The dynamics of filopodia interacting with the surrounding extracellular matrix (ECM) play a key role in various cell-ECM interactions, but their mechanisms of interaction with the ECM in 3D environment remain poorly understood. Based on first principles, here we construct an individual-based, force-based computational model integrating four modules of 1) filopodia penetration dynamics; 2) intr...

In this thesis we investigate nonsmooth classical and continuum mechanics and its discretizations by means of variational numerical and geometric methods. The theory of smooth Lagrangian mechanics is extended to a nonsmooth context appropriate for collisions and it is shown in what sense the system is symplectic and satisfies a Noether-style momentum conservation theorem. Next, we develop the f...

We assume that at the continuum scales of interest here, the mass density ⇢ as well as the the momentum per unit volume ⇢u can be interpreted as well-defined averages of microscopic masses and momenta. That is, they are averages over minute spatial regions and time intervals, which can nevertheless be chosen large enough that there are negligible statistical fluctuations about those averages at...