Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “generalized functions”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,171 records · Page 65

Information divergences to parametrize astrophysical uncertainties in dark matter direct detection

Astrophysical uncertainties in dark matter direct detection experiments are typically addressed by parametrizing the velocity distribution in terms of a few uncertain parameters that vary around some central values. Here we propose a method to optimize over all velocity distributions lying within a given distance measure from a central distribution. We discretize the dark matter velocity distribution as a superposition of streams and use a variety of information divergences to parametrize its uncertainties. With this, we bracket the limits on the dark matter–nucleon and dark matter–electron scattering cross sections, when the true dark matter velocity distribution deviates from the commonly assumed Maxwell-Boltzmann form. The methodology pursued is general and could be applied to other physics scenarios where a given physical observable depends on a function that is uncertain.

particle astrophysics↗

Decoding polymer self-dynamics using a two-step approach

The self-correlation function and corresponding self-intermediate scattering function in Fourier space are important quantities for describing the molecular motions of liquids. This work draws attention to a largely overlooked issue concerning the analysis of these space-time density-density correlation functions of polymers. Here, we show that the interpretation of non-Gaussian behavior of polymers is generally complicated by intrachain averaging of distinct self-dynamics of different segments. By the very nature of the mathematics involved, the averaging process not only conceals critical dynamical information, but also contributes to the observed non-Gaussian dynamics. To fully expose this issue and provide a thorough benchmark of polymer self-dynamics, we perform analyses of coarse-grained molecular dynamics simulations of linear and ring polymer melts as well as several theoretical models using a “two-step” approach, where interchain and intrachain averagings of segmental self-dynamics are separated. While past investigations primarily focused on the average behavior, our results indicate that a more nuanced approach to polymer self-dynamics is clearly required.

36 MATERIALS SCIENCE↗

Freely jointed chain models with extensible links

We report analytical relations for the mechanical response of single polymer chains are valuable for modeling purposes, on both the molecular and the continuum scale. These relations can be obtained using statistical thermodynamics and an idealized single-chain model, such as the freely jointed chain model. To include bond stretching, the rigid links in the freely jointed chain model can be made extensible, but this almost always renders the model analytically intractable. Here, an asymptotically correct statistical thermodynamic theory is used to develop analytic approximations for the single-chain mechanical response of this model. The accuracy of these approximations is demonstrated using several link potential energy functions. This approach can be applied to other single-chain models, and to molecular stretching in general.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Evaluating Physics-Informed Neural Network Performance for Seismic Discrimination between Earthquakes and Explosions

In this article, we evaluate adding a weak physics constraint, that is, a physics‐based empirical relationship, to the loss function with a physics‐informed manner in local distance explosion discrimination in the hope of improving the generalization capability of the machine learning (ML) model. We compare the proposed model with the two‐branch model we previously developed, as well as with a pure data‐driven model. Unexpectedly, the proposed model did not consistently outperform the pure data‐driven model. By varying the level of inconsistency in the training data, we find this approach is modulated by the strength of the physics relationship. In conclusion, this result has important implications for how to best incorporate physical constraints in ML models.

58 GEOSCIENCES↗

Topological order in matrix Ising models

We study a family of models for an N_1 \times N_2 N 1 × N 2 matrix worth of Ising spins S_{aB} S a B . In the large N_i N i limit we show that the spins soften, so that the partition function is described by a bosonic matrix integral with a single ‘spherical’ constraint. In this way we generalize the results of to a wide class of Ising Hamiltonians with O(N_1,\mathbb{Z})\times O(N_2,\mathbb{Z}) O ( N 1 , ℤ ) × O ( N 2 , ℤ ) symmetry. The models can undergo topological large N N phase transitions in which the thermal expectation value of the distribution of singular values of the matrix S_{aB} S a B becomes disconnected. This topological transition competes with low temperature glassy and magnetically ordered phases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The Aemulus Project. V. Cosmological Constraint from Small-scale Clustering of BOSS Galaxies

