SEARCH · Engineering Papers

Results for “spatial heterogeneity”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 199 records · Page 11

All sources NASA NTRS DOE OSTI

DOE OSTI2023

Global assessment of the carbon–water tradeoff of dry cooling for thermal power generation

Water scarcity and climate change are dual challenges that could potentially threaten energy security. Yet, integrated water–carbon management frameworks coupling diverse water- and carbon-mitigation technologies at high spatial heterogeneity are largely underdeveloped. Here we build a global unit-level framework to investigate the CO 2 emission and energy penalty due to the deployment of dry cooling—a critical water mitigation strategy—together with alternative water sourcing and carbon capture and storage under climate scenarios. We find that CO 2 emission and energy penalty for dry cooling units are location and climate specific (for example, 1–15% of power output), often demonstrating notably faster efficiency losses than rising temperature, especially under the high climate change scenario. Despite energy and CO 2 penalties associated with alternative water treatment and carbon capture and storage utilization, increasing wastewater and brine water accessibility provide potential alternatives to dry cooling for water scarcity alleviation, whereas CO 2 storage can help to mitigate dry cooling-associated CO 2 emission tradeoffs when alternative water supply is insufficient. By demonstrating an integrative planning framework, our study highlights the importance of integrated power sector planning under interconnected dual water–carbon challenges.

42 ENGINEERING↗

DOE OSTI2020

Electro-chemo-mechanical evolution of sulfide solid electrolyte/Li metal interfaces: operando analysis and ALD interlayer effects

Sulfide solid electrolytes (SE) show promise for high-performance solid-state batteries because of their high ionic conductivity and ease of processing. However, sulfide electrolytes have suffered from chemical and electrochemical instability against Li metal anodes. In this paper, we use a suite of in situ/operando microscopy and spectroscopy techniques to demonstrate that Al 2 O 3 interlayers deposited using atomic layer deposition (ALD) delay degradation at the Li/LGPS interface by modifying the solid electrolyte interphase (SEI) chemistry and morphology. Optical and scanning electron microscopy are used to rationalize the electrochemical response of the system, which is attributed to a delayed onset of mechanical degradation at the interface when ALD interlayers are used. Operando X-ray photoelectron spectroscopy demonstrates that the dynamic evolution of SEI chemistry is impacted by the presence of the ALD interlayer. In situ Auger spectroscopy and operando optical microscopy provide visual evidence of spatial heterogeneity of Li plating, which is attributed to the chemo-mechanical degradation of the ALD interphase. The implications of these observations provide valuable insights toward the development of robust interlayers for solid-state batteries.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Incorporating the molecular-scale into a hydrodynamic description of confined aqueous systems

Hydrodynamics provides a continuum-level description of fluid motion, but its applicability at the nanoscale becomes uncertain due to the emerging importance of molecular-level effects such as spatial heterogeneity. Hydrodynamic boundary conditions that incorporate molecular details allow us to partition the system into a near-wall region and a bulk fluid region. We identify a hydrodynamic wall located inside the fluid that determines where slip begins. By extending the hydrodynamic wall with the slip length, the position of the extrapolated wall is established. This offers a unified description of both slip and stagnant flow behaviors, with wall hydrophobicity characterized by the relative location of the extrapolated wall with respect to the physical wall. Employing this concept in analyses of equilibrium molecular dynamics (MD) and non-equilibrium MD simulations of Couette and Poiseuille flows, our results demonstrate consistency between equilibrium and non-equilibrium approaches across different flow types and confinement levels. This demonstrates the robust nature of linear response theory. We then explore the effects of fluid-wall and bulk fluid interactions on the hydrodynamic properties. These findings enhance the effectiveness of molecular-based simulations for investigating complex confined systems in nanofluidics, biology, and colloidal science, offering a complementary molecular-scale perspective to traditional continuum approaches.

flow simulations↗

DOE OSTI2021

Nature of dynamic gradients, glass formation, and collective effects in ultrathin freestanding films

