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The hydrostatic Lagrangian approach to the compressible primitive equations
Get PDFThis article develops the hydrostatic Lagrangian approach to the compressible primitive equations. A fundamental aspect in the analysis is the investigation of the compressible hydrostatic Lamé and Stokes operators. Local strong well-posedness for large data and global strong well-posedness for small data are established under various assumptions on the pressure law, both in the presence and absence of gravity
Prevailing triaxial shapes in atomic nuclei and a quantum theory of rotation of composite objects
No full textVirtually any object can rotate: the rotation of a rod or a linear molecule appears evident, but a number of objects, including a simple example of H₂O molecule, are of complex shapes and their rotation is of great interest. For atomic nuclei, rotational bands have been observed in many nuclei, and their basic picture is considered to have been established in the 1950s. We, however, show that there may be substantial changes in the basic picture of nuclear rotation: In the traditional view, as stressed by Aage Bohr in his Nobel lecture with an example of ¹⁶⁶Er nucleus, a large fraction of heavy (mass number A>150) nuclei are like axially-symmetric prolate ellipsoids (i.e., with two shorter axes of equal length), rotating about one of the short axes, like a rod. In an alternative picture, however, the lengths of these three axes are all different, called triaxial. The triaxial shape yields more complex rotations. This alternative picture was also discussed in the past, but has not been recognized as a major picture. We show that substantially triaxial shapes occur in a large number of heavy deformed nuclei. Such prevailing triaxiality results in salient descriptions of experimental data over many nuclei, as confirmed by state-of-the-art Configuration Interaction calculations. Two origins are suggested for the triaxiality in the heavy deformed nuclei: (i) binding-energy gain by the symmetry restoration for triaxial shapes, and (ii) another gain by specific components of the nuclear force, like tensor force and high-multipole (e.g. hexadecupole) central force. While the origin (i) produces small triaxiality for virtually all deformed nuclei, the origin (ii) produces medium triaxiality for a certain class of nuclei. An example of the former is ¹⁵⁴Sm, a typical showcase of axial symmetry but is now suggested to depict a small yet finite triaxiality. The medium triaxiality is discussed from various viewpoints for some exemplified nuclei including ¹⁶⁶Er, and experimental findings, for instance, those by multiple Coulomb excitations decades ago, are re-evaluated to be supportive of the medium triaxiality. Many-body structures of the γ band and the double-γ band are clarified, and the puzzles over them are solved. The well-known J(J + 1) - K² formula of rotational excitation energies, which was derived by Taylor expansion in the past, is derived in an alternative way with polynomial property, including the previous work as an approximation. The rotational states of strongly and triaxially deformed heavy nuclei are described within quantum many-body framework, with K quantum number shown to be practically conserved. Thus, two long-standing open problems for strongly deformed heavy nuclei, (i) occurrence and origins of triaxial shapes and (ii) quantum many-body description of their rotational bands classified by K quantum number are solved. The picture of prevailing triaxial shapes thus emerges, where the empirically known rotational-band pattern appears with good K quantum number, but the internal structure is different from conventional picture à la A. Bohr. As a feasible experimental approach to the triaxiality of the 0⁺ ground state, the Relativistic Heavy-Ion Collision is mentioned. Davydov’s claim of triaxial shapes over many nuclei and the validity of his rigid-triaxial-rotor model are separately assessed with high appreciation of the former
Combined parameter and shape optimization of electric machines with isogeometric analysis
No full textIn structural optimization, both parameters and shape are relevant for the model performance. Yet, conventional optimization techniques usually consider either parameters or the shape separately. This work addresses this problem by proposing a simple yet powerful approach to combine parameter and shape optimization in a framework using Isogeometric Analysis (IGA).The optimization employs sensitivity analysis by determining the gradients of an objective function with respect to parameters and control points that represent the geometry. The gradients with respect to the control points are calculated in an analytical way using the adjoint method, which enables straightforward shape optimization by altering these control points. Given that a change in a single geometry parameter corresponds to modifications in multiple control points, the chain rule is employed to obtain the gradient with respect to the parameters in an efficient semi-analytical way.The presented method is exemplarily applied to nonlinear 2D magnetostatic simulations featuring a permanent magnet synchronous motor and compared to designs, which were optimized using parameter and shape optimization separately. It is numerically shown that the permanent magnet mass can be reduced and the torque ripple can be eliminated almost completely by simultaneously adjusting rotor parameters and shape. The approach allows for novel designs to be created with the potential to reduce the optimization time substantially
Entwicklung von effizienten genetischen Werkzeugen für Vibrio natriegens
No full textAktuell werden in der Biotechnologie nur wenige gut erforschte Mikroorganismen eingesetzt, um beispielsweise Pharmazeutika herzustellen. Die verwendeten Organismen stellen daher nur einen verschwindend geringen Anteil der biologischen Vielfalt dar, was mögliche Anwendungsbereiche begrenzt. Aus diesem Grund ist die Etablierung von neuen Produktionsorganismen ein wichtiges Forschungsfeld
