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At least 1,027 records · Page 57

Transition Analysis for the CRM-NLF Wind Tunnel Configuration

This paper presents the results of an ongoing study into the linear stability characteristics of the boundary layer flow over the common research model with natural laminar flow (CRMNLF) aircraft configuration. The flow conditions match selected test conditions from a recent wind tunnel experiment in the National Transonic Facility at the NASA Langley Research Center. Previous work involving parallel stability computations of a boundary layer flow based on the conical flow approximation has shown that the measured onset of laminar-turbulent transition during the experiments can be correlated with the linear amplification of Tollmien- Schlichting (TS) and stationary crossflow (CF) instabilities in the swept wing boundary layer. Here, we examine the effects of the simplifying approximations in both basic state computation and the stability analysis, with the goal of quantifying the resulting changes in the N-factor correlations. Specifically, the basic states are computed by using full Navier-Stokes equations and the stability analysis is performed by using a nonorthogonal coordinate system that allows a clear distinction between planar TS and CF instabilities. Furthermore, the effects of curvature and nonparallel mean flow have been included in the stability computations based on the parabolized stability equations (PSE). The fully turbulent Reynolds-Averaged-Navier-Stokes (RANS) mean flow solutions show good agreement with the measured wall pressure distribution. Viscous-inviscid interactive effects are observed to be important because the shock fronts along the suction surface are influenced by the imposed transition front. The stability results confirm the previous findings related to TS amplification within the inboard region of the wing and the dominance of stationary CF modes in the outboard region. However, given the close proximity of the measured transition front and the dual shock system within the outer part of the wing, the onset of transition may well be shock limited within the outboard region. In general, the transition criterion based on the dual N-factor method with N TS = N CF = 6 is reasonably successful at correlating with the measured transition fronts at Re MAC = 15 million and AoA = 1.5, 2 degrees; however, the low values of the correlating N-factors at Re MAC = 17.5 million support the hypothesis that the measured transition at the higher Reynolds number may have been strongly influenced by the merging of turbulent wedges that originate from surface imperfections near the leading edge.

Boundary layer transition↗

Transition Analysis for the CRM-NLF Wind Tunnel Configuration

This paper presents the results of an ongoing study into the linear stability characteristics of the boundary layer flow over the common research model with natural laminar flow (CRMNLF) aircraft configuration. The flow conditions match selected test conditions from a recent wind tunnel experiment in the National Transonic Facility at the NASA Langley Research Center. Previous work involving parallel stability computations of a boundary layer flow based on the conical flow approximation has shown that the measured onset of laminar-turbulent transition during the experiments can be correlated with the linear amplification of Tollmien- Schlichting (TS) and stationary crossflow (CF) instabilities in the swept wing boundary layer. Here, we examine the effects of the simplifying approximations in both basic state computation and the stability analysis, with the goal of quantifying the resulting changes in the N-factor correlations. Specifically, the basic states are computed by using full Navier-Stokes equations and the stability analysis is performed by using a nonorthogonal coordinate system that allows a clear distinction between planar TS and CF instabilities. Furthermore, the effects of curvature and nonparallel mean flow have been included in the stability computations based on the parabolized stability equations (PSE). The fully turbulent Reynolds-Averaged-Navier-Stokes (RANS) mean flow solutions show good agreement with the measured wall pressure distribution. Viscous-inviscid interactive effects are observed to be important because the shock fronts along the suction surface are influenced by the imposed transition front. The stability results confirm the previous findings related to TS amplification within the inboard region of the wing and the dominance of stationary CF modes in the outboard region. However, given the close proximity of the measured transition front and the dual shock system within the outer part of the wing, the onset of transition may well be shock limited within the outboard region. In general, the transition criterion based on the dual N-factor method with N TS = N CF = 6 is reasonably successful at correlating with the measured transition fronts at Re MAC = 15 million and AoA = 1.5, 2 degrees; however, the low values of the correlating N-factors at Re MAC = 17.5 million support the hypothesis that the measured transition at the higher Reynolds number may have been strongly influenced by the merging of turbulent wedges that originate from surface imperfections near the leading edge.

