SEARCH · Engineering Papers

Results for “SERIES EXPANSION”

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.

SourceResearch connectionFrom yearThrough year

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

At least 217 records · Page 12

All sources NASA NTRS DOE OSTI

DOE OSTI2021

Heptagon functions and seven-gluon amplitudes in multi-Regge kinematics

We compute all 2 → 5 gluon scattering amplitudes in planar $ \mathcal{N} $ N = 4 super-Yang-Mills theory in the multi-Regge limit that is sensitive to the non-trivial (“long”) Regge cut. We provide the amplitudes through four loops and to all logarithmic accuracy at leading power, in terms of single-valued multiple polylogarithms of two variables. To obtain these results, we leverage the function-level results for the amplitudes in the Steinmann cluster bootstrap. To high powers in the series expansion in the two variables, our results agree with the recently conjectured all-order central emission vertex used in the Fourier-Mellin representation of amplitudes in multi-Regge kinematics. Our results therefore provide a resummation of the Fourier-Mellin residues into single-valued polylogarithms, and constitute an important cross-check between the bootstrap approach and the all-orders multi-Regge proposal.

1/N expansion↗

DOE OSTI2022

A coupling approach for linear elasticity problems with spatially non-coincident discretized interfaces

Here we present a new method for coupled linear elasticity problems whose finite element discretization may lead to spatially non-coincident discretized interfaces. Our approach combines the classical Dirichlet–Neumann coupling formulation with a new set of discretized interface conditions obtained through Taylor series expansions. We show that these conditions ensure linear consistency of the coupled finite element solution. We then formulate an iterative solution method for the coupled discrete system and apply the new coupling approach to two representative settings for which we also provide several numerical illustrations. The first setting is a mesh-tying problem in which both coupled structures have the same Lamé parameters whereas the second setting is an interface problem for which the Lamé parameters in the two coupled structures are different.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

An energy-stable time-integrator for phase-field models

Here, we introduce a provably energy-stable time-integration method for general classes of phase-field models with polynomial potentials. We demonstrate how Taylor series expansions of the nonlinear terms present in the partial differential equations of these models can lead to expressions that guarantee energy-stability implicitly, which are second-order accurate in time. The spatial discretization relies on a mixed finite element formulation and isogeometric analysis. We also propose an adaptive time-stepping discretization that relies on a first-order backward approximation to give an error-estimator. This error estimator is accurate, robust, and does not require the computation of extra solutions to estimate the error. This methodology can be applied to any second-order accurate time-integration scheme. We present numerical examples in two and three spatial dimensions, which confirm the stability and robustness of the method. The implementation of the numerical schemes is done in PetIGA, a high-performance isogeometric analysis framework.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Calculating elements of matrix functions using divided differences

In this work, we introduce a method for calculating individual elements of matrix functions. Our technique makes use of a novel series expansion for the action of matrix functions on basis vectors that is memory efficient even for very large matrices. We showcase our approach by calculating the matrix elements of the exponential of a transverse-field Ising model and evaluating quantum transition amplitudes for large many-body Hamiltonians of sizes up to 2 64 x 2 64 on a single workstation. We also discuss the application of the method to matrix inverses. We relate and compare our method to the state-of-the-art and demonstrate its advantages. We also discuss practical applications of our method.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Discretizing singular point sources in hyperbolic wave propagation problems

Here, we develop high order accurate source discretizations for hyperbolic wave propagation problems in first order formulation that are discretized by finite difference schemes. By studying the Fourier series expansions of the source discretization and the finite difference operator, we derive sufficient conditions for achieving design accuracy in the numerical solution. Only half of the conditions in Fourier space can be satisfied through moment conditions on the source discretization, and we develop smoothness conditions for satisfying the remaining accuracy conditions. The resulting source discretization has compact support in physical space, and is spread over as many grid points as the number of moment and smoothness conditions. In numerical experiments we demonstrate high order of accuracy in the numerical solution of the 1-D advection equation (both in the interior and near a boundary), the 3-D elastic wave equation, and the 3-D linearized Euler equations.

