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Results for “Extremal set theory”

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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DOE OSTI2022

Bootstrapping 2d ϕ 4 theory with Hamiltonian truncation data

We combine the methods of Hamiltonian Truncation and the recently proposed generalisation of the S-matrix bootstrap that includes local operators to determine the two-particle scattering amplitude and the two-particle form factor of the stress tensor at s > 0 in the 2d Φ 4 theory. We use the form factor of the stress tensor at s ≤ 0 and its spectral density computed using Lightcone Conformal Truncation (LCT), and inject them into the generalized S-matrix bootstrap set-up. The obtained results for the scattering amplitude and the form factor are fully reliable only in the elastic regime. We independently construct the “pure” S-matrix bootstrap bounds (bootstrap without including matrix elements of local operators), and find that the sinh-Gordon model and its analytic continuation the “staircase model” saturate these bounds. Surprisingly, the Φ 4 two-particle scattering amplitude also very nearly saturates these bounds, and moreover is extremely close to that of the sinh-Gordon/staircase model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Universality in logarithmic temperature corrections to near-extremal rotating black hole thermodynamics in various dimensions

The low-temperature thermodynamics of near-extremal rotating black holes has recently been revisited to incorporate one-loop contributions that are dominant in this regime. We discuss these quantum corrections to the gravitational path integral for asymptotically Anti de-Sitter black holes in four and five dimensions. In four dimensions we explicitly consider Kerr-AdS 4 , Kerr-Newman-AdS 4 and the rotating black hole in $\mathcal{N}$ = 4 gauged supergravity with two scalars and two electric charges turned on. In five dimensions we explicitly address the asymptotically flat Myers-Perry black hole and the Kerr-AdS5 black hole. In every case we find that tensor modes contribute $\frac{3}{2}$logT Hawking to the low-temperature thermodynamics. We identify the root cause of this universality in two facts: (i) the universal presence of a SL(2, $\mathbb{R}$) subgroup of isometries in the near-horizon geometry and (ii) a set of cancellations in the Lichnerowicz operator. We show that these two conditions hold for near-extremal black holes in asymptotically flat and asymptotically AdS spacetimes of various dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Minimal-Area Metrics on the Swiss Cross and Punctured Torus

The closed string theory minimal-area problem asks for the conformal metric of least area on a Riemann surface with the condition that all non-contractible closed curves have length greater than or equal to an arbitrary constant that can be set to one. Through every point in such a metric there is a geodesic that saturates the length condition, and the saturating geodesics in a given homotopy class form a band. The extremal metric is unknown when bands of geodesics cross, as it happens for surfaces of non-zero genus. Here, we use recently proposed convex programs to numerically find the minimal-area metric on the square torus with a square boundary, for various sizes of the boundary. For large enough boundary the problem is equivalent to the “Swiss cross” challenge posed by Strebel. We find that the metric is positively curved in the two-band region and flat in the single-band regions. For small boundary the metric develops a third band of geodesics wrapping around it, and has both regions of positive and of negative curvature. This surface can be completed to provide the minimal-area metric on a once-punctured torus, representing a closed-string tadpole diagram.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Predicting Device Parameters for Dye-Sensitized Solar Cells from Electronic Structure Calculations to Reproduce Experiment.

Given that improvements to the power-conversion efficiency (PCE) of dye-sensitized solar cells (DSSCs) have slowed in recent years, a means to accurately predict the device parameters yielded by trial dyes in silico, without having to synthesize them, would be extremely valuable to speed up the design process. Currently, the best-performing methods of calculating device parameters rely on a set of experimentally determined kinetic coefficients. In practice, it is very difficult to measure these kinetic parameters accurately, limiting the overall accuracy of such predictive methods. This work proposes a model to obtain key parameters such as J(SC), V-OC, and PCE using only the results from density functional theory (DFT) and time-dependent DFT calculations, noting that rates of electron-transfer steps are ultimately linked to the electronic structure of the dye center dot center dot center dot TiO2 working electrode. Six organic DSSC dyes from dissimilar chemical classes (L0, L1, L2, WS-2, WS-92, and C281) were chosen to demonstrate the power of this approach. Their a priori known experimentally determined device performance metrics served to validate our predictions. The greatest absolute error in our predicted PCE values was 0.36% relative to the experiment, while the greatest fractional error was 0.042. This indicates that the proposed model offers a dramatic improvement on previous predictive methods for DSSC device parameters, both in accuracy and in consistency. Moreover, such a predictive model has great potential to be applied to other photovoltaic applications, further enabling the design of novel, highly efficient photoactive materials.

