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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.

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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS2009

Local-in-Time Adjoint-Based Method for Optimal Control/Design Optimization of Unsteady Compressible Flows

.We study local-in-time adjoint-based methods for minimization of ow matching functionals subject to the 2-D unsteady compressible Euler equations. The key idea of the local-in-time method is to construct a very accurate approximation of the global-in-time adjoint equations and the corresponding sensitivity derivative by using only local information available on each time subinterval. In contrast to conventional time-dependent adjoint-based optimization methods which require backward-in-time integration of the adjoint equations over the entire time interval, the local-in-time method solves local adjoint equations sequentially over each time subinterval. Since each subinterval contains relatively few time steps, the storage cost of the local-in-time method is much lower than that of the global adjoint formulation, thus making the time-dependent optimization feasible for practical applications. The paper presents a detailed comparison of the local- and global-in-time adjoint-based methods for minimization of a tracking functional governed by the Euler equations describing the ow around a circular bump. Our numerical results show that the local-in-time method converges to the same optimal solution obtained with the global counterpart, while drastically reducing the memory cost as compared to the global-in-time adjoint formulation.

Yamaleev, N. K.↗
NASA NTRS2013

The Effect of Fiber Strength Stochastics and Local Fiber Volume Fraction on Multiscale Progressive Failure of Composites

Continuous fiber unidirectional polymer matrix composites (PMCs) can exhibit significant local variations in fiber volume fraction as a result of processing conditions that can lead to further local differences in material properties and failure behavior. In this work, the coupled effects of both local variations in fiber volume fraction and the empirically-based statistical distribution of fiber strengths on the predicted longitudinal modulus and local tensile strength of a unidirectional AS4 carbon fiber/ Hercules 3502 epoxy composite were investigated using the special purpose NASA Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC); local effective composite properties were obtained by homogenizing the material behavior over repeating units cells (RUCs). The predicted effective longitudinal modulus was relatively insensitive to small (~8%) variations in local fiber volume fraction. The composite tensile strength, however, was highly dependent on the local distribution in fiber strengths. The RUC-averaged constitutive response can be used to characterize lower length scale material behavior within a multiscale analysis framework that couples the NASA code FEAMAC and the ABAQUS finite element solver. Such an approach can be effectively used to analyze the progressive failure of PMC structures whose failure initiates at the RUC level. Consideration of the effect of local variations in constituent properties and morphologies on progressive failure of PMCs is a central aspect of the application of Integrated Computational Materials Engineering (ICME) principles for composite materials.

multiscale analysis↗
NASA NTRS2021

Local Time Dependence of Jupiter's Polar Auroral Emissions Observed by Juno UVS

Auroral brightness and color ratio imagery, captured using the Juno mission's Ultraviolet Spectrograph, display intense emissions poleward of Jupiter's northern main emission, and these are split into two distinctly different spectral or “color ratio” regimes. The most poleward region, designated the “swirl region” by Grodent et al. (2003), https://doi.org/10.1029/2003ja010017, exhibits a high color ratio, while low color ratio emissions are found within the collar around the swirl region but still poleward of the main emission. We confirm the apparent strong magnetospheric local time control within the polar collar (Grodent et al., 2003, https://doi.org/10.1029/2003ja010017), with the dusk side bright “active region” emissions extending from ∼11 to 22 hr of magnetospheric local time. These bright emissions dim by at least an order of magnitude between ∼0 and 11 hr magnetospheric local time, in the midnight to dawn side “dark region.” This magnetospheric local time structure holds true even when the entire northern oval is located on the night side of the planet (in ionospheric local time), a geometry unstudied prior to Juno, as it is unobservable from Earth. The swirl region brightens at ionospheric dawn (∼5–7 ionospheric local time) and diminishes or completely disappears at ionospheric local times of ∼20–22 hr. Finally, the southern auroral polar emissions appear to share all of the local time dependencies of its northern counterpart, but at a reduced intensity

Thomas Greathouse↗
DOE OSTI2020

Resolution system that provides access to remote data locally

A system and method that provides access to remote data locally by identifying and downloading linked content from a plurality of remote sources through a communication network; decomposing the downloaded content into local content elements by intercepting links between the content elements and mapping the intercepted links to redirected links that locate the same download content in a local cache or a local server proxy; identifying remote devices requesting access to the local cache or the local server proxy and the device's functionality through a tracking code stored on the remote devices and a probabilistic tracking; and providing access to the local cache or the local server proxy in response to authorizations associated with the identified devices and a user.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Strain localization criteria for viscoplastic geomaterials

