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 883 records · Page 49

Heavy states in 3d gravity and 2d CFT

We discuss correlators of light fields in heavy states in AdS 3 gravity and holographic 2d CFTs. In the bulk, the propagator of free fields in AdS backgrounds containing a conical defect or a BTZ black hole can be obtained by solving a wave equation, as well as by the method of images. On the boundary, these geometries are sourced by heavy operator insertions, and the propagator is dual to a heavy-light (HHLL) correlator. By matching its expansion in Virasoro blocks to our bulk results, we determine the OPE coefficients of all contributing states in both the s and t channels. In the s channel, these states are excitations of the light field on top of the heavy state, and their OPE coefficients are the amplitudes to create them. The t-channel OPE is dominated by the Virasoro vacuum block, but there is also an infinite family of light two-particle states that contribute to the correlator. The OPE coefficients that couple these states to heavy operators represent their expectation values in heavy backgrounds. We determine them exactly, derive their asymptotic form at large twist, and discuss their behavior near and above the BTZ threshold, where they become thermal one-point functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

New solutions of nonlocal NLS, mKdV and Hirota equations

In this paper, we provide several novel solutions of the Ablowitz–Musslimani and Yang’s versions of the nonlocal nonlinear Schrödinger (NLS) equation, nonlocal modified Korteweg–de Vries (mKdV) as well as nonlocal Hirota equations. Further, in each case we compare and contrast with the corresponding solutions of the relevant local equation. In addition, we provide new solutions of the local NLS, local mKdV and local Hirota equations which are not the solutions of the corresponding nonlocal equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Learning functional priors and posteriors from data and physics

In this work, we develop a new Bayesian framework based on deep neural networks to be able to extrapolate in space-time using historical data and to quantify uncertainties arising from both noisy and gappy data in physical problems. Specifically, the proposed approach has two stages: (1) prior learning and (2) posterior estimation. At the first stage, we employ the physics-informed Generative Adversarial Networks (PI-GAN) to learn a functional prior either from a prescribed function distribution, e.g., Gaussian process, or from historical data and physics. At the second stage, we employ the Hamiltonian Monte Carlo (HMC) method to estimate the posterior in the latent space of PI-GANs. In addition, we use two different approaches to encode the physics: (1) automatic differentiation, used in the physicsinformed neural networks (PINNs) for scenarios with explicitly known partial differential equations (PDEs), and (2) operator regression using the deep operator network (DeepONet) for PDE-agnostic scenarios. We then test the proposed method for (1) meta-learning for one-dimensional regression, and forward/inverse PDE problems (combined with PINNs); (2) PDE-agnostic physical problems (combined with DeepONet), e.g., fractional diffusion as well as saturated stochastic (100-dimensional) flows in heterogeneous porous media; and (3) spatial-temporal regression problems, i.e., inference of a marine riser displacement field using experimental data from the Norwegian Deepwater Programme (NDP). The results demonstrate that the proposed approach can provide accurate predictions as well as uncertainty quantification given very limited scattered and noisy data, since historical data could be available to provide informative priors. In summary, the proposed method is capable of learning flexible functional priors, e.g., both Gaussian and non-Gaussian process, and can be readily extended to big data problems by enabling mini-batch training using stochastic HMC or normalizing flows since the latent space is generally characterized as low dimensional.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Direct numerical simulations of three-component Rayleigh–Taylor mixing and an improved model for multicomponent reacting mixtures