58 GEOSCIENCES↗

DOE OSTI2019

Conservative explicit local time-stepping schemes for the shallow water equations

Here we develop explicit local time-stepping (LTS) schemes with second and third order accuracy for the shallow water equations. The system is discretized in space by a C-grid staggering method, namely the TRiSK scheme adopted in MPAS-Ocean, a global ocean model with the capability of resolving multiple resolutions within a single simulation. The time integration is designed based on the strong stability preserving Runge–Kutta (SSP-RK) methods, but different time step sizes can be used in different regions of the domain through the coupling of coarse-fine time discretizations on the interface, and are only restricted by respective local CFL conditions. The proposed LTS schemes are of predictor–corrector type in which the predictors are constructed based on Taylor series expansions and SSP-RK stepping algorithms. The schemes preserve some important physical quantities in the discrete sense, such as exact conservation of the mass and potential vorticity and conservation of the total energy within time truncation errors. Moreover, they inherit the natural parallelism of the original explicit global time-stepping schemes. Extensive numerical tests are presented to illustrate the performance of the proposed algorithms.

58 GEOSCIENCES↗

DOE OSTI2022

Modeling multiple scattering transient of an ultrashort laser pulse by spherical particles

The multiple scattering of an ultrashort laser pulse by a turbid dispersive medium (namely a cloud of bubbles in water) is investigated by means of Monte Carlo simulations. The theory of Gouesbet and Gréhan (2000) is used to derive an energetic model of the scattering transient. It is shown that the spreading and extinction of the pulse can be decoupled from the transient of scattering, which allows to describe each phenomenon individually. The transient of scattering is modeled with the Lorenz-Mie Theory and thus is also valid for a relative refractive index lower than one, contrary to the Debye series expansion which does not converge close to the critical angle. This is made possible after the introduction of a new physical object, the Scattering Impulse Response Function (SIRF) which allows to detect the different modes of scattering transient, in time and direction. Here the present approach is more generic, as it enables to simulate clouds of air bubbles in water, which was not possible previously. Two different approaches are proposed within the Monte Carlo framework. The first is a pure Monte Carlo approach where the delay due to the scattering is randomly drawn at each event, while the second is based on the transport of the whole scattering signal. They are both embedded in the Monte Carlo code Scatter3D. Both models produce equivalent trends and are validated against published numerical results. They are then applied to the multiple scattering of ultra short pulse by a cloud of bubble in water in the forward direction. The pulse spread due to the propagation in water is computed for a wide range of traveled distances and pulse durations, and the optimal pulse duration is given to minimize the pulse spread at a given distance. The main result is that the scattered photons exit the turbid medium earlier than the ballistic photons and produce a double peak related to the refraction in the bubble. This demonstrates the possibility to develop new diagnostics to characterize dynamic bubbly flows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

A high order Cartesian grid, finite volume method for elliptic interface problems

We present a higher-order finite volume method for solving elliptic PDEs with jump conditions on interfaces embedded in a 2D Cartesian grid. Second, fourth, and sixth order accuracy is demonstrated on a variety of tests including problems with high-contrast and spatially varying coefficients, large discontinuities in the source term, and complex interface geometries. We include a generalized truncation error analysis based on cell-centered Taylor series expansions, which then define stencils in terms of local discrete solution data and geometric information. In the process, we develop a simple method based on Green's theorem for computing exact geometric moments directly from an implicit function definition of the embedded interface. This approach produces stencils with a simple bilinear representation, where spatially-varying coefficients and jump conditions can be easily included and finite volume conservation can be enforced.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Universality driven analytic structure of QCD crossover: radius of convergence and QCD critical point

Recent lattice QCD calculations show strong indications that the crossover of QCD at zero baryon chemical potential (µB) is a remnant of the second order chiral phase transition. The non-universal parameters needed to map temperature T and µ B to the universal properties of the second order chiral phase transition were determined by lattice QCD calculations. Motivated by these advances, first, we discuss the analytic structure of the partition function - the so-called Yang-Lee edge singularity - in the QCD crossover regime, solely based on universal properties. Then, utilizing the lattice calculated non-universal parameters, we map this singularity to the real T and complex µ B plane, in order to find the radius of convergence for a Taylor series expansion of QCD partition function around µ B = 0 in the QCD crossover regime. Our most important findings are: (i) An universality-based estimate of the radius of convergence around µ B = 0; (ii) Universality and lattice QCD based constraints on the location of the QCD critical point in the T - µ B plane.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Factorization for jet production in heavy-ion collisions

We develop an Effective Field Theory approach for jet observables in heavy-ion collisions, where the jet is treated as an open quantum system interacting with a hot and dense QCD medium. Within this framework, we derive a novel factorization formula for inclusive jet production, expressed as a series expansion with an increasing number of radiating subjet functions that encode forward scattering with the Quark-Gluon Plasma, convolved with perturbative matching coefficients. This work provides a systematic framework for computing jet observables at higher order and understanding their non-perturbative aspects, paving the way for future applications in heavy-ion phenomenology.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Imaging Polarity in Two Dimensional Materials by Breaking Friedel's Law