This report presents a viscoplastic localization criterion to detect quasi-instantaneous (i.e., load-induced) and delayed (creep-induced) strain localization in rate-dependent solids. The study is based on the theory of controllability and a viscoplastic description of the mechanical response. Analytical precursors of unstable states are defined through systems of ordinary differential equations (OEDs). The use of the proposed criteria is illustrated at the material point level through a set of strain localization analyses simulating active strain localization of a porous rock. In addition, full-field finite element simulations of compression tests conducted under various pressures are reported to demonstrate the role of local unstable viscoplasticity in the spontaneous propagation of deformation bands under stationary boundary conditions. The study shows that the viscoplastic localization criterion maintains a negative sign as long as the behavior is unstable, that is, the rate of deformation is accelerating. The sign switch coincides with the transition to decelerating deformation. The analyses revealed that pulses of overstress always emerge in correspondence with the growth of unstable behavior, and the peak matches the transition to stable behavior. The local responses recovered from full-field analyses were consistent with those observed in analyses at material point level and the predictions of the presented theory.

36 MATERIALS SCIENCE↗
DOE OSTI2021

The influence of preexisting host rock damage on fault network localization

The transition from stable to unstable fracture propagation occurs when fractures begin to interact and link. Thus, fracture network coalescence controls how rocks and engineered structures fail. Here, to constrain the factors that influence localization in shear zones under brittle conditions, we build discrete element method models with a rough fault embedded in a shear zone. We add varying numbers of diffuse, randomly-placed weaknesses to examine the influence of diffuse damage on fracture network localization. The number of weaknesses controls the localization behavior of the fault network and the final fault geometry. We quantify localization using the Gini coefficient of the fracture volume, which measures the nonuniformity in a population. Each model generally increases in localization toward failure. However, models with more diffuse damage experience delocalization phases that are superimposed on the overall trend of increasing localization. The observed link between delocalization and host rock damage may help explain the varying localization of low magnitude seismicity in southern California. Models with more diffuse damage produce more complex fault geometries comprised of several parallel strands of wing cracks. The propagation of these wing cracks reduces the shear stress acting on the model boundaries, indicating that this fracture development increases the mechanical efficiency of the system.

58 GEOSCIENCES↗
DOE OSTI2023

Transforming our understanding of chloroplast-associated genes through comprehensive characterization of protein localizations and protein-protein interactions

Bioenergy crops are a renewable source of fuels and are a critical base for building a carbon-neutral economy. Rational engineering of bioenergy crops has the potential to enhance the yields. However, our ability to engineer plants is limited because the functions of most genes remain unknown. Systematic characterization of gene function in plants thus has the potential to greatly accelerate bioenergy research. Here, we focus on the chloroplast, an underexplored energy-producing organelle that is a hallmark of plants. The chloroplast is one of the promising targets of biofuel crop engineering efforts because of its central role in photosynthesis, metabolism, and intracellular signaling. However, the protein composition of the chloroplast and the functions of most of its proteins remain poorly characterized. At the core of this project, we sought to comprehensively determine the localization of chloroplast-associated proteins and generate a spatially defined protein-protein interaction network for chloroplast. For this purpose, we used the leading model alga Chlamydomonas reinhardtii, which greatly increased experimental speed and throughput. We illustrated the value of our findings to land plants by determining the localization of Arabidopsis thaliana land plant homologs of the Chlamydomonas proteins. Altogether, we were successful in determining the localization of 1,034 chloroplast-associated proteins in Chlamydomonas. The localizations provide numerous insights into the spatial organization of chloroplasts and how they function to support photosynthesis. The localization patterns of distinct proteins revealed new chloroplast structures and revealed new spatial organization inside the chloroplast. We also identified new components of known chloroplast structures, such as the chloroplast envelope, nucleoid, plastoglobuli, and pyrenoid. We identified these new components by investigating the interacting partners of known proteins. Many proteins localized in both the chloroplast and other cellular structures, thereby hinting at new functions and communication between cellular structures. We also applied machine learning on the atlas to generate predictions for the location of all of the proteins in Chlamydomonas. This enabled us to assign putative functions to many uncharacterized proteins based on their cellular location. Altogether, this research establishes a rich resource that opens new avenues of investigation and guides future work in deciphering and manipulating chloroplast function. Next, we developed an extensive protein-protein interaction network for the chloroplast by performing affinity purification-mass spectrometry on ~1,150 tagged chloroplast-associated proteins, the first such large-scale study in any photosynthetic organism. This dataset reveals 4,694 high-confidence protein-protein interactions, offering insights into the functions of thousands of conserved poorly-characterized chloroplast proteins. This systematic identification of protein-protein interactions in the chloroplast also provides multiple exciting new research directions and a detailed blueprint of the chloroplast's operation. This research lays the groundwork to decipher the inner workings of the chloroplast, the cell structure at the heart of photosynthesis. The spatial atlas and protein-protein interactions reveal chloroplast organizational features that would not have been accessible with traditional approaches. The localization mapping, insights into the function, and research materials generated further provide a rich resource for the research community to advance the understanding of how the chloroplast is organized to enable engineering of enhanced photosynthetic organisms.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Concurrent two-way coupling of global and local models across internal boundaries with non-matching discretizations

