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At least 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Analytical Approximations for Beamstrahlung at Very High Energy Electron-Positron Colliders

Among the many effects that occur in beam-beam electron-positron collisions at TeV energies, emission of hard synchrotron radiation, or beamstrahlung, has special importance. Beamstrahlung determines the energy spectrum of the most energetic electrons, positrons, and photons and supplies the initial condition for the calculation of all other QED processes. In this paper, we show that the description of beamstrahlung simplifies in the limit of large quantum parameter $Υ$, which is realized in 10 TeV collider designs. The beamstrahlung spectra for electrons and photons are given in terms of universal functions. We supply approximations to these functions that will be useful for more general studies of the beam-beam interaction at very high energies.

Accelerator Physics (physics.acc-ph)↗
DOE OSTI2020

Thermal hybrid exchange-correlation density functional for improving the description of warm dense matter

Finite-temperature density functional theory (FT-DFT) has become a standard tool for first principles calculations of the properties of warm dense matter (WDM) relevant to high-energy density physics (HEDP) applications. In this work we introduce theoretical grounds of thermal hybrid exchange-correlation (XC) functionals within the generalized Mermin-Kohn-Sham scheme for an improved description of WDM. Building on the previously developed KSDT (Karasiev-Sjostrom-Dufty-Trickey) [Karasiev et al., Phys. Rev. Lett. 112, 076403 (2014)] local density approximation (LDA) and the KDT16 (Karasiev-Dufty-Trickey 2016) [Karasiev et al., Phys. Rev. Lett. 120, 076402 (2018)] generalized-gradient approximation (GGA) XC free-energy density functionals, we construct a new thermal hybrid XC functional, referred to here as KDT0. The KDT0 model at low temperature reduces to the popular ground-state PBE0 hybrid due to properties of the used KDT16 density functional approximation. Application to static calculations of electronic band gap and band structure at a wide range of temperatures for various systems of interest to HEDP show that KDT0 provides a significant improvement to the lower LDA and GGA rung XC functionals and to the ground-state PBE0 hybrid.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Ab initio electronic structure of quasi-two-dimensional materials: A “native” Gaussian–plane wave approach

Ab initio electronic structure calculations of two-dimensional layered structures are typically performed using codes that were developed for three-dimensional structures, which are periodic in all three directions. The introduction of a periodicity in the third direction (perpendicular to the layer) is completely artificial and may lead in some cases to spurious results and to difficulties in treating the action of external fields. In this paper we develop a new approach, which is “native” to quasi-2D materials, making use of basis function that are periodic in the plane, but atomic-like in the perpendicular direction. We show how some of the basic tools of ab initio electronic structure theory — density functional theory, GW approximation and Bethe-Salpeter equation — are implemented in the new basis. We argue that the new approach will be preferable to the conventional one in treating the peculiarities of layered materials, including the long range of the unscreened Coulomb interaction in insulators, and the effects of strain, corrugations, and external fields.

Trevisanutto, Paolo E.↗
DOE OSTI2018

Study of the Electronic Structure, Magnetic and Elastic Properties and Half-Metallic Stability on Variation of Lattice Constants for CoFeCrZ (Z = P, As, Sb) Heusler Alloys

Structural, elastic, magnetic and electronic properties of CoFeCrZ (Z = P, As, Sb) Heusler alloys in their YI-type structure have been computed by density functional theory-based WIEN2k code within generalized gradient approximation for exchange correlation functions. Values of formation energy and elastic constants verify the stability of these alloys. True half metallic ferromagnetic behaviour with 100% spin polarization and good band gap in the minority spin are obtained for all the alloys. Magnetic moment of these alloys is 4.00 μ{sub B}, which matches well with the value predicted from Slater-Pauling rule. Half-metallicity is maintained over a wide range of lattice constants making these alloys promising for spintronics device applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

