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DOE OSTI2024

Differentiating Three-Dimensional Molecular Structures Using Laser-Induced Coulomb Explosion Imaging

Coulomb explosion imaging (CEI) with x-ray free electron lasers has recently been shown to be a powerful method for obtaining detailed structural information of gas-phase planar ring molecules [R. Boll et al., X-ray multiphoton-induced Coulomb explosion images complex single molecules, Nat. Phys. 18, 423 (2022).]. In this Letter, we investigate the potential of CEI driven by a tabletop laser and extend this approach to differentiating three-dimensional structures. We study the static CEI patterns of planar and nonplanar organic molecules that resemble the structures of typical products formed in ring-opening reactions. Here, our results reveal that each molecule exhibits a well-localized and distinctive pattern in three-dimensional fragment-ion momentum space. We find that these patterns yield direct information about the molecular structures and can be qualitatively reproduced using a classical Coulomb explosion simulation. Our findings suggest that laser-induced CEI can serve as a robust method for differentiating molecular structures of organic ring and chain molecules. As such, it holds great promise as a method for following ultrafast structural changes, e.g., during ring-opening reactions, by tracking the motion of individual atoms in pump-probe experiments.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2024

The influence of the shock-to-reshock time on the Richtmyer–Meshkov instability in reshock

Experiments on the Richtmyer–Meshkov instability (RMI) in a dual driver vertical shock tube (DDVST) are described. An initially planar, stably stratified membraneless interface is formed by flowing air from above and sulfur hexafluoride from below the interface location using the method of Jones & Jacobs ( Phys. Fluids , vol. 9, issue 1997, 1997, pp. 3078–3085). A random three-dimensional, multi-modal initial perturbation is imposed by vertically oscillating the gas column to produce Faraday waves. The DDVST design generates two shock waves, one originating above and one below the interface, with these shocks having independently controllable strengths and interface arrival times. The shock waves have nominal strengths of $M_L=1.17$ and $M_H=1.18$ for the shock wave originating in the light and heavy gas, respectively, with these strengths chosen to result in arrested bulk interface motion following reshock. The influence of the length of the shock-to-reshock time, as well as the order of shock arrival, on the post-reshock RMI is examined. The mixing layer width grows according to $h\propto t^\theta$ , where $\theta _H=0.36\pm 0.018$ (95 %) and $\theta _L=0.38\pm 0.02$ (95 %) for heavy and light shock first experiments, respectively, indicating no strong dependence on the order of shock wave arrival. Volume integrated specific turbulent kinetic energy (TKE) in the mixing layer versus time is found to decay according to $E_{tot}/\bar {\rho }\propto t^p$ with $p_H=-0.823\pm 0.06$ (95 %) and $p_L=-1.061\pm 0.032$ (95 %) for heavy and light shock first experiments, respectively. Notably, the 95 % confidence intervals do not overlap. Analysis on the influence of the shock-to-reshock time on turbulent length scales, transition criteria, spectra and mixing layer anisotropy are also presented.

Ferguson, Kevin (ORCID:0000000166537482)↗

DOE OSTI2025

Collective behavior of “flexicles”

In recent years the functionality of synthetic active microparticles has edged even closer to that of their biological counterparts. However, we still lack the understanding needed to recreate at the microscale key features of autonomous behavior exhibited by microorganisms or swarms of macroscopic robots. In this study, we propose a model for a three-dimensional deformable cellular composite particle consisting of self-propelled rod-shaped colloids confined within a flexible vesicle—representing a superstructure we call a “flexicle” that couples particle deformation to the internal dynamics of the internal active components. Using molecular dynamics simulations, we investigate the collective behavior of dense systems composed of many flexicles. We show that individual flexicles exhibit shape changes upon collisions with other flexicles that lead to rearrangements of the internal active rods, which slows flexicle motion. This shape deformability gives rise to a diverse set of motility-induced phase separation phenomena and the spontaneous flow of flexicles reminiscent of the migration of cells in dense tissues. Our findings establish a foundation for designing responsive, cell-like active particles and developing strategies for controlling swarm migration and other autonomous swarm behaviors at cellular and colloidal scales.

