Characteristic Scale Research Articles

Computational integration and experimental validation of a two-length scale model for accurate prediction of steels’ plastic behavior during phase transformation

Transformation plasticity, essential during solid–solid phase transitions, significantly impacts industrial processes like welding and quenching. Accurately simulating these procedures necessitates understanding thermal, metallurgical, and mechanical effects. Leblond et al.’s model offers a foundation, but refinement for mixed isotropic/kinematic hardening is crucial. We enhance this model by introducing characteristic length scales through nonlocal variables, illuminating plastic deformation mechanisms in both phases. Our work includes numerical implementation within a finite element analysis framework and practical applications to phase transformation scenarios involving A.508 cl. 3 and A533 low-alloy steels. Results affirm model robustness and efficiency in predicting phase transformation phenomena, benefiting industrial applications.

On the importance of slow ions in the kinetic Bohm criterion

Between a plasma and a solid target lies a positively charged sheath of several Debye lengths $\lambda _{D}$ width, typically much smaller than the characteristic length scale $L$ of the main plasma. This scale separation implies that the asymptotic limit $\epsilon = \lambda _{D} / L \rightarrow 0$ is useful to solve for the plasma-sheath system. In this limit, the Bohm criterion must be satisfied at the sheath entrance. A new derivation of the kinetic criterion, admitting a general ion velocity distribution, is presented. It is proven that, for $\epsilon \rightarrow 0$ , the distribution of the velocity component normal to the target, $v_x$ , and its first derivative must vanish for $|v_x| \rightarrow 0$ at the sheath entrance. These two conditions can be subsumed into a third integral one after it is integrated by parts twice. A subsequent interchange of the limits $\epsilon \rightarrow 0$ and $|v_x| \rightarrow 0$ is invalid, leading to a divergence which underlies the misconception that the criterion gives undue importance to slow ions.

Multi-physics metasurface with reduced characteristic scales simultaneously for microwave，infrared and acoustic compatibility

Multi-physics metasurface with reduced characteristic scales simultaneously for microwave，infrared and acoustic compatibility

A revised elastic-plastic contact model of cycloidal pinwheel based on length scale

This study explores the relationship between surface roughness and characteristic scale through theoretical analyses and experimental data. Considering the concavity and convexity of cycloidal gear tooth profile curvatures, a curved surface contact coefficient model suitable for both inner and outer contacts, with either equal or unequal curvatures, has been developed. Moreover, a fractal contact model is constructed for cycloidal pinwheels. This model considers scale correlation and analyzes the influence of microscopic parameters on the elastic-plastic critical grade and the behavior of the contact area. Additionally, the influence of the micro-convex body frequency index on surface contact performance is explored to provide theoretical insights for improving the elastic contact ratio and reducing wear on contact surfaces.

Forecasts and Statistical Insights for Line Intensity Mapping Cross-correlations: A Case Study with 21 cm × [C ii]

Intensity mapping—the large-scale mapping of selected spectral lines without resolving individual sources—is quickly emerging as an efficient way to conduct large cosmological surveys. Multiple surveys covering a variety of lines (such as the hydrogen 21 cm hyperfine line, carbon-monoxide rotational lines, and [C ii] fine-structure lines, among others) are either observing or will soon be online, promising a panchromatic view of our Universe over a broad redshift range. With multiple lines potentially covering the same volume, cross-correlations have become an attractive prospect, both for probing the underlying astrophysics and for mitigating observational systematics. For example, cross-correlating 21 cm and [C ii] intensity maps during reionization could reveal the characteristic scale of ionized bubbles around the first galaxies, while simultaneously providing a convenient way to reduce independent foreground contaminants between the two surveys. However, many of the desirable properties of cross-correlations in principle emerge only under ideal conditions, such as infinite ensemble averages. In this paper, we construct an end-to-end pipeline for analyzing intensity mapping cross-correlations, enabling instrumental effects, foreground residuals, and analysis choices to be propagated through Monte Carlo simulations to a set of rigorous error properties, including error covariances, window functions, and full probability distributions for power-spectrum estimates. We use this framework to critically examine the applicability of simplifying assumptions such as the independence and Gaussianity of power-spectrum errors. As worked examples, we forecast the sensitivity of near-term and futuristic 21 cm × [C ii] cross-correlation measurements, providing recommendations for survey design.