density functional theory↗
DOE OSTI2020

Polarizabilities of neutral atoms and atomic ions with a noble gas electron configuration

Atomic polarizabilities play an important role in the development of force fields for molecular simulations, as well as for the development of qualitative concepts of atomic and molecular behavior. Coupled cluster theory at the coupled cluster singles doubles triples level with very large correlation-consistent basis sets with extended diffuse functions has been used to predict the polarizabilities of the atomic neutrals, mono-cations and mono-anions with a noble gas configuration. Additional corrections for scalar relativistic and spin–orbit effects were also included for the electron configurations of Kr, Xe, and Rn. The results are in excellent agreement with experiment or with other high level calculations where available. The current results for most of these species represent the best available values for the polarizabilities. The results show that the polarizability of H - is very difficult to calculate without extremely diffuse functions. The polarizability of H - is the largest value, 34.05 Å 3 , calculated for all species in the current study. The polarizabilities of the remaining halogen anions are also the best available values. The polarizabilities of the halogen anions (excluding F - ) and H - have a linear correlation with the electron affinity of the neutral atom. Spin– orbit effects, even for closed shell species, cannot be ignored for quantitative accuracy, and the inclusion of spin–orbit effects for Fr + , Rn, and At - increases the polarizability by 4%, 6%, and 15%, respectively.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

A Machine Learning Assisted Development of a Model for the Populations of Convective and Stratiform Clouds

Abstract Traditional parameterizations of the interaction between convection and the environment have relied on an assumption that the slowly varying large‐scale environment is in statistical equilibrium with a large number of small and short‐lived convective clouds. They fail to capture nonequilibrium transitions such as the diurnal cycle and the formation of mesoscale convective systems as well as observed precipitation statistics and extremes. Informed by analysis of radar observations, cloud‐permitting model simulation, theory, and machine learning, this work presents a new stochastic cloud population dynamics model for characterizing the interactions between convective and stratiform clouds, with the goal of informing the representation of these interactions in global climate models. Fifteen wet seasons of precipitating cloud observations by a C‐band radar at Darwin, Australia are fed into a machine learning algorithm to obtain transition functions that close a set of coupled equations relating large‐scale forcing, mass flux, the convective cell size distribution, and the stratiform area. Under realistic large‐scale forcing, the derived transition functions show that, on the one hand, interactions with stratiform clouds act to dampen the variability in the size and number of convective cells and therefore in the convective mass flux. On the other, for a given convective area fraction, a larger number of smaller cells is more favorable for the growth of stratiform area than a smaller number of larger cells. The combination of these two factors gives rise to solutions with a few convective cells embedded in a large stratiform area, reminiscent of mesoscale convective systems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Phenomenology of magnetic black holes with electroweak-symmetric coronas

Magnetically charged black holes (MBHs) are interesting solutions of the Standard Model and general relativity. They may possess a “hairy” electroweak-symmetric corona outside the event horizon, which speeds up their Hawking radiation and leads them to become nearly extremal on short timescales. Their masses could range from the Planck scale up to the Earth mass. We study various methods to search for primordially produced MBHs and estimate the upper limits on their abundance. We revisit the Parker bound on magnetic monopoles and show that it can be extended by several orders of magnitude using the large-scale coherent magnetic fields in Andromeda. This sets a mass-independent constraint that MBHs have an abundance less than 4 × 10 -4 times that of dark matter. MBHs can also be captured in astrophysical systems like the Sun, the Earth, or neutron stars. There, they can become non-extremal either from merging with an oppositely charged MBH or absorbing nucleons. The resulting Hawking radiation can be detected as neutrinos, photons, or heat. High-energy neutrino searches in particular can set a stronger bound than the Parker bound for some MBH masses, down to an abundance 10 -7 of dark matter.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Leading order corrections to the quantum extremal surface prescription

