Large Length Scales Research Articles

Hydrodynamic and Ballistic Transport over Large Length Scales in GaAs/AlGaAs.

We study hydrodynamic and ballistic transport regimes through nonlocal resistance measurements and high-resolution kinetic simulations in a mesoscopic structure on a high-mobility two-dimensional electron system in a GaAs/AlGaAs heterostructure. We evince the existence of collective transport phenomena in both regimes and demonstrate that negative nonlocal resistances and current vortices are not exclusive to only the hydrodynamic regime. The combined experiments and simulations highlight the importance of device design, measurement schemes, and one-to-one modeling of experimental devices to demarcate various transport regimes.

Upscaling the porosity\u2013permeability relationship of a microporous carbonate for Darcy-scale flow with machine learning

The permeability of a pore structure is typically described by stochastic representations of its geometrical attributes (e.g. pore-size distribution, porosity, coordination number). Database-driven numerical solvers for large model domains can only accurately predict large-scale flow behavior when they incorporate upscaled descriptions of that structure. The upscaling is particularly challenging for rocks with multimodal porosity structures such as carbonates, where several different type of structures (e.g. micro-porosity, cavities, fractures) are interacting. It is the connectivity both within and between these fundamentally different structures that ultimately controls the porosity–permeability relationship at the larger length scales. Recent advances in machine learning techniques combined with both numerical modelling and informed structural analysis have allowed us to probe the relationship between structure and permeability much more deeply. We have used this integrated approach to tackle the challenge of upscaling multimodal and multiscale porous media. We present a novel method for upscaling multimodal porosity–permeability relationships using machine learning based multivariate structural regression. A micro-CT image of Estaillades limestone was divided into small 603 and 1203 sub-volumes and permeability was computed using the Darcy–Brinkman–Stokes (DBS) model. The microporosity–porosity–permeability relationship from Menke et al. (Earth Arxiv, https://doi.org/10.31223/osf.io/ubg6p, 2019) was used to assign permeability values to the cells containing microporosity. Structural attributes (porosity, phase connectivity, volume fraction, etc.) of each sub-volume were extracted using image analysis tools and then regressed against the solved DBS permeability using an Extra-Trees regression model to derive an upscaled porosity–permeability relationship. Ten test cases of 3603 voxels were then modeled using Darcy-scale flow with this machine learning predicted upscaled porosity–permeability relationship and benchmarked against full DBS simulations, a numerically upscaled Darcy flow model, and a Kozeny–Carman model. All numerical simulations were performed using GeoChemFoam, our in-house open source pore-scale simulator based on OpenFOAM. We found good agreement between the full DBS simulations and both the numerical and machine learning upscaled models, with the machine learning model being 80 times less computationally expensive. The Kozeny–Carman model was a poor predictor of upscaled permeability in all cases.

Deep learning of accurate force field of ferroelectric HfO2

The discovery of ferroelectricity in HfO$_2$-based thin films opens up new opportunities for using this silicon-compatible ferroelectric to realize low-power logic circuits and high-density non-volatile memories. The functional performances of ferroelectrics are intimately related to their dynamic responses to external stimuli such as electric fields at finite temperatures. Molecular dynamics is an ideal technique for investigating dynamical processes on large length and time scales, though its applications to new materials is often hindered by the limited availability and accuracy of classical force fields. Here we present a deep neural network-based interatomic force field of HfO$_2$ learned from {\em ab initio} data using a concurrent learning procedure. The model potential is able to predict structural properties such as elastic constants, equation of states, phonon dispersion relationships, and phase transition barriers of various hafnia polymorphs with accuracy comparable with density functional theory calculations. The validity of this model potential is further confirmed by the reproduction of experimental sequences of temperature-driven ferroelectric-paraelectric phase transitions of HfO$_2$ with isobaric-isothermal ensemble molecular dynamics simulations. We suggest a general approach to extend the model potential of HfO$_2$ to related material systems including dopants and defects.