THE MIRA–TITAN UNIVERSE: PRECISION PREDICTIONS FOR DARK ENERGY SURVEYS

Large-scale simulations of cosmic structure formation play an important role in interpreting cosmological observations at high precision. The simulations must cover a parameter range beyond the standard six cosmological parameters and need to be run at high mass and force resolution. A key simulation-based task is the generation of accurate theoretical predictions for observables using a finite number of simulation runs, via the method of emulation. Using a new sampling technique, we explore an eight-dimensional parameter space including massive neutrinos and a variable equation of state of dark energy. We construct trial emulators using two surrogate models (the linear power spectrum and an approximate halo mass function). The new sampling method allows us to build precision emulators from just 26 cosmological models and to systematically increase the emulator accuracy by adding new sets of simulations in a prescribed way. Emulator fidelity can now be continuously improved as new observational data sets become available and higher accuracy is required. Finally, using one ΛCDM cosmology as an example, we study the demands imposed on a simulation campaign to achieve the required statistics and accuracy when building emulators for investigations of dark energy.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Introducing the embedded random phase approximation: H 2 dissociative adsorption on Cu(111) as an exemplar

The random phase approximation (RPA) as a means of treating electron correlation recently has been shown to outperform standard density functional theory (DFT) approximations in a variety of cases. However, the computational cost of the RPA is substantially more than DFT, especially when aiming to study extended surfaces. Properly accounting for sufficient surface ensemble size, Brillouin zone sampling, and vacuum separation of periodic images in standard periodic-planewave-based DFT code raises the cost to achieve converged results. Here, we show that sub-system embedding schemes enable use of the RPA for modeling heterogeneous reactions at reduced computational cost. Further, we explore two different embedded RPA (emb-RPA) approaches, periodic emb-RPA and cluster emb-RPA. We use the (experimentally and theoretically) well-studied H 2 dissociative adsorption on Cu(111) as our exemplar, and first perform full periodic RPA calculations as a benchmark. The full RPA results match well the semi-empirical barrier fit to experimental observables and others derived from high-level computations, e.g., from recent embedded n-electron valence second order perturbation theory [Zhao et al., J. Chem. Theory Comput. 16(11), 7078–7088 (2020)] and quantum Monte Carlo [Doblhoff-Dier et al., J. Chem. Theory Comput. 13(7), 3208–3219 (2017)] simulations. Among the two emb-RPA approaches tested, the cluster emb-RPA accurately reproduces the energy profile (maximum error of 50 meV along the reaction pathway) while reducing the computational cost by approximately two orders of magnitude. We therefore expect that the embedded cluster approach will enable wider RPA implementation in heterogeneous catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Statistics of Green's functions on a disordered Cayley tree and the validity of forward scattering approximation

The accuracy of the forward scattering approximation for two-point Green's functions of the Anderson localization model on the Cayley tree is studied. A relationship between the moments of the Green's function and the largest eigenvalue of the linearized transfer-matrix equation is proved in the framework of the supersymmetric functional-integral method. The new large-disorder approximation for this eigenvalue is derived and its accuracy is established. Using this approximation the probability distribution of the two-point Green's function is found and compared with that in the forward scattering approximation (FSA). It is shown that FSA overestimates the role of resonances and thus the probability for the Green's function to be significantly larger than its typical value. The error of FSA increases with increasing the distance between points in a two-point Green's function.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Spectral-partitioned Kohn-Sham density functional theory

Here we introduce a general, variational scheme for systematic approximation of a given Kohn-Sham free-energy functional by partitioning the density matrix into distinct spectral domains, each of which may be spanned by an independent diagonal representation without requirement of mutual orthogonality. It is shown that by generalizing the entropic contribution to the free energy to allow for independent representations in each spectral domain, the free energy becomes an upper bound to the exact (unpartitioned) Kohn-Sham free energy, attaining this limit as the representations approach Kohn-Sham eigenfunctions. A numerical procedure is devised for calculation of the generalized entropy associated with spectral partitioning of the density matrix. The result is a powerful framework for Kohn-Sham calculations of systems whose occupied subspaces span multiple energy regimes. As a case in point, we apply the proposed framework to warm- and hot-dense matter described by finite-temperature density functional theory, where at high energies the density matrix is represented by that of the free-electron gas, while at low energies it is variationally optimized. We derive expressions for the spectral-partitioned Kohn-Sham Hamiltonian, atomic forces, and macroscopic stresses within the projector-augmented wave (PAW) and the norm-conserving pseudopotential methods. It is demonstrated that at high temperatures, spectral partitioning facilitates accurate calculations at dramatically reduced computational cost. Moreover, as temperature is increased, fewer exact Kohn-Sham states are required for a given accuracy, leading to further reductions in computational cost. Finally, it is shown that standard multiprojector expansions of electronic orbitals within atomic spheres in the PAW method lack sufficient completeness at high temperatures. Spectral partitioning provides a systematic solution for this fundamental problem.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Can Convolution and Deconvolution Be Used as Tools for Modeling Multicomponent, Mixing-Limited Reaction Networks?

