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Asymptotics on the dynamics of the hanging chain pendulum
No full textThe dynamics of a hanging chain pendulum, long treated as a textbook problem in classical mechanics, are revisited from a fresh and rigorous analytical perspective. By systematically deriving and comparing the continuum and discrete formulations, subtle but significant differences in the vibrational spectrum, particularly in the high-frequency regime are uncovered. Using asymptotic expansions, boundary layer theory, and matched scaling arguments, a comprehensive description of the eigenmodes and their scaling behavior is developed. In the discrete model, we reveal a striking two-regime structure: low-frequency modes governed by Bessel-type equations, and high-frequency modes localized near the free end, described by Airy-type asymptotics. The transition between these regimes emerges naturally from a balance of competing terms in the governing equations, yielding a characteristic crossover scaling. This analysis clarifies the limitations of discrete and continuum approximations and exposes the deeper mathematical structure underlying the system. Ultimately, the followed approach provides a dual perspective and case study, demonstrating how rigorous asymptotics bridge discrete and continuum models and yield fresh insight into seemingly well-understood mechanics of the chain pendulum
Unraveling and Sliding of Polypeptide Strands Underlies the Exceptional Toughness of the Triple-Helix Collagen Molecule
No full textFibril-forming tropocollagens (TCs) play an essential role in tissue biomechanics. They are ubiquitous in mammals and other animal tissues, where they provide passive mechanical functions. While molecular dynamics simulations have targeted the mechanics of individual TCs, experimental data on their tensile mechanical properties remain scarce. As a consequence, the link between the unique triple-helix structure of the collagen molecule and macro-mechanical properties of collagenous tissues is not well understood. To close this gap, we have investigated isolated TCs grafted on the tip of atomic force microscopy (AFM) probes as well as adsorbed TC films using a surface force apparatus (SFA). AFM force spectroscopy showed that an individual TC can be stretched without failing to a contour length of up to 900 nm─nearly three times its native length─over thousands of stretching cycles. The molecule was retracted from a strongly adhering mica surface by pulling on one of the α-chains, forcing the triple-helix to unravel. During this process, the α-chains slipped progressively, irreversibly, and almost entirely past each other before being caught by strong physical interactions between overlapping chain ends. SFA measurements showed that strong electrostatic interactions bind TC to mica and prevent TC aggregation, supporting the AFM results. These findings indicate that a controlled slippage mechanism underpins the exceptional toughness of TCs, collagen fibrils, and collagen-rich tissues such as tendons and skin
Refractive Index Mapping below the Diffraction Limit via Single Molecule Localization Microscopy
No full textSingle molecule localization microscopy (SMLM) is a powerful method to image biological samples in three dimensions, below the diffraction limit of light microscopy. Beyond the position of the emitter, the shape of the single-molecule point spread function provides additional information, for example, about the refractive properties of the sample between the emitter and the glass coverslip. Here, we show that the combination of SMLM with atomic force microscopy (AFM) allows mapping of the refractive index of a biological sample at subdiffraction resolution and at a precision only limited by measurement errors of SMLM and AFM. We showcase the method by the determination of the refractive index of isolated single collagen fibrils. Variabilities both in refractive index and the swelling behavior of single fibrils upon drying and rehydration exposed deviations from the ensemble behavior, demonstrating differential hydration of single collagen fibrils. Mapping the refractive index along single collagen fibrils revealed substantial fluctuations at characteristic length scales below 500 nm, which indicates the structural heterogeneity of collagen fibrils at the length scale of single collagen molecules
Determination Problems for Orbit Closures and Matrix Groups
No full textComputational problems concerning the orbit of a point under the action of a matrix group occur throughout computer science, including in program analysis, complexity theory, quantum computation, and automata theory. In many cases the focus extends beyond orbits proper to orbit closures under a suitable topology. Typically one starts from a group and a set of points and asks questions about the orbit closure of the set under the action of the group, e.g., whether two given orbit closures intersect.
In this paper we consider a collection of what we call determination problems concerning matrix groups and orbit closures. These problems begin with a given variety and seek to understand whether and how it arises either as an algebraic matrix group or as an orbit closure. The how question asks whether the underlying group is s-generated, meaning it is topologically generated by s matrices for a given number s. Among other applications, problems of this type have recently been studied in the context of synthesising loops subject to certain specified invariants on program variables.