Science & Technology - Other Topics↗

DOE OSTI2024

The MOSAiC Distributed Network: Observing the coupled Arctic system with multidisciplinary, coordinated platforms

Central Arctic properties and processes are important to the regional and global coupled climate system. The Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) Distributed Network (DN) of autonomous ice-tethered systems aimed to bridge gaps in our understanding of temporal and spatial scales, in particular with respect to the resolution of Earth system models. By characterizing variability around local measurements made at a Central Observatory, the DN covers both the coupled system interactions involving the ocean-ice-atmosphere interfaces as well as three-dimensional processes in the ocean, sea ice, and atmosphere. The more than 200 autonomous instruments (“buoys”) were of varying complexity and set up at different sites mostly within 50 km of the Central Observatory. During an exemplary midwinter month, the DN observations captured the spatial variability of atmospheric processes on sub-monthly time scales, but less so for monthly means. They show significant variability in snow depth and ice thickness, and provide a temporally and spatially resolved characterization of ice motion and deformation, showing coherency at the DN scale but less at smaller spatial scales. Ocean data show the background gradient across the DN as well as spatially dependent time variability due to local mixed layer sub-mesoscale and mesoscale processes, influenced by a variable ice cover. The second case (May–June 2020) illustrates the utility of the DN during the absence of manually obtained data by providing continuity of physical and biological observations during this key transitional period. We show examples of synergies between the extensive MOSAiC remote sensing observations and numerical modeling, such as estimating the skill of ice drift forecasts and evaluating coupled system modeling. The MOSAiC DN has been proven to enable analysis of local to mesoscale processes in the coupled atmosphere-ice-ocean system and has the potential to improve model parameterizations of important, unresolved processes in the future.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Terahertz Circular Dichroism Spectroscopy of Molecular Assemblies and Nanostructures

Chemical, physical, biological and materials engineering disciplines use a variety of chiroptical spectroscopies to probe geometrical and optical asymmetry in molecules and particles. Electronic (ECD) and vibrational (VCD) circular dichroism are the most common of these techniques and collectively enable the studies of electronic and vibronic transitions with energies between 0.1 and 5.0 eV. The vibrational states with characteristic energies in the range of 0.001–0.01 eV carry valuable information about concerted intermolecular motions in molecules and crystals involving multiple atoms. These vibronic transitions located in the terahertz (THz) part of the spectrum become increasingly more important for the chemistry, physics, and biology of complex molecules and materials However, the methodology and hardware of THz circular dichroism (TCD) are much less developed than the chiroptical spectroscopies for ultraviolet, visible, near- and mid infrared photons. In this report we provide theoretical foundations, practical implementations, comparative assessments, and exemplary applications of TCD spectroscopy. We show that the sign, intensity, and position of TCD peaks are highly sensitive to the three-dimensional structure and long-range organization of molecular crystals, which offer unique capabilities to study (bio) molecules, their crystals, and nanoscale assemblies and apply the novel data processing methodologies. TCD also offers a convenient toolbox to identify new physical phenomena, such as chiral phonons and their propagation in nanostructured matter. We also discuss the major challenges, emerging opportunities and promising research directions, including broad investigation of chiral phonons observed in chiral (nano) crystals and emerging machine learning methodologies for TCD in biological and nanoscale structures. Ubiquity of low-frequency vibrations with rotational components in biomolecular structures, combined with sharpness of peaks in TCD spectra, enables a variety of technological translations.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Statistical characterization of a shock interacting with an inclined gas column

We present a statistical characterization of the interaction between a planar shock and a finite-diameter, cylindrical column of dense gas based on three-dimensional, large-eddy simulation results. In the simulation, the column of gas is initially inclined at an angle $\alpha _0$ with respect to the shock plane. Effects of the initial column angle on the mixing characteristics are examined at Mach number 2.0 for column incline angles $1^\circ$ , $5^\circ$ , $10^\circ$ and $30^\circ$ . Mean velocity profiles show that the column angle affects the gas velocity components in the vertical plane, but not in the spanwise direction. The gas undergoes higher initial upward acceleration at larger initial column incline angles. With time, the gas motion tends to become one-dimensional in the streamwise direction. Initially, velocity fluctuations are most intense within the interior of the column, but concentrate near the column leading edge over time. At high wavenumbers $\kappa$ , the turbulent kinetic energy spectra follow a power-law scaling of $\kappa ^{-1}$ . The structure functions of the mass fraction do not clearly demonstrate power-law scaling except at early times for $\alpha _0=30^\circ$ , manifesting overall trends very similar to those observed in earlier experiments. Probability distributions of the mass fraction show independence of the mean and the standard deviation of the mixed gas on $\alpha _0$ . The column angle was also found to have little effect on the mixing efficiency characterized by the molecular mixedness. Velocity components in the streamwise and transverse directions tend towards a bimodal distribution for larger $\alpha _{0}$ .

