Vorträge

We discuss spectral inequalities and observability for the harmonic oscillator and more general Schrödinger operators with confinement potentials on the whole space. It turns out that the (super-)exponential decay of the corresponding eigenfunctions allows to consider sensor sets with a density that exhibits a certain decay. This, in particular, permits sensors with finite measure.

Nuclear fusion reactor design crucially depends on numerical simulation. The plasma can usually be modeled using fluid equations (for mass, momentum and energy). However, the reactor also contains neutral (non-charged) particles (which are important in its operation), of which both the position and velocity distribution is important. This leads to a Boltzmann-type transport equation that needs to be discretised with a Monte Carlo method. In high-collisional regimes, the Monte Carlo simulation describing the evolution of neutral particles becomes prohibitively expensive, because each individual collision needs to be tracked.
In this presentation, we overview a number of approaches that can alleviate the computational burden associated with the high-collisional regime. One option is to avoid simulating each invididual collision. In the limit of infinite collision rate, the law of large numbers dictates the approach of an advection-diffusion like particle behaviour, in which the accumulated effect of an infinite amount of collisions is aggregated in a Brownian motion (diffusion). To maintain accuracy and remove exploding simulation costs in high-collisional regimes, one can define hybridized particles that exhibit both kinetic behaviour and diffusive behaviour depending on the local collisionality [3].
Additionally, we can reduce the number of Monte Carlo particles that needs to be simulated via the multilevel Monte Carlo method[5]. Finally, one can also reduce the variance of the simulation by using an approximate fluid model for the neutral particles, discretized with a finite volume methods. This deterministic simulation can be used as a control variate, allowing the Monte Carlo simulation to focus on solely the deviation of the kinetic model with respect to the approximate fluid model.
References
[1] KukushkinA.S.,PacherH.D.,KotovV.,PacherG.W.,andReiterD.(2011)FinalizingtheITERdivertordesign:thekeyroleofSOLPSmodeling Fusion Eng. Des. 86:2865-2873.
[2] ReiterD.,BaelmansM.,andBörner,P.(2005)TheEIRENEandB2-EIRENEcodes,FusionSci.Technol.47:172-186.
[3] MortierB.,SamaeyG.,BaelmansM.(2019)Kinetic-diffusionasymptotic-preservingMonteCarloalgorithmsforplasmaedgeneutralsimulation.
Contributions to Plasma Physics, in press.
[4] Horsten N., Samaey G., Baelmans M. (2019) Hybrid fluid-kinetic model for neutral particles in the plasma edge. Nuclear Materials and Energy
18:201-207.
[5] Løvbak E., Samaey G., Vandewalle S. (2019) A multilevel Monte Carlo method for asymptotic-preserving particle schemes. Submitted. https://arxiv.org/abs/1907.04610.

Zoomlink: https://tuhh.zoom.us/j/84729171896?pwd=ODArbForaUxMM3Q3VTJsNG1kaVNYQT09

Aufgrund des zunehmenden Wachstums im E-Commerce-Sektor haben robotisierte Lagerhaltungs-
systeme – Robotic mobile fulfillment systems (RMFS) – für die Auftragsabwicklung in letzter Zeit
mehr Aufmerksamkeit erhalten. Dabei handelt es sich um eine neue Art von Lagerhaltungssyste-
men, bei denen nicht mehr Kommissionierer:innen in den Lagerbereich geschickt werden, um die
bestellten Artikel zu suchen und zu kommissionieren, sondern Roboter die Regale mit den bestell-
ten Artikeln aus dem Lagerbereich zu den Kommissionierstationen, auch Packstationen genannt,
tragen. An jeder Packstation steht eine Person – der oder die Kommissionierer:in (Packer:in) – die
die Artikel aus den Regalen nimmt und sie entsprechend der Kundenbestellung in Kartons verpackt.
Ein solches RMFS wirft viele Entscheidungsprobleme auf. Wir konzentrieren uns auf Entscheidun-
gen über die optimale Anzahl von Robotern. Wir modellieren das RMFS als ein Warteschlangen-
netzwerk, analysieren seine Stabilität und bestimmen die minimale Anzahl von Robotern für ein
stabiles System.
Dieser Vortrag basiert auf der gemeinsamen Arbeit [1] mit Sonja Otten, Ruslan Krenzler, Lin Xie
und Hans Daduna.

LITERATUR
[1] Otten, S., Krenzler, R., Xie, L., Daduna, H., und Kruse, K. Analysis of semi-open queueing
networks using lost customers approximation with an application to robotic mobile fulfilment
systems, OR Spectrum, 1–46, 2021. DOI: 10.1007/s00291-021-00662-9.

We discuss recent developments around approaches to Crouzeix's conjecture, the statement that the numerical range is a 2 spectral set for any complex square matrix. This includes spectral constants for specific classes of operators.

Zoomlink:
https://tuhh.zoom.us/j/84729171896?pwd=ODArbForaUxMM3Q3VTJsNG1kaVNYQT09

The Maxey-Riley Equation (MRE) models the motion of a finite-sized, spherical particle moving in a fluid. Applications using the MRE are, for example, the study of the spread of Coronavirus particles in a room, the formation of clouds and the so-called marine snow. The MRE is a second-order, implicit integro-differential equation with a singular kernel at initial time. For over 35 years, researchers used approximations and numerical schemes with high storage requirements or ignored the integral term, although its impact can be relevant. A major break-through was reached in 2019, when Prasath et al. mapped the MRE to a time-dependent Robin-type boundary condition of the 1D Heat equation, thus removing the requirement to store the full history. They provided an implicit integral form of the solution by using the so-called Fokas method that could be later solved with numerical scheme and a nonlinear solver. While Prasath et al.’s method can deliver numerical solutions of very high accuracy, the need to evaluate nested integrals makes it computationally costly and it becomes impractical for computing trajectories of a large number of particles. In the talk, we will present a finite differences approach that it is not only storage efficient but also much faster. We will compare our approach to both Prasath et al.’s method as well as a to the numerical schemes developed by A. Daitche in 2013 for direct integration of the original Maxey-Riley equation with integral term.