Our main result is a polynomial-space procedure that inputs a variety and a number s and determines whether the given variety arises as an orbit closure of a point under an s-generated commutative algebraic matrix group. The main tools in our approach are structural properties of commutative algebraic matrix groups and module theory. We leave open the question of determining whether a variety is an orbit closure of a point under an s-generated algebraic matrix group (without the requirement of commutativity)
Mechanical properties and thermal stability of refractory metal-alloyed (Al,V)N-based high-entropy nitrides and oxynitrides
No full textThis study explores the thermal stability and mechanical properties of (Al,V)-based high-entropy sublattice nitride (HESN) and oxynitride (HESON) coatings alloyed with various refractory metals, including Ti, Cr, Mo, W, Hf, and Zr. Through systematic annealing treatments at 800 °C, we examine the influence of alloying elements on the hardness and indentation modulus of these coatings. The results show that coatings alloyed with Ti-Hf-Cr, Ti-Hf-W, Zr-Hf-Cr, and Ti-Cr-W exhibit excellent retention of mechanical properties under prolonged thermal exposure. In particular, the Ti-Hf-W-alloyed (Al,V)N and its oxynitride variant maintain the highest hardness of ∼32 GPa during 50 h vacuum annealing at 800 °C. Conversely, the Cr-Mo-W-alloyed variants exhibit significant degradation and the formation of an Me₂N phase. X-ray diffraction analyses reveal changes in preferred crystallographic orientations and the emergence of fcc-structured domains, influencing mechanical behavior. Despite their thermal degradation, the Cr-Mo-W-alloyed (Al,V)N showed the most promising fracture toughness behavior. The findings highlight the importance of careful selection of alloying elements and compositions to optimize the performance of HESN and HESON coatings for high-temperature applications. This research provides valuable insights into the underlying mechanisms affecting the thermal and mechanical properties of advanced coatings, paving the way for future advancements in materials designed for extreme environments
Approach for redefining the damping factor of railway bridges with ballast superstructure: model calibration and guidelines for practical application
No full textTo ensure the compatibility between rolling stock and infrastructure when dynamically assessing railway bridges under high-speed traffic, the damping properties considered in the calculation model significantly influence the predicted acceleration amplitude at resonance. However, due to the normative specifications of EN 1991-2, which are considered to be overly conservative, damping factors that are far below the actual damping have to be used when predicting vibrations of railway bridges, which means that accelerations at resonance tend to be overestimated to an uneconomical extent. Comparisons between damping factors prescribed by the standard and those identified based on in situ structure measurements always reveal a large discrepancy between reality and regulation. Given this background, this contribution presents a novel approach for defining the damping factor of railway bridges with ballasted tracks, where the damping factor for bridges is mathematically determined based on three different two-dimensional mechanical models. The basic principle of the approach for mathematically determining the damping factor is to separately define and superimpose the dissipative contributions of the supporting structure (including the substructure) and the superstructure. Using the results of a measurement campaign on 15 existing steel railway bridges in the Austrian rail network, the presented mechanical models are calibrated, and by analysing the energy dissipation in the ballasted track, guiding principles for practical application are defined. This guideline is intended to establish an alternative to the currently valid specifications of EN 1991-2, enabling the damping factor of railway bridges to be assessed in a realistic range by mathematical calculation and thus without the need for extensive in situ measurements on the individual structure. In this way, the existing potential of the infrastructure with regard to the damping properties of bridges can be utilised. This contribution focuses on steel bridges, but the mathematical approach for determining the damping factor applies equally to other bridge types (concrete, composite, or filler beam)
Influence of the Rail Vehicle Layout on Efficiency and Railway Operation
Get PDFRailway efficiency is increasingly significant given the competition with road and air transport, where usability of travel time, passenger comfort and operational reliability play key roles. This study investigates the influence of passenger rail vehicle layout on efficiency, focusing on aspects such as passenger changeover time, luggage storage, seating usability and overall comfort. Since 2001, empirical research at TU Wienhas combined extensive passenger observations, surveys of more than 60,000 travellers, detailed luggage measurements and video analyses of over 20,000 boarding and alighting processes, complemented by controlled changeover tests in multiple vehicle layouts. These data informed the development of a calculation model and the TrainOptimizer software to evaluate and optimiselayouts. Findings show that maximisingseating capacity often reduces efficiency by limiting luggage storage, blocking seats and extending changeover times, whereas layouts with fewer but better-positioned seats and distributed luggage racks increase usable capacity and passenger satisfaction. Results also indicate that interior design directly affects time use, stress and well-being during travel. The study concludes that vehicle design has a significant impact on operational performance, energy use and the competitive position of railways, with well-balanced layouts offering both higher efficiency and an enhanced passenger experience
Deconvolution of superimposing reaction signals from DSC curves in selected Al-Mg-Si-(Cu) alloys by mean-field modeling and HEXRD
No full textThe present work describes a systematic approach to improve mean-field simulations of dissolution and precipitation of precipitates from the late stages in the precipitation sequence in AlMgSiCu alloys for processing simulations. In addition to metastable precipitates, it considers the evolution of two populations (coarse and fine) of the thermodynamically stable phases in EN AW-6061 and EN AW-6016, β-Mg2Si and Si respectively. The setup is based on two previous publications using heterogeneous nucleation site energies and their distribution. The simulations are calibrated using data from continuous cooling and heating experiments obtained with differential scanning calorimetry (DSC) and high-energy X-ray diffraction (HEXRD). We show that mean-field simulations combined with DSC and HEXRD can provide valuable information to eliminate uncertainties related to, for instance, the thermodynamic description of metastable precipitates. The method described in this paper also delivers very reasonable results for the evolution of the individual phase fractions. It potentially facilitates the assessment of the influence of different types of nucleation sites and their densities
Quality in the circular economy: What does it mean, and how is it measured?
No full textQuality is increasingly recognized as a critical factor for achieving functional value retention in the circular economy. However, the concept remains poorly defined and inconsistently measured, limiting its integration into circularity assessments. This article develops a typology that distinguishes six types of quality metrics based on two dimensions: the targeted resource state (material, component, or product) and the nature of the quality characteristics assessed (intrinsic or extrinsic). It also identifies three assessment levels (generic, application-specific, and indirect) reflecting how quality is evaluated in practice. To illustrate the typology, existing approaches that quantify changes in resource quality were collected and positioned within the typology. This analysis highlights the diversity of methodological strategies and provides guidance on when to use which type of metric. While no single metric can fully capture the multifaceted nature of resource quality, the typology provides a practical foundation for more consistent quality assessments in circular economy research