We present direct numerical simulations of a three-layer Rayleigh–Taylor instability (RTI) problem with a configuration based on the experiments of Suchandra & Ranjan ( J. Fluid Mech. , vol. 974, 2023, A35) and Jacobs & Dalziel ( J. Fluid Mech. , vol. 542, 2005, pp. 251–279). The problem consists of a layer of light fluid between two layers of heavy fluid with an Atwood number of 0.3. These simulations are first validated through comparison with available experimental data. The validated simulations are then utilized to analyse statistics in this three-component flow. First, length scales are examined utilizing spectra and two-point spatial correlations of velocity and species concentration fluctuations. Next, joint probability density functions (p.d.f.s) of species concentration are compared against several model p.d.f.s representing generalizations of the bivariate beta distribution. Notably, the joint p.d.f.s do not appear to be accurately described by a Dirichlet distribution, indicating the marginal distributions do not conform to a beta distribution. Finally, similarity of the present configuration to three-component mixing found in inertial confinement fusion (ICF) applications is exploited to develop and validate an improved model for the impact of multicomponent mixing on thermonuclear (TN) reaction rates. A single time instant from the present simulations is chosen for a TN burn calculation under the hypothetical assumption of ICF materials and temperatures. Total TN output from this second calculation is then compared against the prediction of the improved model. The new model is found to accurately predict TN reaction rates in both premixed and non-premixed configurations.

42 ENGINEERING↗

Comparing Classical and Machine Learning Force Fields for Modeling Deformation of Metal–Organic Frameworks Relevant for Direct Air Capture

Deformation of metal–organic frameworks (MOFs) induced by adsorbate molecules can affect adsorption properties such as capacity and selectivity, but most computational studies of MOFs assume framework rigidity to simplify calculations. Although flexible force fields (FFs) for MOFs have been parametrized for specific materials, the generality of FFs for reliably modeling adsorbate-induced deformation to accuracy nearing that of density functional theory (DFT) has not been established. This work confirms using DFT calculations that adsorbate-induced deformation can affect CO 2 and H 2 O adsorption energies in a considerable fraction of MOFs promising for direct air capture (DAC). We then benchmark the efficacy of several general-purpose FFs in describing adsorbate-induced deformation for DAC against DFT. Our results show that current classical FFs are insufficient for describing MOF deformation, especially in cases of interest for DAC where strong interactions exist between adsorbed molecules and MOF frameworks. Some emerging machine learning force fields (MLFFs) we tested, particularly CHGNet, MACE-MP-0, and Equiformer V2, appear to be more promising than the classical FF for emulating the deformation behavior described by DFT. The best performing FF (CHGNet), however, fails to achieve the accuracy required for practical predictions with a mean absolute adsorption energy error of 0.124 eV.

adsorption↗

New Dimension in Ab Initio Electronic Structure Theory: Temperature, Pressure, and Chemical Potential

Ab initio electronic structure theory has transformed gas-phase molecular science with its predictive ability. In the attempt to bring such predictive ability to macroscopic systems and condensed matter, the theory must integrate quantum mechanics with statistical thermodynamics, so that thermodynamic functions such as free energy, internal energy, entropy, and chemical potentials are computed as functions of temperature in a systematically converging series of approximations. Here, a general, versatile strategy of elevating ab initio electronic structure theory to nonzero temperatures is introduced and discussed.

74 ATOMIC AND MOLECULAR PHYSICS↗

leapR: An R Package for Multiomic Pathway Analysis

A generalized goal of many high-throughput data studies is to identify functional mecha-nisms that underlie observed biological phenomena, whether disease outcomes or metabolic out-put. Increasingly, studies that rely on multiple sources of high-throughput data (genomic, tran-scriptomic, proteomic, metabolomic) are faced with a challenge of utilizing the data in a way that maximizes utility. However, methods for integration of multiple forms of molecular data into a biolog-ically coherent frameworks are needed. Furthermore, we have developed a framework to assess biological pathway activity that relates to phenotypic outcome using multi-source data. Availability and implementation: The leapR package with user manual and example workflow is available for download from GitHub (https://github.com/biodataganache/leapR).