Coupling local and global models enables efficient simulation of multiscale systems, where global models capture large-scale behavior and local models, with enhanced physics, resolve finer details over a smaller region. Here, this paper presents a mathematically consistent method for coupling physics-based models of varying fidelity across adjacent, non-overlapping subdomains, even when discretizations do not match at the immersed interdomain interfaces. Incompressible Navier-Stokes equations (NSE) constitute the global model while residual-based turbulence model serves as the local high-fidelity model. In addition, a scalar advection-diffusion equation that models the convection of an active scalar field is appended to the turbulence model in the local domain. This scalar field does not have its complement in the global model, giving rise to unequal number of equations at the immersed boundary between local and global models. Interdomain coupling terms are derived via the Variational Multiscale Discontinuous Galerkin (VMDG) method with new developments in scale representation and efficient fine-scale estimation. While transient laminar flows modeled with NSE in the global domain can be resolved with relatively coarse mesh, turbulent flow calculations in the local model require much finer spatial discretizations as well as smaller time-step for appropriately resolving the turbulent flow physics. The proposed framework also accommodates non-matching meshes at the immersed boundaries. Test problems in 2D and 3D numerically showcase the concurrent two-way coupling of unknown fields across the immersed boundaries. The 3D test presents a case with an unequal number of equations, where the scalar field represents the convection of contaminant concentration. This provides more detailed physics in the local region and highlights its application in climate modeling and atmospheric sciences.

Variational Multiscale Discontinuous Galerkin (VMD↗
DOE OSTI2020

The Role of Electron Localization in Covalency and Electrochemical Properties of Lithium-Ion Battery Cathode Materials

Following the fundamental research conducted by J. B. Goodenough, the important role of electron localization induced by elemental substitution is studied. The size and electron negativity of host and substituting ions are two important factors in tuning material properties such as local structure and transition metal (TM) oxygen covalency. However, another factor, electron localization, which is widely studied in catalyst research but largely overlooked for battery materials, deserves systematic studies. A combined investigation using synchrotronbased X-ray spectroscopy and theoretical calculations is carried out on the Li-Co-Mn-O model system in which the substituting cation Mn 4+ , with its 3d 3 electronic structure, is used as a promoter for electron localization. Results indicate that electron localization greatly influences the Co - O bond by making it less covalent, which increases the delithiation voltage. It is also found that during charge/discharge, electron localization tends to make TM K-edge X-ray absorption near edge spectroscopy (XANES) spectra show a more “rigid shift” behavior while electron delocalization makes the XANES exhibit a “shape change.” It clearly explains why the K-edge XANES data of some TM oxides show no “rigid shift” while the nominal valence states changed. This work highlights the importance of electron localization with guidance for XANES interpretation.