Dissipation at limited resolutions: power law and detection of hidden dissipative scales

Abstract Non-equilibrium systems, in particular, living organisms, are maintained by irreversible transformations of energy that drive diverse functions. Quantifying their irreversibility, as measured by energy dissipation, is essential for understanding the underlying mechanisms. However, existing techniques usually overlook experimental limitations, either by assuming full information or by employing a coarse-graining method that requires knowledge of the structure behind hidden degrees of freedom. Here, we study the inference of dissipation from finite-resolution measurements by employing a recently developed model-free estimator that considers both the sequence of coarse-grained transitions and the waiting time distributions: σ 2 = σ 2 ℓ + σ 2 t . The dominant term σ 2 ℓ originates from the sequence of observed transitions. We find that it scales with resolution following a power law. Comparing the scaling exponent with a previous estimator highlights the importance of accounting for flux correlations at lower resolutions. σ 2 t comes from asymmetries in waiting time distributions. It is non-monotonic in resolution, with its peak position revealing characteristic scales of the underlying dissipative process, consistent with observations in the actomyosin cortex of starfish oocytes. Alternatively, the characteristic scale can be detected in a crossover of the scaling of σ 2 ℓ . This provides a novel perspective for extracting otherwise hidden characteristic dissipative scales directly from dissipation measurements. We illustrate these results in biochemical models as well as complex networks. Overall, this study highlights the significance of resolution considerations in non-equilibrium systems, providing insight into the interplay between experimental resolution, entropy production and underlying complexity.

Revealing membrane integrity and cell size from diffusion kurtosis time dependence.

The nonmonotonic dependence of diffusion kurtosis on diffusion time has been observed in biological tissues, yet its relation to membrane integrity and cellular geometry remains to be clarified. Here we establish and explain the characteristic asymmetric shape of the kurtosis peak. We also derive the relation between the peak time , when kurtosis reaches its maximum, and tissue parameters. The peak shape and its position qualitatively follow from the adiabatic extension of the Kärger model onto the case of intra-cellular diffusivity time-dependence. This intuition is corroborated by the effective medium theory-based calculation, as well as by Monte Carlo simulations of diffusion and exchange in randomly and densely packed spheres for various values of permeability, cell fractions and sizes, and intrinsic diffusivity. We establish that is proportional to the geometric mean of two characteristic time scales: extra-cellular correlation time (determined by cell size) and intra-cellular residence time (determined by membrane permeability). When exchange is barrier-limited, the peak shape approaches a universal scaling form determined by the ratio . Numerical simulations and theory provide an interpretation of a specific feature of kurtosis time-dependence, offering a potential biomarker for in vivo evaluation of pathology by disentangling the functional (permeability) and structural (cell size) integrity in tissues. This is relevant as the time-dependent diffusion cumulants are sensitive to pathological changes in membrane integrity and cellular structure in diseases, such as ischemic stroke, tumors, and Alzheimer's disease.

Characterization of rapeseed protein supramolecular structures obtained by aqueous extractions

Aqueous extraction of rapeseed has the potential to produce mildly refined yet functional protein ingredients. However, the colloidal structures of these mildly refined ingredients are still not fully understood. Therefore, the aim of this work was to examine the structures present in rapeseed extracts by analyzing their scattering characteristics across different length scales. Rapeseed protein concentrates were obtained after aqueous extractions at acidic (pH 5.7) or alkaline (pH 8.5) conditions. The structures were investigated using complementary techniques, cryo-transmission electron microscopy, small angle X-ray scattering and small angle neutron scattering. To understand the scattering contribution of various components at characteristic length scales, D2O contrast variation was performed, and SAXS analysis for extracts at pH 5.7 treated with pectinase were compared to those untreated. All suspensions contained globular proteins within a network of soluble polysaccharides as observed by Cryo-TEM. SANS analysis with different D2O/H2O ratios demonstrated that at low q, both proteins and polysaccharide contributed to scattering, suggesting the presence of large complexes containing both. The signal for pH 8.5 suspensions was mainly attributed to oleosomes. SAXS measurements agreed with the SANS data, and pH 5.7 suspensions measured after pectin hydrolysis revealed that the complexes were formed by rapeseed globulins (∼4 nm) and polysaccharide chains. This research highlights the importance of understanding the protein-polysaccharide interactions occurring in rapeseed aqueous extracts, to fully utilize these less refined fractions as value-added ingredients in future sustainable foods.

