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Universal scaling in the aging of the strong glass former SiO{sub 2}

We show that the aging dynamics of a strong glass former displays a strikingly simple scaling behavior, connecting the average dynamics with its fluctuations, namely, the dynamical heterogeneities. We perform molecular dynamics simulations of SiO{sub 2} with van Beest-Kramer-van Santen interactions, quenching the system from high to low temperature, and study the evolution of the system as a function of the waiting time t{sub w} measured from the instant of the quench. We find that both the aging behavior of the dynamic susceptibility χ{sub 4} and the aging behavior of the probability distribution P(f{sub s,r}) of the local incoherent intermediate scattering function f{sub s,r} can be described by simple scaling forms in terms of the global incoherent intermediate scattering function C. The scaling forms are the same that have been found to describe the aging of several fragile glass formers and that, in the case of P(f{sub s,r}), have been also predicted theoretically. A thorough study of the length scales involved highlights the importance of intermediate length scales. We also analyze directly the scaling dependence on particle type and on wavevector q and find that both the average and the fluctuations of the slow aging dynamics are controlled by a unique aging clock, which is not only independent of the wavevector q, but is also the same for O and Si atoms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Comparison of a Full-Scale and a 1:10 Scale Low-Speed Two-Stroke Marine Engine Using Computational Fluid Dynamics

International marine shipping is a growing component of international trade; a vast majority of all the world’s goods are being transported on large ocean-going vessels. The International Maritime Organization (IMO) introduced the Energy Efficiency Design Index in 2013, a regulatory framework of associated metrics for reducing emissions of CO 2 per tonne-mile from shipping by approximately 10% each decade. Therefore, decarbonizing the maritime sector requires the development of new fuel sources. Because of the extremely large physical size of the internal combustion engines present in shipping vessels, experimental iterative development of the engine and fuel system is cost-prohibitive. Thus, the ability to perform combustion system development in a scaled platform that can be more easily operated and modeled computationally is of interest. To that end, scaling relationships are needed to translate the results from a smaller engine to a larger counterpart. Scaling studies to date have been restricted to low scaling ratios, four-stroke light-duty engines, and under-resolved computational fluid dynamic simulations that likely do not accurately capture the physics of scaling. In this work, computational models of a 1:10 scale and a full-scale two-stroke crosshead low-speed marine engine were created and validated against experiments obtained in a real 1:10 scale engine installed at Oak Ridge National Laboratory. Further, due to the large size of the full-scale engine, the model required large high-performance computing resources to be evaluated. The availability of high-performance computing resources at the Department of Energy’s Leadership Computing Facilities is an enabler of the current work. The results of the small- and large-scale engine simulations were compared to analyze the effectiveness of the appropriate scaling laws under these extreme scaling ratio conditions.

33 ADVANCED PROPULSION SYSTEMS↗

Adaptive Control and Scaling Approach for the Emulation of Dynamic Sub-scale Torque Loads

Previous research by the authors proposed a control and scaling approach for emulating dynamic sub-scale torque loads. This approach produced an emulation controller that successfully regulated the dynamic behavior of a sub-scale electro-mechanical system intended to be a dynamical representation of the sub-scale turboelectric powertrain of a single-aisle commercial aircraft. The sub-scale system provides an environment without turbomachinery or rotors for the initial testing of electrified aircraft propulsion (EAP) control algorithms as they would be applied to a full-scale EAP system. The sub-scale turbomachinery/rotor torque loads were produced by electric machines (EMs) driven by the control and scaling approach, a full-scale turboelectric powertrain model, and an advanced EAP control algorithm. Although successfully tested, this approach produces an emulation controller that does not guarantee asymptotic stability. Modifying the original control law and integrating adaptive control techniques into the emulation controller allows the designer to guarantee asymptotic stability. This paper introduces the idea behind the emulation controller modifications, derives the controller, proves asymptotic stability, describes the implementation of the controller on a sub-scale electro-mechanical system intended to represent a parallel hybrid-electric turbofan engine, and describes the testing of a full-scale advanced EAP control algorithm. The turbofan engine and emulation controller performance are compared to results obtained using the previous, non-adaptive control and scaling approach.