42 ENGINEERING↗

DOE OSTI2025

Three-Dimensional Heat Flux and Thermal Analysis of Angled Tungsten Samples on DIII-D

ITER-grade tungsten and dispersoid-strengthened tungsten samples with the top surface angled at ~15° towards the incident plasma flux were exposed to 9 H-mode discharges with edge-localized modes (ELMs) in the lower divertor of DIII-D tokamak using the Divertor Material Evaluation System (DiMES). Surface damage included cracking and flaking of material on the two samples farthest away from the plasma strike point, and significant melting of the two samples closest to the strike point. Heat flux and thermal analysis tools new to DIII-D have been applied to better understand this material response and to help optimize the exposure conditions for future experiments. SMITER field-line tracing simulations based on IRTV data and EFIT equilibria estimate an average inter-ELM perpendicular heat flux, 𝑞⊥,𝑖nter−𝐸LM , on the angled surfaces of 10.1 – 19.6 MW/m² for a majority of the 9 discharges, increasing to 15.6 – 24.5 MW/m² for the single, higher-power shot where samples melted. Fast camera data showed shallow intra-ELM melting and re-solidification, which transitioned to bulk inter-ELM melting with melt motion in the 𝐽⃗ 𝑥 𝐵⃗ direction. About 50% of the protruding volume of the most affected sample was displaced via melt-motion. SIERRA thermal modeling software was able to reproduce an onset time of melting consistent with fast camera data and final sample conditions, within < 200 ms. Maximum surface temperatures of 3122 K and 2787 K are estimated for the samples farthest away from the strike point, while the closest samples achieve melting at 4067 ms and 4750 ms into the ~5000 ms plasma exposure. A +10% increase in both the SMITER 𝑞⊥,𝑖nter−𝐸LM calculations and the estimated ELM heat loads 𝑞⊥, 𝐸LM was required to achieve this result, which is within the uncertainty of the diagnostic data but likely accounts for non-ideal geometry effects plus other physics uncertainties not included in this first iteration of modeling. This work provided valuable estimates of the 3D temperature evolution to help better understand the observed surface morphology and internal recrystallization of samples, which are discussed in detail in a complementary manuscript [1]. Benchmarking efforts with more diagnosed DIII-D experiments are underway to further refine the SMITER and SIERRA models for DiMES. Future use of these tools will enable researchers to precisely target heat flux exposure conditions in DIII-D to test, but not exceed, the thermomechanical limitations of novel plasma-facing materials.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Oblique and rippled heliosphere structures from the Interstellar Boundary Explorer

Abstract Past analysis has shown that the heliosphere structure can be deduced from correlations between long-scale solar wind pressure evolution and energetic neutral atom emissions. However, this required spatial and temporal averaging that smoothed out small or dynamic features of the heliosphere. In late 2014, the solar wind dynamic pressure increased by roughly 50% over a period of 6 months, causing a time and directional-dependent rise in around 2–6 keV energetic neutral atom fluxes from the heliosphere observed by the Interstellar Boundary Explorer. Here, we use the 2014 pressure enhancement to provide a simultaneous derivation of the three-dimensional heliospheric termination shock (HTS) and heliopause (HP) distances at high resolution from Interstellar Boundary Explorer measurements. The analysis reveals rippled HTS and HP surfaces that are oblique with respect to the local interstellar medium upwind direction, with significant asymmetries in the heliosphere structure compared to steady-state heliosphere models. We estimate that the heliosphere boundaries contain roughly ten astronomical unit-sized spatial variations, with slightly larger variations on the HTS surface than the HP and a large-scale, southwards-directed obliquity of the surfaces in the meridional plane. Comparisons of the derived HTS and HP distances with Voyager observations indicate substantial differences in the heliosphere boundaries in the northern versus southern hemispheres and their motion over time.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Modeling of injected current stream-induced 3D perturbations in local helicity injection plasmas