Boundary layer transition↗

New description of charged particle propagation in random magnetic fields

When charged particles spiral along a large constant magnetic field, their trajectories are scattered by random components that are superposed on the guiding field. In the simplest analysis of this situation, scattering causes the particles to diffuse parallel to the guiding field. At the next level of approximation, moving pulses that correspond to a coherent mode of propagation are present, but they are represented by delta-functions whose infinitely narrow width makes no sense physically and is inconsistent with the finite duration of coherent pulses observed in solar energetic particle events. To derive a more realistic description, the transport problem is formulated in terms of 4 x 4 matrices, which derive from a representation of the particle distribution function in terms of eigenfunctions of the scattering operator, and which lead to useful approximations that give explicit predictions of the detailed evolution not only of the coherent pulses, but also of the diffusive wake. More specifically, the new description embodies a simple convolution of a narrow Gaussian with the solutions above that involve delta-functions, but with a slightly reduced coherent velocity. The validity of these approximations, which can easily be calculated on a desktop computer, has been exhaustively confirmed by comparison with results of Monte Carlo simulations which kept track of 50 million particles and which were carried out on the Maspar computer at Goddard Space Flight Center.

Earl, James A.↗

The characteristic of the magnetopause reconnection X-line deduced from low-altitude satellite observations of cusp ions

We present an analysis of a 'quasi-steady' cusp ion dispersion signature observed at low altitudes. We reconstruct the field-parallel part of the Cowley-D ion distribution function, injected into the open low-latitude boundary layer (LLBL) in the vicinity of the reconnection X-line. From this we find the field parallel magnetosheath flow at the X-line was only 20 +/- 60 km/s, placing the reconnection site close to the flow streamline which is perpendicular to the magnetosheath field. Using interplanetary data and assuming the subsolar magnetopause is in pressure balance, we derive a wealth of information about the X-line, including: the density, flow, magnetic field and Alfven speed of the magnetosheath; the magnetic shear across the X-line; the de-Hoffman Teller speed with which field lines emerge from the X-line; the magnetospheric field; and the ion transmission factor across the magnetopause. The results indicate that some heating takes place near the X-line as the ions cross the magnetopause, and that sheath densities may be reduced in a plasma depletion layer. We also compute the reconnection rate. Despite its quasi-steady appearance on an ion spectrogram, this cusp is found to reveal a large pulse of enhanced reconnection rate.

Lockwood, M.↗

Volumetric 3D Display System with Static Screen

Current display technology has relied on flat, 2D screens that cannot truly convey the third dimension of visual information: depth. In contrast to conventional visualization that is primarily based on 2D flat screens, the volumetric 3D display possesses a true 3D display volume, and places physically each 3D voxel in displayed 3D images at the true 3D (x,y,z) spatial position. Each voxel, analogous to a pixel in a 2D image, emits light from that position to form a real 3D image in the eyes of the viewers. Such true volumetric 3D display technology provides both physiological (accommodation, convergence, binocular disparity, and motion parallax) and psychological (image size, linear perspective, shading, brightness, etc.) depth cues to human visual systems to help in the perception of 3D objects. In a volumetric 3D display, viewers can watch the displayed 3D images from a completely 360 view without using any special eyewear. The volumetric 3D display techniques may lead to a quantum leap in information display technology and can dramatically change the ways humans interact with computers, which can lead to significant improvements in the efficiency of learning and knowledge management processes. Within a block of glass, a large amount of tiny dots of voxels are created by using a recently available machining technique called laser subsurface engraving (LSE). The LSE is able to produce tiny physical crack points (as small as 0.05 mm in diameter) at any (x,y,z) location within the cube of transparent material. The crack dots, when illuminated by a light source, scatter the light around and form visible voxels within the 3D volume. The locations of these tiny voxels are strategically determined such that each can be illuminated by a light ray from a high-resolution digital mirror device (DMD) light engine. The distribution of these voxels occupies the full display volume within the static 3D glass screen. This design eliminates any moving screen seen in previous approaches, so there is no image jitter, and has an inherent parallel mechanism for 3D voxel addressing. High spatial resolution is possible with a full color display being easy to implement. The system is low-cost and low-maintenance.