adaptive↗

Scale in Remote Sensing and GIS: An Advancement in Methods Towards a Science of Scale

The term "scale", both in space and time, is central to remote sensing and Geographic Information Systems (GIS). The emergence and widespread use of GIS technologies, including remote sensing, has generated significant interest in addressing scale as a generic topic, and in the development and implementation of techniques for dealing explicitly with the vicissitudes of scale as a multidisciplinary issue. As science becomes more complex and utilizes databases that are capable of performing complex space-time data analyses, it becomes paramount that we develop the tools and techniques needed to operate at multiple scales, to work with data whose scales are not necessarily ideal, and to produce results that can be aggregated or disaggregated ways that suit the decision-making process. Contemporary science is constantly coping with compromises, and the data available for a particular study rarely fit perfectly with the scales at which the processes being investigated operate, or the scales that policy-makers require to make sound, rational decisions. This presentation discusses some of the problems associated with scale as related to remote sensing and GIS, and describes some of the questions that need to be addressed in approaching the development of a multidisciplinary "science of scale". Techniques for dealing with multiple scaled data that have been developed or explored recently are described as a means for recognizing scale as a generic issue, along with associated theory and tools that can be of simultaneous value to a large number of disciplines. These can be used to seek answers to a host of interrelated questions in the interest of providing a formal structure for the management and manipulation of scale and its universality as a key concept from a multidisciplinary perspective.

Quattrochi, D. A.↗

Scale in Remote Sensing and GIS: An Advancement in Methods Towards a Science of Scale

The term "scale", both in space and time, is central to remote sensing and geographic information systems (GIS). The emergence and widespread use of GIS technologies, including remote sensing, has generated significant interest in addressing scale as a generic topic, and in the development and implementation of techniques for dealing explicitly with the vicissitudes of scale as a multidisciplinary issue. As science becomes more complex and utilizes databases that are capable of performing complex space-time data analyses, it becomes paramount that we develop the tools and techniques needed to operate at multiple scales, to work with data whose scales are not necessarily ideal, and to produce results that can be aggregated or disaggregated in ways that suit the decision-making process. Contemporary science is constantly coping with compromises, and the data available for a particular study rarely fit perfectly with the scales at which the processes being investigated operate, or the scales that policy-makers require to make sound, rational decisions. This presentation discusses some of the problems associated with scale as related to remote sensing and GIS, and describes some of the questions that need to be addressed in approaching the development of a multidisciplinary "science of scale". Techniques for dealing with multiple scaled data that have been developed or explored recently are described as a means for recognizing scale as a generic issue, along with associated theory and tools that can be of simultaneous value to a large number of disciplines. These can be used to seek answers to a host of interrelated questions in the interest of providing a formal structure for the management and manipulation of scale and its universality as a key concept from a multidisciplinary perspective.

Quattrochi, Dale A.↗

A gravo-aeroelastically scaled wind turbine rotor at field-prototype scale with strict structural requirements

A new sub-scale field-prototype design solution is developed to realize the dynamics, structural response, and distributed loads (gravitational, aerodynamic, centrifugal) that are characteristic of a full-scale large, modern wind turbine rotor. Prior work in sub-scale wind turbine testing has focused on matching aerodynamic/aero-elastic characteristics of full-scale rotors at wind tunnel scale. However, large-scale rotor designs must expand beyond this limited set of scaling parameters for cost-effective prototyping and meet strict requirements for structural safety for field testing. Here, the challenge lies in producing a structural design meeting two competing objectives: novel scaling objectives that prescribe the sub-scale blade to have low mass and stiffness; and traditional structural safety objectives that drive the design to have higher stiffness and mass. A 20% gravo-aeroelastically scaled wind turbine blade is developed successfully that satisfies these competing objectives. First, it achieved close agreement for non-dimensional tip deflection and flap-wise blade frequency (both within 2.1%) with a blade mass distribution constrained to produce target gravitational and centrifugal loads. Second, the entire blade structure was optimized to ensure a safe, manufacturable solution meeting strict strength requirements for a testing site that can experience up to 45 m/s wind gusts. The prototype-scale blade was fabricated and successfully proof-load tested.

