Macroscopic Length Scales Research Articles

Exact fluctuating hydrodynamics of active lattice gases—typical fluctuations

We extend recent results on the exact hydrodynamics of a system of diffusive active particles displaying a motility-induced phase separation to account for typical fluctuations of the dynamical fields. By calculating correlation functions exactly in the homogeneous phase, we find that two macroscopic length scales develop in the system. The first is related to the diffusive length of the particles and the other to the collective behavior of the particles. The latter diverges as the critical point is approached. Our results show that the critical behavior of the model in one dimension belongs to the universality class of a mean-field Ising model, both for static and dynamic properties, when the thermodynamic limit is taken in a specified manner. The results are compared to the critical behavior exhibited by the ABC model. In particular, we find that in contrast to the ABC model the density large deviation function, at its Gaussian approximation, does not contain algebraically decaying interactions but is of a finite, macroscopic, extent which is dictated by the diverging correlation length.

Nanoparticles exploring the macroscopic world

Nanoparticles exploring the macroscopic world

Topology Protects Chiral Edge Currents in Stochastic Systems

Constructing systems that exhibit time-scales much longer than those of the underlying components, as well as emergent dynamical and collective behavior, is a key goal in fields such as synthetic biology and materials self-assembly. Inspiration often comes from living systems, in which robust global behavior prevails despite the stochasticity of the underlying processes. Here, we present two-dimensional stochastic networks that consist of minimal motifs representing out-of-equilibrium cycles at the molecular scale and support chiral edge currents in configuration space. These currents arise in the topological phase due to the bulk-boundary correspondence and dominate the system dynamics in the steady-state, further proving robust to defects or blockages. We demonstrate the topological properties of these networks and their uniquely non-Hermitian features such as exceptional points and vorticity, while characterizing the edge state localization. As these emergent edge currents are associated to macroscopic timescales and length scales, simply tuning a small number of parameters enables varied dynamical phenomena including a global clock, dynamical growth and shrinkage, and synchronization. Our construction provides a novel topological formalism for stochastic systems and fresh insights into non-Hermitian physics, paving the way for the prediction of robust dynamical states in new classical and quantum platforms.

Characterizing bulk liquids with zero-group-velocity Lamb modes

In this work we study the coupled response of zero-group-velocity (ZGV) modes and test liquids. In particular, we assess the viability of exploiting the spatiotemporal constraint of ZGV modes to derive techniques for non-contact, non-invasive liquid characterization to support process optimization. The results demonstrate that the ZGV resonance behaves like a baffled piston source that couples into standing waves in the test liquid. Moreover the particle displacement associated with the liquid resonance extends over macroscopic length scales (∼cm). The resonance frequencies are governed by the acoustic properties and depth, h, of the test liquid. Therefore, the test liquid sound speed, cL , can be determined by analysing the spectral content of the system response. While the technique provides an accurate measure of sound speed, the morphology of immiscible mixtures (e.g. buoyancy separated or emulsion) affects the variation in sound speed with composition. In this case, it is necessary to know the mixture morphology in order to utilize the sound speed as a proxy for composition. The technology is applicable to any thin-walled (mm–cm) structure (pipe, tank, etc) commonly utilized for liquid handling. As a result, the measurement is broadly applicable to many industrial settings that require convenient and accurate methods to determine liquid composition in support of process evaluation and optimization.

Turbulent Flows With Drops and Bubbles: What Numerical Simulations Can Tell Us—Freeman Scholar Lecture

AbstractTurbulent flows laden withlarge, deformable drops or bubbles are ubiquitous in nature and a number of industrial processes. These flows are characterized by physics acting at many different scales: from the macroscopic length scale of the problem down to the microscopic molecular scale of the interface. Naturally, the numerical resolution of all the scales of the problem, which span about eight to nine orders of magnitude, is not possible, with the consequence that numerical simulations of turbulent multiphase flows impose challenges and require methods able to capture the multiscale nature of the flow. In this review, we start by describing the numerical methods commonly employed and by discussing their advantages and limitations, and then we focus on the issues arising from the limited range of scales that can be possibly solved. Ultimately, the droplet size distribution, a key result of interest for turbulent multiphase flows, is used as a benchmark to compare the capabilities of the different methods and to discuss the main insights that can be drawn from these simulations. Based on this, we define a series of guidelines and best practices that we believe to be important in the analysis of the simulations and the development of new numerical methods.

