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DOE OSTI2021

On the canonical formulation of gauge field theories and Poincaré transformations

We address the Hamiltonian formulation of classical gauge field theories while putting forward results some of which are not entirely new, though they do not appear to be well known. We refer in particular to the fact that neither the canonical energy momentum vector ( P μ ) nor the gauge invariant energy momentum vector ( P inv μ ) do generate space-time translations of the gauge field by means of the Poisson brackets: In a general gauge, one has to consider the so-called kinematical energy momentum vector and, in a specific gauge (like the radiation gauge in electrodynamics), one has to consider the Dirac brackets rather than the Poisson brackets. Similar arguments apply to rotations and to Lorentz boosts and are of direct relevance to the “nucleon spin crisis” since the spin of the proton involves a contribution which is due to the angular momentum vector of gluons and thereby requires a proper treatment of the latter. We conclude with some comments on the relationships between the different approaches to quantization (canonical quantization based on the classical Hamiltonian formulation, Gupta-Bleuler, path integrals, BRST, covariant canonical approaches).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

A nonhydrostatic formulation for MPAS-Ocean

The Model for Prediction Across Scales-Ocean (MPAS-Ocean) is an open-source, global ocean model and is one component of a family of climate models within the MPAS framework, including atmosphere, sea-ice, and land-ice models. Here, in this work, a new formulation for the ocean model is presented that solves the nonhydrostatic, incompressible Boussinesq equations on an unstructured, staggered, z-level grid. The introduction of this nonhydrostatic capability is necessary for the resolution of internal wave dynamics and large eddy simulations. Compared to the standard, hydrostatic formulation, a nonhydrostatic pressure solver and a vertical momentum equation are added, where the PETSc (Portable Extensible Toolkit for Scientific Computation) library is used for the inversion of a large sparse system for the nonhydrostatic pressure. Numerical results on a stratified seiche, internal solitary wave, overflow and lock-exchange test cases are presented, and the parallel efficiency of the code is evaluated using up to 1024 processors.

3D Poisson equation↗

DOE OSTI2025

A nonhydrostatic formulation for MPAS-Ocean

3D Poisson equation↗

DOE OSTI2016

An indirect latent informational conformity social influence choice model: Formulation and case study

The current state-of-the-art in social influence models of travel behavior is conformity models with direct benefit social influence effects. Indirect effects have seen limited development, but this paper presents a latent class discrete choice model of an indirect informational conformity hypothesis. Moreover, class membership depends on the proportion of group members who adopt a behavior. Membership into the more informed class causes changes in the preferences of those individuals thus making adoption more attractive. Equilibrium properties are derived for this model showing the possibility of multiple equilibria but under different conditions than the direct-benefit formulations. Social influence elasticity is derived for both models types. The informational conformity model can represent non-linear elasticity behavior unlike the direct-benefit formulation. Additionally, a two-stage control function is developed to obtain consistent parameter estimates in the presence of an endogenous class membership model covariate that is correlated with choice model unobservables. A case study to study social influence in bicycle ownership in the United States is presented. Our results showed that more informed households had a greater chance of owning a bike due to preference changes with less sensitivity to smaller home footprints and limited incomes. The behavioral hypothesis of positive preference change due to information transfer was confirmed. Observed ownership share closely matched predicted local-level equilibrium in some metropolitan areas but was unable to achieve expected prediction rate within confidence intervals. Finally, the elasticity of social influence was found to range locally from about 0.5% to 1.0%.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2020

Formulation and solution approach for calibrating activity-based travel demand model-system via microsimulation

This study addresses the problem of calibrating utility-maximizing nested logit activity-based travel demand model-systems. After estimation, it is common practice to use aggregate measurements to calibrate the estimated model-system’s parameters prior to their application in transportation planning, policy making, and operations. However, calibration of activity-based model-systems has received much less attention. Existing calibration approaches are myopic heuristics in the sense that they do not consider the fundamental inter-dependencies among choice-models and do not have a systematic way to adjust model parameters. Also, other purely simulation-based approaches do not perform well in large-scale applications. In this study, we focus on utility-maximizing nested logit activity-based model-systems and calibrating aggregate statistics such as activity shares, mode shares, time-dependent & mode-specific OD flows, and time-dependent & mode-specific sensor counts. We formulate the calibration problem as a simulation-based optimization problem and propose a stochastic gradient-based solution procedure to solve it. The solution procedure relies on microsimulation to calculate expectations of the aggregate statistics of interest to the calibration problem. Additionally, we derive approximate analytical expressions for the gradient of the objective function —that are evaluated through microsimulation on mini-batches of the population. The proposed solution procedure is sensitive to the fundamental structure of the activity-based model-system and is non-myopic in considering the dependencies across its model components. The formulated optimization problem is non-convex, highly nonlinear, and potentially has multiple-minima. Lastly, we show —through a real-world application— that the proposed solution procedure outperforms other state-of-the-art purely simulation-based optimization approaches in terms of computational efficiency, stability, and convergence. We also compare various gradient-based solution algorithms to determine the best algorithm to update the parameters. This work has the potential to facilitate wider and easier application of activity-based model-systems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Differential formulation of the gyrokinetic Landau operator

