# Karlstad Applied Analysis Seminar (KAAS)

*Subscribe to the KAAS calendar and stay updated automatically. Copy the link and add it to your online calendar.*

## Future seminars:

**Talk-142**

**When:** T.B.D, 29 May 2024

**What: **Studying cell ecology with spatial cumulant models.

**Who: **Mykola Tkachuk, Karlstad University, Karlstad, Sweden.

Where: T.B.D and **online:**https://kau-se.zoom.us/j/61616693592

**Abstract: **Spatial cumulant models (SCMs) are spatially resolved population models, formulated by differential equations. SCMs approximate the dynamics of two summary statistics generated by spatio-temporal point processes (STPPs): first-order spatial cumulants (densities), and second-order spatial cumulants (spatial covariances).

In this talk, I’ll exemplify how SCMs can be used to predict and control STPP-generated population dynamics. With a worked example, I’ll demonstrate that (1) SCMs can capture STPP-generated density dynamics, even when mean-field population models (MFPMs) fail to do so, and (2) SCM-informed treatment strategies outperform MFPM-informed strategies in terms of inhibiting population growths. Overall, our work demonstrates that SCMs provide a new framework in which to study cell-to-cell interactions and treatments that take cell-to-cell interactions into account.

**Talk-143**

**When:** T.B.D

**What: **Nonsmooth mathematical programming in mechanics

**Who: **Sara Hamis, Department of Information Technology, Uppsala Univeristy, Sweden.

Where: T.B.D and **online:**https://kau-se.zoom.us/j/61616693592

**Abstract:**

We wish to present the case that many problems in mechanics can be posed as mathematical programming. There is a great variety of possible objective functions and types of constraints that can be put into the formulation. There are extremely effective interior point methods that allow to solve quite large problems numerically.

Equilibrium of various structures can be determined via minimization of the potential energy or other suitable mechanical functional. The rate-independent sliding and the quasi-static loading of fiber networks found in nonwoven materials are constituted within the theory of standard dissipative systems. A minimum principle for incremental potential is formulated with respect to the displacement-based variables as a second-order cone programming (SOCP) problem. A pure complementary energy principle is derived as the dual formulation in terms of stress-like variables. The model captures large irreversible deformations of nonwoven materials.

Form finding problems can be stated as nonsmooth mathematical programming problems as well. The effect of stiffness and strength reduction for 2D truss structures due to corrosion is accounted through a simple cross-sectional correction law. The formulation is presented either for fixed width or fixed aspect ratio rectangular cross-sections with affine or nearly affine dependency of the weight objective and the compliance constraint on the design parameters. The compliance constraint for the quasi-static problem is treated as a linear matrix inequality.