59 BASIC BIOLOGICAL SCIENCES↗

Cation–Ligand Interactions Dictate Salt Partitioning and Diffusivity in Ligand-Functionalized Polymer Membranes

Membranes are an attractive alternative to current thermal separations due to their scalability and energy efficiency in desalinating water. Unfortunately, many of the conventional membrane materials available today are unable to differentiate between ionic solutes, especially alkali cations, compromising their use in ion–ion separations. Inspired by the ion-specific interactions exhibited by biological ion channels, recent research efforts have focused on synthesizing and characterizing new polymeric materials that incorporate ligands into polymer networks to bias solubility and/or diffusivity of one cationic species over another. Despite these efforts, little is known about the influence of incorporating ligands into polymer membranes on solubility and diffusivity of the complexing species. In this study, we first build a qualitative model of salt partitioning, diffusivity, and permeability in generic cation-complexing ligand-functionalized polymer membranes. Next, to validate our model and hypotheses, we perform atomistic molecular dynamics simulations of a 12-crown-4-functionalized membrane in the presence of alkali halide salts at low concentration. Generally, cation complexation enhances cation solubility but decreases diffusivity. Interestingly, the reduction in diffusivity is predicted to be larger than the enhancement in solubility for materials which operate by the mechanisms proposed in our physical picture, ultimately resulting in a reduction in the permeability of the selectively complexing ion.

36 MATERIALS SCIENCE↗

On the Interplay of Electronic and Lattice Screening on Exciton Binding in Two-Dimensional Lead Halide Perovskites

We use path integral Monte Carlo to study the energetics of excitons in layered, hybrid organic–inorganic perovskites in order to elucidate the relative contributions of dielectric confinement and electron–phonon coupling. While the dielectric mismatch between polar perovskite layers and nonpolar ligand layers significantly increases the exciton binding energy relative to their three-dimensional bulk crystal counterparts, formation of exciton polarons attenuates this effect. The contribution from polaron formation is found to be a nonmonotonic function of the lead halide layer thickness, which is clarified by a general variational theory. Accounting for both of these effects provides a description of exciton binding energies in good agreement with experimental measurements. By studying isolated layers and stacked layered crystals of various thicknesses, with ligands of varying polarity, we provide a systematic understanding of the excitonic behavior of this class of materials and how to engineer their photophysics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Exploration of lattice Hamiltonians for functional and structural discovery via Gaussian process-based exploration–exploitation

Statistical physics models ranging from simple lattice to complex quantum Hamiltonians are one of the mainstays of modern physics that have allowed both decades of scientific discovery and provided a universal framework to understand a broad range of phenomena from alloying to frustrated and phase separated materials to quantum systems. Traditionally, exploration of the phase diagrams corresponding to multidimensional parameter spaces of Hamiltonians was performed using a combination of basic physical principles, analytical approximations, and extensive numerical modeling. However, exploration of complex multidimensional parameter spaces is subject to the classic dimensionality problem, and the behaviors of interest concentrated on low dimensional manifolds remain undiscovered. Here, we demonstrate that a combination of exploration and exploration–exploitation with Gaussian process modeling and Bayesian optimization allows effective exploration of the parameter space for lattice Hamiltonians and effectively maps the regions at which specific macroscopic functionalities or local structures are maximized. We argue that this approach is general and can be further extended well beyond the lattice Hamiltonians to effectively explore the parameter space of more complex off-lattice and dynamic models.

42 ENGINEERING↗

Calculation of spin–orbit couplings using RASCI spinless one-particle density matrices: Theory and applications

Here we present the formalism and implementation for calculations of spin–orbit couplings (SOCs) using the Breit–Pauli Hamiltonian and non-relativistic wave functions described by the restricted active space configuration interaction (RASCI) method with general excitation operators of spin-conserving spin-flipping, ionizing, and electron-attaching types. The implementation is based on the application of the Wigner–Eckart theorem within the spin space, which enables the calculation of the entire SOC matrix based on the explicit calculation of just one transition between the two spin multiplets. Numeric results for a diverse set of atoms and molecules highlight the importance of a balanced treatment of correlation and adequate basis sets and illustrate the overall robust performance of RASCI SOCs. The new implementation is a useful addition to the methodological toolkit for studying spin-forbidden processes and molecular magnetism.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Mason–Weaver theory: Revised and extended for a semi-infinite domain

