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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Fracture-based shape optimization built upon the topological derivative

In Silva et al. (2011) and Alidoost et al. (2020), the authors developed an approximation of the energy release rate field associated with a small edge or surface crack at any boundary location and with any orientation using the topological derivative. The approximation is computationally attractive because it requires only a single analysis on the non-cracked domain in contrast with conventional boundary-element and finite-element-based methods, which require a separate and costlier analysis for each crack length-location-orientation combination. Here, a shape optimization scheme for fracture-resistant structures is developed using the energy release rate approximation. In the gradient-based optimization scheme, the domain and its boundary are defined implicitly using level-set functions. The level-set functions of arbitrary geometries are constructed using Boolean operations from the level-set functions of simple primitives. This geometrical representation has the dual advantage of (i) allowing shapes to intersect and/or separate during the optimization and (ii) simplifying the computation of the shape sensitivities.

42 ENGINEERING↗
DOE OSTI2020

Topologically derived dislocation theory for twist and stretch moiré superlattices in bilayer graphene

In this work, we develop a continuum dislocation description of twist and stretch moiré superlattices in two-dimensional material bilayers. The continuum formulation is based on the topological constraints introduced by the periodic dislocation network associated with the moiré structure. The approach is based on solving analytically for the structural distortion and displacement fields that satisfy the topological constraints and that minimize the total energy. The total energy is described by both the strain energy of each individual distorted layer and a Peierls-Nabarro-like interfacial contribution arising from stacking disregistry. The dislocation core emerges naturally within the formalism as a result of the competition between the two contributions. The approach presented here captures the structure and energetics of twist and stretch moiré superlattices of dislocations with arbitrary direction and character, without assuming an analytical solution a priori and while accounting naturally for dislocation-dislocation image interactions. In comparisons to atomistic simulations using classical potentials, the maximum structure deviation is 6%, while the maximum line energy deviation is 0.019 eV/Å. Several applications of our model are shown, including predicting the variation of structure with twist angle and describing dislocation line tension and junction energies.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Noether currents for Eulerian variational principles in non-barotropic magnetohydrodynamics and topological conservations laws

We derive a Noether current for the Eulerian variational principle of ideal non-barotropic magnetohydrodynamics (MHD). It was shown previously that ideal non-barotropic MHD is mathematically equivalent to a five function field theory with an induced geometrical structure in the case that field lines cover surfaces and this theory can be described using a variational principle. Here we use various symmetries of the flow to derive topological constants of motion through the derived Noether current and discuss their implication for non-barotropic MHD.

42 ENGINEERING↗
DOE OSTI2024

Evidence for Topological Protection Derived from Six-Flux Composite Fermions

The composite fermion theory opened a new chapter in understanding many-body correlations through the formation of emergent particles. The formation of two-flux and four-flux composite fermions is well established. While there are limited data linked to the formation of six-flux composite fermions, topological protection associated with them is conspicuously lacking. Here we report evidence for the formation of a quantized and gapped fractional quantum Hall state at the filling factor ν = 9/11, which we associate with the formation of six-flux composite fermions. Our result provides evidence for the most intricate composite fermion with six fluxes and expands the already diverse family of highly correlated topological phases with a new member that cannot be characterized by correlations present in other known members. Our observations pave the way towards the study of higher order correlations in the fractional quantum Hall regime.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

TopoSZ: Preserving Topology in Error-Bounded Lossy Compression

Existing error-bounded lossy compression techniques control the pointwise error during compression to guarantee the integrity of the decompressed data. However, they typically do not explicitly preserve the topological features in data. When performing post hoc analysis with decompressed data using topological methods, preserving topology in the compression process to obtain topologically consistent and correct scientific insights is desirable. In this paper, we introduce TopoSZ, an error-bounded lossy compression method that preserves the topological features in 2D and 3D scalar fields. Specifically, we aim to preserve the types and locations of local extrema as well as the level set relations among critical points captured by contour trees in the decompressed data. The main idea is to derive topological constraints from contour-tree-induced segmentation from the data domain, and incorporate such constraints with a customized error-controlled quantization strategy from the SZ compressor (version 1.4). In conclusion, our method allows users to control the pointwise error and the loss of topological features during the compression process with a global error bound and a persistence threshold.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