25 ENERGY STORAGE↗
DOE OSTI2026

Revealing Local Structures through Machine-Learning-Fused Multimodal Spectroscopy

Atomistic structures of materials offer valuable insights into their functionality. Determining these structures remains a fundamental challenge in materials science, especially for systems with defects. While both experimental and computational methods exist, each has limitations in resolving nanoscale structures. Core-level spectroscopies, such as X-ray absorption (XAS) or electron energy-loss spectroscopies (EELS), have been used to determine the local bonding environment and structure of materials. Recently, machine learning (ML) methods have been applied to extract structural and bonding information from XAS/EELS data. However, frameworks relying solely on a single data stream, defined as characterization data derived from a single element using one technique, are often insufficient because multiple local environments can yield similar spectral features, making it challenging to differentiate between competing structural hypotheses. Here, in this work, we address this challenge by integrating multimodal ab initio simulations, experimental data acquisition, and ML techniques for structure characterization. Our goal is to determine local structures and properties using EELS and XAS data from multiple elements and edges. To showcase our approach, we use various lithium nickel manganese cobalt (NMC) oxide compounds which are used for lithium ion batteries, including those with oxygen vacancies and antisite defects, as the sample material system. We successfully inferred local element content, ranging from lithium to transition metals, with quantitative agreement with experimental data. Beyond local element inference, we find that ML model based on multimodal spectroscopic data is able to determine whether local defects such as oxygen vacancy and antisites are present, a task which is impossible for single mode spectra or other experimental techniques. Furthermore, our framework is able to provide physical interpretability, bridging spectroscopy with the local atomic and electronic structures.

battery↗
DOE OSTI2024

A Straightforward Model for Quantifying Local pH Gradients Governing the Oxygen Evolution Reaction

The production and consumption of protons by an electrocatalyst will, under certain conditions, generate localized microenvironments with properties distinct from those of the bulk solution. These local properties are particularly impactful for reactions involving proton-coupled electron transfer, where the generation of locally basic or acidic environments may significantly influence the energy efficiency and reaction selectivity of the electrocatalyst. Whereas local pH environments have been observed and characterized in reductive half-reactions, including the CO 2 reduction and hydrogen evolution reactions, the incompatibility of conventional techniques and materials has limited studies in oxidative half-reactions, including the oxygen evolution reaction (OER), which provides the reducing equivalents for solar-to-fuels electrolysis. With the straightforward parameters bulk pH, buffer composition and pK a , and mass transport, we develop a model for describing local pH as a function of current density regardless of the microscopic details of the mechanism. Using an acid-stable PbO x OER catalyst, we observe the formation and dissipation of pH gradients during the OER and validate the model with voltammetric and potentiometric studies. Here, the model predicts how local acidic environments can develop over a narrow OER current density window, thus providing further motivation for the development of OER catalysts that are stable to acid, even when operating in basic aqueous conditions. More generally, the model is not restricted to the OER and is useful for determining the onset of local pH gradients for other electrocatalytic reactions that involve the consumption or generation of protons in energy conversion reactions.

Anions↗
DOE OSTI2024

Expanded Understanding of the Western Antarctic Peninsula Sea‐Ice Environment Through Local and Regional Observations at Palmer Station

Abstract The Western Antarctic Peninsula (WAP) has been experiencing rapid regional warming since at least the 1950s, however, the impacts of this warming at the local scale are variable and nuanced. Previous studies that have linked sea‐ice variability to biogeochemical cycles and food web dynamics often combine local‐scale biogeochemical data with coarse‐resolution regional satellite sea‐ice data, which may not adequately capture local sea‐ice conditions. In this study, we analyzed local‐scale in situ sea‐ice observations collected as part of a 28‐year record (1992–2020) from the Palmer Long‐Term Ecological Research site at Anvers Island, mid‐WAP, in conjunction with isotopically‐derived sea‐ice meltwater (SIM) fractions and satellite‐derived sea‐ice motion and concentration, to quantify the variability and long‐term trends in local sea‐ice behavior. In situ sea ice observations at Palmer Station displayed higher variability than satellite observations and showed no significant declines over this time, despite region‐wide declines identified in prior studies. Higher spring SIM fractions were attributed to strong northward sea‐ice motion throughout the winter. Applying these local‐scale sea‐ice insights to similarly scaled stratification and chlorophyll‐ a measurements, we found that a longer‐lasting, more consistent sea‐ice pack led to greater water column stratification following the spring sea‐ice retreat. Greater sea‐ice persistence and stronger stratification led to larger peaks in chlorophyll‐ a , though sea‐ice metrics did not explain the positive temporal trends in either stratification strength or chlorophyll‐ a . Through this study, we identify how local sea‐ice observations and meltwater data can enhance satellite data to build an understanding of the intricate connections between ice, water column dynamics, and phytoplankton.