Mason and Weaver developed equations to describe small particles settling under the influence of gravity and Brownian motion, including the limiting case for an infinitely deep suspension. We encountered this common convection–diffusion equation and no-flux boundary conditions in a model for dynamics of adsorbed polymers in dead end pores of a depolymerization catalyst. Close examination reveals that the Mason–Weaver solution is not correct for the infinite domain with a non-uniform initial condition. In this paper, we obtain the time dependent Green’s function for the no flux boundary condition and also for a more general reactive boundary condition. We demonstrate how the results provide solutions, via superposition, which provide solutions for several boundary conditions and all initial conditions.

Chen, Ziqiu↗

An implicit solution for Asay foil trajectories generated by separable, sustained-production ejecta source models

We present a simple implicit solution for the time-dependent trajectory of a thin Asay foil ejecta diagnostic for the general case where the impinging ejecta cloud is generated by a source function characterized by an arbitrary (sustained) time dependence and a time-independent (stationary) particle velocity distribution. In the limit that the source function time dependence becomes a delta function, this solution—which is amenable to rapid numerical calculations of arbitrary accuracy—exactly recovers a previously published solution for the special case of instantaneous ejecta production. We also derive simple expressions for the free-surface arrival (catch-up) time as well as the true ejecta areal mass accumulation on the accelerating foil and place bounds on the level of error incurred when applying instant-production mass solutions to a sustained-production trajectory. We demonstrate these solutions with example calculations for hypothetical source functions spanning a wide range of ejecta production durations, velocity distributions, and temporal behaviors. These calculations demonstrate how the foil trajectory is often insensitive to the temporal dependence of the source function, instead being dominated by the velocity distribution. We quantify this insensitivity using a “compatibility score” metric. Under certain conditions, one may capitalize upon this insensitivity to obtain a good approximation of the second integral of the velocity distribution from the observed foil trajectory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Lagrangian large eddy simulations via physics-informed machine learning

High-Reynolds number homogeneous isotropic turbulence (HIT) is fully described within the Navier–Stokes (NS) equations, which are notoriously difficult to solve numerically. Engineers, interested primarily in describing turbulence at a reduced range of resolved scales, have designed heuristics, known as large eddy simulation (LES). LES is described in terms of the temporally evolving Eulerian velocity field defined over a spatial grid with the mean-spacing correspondent to the resolved scale. This classic Eulerian LES depends on assumptions about effects of subgrid scales on the resolved scales. Here, we take an alternative approach and design LES heuristics stated in terms of Lagrangian particles moving with the flow. Our Lagrangian LES, thus L-LES, is described by equations generalizing the weakly compressible smoothed particle hydrodynamics formulation with extended parametric and functional freedom, which is then resolved via Machine Learning training on Lagrangian data from direct numerical simulations of the NS equations. The L-LES model includes physics-informed parameterization and functional form, by combining physics-based parameters and physics-inspired Neural Networks to describe the evolution of turbulence within the resolved range of scales. The subgrid-scale contributions are modeled separately with physical constraints to account for the effects from unresolved scales. We build the resulting model under the differentiable programming framework to facilitate efficient training. We experiment with loss functions of different types, including physics-informed ones accounting for statistics of Lagrangian particles. We show that our L-LES model is capable of reproducing Eulerian and unique Lagrangian turbulence structures and statistics over a range of turbulent Mach numbers.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Machine learning enabled discovery of application dependent design principles for two-dimensional materials