We analyze clustering measurements of BOSS galaxies using a simulation-based emulator of two-point statistics. We focus on the monopole and quadrupole of the redshift-space correlation function, and the projected correlation function, at scales of 0.1 ~ 60 h -1 Mpc. Although our simulations are based on wCDM with general relativity (GR), we include a scaling parameter of the halo velocity field, γ f , defined as the amplitude of the halo velocity field relative to the GR prediction. We divide the BOSS data into three redshift bins. After marginalizing over other cosmological parameters, galaxy bias parameters, and the velocity scaling parameter, we find fσ 8 (z = 0.25) = 0.413 ± 0.031, fσ 8 (z = 0.4) = 0.470 ± 0.026, and fσ 8 (z = 0.55) = 0.396 ± 0.022. Compared with Planck observations using a flat Lambda cold dark matter model, our results are lower by 1.9σ, 0.3σ, and 3.4σ, respectively. These results are consistent with other recent simulation-based results at nonlinear scales, including weak lensing measurements of BOSS LOWZ galaxies, two-point clustering of eBOSS LRGs, and an independent clustering analysis of BOSS LOWZ. All these results are generally consistent with a combination of ${\gamma }_{f}^{1/2}{\sigma }_{8}\approx 0.75$. We note, however, that the BOSS data is well fit assuming GR, i.e., γf = 1. We cannot rule out an unknown systematic error in the galaxy bias model at nonlinear scales, but near-future data and modeling will enhance our understanding of the galaxy–halo connection, and provide a strong test of new physics beyond the standard model.

79 ASTRONOMY AND ASTROPHYSICS↗

The cosmic web around the Coma cluster from constrained cosmological simulations

Galaxy clusters in the Universe occupy the important position of nodes of the cosmic web. They are connected among them by filaments, elongated structures composed of dark matter, galaxies, and gas. The connection of galaxy clusters to filaments is important, as it is related to the process of matter accretion onto the former. For this reason, investigating the connections to the cosmic web of massive clusters, especially well-known ones for which a lot of information is available, is a hot topic in astrophysics. In a previous work, we performed an analysis of the filament connections of the Coma cluster of galaxies, as detected from the observed galaxy distribution. In this work we resort to a numerical simulation whose initial conditions are constrained to reproduce the local Universe, including the region of the Coma cluster to interpret our observations in an evolutionary context. We detect the filaments connected to the simulated Coma cluster and perform an accurate comparison with the cosmic web configuration we detect in observations. We perform an analysis of the halos’ spatial and velocity distributions close to the filaments in the cluster outskirts. We conclude that, although not significantly larger than the average, the flux of accreting matter on the simulated Coma cluster is significantly more collimated close to the filaments with respect to the general isotropic accretion flux. This paper is the first example of such a result and the first installment in a series of publications which will explore the build-up of the Coma cluster system in connection to the filaments of the cosmic web as a function of redshift.

79 ASTRONOMY AND ASTROPHYSICS↗

Three-point functions in $\mathrm{ABJM}$ and Bethe Ansatz

We develop an integrability-based framework to compute structure constants of two sub-determinant operators and a single-trace non-BPS operator in ABJM theory in the planar limit. In this first paper, we study them at weak coupling using a relation to an integrable spin chain. We first develop a nested Bethe ansatz for an alternating SU(4) spin chain that describes single-trace operators made out of scalar fields. We then apply it to the computation of the structure constants and show that they are given by overlaps between a Bethe eigenstate and a matrix product state. We conjecture that the determinant operator corresponds to an integrable matrix product state and present a closed-form expression for the overlap, which resembles the so-called Gaudin determinant. We also provide evidence for the integrability of general sub-determinant operators. The techniques developed in this paper can be applied to other quantities in ABJM theory including three-point functions of single-trace operators.

1/N Expansion↗

A review on experimentally observed mechanical and microstructural characteristics of interfaces in multi-material laser powder bed fusion

Additive manufacturing (AM) is a revolutionary technology. One of the key AM categories, metal powder-based fusion processes, has many advantages compared to conventional methods for fabricating structural materials, such as permitting increased geometric complexity. While single material metal powder AM has advanced significantly in the past decade, multi-material AM is gradually attracting more attention owing to the recent breakthrough in multi-material feedstock delivery and the growing interest of fabricating functionally graded components. Multi-material AM offers an alternative route for applications that require location dependent material properties and high geometrical complexity. The AM community has invented several ways to achieve compositional gradients and discrete boundaries in two and three dimensions using mechanical spreading, nozzle-based, electrophotographic, and hybrid techniques. This article reviews the current state of laser powder bed fusion based multi-material AM of metals with focuses on the characteristics of the material interface as well as the properties and performance of the AM built functionally graded materials. We show the common challenges and issues related to material transitions, such as defects, segregation, phase separation, and the efficacy of some potential solutions including material and process optimizations. Additionally, this study evaluates the applicability and limitations of the existing testing standards and methods for measuring mechanical performance of functionally graded materials. Finally, we discuss mechanical testing development opportunities, which can help multi-material AM move towards higher technological maturity. In general, we find that the link between gradient microstructure and mechanical properties is not well understood or studied and suggest several mechanical tests that may better inform this knowledge gap.