17 WIND ENERGY↗

Cloud Structure and Cloud-Radiation Interaction: From Smallest Observable Scales (Less than 10 m) to GCM Grid Scales (More than 100 km)

In this presentation we review the fractal nature of internal cloud structure from cm- to km-scales as captured by in-situ probes during long horizontal penetrations by aircraft. We uncover the non-Poissonian spatial distribution of cloud droplets at submeter scales and confirm scale-invariant behavior for large scales. Based on these structural characteristics, we generate simple fractal cloud models that reproduce statistical scaling properties of real clouds. These stochastic models represent a link between nonlinear science, in general, and cloud-radiation interaction, in particular. Next we run three-dimensional radiative transfer computations on these synthetic fractal clouds and compare the structure of the resulting radiation fields with the known structure of the cloud model and with satellite images of real clouds. The different behaviors observed for small and large-scale variabilities will be discussed in detail. We find that while the large-scale fluctuations of the resulting radiation fields resemble those in the original scale-invariant cloud structure, the radiation at small scales is much smoother than its cloud liquid water counterpart. This violates scale-invariance and produces a scale-break at 0.2-0.5 km that is clearly observed in high-resolution satellite data such as from Landsat. Finally, we show how radiative transfer Green function theory in the photon diffusion limit explains (and predicts) the above phenomena of "radiative smoothing."

Marshak, Alexander↗

Evaluation of Methods to Select Scale Velocities in Icing Scaling Tests

A series of tests were made in the NASA Glenn Icing Research Tunnel to determine how icing scaling results were affected by the choice of scale velocity. Reference tests were performed with a 53.3-cm-chord NACA 0012 airfoil model, while scale tests used a 27.7-cm-chord 0012 model. Tests were made with rime, mixed, and glaze ice. Reference test conditions included airspeeds of 67 and 89 m/s, an MVD of 40 microns, and LWCs of 0.5 and 0.6 g/cu m. Scale test conditions were established by the modified Ruff (AEDC) scaling method with the scale velocity determined in five ways. The resulting scale velocities ranged from 85 to 220 percent of the reference velocity. This paper presents the ice shapes that resulted from those scale tests and compares them to the reference shapes. It was concluded that for freezing fractions greater than 0.8 as well as for a freezing fraction of 0.3, the value of the scale velocity had no effect on how well the scale ice shape simulated the reference shape. For freezing fractions of 0.5 and 0.7, the simulation of the reference shape appeared to improve as the scale velocity increased.

Anderson, David N.↗

Pore-scale supercritical CO 2 dissolution and mass transfer under drainage conditions