Dissipation and adhesion in collisions between amorphous FeO nanoparticles

How dust grains aggregate into planetesimals is still an open question. It is experimentally observed that binary collisions between micron-sized dust grains result in adhesion for collisions up to ∼1 ms−1. However, aggregates at scales ∼1 mm and above have been shown to exhibit fragmentation or bouncing at relevant collision velocities, resulting in a barrier preventing the formation of larger aggregates. One key factor is the weak adhesion observed between dust particles in aggregates leading to ruptures even in low-velocity collisions. To better understand the structure and strength of the adhered interface resulting from collisions, we performed molecular-dynamics simulations of head-on collisions between amorphous FeO nanoparticles. The results demonstrate several important phenomena which indicate how bonding between aggregates might become stronger than is often observed in experiments. For nanograins, it is shown that strong attractive interactions result in a minimum relative collision speed vc determined just before impact. The values of vc for particle radii 7 nm and below are computed to be in the range 40–100 ms−1. This high collision speed is shown to result in strong bond reordering at the interface. Moreover, increasing the incident collision speed vrel is shown to increase the work of adhesion Wadh, which is correlated to substantial bond rearrangement. Specifically, for values of vrel in the range between 10–90 ms−1, the interface between adhered grains is structured very closely to perfectly coordinated FeO amorphous solid. The reported results suggest stronger bonding results from collisions between particles with unpassivated surfaces, especially when particles are small, have amorphous surface structures, or when collisions occur at higher relative speeds. These factors should generate aggregates with stronger bonds that are less easily broken in subsequent collisions, and hence might be responsible for aggregates less likely to fragment at larger length scales.

Observations on decadal sandbar behaviour along a large‐scale curved shoreline

AbstractNearshore sandbars are characteristic features of sandy surf zones and have been observed with a variety of geometries in cross‐shore (e.g. location) and longshore direction (e.g. planform). Although the behaviour of sandbars has been studied extensively on spatial scales up to kilometres and timescales up to years, it remains challenging to observe and explain their behaviour on larger spatial and temporal scales, especially in locations where coastline curvature can be prominent. In this paper, we study a data set with 38 years of coastal profiles, collected with alongshore intervals of 50 m, along the 34 km‐long curved sandy shoreline of Sylt island, Germany. Sylt's shoreline has an orientation difference of ~20° between the northern and southern half of the island. We found that the decadal coastal profiles on the southern half show features of a low‐tide terrace and a sandbar located further from the shoreline (~441 m). On the nothern half, the sandbar was located closer to the shoreline (~267 m) and was less pronounced, while the profiles show transverse bar and rip features. The alongshore planform also differed systematically and significantly along the two island sides. The sandbar on the southern island half, with alongshore periodicity on a larger length scale (~2240 m), was coupled out‐of‐phase to the shoreline, while no phase coupling was observed for the sandbar with periodicity on a shorter length scale (~670 m) on the northern half. We related the observed geometric differences of the sandbars to the difference in the local wave climate along Sylt, imposed by the shoreline shape. Our observations imply that small alongshore variations in wave climate, due to the increasing shoreline curvature on larger spatial scales, can lead to significant alongshore differences in the decadal evolution of coastal profiles, sandbars and shorelines. © 2020 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd

On the strength of nanoporous materials with the account of surface effects

The increasing applications of nanoporous materials in engineering structures call for robust strength criteria that are able to model the size effects of multiscale voids inherent to these materials. Many literature works have devoted to this line of research by either employing the classical homogenization approach or extending Gurson’s model to incorporate the nanovoid surface mechanics. However, few studies are able to simultaneously account for the multiscale effects of both nanovoid and microvoid porosities. This work presents a two-level hierarchical strength theory for nanoporous materials accommodating the effects of nanovoid surface and multiscale porosities. No surface effects exist for microvoids because of their sufficiently large length scale. The lower level representative volume element (RVE) is modeled as a homogeneous, incompressible and rigid-perfectly plastic matrix embedded with multiple nanovoids of similar size. The lower level RVE is then treated as a material point in the upper level RVE made by a hollow sphere. By the coupling of homogenization method for the lower level RVE and the limit analysis of Gurson type at the upper level, an implicit closed-form macroscopic strength criterion is derived. Parametric studies about the significance of nanovoid surface properties, nanovoid size, nanovoid porosity and microvoid porosity on yield loci reveal that the proposed two-level hierarchical model is a substantial reinforcement to the conventional single level strength criteria available in the open literature.

