Length Scales Research Articles

Turbulent diffusion and air pollution: A comprehensive review of mechanisms, impacts, and modeling approaches

Turbulent diffusion is often a desirable phenomenon in many contexts, but it also presents significant challenges, particularly in the realm of air pollution. Air pollution, a universally recognized and frowned upon issue, degrades air quality and poses serious long-term health risks. Turbulent flows, characterized by chaotic and random fluid motions, give rise to turbulent diffusion, a process that acts as a transport mechanism for dispersing pollutants in the atmosphere. Despite its inherent complexities, the study of turbulent diffusion has advanced significantly, building on foundational concepts like Osborne Reynolds' decomposition in the 1850s and extending to Kolmogorov's length scale framework. These developments have enabled a deeper understanding of turbulent diffusion and its wide-ranging applications across various fields as new methods are continuously employed to broaden the scope of research and application.

Sheared turbulent flows and wake dynamics of an idled floating tidal turbine

Ocean energy extraction is on the rise. While tides are the most predictable amongst marine renewable resources, turbulent and complex flows still challenge reliable tidal stream energy extraction and there is also uncertainty in how devices change the natural environment. To ensure the long-term integrity of emergent floating tidal turbine technologies, advances in field measurements are required to capture multiscale, real-world flow interactions. Here we use aerial drones and acoustic profiling transects to quantify the site- and scale-dependent complexities of actual turbulent flows around an idled, utility-scale floating tidal turbine (20 m rotor diameter, D). The combined spatial resolution of our baseline measurements is sufficiently high to quantify sheared, turbulent inflow conditions (reversed shear profiles, turbulence intensity >20%, and turbulence length scales > 0.4D). We also detect downstream velocity deficits (approaching 20% at 4D) and trace the far-wake propagation using acoustic backscattering techniques in excess of 30D. Addressing the energy-environment nexus, our oceanographic lens on flow characterisation will help to validate multiscale flow physics around offshore energy platforms that have thus far only been simulated.

Green Synthesis of Catalytic 3D Platinum Nanostructures from a Body‐Centered Cubic Pluronic Micellar Array Template

AbstractOrdered and well‐interconnected 3D electrode nanostructures open up exciting perspectives in catalysis, sensing and energy harvesting. Here, highly ordered 3D nano‐sized Pt mesoporous structures based on the I‐Wrapped Package (I‐WP) architecture with 13.5 nm unit cell size, previously unreported for metal nanomaterials, are presented. The samples are synthetized by soft‐template electrodeposition, using the body‐centred cubic (BCC) lyotropic crystalline micellar phase of Pluronic F68 as the template. The specific surface area of the resulting Pt nanoarchitecture is 36 ± 13 m2 g−1. The oxygen reduction reaction kinetic current is 0.98 mA cm−2; the current density normalized by the electrochemical active surface area and the weight of deposited Pt are 0.92 mA cm−2 and 153.53 A g−1, respectively, showing superior properties than conventional Pt nanostructures produced by surfactant templates. These results suggest a nanostructure based on the topology of the I‐WP minimal surface, representing the first case at this length scale from a metallic material, opening up new research directions in fundamental physics based on predicted thermal and phononic properties for this topology. The water‐based template provides a chemical‐free, eco‐friendly route for ordered mesoporous conductive nanomaterials manufacturing, inspiring future trends in the field.

Dissipation Effects in the Tea Leaf Paradox

The Tea Leaf Paradox (TLP) describes unsteady fluid motions which help entrain and deposit suspended particles at the center of rotation. Various applications depend on the TLP for particle separations—spanning orders of magnitude in length scales—making it an important problem in fluid mechanics. Despite papers describing the phenomenon, the efficacy of particle separation using the TLP remains unclear as to the relative importance of, for example, hydrostatics, particle-fluid density ratio, wall friction, liquid bath aspect ratio and the rotation speed. The dynamics involved are notably complex and require a careful tuning of each variable. In this study, we have investigated the role of the limit of the aggregation dynamics in rotational flows within 3D-printed vessels of various sizes in tandem with particle imaging to probe the dissipation effects on the particle motions. We have found that the liquid bath aspect ratio limits how much aggregation may occur for a particle-fluid density ratio greater than unity (e.g., ρp/ρf>1), where ρp is the density of the particle and ρf is the ambient fluid density.