Significance The origin of spatially heterogeneous alterations in the dynamics of nanoconfined liquids has been a major question in physics, chemistry, and materials science for over 30 y. We combine simulation and theory to establish a unified predictive microscopic understanding in freestanding films at low to medium molecular weight, spanning from thick to ultrathin films. The simulation-based phenomenology of altered dynamics is theoretically predicted and understood based on a combination of coupled near-interface gradients of local caging constraints and interfacial and finite size-induced changes in a collective elastic barrier to motion. No invocation of any realized or incipient critical-like phenomenon is necessary, which may have broad implications for other confined systems and the mechanism of the bulk glass transition.

nanoconfinement↗

DOE OSTI2021

Early warm-season mesoscale convective systems dominate soil moisture–precipitation feedback for summer rainfall in central United States

Land–atmosphere interactions play an important role in summer rainfall in the central United States, where mesoscale convective systems (MCSs) contribute to 30 to 70% of warm-season precipitation. Previous studies of soil moisture–precipitation feedbacks focused on the total precipitation, confounding the distinct roles of rainfall from different convective storm types. Here, we investigate the soil moisture–precipitation feedbacks associated with MCS and non-MCS rainfall and their surface hydrological footprints using a unique combination of these rainfall events in observations and land surface simulations with numerical tracers to quantify soil moisture sourced from MCS and non-MCS rainfall. Furthermore, we find that early warm-season (April to June) MCS rainfall, which is characterized by higher intensity and larger area per storm, produces coherent mesoscale spatial heterogeneity in soil moisture that is important for initiating summer (July) afternoon rainfall dominated by non-MCS events. On the other hand, soil moisture sourced from both early warm-season MCS and non-MCS rainfall contributes to lower-level atmospheric moistening favorable for upscale growth of MCSs at night. However, soil moisture sourced from MCS rainfall contributes to July MCS rainfall with a longer lead time because with higher intensity, MCS rainfall percolates into deeper soil that has a longer memory. Therefore, early warm-season MCS rainfall dominates soil moisture–precipitation feedback. This motivates future studies to examine the contribution of early warm-season MCS rainfall and associated soil moisture anomalies to predictability of summer rainfall in the major agricultural region of the central United States and other continental regions frequented by MCSs.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Probing multiscale dissolution dynamics in natural rocks through microfluidics and compositional analysis

Mineral dissolution significantly impacts many geological systems. Carbon released by diagenesis, carbon sequestration, and acid injection are examples where geochemical reactions, fluid flow, and solute transport are strongly coupled. The complexity in these systems involves interplay between various mechanisms that operate at timescales ranging from microseconds to years. Current experimental techniques characterize dissolution processes using static images that are acquired with long measurement times and/or low spatial resolution. These limitations prevent direct observation of how dissolution reactions progress within an intact rock with spatially heterogeneous mineralogy and morphology. We utilize microfluidic cells embedded with thin rock samples to visualize dissolution with significant temporal resolution (100 ms) in a large observation window (3 × 3 mm). Here we injected acidic fluid into eight shale samples ranging from 8 to 86 wt % carbonate. The pre- and postreaction microstructures are characterized at the scale of pores (0.1 to 1 µm) and fractures (1 to 1,000 µm). We observe that nonreactive particle exposure, fracture morphology, and loss of rock strength are strongly dependent on both the relative volume of reactive grains and their distribution. Time-resolved images of the rock unveil the spatiotemporal dynamics of dissolution, including two-phase flow effects in real time and illustrate the changes in the fracture interface across the range of compositions. Moreover, the dynamical data provide an approach for characterizing reactivity parameters of natural heterogeneous samples when porous media effects are not negligible. The platform and workflow provide real-time characterization of geochemical reactions and inform various subsurface engineering processes.