Nanostructural deformation of high-stiffness spruce wood under tension

Conifer wood is an exceptionally stiff and strong material when its cellulose microfibrils are well aligned. However, it is not well understood how the polymer components cellulose, hemicelluloses and lignin co-operate to resist tensile stress in wood. From X-ray scattering, neutron scattering and spectroscopic data, collected under tension and processed by novel methods, the ordered, disordered and hemicellulose-coated cellulose components comprising each microfibril were shown to stretch together and demonstrated concerted, viscous stress relaxation facilitated by water. Different cellulose microfibrils did not all stretch to the same degree. Attempts were made to distinguish between microfibrils showing large and small elongation but these domains were shown to be similar with respect to orientation, crystalline disorder, hydration and the presence of bound xylan. These observations are consistent with a major stress transfer process between microfibrils being shear at interfaces in direct, hydrogen-bonded contact, as demonstrated by small-angle neutron scattering. If stress were transmitted between microfibrils by bridging hemicelluloses these might have been expected to show divergent stretching and relaxation behaviour, which was not observed. However lignin and hemicellulosic glucomannans may contribute to stress transfer on a larger length scale between microfibril bundles (macrofibrils).

A nonlinear geometric couple stress based strain gradient Kirchhoff–Love shell formulation for microscale thin-wall structures

We present a nonlinear Kirchhoff–Love micro-shell element based on isogeometric analysis (IGA) and couple stress theory. Higher-order NURBS functions are exploited for analyzing the strain gradient effect which automatically fulfill the higher-order continuity requirements. We express the strain gradient elastic formulation in natural curvilinear coordinates, which leads to an efficient numerical tool to examine geometric nonlinearities of thin micro-shell structures. The presented IGA formulation is verified through comparisons to analytical solution, experimental data as well as other popular benchmark problems of nonlinear geometric shells. We believe that the presented formulation is particularly suitable for analyzing two-dimensional materials at larger length scales, which are commonly studied at nanoscale.

Collagen Fiber Orientation Is Coupled with Specific Nano-Compositional Patterns in Dark and Bright Osteons Modulating Their Biomechanical Properties.

Bone continuously adapts to its mechanical environment by structural reorganization to maintain mechanical strength. As the adaptive capabilities of bone are portrayed in its nano- and microstructure, the existence of dark and bright osteons with contrasting preferential collagen fiber orientation (longitudinal and oblique-angled, respectively) points at a required tissue heterogeneity that contributes to the excellent fracture resistance mechanisms in bone. Dark and bright osteons provide an exceptional opportunity to deepen our understanding of how nanoscale tissue properties influence and guide fracture mechanisms at larger length scales. To this end, a comprehensive structural, compositional, and mechanical assessment is performed using circularly polarized light microscopy, synchrotron nanocomputed tomography, focused ion beam/scanning electron microscopy, quantitative backscattered electron imaging, Fourier transform infrared spectroscopy, and nanoindentation testing. To predict how the mechanical behavior of osteons is affected by shifts in collagen fiber orientation, finite element models are generated. Fundamental disparities between both osteon types are observed: dark osteons are characterized by a higher degree of mineralization along with a higher ratio of inorganic to organic matrix components that lead to higher stiffness and the ability to resist plastic deformation under compression. On the contrary, bright osteons contain a higher fraction of collagen and provide enhanced ductility and energy dissipation due to lower stiffness and hardness.

Implementation and validation of finite element model of skull deformation and failure response during uniaxial compression

