arXiv subjects

Erik Bertram

Publications and source records attributed to Erik Bertram.

13 recordsLinked to original sources

arXiv2026

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), which restricts entropy evolution along null directions, we derive a Raychaudhuri-type differential inequality for the generalized expansion that makes its local dependence on expansion and shear explicit. The resulting relation, $\frac{d\Theta}{d\lambda} \le -\theta \Theta + \tfrac{1}{2}\theta^2 - \sigma^2$, reveals a direct interplay between expansion and shear in controlling entropy flow: shear contributes negatively and yields a monotonic suppression of the generalized expansion in shear-dominated regimes, while expansion provides a competing geometric source term. This structure provides a local geometric formulation consistent with the QFC and clarifies its interpretation as a constraint on entropy evolution. We further show that quantum extremal surfaces correspond to configurations characterized by $\Theta=0$, whose local stability properties are governed by the same geometric data. In addition, we derive a bound on the exponential separation of nearby null generators, indicating that the same combination of expansion and shear also controls geometric instability. Our results provide a local geometric refinement of entropy bounds in semiclassical gravity and establish a direct connection between null geometry, quantum energy conditions, and entropy flow, offering a local geometric perspective on horizon thermodynamics beyond global formulations.

gr-qc↗

arXiv2026

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 and organize it in terms of interactions between well-defined scale components. Under suitable smoothness assumptions, we obtain an absolutely convergent triadic expansion and quantitative bounds that distinguish local and nonlocal contributions in scale space. This framework provides a transparent and fully explicit description of how energy transfer is mediated by triadic interactions and how scale locality emerges as a structural property of the nonlinearity. Building on this formulation, we revisit the classical inertial-range picture of turbulence from a deterministic perspective. We show that, under a scale-invariant flux assumption, the Kolmogorov $-5/3$ scaling is formally consistent with the triadic energy-transfer mechanism at a structural level. The result does not rely on statistical assumptions, but instead follows from the structural properties of the Navier-Stokes equations combined with a scale-resolved representation of the energy flux. The present work thus provides a coherent synthesis of triadic interaction analysis, dyadic scale decomposition, and classical turbulence phenomenology, offering a deterministic framework that clarifies how Kolmogorov-type scaling constraints arise in the scale-resolved structure of the underlying equations.

physics.flu-dyn↗

arXiv2026

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, and show that this generically leads to a stable low-efficiency equilibrium with only weak dependence on global cloud properties. We extend the framework by including a phenomenological contribution from gravity-driven turbulence and find that both feedback- and gravity-driven motions converge to similar equilibrium states under typical GMC conditions. The efficiency can be expressed as the ratio between a gravitational velocity scale and an effective feedback velocity scale, providing a physically transparent interpretation of self-regulated star formation. The model provides a simple, physically motivated interpretation of observed gas-star formation scaling relations, including a Schmidt-like scaling at cloud scales and a Kennicutt-like scaling when averaged over cloud populations. Comparison with observed GMC properties shows agreement within a factor of a few and highlights the weak sensitivity of $\epsilon_{\rm ff}$ to cloud parameters. Despite its simplicity, the framework captures the leading-order interplay between turbulence, gravity, and feedback, and provides a physically transparent explanation for the origin and robustness of low star formation efficiencies in GMCs.

astro-ph.SR↗

arXiv2026

The impact of artificial intelligence on enterprise software user roles

Artificial Intelligence (AI) is rapidly reshaping the nature of work in software development, transforming user roles, workflows, and collaboration patterns across enterprise platforms. This qualitative study investigates how AI alters professional responsibilities within the context of SAP's Business Technology Platform (BTP), combining expert interviews (n=20) and a participatory workshop (n=24). The results reveal substantial shifts in day-to-day tasks and roles in the development domain, characterized by increasing automation of operational tasks, expanding human-AI collaboration, and growing reliance on agentic AI systems. The study further identifies significant implications for existing user-role frameworks, such as the BTP User Type Matrix, which requires adaptation as the workforce is undergoing significant role specific changes. Collectively, these findings highlight a workforce landscape in transition and underscore the need for revised role taxonomies, new governance and oversight functions, and updated design approaches for AI-native enterprise software systems.

cs.SE↗

arXiv2026

Integrating Multi-Label Classification and Generative AI for Scalable Analysis of User Feedback

In highly competitive software markets, user experience (UX) evaluation is crucial for ensuring software quality and fostering long-term product success. Such UX evaluations typically combine quantitative metrics from standardized questionnaires with qualitative feedback collected through open-ended questions. While open-ended feedback offers valuable insights for improvement and helps explain quantitative results, analyzing large volumes of user comments is challenging and time-consuming. In this paper, we present techniques developed during a long-term UX measurement project at a major software company to efficiently process and interpret extensive volumes of user comments. To provide a high-level overview of the collected comments, we employ a supervised machine learning approach that assigns meaningful, pre-defined topic labels to each comment. Additionally, we demonstrate how generative AI (GenAI) can be leveraged to create concise and informative summaries of user feedback, facilitating effective communication of findings to the organization and especially upper management. Finally, we investigate whether the sentiment expressed in user comments can serve as an indicator for overall product satisfaction. Our results show that sentiment analysis alone does not reliably reflect user satisfaction. Instead, product satisfaction needs to be assessed explicitly in surveys to measure the user's perception of the product.