58 GEOSCIENCES↗

DOE OSTI2024

Emergent facilitation and glassy dynamics in supercooled liquids

In supercooled liquids, dynamical facilitation refers to a phenomenon where microscopic motion begets further motion nearby, resulting in spatially heterogeneous dynamics. This is central to the glassy relaxation dynamics of such liquids, which show super-Arrhenius growth of relaxation timescales with decreasing temperature. Despite the importance of dynamical facilitation, there is no theoretical understanding of how facilitation emerges and impacts relaxation dynamics. Here, we present a theory that explains the microscopic origins of dynamical facilitation. We show that dynamics proceeds by localized bond-exchange events, also known as excitations, resulting in the accumulation of elastic stresses with which new excitations can interact. At low temperatures, these elastic interactions dominate and facilitate the creation of new excitations near prior excitations. Using the theory of linear elasticity and Markov processes, we simulate a model, which reproduces multiple aspects of glassy dynamics observed in experiments and molecular simulations, including the stretched exponential decay of relaxation functions, the super-Arrhenius behavior of relaxation timescales as well as their two-dimensional finite-size effects. The model also predicts the subdiffusive behavior of the mean squared displacement (MSD) on short, intermediate timescales. Furthermore, we derive the phonon contributions to diffusion and relaxation, which when combined with the excitation contributions produce the two-step relaxation processes, and the ballistic–subdiffusive–diffusive crossover MSD behaviors commonly found in supercooled liquids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

The implications of future climate change on the blue water footprint of hydropower in the contiguous US

As the largest renewable energy source, hydropower is essential to the sustainability of the global energy market. However, a considerable amount of water can be lost in the form of evaporation from the associated multipurpose reservoirs, and hence enlarge the blue water footprint (BWF) of hydropower in a warming climate. To facilitate the sustainable management of both water and energy resources under the impact of climate change in the contiguous United States (CONUS), the BWF values of 143 major multipurpose reservoirs were evaluated during the historical period (1985–2014) and two future periods (2020–2049 and 2070–2099). The historical reservoir evaporation loss was calculated using the Landsat-based reservoir surface area and a new evaporation rate algorithm that considers the heat storage effect. Future projections of runoff availability, hydropower generation, and reservoir evaporation were estimated based on the downscaled climate model ensemble from phase 5 of the Coupled Model Intercomparison Project (CMIP5). It was found that the BWF for the CONUS is highly spatially heterogeneous, with an average value of 26.2 m 3 /MWh in the historical period. In the future, the BWF values are projected to increase under both Representative Concentration Pathway (RCP) 4.5 and 8.5 scenarios. This is especially noticeable under RCP 8.5, which has an average BWF value of 30.2 m 3 /MWh for 2070–2099 (increasing by 15.3% from 26.2 m 3 /MWh). The uncertainty ranges increase even more, from 3.4 m 3 /MWh during 2020–2049 to 5.7 m 3 /MWh during 2070–2099. These findings can benefit water and energy resources management in identifying suitable environmental, economic, operational, and investment strategies for multipurpose reservoirs in a changing environment.

13 HYDRO ENERGY↗

DOE OSTI2022

A review of carbon monitoring in wet carbon systems using remote sensing

Carbon monitoring is critical for the reporting and verification of carbon stocks and change. Remote sensing is a tool increasingly used to estimate the spatial heterogeneity, extent and change of carbon stocks within and across various systems. We designate the use of the term wet carbon system to the interconnected wetlands, ocean, river and streams, lakes and ponds, and permafrost, which are carbon-dense and vital conduits for carbon throughout the terrestrial and aquatic sections of the carbon cycle. We reviewed wet carbon monitoring studies that utilize earth observation to improve our knowledge of data gaps, methods, and future research recommendations. To achieve this, we conducted a systematic review collecting 1622 references and screening them with a combination of text matching and a panel of three experts. The search found 496 references, with an additional 78 references added by experts. Our study found considerable variability of the utilization of remote sensing and global wet carbon monitoring progress across the nine systems analyzed. The review highlighted that remote sensing is routinely used to globally map carbon in mangroves and oceans, whereas seagrass, terrestrial wetlands, tidal marshes, rivers, and permafrost would benefit from more accurate and comprehensive global maps of extent. We identified three critical gaps and twelve recommendations to continue progressing wet carbon systems and increase cross system scientific inquiry.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Arctic extreme precipitation changes from 1980 to 2022 in response to sea ice decline and enhanced atmospheric rivers

