Technical University of Darmstadt

We consider elliptic transmission problems in several space dimensions near an interface which is C 1,1 -diffeomorphic to an axisymmetric reference interface with a singular point of cusp type. We establish the regularity of the gradient and of the Hessian in L p spaces up to the cusp point for local weak solutions. We obtain regularity thresholds which are different according to whether the cusp is inward or outward to the subdomain, and which depend explicitly on the opening of the interface at the cusp. Our results allow for source terms in the bulk and on the interface.

This paper presents a digital-twin-based model predictive control framework for autonomous process control, demonstrated in a virtual experiment on thermal food processing in a convection oven. In combination with prior work, this approach enables simulation-centered food scientists to deploy physics-based simulation models in live process control environments. The digital twin is realized as a physics-based, data-driven reduced-order model (ROM) that provides faster-than-real-time predictions. The ROM is trained on trajectories from a high-fidelity multiphysics finite-element model of chicken fillets. A central contribution is a model predictive control scheme that overcomes the common fixed-initial-condition limitation of augmented neural ordinary differential equation ROMs: a dedicated sub-optimization step re-synchronizes the surrogate to the measured state of the food item at each control instant, allowing reliable live re-optimization without access to internal ROM states. The controller optimizes oven temperature setpoints to meet target food-quality metrics (core temperature, moisture content, texture) and autonomously accommodates changes to the planned end time during operation. Quantitatively, the ROM achieves relative time-series errors of 0.18–0.49%, and the control algorithm evaluates 501 trajectories of 1800 s real time in a total of 46.6 s on a single core of a processor, demonstrating on-device feasibility without cloud or edge resources. Receding-horizon model predictive control of the remaining setpoints mitigates model–reality mismatch, enforces user-defined food metrics, and sustains closed-loop performance under autonomous operation. • Software-agnostic pipeline to deploy digital-twin surrogates for online control. • Accurate, faster-than-real-time predictions enable autonomous operation. • Online sub-optimization re-synchronizes predictions to measured core temperature. • Level 5 autonomy case beyond the trained time window. • On-device digital twin operation possible without cloud or edge resources.

We study the global geometry of families of tubes of constant mean curvature invariant under screw-motions in homogeneous E ( κ , τ ) -spaces. In particular, we study embeddedness and prove a foliation result. Moreover, we numerically analyze the isoperimetric profile in the compact case. • We prove existence of a continuous family of CMC tubes around any screw motion geodesic in E ( κ , τ ) , that converges to this geodesic. • For κ > 0 , we prove that a subfamily always foliates an open set of ambient space. In some cases the foliation is global. • For κ ≤ 0 , we prove the embeddedness of some tubes. • Unlike all other tubes previously described in the literature, some of these tubes do not admit a dihedral symmetry of order 4. • For Heisenberg space Nil 3 we proof a partial uniqueness result.

Permanent magnets containing rare earth elements are essential components for the electrification of society. Ce(Co 1-x Cu x ) 5 permanent magnets are a model system known for their substantial coercivity, yet the underlying mechanism remains unclear. Here, we investigate Ce(Co 0.8 Cu 0.2 ) 5.4 magnets with a coercivity of ∼1 T. Using transmission electron microscopy (TEM) and atom probe tomography (APT), we identify a nanoscale cellular structure formed by spinodal decomposition. Cu-poor cylindrical cells (∼5-10 nm in diameter, ∼20 nm long) have a disordered CeCo 5 -type structure and a composition Ce(Co 0.9 Cu 0.1 ) 5.3 . Cu-rich cell boundaries are ∼ 5 nm thick and exhibit a modified CeCo 5 structure, with Cu ordered on the Co sites and a composition Ce(Co 0.7 Cu 0.3 ) 5.0 . Micromagnetic simulations demonstrate that the intrinsic Cu concentration gradients up to 12 at.% Cu/nm lead to a spatial variation in magnetocrystalline anisotropy and domain wall energy, resulting in effective pinning and high coercivity. Compared to Sm 2 Co 17 -type magnets, Ce(Co 0.8 Cu 0.2 ) 5.4 displays a finer-scale variation of conventional pinning with lower structural and chemical contrast in its underlying nanostructure. The identification of nanoscale chemical segregation in nearly single-phase Ce(Co 0.8 Cu 0.2 ) 5.4 magnets provides a microstructural basis for the long-standing phenomenon of "giant intrinsic magnetic hardness" in systems such as SmCo 5-x M x , highlighting avenues for designing rare-earth-lean permanent magnets via controlled nanoscale segregation.

Critical-size femoral defects in rats are a well-established model for preclinical bone regeneration research. Histological evaluation is essential for assessing healing but remains time-consuming and subject to observer variability. Machine learning, particularly convolutional neural networks (CNNs), offers potential for objective and scalable analysis of histological sections. We developed a modified U-Net model to perform semantic segmentation and classification of bone healing stages based on Movat pentachrome-stained histological sections (n=669). Five tissue classes (bone, cartilage, bone marrow, granulation tissue, background) were manually annotated to train the model. Data were split into training (64%), validation (16%), and test (20%) sets. The model then was used to segment and rank histological images. In addition, a subset of 20 independent test images was scored by four orthopedic experts, seven medical students, and the AI using a refined bone healing score ranging from -10 to +10. The model achieved high segmentation performance, particularly for bone and background. AI-generated healing scores showed strong correlation with expert ratings (Spearman r=0.819, p<0.0001) and similar accuracy to student ratings (mean absolute deviation: AI=0.468 vs. students=0.469; p=0.5753). ICC analysis confirmed excellent agreement between AI and experts (ICC=0.820) and revealed a significant difference favoring AI over students (bootstrap p=0.0466). This study introduces a CNN-based model capable of expert-level performance in the histological assessment of bone healing. It offers a reproducible and time-efficient tool for future preclinical applications.

Lipid transfer proteins (LTPs) maintain the specialized lipid compositions of organellar membranes1,2. In humans, many LTPs are implicated in diseases3, but the cargo and auxiliary lipids that facilitate the transfer of the majority of LTPs remain unknown. Here we combined biochemical, lipidomic and computational methods to systematically characterize LTP-lipid complexes4 and measure how LTP gains of function affect cellular lipidomes. We identified bound lipids for around half of the hundreds of LTPs that we analysed, confirming known ligands and identifying new ones across most LTP families. Gains in LTP function affected the cellular abundance of both their known and newly identified lipid ligands, indicating comparable functional relevance of the two ligand sets. Using structural bioinformatics, we characterized mechanisms that contribute to lipid selectivity and identified preferences based on headgroup or acyl chain. We demonstrate some basic principles of how LTPs mobilize their ligands. They commonly interact with several classes of lipids and exhibit broad but selective preference for particular headgroups and for lipid species with shorter acyl chains that contain one or two unsaturated carbons, suggesting that only subsets of lipid species are efficiently mobilized. The datasets represent a resource for further analysis in different cell types and states, such as those associated with pathologies.