Abstract: Recently, both core- and pore-scale imbibition experiments have shown non-equilibrium dissolution of supercritical CO 2 (scCO 2 ) and a prolonged depletion of residual scCO 2 . In this study, pore-scale scCO 2 dissolution and mass transfer under drainage conditions were investigated using a two-dimensional heterogeneous micromodel and a novel fluorescent water dye with a sensitive pH range between 3.7 and 6.5. Drainage experiments were conducted at 9 MPa and 40 °C by injecting scCO 2 into the sandstone-analogue pore network initially saturated by water without dissolved CO 2 (dsCO 2 ). During the experiments, time-lapse images of dye intensity, reflecting water pH, were obtained. These images show non-uniform pH in individual pores and pore clusters, with average pH levels gradually decreasing with time. Further analysis on selected pores and pore clusters shows that (1) rate-limited mass transfer prevails with slowly decreasing pH over time when the scCO 2 -water interface area is low with respect to the volume of water-filled pores and pore clusters, (2) fast scCO 2 dissolution and phase equilibrium occurs when scCO 2 bubbles invade into water-filled pores, significantly enhancing the area-to-volume ratio, and (3) a transition from rate-limited to diffusion-limited mass transfer occurs in a single pore when a medium area-to-volume ratio is prevalent. The analysis also shows that two fundamental processes – scCO 2 dissolution at phase interfaces and diffusion of dsCO 2 at the pore scale (10-100 µm) observed after scCO 2 bubble invasion into water-filled pores without pore throat constraints – are relatively fast. The overall slow dissolution of scCO 2 in the millimeter-scale micromodel can be attributed to the small area-to-volume ratios that represent pore-throat configurations and characteristics of phase interfaces. This finding is applicable for the behavior of dissolution at pore, core, and field scales when water-filled pores and pore clusters of varying size are surrounded by scCO 2 at narrow pore throats.

54 ENVIRONMENTAL SCIENCES↗

Developing Scaling Relationships for Molecular Electrocatalysis through Studies of Fe-Porphyrin-Catalyzed O 2 Reduction

The oxygen reduction reaction (ORR) is a multiproton/multielectron transformation in which dioxygen (O 2 ) is reduced to water or hydrogen peroxide and serves as the cathode reaction in most fuel cells. The ORR (O 2 + 4e – + 4H + → 2H 2 O) involves up to nine substrates and thus requires navigating a complicated reaction landscape, typically with several high-energy intermediates. Many catalysts can perform this reaction, though few operate with fast rates and at low overpotentials (close to the thermodynamic potential). Attempts to optimize these parameters, both in homogeneous and heterogeneous electrocatalytic systems, have focused on modifying catalyst design and understanding kinetic/thermodynamic relationships between catalytic intermediates. One such method for analyzing and predicting catalyst reactivity and efficiency has been the development of “molecular scaling relationships”. In this work, we share our experience deriving and utilizing molecular scaling relationships for soluble, iron-porphyrin-catalyzed O 2 reduction in organic solvents. These relationships correlate turnover frequencies (TOF max ) and effective overpotentials (η eff ), properties uniquely defined for homogeneous catalysts. Following a general introduction of scaling relationships for both homogeneous and heterogeneous electrocatalysis, we describe the components of such scaling relationships: (i) the overall thermochemistry of the reaction and (ii) the rate and rate law of the catalyzed reaction. We then show how connecting these thermodynamic and kinetic parameters reveals multiple molecular scaling relationships for iron-porphyrin-catalyzed O 2 reduction. For example, the log(TOF max ) responds steeply to changes in ηeff that result from different catalyst reduction potentials (18.5 decades in TOF max /V in η eff ) but much less dramatically to changes in η eff that arise from varying the pKa of the acid buffer (5.1 decades in TOF max /V in η eff ). Thus, a single scaling relationship is not always sufficient for describing molecular electrocatalysis. This is particularly evident when the catalyst identity and reaction conditions are coupled. Using these multiple scaling relationships, we demonstrate that the metrics of turnover frequency and effective overpotential can be predictably tuned to achieve faster rates at lowered overpotentials. This Account uses a collection of related stories describing our research on soluble iron-porphyrin-catalyzed ORR to show how molecular scaling relationships can be derived and used for any electrocatalytic reaction. Such scaling relationships are powerful tools that connect the thermochemistry, mechanism, and rate law for a catalytic system. We hope that this collection shows the utility and simplicity of the molecular scaling approach for understanding catalysis, for enabling direct comparisons between catalyst systems, and for optimizing catalytic processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Immersive Particle Advection: Through the Scales of Renewable Energy: Preprint