42 ENGINEERING↗

Notes on resonances and unitarity from celestial amplitudes

We study the celestial description of the O(N) sigma model in the large N limit as introduced by Coleman, Jackiw and Politzer. Focusing on three dimensions, we analyze the implications of a UV complete, all-loop order 4-point amplitude of pions in terms of correlation functions defined on the celestial circle. We find these retain many key features from the previously studied tree-level case, such as their relation to Generalized Free Field theories and crossing-symmetry, but also incorporate new properties such as IR/UV softness and S-matrix metastable states. In particular, to understand unitarity, we propose a form of the optical theorem that controls the imaginary part of the correlator based solely on the presence of these resonances. We also explicitly analyze the conformal block expansions and factorization of four-point functions into three-point functions. We find that summing over resonances is key for these factorization properties to hold. We end with some topics for future study.

1/N expansion↗

Density Functional Tight-Binding Models for Band Structures of Transition-Metal Alloys and Surfaces across the d -Block

First-principles electronic structure simulations are an invaluable tool for understanding chemical bonding and reactions. While machine-learning models such as interatomic potentials significantly accelerate the exploration of potential energy surfaces, electronic structure information is generally lost. Particularly in the field of heterogeneous catalysis, simulated electron band structures provide fundamental insights into catalytic reactivity. This ab initio knowledge is preserved in semiempirical methods such as density functional tight binding (DFTB), which extend the accessible computational length and time scales beyond first-principles approaches. In this paper here we present Shell-Optimized Atomic Confinement (SOAC) DFTB electronic-part-only parametrizations for bulk and surface band structures of all d-block transition metals that enable efficient predictions of electronic descriptors for large structures or high-throughput studies on complex systems outside the computational reach of density functional theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Describing adsorption of benzene, thiophene, and xenon on coinage metals by using the Zaremba–Kohn theory-based model

Semilocal (SL) density functional approximations (DFAs) are widely applied but have limitations due to their inability to incorporate long-range van der Waals (vdW) interaction. Non-local functionals (vdW-DF, VV10, and rVV10) or empirical methods (DFT+D, DFT+vdW, and DFT+MBD) are used with SL-DFAs to account for such missing interaction. The physisorption of a molecule on the surface of the coinage metals (Cu, Ag, and Au) is a typical example of systems where vdW interaction is significant. However, it is difficult to find a general method that reasonably describes both adsorption energy and geometry of even the simple prototypes of cyclic and heterocyclic aromatic molecules such as benzene (C 6 H 6 ) and thiophene (C 4 H 4 S), respectively, with reasonable accuracy. Here, we present an alternative scheme based on Zaremba–Kohn theory, called DFT+vdW-dZK. We show that unlike other popular methods, DFT+vdW-dZK and particularly SCAN+vdW-dZK give an accurate description of the physisorption of a rare-gas atom (xenon) and two small albeit diverse prototype organic molecules on the (111) surfaces of the coinage metals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Mechanical adaptation of brachiopod shells via hydration-induced structural changes

The function-optimized properties of biominerals arise from the hierarchical organization of primary building blocks. Alteration of properties in response to environmental stresses generally involves time-intensive processes of resorption and reprecipitation of mineral in the underlying organic scaffold. Here, we report that the load-bearing shells of the brachiopod Discinisca tenuis are an exception to this process. These shells can dynamically modulate their mechanical properties in response to a change in environment, switching from hard and stiff when dry to malleable when hydrated within minutes. Using ptychographic X-ray tomography, electron microscopy and spectroscopy, we describe their hierarchical structure and composition as a function of hydration to understand the structural motifs that generate this adaptability. Key is a complementary set of structural modifications, starting with the swelling of an organic matrix on the micron level via nanocrystal reorganization and ending in an intercalation process on the molecular level in response to hydration.

36 MATERIALS SCIENCE↗

Tunable structural color of bottlebrush block copolymers through direct-write 3D printing from solution

Additive manufacturing of functional materials is limited by control of microstructure and assembly at the nanoscale. In this work, we integrate nonequilibrium self-assembly with direct-write three-dimensional (3D) printing to prepare bottlebrush block copolymer (BBCP) photonic crystals (PCs) with tunable structure color. After varying deposition conditions during printing of a single ink solution, peak reflected wavelength for BBCP PCs span a range of 403 to 626 nm (blue to red), corresponding to an estimated change in d-spacing of >70 nm (Bragg- Snell equation). Physical characterization confirms that these vivid optical effects are underpinned by tuning of lamellar domain spacing, which we attribute to modulation of polymer conformation. Using in situ optical microscopy and solvent-vapor annealing, we identify kinetic trapping of metastable microstructures during printing as the mechanism for domain size control. More generally, we present a robust processing scheme with potential for on-the-fly property tuning of a variety of functional materials.