Goodell, E.↗
DOE OSTI2023

Emergence of high piezoelectricity from competing local polar order-disorder in relaxor ferroelectrics

Relaxor ferroelectrics are known for outstanding piezoelectric properties, finding a broad range of applications in advanced electromechanical devices. Decoding the origins of the enhanced properties, however, have long been complicated by the heterogeneous local structures. Here, we employ the advanced big-box refinement method by fitting neutron-, X-ray-based total scattering, and X-ray absorption spectrum simultaneously, to extract local atomic polar displacements and construct 3D polar configurations in the classical relaxor ferroelectric Pb(Mg 1/3 Nb 2/3 )O 3 –PbTiO 3 . Our results demonstrate that prevailing order-disorder character accompanied by the continuous rotation of local polar displacements commands the composition-driven global structure evolution. The omnidirectional local polar disordering appears as an indication of macroscopic relaxor characteristics. Combined with phase-field simulations, it demonstrates that the competing local polar order-disorder between different states with balanced local polar length and direction randomness leads to a flattening free-energy profile over a wide polar length, thus giving rise to high piezoelectricity. Our work clarifies that the critical structural feature required for high piezoelectricity is the competition states of local polar rather than relaxor.

42 ENGINEERING↗
DOE OSTI2023

Three-dimensional atomic structure and local chemical order of medium- and high-entropy nanoalloys

Medium- and high-entropy alloys (M/HEAs) mix several principal elements with near-equiatomic composition and represent a model-shift strategy for designing previously unknown materials in metallurgy, catalysis and other fields. One of the core hypotheses of M/HEAs is lattice distortion, which has been investigated by different numerical and experimental techniques. However, determining the three-dimensional (3D) lattice distortion in M/HEAs remains a challenge. Moreover, the presumed random elemental mixing in M/HEAs has been questioned by X-ray and neutron studies, atomistic simulations, energy dispersive spectroscopy and electron diffraction, which suggest the existence of local chemical order in M/HEAs. However, direct experimental observation of the 3D local chemical order has been difficult because energy dispersive spectroscopy integrates the composition of atomic columns along the zone axes and diffuse electron reflections may originate from planar defects instead of local chemical order. Here, in this work, we determine the 3D atomic positions of M/HEA nanoparticles using atomic electron tomography and quantitatively characterize the local lattice distortion, strain tensor, twin boundaries, dislocation cores and chemical short-range order (CSRO). We find that the high-entropy alloys have larger local lattice distortion and more heterogeneous strain than the medium-entropy alloys and that strain is correlated to CSRO. We also observe CSRO-mediated twinning in the medium-entropy alloys, that is, twinning occurs in energetically unfavoured CSRO regions but not in energetically favoured CSRO ones, which represents, to our knowledge, the first experimental observation of correlating local chemical order with structural defects in any material. We expect that this work will not only expand our fundamental understanding of this important class of materials but also provide the foundation for tailoring M/HEA properties through engineering lattice distortion and local chemical order.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Direct observation of the local microenvironment in inhomogeneous CO 2 reduction gas diffusion electrodes via versatile pOH imaging

In this study, we report how the micrometer-scale morphology of a carbon dioxide reduction (CO 2 R) gas diffusion electrode (GDE) affects the mass transport properties and with it, the local CO 2 R performance. We developed a technique to probe the microenvironment in a CO 2 R GDE via local pOH imaging with time- and three-dimensional spatial, micrometer-scale resolution. The local activity of hydroxide anions (OH - ), represented by the pOH value, around a GDE in contact with an aqueous electrolyte is a crucial parameter that governs the catalytic activity and CO 2 R selectivity. Here, we use fluorescence confocal laser scanning microscopy (CLSM) to create maps of the local pOH around a copper GDE by combining two ratiometric fluorescent dyes, one of which is demonstrated as a pOH sensor for the first time in this work. We observe that the local pOH decreases when current is applied due to the creation of OH - as a byproduct of CO 2 R. Interestingly, the pOH is lower inside microtrenches compared to the electrode surface and decreases further as trenches become more narrow due to enhanced trapping of OH - . We support our experimental results with multiphysics simulations that correlate exceptionally well with measurements. These simulations additionally suggest that the decreased pOH inside microcavities in the surface of a CO 2 R GDE leads to locally enhanced selectivity towards multicarbon (C 2+ ) products. This study suggests that narrow microstructures on the length scale of 5 μm in a GDE surface serve as local CO 2 R hotspots, and thus highlights the importance of a GDE's micromorphology on the CO 2 R performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Validity condition for the local sheath impedance boundary condition and a nonlocal generalization