The impact of turbulent transport efficiency on surface vertical heat fluxes in the Arctic stable boundary layer predicted from similarity theory and machine-learning

Abstract We analyzed 14 days of observations from sonic anemometry and high-resolution fiber optic distributed sensing collected in the stable polar boundary layer (SBL). The study sought to evaluate if and under which conditions the sensible heat flux is related to the temperature gradient. Machine learning methods were employed to identify drivers of and model heat fluxes. We found the recently proposed coupling metric Ω defined as the ratio of the buoyancy length scale and measurement height to delineate physically meaningful transport regimes. The regime transition marks the point where static stability in addition to the vertical turbulence strength control the heat transport, which is rather gradual than abrupt. The maximum downward heat flux is reached when one third of turbulent eddies exceed the opposing buoyancy forces in the SBL. We found evidence that even for large Ω a substantial fraction of the turbulent transport is non-equilibrium. The non-dimensional temperature gradient is better explained by variations in Ω than ζ = zL−1 from Monin-Obukhov Similarity theory. Its continuous organization with Ω across stabilities suggest that the vertical heat transport always remains coupled to the surface, but its efficiency and the resulting flux vary. 43% of the total enthalpy is exchanged during conditions of limited transport efficiency in the very SBL despite the small flux magnitude of ≤ 7 W m−2, which underlines the importance of quantifying the weak surface exchange for polar regions. When predicting sensible heat fluxes using mean quantities from weather stations, the net longwave radiative forcing and the horizontal wind speed are the most important predictors representing stratification and bulk shear.

Observation of quantum entanglement with top quarks at the ATLAS detector

Entanglement is a key feature of quantum mechanics1–3, with applications in fields such as metrology, cryptography, quantum information and quantum computation4–8. It has been observed in a wide variety of systems and length scales, ranging from the microscopic9–13 to the macroscopic14–16. However, entanglement remains largely unexplored at the highest accessible energy scales. Here we report the highest-energy observation of entanglement, in top–antitop quark events produced at the Large Hadron Collider, using a proton–proton collision dataset with a centre-of-mass energy of √s = 13 TeV and an integrated luminosity of 140 inverse femtobarns (fb)−1 recorded with the ATLAS experiment. Spin entanglement is detected from the measurement of a single observable D, inferred from the angle between the charged leptons in their parent top- and antitop-quark rest frames. The observable is measured in a narrow interval around the top–antitop quark production threshold, at which the entanglement detection is expected to be significant. It is reported in a fiducial phase space defined with stable particles to minimize the uncertainties that stem from the limitations of the Monte Carlo event generators and the parton shower model in modelling top-quark pair production. The entanglement marker is measured to be D = −0.537 ± 0.002 (stat.) ± 0.019 (syst.) for 340GeV<mtt¯<380GeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$340\\,{\\rm{GeV}} < {m}_{t\\bar{t}} < 380\\,{\\rm{GeV}}$$\\end{document}. The observed result is more than five standard deviations from a scenario without entanglement and hence constitutes the first observation of entanglement in a pair of quarks and the highest-energy observation of entanglement so far.

Machine learning the electric field response of condensed phase systems using perturbed neural network potentials

The interaction of condensed phase systems with external electric fields is of major importance in a myriad of processes in nature and technology, ranging from the field-directed motion of cells (galvanotaxis), to geochemistry and the formation of ice phases on planets, to field-directed chemical catalysis and energy storage and conversion systems including supercapacitors, batteries and solar cells. Molecular simulation in the presence of electric fields would give important atomistic insight into these processes but applications of the most accurate methods such as ab-initio molecular dynamics (AIMD) are limited in scope by their computational expense. Here we introduce Perturbed Neural Network Potential Molecular Dynamics (PNNP MD) to push back the accessible time and length scales of such simulations. We demonstrate that important dielectric properties of liquid water including the field-induced relaxation dynamics, the dielectric constant and the field-dependent IR spectrum can be machine learned up to surprisingly high field strengths of about 0.2 V Å−1 without loss in accuracy when compared to ab-initio molecular dynamics. This is remarkable because, in contrast to most previous approaches, the two neural networks on which PNNP MD is based are exclusively trained on molecular configurations sampled from zero-field MD simulations, demonstrating that the networks not only interpolate but also reliably extrapolate the field response. PNNP MD is based on rigorous theory yet it is simple, general, modular, and systematically improvable allowing us to obtain atomistic insight into the interaction of a wide range of condensed phase systems with external electric fields.