cs.HC↗

arXiv2025

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. Despite the improvements on this field, a major obstacle often remains when drawing the right conclusions out of the data and channeling them into the software development process. In this paper we present a practical end-to-end approach of how to extract useful information out of a data set and leverage the information to drive change. We describe how to choose the right metrics to measure, gather appropriate feedback from customer end-users, analyze the data by leveraging methods from inferential statistics, make the data transparent, and finally drive change with the results. Furthermore, we present an example of a UX prototype dashboard that can be used to communicate the analyses to stakeholders within the company.

cs.HC↗

arXiv2015

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

We run numerical simulations of molecular clouds (MCs), adopting properties similar to those found in the Central Molecular Zone (CMZ) of the Milky Way. For this, we employ the moving mesh code Arepo and perform simulations which account for a simplified treatment of time-dependent chemistry and the non-isothermal nature of gas and dust. We perform simulations using an initial density of n_0 = 10^3 cm^{-3} and a mass of 1.3x10^5 M_sun. Furthermore, we vary the virial parameter, defined as the ratio of kinetic and potential energy, alpha = E_{kin} / |E_{pot}|, by adjusting the velocity dispersion. We set it to alpha = 0.5, 2.0 and 8.0, in order to analyze the impact of the kinetic energy on our results. We account for the extreme conditions in the CMZ and increase both the interstellar radiation field (ISRF) and the cosmic-ray flux (CRF) by a factor of 1000 compared to the values found in the solar neighbourhood. We use the radiative transfer code RADMC-3D to compute synthetic images in various diagnostic lines. These are [CII] at 158 micron, [OI] (145 micron), [OI] (63 micron), 12CO (J = 1 -> 0) and 13CO (J = 1 -> 0) at 2600 micron and 2720 micron, respectively. When alpha is large, the turbulence disperses much of the gas in the cloud, reducing its mean density and allowing the ISRF to penetrate more deeply into the cloud's interior. This significantly alters the chemical composition of the cloud, leading to the dissociation of a significant amount of the molecular gas. On the other hand, when alpha is small, the cloud remains compact, allowing more of the molecular gas to survive. We show that in each case the atomic tracers accurately reflect most of the physical properties of both the H2 and the total gas of the cloud and that they provide a useful alternative to molecular lines when studying the ISM in the CMZ.

astro-ph.GA↗

arXiv2015

Star formation efficiencies of molecular clouds in a galactic center environment

We use the Arepo moving mesh code to simulate the evolution of molecular clouds exposed to a harsh environment similar to that found in the galactic center (GC), in an effort to understand why the star formation efficiency (SFE) of clouds in this environment is so small. Our simulations include a simplified treatment of time-dependent chemistry and account for the highly non-isothermal nature of the gas and the dust. We model clouds with a total mass of 1.3x10^5 M_{sun} and explore the effects of varying the mean cloud density and the virial parameter, alpha = E_{kin}/|E_{pot}|. We vary the latter from alpha = 0.5 to alpha = 8.0, and so many of the clouds that we simulate are gravitationally unbound. We expose our model clouds to an interstellar radiation field (ISRF) and cosmic ray flux (CRF) that are both a factor of 1000 higher than the values found in the solar neighbourhood. As a reference, we also run simulations with local solar neighbourhood values of the ISRF and the CRF in order to better constrain the effects of the extreme conditions in the GC on the SFE. Despite the harsh environment and the large turbulent velocity dispersions adopted, we find that all of the simulated clouds form stars within less than a gravitational free-fall time. Increasing the virial parameter from alpha = 0.5 to alpha = 8.0 decreases the SFE by a factor ~4-10, while increasing the ISRF/CRF by a factor of 1000 decreases the SFE again by a factor ~2-6. However, even in our most unbound clouds, the SFE remains higher than that inferred for real GC clouds. We therefore conclude that high levels of turbulence and strong external heating are not enough by themselves to lead to a persistently low SFE at the center of the Galaxy.

astro-ph.SR↗

arXiv2015

Structure analysis of simulated molecular clouds with the Delta-variance

We employ the Delta-variance analysis and study the turbulent gas dynamics of simulated molecular clouds (MCs). Our models account for a simplified treatment of time-dependent chemistry and the non-isothermal nature of the gas. We investigate simulations using three different initial mean number densities of n_0 = 30, 100 and 300 cm^{-3} that span the range of values typical for MCs in the solar neighbourhood. Furthermore, we model the CO line emission in a post-processing step using a radiative transfer code. We evaluate Delta-variance spectra for centroid velocity (CV) maps as well as for integrated intensity and column density maps for various chemical components: the total, H2 and 12CO number density and the integrated intensity of both the 12CO and 13CO (J = 1 -> 0) lines. The spectral slopes of the Delta-variance computed on the CV maps for the total and H2 number density are significantly steeper compared to the different CO tracers. We find slopes for the linewidth-size relation ranging from 0.4 to 0.7 for the total and H2 density models, while the slopes for the various CO tracers range from 0.2 to 0.4 and underestimate the values for the total and H2 density by a factor of 1.5-3.0. We demonstrate that optical depth effects can significantly alter the Delta-variance spectra. Furthermore, we report a critical density threshold of ~100 cm^{-3} at which the Delta-variance slopes of the various CO tracers change sign. We thus conclude that carbon monoxide traces the total cloud structure well only if the average cloud density lies above this limit.