Geng, Jason↗

Integrating Cache Performance Modeling and Tuning Support in Parallelization Tools

With the resurgence of distributed shared memory (DSM) systems based on cache-coherent Non Uniform Memory Access (ccNUMA) architectures and increasing disparity between memory and processors speeds, data locality overheads are becoming the greatest bottlenecks in the way of realizing potential high performance of these systems. While parallelization tools and compilers facilitate the users in porting their sequential applications to a DSM system, a lot of time and effort is needed to tune the memory performance of these applications to achieve reasonable speedup. In this paper, we show that integrating cache performance modeling and tuning support within a parallelization environment can alleviate this problem. The Cache Performance Modeling and Prediction Tool (CPMP), employs trace-driven simulation techniques without the overhead of generating and managing detailed address traces. CPMP predicts the cache performance impact of source code level "what-if" modifications in a program to assist a user in the tuning process. CPMP is built on top of a customized version of the Computer Aided Parallelization Tools (CAPTools) environment. Finally, we demonstrate how CPMP can be applied to tune a real Computational Fluid Dynamics (CFD) application.

Waheed, Abdul↗

Modeling transient edge plasma transport with dynamic recycling

The work presents numerical simulation studies of the role that dynamic plasma recycling on the main wall and divertor target surfaces plays in transient edge plasma transport phenomena, such as edge localized modes (ELMs). The studies are performed by coupling the edge plasma transport code UEDGE [Rognlien et al., J. Nucl. Mater. 196–198, 347 (1992)] and the wall reaction–diffusion transport code FACE [Smirnov et al., Fusion Sci. Technol. 71, 75 (2017)]. The two-dimensional, time-dependent, two-way coupling of the codes, in a realistic tokamak geometry, is accomplished using the Integrated Plasma Simulator framework [Elwasif et al., in 18th Euromicro Conference on Parallel, Distributed and Network-Based Processing (PDP 2010), Pisa, Italy (IEEE, 2010), pp. 419–427] for all modeled material plasma boundaries. The simulations show that dynamic plasma recycling has substantially different characteristics on the main wall and on the divertor plates. It is demonstrated that during an ELM cycle the outer wall can dynamically absorb and release a number of particles comparable to that expelled by the ELM from the core plasma, by far exceeding the dynamic retention capacity of the divertor surfaces. The resulting evolution of the edge and divertor plasma conditions during an ELM cycle is analyzed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Effect of current on spectrum of breaking waves in water of finite depth

This paper presents an approximate method to compute the mean value, the mean square value and the spectrum of waves in water of finite depth taking into account the effect of wave breaking with or without the presence of current. It is assumed that there exists a linear and Gaussian ideal wave train whose spectrum is first obtained using the wave energy flux balance equation without considering wave breaking. The Miche wave breaking criterion for waves in finite water depth is used to limit the wave elevation and establish an expression for the breaking wave elevation in terms of the elevation and its second time derivative of the ideal waves. Simple expressions for the mean value, the mean square value and the spectrum are obtained. These results are applied to the case in which a deep water unidirectional wave train, propagating normally towards a straight shoreline over gently varying sea bottom of parallel and straight contours, encounters an adverse steady current whose velocity is assumed to be uniformly distributed with depth. Numerical results are obtained and presented in graphical form.

Tung, C. C.↗

Learning local equivariant representations for large-scale atomistic dynamics

Abstract A simultaneously accurate and computationally efficient parametrization of the potential energy surface of molecules and materials is a long-standing goal in the natural sciences. While atom-centered message passing neural networks (MPNNs) have shown remarkable accuracy, their information propagation has limited the accessible length-scales. Local methods, conversely, scale to large simulations but have suffered from inferior accuracy. This work introduces Allegro, a strictly local equivariant deep neural network interatomic potential architecture that simultaneously exhibits excellent accuracy and scalability. Allegro represents a many-body potential using iterated tensor products of learned equivariant representations without atom-centered message passing. Allegro obtains improvements over state-of-the-art methods on QM9 and revMD17. A single tensor product layer outperforms existing deep MPNNs and transformers on QM9. Furthermore, Allegro displays remarkable generalization to out-of-distribution data. Molecular simulations using Allegro recover structural and kinetic properties of an amorphous electrolyte in excellent agreement with ab-initio simulations. Finally, we demonstrate parallelization with a simulation of 100 million atoms.