Variational damage model: A novel consistent approach to fracture

The computational modeling of fractures in solids using damage mechanics faces challenge when dealing with complex crack topologies. One effective approach to address this challenge is by reformulating damage mechanics within a variational framework. In this paper, we present a novel variational damage model that incorporates a threshold value to prevent damage initiation at low energy levels. The proposed model defines fracture energy density (ϕ˜) and damage field (s) based on the energy density (ϕ), crack energy release rate (Gc), and crack length scale (ℓ). Specifically, if ϕ≤Gc2ℓ, then ϕ˜=ϕ and s=0; otherwise, ϕ˜=−Gc24ℓ21ϕ+Gcℓ and s=1−Gc2ℓ1ϕ. Furthermore, we extend the model with a threshold value to a higher-order version. Utilizing this functional, we derive the governing equation for fractures that evolve automatically with ease. The formulation can be seamlessly integrated into conventional finite element methods for elastic solids with minimal modifications. The proposed formulation offers sharper crack interfaces compared to phase field methods using the same mesh density. We demonstrate the capabilities of our approach through representative numerical examples in both 2D and 3D, including static fracture problems, cohesive fractures, and dynamic fractures. The open-source code is available on GitHub via the link https://github.com/hl-ren/vdm.

A hybrid mesoscale-continuum approach to understand and predict melting kinetics of Al powders during laser processing

Abstract Laser interaction with metallic powders during additive manufacturing (AM) leads to fast heating and cooling rates that can affect the quality of the final products due to the formation of defects. One of the first steps towards predicting microstructures generated during AM, therefore, requires an accurate understanding of the laser energy deposition mechanisms that determine the melting kinetics at the level of individual powders. The critical challenge, however, is the availability of computational methods that can model the laser energy absorption, heat transfer, and the related microstructure evolution in individual metal powders at the length and time scales of AM. This manuscript demonstrates the capability of a novel scale-bridging methodology that combines the mesoscale quasi-coarse-grained dynamics (QCGD) simulations with a continuum two-temperature model (TTM) to account for the atomistic mechanisms of laser energy deposition and microstructure evolution and predict the kinetics of melting of individual powders at the experimental time and length scales. The scale-bridging capability of the hybrid QCGD-TTM simulations is demonstrated here by investigating the laser-induced microstructure evolution in aluminum powders with various sizes ranging from 200 nm to 20 µm. The analysis of the evolution of temperature, pressure, phase fraction, and melt fronts suggests the melting mechanism is heterogeneous due to the interaction with a laser, and the melting time is observed to decrease exponentially as the laser intensity increases. The solid-liquid interface velocity can be quantified to identify correlations with interface temperatures, and the predicted values satisfy the theoretically reported limits of crystal stability of metals against homogeneous melting. In addition, the pre-melting is found at the grain boundaries of 20 µm polycrystalline aluminum powder, while a minute contribution to melting is observed. This manuscript demonstrates the capability of the QCGD-TTM method to capture laser-powder interaction and allow the investigation of the kinetics of laser melting.

Establishing coherent momentum-space electronic states in locally ordered materials

Rich momentum-dependent electronic structure naturally arises in solids with long-range crystalline symmetry. Reliable and scalable quantum technologies rely on materials that are either not perfect crystals or non-crystalline, breaking translational symmetry. This poses the fundamental questions of whether coherent momentum-dependent electronic states can arise without long-range order, and how they can be characterized. Here we investigate Bi2Se3, which exists in crystalline, nanocrystalline, and amorphous forms, allowing direct comparisons between varying degrees of spatial ordering. Through angle-resolved photoemission spectroscopy, we show for the first time momentum-dependent band structure with Fermi surface repetitions in an amorphous solid. The experimental data is complemented by a model that accurately reproduces the vertical, dispersive features as well as the replication at higher momenta in the amorphous form. These results reveal that well-defined real-space length scales are sufficient to produce dispersive band structures, and that photoemission can expose the imprint of these length scales on the electronic structure.