Solenoid-free tokamak startup techniques are essential for spherical tokamaks and offer a pathway to cost reduction and design simplification in fusion energy systems. Local helicity injection (LHI) is one such approach, employing compact edge current sources to drive open field line current that initiates and sustains tokamak plasmas. The recently commissioned Pegasus-III Experiment provides a platform for advancing this and other solenoid-free startup methods. This study investigates the effect of LHI on magnetic topology in Pegasus-III plasmas. A helical filament model represents the injected current, and the linear plasma response to its three-dimensional field is calculated with M3D-C1. Poincaré mapping reveals substantial flux surface degradation in all modeled cases. The onset of overlapping magnetic structures and large-scale surface deformation begins near Ψ N ≈ 0.37, indicating a broad region of perturbed topology extending toward the edge. In rotating plasmas, both single-fluid and two-fluid models exhibit partial screening of the n = 1 perturbation, with two-fluid calculations showing stronger suppression near the edge. In contrast, the absence of rotation leads to strong resonant field amplification in the single-fluid case, while the two-fluid case with zero electron rotation mitigates this amplification and preserves edge screening. Magnetic probe measurements indicate that modeling the stream with spatial spreading—representing distributed current and/or oscillatory motion—better reproduces measured magnetic power profiles than a rigid filament model. The results underscore the role of rotation and two-fluid physics in screening stream perturbations and point to plasma flow measurements and refined stream models as key steps toward improving predictive fidelity.

Schaefer, Carolyn E. [Univ. of Wisconsin, Madison,↗

DOE OSTI2024

Approach and rotation of reconnecting topological defect lines in liquid crystal

Topological defects are a universal concept across many disciplines, such as crystallography, liquid-crystalline physics, low-temperature physics, cosmology, and even biology. In nematic liquid crystals, topological defects called disclinations have been widely studied. For their three-dimensional (3D) dynamics, however, only recently have theoretical approaches dealing with fully 3D configurations been reported. Further, recent experiments have observed 3D disclination line reconnections, a phenomenon characteristic of defect line dynamics, but detailed discussions were limited to the case of approximately parallel defects. In this paper, we focus on the case of two disclination lines that approach at finite angles and lie in separate planes, a more fundamentally 3D reconnection configuration. Observing and analyzing such reconnection events, we find the square-root law of the distance between disclinations and the decrease of the interdisclination angle over time. We compare the experimental results with theory and find qualitative agreement on the scaling of distance and angle with time, but quantitative disagreement on distance and angle relative mobilities. To probe this disagreement, we derive the equations of motion for systems with reduced twist constant and also carry out simulations for this case. These, together with the experimental results, suggest that deformations of disclinations may be responsible for the disagreement. Published by the American Physical Society 2024

36 MATERIALS SCIENCE↗

DOE OSTI2024

Approach and rotation of reconnecting topological defect lines in liquid crystal

36 MATERIALS SCIENCE↗

DOE OSTI2024

Dynamical Inference and 3D Imaging of Magnetized Dusty Plasmas

This is the final technical report for this DOE award. The motion of dust particles in a laboratory plasma has been studied for nearly 30 years and has led to the discovery of strongly-coupled crystalline structures and nonequilibrium dynamics governed by gravitational, hydrodynamic, and electrostatic forces. Many of the inter-particle forces are complex; they can be non-reciprocal, and non-additive. Deciphering the mélange of particle interactions has been a challenging task, nevertheless, magnetized dusty plasmas remains an open challenge with limited understanding. With applications ranging from magnetically-confined plasmas for fusion to near-surface planetary environments, this research field is ripe for well-controlled, laboratory experiments and new theoretical tools. In collaboration with the MDPX experiment at Auburn University, this proposal aims to tease apart both the known and unknown forces that drive dusty plasmas in magnetized environments using high-resolution, three-dimensional imaging and particle tracking coupled with modern dynamical inference and machine learning techniques.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Mapping 3D grain and precipitate structure during in situ mechanical testing of open-cell metal foam using micro-computed tomography and high-energy X-ray diffraction microscopy