74 ATOMIC AND MOLECULAR PHYSICS↗

Snow ALbedo eVOlution (SALVO) Campaign Spectral Albedo and Related Measurements from April - June, 2024 in Utqiagivk, AK

A field-portable spectroradiometer, referred to herein as an ‘ASD’, was used to make spatially-distributed spectral albedo (350 – 2500 nm) measurements on tundra and sea ice surfaces. The ASD detector is carried in a backpack and controlled via a computer mounted on the front of the operator (see Figure 1). The ASD measures the spectral irradiance from a fiber optic cable that is routed from the backpack to a custom, gooseneck cosine collector mounted on the end of a 1-m long boom (Grenfell and Perovich, 2008). The boom was held at hip height (approximately 1 m) and had an integrated bubble level for levelling. To make an albedo measurement, first the operator collect an incident (down-welling) irradiance, followed by a reflected (up-welling) measurement. The time between incident and reflected measurements was typically between 11 and 26 seconds (interquartile range). For each measurement, 10 spectra are averaged together. Albedo is calculated as the ratio of the reflected to incident measurement, which obviates the need for absolute radiometric calibration. Albedo measurements were taken parallel to the 200-m albedo lines at 5-m increments (41 measurements) ~1 m south of the line. While the ASD operator was making measurements, an assistant kept notes on the scan number associated with each measurement, the surface type (see below), and collected photos of each measurement (see companion oblique photos data archive). Measurements were made within 3 hours of solar noon.

ASD Spectroradiometer↗

Transient cycling of nitrogen, organic carbon and oxygen within the free-flowing Columbia River corridor: Linking exposure time dependent biogeochemical reactions to river stage fluctuations (Final project report)

The objective of this project was to develop next-generation techniques for representing the transformations of complex reaction networks like those impacting transient river-corridors, then apply them to develop upscaling tools. The project contributed significantly to the development of Lagrangian “mass transfer particle tracking” (MTPT) tools that are the first numerical framework that explicitly separates mixing and spreading processes; a crucial distinction for accurate representations of reaction rates across scales. The MTPT approach uses an operator splitting scheme where physical transport processes are simulated using classical random walk methods and each particle is treated as a “container” that carries with it any number of chemical species. Mixing between particles is simulated using a colocation-probability based mass transfer kernel and reactions are evaluated on each particle after mixing. The method is stable, accurate, and also allows the explicit modeling of residence time distributions of the individual containers of mass. The MTPT scheme allowed us to explore several research questions related to reactive transport in river corridors and complex reaction networks. We found that it is possible to quantify the exposure time distributions (ETDs) of reactants and that this does suggest some pathways to upscaling. However, comparable approximations can be obtained using simplified (reduced dimensionality) MTPT simulations in less time with similar uncertainty, so development of extensive ETD-based methods was not productive. The major findings are that i) the MTPT schemes are robust and highly accurate across a range of arbitrarily complex reactions, ii) the methods can be efficiently parallelized and the parallel performance characteristics of MTPT are predictable, and iii) the MTPT tools allow simultaneous tracking of residence time. The development of these research tools into efficient software packages continues. The methods are already available to the community because open-source, working examples have been included with all publications.

54 ENVIRONMENTAL SCIENCES↗

¬¬Integration of Quantification of Margins and Uncertainties Methodology into Parallel Discrete Event Simulator Framework

Parallel Discrete Events Simulation (PDES) is becoming increasingly important to lab efforts in security and intelligence. It is used to model complex asynchronous systems such as computer networks, satellite systems, vehicular traffic, and human performance. Uncertainty Quantification (UQ) techniques have become a mainstay of Verification and Validation (V&V) efforts on physics simulations. However, PDES models are very different from traditional physics simulations, and research into UQ techniques for PDES is in its infancy. It is not clear which traditional UQ techniques can be applied to PDES, or what new techniques will need to be developed. The goal of this project was to identify existing UQ techniques that can be applied to PDES, and to develop new techniques as necessary. The project implemented or developed techniques to handle issues that do not appear in traditional physics simulations, but are common among PDES, including sampling techniques for high-dimensional homogenous inputs, response surfaces for high-variance heteroskedastic output, and characterization of skewed output distributions. These are foundational UQ techniques that must be used in any complete UQ analysis (Tong 2018).