We describe the benefits of immersive flow analysis for three large-scale computational science studies in the field of renewable energy. The studies encompass a range of scales, spanning from the large atmospheric scale of a wind farm to the human scale of an electric vehicle cabin down to the microscopic scale of battery material science. In these studies, users explored the flow patterns and dynamics through immersive particle advection. The integration of high-performance computing with immersive analysis provided a deeper understanding of these systems, helping develop more effective solutions for a sustainable energy future.

computational fluid dynamics↗

Tornadoes in Southeast South America: Mesoscale to Planetary-Scale Environments

Abstract A multiscale analysis of the environment supporting tornadoes in southeast South America (SESA) was conducted based on a self-constructed database of 74 reports. Composites of environmental and convective parameters from ERA5 were generated relative to tornado events. The distribution of the reported tornadoes maximizes over the Argentine plains, while events are rare close to the Andes and south of Sierras de Córdoba. Events are relatively common in all seasons except in winter. Proximity environment evolution shows enhanced instability, deep-layer vertical wind shear, storm-relative helicity, reduced convective inhibition, and a lowered lifting condensation level before or during the development of tornadic storms in SESA. No consistent signal in low-level wind shear is seen during tornado occurrence. However, a curved hodograph with counterclockwise rotation is present. The Significant Tornado Parameter (STP) is also maximized prior to tornadogenesis, most strongly associated with enhanced CAPE. Differences in the convective environment between tornadoes in SESA and the U.S. Great Plains are discussed. On the synoptic scale, tornado events are associated with a strong anomalous trough crossing the southern Andes that triggers lee cyclogenesis, subsequently enhancing the South American low-level jet (SALLJ) that increases moisture advection to support deep convection. This synoptic trough also enhances vertical shear that, along with enhanced instability, sustains organized convection capable of producing tornadic storms. At planetary scales, the tornadic environment is modulated by Rossby wave trains that appear to be forced by convection near northern Australia. Madden–Julian oscillation phase 3 preferentially occurs 1–2 weeks ahead of tornado occurrence. Significance Statement The main goal of this study is to describe what atmospheric conditions (from local to global scales) are present prior to and during tornadic storms impacting southeast South America (SESA). Increasing potential for deep convection, wind shear, and potential for rotating updrafts, as well as reducing convective inhibition and cloud-base height, are predominant a few hours before and during the events in connection to low-level northerly winds enhancing moisture transport to the region. Remote convective activity near northern Australia appears to influence large-scale atmospheric circulation that subsequently triggers convective storms supporting tornadogenesis 1–2 weeks later in SESA. Our findings highlight the importance of accounting for atmospheric processes occurring at different scales to understand and predict tornado occurrences.

Meteorology & Atmospheric Sciences↗

Development and analysis of prognostic equations for mesoscale kinetic energy and mesoscale (subgrid scale) fluxes for large-scale atmospheric models

Generated by landscape discontinuities (e.g., sea breezes) mesoscale circulation processes are not represented in large-scale atmospheric models (e.g., general circulation models), which have an inappropiate grid-scale resolution. With the assumption that atmospheric variables can be separated into large scale, mesoscale, and turbulent scale, a set of prognostic equations applicable in large-scale atmospheric models for momentum, temperature, moisture, and any other gaseous or aerosol material, which includes both mesoscale and turbulent fluxes is developed. Prognostic equations are also developed for these mesoscale fluxes, which indicate a closure problem and, therefore, require a parameterization. For this purpose, the mean mesoscale kinetic energy (MKE) per unit of mass is used, defined as E-tilde = 0.5 (the mean value of u'(sub i exp 2), where u'(sub i) represents the three Cartesian components of a mesoscale circulation (the angle bracket symbol is the grid-scale, horizontal averaging operator in the large-scale model, and a tilde indicates a corresponding large-scale mean value). A prognostic equation is developed for E-tilde, and an analysis of the different terms of this equation indicates that the mesoscale vertical heat flux, the mesoscale pressure correlation, and the interaction between turbulence and mesoscale perturbations are the major terms that affect the time tendency of E-tilde. A-state-of-the-art mesoscale atmospheric model is used to investigate the relationship between MKE, landscape discontinuities (as characterized by the spatial distribution of heat fluxes at the earth's surface), and mesoscale sensible and latent heat fluxes in the atmosphere. MKE is compared with turbulence kinetic energy to illustrate the importance of mesoscale processes as compared to turbulent processes. This analysis emphasizes the potential use of MKE to bridge between landscape discontinuities and mesoscale fluxes and, therefore, to parameterize mesoscale fluxes generated by such subgrid-scale landscape discontinuities in large-scale atmospheric models.