The interfacial energy penalty to crystal growth close to equilibrium

AbstractUnderstanding the origin of rock microstructure is critical for refining models of the geodynamics of the Earth. We use the geometry of compositional growth zoning of a population of garnet porphyroblasts in a mica schist to gain quantitative insight into (1) the relative growth rates of individual crystals, (2) the departure from equilibrium during their growth, and (3) the mobility of the porphyroblast-matrix interface. The driving force for garnet growth in the studied sample was exceedingly small and is comparable in magnitude to the interfacial energy associated with the garnet-matrix interface. This resulted in size-dependent garnet growth at macroscopic length scales, with a decrease in radial growth rates for smaller crystals caused by the penalty effect of the interfacial energy. The difference in growth rate between the largest and the smallest crystal is ~45%, and the interface mobility for garnet growth from ~535°C, 480 MPa to 565°C, 560 MPa in the phyllosilicate-dominated rock matrix ranged between ~10−19 and 10−20 m4 J−1 s−1. This is the first estimation of interface mobility in natural rock samples. In addition to the complex structural and chemical reorganization associated with the formation of dodecahedral coordination polyhedra in garnet, the presence of abundant graphite may have exerted drag on the garnet-matrix interface, further decreasing its mobility.

Linking the length scales

A challenge for multiscale simulations is how to link the macroscopic and microscopic length scales effectively. A new machine-learning-based sampling approach enables full exploration of macro configurations while retaining the precision of a microscale model.

A review of phase-field models, fundamentals and their applications to composite laminates

Innovations of advanced materials have been at the core of most engineering technologies, devices and systems. Composite laminates in particular have been extensively employed in many major and advanced industries including aircraft, maritime transport, and automobiles. Failure in composite structures is critical and often complicated, and that is the consequence of the evolution of and interactions among the constitutive fracture events (e.g., matrix cracking, fibre/matrix debonding, delamination, fibre breakage, fibre kinking). Accurate prediction of progressive failure in composite laminates is crucial for the development and design of most lightweight components and structures. This paper, for the first time, outlines a critical review on the developments and recent applications of regularized phase field models for failure problems in composite laminates and structures. Fundamentals of the phase field models are introduced and the developments of the regularized model from different aspects for the modeling are reviewed. Phase field models as well as the modeling strategies from different levels of idealization, i.e., microscopic, mesoscopic and macroscopic length scales are presented. The realization of existing widely used models such as cohesive zone model, plasticity, and damage initiation criterion and energy decomposition into the phase field model is also addressed. Typical applications of the phase field models in composite laminate modeling are discussed.

Hierarchical carrier transport simulator for defected nanoparticle solids

The efficiency of nanoparticle (NP) solar cells has grown impressively in recent years, exceeding 16%. However, the carrier mobility in NP solar cells, and in other optoelectronic applications remains low, thus critically limiting their performance. Therefore, carrier transport in NP solids needs to be better understood to further improve the overall efficiency of NP solar cell technology. However, it is technically challenging to simulate experimental scale samples, as physical processes from atomic to mesoscopic scales all crucially impact transport. To rise to this challenge, here we report the development of TRIDENS: the Transport in Defected Nanoparticle Solids Simulator, that adds three more hierarchical layers to our previously developed HINTS code for nanoparticle solar cells. In TRIDENS, we first introduced planar defects, such as twin planes and grain boundaries into individual NP SLs superlattices (SLs) that comprised the order of 103 NPs. Then we used HINTS to simulate the transport across tens of thousands of defected NP SLs, and constructed the distribution of the NP SL mobilities with planar defects. Second, the defected NP SLs were assembled into a resistor network with more than 104 NP SLs, thus representing about 107 individual NPs. Finally, the TRIDENS results were analyzed by finite size scaling to explore whether the percolation transition, separating the phase where the low mobility defected NP SLs percolate, from the phase where the high mobility undefected NP SLs percolate drives a low-mobility-to-highmobility transport crossover that can be extrapolated to genuinely macroscopic length scales. For the theoretical description, we adapted the Efros-Shklovskii bimodal mobility distribution percolation model. We demonstrated that the ES bimodal theory’s two-variable scaling function is an effective tool to quantitatively characterize this low-mobility-to-high-mobility transport crossover.