97 MATHEMATICS AND COMPUTING↗

Parallel Simulation of Quantum Networks with Distributed Quantum State Management

Quantum network simulators offer the opportunity to cost-efficiently investigate potential avenues for building networks that scale with the number of users, communication distance, and application demands by simulating alternative hardware designs and control protocols. Several quantum network simulators have been recently developed with these goals in mind. As the size of the simulated networks increases, however, sequential execution becomes time-consuming. Parallel execution presents a suitable method for scalable simulations of large-scale quantum networks, but the unique attributes of quantum information create unexpected challenges. In this work, we identify requirements for parallel simulation of quantum networks and develop the first parallel discrete-event quantum network simulator by modifying the existing serial simulator SeQUeNCe. Our contributions include the design and development of a quantum state manager (QSM) that maintains shared quantum information distributed across multiple processes. We also optimize our parallel code by minimizing the overhead of the QSM and decreasing the amount of synchronization needed among processes. Using these techniques, we observe a speedup of 2 to 25 times when simulating a 1,024-node linear network topology using 2 to 128 processes. We also observe an efficiency greater than 0.5 for up to 32 processes in a linear network topology of the same size and with the same workload. We repeat this evaluation with a randomized workload on a caveman network. We also introduce several methods for partitioning networks by mapping them to different parallel simulation processes. We have released the parallel SeQUeNCe simulator as an open source tool alongside the existing sequential version.

97 MATHEMATICS AND COMPUTING↗

Regional-scale fault-to-structure earthquake simulations with the EQSIM framework: Workflow maturation and computational performance on GPU-accelerated exascale platforms

Continuous advancements in scientific and engineering understanding of earthquake phenomena, combined with the associated development of representative physics-based models, is providing a foundation for high-performance, fault-to-structure earthquake simulations. However, regional-scale applications of high-performance models have been challenged by the computational requirements at the resolutions required for engineering risk assessments. The EarthQuake SIMulation (EQSIM) framework, a software application development under the US Department of Energy (DOE) Exascale Computing Project, is focused on overcoming the existing computational barriers and enabling routine regional-scale simulations at resolutions relevant to a breadth of engineered systems. This multidisciplinary software development—drawing upon expertise in geophysics, engineering, applied math and computer science—is preparing the advanced computational workflow necessary to fully exploit the DOE’s exaflop computer platforms coming online in the 2023 to 2024 timeframe. Achievement of the computational performance required for high-resolution regional models containing upward of hundreds of billions to trillions of model grid points requires numerical efficiency in every phase of a regional simulation. This includes run time start-up and regional model generation, effective distribution of the computational workload across thousands of computer nodes, efficient coupling of regional geophysics and local engineering models, and application-tailored highly efficient transfer, storage, and interrogation of very large volumes of simulation data. This article summarizes the most recent advancements and refinements incorporated in the workflow design for the EQSIM integrated fault-to-structure framework, which are based on extensive numerical testing across multiple graphics processing unit (GPU)-accelerated platforms, and demonstrates the computational performance achieved on the world’s first exaflop computer platform through representative regional-scale earthquake simulations for the San Francisco Bay Area in California, USA.

58 GEOSCIENCES↗

High-Resolution Comonomer Sequencing of Blocky Brominated Syndiotactic Polystyrene Copolymers Using 13C NMR Spectroscopy and Computer Simulations

This work demonstrates the first high-resolution comonomer sequencing of Blocky brominated syndiotactic polystyrene (sPS-co-sPS-Br) copolymers based on pentad assign- ments of the quaternary carbon region of the nuclear magnetic resonance spectrum. Copolymers containing p-bromostyrene (Br-Sty) units were prepared in matched sets using postpolymerization bromination methods carried out in the heterogeneous gel state (Blocky) and homogeneous solution state (Random). Quantitative information from the quaternary carbon spectra, heteronuclear multiple bond correlation spectroscopy, electronic structure calculations, and simulated statistically random copolymers was correlated to confirm the carbon resonance assignments for all 20 possible pentad comonomer sequences. Using the experimental pentad sequence prevalences, a computer code was developed to simulate chains with microstructures typical of each sample as a means to visually represent the copolymer blockiness with quantitative precision. Based on the microstructure and distribution of run lengths in these chains, the simulations revealed that the Blocky copolymers contain a high degree of blockiness. By comparing the run lengths in the simulated chains to the average number of styrene units in a crystalline segment of sPS (found by small-angle X-ray scattering), copolymer crystallizability was predicted. For the simulated Blocky B-21% (21 mol % Br-Sty) chain, the probability of randomly selecting a styrene unit in a crystallizable block was 25.8%, while that in the simulated Random R-18% was zero, in excellent agreement with the experimental crystallization behavior measured by differential scanning calorimetry. Additionally, these predictions confirmed that the simulated chains accurately represent the ensemble of chains in their respective copolymer samples. Furthermore, each simulated Blocky chain contained one or more long sPS blocks that paralleled the measured 38-40 styrene units spanning a crystalline segment within the sPS/CCl4 gel. This finding affirmed that the long sPS segments originated from the precise lamellar structure within the heterogeneous gel morphology (i.e., block length is correlated with lamellar thickness). Overall, the ability to tailor the copolymer microstructure through control of the semicrystalline gel morphology opens the door to synthesizing ordered copolymers by postpolymerization functionalization processes with unprecedented levels of compositional control.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A DSMC Surface Chemistry Model for Carbon-Based Ablators