Elucidating linear programs by neural encodings
No full textLinear Programs (LPs) are one of the major building blocks of AI and have championed recent strides in differentiable optimizers for learning systems. While efficient solvers exist for even high-dimensional LPs, explaining their solutions has not received much attention yet, as explainable artificial intelligence (XAI) has mostly focused on deep learning models. LPs are mostly considered white-box and thus assumed simple to explain, but we argue that they are not easy to understand in terms of relationships between inputs and outputs. To mitigate this rather non-explainability of LPs we show how to adapt attribution methods by encoding LPs in a neural fashion. The encoding functions consider aspects such as the feasibility of the decision space, the cost attached to each input, and the distance to special points of interest. Using a variety of LPs, including a very large-scale LP with 10k dimensions, we demonstrate the usefulness of explanation methods using our neural LP encodings, although the attribution methods Saliency and LIME are indistinguishable for low perturbation levels. In essence, we demonstrate that LPs can and should be explained, which can be achieved by representing an LP as a neural network
Theologie an der Uni
Get PDFDas »Institut für Theologie und Sozialethik« feiert in diesem Jahr sein 40-jähriges Bestehen im Fachbereich Gesellschafts- und Geschichtswissenschaften. Ein Rückblick im Zeitraffer
Influence of Surface Damage on Weld Quality and Joint Strength of Collision-Welded Aluminium Joints
Get PDFCollision welding represents a promising solid-state joining technique for combining both similar and dissimilar metals without the thermal degradation of mechanical properties typically associated with fusion-based methods. This makes it particularly attractive for lightweight structural applications. In the context of collision welding, it is typically assumed that ideally smooth and defect-free surface conditions exist prior to welding. However, this does not consistently reflect industrial realities, where surface imperfections such as scratches are often unavoidable. Despite this, the influence of such surface irregularities on weld integrity and quality has not been comprehensively investigated to date. In this study, collision welding is applied to the material combination of AA6110A-T6 and AA6060-T6. Initially, the process window for this material combination is determined by systematically varying the collision velocity and collision angle—the two primary process parameters—using a special model test rig. Subsequently, the effect of surface imperfections in the form of defined scratch geometries on the resulting weld quality is investigated. In addition to evaluating the welding ratio and tensile shear strength, weld quality is assessed through scanning electron microscopy (SEM) of the bonding interface and high-speed imaging of jet formation during the collision process
Banking market consolidation in Asia: Evidence from acquirers, targets, and rivals
Get PDFWe analyse the financial sector consolidation in Asia by using a comprehensive sample of bank M&As from 1995 to 2021. Our results show that M&A announcements by Asian domestic acquirers are associated with significant positive stock price returns to both acquirers and their rivals. In contrast, cross‐border acquirers and their rivals experience negative but insignificant returns, while targets and their rivals record gains, regardless whether it is a domestic or cross‐border transaction. Further analyses reveal that domestic acquirers obtaining larger relative increases in their market share benefit the most, indicating that market power considerations are the primary driver behind acquirers' positive returns. For cross‐border acquirers, neither cultural differences nor regulatory arbitrage considerations can explain return patterns surrounding M&A announcements
The three limits of the hydrostatic approximation
No full textThe primitive equations are derived from the 3D Navier–Stokes equations by the hydrostatic approximation. Formally, assuming an ε‐thin domain and anisotropic viscosities with vertical viscosity νz=O(εᵞ) where γ=2, one obtains the primitive equations with full viscosity as ε→0. Here, we take two more limit equations into consideration: For γ2 the primitive equations with only horizontal viscosity −ΔH as ε→0. Thus, there are three possible limits of the hydrostatic approximation depending on the assumption on the vertical viscosity. The latter convergence has been proven recently by Li, Titi, and Yuan using energy estimates. Here, we consider more generally νz=ε²δ and show how maximal regularity methods and quadratic inequalities can be an efficient approach to the same end for ε,δ→0. The flexibility of our methods is also illustrated by the convergence for δ→∞ and ε→0 to the 2D Navier–Stokes equations
Data‐Driven Design of Mechanically Hard Soft Magnetic High‐Entropy Alloys
Get PDFThe design and optimization of mechanically hard soft magnetic materials, which combine high hardness with magnetically soft properties, represent a critical frontier in materials science for advanced technological applications. To address this challenge, a data‐driven framework is presented for exploring the vast compositional space of high‐entropy alloys (HEAs) and identifying candidates optimized for multifunctionality. The study employs a comprehensive dataset of 1 842 628 density functional theory calculations, comprising 45 886 quaternary and 414 771 quinary equimolar HEAs derived from 42 elements. Using ensemble learning, predictive models are integrated to capture the relationships between composition, crystal structure, mechanical, and magnetic properties. This framework offers a robust pathway for accelerating the discovery of next‐generation alloys with high hardness and magnetic softness, highlighting the transformative impact of data‐driven strategies in material design