Avissar, Roni↗

Prognostic Power of Extreme Rainfall Scaling Formulas Across Space and Time Scales

Some studies documenting changes in extreme precipitation use scaling formulas to approximate the large percentiles of the rainfall distribution from average dynamical and thermodynamical variables, called predictors. Here we instead assess the performance of these formulas as approximations to the rain rates in individual events. We evaluate the accuracies of the scaling relationships as functions of spatial and temporal scales by analyzing tropical rainfall in a superparameterized model. Relationships using full vertical profiles of the predictors are more accurate than those using their values at specific vertical levels because they better characterize the specific dynamics of each event. Both types of scaling relationships perform well over a range of length scales from 200 to 2,000 km and time scales from an hour to a week, and their precision is higher in the case of simulations with superparameterization than with parameterized convection. Uncertainties emerging from the local use of the scaling relationships suggest that they may only characterize the intensification of individual extremes for a warming of 4–5 K or larger. Finally, we argue that these formulas can be used to reconstruct the tail of the rainfall distribution directly from its predictors without prior information on P. While scalings have been used as diagnostic equations conditioned on the occurrence of extreme rainfall, they are actually able to mimic the prognostic behavior of climate model parameterizations on a variety of scales when estimating the intensity, frequency, and spatial patterns of extremes.

54 ENVIRONMENTAL SCIENCES↗

Exploring the parameter space of MagLIF implosions using similarity scaling. II. Current scaling

Magnetized liner inertial fusion (MagLIF) is a magneto-inertial-fusion (MIF) concept, which is presently being studied on the Z pulsed power facility. The MagLIF platform has achieved interesting plasma conditions at stagnation and produced significant fusion yields in the laboratory. Given the relative success of MagLIF, there is a strong interest to scale the platform to higher peak currents. However, scaling MagLIF is not entirely straightforward due to the large dimensionality of the experimental input parameter space and the numerous physical processes involved in MIF implosions. Here, in this work, we propose a novel method to scale MagLIF loads to higher currents. Our method is based on similarity (or similitude) scaling and attempts to preserve much of the physics regimes already known or being studied on today's Z pulsed-power driver. By avoiding significant deviations into unexplored and/or less well-understood regimes, the risk of unexpected outcomes on future scaled-up experiments is reduced. Using arguments based on similarity scaling, we derive the scaling rules for the experimental input parameters characterizing a MagLIF load (as functions of the characteristic current driving the implosion). We then test the estimated scaling laws for various metrics measuring performance against results of 2D radiation–magneto-hydrodynamic hydra simulations. Agreement is found between the scaling theory and the simulation results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A subgrid model for electron-scale turbulent transport in global ion-scale gyrokinetic simulations of tokamak plasmas

A subgrid electron–temperature–gradient (ETG) model is demonstrated here which averages local electron-scale turbulence over intermediate scales in space and time to include in global ion–temperature–gradient (ITG) simulations. This approach results in ion-scale equations, which incorporate the electron heat transport from ETG turbulence and the effects of electron-scale turbulence on the ion scale. Flux-tube ETG Cyclone Base Case simulations are performed at different radial locations and a kinetic form of the flux is added to global ion-scale (IS) simulations as a source term. Analytic radial profiles of ETG heat flux are constructed and compared to flux-tube results at multiple radial locations. Different ratios of ITG to ETG heat flux levels are considered and the results of capturing ETG heat transport in global ion-scale simulations are discussed. The potential coupling of the ETG streamer potential and intermediate-scale zonal flows to the ion scale is further addressed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Linking Large-Scale Double-ITCZ Bias to Local-Scale Drizzling Bias in Climate Models