ICRF sheaths can cause unwanted interactions of high-power RF waves with material surfaces in magnetic fusion devices. In previous work, a local RF sheath impedance boundary condition (BC) was derived for use in ICRF codes together with a microscale (i.e., Debye or sheath width scale) model for obtaining the sheath impedance used in that BC. This local RF sheath BC matches the normal component of current and electrostatic potential across the sheath-plasma interface. Collapsing the matching conditions at the sheath-plasma interface to a BC depends on the assumption of scale separation, which can be violated when conditions along the local radius of curvature of the surface vary sufficiently rapidly. The validity condition is explored in this contribution, with special attention to the case where the magnetic field approaches being tangent to the surface. When the local sheath BC no longer applies, a non-local sheath BC is developed under the assumption of a more relaxed scale separation assumption. It is shown that the non-local sheath BC reduces to the previous local sheath BC under appropriate conditions. Furthermore, a surface-integrated sheath admittance parameter describes the 2D physics in the new BC.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Prevalence and scalable control of localized networks

The ability to control network dynamics is essential for ensuring desirable functionality of many technological, biological, and social systems. Such systems often consist of a large number of network elements, and controlling large-scale networks remains challenging because the computation and communication requirements increase prohibitively fast with network size. Here, we introduce a notion of network locality that can be exploited to make the control of networks scalable, even when the dynamics are nonlinear. We show that network locality is captured by an information metric and is almost universally observed across real and model networks. In localized networks, the optimal control actions and system responses are both shown to be necessarily concentrated in small neighborhoods induced by the information metric. This allows us to develop localized algorithms for determining network controllability and optimizing the placement of driver nodes. This also allows us to develop a localized algorithm for designing local feedback controllers that approach the performance of the corresponding best global controllers, while incurring a computational cost orders-of-magnitude lower. Here, we validate the locality, performance, and efficiency of the algorithms in Kuramoto oscillator networks, as well as three large empirical networks: synchronization dynamics in the Eastern US power grid, epidemic spreading mediated by the global air-transportation network, and Alzheimer’s disease dynamics in a human brain network. Taken together, our results establish that large networks can be controlled with computation and communication costs comparable to those for small networks.

42 ENGINEERING↗
DOE OSTI2021

Iterated projected position algorithm for constructing exponentially localized generalized Wannier functions for periodic and nonperiodic insulators in two dimensions and higher

Localized bases play an important role in understanding electronic structure. In periodic insulators, a natural choice of localized basis is given by the Wannier functions which depend on a choice of unitary transform known as a gauge transformation. Over the past few decades, there have been many works that have focused on optimizing the choice of the gauge so that the corresponding Wannier functions are maximally localized or reflect some symmetry of the underlying system. In this work, we consider fully nonperiodic materials where the usual Wannier functions are not well defined and gauge optimization is impractical. To tackle the problem of calculating exponentially localized generalized Wannier functions in both periodic and nonperiodic systems, we discuss the ‘iterated projected position (IPP)” algorithm. Here, the IPP algorithm is based on matrix diagonalization and therefore unlike optimization-based approaches, it does not require initialization and cannot get stuck at a local minimum. Furthermore, the IPP algorithm is guaranteed by a rigorous analysis to produce exponentially localized functions under certain mild assumptions. We numerically demonstrate that the IPP algorithm can be used to calculate exponentially localized bases for the Haldane model, the Kane-Mele model (in both Z 2 invariant even and Z 2 invariant odd phases), and the p x + ip y model on a quasicrystal lattice.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