Adsorption and self-assembly properties of the plant based biosurfactant, Glycyrrhizic acid

There is an increased interest in the use of natural surfactant as replacements for synthetic surfactants due to their biosustainable and biocompatible properties. A category of natural surfactants which are attracting much current interest is the triterpenoid saponins; surface active components found extensively in a wide range of plant species. A wide range of different saponin structures exist, depending upon the plant species they are extracted from; but regardless of the variation in structural details they are all highly surface active glycosides. Greater exploitation and application requires a characterisation and understanding of their basic adsorption and self-assembly properties. HypothesisGlycyrrhizic acid, extracted from Licorice root, is a monodesmosidic triterpenoid saponin. It is widely used in cosmetic and pharmaceutical applications due to its anti-inflammatory properties, and is an ingredient in foods as a sweetener additive. It has an additional attraction due to its gel forming properties at relatively low concentrations. Although it has attracted much recent attention, many of its basic surface active characteristics, adsorption and self-assembly, remain relatively unexplored. How the structure of the Glycyrrhizic acid saponin affects its surface active properties and the impact of gelation on these properties are important considerations, and to investigate these are the focus of the study. ExperimentsIn this paper the adsorption properties at the air–water interface and the self-assembly in solution have been investigated using by neutron reflectivity and small angle neutron scattering; in non-gelling and gelling conditions. FindingsThe adsorption isotherm is determined in water and in the presence of gelling additives, and compared with the adsorption behaviour of other saponins. Gelation has minimal impact on the adsorption; apart from producing a rougher surface with a surface texture on a macroscopic length scale. Globular micelles are formed in aqueous solution with modest anisotropy, and are compared with the structure of other saponin micelles. The addition of gelling agents results in only minimal micelle growth, and the solutions remain isotropic under applied shear flow.

Macroscopic materials assembled from nanoparticle superlattices.

Nanoparticle assembly has been proposed as an ideal means to program the hierarchical organization of a material by using a selection of nanoscale components to build the entire material from the bottom up. Multiscale structural control is highly desirable because chemical composition, nanoscale ordering, microstructure and macroscopic form all affect physical properties1,2. However, the chemical interactions that typically dictate nanoparticle ordering3-5 do not inherently provide any means to manipulate structure at larger length scales6-9. Nanoparticle-based materials development therefore requires processing strategies to tailor micro- and macrostructure without sacrificing their self-assembled nanoscale arrangements. Here we demonstrate methods to rapidly assemble gram-scale quantities of faceted nanoparticle superlattice crystallites that can be further shaped into macroscopic objects in a manner analogous to the sintering of bulk solids. The key advance of this method is that the chemical interactions that govern nanoparticle assembly remain active during the subsequent processing steps, which enables the local nanoscale ordering of the particles to be preserved as the macroscopic materials are formed. The nano- and microstructure of the bulk solids can be tuned as a function of the size, chemical makeup and crystallographic symmetry of the superlattice crystallites, and the micro- and macrostructures can be controlled via subsequent processing steps. This work therefore provides a versatile method to simultaneously control structural organization across the molecular to macroscopic length scales.