Friedel's law guarantees an inversion-symmetric diffraction pattern for thin, light materials where a kinematic approximation or a single-scattering model holds. Typically, breaking Friedel symmetry is ascribed to multiple scattering events within thick, non-centrosymmetric crystals. However, two-dimensional (2D) materials such as a single monolayer of MoS 2 can also violate Friedel's law, with unexpected contrast between conjugate Bragg peaks. Here, we show analytically that retaining higher order terms in the power series expansion of the scattered wavefunction can describe the anomalous contrast between hkl and $\bar{hkl}$ peaks that occurs in 2D crystals with broken in-plane inversion symmetry. These higher-order terms describe multiple scattering paths starting from the same atom in an atomically thin material. Furthermore, 2D materials containing heavy elements, such as WS 2 , always act as strong phase objects, violating Friedel's law no matter how high the energy of the incident electron beam. Experimentally, this understanding can enhance diffraction-based techniques to provide rapid imaging of polarity, twin domains, in-plane rotations, or other polar textures in 2D materials.

2D materials↗

DOE OSTI2021

A vortex sheet based analytical model of the curled wake behind yawed wind turbines

Motivated by the need for compact descriptions of the evolution of non-classical wakes behind yawed wind turbines, we develop an analytical model to predict the shape of curled wakes. Interest in such modelling arises due to the potential of wake steering as a strategy for mitigating power reduction and unsteady loading of downstream turbines in wind farms. We first estimate the distribution of the shed vorticity at the wake edge due to both yaw offset and rotating blades. By considering the wake edge as an ideally thin vortex sheet, we describe its evolution in time moving with the flow. Vortex sheet equations are solved using a power series expansion method, and an approximate solution for the wake shape is obtained. The vortex sheet time evolution is then mapped into a spatial evolution by using a convection velocity. Apart from the wake shape, the lateral deflection of the wake including ground effects is modelled. Our results show that there exists a universal solution for the shape of curled wakes if suitable dimensionless variables are employed. For the case of turbulent boundary layer inflow, the decay of vortex sheet circulation due to turbulent diffusion is included. Finally, we modify the Gaussian wake model by incorporating the predicted shape and deflection of the curled wake, so that we can calculate the wake profiles behind yawed turbines. Model predictions are validated against large-eddy simulations and laboratory experiments for turbines with various operating conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

The DESC stellarator code suite. Part 2. Perturbation and continuation methods

A new perturbation and continuation method is presented for computing and analysing stellarator equilibria. The method is formally derived from a series expansion about the equilibrium condition $\boldsymbol {F} \equiv \boldsymbol {J}\times \boldsymbol {B} - \boldsymbol {\nabla } p = 0$ , and an efficient algorithm for computing solutions to second- and third-order perturbations is developed. The method has been implemented in the DESC stellarator equilibrium code, using automatic differentiation to compute the required derivatives. Examples are shown demonstrating its use for computing complicated equilibria, perturbing a tokamak into a stellarator and performing parameter scans in pressure, rotational transform and boundary shape in a fraction of the time required for a full solution.

Conlin, Rory (ORCID:0000000183662111)↗

DOE OSTI2021

Connection Between Mass Flux Transport and Eddy Diffusivity in Convective Atmospheric Boundary Layers

Turbulence parameterizations for convective boundary layer in coarse-scale atmospheric models usually consider a combination of the eddy-diffusive transport and a non-local transport, typically in the form of a mass flux term, such as the widely adopted eddy-diffusivity mass-flux (EDMF) approach. These two types of turbulent transport are generally considered to be independent of each other. Using results from large-eddy simulations, here, we show that a Taylor series expansion of the updraft and downdraft mass-flux transport can be used to approximate the eddy-diffusivity transport in the atmospheric surface layer and the lower part of the mixed layer, connecting both eddy-diffusivity and mass-flux transport theories in convective conditions, which also quantifies departure from the Monin-Obukhov similarity (MOS) in the surface layer. This study provides a theoretical support for a unified EDMF parameterization applied to both the surface layer and mixed layer and highlights important correction required for surface models relying on MOS

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Multiscale Temporal Variability of the Global Air‐Sea CO 2 Flux Anomaly

