Steven M. Wise

TL;DR: In this paper, the authors provide an overview of multiscale modelling focusing on the growth phase of tumours and bypassing the initial stage of tumourigenesis, and limit the scope further by considering models of tumor progression that do not distinguish tumour cells by their age and do not consider immune system interactions nor do they describe models of therapy.

TL;DR: This is the first paper in a two-part series in which a diffuse interface continuum model of multispecies tumor growth and tumor-induced angiogenesis in two and three dimensions is developed, analyzed, and simulated.

TL;DR: Most of the theoretical results hold for the related Swift-Hohenberg equation as well and local-in-time error estimates that ensure the convergence of the scheme are presented.

TL;DR: This work shows that taxis may play a role in tumor invasion and that when nutrient plays the role of a chemoattractant, the diffusional instability is exacerbated by nutrient gradients, as predicted by linear stability theory.

TL;DR: This paper presents and compares two unconditionally energy stable finite-difference schemes for the phase field crystal equation and considers a new, fully second-order two-step algorithm that solves the nonlinear equations using an efficient nonlinear multigrid method.