Numerical studies aimed at evaluating head injury due to externally applied loading can be made more biofidelic by incorporating nonlinear mechanism-based and microstructurally-inspired material models representing the mechanical response and fracture (failure or injury) of the human skull bone. Thus, incorporation of these mechanism-based models would increase the ability of simulations of mechanical impact to identify more realistic fracture-based injuries at clinical relevancy, such as linear (tensile), depressed (compressive), or penetration (shear). One of the challenges for accurate modeling of the mechanical response of the human skull is the intricate location dependent heterogeneous mesostructural arrangement of bone within the structure of the skull. Recently, a power-law relationship between the localized bone volume fraction (BVF) and modulus (E) within the human skull was developed based on quasi-static compression experiments. However, the parameters of the power-law were optimized and obtained using approximations which were not experimentally or computationally validated for the actual heterogeneous 3D bone structure. Here, a hybrid experimental-modeling-computational (HEMC) based concept was used to develop a microstructurally compatible detailed meso-scale finite element (FE) model of the heterogeneous microstructure of one of the human skull bone coupons previously used to derive the E-BVF relationship. Finite elements were mapped to the corresponding regions from microcomputed tomography images, and the BVF of each element was identified. Then, element-specific moduli were calculated from the E-BVF power relationship. The goal of the simulations was twofold: to assess the assumptions used to derive the E-BVF relationship from the linear regime of the experimental response, and also to model the subsequent deviation from linearity. Using the E-BVF relationship, the 3D simulation was able to match the experimentally measured global modulus to within 3%. After validating the E-BVF power law using the initial linear response, to develop and validate failure models, the following steps were completed. The subsequent deviation of the mechanical response from its initial linearity was assumed to be due to failure of elements either by compression or tension. Elemental microstructure-specific compressive and tensile failure thresholds (σf) for each element were modeled by BVF (fBV) power functional relationships of the form: σf=σf,0(fBV)2 MPa. The initial leading coefficients (σf,0) for compression and tension were derived from prior reported experimental work. Through incorporating element-level failure and then iterating the leading coefficients, the simulation was able to represent the nonlinearity of the stress-strain curve and its catastrophic failure in the experiment. Evolution of the measured non-uniform full-strain-fields on two surfaces of the coupon, showing the localized regions of failure, was compared between experiment and simulation, and was approximately similar, thus validating the developed HEMC procedure and failure models. The simulation methodology developed here allowed for identification of failure location within the skull coupon specimen, thereby providing a tool to predict the localized failure (fracture or injury) initiation within the human skull in FE simulations at larger length scales.

Colloidal aggregation in anisotropic liquid crystal solvent.

The mutual attraction between colloidal particles in an anisotropic fluid, such as the nematic liquid crystal phase, leads to the formation of hierarchical aggregate morphologies distinct from those that tend to form in isotropic fluids. Previously it was difficult to study this aggregation process for a large number of colloids due to the difficulty of achieving a well dispersed initial colloid distribution under good imaging conditions. In this paper, we report the use of a recently developed self-assembling colloidal system to investigate this process. Hollow, micron-scale colloids are formed in situ in the nematic phase and subsequently aggregate to produce fractal structures and colloidal gels, the structures of which are determined by colloid concentration and temperature quench depth through the isotropic to nematic phase transition point. This self-assembling colloidal system provides a unique method to study particle aggregation in liquid crystal over large length scales. We use fluorescence microscopy over a range of length scales to measure aggregate structure as a function of temperature quench depth, observe ageing mechanisms and explore the driving mechanisms in this unique system. Our analyses suggest that aggregate dynamics depend on a combination of Frank elasticity relaxation, spontaneous defect line annihilation and internal aggregate fracturing.

Eigenvector-spatial localisation

We present a new multiscale covariance localisation method for ensemble data assimilation that is based on the estimation of eigenvectors and subsequent projections, together with traditional spatial localisation applied with a range of localisation lengths. In short, we estimate the leading, large-scale eigenvectors from the sample covariance matrix obtained by spatially smoothing the ensemble (treating small scales as noise) and then localise the resulting sample covariances with a large length scale. After removing the projection of each ensemble member onto the leading eigenvectors, the process may be repeated using less smoothing and tighter localizations or, in a final step, using the resulting, residual ensemble and tight localisation to represent covariances in the remaining subspace. We illustrate the use of the new multiscale localisation method in simple numerical examples and in cycling data assimilation experiments with the Lorenz Model III. We also compare the proposed new method to existing multiscale localisation and to single-scale localisation.

Effects of fuel spatial distribution on wildland fire behaviour

The distribution of fuels is recognised as a key driver of wildland fire behaviour. However, our understanding of how fuel density heterogeneity affects fire behaviour is limited because of the challenges associated with experiments that isolate fuel heterogeneity from other factors. Advances in fire behaviour modelling and computational resources provide a means to explore fire behaviour responses to fuel heterogeneity. Using an ensemble approach to simulate fire behaviour in a coupled fire–atmosphere model, we systematically tested how fuel density fidelity and heterogeneity shape effective wind characteristics that ultimately affect fire behaviour. Results showed that with increased fuel density fidelity and heterogeneity, fire spread and area burned decreased owing to a combination of fuel discontinuities and increased fine-scale turbulent wind structures that blocked forward fire spread. However, at large characteristic length scales of spatial fuel density, the fire spread and area burned increased because local fuel discontinuity decreased, and wind entrainment into the forest canopy maintained near-surface wind speeds that drove forward fire spread. These results demonstrate the importance of incorporating high-resolution fuel fidelity and heterogeneity information to capture effective wind conditions that improve fire behaviour forecasts.