A detailed molecular surface chemistry model for the DSMC (Direct Simulation Monte Carlo) method is proposed and implemented into the SPARTA (Stochastic PArallel Rarefied-gas Time-accurate Analyzer) DSMC solver. Molchanova et al. constructed a molecular model for surface recombination in DSMC that includes different surface processes (adsorption, desoprtion, Eley-Rideal and Langmuir-Hinshelwood). All surface processes can be divided into two groups: surface mechanisms, which involve only the particle adsorbed by the surface (desorption and Langmuir-Hinshelwood), and impact mechanisms, which also involve gas-phase particles (adsorption, Eley-Rideal). Using a similar approach, the 14-reaction kinetic model of oxygen-carbon interaction suggested by Zhlukhtov and Abe, as well as more recent models by Alba et al., Poovathinghal et al., and a new model developed in the scope of this work, are implemented in SPARTA. The computational results for the different oxidation models are compared with experimental results from Murray et al. (oxidation of a vitreous carbon surface due to a hyperthermal beam of O and O2), with a particular focus on fluxes, angular and Time-Of-Flight distributions of scattered particles.

oxidation↗

Ab-Initio Investigation of Finite Size Effects in Rutile Titania Nanoparticles with Semilocal and Nonlocal Density Functionals

In this work, we employ hybrid and generalized gradient approximation (GGA) level density functional theory (DFT) calculations to investigate the convergence of surface properties and electronic gap of rutile titania nanoparticles with particle size. The surface energies and electronic gaps are calculated for cuboidal particles with minimum dimension ranging from 3.7 Angstrom (24 atoms) to 10.3 Angstrom (384 atoms) using a highly-parallel real-space DFT code to enable hybrid level DFT calculations of larger nanoparticles than are typically practical. We deconvolute the geometric and electronic finite size effects in surface energy, and evaluate the influence of defects on electronic gap and density of states (DOS). The electronic finite size effects in surface energy vanish when the minimum length scale of the nanoparticles becomes greater than 10 Angstrom. We show that this length scale is consistent with a computationally efficient numerical analysis of the characteristic length scale of electronic interactions. The surface energy of nanoparticles having minimum dimension beyond this characteristic length can be approximated using slab calculations that account for the geometric defects. In contrast, the finite size effects on the electronic gap and DOS is highly dependent on the shape and size of these particles. Furthermore, the DOS for cuboidal particles and more realistic particles constructed using the Wulff algorithm reveal that defect states within the electronic gap play a key role in determining the eigen value distribution of nanoparticles and the electronic gap does not converge to the bulk limit for the particle sizes investigated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Weak scaling of the contact distance between two fluctuating interfaces with system size

A pair of flat parallel surfaces, each freely diffusing along the direction of their separation, will eventually come into contact. If the shapes of these surfaces also fluctuate, then contact will occur when their centers-of-mass remain separated by a nonzero distance ℓ. An example of such a situation is the motion of interfaces between two phases at conditions of thermodynamic coexistence, and in particular the annihilation of domain wall pairs under periodic boundary conditions. Here we present a general approach to calculate the probability distribution of the contact distance ℓ and determine how its most likely value ℓ* depends on the surfaces' lateral size L. Using the Edward-Wilkinson equation as a model for interfaces, we demonstrate that ℓ* scales weakly with system size, i.e., the dependence of ℓ* on L for both (1+1)- and (2+1)-dimensional interfaces is such that lim L→∞ (ℓ*/L) = 0. In particular, for (2+1)-dimensional interfaces ℓ* is an algebraic function of logL, a result that is confirmed by computer simulations of slab-shaped domains formed under periodic boundary conditions. Overall, this weak scaling implies that such domains remain topologically intact until ℓ becomes very small compared to the lateral size of the interface, contradicting expectations from equilibrium thermodynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