLICATION TO A VARIATIONAL MODEL FOR DISLOCATIONS

In this paper, we provide an existence result for the energetic evolution of a set of dislocation lines in a three-dimensional single crystal. The variational problem consists of a polyconvex stored elastic energy plus a dislocation energy and some higher-order terms. The dislocations are modeled by means of integral one-currents. Moreover, we discuss a novel dissipation structure for such currents, namely the flat distance, that will serve to drive the evolution of the dislocation clusters.