We show that a naïve application of the quantum extremal surface (QES) prescription can lead to paradoxical results and must be corrected at leading order. The corrections arise when there is a second QES (with strictly larger generalized entropy at leading order than the minimal QES), together with a large amount of highly incompressible bulk entropy between the two surfaces. We trace the source of the corrections to a failure of the assumptions used in the replica trick derivation of the QES prescription, and show that a more careful derivation correctly computes the corrections. Using tools from one-shot quantum Shannon theory (smooth min- and max-entropies), we generalize these results to a set of refined conditions that determine whether the QES prescription holds. We find similar refinements to the conditions needed for entanglement wedge reconstruction (EWR), and show how EWR can be reinterpreted as the task of one-shot quantum state merging (using zero-bits rather than classical bits), a task gravity is able to achieve optimally efficiently.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Automated Detection of Instability-Inducing Channel Geometry Transitions in Saint-Venant Simulation of Large-Scale River Networks

A new sweep-search algorithm (SSA) is developed and tested to identify the channel geometry transitions responsible for numerical convergence failure in a Saint-Venant equation (SVE) simulation of a large-scale open-channel network. Numerical instabilities are known to occur at “sharp” transitions in discrete geometry, but the identification of problem locations has been a matter of modeler’s art and a roadblock to implementing large-scale SVE simulations. The new method implements techniques from graph theory applied to a steady-state 1D shallow-water equation solver to recursively examine the numerical stability of each flowpath through the channel network. The SSA is validated with a short river reach and tested by the simulation of ten complete river systems of the Texas–Gulf Coast region by using the extreme hydrological conditions recorded during hurricane Harvey. The SSA successfully identified the problematic channel sections in all tested river systems. Subsequent modification of the problem sections allowed stable solution by an unsteady SVE numerical solver. The new SSA approach permits automated and consistent identification of problem channel geometry in large open-channel network data sets, which is necessary to effectively apply the fully dynamic Saint-Venant equations to large-scale river networks or for city-wide stormwater networks.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Nanoscale Turing patterns in a bismuth monolayer

Turing’s reaction–diffusion theory of morphogenesis has been very successful for understanding macroscopic patterns within complex objects ranging from biological systems to sand dunes. However, Turing patterns on microscopic length scales are extremely rare. Here we show that a strained atomic bismuth monolayer assembled on the surface of NbSe 2 —and subject to interatomic interactions and kinetics—displays Turing patterns. Our reaction–diffusion model produces stripe patterns with a period of five atoms (approximately 2 nm) and domain walls with Y-shaped junctions that bear a striking resemblance to what has been experimentally observed. Our work establishes that Turing patterns can occur at the atomic scale in a hard condensed-matter setting.

36 MATERIALS SCIENCE↗
DOE OSTI2021

The great escape: tunneling out of microstate geometries

We compute the quasi-normal frequencies of scalars in asymptotically-flat microstate geometries that have the same charge as a D1-D5-P black hole, but whose long BTZ-like throat ends in a smooth cap. In general the wave equation is not separable, but we find a class of geometries in which the non-separable term is negligible and we can compute the quasi-normal frequencies using WKB methods. We argue that our results are a universal property of all microstate geometries with deeply-capped BTZ throats. These throats generate large redshifts, which lead to exceptionally-low-energy states with extremely long decay times, set by the central charge of the dual CFT to the power of twice the dimension of the operator dual to the mode. While these decay times are extremely long, we also argue that the energy decay is bounded, at large t , by (log( t )) – 2 and is comparable with the behavior of ultracompact stars, as one should expect for microstate geometries.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Effective Field Theory for Extreme Mass Ratio Binaries