Open-cell metal foams are ultra-low-density cellular metals with complex hierarchical structures that span bulk, cell, ligament, and sub-ligament scales and give rise to desirable properties such as high strength-to-weight ratio and excellent energy absorption. Although literature suggests that intrinsic material structures at sub-ligament length scales (e.g., grains and precipitates) play an important role in mechanical behavior of open-cell metal foams, there are very few experimental measurements of such structures in three dimensions and for meaningful volumes of foam. This study seeks to map and track the three-dimensional (3D) grain and precipitate structures of an intact volume of open-cell aluminum foam by advancing microstructural characterization techniques that leverage X-ray micro-computed tomography (μCT) and far-field high-energy X-ray diffraction microscopy (FF-HEDM). A 6%-relative-density aluminum foam sample was mechanically tested in compression while μCT and FF-HEDM measurements were collected at interrupted loading states at beamline 1-ID of the Advanced Photon Source. Further, a new scanning strategy and reconstruction algorithm were established to enable characterization of a foam volume with diameter approximately four times wider than the nominal width of the X-ray beam. The result is a set of maps that detail both the 3D grain and precipitate structures throughout the foam volume at successive strain steps. A novel grain tracking procedure was developed to track individual grains within the foam volume by accounting for the large rigid-body motions that individual ligaments can undergo during mechanical loading. The ability to track grains and precipitate structures in three dimensions throughout large bulk deformation of ultra-low-density polycrystalline materials enables new possibilities for validating numerical models and investigating local failure mechanisms. Furthermore, the methods and procedures developed in this study could be applied to other ultra-low-density structures, such as additively manufactured lattices.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Numerical simulation of vortex-induced vibration response of a single IEA 10-MW wind turbine blade

Three-dimensional simulation of vortex-induced vibration (VIV) of a single International Energy Agency (IEA) 10-MW reference wind turbine blade with a length of 97.325 m is performed using the ExaWind stack, an open-source suite of codes. This study aims to illustrate the spanwise VIV response characteristics and cross-validate the results with an existing commercial framework. Five near-body meshes and three time steps are selected for the convergence study. To improve computational efficiency, several VIV triggering methods are also compared to shorten the VIV development period. The ExaWind-based VIV simulation strategy for a single IEA 10-MW blade is determined. First, the modal shape is validated against published results. Then, spanwise VIV responses of four blade configurations under a fixed and varied incoming flow velocity are analyzed. Results show that the VIV response is dominated by the first edgewise (second overall) mode. Little first-mode contributions appear near the second-mode node, producing a pi phase jump, and a higher harmonics response occurs near the blade root. Rotational degrees of freedom are minor compared with translational motion. The response versus reduced velocity is analyzed, showing a two-branch behavior similar to that of VIV for a bluff cylinder. Across all tested cases, the dominant frequency remains locked to the natural frequency of the second mode with no observed desynchronization. A mild deviation is observed for the case of 90-degree pitch and 310-degree azimuth rotation near a reduced velocity of 6, which will be examined with additional cases in future work. These findings indicate that severe VIV responses can arise under specific configurations and flow conditions, thereby increasing the potential for VIV fatigue damage and requiring greater attention during operation.

17 WIND ENERGY↗

DOE OSTI2022

Nanoscale defect evaluation framework combining real-time transmission electron microscopy and integrated machine learning-particle filter estimation