The effect of crystallographic orientation and interfaces on thermo-mechanical softening of a martensitic steel

Thermo-mechanical softening forms the basis for hot working of metallic materials. In materials with hierarchical microstructures such as martensite, softening processes can be mediated or restricted by interfaces. In the present study, the operation of three distinct softening mechanisms in P91 martensitic steel during thermo-mechanical processing (TMP) has been investigated. The softening in the present case is found to arise from the interplay between microstructural strain, texture, and phase transformation. Further, softening characteristics vary with the TMP parameters. The manifestation of softening has been explored at the macroscopic, mesoscopic, and microscopic length scales. It has been found that each softening mechanism is differently mediated by the interfaces and is governed by local crystallographic orientation. Thermo-mechanical softening of martensite proceeds through orientation-dependent dynamic recrystallization. The role of specific interfaces in impeding this mechanism has been highlighted. In contrast, TMP of austenite proceeds through interface-mediated softening, combining the phenomena of recrystallization and phase transformation.

Particles to partial differential equations parsimoniously.

Equations governing physico-chemical processes are usually known at microscopic spatial scales, yet one suspects that there exist equations, e.g., in the form of partial differential equations (PDEs), that can explain the system evolution at much coarser, meso-, or macroscopic length scales. Discovering those coarse-grained effective PDEs can lead to considerable savings in computation-intensive tasks like prediction or control. We propose a framework combining artificial neural networks with multiscale computation, in the form of equation-free numerics, for the efficient discovery of such macro-scale PDEs directly from microscopic simulations. Gathering sufficient microscopic data for training neural networks can be computationally prohibitive; equation-free numerics enable a more parsimonious collection of training data by only operating in a sparse subset of the space-time domain. We also propose using a data-driven approach, based on manifold learning (including one using the notion of unnormalized optimal transport of distributions and one based on moment-based description of the distributions), to identify macro-scale dependent variable(s) suitable for the data-driven discovery of said PDEs. This approach can corroborate physically motivated candidate variables or introduce new data-driven variables, in terms of which the coarse-grained effective PDE can be formulated. We illustrate our approach by extracting coarse-grained evolution equations from particle-based simulations with a priori unknown macro-scale variable(s) while significantly reducing the requisite data collection computational effort.

Hyperelastic material properties of axonal fibers in brain white matter

Accurate characterization of the mechanical properties of the human brain at both microscopic and macroscopic length scales is a critical requirement for modeling of traumatic brain injury and brain folding. To date, most experimental studies that employ classical tension/compression/shear tests report the mechanical properties of the brain averaged over both the gray and white matter within the macroscopic regions of interest. As a result, there is a missing correlation between the independent mechanical properties of the microscopic constituent elements and the composite bulk macroscopic mechanical properties of the tissue. This microstructural computational study aims to inversely predict the hyperelastic mechanical properties of the axonal fibers and their surrounding extracellular matrix (ECM) from the bulk tissue's mechanical properties. We develop a representative volume element (RVE) model of the bulk tissue consisting of axonal fibers and ECM with the embedded element technique. A multiobjective optimization technique is implemented to calibrate the model and establish the independent mechanical properties of axonal fibers and ECM based on seven previously reported experimental mechanical tests for bulk white matter tissue from the corpus callosum. The result of the study shows that the discrepancy between the reported values for the elastic behavior of white matter in literature stems from the anisotropy of the tissue at the microscale. The shear modulus of the axonal fiber is seven times larger than the ECM, with axonal fibers that also show greater nonlinearity, contrary to the common assumption that both components exhibit identical nonlinear characteristics. Statement of significanceThe reported mechanical properties of white matter microstructure used in traumatic brain injury or brain mechanics studies vary widely, in some cases by up to two orders of magnitude. Currently, the material parameters of the white matter microstructure are identified by a single loading mode or ultimately two modes of the bulk tissue. The presented material models only define the response of the bulk and homogenized white matter at a macroscopic scale and cannot explicitly capture the connection between the material properties of microstructure and bulk structure. To fill this knowledge gap, our study characterizes the hyperelastic material properties of axonal fibers and ECM using microscale computational modeling and multiobjective optimization. The hyperelastic material properties for axonal fibers and ECM presented in this study are more accurate than previously proposed because they have been optimized using seven or six loading modes of the bulk tissue, which were previously limited to only two of the seven possible loading modes. As such, the predicted values with high accuracy could be used in various computational modeling studies. The systematic characterization of the material properties of the human brain tissue at both macro- and microscales will lead to more accurate computational predictions, which will enable a better understanding of injury criteria, and has a positive impact on the improved development of smart protection systems, and more accurate prediction of brain development and disease progression.