Arctic extreme precipitation (EP) broadly impacts permafrost degradation, glacier and snow cover changes, and ice sheet mass balance as well as ecosystems. However, investigation of EP spatiotemporal variations over the Arctic remains challenging, and their primary drivers are still poorly understood. Performance estimation of three state-of-the-art reanalysis products (Climate Forecast System Reanalysis (CFSR), European Centre for Medium-Range Weather Forecasts Reanalysis version 5 (ERA-5), and Modern-Era Retrospective analysis for Research and Applications, version 2 (MERRA-2)) against gauge-based precipitation observations reveals that MERRA-2 outperforms other reanalysis for Arctic EP changes. Based on MERRA-2 data, both annual EP amount and occurrence days averaged over the Arctic show statistically significant positive trends during 1980–2022 (3.37 ± 1.03 mm dec −1 and 0.42 ± 0.17 d dec −1 , respectively), with the most pronounced increase in the autumn. Spatial heterogeneity in annual and seasonal EP trends is found across the Arctic, with the largest positive annual trends of 30 mm dec −1 over the Bering Sea and the Denmark Strait. The significant EP increase is closely associated with intensified atmospheric rivers (ARs) and widespread decline in sea ice concentration (SIC). Specially, SIC and ARs are responsible for 12% and 50% of Arctic EP inter-annual variance, respectively, while ARs directly contribute 28.3% of the total annual EP amounts. These findings explain the mechanistic controls on Arctic EP, providing critical insights for projecting polar weather and climate extremes and their impacts on the Arctic environment.

atmospheric rivers↗

DOE OSTI2025

Near-term heatwave risk in HighResMIP models across different temperature zones of West Africa

This study projects near-future (2031–2050) changes in heatwave (HW) risk across West Africa (WA) using an ensemble of eight high-resolution global climate models from the High-Resolution Model Intercomparison Project under a high-emission scenario. Using K-means clustering, we divided WA into four unique temperature zones and examined projected changes in extreme temperatures, HW occurrence and magnitude. Our results indicate a statistically significant increase in future HW events across most parts of WA, although considerable spread exists over the region and among individual models. The most pronounced increases are evident in the Sahel/Sahara and the Guinea Highlands subregions, with an ensemble mean increase of ∼10 HW events per year. In contrast, the lowest increase in HW events is projected in central WA, with increases ranging between 1 and 5 events per year. Similarly, the magnitude of HW events is projected to increase in most models, with Sahel/Sahara exhibiting the largest increases. Additionally, projections suggest that the strongest HWs will become more frequent, particularly in northern and southwestern WA. These findings highlight significant spatial heterogeneity in future HW risk across WA, emphasizing the need for targeted adaptation strategies.

HighResMIP↗

DOE OSTI2023

The Determination of the Spatial Distribution of Indigenous Lipid Biomarkers in an Immature Jurassic Sediment Using Time-of-Flight–Secondary Ion Mass Spectrometry

The ability to detect and map lipids, including potential lipid biomarkers, within a sedimentary matrix using mass spectrometry (MS) imaging may be critical to determine whether potential lipids detected in samples returned from Mars are indigenous to Mars or are contaminants. Here, we use gas chromatography–mass spectrometry (GC-MS) and time-of-flight–secondary ion mass spectrometry (ToF-SIMS) datasets collected from an organic-rich, thermally immature Jurassic geologic sample to constrain MS imaging analysis of indigenous lipid biomarkers in geologic samples. GC-MS data show that the extractable fractions are dominated by C 27 –C 30 steranes and sterenes as well as isorenieratene derivatives. ToF-SIMS spectra from organic matter-rich laminae contain a strong, spatially restricted signal for ions m/z 370.3, m/z 372.3, and m/z 386.3, which we assign to C 27 sterenes, cholestane (C 27 ), and 4- or 24-methyl steranes (C 28 ), respectively, as well as characteristic fragment ions of isorenieratene derivatives, including m/z 133.1, m/z 171.1, and m/z 237.1. We observed individual steroid spatial heterogeneity at the scale of 10's to 100's of microns. The fine-scale heterogeneity observed implies that indigenous lipid biomarkers concentrated within specific regions may be detectable via ToF-SIMS in samples with even low amounts of organic carbon, including in samples returned from Mars.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2025

Mesoscale variations of the chemical and electronic landscape on the surface of the Weyl semimetal Co 3 ⁢Sn 2⁢ S 2 visualized by ARPES and XPS