High-temperature Majorana fermions in magnet-superconductor hybrid systems

Magnet-superconductor hybrid (MSH) structures represent one of the most promising platforms to realize, control, and manipulate Majorana modes using scanning tunneling methods. By depositing either chains or islands of magnetic atoms on the surface of a conventional, elemental superconductor such as Pb or Re, topological superconducting phases can emerge. They feature either localized Majorana bound states at the chain ends or dispersing chiral Majorana modes at the island's boundary. However, some of these experiments have not reached the spectral resolution to clearly distinguish between topological Majorana and trivial Shiba states due to very small superconducting gap sizes and experiments performed at sub-Kelvin temperatures. Here we consider superconducting substrates with unconventional spin-singlet pairing, including high-temperature d -wave and extended s -wave superconductors. We derive topological phase diagrams and compute edge states for cylinder and island geometries and discuss their properties. Several time-reversal invariant topological superconducting phases of the Zhang-Kane-Mele type are found and discussed. Addiotnally, we review one-dimensional MSH structures and show that parameters to realize topologically nontrivial magnetic chains embedded into a larger, two-dimensional substrate differ from the purely one-dimensional case. Quite generally we find that unconventional superconducting substrates work as well as the conventional s -wave substrates to realize topological phases. In particular, iron-based pnictide and chalcogenide superconductors are the most promising class of substrates for future high-temperature MSH systems.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Interplay between magnetism and band topology in the kagome magnets R Mn 6 Sn 6

Kagome-lattice magnets R Mn 6 Sn 6 recently emerged as a new platform to exploit the interplay between magnetism and topological electronic states. Some of the most exciting features of this family are the dramatic dependence of the easy magnetization direction on the rare-earth specie, despite other magnetic and electronic properties being essentially unchanged, and the kagome geometry of the Mn planes that in principle can generate flat bands and Dirac points; gapping of the Dirac points by spin-orbit coupling has been suggested recently to be responsible for the observed anomalous Hall response in the member TbMn 6 Sn 6 . In this paper, we address both issues with ab initio calculations. We have discovered the significant role played by higher-order crystal-field parameters and rare-earth magnetic anisotropy constants in these systems. Further, we demonstrate that the microscopic origin of rare-earth magnetic anisotropy can also be quantified and understood at various levels: ab initio, phenomenological, and analytical. In particular, using a simple and physically transparent analytical model based on perturbation theory, we are able to explain, with full quantitative agreement, the evolution of rare-earth magnetic anisotropy across the series. We analyze in detail the topological properties of Mn-dominated bands and demonstrate how they emerge from the multiorbital planar kagome model. We further show that, despite this fact, most of the topological features at the Brillouin zone corner K are strongly 3D and therefore cannot explain the observed quasi-2D anomalous Hall effect, while the most pronounced quasi-2D dispersion are too far removed from the Fermi level. By employing self-consistent calculations with ab initio many-body approaches, we demonstrate that the exchange-correlation effects beyond the density functional theory for itinerant Mn- d electrons do not significantly alter the obtained electronic and magnetic structure. Therefore, we conclude that, contrary to previous claims, the most pronounced 2D kagome-derived topological band features bear little relevance to transport in RMn 6 Sn 6 , albeit they may possibly be brought to focus by electron or hole doping.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Characterization and classification of interacting ( 2 + 1 )-dimensional topological crystalline insulators with orientation-preserving wallpaper groups

While free fermion topological crystalline insulators have been largely classified, the analogous problem in the strongly interacting case has been only partially solved. In this work, we develop a characterization and classification of interacting, invertible fermionic topological phases in (2+1) dimensions with charge conservation, discrete magnetic translation and M-fold point group rotation symmetries, which form the group G f = U(1) f × Φ [Z 2 $\rtimes$Z M ] for M = 1,2,3,4, and 6. Φ is the magnetic flux per unit cell. We derive a topological response theory in terms of background crystalline gauge fields, which gives a complete classification of different phases and a physical characterization in terms of quantized response to symmetry defects. We then derive the same classification in terms of a set of real space invariants {$Θ^±_o$} that can be obtained from ground state expectation values of suitable partial rotation operators. We explicitly relate these real space invariants to the quantized coefficients in the topological response theory, and find the dependence of the invariants on the chiral central charge c – of the invertible phase. Finally, when Φ = 0 we derive an explicit map between the free and interacting classifications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