Large and Local Magnetoresistance in a State-of-the-Art Perpendicular Magnetic Medium.

PurposeMagnetotransport properties of granular oxide-segregated CoPtCr films were studied on both macroscopic and microscopic length scales by performing bulk and point-contact magnetoresistance measurements, respectively. Such a perpendicular magnetic medium is used in state-of-the-art hard disc drives and, when combined with magnetotransport phenomena for read/write operations, may lead to a novel concept for magnetic recording with high areal density.Materials and MethodsThe CoPtCr films were deposited by an epitaxy-like sputtering and contained several perpendicularly magnetized granular-media layers with different coercivities; they are very much like the state-of-the-art perpendicular magnetic medium, which can be found in today’s hard disc drives. Magnetoresistive properties of bulk films were assessed by measuring the film resistance in the standard Van der Pauw geometry, while the local transport was probed by the point-contact technique.ResultsThe bulk measurements showed only a negligible magnetoresistance of less than 0.02%. In contrast, the local point-contact measurements revealed giant-magnetoresistance-like changes ΔR in local resistance of the contact R with more than 10,000% ratio ΔR/R.ConclusionThe observed large and local magnetoresistive effect could be tentatively attributed to a tunnel magnetoresistance between oxide-segregated CoPtCr grains with different coercivities. The tunneling picture of electronic transport in our granular medium was confirmed by the observation of tunneling-like current–voltage characteristics of the contacts and bias dependence of the contact magnetoresistance – both the local point-contact resistance and magnetoresistance were found to decrease with the applied dc bias.

Xolography for linear volumetric 3D printing.

The range of applications for additive manufacturing is expanding quickly, including mass production of athletic footwear parts1, dental ceramics2 and aerospace components3 as well as fabrication of microfluidics4, medical devices5, and artificial organs6. The light-induced additive manufacturing techniques7 used are particularly successful owing to their high spatial and temporal control, but such techniques still share the common motifs of pointwise or layered generation, as do stereolithography8, laser powder bed fusion9, and continuous liquid interface production10 and its successors11,12. Volumetric 3D printing13-20 is the next step onward from sequential additive manufacturing methods. Here we introduce xolography, a dual colour technique using photoswitchable photoinitiators to induce local polymerization inside a confined monomer volume upon linear excitation by intersecting light beams of different wavelengths. We demonstrate this concept with a volumetric printer designed to generate three-dimensional objects with complex structural features as well as mechanical and optical functions. Compared to state-of-the-art volumetric printing methods, our technique has a resolution about ten times higher than computed axial lithography without feedback optimization, and a volume generation rate four to five orders of magnitude higher than two-photon photopolymerization. We expect this technology to transform rapid volumetric production for objects at the nanoscopic to macroscopic length scales.

Phase field modelling of microscopic failure in composite laminates

The previous study of the authors on a phase field method for modelling progressive failure in multi-phase materials is further extended in this study to capture microscopic failure processes in composite laminates. The auxiliary phase field model for the regularization of material interface is re-formulated. In the computational model, a small part of the model is built from microscopic length scale to explicitly consider the microstructure of the material while the other area is built from macroscopic length scale to improve the efficiency. Cohesive elements are employed to link the two mesh parts with different length scales and also to capture the intralaminar failure. The existing ABAQUS subroutine “UEL” has been rewritten for the present study due to the introduction of cohesive elements and a BFGS solver is used to improve the iteration stability. The thickness effect of a thin ply made laminate is considered and the crack suppression effect is investigated.