The multiple crystalline terminations in magnetic Weyl semimetal Co 3 Sn 2 S 2 display distinct topological and trivial surface states, which have successfully been distinguished experimentally. However, a model of pure terminations is known to be inadequate because these surfaces exhibit a high degree of spatial heterogeneity and point disorder. Here, in this study, we perform a spectromicroscopy study of the surface chemistry and surface electronic structure using photoemission measurements in combination with first-principles calculations of core levels. We identify an intermediate region with properties distinct from both the sulfur and tin terminations, and demonstrate that the spectral features in this region can be associated with a disordered termination with a varying density of surface tin vacancies. This work establishes heuristics for identifying variable surface disorder using photoemission, an important prerequisite to experimentally establishing the behavior of momentum-space topological surface features subject to variable surface disorder on a single cleave.

Sreedhar, Sudheer Anand [Univ. of California, Davi↗

DOE OSTI2021

Phase transitions in Schloegl's second model for autocatalysis on a Bethe lattice

Schloegl's second model (also known as the quadratic contact process) on a lattice involves spontaneous particle annihilation at rate p and autocatalytic particle creation at empty sites with n ≥ 2 occupied neighbors. The particle creation rate for exactly n occupied neighbors is selected here as n(n - 1)/[z(z - 1)] for lattice coordination number z. We analyze this model on a Bethe lattice. Precise behavior for stochastic models on regular periodic infinite lattices is usually surmised from kinetic Monte Carlo simulation on a finite lattice with periodic boundary conditions. However, the persistence of boundary effects for a Bethe lattice complicates this process, e.g., by inducing spatially heterogenous states. This motivates the exploration of various boundary conditions and unconventional simulation ensembles on the Bethe lattice to predict behavior for infinite size. Here, we focus on z = 3, and predict a discontinuous transition to the vacuum state on the infinite lattice when p exceeds a threshold value of around 0.053.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Unveiling the mechanism of phase and morphology selections during the devitrification of Al-Sm amorphous ribbon

The complex interplay between energetic and kinetic factors that governs the phase and morphology selections can originate at the earliest stage of crystallization in the amorphous parent phases. Because of the extreme difficulties in capturing the microscopic nucleation process, a detailed picture of how initial disordered structures affect the transformation pathway remains unclear. Here, we report the experimental observation of widely varying phase selection and grain size evolution during the devitrification of a homogeneous melt-spun glassy ribbon. Two different crystalline phases, θ-Al 5 Sm and ε-Al 60 Sm 11 , are found to form in the different regions of the same metallic glass ribbon during the devitrification. The grain size of ε-Al 60 Sm 11 phase shows a strong spatial heterogeneity. Coarse-grained ε-Al 60 Sm 11 phase coupled with the small volume fraction of θ-Al 5 Sm phase is preferably formed close to wheel side of the melt-spun ribbon. Combining experimental characterization and computational simulations, we show that phase selection and microstructure evolution can be traced back to different types and populations of atomic clusters that serve as precursors for the nucleation of different crystalline phases. Inhomogeneous cooling rates cause different structure orders across the glass sample during the quenching process. Our findings provide direct insight into the effect of structural order on the crystallization pathways during the devitrification of metallic glass. It also opens an avenue to study the detailed nucleation process at the atomic level using the metallic glass as a platform and suggests the opportunity of microstructure and property design via controlling the cooling process.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Imaging coherent phonons and precursor dynamics in LaFeAsO with 4D ultrafast electron microscopy