Abstract The global air‐sea CO 2 flux (F) impacts and is impacted by a plethora of climate‐related processes operating at multiple time scales. In bulk mass transfer formulations, F is driven by physico‐ and bio‐chemical factors such as the air‐sea partial pressure difference (∆pCO 2 ), gas transfer velocity, sea surface temperature, and salinity–all varying at multiple time scales. To de‐convolve the impact of these factors on variability in F at different time scales, time‐resolved estimates of F were computed using a global data set assembled between 1988 and 2015. The F anomalies were defined as temporal deviations from the 28‐year time‐averaged value. Spectral analysis revealed four dominant timescales of variability in F–subseasonal, seasonal, interannual, and decadal with relative amplitude differences varying across regions. A second‐order Taylor series expansion was then conducted along these four timescales to separate drivers across differing regions. The analysis showed that on subseasonal timescales, wind speed variability explains some 66% of the global F anomaly and is the dominant driver. On seasonal, interannual, and decadal timescales, the ∆pCO 2 effect controlled by the ∆pCO 2 anomaly, explained much of the F anomaly. On decadal timescales, the F anomaly was almost entirely governed by the ∆pCO 2 effect with large contributions from high latitudes. The main drivers across timescales also dominate the regional F anomaly, particularly in the mid‐high latitude regions. Finally, the driver of the ∆pCO 2 effect was closely connected with the relative strength of atmospheric pCO 2 and the nonthermal component of oceanic pCO 2 anomaly associated with dissolved inorganic carbon and alkalinity.

Environmental Sciences & Ecology↗

DOE OSTI2023

A Gradient Based Subgrid-Scale Parameterization for Ocean Mesoscale Eddies

Mesoscale eddies play an important role in transport of heat and biogeochemical tracers in the global ocean circulation. Resolving these energetic eddies, however, is challenging in ocean general circulation models (OGCM) because it requires a horizontal grid spacing of ≲1/8° that is computationally expensive. As a result, we are required to parameterize mesoscale eddy effects on large-scale ocean flows. In this work, we introduce a new subgrid-scale (SGS) model that is developed based on a Taylor series expansion of resolved variables to parameterize subgrid mesoscale eddy transports and momentum fluxes in OGCM. We have performed an a priori study to evaluate the performance of our new gradient model using high-resolution ocean simulations. Our results show that the gradient model well predicts the actual SGS thickness fluxes in the zonal and meridional directions in coarse-resolution simulations with the grid spacing ≳1/4°. The unresolved kinetic energy at the ocean surface is also skillfully estimated. More importantly, unlike current mesoscale eddy parameterizations, which are mainly developed based on an assumption of flat bottom ocean, our new SGS model can capture the structure of unresolved standing meanders at the ocean surface. We have also developed a dynamic procedure for setting in non-dimensional parameters in our new parameterization through a non-ad hoc and tuning-free method. Overall, this work suggests that implementing the gradient model in OGCM can improve the model accuracy with an affordable computational cost in eddy-permitting and non-eddying simulations.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2012

The dispersion interaction between quantum mechanics and effective fragment potential molecules

A method for calculating the dispersion energy between molecules modeled with the general effective fragment potential (EFP2) method and those modeled using a full quantum mechanics (QM) method, e.g., Hartree-Fock (HF) or second-order perturbation theory, is presented. C6 dispersion coefficients are calculated for pairs of orbitals using dynamic polarizabilities from the EFP2 portion, and dipole integrals and orbital energies from the QM portion of the system. Dividing by the sixth power of the distance between localized molecular orbital centroids yields the first term in the commonly employed London series expansion. A C8 term is estimated from the C6 term to achieve closer agreement with symmetry adapted perturbation theory values. Two damping functions for the dispersion energy are evaluated. By using terms that are already computed during an ordinary HF or EFP2 calculation, the new method enables accurate and extremely rapid evaluation of the dispersion interaction between EFP2 and QM molecules.

36 MATERIALS SCIENCE↗

DOE OSTI2013

Ab initio potential energy surface for the highly nonlinear dynamics of the KCN molecule

An accurate ab initio quantum chemistry study at level of quadratic configuration interaction method of the electronic ground state of the KCN molecule is presented. A fitting of the results to an analytical series expansion was performed to obtain a global potential energy surface suitable for the study of the associated vibrational dynamics. Additionally, classical Poincaré surfaces of section for different energies and quantum eigenstates were calculated, showing the highly nonlinear behavior of this system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