Karlstad Applied Analysis Seminar (KAAS)

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Future seminars:

Talk-150

When: 28 May 2025, 14:00-14:45
What: Quantum theory and mathematics. A 100-year success story
Who: Christoph Schweigert, Department of Mathematics, Division of Algebra and Number Theory, Center for Mathematical Physics, University of Hamburg, Hamburg, Germany
Where: 21D302

It is our pleasure to invite you to the following joint KAAS seminar & Research Seminars in Physics. Note that the presentation will be "in presence" in 21D302.
Abstract:

The year 2025 marks the 100th anniversary of the papers by Heisenberg, Schrödinger, and Born-Jordan, which laid the foundations of modern quantum mechanics. In recognition of these seminal papers, UNESCO has declared 2025 the International Year of Quantum Science and Technology.

In this talk, we will explore the interplay between quantum theories and mathematics. Through several examples, we will show that mathematics provides crucial technology for the study of quantum theories and how quantum theories stimulate the development of new mathematics.

Talk-151

When: T.B.D
What: Nonsmooth mechanics of fiber network microstructures
Who: Mykola Tkachuk, Karlstad University, Karlstad, 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.

Equilibrium of various structures can be determined via minimization of the potential energy or other suitable mechanical functional. We have developed a new discrete network model [2] for nonwoven materials.

The rate-independent sliding and the quasi-static equilibrium loading of such network structure are constituted within the theory of standard dissipative systems. A minimum principle for incremental potential is formulated with respect to the displacement-based variables: nodal coordinates, segment end-to-end vectors, segment lengths and incremental fiber slidings. It takes the form of second-order cone programming (SOCP) similarly to the case of elastic cable networks. A pure complementary energy principle is derived as the dual formulation in terms of stress-like variables: nodal reactions, fiber force vectors, axial forces and friction forces.

The model capture large irreversible deformations of nonwoven materials. The damage mechanism is implemented in the form of fiber pull-out. The network becomes disjoint as more and more sections of free tails are pulled through the end knots.