In this work, we used 4D ultrafast electron microscopy (UEM) to directly image femtosecond photoinduced structural dynamics in single-crystal LaFeAsO at initial temperatures of 300 and 100 K, above and below the known structural and magnetic phase-transition temperatures, respectively. With nanometer-picosecond resolution, we resolved an initial (precursor) sigmoidlike response arising from photothermal expansion and lattice reorientation that precedes the onset of propagating coherent acoustic phonons (CAPs). In the specific regions probed, the precursor response at 100 K is shorter than at 300 K ($t$ 0.5;100 K = 11.3ps vs $t$ 0.5;300 K = 17.8ps), and the CAP oscillation frequency is lowered with cooling (ƒ CAP;100 K = 12 GHz vs ƒ CAP;300 K = 21 GHz), correlated to known lattice softening due to the structural phase change. The transient CAP behaviors at 300 K are dispersive, displaying an exponentially decaying phase velocity over the first nanosecond. Further, the CAP symmetry at 300 K matches a first-order antisymmetric shear mode (A 1 ), while at 100 K it is best matched by a mostly nondispersive zero-order symmetric mode (S 0 ). These findings illustrate the sensitivity of UEM imaging to spatially heterogeneous dynamics in the Fe-pnictide materials and more broadly in other quantum materials.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Intricate short-range order in GeSn alloys revealed by atomistic simulations with highly accurate and efficient machine-learning potentials

GeSn alloys hold promise for silicon-compatible integrated applications in electronics, photonics, and topological quantum devices. However, understanding their intricate structures using density functional theory (DFT) calculations is hindered by spatiotemporal constraints. To overcome this limitation, we develop highly accurate and efficient machine-learning interatomic potentials based on a neuroevolution potential approach with farthest point sampling on a comprehensive DFT data set. The application of the developed machine-learning potential in large-scale atomistic simulations bridges the spatiotemporal gap between modeling and advanced characterizations, and facilitates the discovery of structural intricacies in GeSn alloys. Through extensive statistical sampling, we identify a type of short-range order (SRO) that is distinguished by both its structural signature and electronic band gap from the SRO structure previously predicted. Modeling based on a large simulation cell reveals the coexistence of nano SRO domains with various degrees of ordering, demonstrating a complex spatial heterogeneity of SRO structure. Finally, our study not only reinforces the significance of fine-level structural information in alloys, but it also constitutes an effective framework for exploring SRO in a broad range of complex alloys based on highly accurate and effective machine-learning potentials.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Trends in spatial correlations, two-phase coexistence, and criticality in a class of type-2 Schloegl models for autocatalysis

A class of type-2 Schloegl models is considered for particles on a square lattice with variable-range cooperativity. These models involve: (i) spontaneous particle annihilation at rate p; (ii) autocatalytic particle creation at unoccupied sites (i, j) with n ⩾ 2 particles within a specified neighborhood, Ω 𝑁 (i, j), of sites at rate $k_n$ = $\frac{^{(^n_2)}}{_{(^N_2)}}$ = $\frac{n{(n-1)}}{_{N(N-1)}}$; and (iii) possible spontaneous particle creation at unoccupied sites at “small” rate ɛ ⩾ 0. In some cases, Ω 𝑁 just includes all symmetry-equivalent sites at a single specific distance 𝑑 (in units of lattice constants) from the unoccupied site, e.g., 𝑑 = 1 (nearest-neighbor sites) where 𝑁 = 4, or 𝑑 = √5 (or √13 or…) where 𝑁 = 8. In other cases, Ω 𝑁 includes sites multiple distances from the unoccupied site, e.g., 𝑑 = {1,√2}, where 𝑁 = 8. Kinetic Monte Carlo (KMC) simulation reveals that these models exhibit a nonequilibrium discontinuous phase transition between high- and low-density states below a critical point, ɛ < ɛ c , with generic two-phase coexistence (2PC) at least for smaller 𝑁. With some exceptions, there is an approach toward mean-field behavior with increasing 𝑁 (so the regime of generic 2PC shrinks, and ɛ c approaches the mean-field value of 1/27). Additional insight into trends is provided by analysis of the exact master equations for the models via hierarchical truncation. These truncations utilize suitably tailored pair approximations which reflect the dominant nonequilibrium spatial correlations. These correlations in turn are shown to reflect the details of the autocatalytic particle creation process. For spatially heterogeneous states, the truncations produce coupled sets of lattice differential equations (LDE) which can describe orientation-dependent propagation of an interface between high- and low-density steady states for ɛ < ɛ c . Pair approximation values of 𝑝 = 𝑝 eq where the interface is stationary, and its orientation-dependence, are in semiquantitative agreement with KMC results. In conclusion, this comparison accounts for propagation failure in the LDE which complicates interpretation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