Requirements for partial turbulence simulations using nondimensional turbulence energy contributions

Quantifying turbulence effects is crucial for understanding building aerodynamics and for ensuring accurate wind tunnel test methods. This is especially important in wind tunnel methods that require post-experiment adjustments because approximate wind fields are used, such as the Partial Turbulence Simulation (PTS) approach. Understanding and analyzing these effects enables load adjustments since the PTS method only requires matching the high frequency portions of the upstream spectra of the longitudinal velocity component in model and full-scale. However, the limits for which the PTS method is applicable are unclear in terms of the allowable range of wind field characteristics that can be used in the wind tunnel simulation. To address this, the paper utilizes two nondimensional parameters, one representing the small-scale turbulence energy, ES, and the other the large-scale turbulence energy, EL, to elaborate the aerodynamic effects of turbulence intensity and integral length scales in the upstream wind. The results show that the maximum allowable mismatch ratio of integral length scales and of Jensen numbers between model and full-scale simulations depend on the target small-scale turbulence energy and the maximum allowable deviation of small-scale energy. By quantifying the effects of ES and EL on area-averaged pressure coefficients, the allowable limits are identified for wind tunnel test parameters that lead to negligible differences in the resultant pressure coefficient statistics in regions of separated-reattaching flow on the roof of a low-rise building.

The intrinsic distribution of Lyman-alpha halos

The emission and escape of Lyman-alpha photons from star-forming galaxies is determined through complex interactions between the emitted photons and a galaxy's interstellar and circumgalactic gas.\ This causes Lyman-alpha emitters (LAEs) to commonly appear not as point sources but in spatially extended halos with complex spectral profiles. We developed a 3D spatial-spectral model of Lyman-alpha halos (LAHs) to replicate LAH observations in integral field spectroscopic studies, such as those made with VLT/MUSE. The profile of this model is a function of six key halo properties: the halo- and compact-source exponential scale lengths sH $ and $r_ sC $), the halo flux fraction ($f_H$), the compact component ellipticity ($q$), the spectral line width (sigma ), and the spectral line skewness parameter (gamma ). Placing a series of model LAHs into datacubes that reflect observing conditions in the MUSE UDF-Mosaic survey, we tested their detection recoverability and determine that sigma , $r_ sH $, and $f_H$ are expected to have the most significant effect on the detectability of the overall LAH at a given central wavelength and intrinsic line luminosity. We developed a general selection function model that spans a grid of these halo parameters. Using it with a sample of 145 LAHs with measured halo properties observed in the UDF-Mosaic survey, we derived completeness-corrected, intrinsic distributions of the values of sigma , $r_ sH $, and $f_H$ for $3&lt;z&lt;5$ LAHs. We present the best-fit functional forms of the distributions as well as a sigma distribution corrected for instrumental line-spread function broadening, and thereby show the physical line-spread distribution of the intrinsic population. Finally, we discuss possible implications for these distributions for the nature of Lyalpha emission through the circumgalactic medium, finding that observations may undercount LAHs with extended halo scale lengths compared to the intrinsic population.

Characterization of human trabecular bone across multiple length scales using a correlative approach combining X-ray tomography with LaserFIB and plasma FIB-SEM

Three-dimensional correlative multimodal and multiscale imaging is an emerging method for investigating the complex hierarchical structure of biological materials such as bone. This approach synthesizes images acquired across multiple length scales, for the same region of interest, to provide a comprehensive view of the material structure of a sample. Here, we develop a workflow for the structural analysis of human trabecular bone using a femtosecond laser to produce a precise grid to facilitate correlation between imaging modalities and identification of structures of interest, in this case, a single trabecula within a volume of trabecular bone. Through such image registration, high resolution X-ray microscopy imaging revealed fine architectural details, including the cement sheath and bone cell lacunae of the selected bone trabecula. The selected bone volume was exposed with a combination of manual polishing and site-specific femtosecond laser ablation and then examined with plasma focused ion beam-scanning electron microscopy. This reliable and versatile correlation approach has the potential to be applied to a variety of biological tissues and traditional engineered materials. The proposed workflow has the enhanced capability for generating highly resolved and broadly contextualized structural data for a better understanding of the architectural features of a material spanning its macroscopic to nanoscopic levels.