Subsequent to the recent rigorous derivation of an energetically consistent gyrokinetic collision operator in the so-called Landau representation, this work investigates the possibility of finding a differential formulation of the gyrokinetic Landau collision operator. It is observed that, while a differential formulation is possible in the gyrokinetic phase space, reduction of the resulting system of partial differential equations to five dimensions via gyroaveraging poses a challenge. Finally, based on the present work, it is likely that the gyrocentre analogues of the Rosenbluth–MacDonald–Judd potential functions must be kept gyroangle dependent.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Mixed-Integer Linear Programming Formulation with Embedded Machine Learning Surrogates for the Design of Chemical Process Families

In previous work, we introduced process family design. The main idea is to design a platform of common elements, and, allowing us to capture additional cost savings, simultaneously design a family of processes, and reducing both engineering and deployment timelines. We formulate this as an optimization problem, specifically a nonlinear generalized disjunctive program (GDP). We have proposed two approaches for reformulating and solving this problem: one based on full-discretization of the design space and one that uses Machine Learning (ML) surrogates to replace the nonlinear process models. Using ML surrogates to predict required system costs and performance indicators allows us to reformulate the nonlinearities in the GDP generate an efficient MILP formulation. In this work, we apply the ML surrogate approach to two case studies. One case study involves designing a family of carbon capture systems to cover a set of different flue gas flow rates and inlet CO 2 concentrations, where we consider the absorber and stripper as common unit module types. The second case study focuses on a water-desalination process, where we design a family of these processes for a variety of salt concentrations and flow rates. In both of these case studies, we demonstrate a scalable optimization approach that enables the design of multiple processes simultaneously, reducing the time-to-market and overall costs by maximizing the cost savings due to both economies of scale and economies of numbers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Multifidelity Neural Network Formulations for Prediction of Reactive Molecular Potential Energy Surfaces

Here, this paper focuses on the development of multifidelity modeling approaches using neural network surrogates, where training data arising from multiple model forms and resolutions are integrated to predict high-fidelity response quantities of interest at lower cost. We focus on the context of quantum chemistry and the integration of information from multiple levels of theory. Important foundations include the use of symmetry function-based atomic energy vector constructions as feature vectors for representing structures across families of molecules and single-fidelity neural network training capabilities that learn the relationships needed to map feature vectors to potential energy predictions. These foundations are embedded within several multifidelity topologies that decompose the high-fidelity mapping into model-based components, including sequential formulations that admit a general nonlinear mapping across fidelities and discrepancy-based formulations that presume an additive decomposition. Methodologies are first explored and demonstrated on a pair of simple analytical test problems and then deployed for potential energy prediction for C 5 H 5 using B2PLYP-D3/6-311++G(d,p) for high-fidelity simulation data and Hartree–Fock 6-31G for low-fidelity data. For the common case of limited access to high-fidelity data, our computational results demonstrate that multifidelity neural network potential energy surface constructions achieve roughly an order of magnitude improvement, either in terms of test error reduction for equivalent total simulation cost or reduction in total cost for equivalent error.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Quadratic Unitary Coupled-Cluster Singles and Doubles Scheme: Efficient Implementation, Benchmark Study, and Formulation of an Extended Version

An efficient implementation of the quadratic unitary coupled-cluster singles and doubles (qUCCSD) scheme for calculations of electronic ground and excited states using an unrestricted molecular spin–orbital formulation and an efficient tensor contraction library is reported. The accuracy of the qUCCSD scheme and the efficiency of the present implementation are demonstrated using extensive benchmark calculations of excitation energies and an application to S o → S 1 vertical excitation energies for cis- and trans-4a,4b-dihydrotriphenylene. The qUCCSD scheme has been shown to provide improved excitation energies compared with the UCC3 scheme formulated based on perturbation theory. Here, a UCC truncation scheme that can provide excitation energies correct through the fourth order is also presented to further improve the accuracy of the qUCCSD scheme.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Simple Flux-Side Formulation of State-Resolved Thermal Reaction Rates for Ring-Polymer Surface Hopping

