Talks

Given an elliptic operator L=-divA∇ on L^2(R^n) one has by the Kato square root property that dom L^½=H^1(R^n) and

c||∇f||_2 ≤ ||L^½f||_2 ≤ C||∇f||_2

for some c,C>0 and f∈H^1(R^n). The right inequality above beeing equivalent to the Riesz transform ∇L^(-½) being bounded on L^2(R^n). The subject of the talk will be for what other p-norms the above inequality, specifically boundedness of the Riesz transform holds. It turns out that they are essentially the same p as for which the semigroup generated by -L is bounded on L^p(R^n).

Zoomlink:
https://tuhh.zoom.us/j/83250070589?pwd=UZ52e5cgqaexuY9SnleyZo01MmukYW.1

In this talk, we will discuss a very recent operator-theoretic result concerning second-order elliptic equations that yields a compactness theorem in the homogenization theory of the biharmonic equation, i.e., a fourth-order problem.

Spectral theory and functional calculus for unbounded self-adjoint operators on a Hilbert space are usually treated through von Neumann’s Cayley transform. Using ideas of Woronowicz, we redevelop this theory from the point of view of multiplier algebras and the so-called bounded transform (which establishes a bijective correspondence between closed operators and pure contractions). This also leads to a simple account of the affiliation relation between von Neumann algebras and self-adjoint operators. This is joint work with K. Landsman (Nijmegen, Netherlands).

Zoomlink:
https://tuhh.zoom.us/j/81617046707?pwd=tTkia9CCoCuaiEaEsrCmTqlMr1cfOT.1

Suppose that A, B, and C are compact selfadjoint operators on a Hilbert space such that A+B+C=0. We show that the possible eigenvalues of these operators are described by certain combinatorial objects called hives. We will also see that the Horn inequalities (first described in the compact case in joint work with Li and Timotin) can also be obtained from this hive model.

In this colloquium talk, we will explore the interplay between expectations and reality in computational fluid dynamics, with a particular focus on structure-preserving properties and the development of suitable finite element methods for incompressible and compressible flows. Specifically, we will discuss the continuity requirements that arise in approximating key physical quantities such as pressure and velocity. We will examine how these requirements can be effectively realized — whether by "cutting, gluing, or weakly connecting via rubber bands" — and support our approach with computational examples to motivate and illustrate the findings.

Additionally, I will take this opportunity to share insights into my current research and outline potential future research directions.

Zoomlink:
https://tuhh.zoom.us/j/81920578609?pwd=TjBmYldRdXVDT1VkamZmc1BOajREZz09

Model-based optimization is a central element of Process Systems Engineering and supports decision-making across different stages of process development. This talk will provide a brief overview of current work at the Institute of Process Systems Engineering, with a focus on process synthesis and model-based experimental design. The examples will address challenges in the design and evaluation of distillation processes as well as in reactor design and optimization. The underlying mathematical problems range from mixed-integer nonlinear programming to nonlinear dynamic optimization. Based on selected applications, the talk will discuss problem-specific challenges, current solution approaches, and open questions.

Zoomlink:
https://tuhh.zoom.us/j/81920578609?pwd=TjBmYldRdXVDT1VkamZmc1BOajREZz09

Hierarchic formulations for shear-deformable beams, plates and shells are based on a clever reparametrization of the kinematic equations and possess distinct variables for transverse shear. This results in several interesting and promising properties:
1. Hierarchic formulations are intrinsically free from transverse shear locking. That is, transverse shear locking is avoided a priori, independent of the utilized discretization scheme.
2. The hierarchic structure can be exploited towards an intrinsically selective mass scaling (ISMS) scheme. ISMS enables efficient and accurate simulations in explicit dynamics.
3. Hierarchic parametrizations enable intrinsically selective loss scaling (ISLS), which helps improve efficiency when solving problems in structural mechanics using physics-informed neural networks (PINNs).

This talk will introduce the key concepts behind hierarchic formulations for beams, plates and shells. Examples illustrate the applicability to small and large rotations, statics and explicit dynamics, and various discretization schemes and solution strategies. In addition, the talk will provide a brief overview on other current research topics from the Institute for Structural Analysis at TUHH.

Zoomlink:
https://tuhh.zoom.us/j/81920578609?pwd=TjBmYldRdXVDT1VkamZmc1BOajREZz09