A Topological Approach for Motion Track Discrimination

Detecting small targets at range is difficult because there is not enough spatial information present in an image sub-region containing the target to use correlation-based methods to differentiate it from dynamic confusers present in the scene. Moreover, this lack of spatial information also disqualifies the use of most state-of-the-art deep learning image-based classifiers. Here, we use characteristics of target tracks extracted from video sequences as data from which to derive distinguishing topological features that help robustly differentiate targets of interest from confusers. In particular, we calculate persistent homology from time-delayed embeddings of dynamic statistics calculated from motion tracks extracted from a wide field-of-view video stream. In short, we use topological methods to extract features related to target motion dynamics that are useful for classification and disambiguation and show that small targets can be detected at range with high probability.

Emerson, Tegan H.↗
DOE OSTI2023

Topological Guided Detection of Extreme Wind Phenomena: Implications for Wind Energy

Extreme wind phenomena play a crucial role in the efficient operation of wind farms for renewable energy generation. However, existing detection methods are computationally expensive, limited to specific coordinate. In real-world scenarios, understanding the occurrence of these phenomena over a large area is essential. Therefore, there is a significant demand for a fast and accurate approach to forecast such events. In this paper, we propose a novel method for detecting wind phenomena using topological analysis, leveraging the gradient of wind speed or critical points in a topological framework. By extracting topological features from the wind speed profile within a defined region, we employ topological distance to identify extreme wind phenomena. Our results demonstrate the effectiveness of utilizing topological features derived from regional wind speed profiles. We validate our approach using high-resolution simulations with the Weather Research and Forecasting model (WRF) over a month in the US East Coast.

MATHEMATICS AND COMPUTING,WIND ENERGY↗
DOE OSTI2023

Topological Guided Detection of Extreme Wind Phenomena: Implications for Wind Energy: Preprint

Extreme wind phenomena play a crucial role in the efficient operation of wind farms for renewable energy generation. However, existing detection methods are computationally expensive, limited to specific coordinate. In real-world scenarios, understanding the occurrence of these phenomena over a large area is essential. Therefore, there is a significant demand for a fast and accurate approach to forecast such events. In this paper, we propose a novel method for detecting wind phenomena using topological analysis, leveraging the gradient of wind speed or critical points in a topological framework. By extracting topological features from the wind speed profile within a defined region, we employ topological distance to identify extreme wind phenomena. Our results demonstrate the effectiveness of utilizing topological features derived from regional wind speed profiles. We validate our approach using high-resolution simulations with the Weather Research and Forecasting model (WRF) over a month in the US East Coast.

MATHEMATICS AND COMPUTING,WIND ENERGY↗
DOE OSTI2025

Autonomous direct freeform fabrication strategy for multi-axis additive manufacturing

Multi-axis additive manufacturing (M-AM) enables precise material deposition along both planar and curved layers, eliminating the need for support structures through a continuous material deposition approach. In contrast to conventional 2-dimensional planar layers constrained to a fixed building orientation, the deposition on freeform layers demands the specification of guided curves to determine material deposition directions which are no longer to be fixed to a build direction. There are challenges that arise when fabricating components with multiple “build” directions, necessitating the decomposition of geometries and the specification of guided curves for the resulting volumes. Furthermore, multi-axis systems introduce heightened challenges due to an increased degree of freedom in motion. Consequently, the potential risks of collision between the deposited geometry and the motion platform become a notable concern. This research proposes a freeform layering algorithm to address the challenge of seamless transitions between planar and curved layers in the process planning of M-AM. The algorithm computes 3D “printable” layers by leveraging topological information derived from the geometry to be built and integrates collision-free manufacturability considerations into the computational process. These accumulated volumes serve as a “substrate” and support volumes for subsequent deposition, allowing later layers to be built without the need for additional support material. In conclusion, the proposed method successfully devises a freeform layering approach suitable for intricate models that demand substantial support, thus enabling the fabrication of diverse geometries in a manner previously unachievable.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Long-distance coherence of Majorana wires