Additively-manufactured shear tri-coaxial rocket injector mixing and combustion characteristics

A monolithic tri-coaxial propellant injection scheme for enhanced mixing of methane-oxygen in liquid-propellant rocket systems is enabled by additive manufacturing. Mixing and combustion characteristics of the tri-coaxial design are assessed experimentally from 1–69 bar using laser absorption tomography and chemiluminescence imaging, and are compared to a traditionally-manufactured bi-coaxial design. Quantitative two-dimensional images of temperature and carbon monoxide mole fraction are generated from the laser absorption spectroscopy methods, while OH* chemiluminescence provides an approximate metric for combustion heat release defining flame length and injector standoff distance. At similar pressures and oxidizer-to-fuel ratios, the tri-coaxial injector design is shown to enhance mixing and combustion progress, reducing characteristic mixing length scales and achieving improved combustion performance relative to more conventional bi-coaxial designs. Despite enhanced mixing, the tri-coaxial design exhibits more limited reduction in flame standoff distance from the injector face, suggesting that increased heat flux to the injector face can be managed. The tri-coaxial injector highlights the potential to leverage additive manufacturing to enhance performance and simplify the fabrication of liquid-propellant rocket engines.

Development and Validation of an AI Virtual Streamer Scale for Live-Streaming E-Commerce

In recent years, AI virtual streamers (i.e., digital characters with human-like appearances) have become a pervasive e-commerce phenomenon but remain almost unexplored in the literature on e-commerce marketing. The possible reasons for this deficiency are the vagueness of the AI virtual streamer concept and the lack of a measurement tool. Therefore, this study aimed to conceptualize AI virtual streamers and develop an AI virtual streamer characteristic scale through five stages based on social response theory. Following item generation, measurement refinement, exploratory factor analysis, confirmatory factory analysis and nomological validity, a third-dimensional (persona, anthropomorphism, and interactivity) scale with 10 items was established. Empirical results reveal sound measurement qualities in terms of reliability and validity, and demonstrate its unique position in respect to established marketing concepts. The developed scale has managerial implications for designing and applying virtual humans or avatars, such as virtual employees, virtual spokespersons, virtual idols, and virtual guided tours. This tool also enables future research on virtual live streaming, such as virtual destination live streaming, virtual education live streaming, or virtual live concerts.

Performance degradation modeling of civil aviation engines based on component characteristic map optimization

In order to provide a theoretical basis for the degradation of the air path performance of civil aviation engines at the unit level, the CFM56-3 engine was used as the research object. First, on the basis of using the characteristic map scaling method to obtain the component characteristic equation, the selection process of the scaling reference point of the fan general characteristic map was optimized, and a surface fitting method of the characteristic map was proposed to construct an engine component-level benchmark performance model that meets specific speed conditions under steady-state conditions. Then, by introducing the fault factor to generate the fault coefficient matrix, the deviation of the engine monitoring parameters as the component efficiency decreases was calculated, and compared with the fingerprint map data of the GE training manual, it was verified that the engine steady-state performance model that integrates the fan characteristic map scaling reference point optimization and the characteristic map surface fitting method has good accuracy and use in the analysis of air path performance degradation.

A Branched Convolutional Neural Network for Forecasting the Occurrence of Hazes in Paris Using Meteorological Maps with Different Characteristic Spatial Scales

A Branched Convolutional Neural Network for Forecasting the Occurrence of Hazes in Paris Using Meteorological Maps with Different Characteristic Spatial Scales

Adaptive resolution force probe simulations: Coarse graining in the ideal gas approximation.