Effect of matrix heterogeneity on cell mechanosensing.

Cells sense mechanical signals within the extracellular matrix, the most familiar being stiffness, but matrix stiffness cannot be simply described by a single value. Randomness in matrix structure causes stiffness at the scale of a cell to vary by more than an order of magnitude. Additionally, the extracellular matrix contains ducts, blood vessels, and, in cancer or fibrosis, regions with abnormally high stiffness. These different features could alter the stiffness sensed by a cell, but it is unclear whether the change in stiffness is large enough to overcome the noise caused by heterogeneity due to the random fibrous structure. Here we used a combination of experiments and modeling to determine the extent to which matrix heterogeneity disrupts the potential for cell sensing of a locally stiff feature in the matrix. Results showed that, at the scale of a single cell, spatial heterogeneity in local stiffness was larger than the increase in stiffness due to a stiff feature. The heterogeneity was reduced only for large length scales compared to the fiber length. Experiments verified this conclusion, showing spheroids of cells, which were large compared to the average fiber length, spreading preferentially toward stiff inclusions. Hence, the propagation of mechanical cues through the matrix depends on length scale, with single cells being able to sense only the stiffness of the nearby fibers and multicellular structures, such as tumors, also sensing the stiffness of distant matrix features.

NACore Amyloid Formation in the Presence of Phospholipids.

Amyloids are implicated in many diseases, and disruption of lipid membrane structures is considered as one possible mechanism of pathology. In this paper we investigate interactions between an aggregating peptide and phospholipid membranes, focusing on the nanometer-scale structures of the aggregates formed, as well as on the effect on the aggregation process. As a model system, we use the small amyloid-forming peptide named NACore, which is a fragment of the central region of the protein α-synuclein that is associated with Parkinson’s disease. We find that phospholipid vesicles readily associate with the amyloid fibril network in the form of highly distorted and trapped vesicles that also may wet the surface of the fibrils. This effect is most pronounced for model lipid systems containing only zwitterionic lipids. Fibrillation is found to be retarded by the presence of the vesicles. At the resolution of our measurements, which are based mainly on cryogenic transmission electron microscopy (cryo-TEM), X-ray scattering, and circular dichroism (CD) spectroscopy, we find that the resulting aggregates can be well fitted as linear combinations of peptide fibrils and phospholipid bilayers. There are no detectable effects on the cross-β packing of the peptide molecules in the fibrils, or on the thickness of the phospholipid bilayers. This suggests that while the peptide fibrils and lipid bilayers readily co-assemble on large length-scales, most of them still retain their separate structural identities on molecular length-scales. Comparison between this relatively simple model system and other amyloid systems might help distinguish aspects of amyloid-lipid interactions that are generic from aspects that are more protein specific. Finally, we briefly consider possible implications of the obtained results for in-vivo amyloid toxicity.

Quantitative phase-field modeling of solute trapping in rapid solidification

A quantitative phase-field model is developed for prediction of solute trapping for solidification velocities relevant to the additive manufacturing. An anti-trapping flux is proposed to generate a chemical potential jump independent of the interface width and consistent with the sharp interface continuous growth (CG) model. The thin-interface analysis up to the second order is implemented to quantitatively parametrize the phase-field model based on the material properties for both full and zero solute drag limits of the CG model. As a benchmark example, the experimental data on Si-9at.%As (Kittl et al., Acta Materialia, 2000) is used to compare the partition coefficient and kinetic undercooling predicted by this phase-field model with those of the CG model. Our results, especially with the full-drag limit, present a very good agreement with the experimental data and theoretical models for solidification velocities up to the diffusive velocity. Unlike other phase-field models, this proposed model predicts accurate partition coefficient and kinetic undercooling for a wide range of solidification velocities, and the results are less sensitive to the diffusive interface width, enabling quantitative simulations in larger length scales. The model performance in prediction of the cellular growth is highlighted by showing that the primary dendritic arm spacing is also weakly dependent on the diffusive interface width.