We derive an effective field theory describing a pair of gravitationally interacting point particles in an expansion in their mass ratio, also known as the self-force (SF) expansion. The 0SF dynamics are trivially obtained to all orders in Newton’s constant by the geodesic motion of the light body in a Schwarzschild background encoding the gravitational field of the heavy body. The corrections at 1SF and higher are generated by perturbations about this configuration—that is, the geodesic deviation of the light body and the fluctuation graviton—but crucially supplemented by an operator describing the recoil of the heavy body as it interacts with the smaller companion. Using this formalism we compute new results at third post-Minkowskian order for the conservative dynamics of a system of gravitationally interacting massive particles coupled to a set of additional scalar and vector fields.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

On the relation between the subadditivity cone and the quantum entropy cone

Given a multipartite quantum system, what are the possible ways to impose mutual independence among some subsystems, and the presence of correlations among others, such that there exists a quantum state which satisfies these demands? This question and the related notion of a pattern of marginal independence (PMI) were introduced in [1], and then argued in [2] to be central in the derivation of the holographic entropy cone. Here we continue the general information theoretic analysis of the PMIs allowed by strong subadditivity (SSA) initiated in [1]. We show how the computation of these PMIs simplifies when SSA is replaced by a weaker constraint, dubbed Klein’s condition (KC), which follows from the necessary condition for the saturation of subadditivity (SA). Formulating KC in the language of partially ordered sets, we show that the set of PMIs compatible with KC forms a lattice, and we investigate several of its structural properties. One of our main results is the identification of a specific lower dimensional face of the SA cone that contains on its boundary all the extreme rays (beyond Bell pairs) that can possibly be realized by quantum states. We verify that for four or more parties, KC is strictly weaker than SSA, but nonetheless the PMIs compatible with SSA can easily be derived from the KC-compatible ones. For the special case of 1-dimensional PMIs, we conjecture that KC and SSA are in fact equivalent. To make the presentation self-contained, we review the key ingredients from lattice theory as needed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Universal construction of black hole microstates

We refine and extend a recent construction of sets of black hole microstates with semiclassical interiors that span a Hilbert space of dimension e S , where S is the black hole entropy. We elaborate on the definition and properties of microstates in statistical and black hole mechanics. The gravitational description of microstates employs matter shells in the interior of the black hole, and we argue that in the limit where the shells are very heavy, the construction acquires universal validity. To this end, we show it for very wide classes of black holes; we first extend the construction to rotating and charged black holes, including extremal and near-extremal solutions, with or without supersymmetry, and we sketch how the construction of microstates can be embedded in string theory. We then describe how the approach can include general quantum corrections, near or far from extremality. For supersymmetric black holes, the microstates we construct differ from other recent constructions in that the interior excitations are not confined within the near-extremal throat. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2025

Generalizable machine learning potentials for quantum-accurate predictions of non-equilibrium behavior in 2D materials

Machine learning interatomic potentials (ML-IAPs) are emerging as transformative tools in materials modeling, promising quantum-level accuracy at a fraction of the computational cost. However, their ability to generalize beyond equilibrium configurations and to reliably capture defect- and temperature-driven behavior remains underexplored. Here, we develop and benchmark two state-of-the-art ML-IAPs, Spectral Neighbor Analysis Potential (SNAP) and Allegro, on a comprehensive dataset for monolayer MoSe₂. Using density functional theory (DFT) as the reference, we evaluate their performance in capturing stress–strain behavior, phase transition energetics, defect evolution, edge stability, and fracture toughness. Allegro, a deep equivariant neural network potential, surpasses both SNAP and the classical Tersoff potential in accuracy, efficiency, and transferability. Importantly, both ML potentials accurately reproduce experimental fracture measurements and ab initio predictions of inversion domain formation—phenomena well beyond their training sets. Our findings establish ML-IAPs as viable replacements for traditional force fields in the study of non-equilibrium mechanical phenomena, enabling large-scale, high-fidelity simulations in 2D materials and beyond. In conclusion, this work provides a broadly applicable framework for data-driven modeling of structural and functional transformations under extreme conditions.