Transfer functions (i.e., convolutions) have been powerful tools for both forward modeling and reconstructing past states of transport systems in a wide range of subsurface flow problems. The advantage of the transfer function is that it is a simple alternative to complicated, distributed parameter models of flow and transport, but the majority of applications of transfer functions in hydrology have been limited to relatively simple cases, like passive tracers or first-order decay. The central question evaluated in this note is whether or not multicomponent mixing-limited reactive transport can be represented within a transfer function framework. Our examples consider forward-in-time predictions and backward-in-time reconstructions of a carbonate system that represents the intrusion of seawater into a freshwater aquifer. The main result is that accurate forward-in-time and backward-in-time models are developed by posing the problem in terms of conservative components. As with all convolution-based methods, the results are sensitive to errors and/or noise in the input functions, but we show that smoothed approximations of the requisite functions provide good representations of transport. Given the vast unknowns in any subsurface transport problem, such generalized, reactive transfer function models may have yet unexplored advantages when the trade-offs between overall computational cost, accuracy, and uncertainty are explored in more detail.

42 ENGINEERING↗
DOE OSTI2018

Efficient manifolds tracing for planar maps

Here, we present an exact calculation method and an approximation technique for tracing the invariant manifolds of unstable periodic orbits of planar maps. The exact approach relies on an adaptive refinement procedure that prevents redundant calculations occurring in other approaches, and the approximated method relies on a novel interpolation approach based on normal displacement functions. The resulting approximated manifold is precise when compared to the exact one, and its relative computational cost falls like the inverse of the manifold length. To present the tracing method, we obtain the invariant manifolds of the Chirikov-Taylor map, and as an application we illustrate the transition from homoclinic to heteroclinic chaos in the Duffing oscillator that leads from localized chaos to global chaotic motion.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2026

Second-order wave excitation forces in WEC-Sim/MOST: Implementation, experimental validation, and code-to-code comparison

Accurate prediction of second-order hydrodynamic loads is essential for floating bodies, including floating offshore wind turbines, wave energy converters, and hybrid wind–wave platforms. These nonlinear effects, arising from both sum- and difference-frequency forcing, are critical for capturing key response characteristics but remain challenging to model efficiently. In this work, we extend the open-source Wave Energy Converter Simulator / MATLAB for Offshore Simulation Tool by implementing second-order wave excitation forces, supporting both the full Quadratic Transfer Function formulation and the Newman approximation. The full Quadratic Transfer Function method is used for all code-to-code comparisons and experimental validation, while the Newman approximation is provided as a computationally lighter alternative. To benchmark the new capability, we perform a code-to-code comparison with OpenFAST and OrcaFlex. We then validate the enhanced model using wave-tank measurements of a 1:96 scale DeepCwind semi-submersible, showing that second-order effects are required to reproduce platform motions. The implementation employs a computationally efficient pre-computation strategy for second-order wave excitation forces, reducing simulation cost while maintaining engineering accuracy. Overall, this work advances the tool as an open-source and versatile tool for modelling floating offshore renewable-energy systems requiring second-order hydrodynamic fidelity.

17 WIND ENERGY↗
DOE OSTI2020

Adaptive Activation Functions Accelerate Convergence in Deep and Physics-informed Neural Networks

We employ adaptive activation functions for regression in deep and physics-informed neural networks (PINNs) to approximate smooth and discontinuous functions as well as solutions of linear and nonlinear partial differential equations. In particular, we solve the nonlinear Klein-Gordon equation, which has smooth solutions, the nonlinear Burgers equation, which can admit high gradient solutions, and the Helmholtz equation. We introduce a scalable hyper-parameter in the activation function, which can be optimized to achieve best performance of the network as it changes dynamically the topology of the loss function involved in the optimization process. The adaptive activation function has better learning capabilities than the traditional one (fixed activation) as it improves greatly the convergence rate, especially at early training, as well as the solution accuracy. To better understand the learning process, we plot the neural network solution in the frequency domain to examine how the network captures successively different frequency bands present in the solution. We consider both forward problems, where the approximate solutions are obtained, as well as inverse problems, where parameters involved in the governing equation are identified. Our simulation results show that the proposed method is a very simple and effective approach to increase the efficiency, robustness and accuracy of the neural network approximation of nonlinear functions as well as solutions of partial differential equations, especially for forward problems. We theoretically prove that in the proposed method, gradient descent algorithms are not attracted to suboptimal critical points or local minima.