Tropical precipitation in climate models presents significant biases in both the large-scale pattern (i.e., double intertropical convergence zone bias) and local-scale characteristics (i.e., drizzling bias with too frequent drizzle/convection and reduced occurrences of no and heavy precipitation). By untangling the coupled system and analyzing the biases in precipitation, cloud, and radiation, this study shows that local-scale drizzling bias in atmospheric models can lead to large-scale double-ITCZ bias in coupled models by inducing convective-regime-dependent biases in precipitation and cloud radiative effects (CRE). The double-ITCZ bias consists of a hemispherically asymmetric component that arises from the asymmetric SST bias and a nearly symmetric component that exists in atmospheric models without the SST bias. By increasing light rain but reducing heavy rain, local-scale drizzling bias induces positive (negative) precipitation bias in the moderate (strong) convective regime, leading to the nearly symmetric wet bias in atmospheric models. By affecting the cloud profile, local-scale drizzling bias induces positive (negative) CRE bias in the stratocumulus (convective) regime in atmospheric models. Because the stratocumulus (convective) region is climatologically more pronounced in the southern (northern) tropics, the CRE bias is deemed to be hemispherically asymmetric and drives warm and wet (cold and dry) biases in the southern (northern) tropics when coupled to ocean. Our results suggest that correcting local-scale drizzling bias is critical for fixing large-scale double-ITCZ bias. Finally, the drizzling and double-ITCZ biases are not alleviated in models with mesoscale (0.25°–0.5°) or even storm-resolving (~3 km) resolution, implying that either large-eddy simulation or fundamental improvement in small-scale subgrid parameterizations is needed.

54 ENVIRONMENTAL SCIENCES↗

A Micromorphic Length-Scale Coupling Framework for the Determination of Higher-Order Constitutive Models and the Multi-Scale Simulation of Heterogeneous Materials [Thesis]

Heterogeneous materials and materials with complex microstructures pose a unique challenge in the development of accurate models of their response to external stimuli. These difficulties principally arise due to the difficulty in characterizing and modeling the constituents and their interactions. It is usually possible, though non-trivial, to construct an explicit representation of the microstructure (a direct numeric simulation or DNS) but the method by which the complex modes of deformation and other processes can be homogenized to a reduced-order approximation is frequently unclear. Many homogenization approaches are ad-hoc and lack a strong justification beyond ease of computation. Furthermore, the homogenization approach can, in some cases, not utilize the full breadth of information available in the computation of the macro-scale stresses and deformation measures. It is also noteworthy that homogenization, by its very nature, will tend to obfuscate details of processes occurring at the lower length-scale. It is therefore of interest to include as much information as possible in the construction of the reduced-order model so as to be predictive in a variety of loading environments. We here present a length-scale bridging technique based upon the micromorphic continuum mechanics of Eringen which incorporates volume and surface area averages as a part of its construction. This approach enforces the balance equations at the micro-scale and then studies the effect of the spatially varying nature on the macro-scale. This leads, naturally, to further balance equations which are solved at the macro-scale. This work details a homogenization framework which arises naturally from the micromorphic construction of Eringen attempting to introduce no definitions beyond which are justifiable from micro-structural considerations. One of the results of this effort is the so-called “micromorphic filter” which has been developed and applied to several DNS to demonstrate its effectively. In order to determine the macroscopic degrees of freedom we utilize the special case of an overlap coupling technique where the macro-scale is fully constrained to the micro-scale. This enables us to study the resulting material properties as expected but also allows us to further study the boundary conditions on the additional degrees of freedom at the macro-scale.

42 ENGINEERING↗