Chemical short-range ordering accompanies shear band initiation in CrCoNi medium entropy alloy

Extended X-ray absorption fine structure (EXAFS), high-resolution transmission electron microscopy (HRTEM), and X-ray diffraction have been used to monitor the structural development, on atomic-to-nanometer scale, prior to and along with shear band initiation in a face-centered-cubic CrCoNi medium-entropy alloy (MEA) under impact punch shear loads. Our findings provide clear evidence of chemical ordering with accompanying compositional inhomogeneity, on the length scale of one nanometer at the beginning of shear banding initiation. This chemical short-range atomic rearrangement of the three constituent elemental species is a result of atomic diffusion during high-strain-rate straining. The increasing chemical/structural inhomogeneity is likely to exert perturbations to cause uneven energy dissipation and encourage dislocation slip plane softening, both promoting strain localization that may have helped to instigate shear banding. Dynamic recrystallization is observed in later mature shear bands.

Reinforcing biomimetic cementitious composites by aligned hierarchical carbon fibers

Cementitious composites reinforced by carbon-based fibers of varied length scales still face limitations of a single dimension, anisotropic alignment, smooth surface, or poor dispersion. In this study, we developed a bioinspired, hierarchical reinforcing structure that enables multiscale coupling of mechanical properties and directional fiber alignment, significantly improving the load-bearing capacity of cementitious composite. The aligned hierarchical reinforcing structure was synthesized by grafting CNTs onto microscale CFs-COOH via an esterification reaction and a nozzle-injected technique. Parameters for synthesizing the CNTs grafted aligned CF (ACF-CNTs) were optimized considering oxidation solutions, grafting techniques, CNTs geometry, and CNTs concentrations. The chemical bond between CF and CNTs was examined by Laser Raman Spectrometer (LRS), Fourier Transform Infrared Spectrometer (FTIR), and X-ray photoelectron spectroscopy (XPS), respectively. Results indicate that CNTs are uniformly and densely grafted onto CF via ester linkage, forming a hierarchical reinforcing structure. Mechanical measurements show that 1 wt% ACF-CNTs results in a maximum flexural strength of 34.76 MPa and a maximum improvement of 297.12 % (compared to plain cement paste) in the biomimetic cementitious composites. Analysis based on fiber alignment, interface transition zone, and failure mode of CF-CNTs/CNTs suggests that multiscale coupling of mechanical properties and directional fiber alignment are the main reinforcing mechanisms.

Review of: "Nano lasers work on length scales 1000 times smaller than the thickness of a human hair"

Review of: "Nano lasers work on length scales 1000 times smaller than the thickness of a human hair"

Size-dependent finite element buckling analysis of porous cylindrical micro-shells reinforced by graphene platelets

This study introduces a spatial shear deformable rectangular element formulation to investigate the size-dependent buckling behavior of porous graphene platelets (GPL) reinforced micro-shells within the framework of the modified couple stress theory (MCST) for the first time in the worldwide term. The rectangular element, characterized by 4 nodes with 19 degrees of freedom each and possessing weak continuity of order C 1 , incorporates a length scale parameter enabling size-dependent analyses of shells. The research considers three distinct functions for the distribution of porosity combined with three different patterns of the GPL distribution (called by patterns A to C) along the micro-shell thickness. The elastic modulus of the nanocomposite in the absence of porosity is obtained using the Halpin-Tsai micromechanics model. Subsequently, the study meticulously validates the modeling accuracy and then investigates variations in the critical buckling load with respect to porosity distribution functions, distribution patterns of GPL, porosity coefficient, weight percentage of GPL, geometric parameters of the cylinder, and the length-scale parameter. The results reveal that the combination of the GPL pattern A with the first symmetric type porosity distribution yields the highest critical buckling loads. On the contrary, if the pattern B is combined with the second symmetric type of porosity distribution, the lowest critical buckling load will be observed. Given the accuracy of the results obtained and the versatility of the finite element method (FEM) in handling complex geometries together with diverse boundary conditions, the developed element holds promise for analyzing shells of various shapes under different boundary conditions.