2D materials↗
DOE OSTI2020

First-principles equations of state and structures of liquid metals in multi-megabar conditions

Liquid metals at extreme pressures and temperatures are widely interested in the high-pressure community. Based on density functional theory molecular dynamics, we conduct first-principles investigations on the equation of state ( EOS) and structures of four metals (Cu, Fe, Pb, and Sn) at 1.5–5 megabar conditions and 5 × 10 3 –4 × 10 4 K. Our first-principles EOS data enable evaluating the performance of four EOS models in predicting Hugoniot densities and temperatures of the four systems. We find the melting temperature of Cu is 1000–2000 K higher and shows a similar Clapeyron slope, in comparison to those of Fe. Our structure, coordination number, and diffusivity analysis indicates all the four liquid metals form similar simple close-packed structures. Our results set theoretical benchmarks for EOS development and structures of metals in their liquid states and under dynamic compression.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Multi-fidelity learning for interatomic potentials: low-level forces and high-level energies are all you need

The promise of machine learning interatomic potentials (MLIPs) has led to an abundance of public quantum mechanical (QM) training datasets. The quality of an MLIP is directly limited by the accuracy of the energies and atomic forces in the training dataset. Unfortunately, most of these datasets are computed with relatively low-accuracy QM methods, e.g. density functional theory with a moderate basis set. Due to the increased computational cost of more accurate QM methods, e.g. coupled-cluster theory with a complete basis set (CBS) extrapolation, most high-accuracy datasets are much smaller and often do not contain atomic forces. The lack of high-accuracy atomic forces is quite troubling, as training with force data greatly improves the stability and quality of the MLIP compared to training to energy alone. Because most datasets are computed with a unique level of theory, traditional single-fidelity (SF) learning is not capable of leveraging the vast amounts of published QM data. In this study, we apply multi-fidelity learning (MFL) to train an MLIP to multiple QM datasets of different levels of accuracy, i.e. levels of fidelity. Specifically, we perform three test cases to demonstrate that MFL with both low-level forces and high-level energies yields an extremely accurate MLIP—far more accurate than a SF MLIP trained solely to high-level energies and almost as accurate as a SF MLIP trained directly to high-level energies and forces. Therefore, MFL greatly alleviates the need for generating large and expensive datasets containing high-accuracy atomic forces and allows for more effective training to existing high-accuracy energy-only datasets. Indeed, low-accuracy atomic forces and high-accuracy energies are all that are needed to achieve a high-accuracy MLIP with MFL.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Electronic structure of intrinsic defects in c -gallium nitride: Density functional theory study without the jellium approximation

Here, we report the first nonjellium, systematic, density functional theory (DFT) study of intrinsic and extrinsic defects and defect levels in zinc-blende (cubic) gallium nitride. We use the local moment counter charge (LMCC) method, the standard Perdew-Becke-Ernzerhoff (PBE) exchange-correlation potential, and two pseudopotentials, where the Ga 3$\textit{d}$ orbitals are either in the core ($d^0$) or explicitly in the valence set ($d^{10}$). We studied 64, 216, 512, and 1000 atom supercells, and demonstrated convergence to the infinite limit, crucial for delineating deep from shallow states near band edges, and for demonstrating the elimination of finite cell-size errors. Contrary to common claims, we find that exact exchange is not required to obtain defect levels across the experimental band gap. As was true in silicon, silicon carbide, and gallium arsenide, the extremal LMCC defect levels of the aggregate of defects yield an effective LMCC defect band gap that is within 10% of the experimental gap (3.3 eV) for both pseudopotentials. We demonstrate that the gallium vacancy is more complicated than previously reported. There is dramatic metastability–a nearest-neighbor nitrogen atom shifts into the gallium site, forming an antisite, nitrogen vacancy pair, which is more stable than the simple vacancy for positive charge states. Our assessment of the $d^0$ and $d^{10}$ pseudopotentials yields minimal differences in defect structures and defect levels. The better agreement of the $d^0$ lattice constant with experiment suggests that the more computationally economical $d^0$ pseudopotentials are sufficient to achieve the fidelity possible within the physical accuracy of DFT, and thereby enable calculations in larger supercells necessary to demonstrate convergence with respect to finite size supercell errors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