Theoretically, a pair of Majorana bound states in a topological superconductor forms a single fermionic level even at large separations, implying that the parity information is stored nonlocally. The nonlocality leads to a long-distance coherence for electrons tunneling through a Coulomb-blockaded Majorana wire, an effect that can be observed, e.g., in an interferometer. Here, we examine theoretically the coherent electron transfer, taking into account that tunneling implies the long-distance transfer of charge, which is carried by one-dimensional plasmons. In this work, we show that the charge dynamics does not affect the coherence of the electron tunneling process in a topological superconductor consisting of a semiconductor wire proximitized by a single bulk superconductor. The coherence may be strongly suppressed, however, if the topological superconductivity derives from a semiconductor wire proximitized by a granular superconductor.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Concurrent Shape and Topology Optimization

The typical topology optimization workflow uses a design domain that does not change during the optimization process. Consequently, features of the design domain, such as the location of loads and constraints, must be determined in advance and are not optimizable. A method is proposed herein that allows the design domain to be optimized along with the topology. This approach uses topology and shape derivatives to guide nested optimizers to the optimal topology and design domain. The details of the method are discussed, and examples are provided that demonstrate the utility of this approach.

42 ENGINEERING↗
DOE OSTI2021

Convergence of sum-up rounding schemes for cloaking problems governed by the Helmholtz equation

In this work, we consider the problem of designing a cloak for waves described by the Helmholtz equation from an integer programming point of view. The problem can be modeled as a PDE-constrained optimization problem with integer-valued control inputs that are distributed in the computational domain. A first-discretize-then-optimize approach results in a large-scale mixed-integer nonlinear program that is in general intractable because of the large number of integer variables that arise from the discretization of the domain. Instead, we propose an efficient algorithm that is able to approximate the local infima of the underlying nonconvex infinite-dimensional problem arbitrarily close without the need to solve the discretized finite-dimensional integer programs to optimality. We optimize only the continuous relaxations of the approximations for local minima and then apply the sum-up rounding methodology to obtain integer-valued controls. If the solutions of the discretized continuous relaxations converge to a local minimizer of the continuous relaxation, then the resulting discrete-valued control sequence converges weakly \(^*\) in \(L^\infty\) to the same local minimizer. These approximation properties follow under suitable refinements of the involved discretization grids. Our results use familiar concepts arising from the analytical properties of the underlying PDE and complement previous results, derived from a topology optimization point of view.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Modeling and Analysis of DC Microgrids as Stochastic Hybrid Systems

This study proposes a method of predicting the influence of random load behavior on the dynamics of dc microgrids and distribution systems. This is accomplished by combining stochastic load models and deterministic microgrid models. Together, these elements constitute a stochastic hybrid system. The resulting model enables straightforward calculation of dynamic state moments, which are used to assess the probability of desirable operating conditions. Specific consideration is given to systems based on the dual active bridge (DAB) topology. Bounds are derived for the probability of zero voltage switching (ZVS) in DAB converters. A simple example is presented to demonstrate how these bounds may be used to improve ZVS performance as an optimization problem. In conclusion, predictions of state moment dynamics and ZVS probability assessments are verified through comparisons to Monte Carlo simulations.

42 ENGINEERING↗
DOE OSTI2025

Magnetic contribution of itinerant electrons to neutron diffraction in the topological antiferromagnet CeAlGe

We report a neutron diffraction study of the magnetic structure of CeAlGe, a candidate topological semimetal that hosts a noncollinear, multi-𝐤 magnetic phase. By measuring both low- and high-momentum-transfer magnetic Bragg peaks within a single experimental setup, we refine a magnetic structure model based solely on localized Ce moments. This model, which differs from that obtained using only high-𝑄 data, quantitatively reproduces the observed intensities, including the (000) zeroth-order magnetic satellites that are especially sensitive to subtle components of the modulation. While a contribution from itinerant electrons to the zeroth satellite cannot be definitively excluded, our analysis reveals no unambiguous evidence for such effects within experimental uncertainty. The refined magnetic structures exhibit topologically nontrivial winding patterns, derived from the fitted magnetic parameters, that support localized, particle-like spin textures with half-integer topological charges. These features provide a natural microscopic origin for the observed topological Hall effect, establishing CeAlGe as a model system where magnetism and topology are intimately linked.

Magnetic coupling↗