Revisiting neutron scattering data from deuterated milk

Deuterated milk (dried milk powder that has been dissolved in deuterated water, 2H2O or D2O) is a valuable material for determining the structure of dairy products by neutron scattering. This has primarily been used in the past to study the internal structure of casein micelles, and when longer length scales have been studied, interparticle interactions have been neglected. This will impact fits to the data over all length scales, which will hamper quantitative data analysis. Previously measured large length scale neutron scattering data from the literature, both ultra-small-angle neutron scattering (USANS) and spin-echo small-angle neutron scattering (SESANS) data, have been reanalyzed and improved fits have been obtained using a recently proposed model describing casein micelles as sticky spheres, rather than as hard spheres. This shows that these interactions will also be necessary for modeling neutron scattering data on deuterated milk.

Discrete Giant Polymeric Chains Based on Nanosized Monomers.

As size-amplified analogues of canonical macromolecules, polymeric chains built up by “giant” monomers represent an experimental realization of the “beads-on-a-string” model at larger length scales, which could provide insights into fundamental principles of polymer science. In this work, we modularly constructed discrete giant polymeric chains using nanosized building blocks (polyhedral oligomeric silsesquioxane, POSS) as basic repeat units through an efficient and robust iterative exponential growth approach, with precise control on molecular parameters, including size, composition, regioconfiguration, and surface functionalities. Their chemical structures were fully characterized by nuclear magnetic resonance spectroscopy, size-exclusion chromatography, and matrix-assisted laser desorption ionization time-of-flight mass spectrometry. With elaborately designed amphiphilic block POSS chains and their analogues made of conventional monomers, the size effects were delicately studied and highlighted. Interesting assembly behaviors emerge as a result of distinct interactions and molecular dynamics. This category of molecules shares general self-assembly characteristics as the conventional counterparts in terms of phase transition and evolution. Meanwhile, it turns out that the monomer size has profound impacts on phase stability, as a trade-off between entropic and enthalpic contributions. It may open up a door for modular and programmable design of interesting materials with complex structures and diverse functions.

Observation of Efimov Universality across a Nonuniversal Feshbach Resonance in ^{39}K.

We study three-atom inelastic scattering in ultracold ^{39}K near a Feshbach resonance of intermediate coupling strength. The nonuniversal character of such resonance leads to an abnormally large Efimov absolute length scale and a relatively small effective range r_{e}, allowing the features of the ^{39}K Efimov spectrum to be better isolated from the short-range physics. Meticulous characterization of and correction for finite-temperature effects ensure high accuracy on the measurements of these features at large-magnitude scattering lengths. For a single Feshbach resonance, we unambiguously locate four distinct features in the Efimov structure. Three of these features form ratios that obey the Efimov universal scaling to within 10%, while the fourth feature, occurring at a value of scattering length closest to r_{e}, instead deviates from the universal value.

Creep Micromechanics in Meso-Length Scale Samples

This study focuses on the creep response of meso-length scale systems, whose smallest dimensions lie in the range of a few hundred micrometers to a few millimeters. Here, uniaxial creep experiments were performed on commercially pure Al polycrystals using samples having the smallest (or, characteristic sample) dimension of 500 μm to 7 mm in the “five”-power law regime. Compared to the interior, the near-surface region developed creep compliant dislocation substructures, marked by lower dislocation density and larger subgrain size. Furthermore, the extent of this surface-affected region (SAR) inversely varied with applied stress and was limited by the grain size. As SAR became comparable to the characteristic sample dimension (CSD), the creep response of the material was significantly affected by the “weaker” surface, thereby reducing the overall creep resistance. This also resulted in a decrease in stress exponent with a decrease in CSD. The differential creep resistance of the surface and the interior leads to load-shedding between the “weak” surface and the “strong” interior. A microstructure-sensitive iso-strain composite model quantifying this load-shedding effect was formulated to explain the observed creep response across various length scales. The critical insights into the creep micro-mechanics obtained in this study, therefore, seamlessly unify the power-law creep response at large and small length scales.