Abstract The unique electronic and mechanical properties of two-dimensional (2D) materials make them promising next-generation candidates for a variety of applications. Large-scale searches for high-performing 2D materials are limited to calculating descriptors with computationally demanding first-principles density functional theory. In this work, we alleviate this issue by extending and generalizing crystal graph convolutional neural networks to systems with planar periodicity and train an ensemble of models to predict thermodynamic, mechanical and electronic properties. We carry out a screening of nearly 45,000 structures for two separate applications: mechanical strength and photovoltaics. By collecting statistics of the screened candidates, we investigate structural and compositional design principles that impact the properties of the structures surveyed. Our approach recovers some well-accepted design rules: hybrid organic-inorganic perovskites with lead and tin tend to be good candidates for solar cell applications and titanium based MXenes usually have high stiffness coefficients. Interestingly, other members of the group 4 elements also contribute to increasing the mechanical strength of MXenes. For all-inorganic perovskites, we discover some compositions that have not been deeply studied in the field of photovoltaics and thus open up paths for further investigation. We open-source the code-base to spur further development in this space.

Venturi, Victor (ORCID:0000000156727549)↗

Electronic structure and two-band superconductivity in unconventional high- T c cuprates Ba 2 CuO 3+δ

We report that the recently discovered cuprate superconductor Ba 2 CuO 3+δ exhibits a high T c ≃73 K at δ ≃ 0.2. The polycrystal grown under high pressure has a structure similar to La 2 CuO 4 but with dramatically different lattice parameters due to the CuO 6 octahedron compression. The crystal field in the compressed Ba 2 CuO 4 leads to an inverted Cu 3d e g complex with the d x 2 -y 2 orbital sitting below the d 3z 2 - r 2 and an electronic structure highly unusual compared to the conventional cuprates. We construct a two-orbital Hubbard model for the Cu d 9 state at hole doping x = 2δ and study the orbital-dependent strong correlation and superconductivity. For the undoped case at x = 0 , we found that strong correlation drives an orbital-polarized Mott-insulating state with the spin-1/2 moment of the localized d 3z 2 - r 2 orbital. In contrast to the single-band cuprates where superconductivity is suppressed in the overdoped regime, hole doping the two-orbital Mott insulator leads to orbital-dependent correlations and the robust spin and orbital exchange interactions produce a high-T c antiphase d-wave superconductor even in the heavily doped regime at x = 0.4 . We conjecture that Ba 2 CuO 3+δ realizes mixtures of such heavily hole-doped superconducting Ba 2 CuO 4 and disordered Ba 2 CuO 3 chains in a single-layer or predominately separated bilayer structure. Our findings suggest that unconventional cuprates with liberated orbitals as doped two-band Mott insulators can be a direction for realizing high-T c superconductivity with enhanced transition temperature T c .

36 MATERIALS SCIENCE↗

SIDIS at small x at next-to-leading order: Gluon contribution

We calculate the contribution of gluons to single inclusive hadron production at next-to-leading order (NLO) accuracy in deep inelastic scattering (DIS) at small x using the color glass condensate formalism. It is shown that the only divergence present is the standard collinear divergence, which is absorbed into scale evolution of quark-hadron fragmentation function. Our calculations are performed at finite N c and we provide general finite N c expressions for the structure of Wilson lines appearing in inclusive dihadron and single hadron production cross sections. We also comment on how one can obtain rapidity distribution of hadron multiplicities from our results. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Supersymmetric Virasoro minimal strings

A random matrix model definition of a family of N = 1 supersymmetric extensions of the Virasoro minimal string of Collier, Eberhardt, Mühlmann, and Rodriguez is presented. An analysis of the defining string equations shows that the models all naturally have unambiguous nonperturbative completions, which are explicitly supplied by the double-scaled orthogonal polynomial techniques employed. Perturbatively, the multiloop correlation functions of the model define a special supersymmetric class of “quantum volumes,” generalizing the prototype case, some of which are computed. Published by the American Physical Society 2024

Astronomy & Astrophysics↗