The unfolding of molecular complexes or biomolecules under the influence of external mechanical forces can routinely be simulated with atomistic resolution. To obtain a match of the characteristic time scales with those of experimental force spectroscopy, often coarse graining procedures are employed. Here, building on a previous study, we apply the adaptive resolution scheme (AdResS) to force probe molecular dynamics (FPMD) simulations using two model systems as examples: One system is the previously investigated calix[4]arene dimer that shows reversible one-step unfolding, and the other example is provided by a small peptide, a β-alanine octamer in methanol solvent. The mechanical unfolding of this peptide proceeds via a metastable intermediate and, therefore, represents a first step toward a complex unfolding pathway. We show that the average number of native contacts serves as a robust order parameter for the forced unfolding of this small peptide. In addition to increasing the complexity of the relevant conformational changes, we study the impact of the methodology used for coarse graining. Apart from the iterative Boltzmann inversion method, we apply an ideal gas approximation, and therefore, we replace the solvent by a non-interacting system of spherical particles. In all cases, we find excellent agreement between the results of FPMD simulations performed fully atomistically and those of the AdResS simulations also in the case of fast pulling. This holds for all details of the unfolding pathways, such as the distributions of the characteristic forces and also the sequence of hydrogen-bond opening in case of the β-alanine octamer. Therefore, the methodology is very well suited to simulate the mechanical unfolding of systems of experimental relevance.

Effective elasto‐(visco)plastic coefficients of a bi‐phasic composite material with scale‐dependent size effects

We employ the theory of asymptotic homogenization (AH) to study the elasto‐plastic behavior of a composite medium comprising two solid phases, separated by a sharp interface and characterized by mechanical properties, such as elastic coefficients and “initial yield stresses” (i.e., a threshold stress above which remodeling is triggered), that may differ up to several orders of magnitude. We speak of “plastic” behavior because we have in mind a material behavior that, to a certain extent, resembles plasticity, although, for biological systems, it embraces a much wider class of inelastic phenomena. In particular, we are interested in studying the influence of gradient effects in the remodeling variable on the homogenized mechanical properties of the composite. The jump of the mechanical properties from one phase to the other makes the composite highly heterogeneous and calls for the determination of effective properties, that is, properties that are associated with a homogenized “version” of the original composite, and that are obtained through a suitable averaging procedure. The determination of the effective properties results convenient, in particular, when it comes to the multiscale description of inelastic processes, such as remodeling in soft or hard tissues, like bones. To accomplish this task with the aid of AH, we assume that the length scale over which the heterogeneities manifest themselves is several orders of magnitude smaller than the characteristic length scale of the composite as a whole. We identify both a fine‐scale problem and a coarse‐scale problem, each of which characterizes the elasto‐plastic dynamics of the composite at the corresponding scale, and we discuss how they are reciprocally coupled through a transfer of information from one scale to the other. In particular, we highlight how the coarse‐scale plastic distortions influence the fine‐scale problem. Moreover, in the limit of negligible hysteresis effects, we individuate two viscoplastic effective coefficients that encode the information of the two‐scale nature of the composite medium in the upscaled equations. Finally, to deal with a case study tractable semi‐analytically, we consider a multilayered composite material with an initial yield stress that is constant in each phase. Such investigation is meant to contribute to the constitution of a robust framework for devising the effective properties of hierarchical biological media.

Characteristic System Time Scales Can Influence the Collective Sequence Development of Nematically Ordered Copolymers

Characteristic System Time Scales Can Influence the Collective Sequence Development of Nematically Ordered Copolymers

Calculation of Dielectric Spectra by Molecular Dynamics: 4-Cyano-4'-hexylbiphenyl in its Nematic Phase.

We employ classical molecular dynamics simulations to predict the experimentally validated dielectric spectra of a bulk 4-cyano-4'-hexylbiphenyl (6CB) system in the nematic phase at temperatures of 300 K and 290 K. We separately analyze the dielectric spectra parallel to the nematic director and perpendicular to it. They show different intensities and different relaxation times, with the parallel relaxation being slower (hundreds of nanoseconds) than the perpendicular (about 1 ns). We investigate various molecular motions as possible mechanisms for the observed macroscopic dielectric behavior by determining their characteristic time scales. We find that the parallel dielectric relaxation is realized by "head-over-heel" flips of 6CB molecules that invert their dipole moment. The perpendicular dielectric relaxation is traced to a combination of the precession of the long molecular axis (dipole axis) around the director and reorientations of the phenylene rings around the long-axis. Dihedral-angle transitions in the n-hexyl tails do not contribute to the dielectric signal.