36 MATERIALS SCIENCE↗

Physically Informed Machine Learning Prediction of Electronic Density of States

The electronic structure of a material, such as its density of states (DOS), provides key insights into its physical and functional properties and serves as a valuable source of high-quality features for many materials screening and discovery workflows. Still, the computational cost of calculating the DOS, most commonly with density functional theory (DFT), becomes prohibitive for meeting high-fidelity or high-throughput requirements, necessitating a cheaper but sufficiently accurate surrogate. To fulfill this demand, we develop a general machine learning method based on graph neural networks for predicting the DOS purely from atomic positions, six orders of magnitude faster than DFT. This approach can effectively use large materials databases and be applied generally across the entire periodic table to materials classes of arbitrary compositional and structural diversity. We furthermore devise a highly adaptable scheme for physically informed learning which encourages the DOS prediction to favor physically reasonable solutions defined by any set of desired constraints. This functionality provides a means for ensuring that the predicted DOS is reliable enough to be used as an input to downstream materials screening workflows to predict more complex functional properties, which rely on accurate physical features.

36 MATERIALS SCIENCE↗

Generalization error guaranteed auto-encoder-based nonlinear model reduction for operator learning

Many physical processes in science and engineering are naturally represented by operators between infinite-dimensional function spaces. The problem of operator learning, in this context, seeks to extract these physical processes from empirical data, which is challenging due to the infinite or high dimensionality of data. An integral component in addressing this challenge is model reduction, which reduces both the data dimensionality and problem size. In this paper, we utilize low-dimensional nonlinear structures in model reduction by investigating Auto-Encoder-based Neural Network (AENet). AENet first learns the latent variables of the input data and then learns the transformation from these latent variables to corresponding output data. Our numerical experiments validate the ability of AENet to accurately learn the solution operator of nonlinear partial differential equations. Furthermore, we establish a mathematical and statistical estimation theory that analyzes the generalization error of AENet. Finally, our theoretical framework shows that the sample complexity of training AENet is intricately tied to the intrinsic dimension of the modeled process, while also demonstrating the robustness of AENet to noise.

Auto-encoder↗

Deriving Transmissibility Functions from Finite Elements for Specifications

This work explores deriving transmissibility functions for a missile from a measured location at the base of the fairing to a desired location within the payload. A pressure on the outside of the fairing and the rocket motor’s excitation creates an acceleration at a measured location and a desired location. Typically, the desired location is not measured. In fact, it is typical that the payload may change, but measured acceleration at the base of the fairing is generally similar to previous test flights. Given this knowledge, it is desired to use a finite-element model to create a transmissibility function which relates acceleration from the previous test flight’s measured location at the base of the fairing to acceleration at a location in the new payload. Four methods are explored for deriving this transmissibility, with the goal of finding an appropriate transmissibility when both the pressure and rocket motor excitation are equally present. In conclusion, these methods are assessed using transient results from a simple example problem, and it is found that one of the methods gives good agreement with the transient results for the full range of loads considered.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

A General Strategy for Bandgap Engineering Via Anion‐Lattice Doping in High‐Entropy Oxides

Bandgap engineering is a critical tool for tailoring the electronic properties of functional materials, traditionally achieved by modifying the cation sublattice. Here, a generalizable strategy is introduced that leverages facile anion-lattice doping in high entropy materials to modulate the bandgap in high-entropy metal oxides (HEMOs). By incorporating nitrogen into a single-phase high-entropy metal oxide/nitride (HEMO:HEMN) solid solution, a substantial bandgap reduction is achieved from 3.55 eV (HEMO) to ≈2.46 eV (HEMO:HEMN), significantly enhancing electronic conductivity. Unlike conventional bandgap tuning approaches that rely on cation substitution or heterojunction formation, this method exploits anion-mediated entropy stabilization, enabling uniform bandgap narrowing across the entire solid solution. This anion-lattice engineering strategy is broadly applicable to high-entropy systems, providing a new pathway for designing energy materials with tailored electronic properties. The resulting HEMO:HEMN solid solution exhibits a tenfold increase in capacitance and capacity compared to HEMO in supercapacitor and lithium-ion battery tests, demonstrating the transformative potential of anion-driven bandgap modulation for next-generation energy storage and conversion technologies.

energy storage↗