arXiv subjects

Martin Stahn

Publications and source records attributed to Martin Stahn.

4 recordsLinked to original sources

arXiv2026

Large-scale wireless network management via Open-RAN Tandem Apps: Cell on/off switching use case

With growing mobile-network complexity, management and optimization have become increasingly difficult. Centralized algorithms face high control-data overhead and computational load, while distributed approaches often perform far from optimally. The O-RAN architecture introduces two tiers of RAN Intelligent Controllers (RICs), enabling hierarchical network-management schemes. This work proposes Tandem Apps: a pair of tightly coupled optimization mechanisms running on both controllers. We show how to design Tandem Apps through architectural and functional splitting to achieve an agile, low-complexity solution that still preserves a global network view. As an example, we implement Tandem Apps for cell on/off switching and evaluate them in a large heterogeneous network using real network data. Although the Tandem Apps concept is new, it remains fully compliant with the O-RAN standard, as validated using commercial network software.

cs.NI↗

arXiv2021

Randomised one-step time integration methods for deterministic operator differential equations

Uncertainty quantification plays an important role in problems that involve inferring a parameter of an initial value problem from observations of the solution. Conrad et al.\ (\textit{Stat.\ Comput.}, 2017) proposed randomisation of deterministic time integration methods as a strategy for quantifying uncertainty due to the unknown time discretisation error. We consider this strategy for systems that are described by deterministic, possibly time-dependent operator differential equations defined on a Banach space or a Gelfand triple. Our main results are strong error bounds on the random trajectories measured in Orlicz norms, proven under a weaker assumption on the local truncation error of the underlying deterministic time integration method. Our analysis establishes the theoretical validity of randomised time integration for differential equations in infinite-dimensional settings.

math.NA↗

arXiv2019

Lagrangian coherent sets in turbulent Rayleigh-B\'enard convection

Coherent circulation rolls and their relevance for the turbulent heat transfer in a two-dimensional Rayleigh--B\'{e}nard convection model are analyzed. The flow is in a closed cell of aspect ratio four at a Rayleigh number ${\rm Ra}=10^6$ and at a Prandtl number ${\rm Pr}=10$. Three different Lagrangian analysis techniques based on graph Laplacians -- distance spectral trajectory clustering, time-averaged diffusion maps and finite-element based dynamic Laplacian discretization -- are used to monitor the turbulent fields along trajectories of massless Lagrangian particles in the evolving turbulent convection flow. The three methods are compared to each other and the obtained coherent sets are related to results from an analysis in the Eulerian frame of reference. We show that the results of these methods agree with each other and that Lagrangian and Eulerian coherent sets form basically a disjoint union of the flow domain. Additionally, a windowed time-averaging of variable interval length is performed to study the degree of coherence as a function of this additional coarse graining which removes small-scale fluctuations that cause trajectories to disperse quickly. Finally, the coherent set framework is extended to study heat transport.

physics.flu-dyn↗

arXiv2019

Computation and optimal perturbation of finite-time coherent sets for aperiodic flows without trajectory integration

Understanding the macroscopic behavior of dynamical systems is an important tool to unravel transport mechanisms in complex flows. A decomposition of the state space into coherent sets is a popular way to reveal this essential macroscopic evolution. To compute coherent sets from an aperiodic time-dependent dynamical system we consider the relevant transfer operators and their infinitesimal generators on an augmented space-time manifold. This space-time generator approach avoids trajectory integration, and creates a convenient linearization of the aperiodic evolution. This linearization can be further exploited to create a simple and effective spectral optimization methodology for diminishing or enhancing coherence. We obtain explicit solutions for these optimization problems using Lagrange multipliers and illustrate this technique by increasing and decreasing mixing of spatial regions through small velocity field perturbations.

math.DS↗