October 17, 2025 Jared Barber (IU Indianapolis)

Viscoelastic computational models of bone cells and migrating cells

Cellular forces, whether due to external or internal sources, have been implicated in a number of important biological processes.  Here we focus on two such processes:  Bone regulation by osteocytes, bone cells that respond to external forces in useful ways, and cell migration, which plays a role in cancer metastasis, wound healing, and other areas.  Our models in both cases use a network of interconnected damped springs, or viscoelastic elements, to model the cell.

With osteocytes, the external and internal fluid is coupled to our viscoelastic meshwork using a lattice-Boltzmann immersed boundary method.  The external fluid surrounds the cell which, in turn, is surrounded by rigid bone material.  Leveraging our approach’s relatively strong ability to handle complex geometries, we constructed four osteocyte models of varying complexity to consider what forces osteocytes tend to experience when in their natural environment.  We will share our approaches and findings that include suggestions that high force may arise where arms or processes of osteocytes connect to the main portion of the cell and that osteocytes may experience higher forces when inlets preferentially outnumber outlets in the region.

We will also shortly share our preliminary cell migration models and their ability to predict motion and force distribution.  In contrast with our osteocyte models, these models do not include fluid and take into account active cellular components that assist with migration.  We will share how we add in such active cellular components, if time allows, for both of our models.  Currently our main result is that such models, despite relative simplicity, can produce reasonable and interesting migratory behaviors.

September 19, 2025 Robert Buckingham (UC Math)

Pattern Formation and Wave Breaking in Nonlinear Dispersive Equations

Wave propagation in optical fibers, bodies of water, the atmosphere, plasmas, and Bose-Einstein condensates can all be described by nonlinear dispersive wave equations.  Solutions of these equations typically display both smooth and highly oscillatory behavior.  While qualitatively similar, the oscillations can be generated by a variety of different mechanisms.  We will discuss recent progress in understanding patterns formed by pure radiation, soliton ensembles, high-order solitons, and interacting energy modes.  We will also consider the onset of wave breaking and look at different types of behavior that can occur in the transition from smooth to oscillatory regions.  Special attention will be paid to a specific type of rogue-wave focusing that in the past few years has been shown to be universal for a number of different equations and initial conditions.