astro-ph.SR↗

arXiv2014

Centroid Velocity Statistics of Molecular Clouds

We compute structure functions and Fourier spectra of 2D centroid velocity (CV) maps in order to study the gas dynamics of typical molecular clouds (MCs) in numerical simulations. We account for a simplified treatment of time-dependent chemistry and the non-isothermal nature of the gas and use a 3D radiative transfer tool to model the CO line emission in a post-processing step. We perform simulations using three different initial mean number densities of n_0 = 30, 100 and 300 cm^{-3} to span a range of typical values for dense gas clouds in the solar neighbourhood. We compute slopes of the centroid velocity increment structure functions (CVISF) and of Fourier spectra for different chemical components: the total density, H2 number density, 12CO number density as well as the integrated intensity of 12CO (J=1-0) and 13CO (J=1-0). We show that optical depth effects can significantly affect the slopes derived for the CVISF, which also leads to different scaling properties for the Fourier spectra. The slopes of CVISF and Fourier spectra for H2 are significantly steeper than those for the different CO tracers, independent of the density and the numerical resolution. This is due to the larger space-filling factor of H2 as it is better able to self-shield in diffuse regions, leading to a larger fractal co-dimension compared to CO.

astro-ph.SR↗

arXiv2014

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

We use Principal Component Analysis (PCA) to study the gas dynamics in numerical simulations of typical MCs. Our simulations account for the non-isothermal nature of the gas and include a simplified treatment of the time-dependent gas chemistry. We model the CO line emission in a post-processing step using a 3D radiative transfer code. We consider mean number densities n_0 = 30, 100, 300 cm^{-3} that span the range of values typical for MCs in the solar neighbourhood and investigate the slope α_{PCA} of the pseudo structure function computed by PCA for several components: the total density, H2 density, 12CO density, 12CO J = 1 -> 0 intensity and 13CO J = 1 -> 0 intensity. We estimate power-law indices α_{PCA} for different chemical species that range from 0.5 to 0.9, in good agreement with observations, and demonstrate that optical depth effects can influence the PCA. We show that when the PCA succeeds, the combination of chemical inhomogeneity and radiative transfer effects can influence the observed PCA slopes by as much as ~ +/- 0.1. The method can fail if the CO distribution is very intermittent, e.g. in low-density clouds where CO is confined to small fragments.

astro-ph.SR↗

arXiv2012

Reliable estimation of the column density in Smoothed Particle Hydrodynamic simulations

We describe a simple method for estimating the vertical column density in Smoothed Particle Hydrodynamics (SPH) simulations of discs. As in the method of Stamatellos et al. (2007), the column density is estimated using pre-computed local quantities and is then used to estimate the radiative cooling rate. The cooling rate is a quantity of considerable importance, for example, in assessing the probability of disc fragmentation. Our method has three steps: (i) the column density from the particle to the mid plane is estimated using the vertical component of the gravitational acceleration, (ii) the "total surface density" from the mid plane to the surface of the disc is calculated, (iii) the column density from each particle to the surface is calculated from the difference between (i) and (ii). This method is shown to greatly improve the accuracy of column density estimates in disc geometry compared with the method of Stamatellos. On the other hand, although the accuracy of our method is still acceptable in the case of high density fragments formed within discs, we find that the Stamatellos method performs better than our method in this regime. Thus, a hybrid method (where the method is switched in regions of large over-density) may be optimal.

astro-ph.IM↗

arXiv2011

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 the (M/Φ)-ratio of core and envelope, R = (M/Φ)_{core}/(M/Φ)_{envelope} can be used to distinguish between theories of ambipolar diffusion and turbulence-regulated star formation. We analyse R for different Lines-of-Sight (LoS) in various sub-cubes of our simulation box. We find that, 1) the average and median values of |R| for different times and initial magnetic field strengths are typically greater, but close to unity, 2) the average and median values of |R| saturate at average values of |R| ~ 1 for smaller magnetic fields, 3) values of |R| < 1 for small magnetic fields in the envelope are caused by field reversals when turbulence twists the field lines such that field components in different directions average out. Finally, we propose two mechanisms for generating values |R| ~< 1 for the weak and strong magnetic field limit in the context of a turbulent model. First, in the weak field limit, the small-scale turbulent dynamo leads to a significantly increased flux in the core and we find |R| ~< 1. Second, in the strong field limit, field reversals in the envelope also lead to values |R| ~< 1. These reversals are less likely to occur in the core region where the velocity field is more coherent and the internal velocity dispersion is typically subsonic.

astro-ph.SR↗