Observation of dynamic processes by transmission electron microscopy (TEM) is an attractive technique to experimentally analyze materials’ nanoscale phenomena and understand the microstructure-properties relationships in nanoscale. Even if spatial and temporal resolutions of real-time TEM increase significantly, it is still difficult to say that the researchers quantitatively evaluate the dynamic behavior of defects. Images in TEM video are a two-dimensional projection of three-dimensional space phenomena, thus missing information must be existed that makes image’s uniquely accurate interpretation challenging. Therefore, even though they are still a clustering high-dimensional data and can be compressed to two-dimensional, conventional statistical methods for analyzing images may not be powerful enough to track nanoscale behavior by removing various artifacts associated with experiment; and automated and unbiased processing tools for such big-data are becoming mission-critical to discover knowledge about unforeseen behavior. We have developed a method to quantitative image analysis framework to resolve these problems, in which machine learning and particle filter estimation are uniquely combined. The quantitative and automated measurement of the dislocation velocity in an Fe-31Mn-3Al-3Si autunitic steel subjected to the tensile deformation was performed to validate the framework, and an intermittent motion of the dislocations was quantitatively analyzed. The framework is successfully classifying, identifying and tracking nanoscale objects; these are not able to be accurately implemented by the conventional mean-path based analysis.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Do chaotic field lines cause fast reconnection in coronal loops?

Over the past decade, Boozer has argued that three-dimensional (3D) magnetic reconnection fundamentally differs from two-dimensional reconnection due to the fact that the separation between any pair of neighboring field lines almost always increases exponentially over distance in a 3D magnetic field. According to Boozer, this feature makes 3D field-line mapping chaotic and exponentially sensitive to small non-ideal effects; consequently, 3D reconnection can occur without intense current sheets. We test Boozer's theory via ideal and resistive reduced magnetohydrodynamic simulations of the Boozer–Elder coronal loop model driven by sub-Alfvénic footpoint motions [A. H. Boozer and T. Elder, Phys. Plasmas 28, 062303 (2021)]. In this work, our simulation results significantly differ from their predictions. The ideal simulation shows that Boozer and Elder under-predict the intensity of current density due to missing terms in their reduced model equations. Furthermore, resistive simulations of varying Lundquist numbers show that the maximal current density scales linearly rather than logarithmically with the Lundquist number.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Diffusion–convection model of runaway electrons due to large magnetohydrodynamic perturbations in post-thermal quench plasmas

Systematic test particle tracing simulations for runaway electrons (REs) are performed for six post-thermal quench equilibria from DIII-D and ITER, where large scale, kink-like n = 1 (n is the toroidal mode number) magnetohydrodynamic (MHD) instabilities are found. The modeled particle guiding center orbits allow extraction of the effective diffusion–convection coefficients of REs in the presence of large three-dimensional (3D) perturbations up to 10% of the equilibrium toroidal field. With a fixed spatial distribution of the field perturbation, the RE transport coefficients along the plasma radial coordinate track reasonably well with the surface-averaged perturbation level. A substantial variation in the value of the transport coefficients—by three orders of magnitude in most cases, however, occurs with varying launching location of REs along the plasma radius. Large 3D perturbations almost always lead to comparable diffusion and convection processes, meaning that diffusion alone is insufficient to describe the particle motion. At lower (but still high) level of perturbation, the RE convection is found to be dominant over diffusion. A similar observation is made when the perturbation is too strong. In the presence of large perturbation, the dependence of the RE transport on the particle energy is sensitive to the spatial distribution of the perturbation. Based on numerically obtained RE transport coefficients, an analytic fitting model is proposed to quantify the particle diffusion and convection processes due to large MHD events in post-thermal quench plasmas. The model is shown to reasonably well reproduce the direct test particle tracing results for the RE loss fraction and can, thus, be useful for incorporating into other kinetic RE codes in order to simulate the RE beam evolution in the presence of large 3D perturbations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Geometric Delocalization in Two Dimensions

We demonstrate the existence of transient two-dimensional surfaces where a random-walking particle escapes to infinity in contrast to localization in standard flat two-dimensional space. We first prove that any rotationally symmetric two-dimensional membrane embedded in flat three-dimensional space cannot be transient. Then we formulate a criterion for the transience of a general asymmetric two-dimensional membrane. We use it to explicitly construct a class of transient two-dimensional manifolds with a nontrivial metric and height function but “zero average curvature,” which we dub “tablecloth manifolds.” The absence of the logarithmic infrared divergence of the Laplace-Beltrami operator in turn implies the absence of weak localization, nonexistence of bound states in shallow potentials, and breakdown of the Mermin-Wagner theorem and Kosterlitz-Thouless transition on the tablecloth manifolds, which may be realizable in both quantum simulators and corrugated two-dimensional materials.

Anderson localization↗