Zigzag instability of columnar Taylor–Green vortices in a strongly stratified fluid

We investigate the dynamics of a columnar Taylor–Green vortex array under strong stratification, focusing on Froude numbers $0.125\leq Fr \leq 1.0$ , with the aim of identifying and understanding the primary instabilities that lead to the vortices’ breakdown. Linear stability analysis reveals that the fastest-growing vertical wavenumber scales with $Fr^{-1}$ , while the dimensionless growth rate remains approximately constant. The most unstable eigenmode, identified as the mixed hyperbolic mode by Hattori et al. (J. Fluid Mech., vol. 909, 2021, A4), bears significant similarities to the zigzag instability, first discovered by Billant & Chomaz (J. Fluid Mech., vol. 418, 2000, pp. 167–188). Direct numerical simulations further confirm that the zigzag instability is crucial in amplifying initial random perturbations to finite amplitude, with the flow structure and modal growth rate consistent with the linear stability analysis. In particular, the characteristic vertical length scale of turbulence matches that of the fastest-growing linear mode. These findings underscore the broader relevance of the zigzag instability mechanism beyond its initial discovery in vortex pairs, demonstrating its role in facilitating direct energy transfer from vertically uniform vortical motions to a characteristic vertical length scale proportional to $Fr$ in strongly stratified flows.

How to infer ocean freezing rates on icy satellites from measurements of ice thickness

Abstract Liquid-water oceans likely underlie the ice shells of Europa and Enceladus, but ocean properties are challenging to measure due to the overlying ice. Here, we consider gravity-driven flow of the ice shells of icy satellites and relate this to ocean freeze and melt rates. We employ a first-principles approach applicable to conductive ice shells in a Cartesian geometry. We derive a scaling law under which ocean freeze/melt rates can be estimated from shell-thickness measurements. Under a steady-state assumption, ocean freeze/melt rates can be inferred from measurements of ice thickness, given a basal viscosity. Depending on a characteristic thickness scale and basal viscosity, characteristic freeze/melt rates range from around O(10−1) to O(10−5) mm/year. Our scaling is validated with ice-penetrating radar measurements of ice thickness and modelled snow accumulation for Roosevelt Island, Antarctica. Our model, coupled with observations of shell thickness, could help estimate the magnitudes of ocean freeze/melt rates on icy satellites.

Liquid fuel cloud detonation and droplet lifetime

The structures and mechanisms of aerosolized liquid-fuel cloud detonations are studied in a detonation facility using simultaneous high-speed optical diagnostics. The characteristic length scale of the droplet lifetime in liquid fuel detonations is not well predicted by established breakup and evaporation models, whereas it captured by calculations of the evaporation time of the droplet cloud. Novelty and significance statementDetonation research has mostly focused on gaseous fuels with limited investigations of purely liquid fueled detonations. This research explores the characteristic length scales of aerosolized liquid fuel droplets’ lifetime showing it does not scale with established breakup and evaporation models. It scales well with the evaporation time of child droplet clouds, highlighting the significance.

Highlighting the effects of gravity in a compact thermoacoustic heat pump

We present a numerical study of gravity impact on thermoacoustic heat pumping effects in a compact cavity used as a refrigeration device. More precisely, we show how gravity acts on the temperature distribution, on the mean temperature heat flux along the stack area and on flow dynamics. Studies are performed in a two-dimensional geometrical configuration which is simplified with respect to common experimental devices but sufficiently detailed to take into account the main physical mechanisms. Fluid motion, heat and mass transfer as well as compression/expansion effects are estimated from the computation of the Navier-Stokes equations in the low-Mach number hypothesis coupled with the heat equation in solid parts. The low-Mach number hypothesis is here relevant because the characteristic scale of the acoustic wavelength is much smaller than the geometrical length scales of the cavity. The operating mode is characterized by a moderate drive ratio, a fluid oscillating motion of moderate amplitude and fixed low frequency, typical of such devices. It is shown that when gravity is included, buoyancy effects modify the temperature and velocity fields as well as heat pumping efficiency.