Taking a closer look: A molecular-dynamics investigation of microscopic and apparent dynamic contact angles

HypothesisMolecular dynamics (MD) may be used to investigate the velocity dependence of both the microscopic and apparent dynamic contact angles (θm and θapp). MethodsWe use large-scale MD to explore the steady displacement of a water-like liquid bridge between two molecularly-smooth solid plates under the influence of an external force F0. A coarse-grained model of water reduces the computational demand and the solid-liquid affinity is varied to adjust the equilibrium contact angle θ0. Protocols are devised to measure θm and θapp as a function of contact-line velocity Ucl. FindingsFor all θ0, θm is velocity-dependent and consistent with the molecular-kinetic theory of dynamic wetting (MKT). However, θapp diverges from θm as F0 is increased, especially at the receding meniscus. The behavior of θapp follows that predicted by Voinov: (θapp)3 = (θm)3 + 9Ca·ln(L/Lm), where Ca is the capillary number and L and Lm are suitably-chosen macroscopic and microscopic length scales. For each θ0, there is a critical velocity Ucrit and contact angle θcrit at which θapp→0 and the receding meniscus deposits a liquid film. Setting θapp=0, θm=θcrit and Ucl=Ucrit in the Voinov equation yields the value of L/Lm. The predicted values of θapp then agree well with those measured from the simulations. Since θm obeys the MKT, we have, therefore, demonstrated the utility of the combined model of dynamic wetting proposed by Petrov and Petrov.

Machine Learning in Computational Surface Science and Catalysis: Case Studies on Water and Metal-Oxide Interfaces.

The goal of many computational physicists and chemists is the ability to bridge the gap between atomistic length scales of about a few multiples of an Ångström (Å), i. e., 10−10 m, and meso- or macroscopic length scales by virtue of simulations. The same applies to timescales. Machine learning techniques appear to bring this goal into reach. This work applies the recently published on-the-fly machine-learned force field techniques using a variant of the Gaussian approximation potentials combined with Bayesian regression and molecular dynamics as efficiently implemented in the Vienna ab initio simulation package, VASP. The generation of these force fields follows active-learning schemes. We apply these force fields to simple oxides such as MgO and more complex reducible oxides such as iron oxide, examine their generalizability, and further increase complexity by studying water adsorption on these metal oxide surfaces. We successfully examined surface properties of pristine and reconstructed MgO and Fe3O4 surfaces. However, the accurate description of water–oxide interfaces by machine-learned force fields, especially for iron oxides, remains a field offering plenty of research opportunities.

Topological Interlocking and Geometric Stiffening as Complementary Strategies for Strong Plant Shells.

Many organisms encapsulate their embryos in hard, protective shells. While birds and reptiles largely rely on mineralized shells, plants often develop highly robust lignocellulosic shells. Despite the abundance of hard plant shells, particularly nutshells, it remains unclear which fundamental properties drive their mechanical stability. This multiscale analysis of six prominent (nut)shells (pine, pistachio, walnut, pecan, hazelnut, and macadamia) reveals geometric and structural strengthening mechanisms on the cellular and macroscopic length scales. The strongest tissues, found in walnut and pistachio, exploit the topological interlocking of 3D-puzzle cells and thereby outperform the fiber-reinforced structure of macadamia under tensile and compressive loading. On the macroscopic scale, strengthening occurs via an increased shell thickness, spherical shape, small size, and a lack of extended sutures. These functional interrelations suggest that simple geometric modifications are a powerful and resource-efficient strategy for plants to enhance the fracture resistance of entire shells and their tissues. Understanding the interplay between structure, geometry, and mechanics in hard plant shells provides new perspectives on the evolutionary diversification of hard seed coats, as well as insights for nutshell-based material applications.