Conveners
Free Boundaries in Active Matter: MS-12-1
- Shawn Walker (Louisiana State University)
Free Boundaries in Active Matter: MS-12-2
- Shawn Walker (Louisiana State University)
Description
Organisers: Ricardo H. Nochetto, Shawn Walker
-
Qi Wang (U of South Carolina)08/09/2026, 14:00Free Boundaries in Active Matter
We propose several linear, fully decoupled numerical schemes with first- and second-order temporal accuracy for a novel Q-tensor-based two-phase hydrodynamic model that describes the coupling of active nematic liquid crystal solutions with isotropic solid substrates. The model is derived from the generalized Onsager principle and includes nontrivial terms that contribute zero to the total free...
Go to contribution page -
Scott Weady (Flatiron Institute)08/09/2026, 14:30Free Boundaries in Active Matter
We develop and analyze a model for a flat microbial droplet growing on the surface of a viscous fluid. The model describes growth-induced stresses at the fluid surface, density variations in the bulk due to nutrient consumption, and the resulting fluid flows that arise. We reformulate this free boundary problem as a system of integro-differential equations defined solely on the microbial...
Go to contribution page -
Dr Ingo Nitschke (TU Dresden - Institute of Scientific Computing)08/09/2026, 15:00Free Boundaries in Active Matter
Many mathematical models for active interfaces, biological membranes, and other free boundary problems combine geometric evolution with conserved quantities living on evolving surfaces. This motivates the development of general variational frameworks for deriving energy-dissipative evolution equations.
In this talk, we present a general variational framework for constructing coupled...
Go to contribution page -
Oleksii Krupchytskyi (The Pennsylvania State University)08/09/2026, 15:30Free Boundaries in Active Matter
We begin with a brief overview of the rapidly developing research area of active matter, a.k.a. active materials. These materials are intrinsically out of equilibrium resulting in novel physical properties whose modeling requires the development of new mathematical tools. We present a free boundary PDE model a cytoskeleton of a moving cell. The key mathematical features of our model are the...
Go to contribution page -
Dmitry Golovaty09/09/2026, 14:00Free Boundaries in Active Matter
I will discuss pattern formation in active matter confined to a thin film of microtubules activated by Adenosine Triphosphate (ATP), focusing on configurations corresponding to high anisotropy of the elastic constants. This is the result of the joint work with M. Carme Calderer (Minnesota), Jordi Ignes-Mullol (Barcelona), Francesc Sagues (Barcelona), Lingxing Yao (Akron), and Longhua Zhao...
Go to contribution page -
Timothy Atherton (Tufts University)09/09/2026, 14:30Free Boundaries in Active Matter
Liquid crystals provide remarkable examples of two-way coupling between internal order and geometry: orientational or layered order responds to confinement and interfaces, while the resulting elastic stresses can reshape the domain itself. I will discuss recent variational and computational work on this coupling in nematic and smectic systems. In nematic droplets, simultaneous optimization of...
Go to contribution page -
Slobodan Zumer (University of Ljubljana, Faculty of Mathematics and Physics)09/09/2026, 15:00Free Boundaries in Active Matter
Topological active soft matter includes fluids characterized by orientational ordering of constituting entities, ranging from anisotropic particles that extract energy from their surroundings to biological and living systems that convert chemical energy. Due to its softness, topological soft matter rarely exhibits homogeneous orientational order. Most of the frustration arising from the...
Go to contribution page -
APALA MAJUMDAR (University of Manchester)09/09/2026, 15:30Free Boundaries in Active Matter
We introduce a diffuse-interface Landau-de Gennes free energy for nematic liquid crystals (NLC) systems, with free boundaries, in three dimensions submerged in isotropic liquid, and a phase field is introduced to model the deformable interface.
Go to contribution page
The energy consists of the original Landau-de Gennes free energy, three penalty terms and a volume constraint.
We prove the existence and regularity...