Forschung & Lehre

Local Geometric Bounds on Generalized Entropy Evolution along Null Horizons

We develop a local and covariant framework for constraining the evolution of generalized entropy along null horizons, combining classical geometric methods with constraints from quantum field theory. Building on the quantum focusing conjecture (QFC), we derive a Raychaudhuri-type differential inequality for the generalized expansion:

\[\frac{d\Theta}{d\lambda} \le -\theta \Theta + \tfrac{1}{2}\theta^2 - \sigma^2\]

This reveals a direct interplay between expansion and shear in controlling entropy flow. We further show that quantum extremal surfaces correspond to configurations characterized by \(\Theta=0\), and derive a bound on the exponential separation of nearby null generators.

Table: Analogy between classical geometric focusing in general relativity and entropy dynamics along black hole horizons.

From Triadic Interactions to Kolmogorov Scaling: A Deterministic, Scale-Resolved Formulation of Energy Flux

We develop a deterministic, scale-resolved formulation of energy transfer in the three-dimensional incompressible Navier–Stokes equations based on an explicit triadic decomposition of the nonlinear term in Fourier space. Using a systematic dyadic localization of the velocity field, we derive an exact representation of the nonlinear energy flux across scales.

We show that, under a scale-invariant flux assumption, the Kolmogorov scaling is formally consistent with the triadic energy-transfer mechanism at a structural level — without relying on statistical assumptions. The result follows from the structural properties of the Navier–Stokes equations combined with a scale-resolved representation of the energy flux.

A Momentum-Regulated Model For Star Formation Efficiency in Giant Molecular Clouds

We present a minimal analytic framework to investigate the star formation efficiency per free-fall time, \(\epsilon_{\rm ff}\), in giant molecular clouds (GMCs), focusing on the origin of the observed clustering around \(\epsilon_{\rm ff} \sim 0.01\). We model the time evolution of the turbulent velocity dispersion through a momentum balance between stellar feedback and turbulent dissipation, showing this generically leads to a stable low-efficiency equilibrium.

The efficiency can be expressed as the ratio between a gravitational velocity scale and an effective feedback velocity scale — a physically transparent interpretation of self-regulated star formation. The model provides a simple, motivated interpretation of observed gas–star formation scaling relations.

Figure: Predicted \(\epsilon_{\rm ff}\) as a function of gas surface density \(\Sigma_{\rm gas}\) for representative cloud models. The shaded orange region indicates the typical observational range.

From customer survey feedback to software improvements: Leveraging the full potential of data

Converting customer survey feedback data into usable insights has always been a great challenge for large software enterprises. We present a practical end-to-end approach of how to extract useful information from a data set and leverage it to drive change — including choosing the right metrics, gathering feedback from end-users, analyzing data with inferential statistics, and efficiently processing large volumes of user comments with Large Language Models.

Figure: UX prototype dashboard showing UEQ scores and their 95% confidence intervals for six products over time.

Synthetic observations of molecular clouds in a galactic center environment: Studying maps of column density and integrated intensity

We run numerical simulations of molecular clouds adopting properties similar to those found in the Central Molecular Zone (CMZ) of the Milky Way, using the moving mesh code Arepo with simplified time-dependent chemistry. Radiative transfer is performed with RADMC-3D in [CII], [OI], ¹²CO, and ¹³CO lines. We show that atomic tracers accurately reflect most physical properties of both the H₂ and total gas of the cloud and provide a useful alternative to molecular lines when studying the ISM in the CMZ.

Figure: Logarithmic maps of the CO-to-H₂ conversion factor for the α = 2.0 model. Only the inner cloud regions yield the canonical X_CO value on average.

Star formation efficiencies of molecular clouds in a galactic center environment

We use the Arepo code to simulate the evolution of molecular clouds exposed to a harsh galactic center environment to understand why the star formation efficiency (SFE) is so small there. We model clouds with total mass 1.3×10⁵ M☉ and vary the virial parameter \(\alpha\) from 0.5 to 8.0, with ISRF and CRF both 1000× higher than solar neighbourhood values. Despite the harsh environment, all simulated clouds form stars within less than a gravitational free-fall time. We conclude that high levels of turbulence and strong external heating alone are not enough to explain the persistently low SFE at the galactic center.

Figure: Star formation efficiencies per free-fall time against the virial parameter for fiducial density models, showing a decreasing trend with increasing \(\alpha\).

Structure analysis of simulated molecular clouds with the Δ-variance

We employ the Δ-variance analysis to study the turbulent gas dynamics of simulated molecular clouds across three initial mean number densities (n₀ = 30, 100, and 300 cm⁻³), spanning the range typical for MCs in the solar neighbourhood. We evaluate Δ-variance spectra for centroid velocity maps and for integrated intensity and column density maps for multiple chemical components.

The spectral slopes of the Δ-variance on centroid velocity maps for total and H₂ density are significantly steeper than for CO tracers. We report a critical density threshold of ~100 cm⁻³ at which the Δ-variance slopes of the CO tracers change sign — CO traces the total cloud structure well only above this limit.

Figure: Δ-variance spectra for the turbulent velocity field of H₂ and CO density models at n₀ = 100 cm⁻³ and 512³ resolution, computed for centroid velocity maps.

Centroid Velocity Statistics of Molecular Clouds

We employ the Δ-variance analysis and study the turbulent gas dynamics of simulated molecular clouds with simplified time-dependent chemistry. We find slopes for the linewidth-size relation ranging from 0.4 to 0.7 for total and H₂ density models, while slopes for CO tracers range from 0.2 to 0.4 — underestimating the values for total and H₂ density by a factor of 1.5–3.0. Optical depth effects can significantly alter the Δ-variance spectra, and we report a critical density threshold of ~100 cm⁻³ for the CO tracers.

Figure: Δ-variance spectra for the turbulent velocity field of H₂ and CO density models, computed for centroid velocity maps.

Principal Component Analysis of Molecular Clouds: Can CO reveal the dynamics?

We use Principal Component Analysis (PCA) to study gas dynamics in numerical simulations of typical MCs, including non-isothermal gas and time-dependent chemistry. We consider mean number densities n₀ = 30, 100, 300 cm⁻³ and investigate the PCA slope for total density, H₂ density, ¹²CO density, and CO intensities. Power-law indices range from 0.5 to 0.9, in good agreement with observations. The method can fail if the CO distribution is very intermittent, e.g. in low-density clouds where CO is confined to small fragments.

Figure: Integrated intensity maps for ¹²CO for different times and turbulent velocity fields for models n100 and n300.

Statistical analysis of the mass-to-flux ratio in turbulent cores: effects of magnetic field reversals and dynamo amplification

We study the mass-to-flux ratio (M/Φ) of clumps and cores in simulations of supersonic magnetohydrodynamical turbulence for different initial magnetic field strengths. We investigate whether R = (M/Φ)_core/(M/Φ)_envelope can distinguish between theories of ambipolar diffusion and turbulence-regulated star formation. Average values of |R| are typically close to unity. We propose two mechanisms for generating |R| ~ 1: in the weak field limit the small-scale turbulent dynamo increases flux in the core; in the strong field limit, field reversals in the envelope lead to |R| ~ 1.

Figure: Logarithmic column density map for plasma beta = 0.01 (very strong field) with positions of 40 density peaks and their envelope diameters.