Chemo-elasto-electro free energy of non-uniform system in the diffuse interface context

In the present work, we propose an alternative approach for deriving the free energy formulation of a non-uniform system. Compared with the work of Cahn and Hilliard (1958 J.Chem. Phys.28258-67), our approach provides a more comprehensive explanation for the individual energy contribution in a non-uniform system, including entropy, interaction energy, and internal energy. By employing a fundamental mathematical calculus, we reformulate the local composition within the interface region. Utilizing the reformulated local composition as well as classic thermodynamic principles, we establish formal expressions for entropy, interaction energy, and the internal energy, which are functions of both composition and composition gradients. We obtain a comprehensive free energy expression for a non-uniform system by integrating these energy density formulations. The obtained free energy expression is consistent with the formula type of Cahn and Hilliard and prodives more deeper physical interpretation. Moreover, using the same approach, we derive formulations for elastic energy and electric potential energy in a non-uniform system. However, the proposed approach encounters a limitation in the special case of a non-uniform fluid contacting a solid substrate. Due to the significant difference in the length scales between the solid-fluid and fluid-fluid interfaces, the wall free energy formulation based on the aforementioned concept is unsuitable for this multi-scale system. To address this limitation, we reformulate the wall free energy as a function of the average composition over the solid-fluid interface. Additionally, the previous derivation relies on an artificial treatment of describing the composition variation across the interface by a smooth monotone function, while the true nature of this variation remains unclear. By utilizing the concept of average composition, we circumvent the open question of how the composition varies across the interface region. Our work provides a thorough understanding for the construction of free energy formulations for a non-uniform system in condensed matter physics.

Effect of alkali treatment and fungal degradation on the nanostructure and cellulose arrangement in Scots pine cell walls – A neutron and X-ray scattering study

Research on new conservation treatments for historical wood requires considerable amounts of appropriate wood material, which is hard to acquire. Thus, we produced biologically and chemically degraded model wood that could be used as a representative material in future research on consolidating agents. Using chemical composition determinations, we found that fungal decay targeted mainly polysaccharides, while alkaline treatment mostly reduced hemicelluloses and lignin content. X-ray and neutron scattering showed that all decayed samples had increased disorder in microfibril alignment and larger elementary fibril cross-sections, and alkaline-treated samples had much larger elementary fibril spacing compared to those decayed by fungi. These nanoscale and chemical differences correlate with physical property changes. For example, decreased cellulose crystallinity and increased disorder of the microfibrils in degraded cell walls likely contribute to the lower elastic moduli measured for these cell walls. The obtained data improves understanding of how degradation alters wood structures and properties across length scales and will be valuable for future studies focusing on archeological wood. Moreover, it leads to the conclusion that it is more appropriate to develop treatments that consider not only spatial variability and degree of wood degradation but also the corresponding molecular and nanoscale changes in the cell walls.

Geometrical incompatibility regulated pattern selection and morphological evolution in growing spherical soft tissues

Surface morphological patterns are widely observed in natural systems, which are closely correlated to vital biological functions and inspire surface morphology designs in soft matter systems. Geometrical incompatibility widely exists in biological tissues across different length scales and plays an important role in growth-induced pattern selection and morphological evolution of soft tissues. However, the underlying physical mechanism of growth-induced pattern formation and post-buckling evolution in geometrically incompatible spherical soft tissues remain elusive. Here, the effect of geometrical incompatibility on the growth-induced pattern selection and post-buckling evolution are investigated through swelling experiment, theoretical analysis and numerical simulation. The results show that not only the instability pattern but also the instability threshold can be regulated by manipulating geometric incompatibility. Notably, when the geometrical incompatibility parameter exceeds a critical value, spontaneous instability is observed before growth. With continuous growth, the core–shell soft sphere buckles into a periodic buckyball pattern and evolves toward a bean-shaped pattern, and then undergoes a wrinkle-to-fold transition into a labyrinth topography. Our results demonstrate, both experimentally and theoretically, that geometrical incompatibility can guide the growth-induced pattern formation and morphological evolution effectively. This study not only enhances our understanding of the growth-induced pattern selection and morphological evolution in spherical soft tissues, but also provides an inspiring insight for the fabrication of morphological patterns on curved surfaces.