machine leaning, Bad minima, Inverse problems, Phy↗
DOE OSTI2017

Measurement of forward-backward multiplicity correlations in lead-lead, proton-lead, and proton-proton collisions with the ATLAS detector

Two-particle pseudorapidity correlations are measured in √ s NN = 2.76TeV Pb + Pb, √ s NN = 5.02TeV p + Pb, and √s = 13 TeV pp collisions at the Large Hadron Collider (LHC), with total integrated luminosities of approximately 7μb –1 , 28 nb –1 , and 65 nb –1 , respectively. The correlation function C N (η 1 ,η 2 ) is measured as a function of event multiplicity using charged particles in the pseudorapidity range |η| < 2.4. The correlation function contains a significant short-range component, which is estimated and subtracted. After removal of the short-range component, the shape of the correlation function is described approximately by 1 + < a2 1 > 1/2 η 1 η 2 in all collision systems over the full multiplicity range. The values of < a 2 1 > 1/2 are consistent for the opposite-charge pairs and same-charge pairs, and for the three collision systems at similar multiplicity. The values of < a 2 1 > 1/2 and the magnitude of the short-range component both follow a power-law dependence on the event multiplicity. Here, the short-range component in p + Pb collisions, after symmetrizing the proton and lead directions, is found to be smaller at a given η than in pp collisions with comparable multiplicity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

A Measure Approximation for Distributionally Robust PDE-Constrained Optimization Problems

In numerous applications, scientists and engineers acquire varied forms of data that partially characterize the inputs to an underlying physical system. This data is then used to inform decisions such as controls and designs. Consequently, it is critical that the resulting control or design is robust to the inherent uncertainties associated with the unknown probabilistic characterization of the model inputs. Here in this work, we consider optimal control and design problems constrained by partial differential equations with uncertain inputs. We do not assume a known probabilistic model for the inputs, but rather we formulate the problem as a distributionally robust optimization problem where the outer minimization problem determines the control or design, while the inner maximization problem determines the worst-case probability measure that matches desired characteristics of the data. We analyze the inner maximization problem in the space of measures and introduce a novel measure approximation technique, based on the approximation of continuous functions, to discretize the unknown probability measure. Finally, we prove consistency of our approximated min-max problem and conclude with numerical results.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Smoothness of Functions in Spaces of the Finite Element Method

We find necessary and sufficient conditions for the generalized smoothness of the coordinate functions obtained from the approximate relations. We show that for the coordinate functions the smoothness on their supports is equivalent to that on the boundaries of supports. We obtain conditions for the continuity of Courant type finite element approximations and conditions for the uniqueness of a linear space of such approximations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Homogenizing atomic dynamics by fractional differential equations

In this paper, we propose two ways to construct fractional differential equations (FDE) for approximating atomic chain dynamics. Taking harmonic chain as an example, we add a power function of fractional order to Taylor expansion of the dispersion relation, and determine the parameters by matching two selected wave numbers. This approximate function leads to an FDE after considering both directions for wave propagation. As an alternative, we consider the symbol of the force term, and approximate it by a similar function. It also induces an FDE. Both approaches produce excellent agreement with the harmonic chain dynamics. The accuracy may be improved by optimizing the selected wave numbers, or starting with higher order Taylor expansions. When resolved in the lattice constant, the resulting FDE's faithfully reproduce the lattice dynamics. When resolved in a coarse grid instead, they systematically generate homogenized algorithms. Numerical tests are performed to verify the proposed approaches. Moreover, FDE's are also constructed for diatomic chain and anharmonic lattice, to illustrate the generality of the proposed approaches. - Highlights: • Match the dispersion relation of linear chain by power function of fractional order, added on low order Taylor expansion. • Design FDE by approximating dispersion relation, or the symbol for the force term. • Solve the FDE by algorithm of spectral accuracy. • Obtain faithful and systematical homogenization when resolved at coarser grid. • Applies to general lattices: complex, nonlinear and multidimensional.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Cycloidal Shaping of Polyhedra in Two-Rotor Systems

A method of solution is proposed for the model of the cycloid shaping of polyhedra. The method is based on reducing the equations to algebraic form by polynomial approximation of transcendental functions.

42 ENGINEERING↗