Employing the recently developed isomorphic Hamiltonian framework for including nuclear quantum effects in mixed quantum–classical nonadiabatic dynamics, we present a flux-side formulation of state-resolved thermal reaction rates for ring-polymer surface hopping (iso-RPSH). An appealing aspect of the new approach is that calculation of multiple state-resolved nonadiabatic thermal reaction rates is enabled with only a single free-energy surface calculation, whereas previous nonadiabatic flux-side formulations for surface hopping involve multiple free-energy surface calculations. In conclusion, the method is shown to be robust and straightforwardly implemented, and numerical results reveal that RPSH in the isomorphic Hamiltonian framework leads to better dividing surface independence than alternative RPSH methods due to improved preservation of the path-integral statistics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

A Formulation of the Many-Body Expansion (MBE) for Periodic Systems: Application to Several Ice Phases

A new formulation of the many-body expansion (MBE) for periodic systems, based on their inherent translational symmetry, is introduced and applied to 7 ice polymorphs. This new formulation is built via a hierarchical procedure connecting gas phase unit cells over finite supercells to infinite solids. For finite supercells, it is demonstrated that this method successfully recovers the energetics while reducing the scaling of the calculation of the many-body terms by a factor of ~N, where N is the system size. Furthermore, the proposed framework delineates a straightforward way to obtain properties of macroscopic systems in the limit of an infinite cell. For periodic systems, the success of this approach is demonstrated by showing that the lattice energies computed (up to the 4-th order in the MBE) reproduce the lattice energies obtained using periodic boundary conditions with an Ewald summation for 7 polymorphs of ice (Ih, II, VIII, IX, XIII, XIV, XV). This development makes it possible to quantify, for the first time, the many-body contributions to the lattice energy of various ice polymorphs. The many-body (three-body and higher) interactions were found to vary significantly among the 7 ice phases, amounting between 7-24% of the total lattice energies. So, this development opens the door for obtaining insights into solid-state properties, while leveraging the computational benefits of the MBE.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Reconciling and Improving Formulations for Thermodynamics and Conservation Principles in Earth System Models (ESMs)

Abstract This paper provides a comprehensive derivation of the total energy equations for the atmospheric components of Earth System Models (ESMs). The assumptions and approximations made in this derivation are motivated and discussed. In particular, it is emphasized that closing the energy budget is conceptually challenging and hard to achieve in practice without resorting to ad hoc fixers. As a concrete example, the energy budget terms are diagnosed in a realistic climate simulation using a global atmosphere model. The largest total energy errors in this example are spurious dynamical core energy dissipation, thermodynamic inconsistencies (e.g., coupling parameterizations with the host model) and missing processes/terms associated with falling precipitation and evaporation (e.g., enthalpy flux between components). The latter two errors are not, in general, reduced by increasing horizontal resolution. They are due to incomplete thermodynamic and dynamic formulations. Future research directions are proposed to reconcile and improve thermodynamics formulations and conservation principles.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2015

Evidence that formulations of the selective MAO-B inhibitor, selegiline, which bypass first-pass metabolism, also inhibit MAO-A in the human brain

Selegiline (L-deprenyl) is a selective, irreversible inhibitor of monoamine oxidase B (MAO-B) at the conventional dose (10 mg/day oral) that is used in the treatment of Parkinson’s disease. However, controlled studies have demonstrated antidepressant activity for high doses of oral selegiline and for transdermal selegiline suggesting that when plasma levels of selegiline are elevated, brain MAO-A might also be inhibited. Zydis selegiline (Zelapar®) is an orally disintegrating formulation of selegiline, which is absorbed through the buccal mucosa producing higher plasma levels of selegiline and reduced amphetamine metabolites compared to equal doses of conventional selegiline. Although there is indirect evidence that Zydis selegiline at high doses loses its selectivity for MAO-B, there is no direct evidence that it also inhibits brain MAO-A in humans. We measured brain MAO-A in 18 healthy men after a 28-day treatment with Zydis selegiline (2.5, 5.0, or 10 mg/day) and in 3 subjects receiving the selegiline transdermal system (Emsam patch, 6 mg/day) using PET and the MAO-A radiotracer [¹¹C]clorgyline. We also measured dopamine transporter (DAT) availability in three subjects from the 10 mg group. The 10 mg Zydis selegiline dose significantly inhibited MAO-A (36.9 ± 19.7%, range 11–70%, p<0.007)) but not DAT; and while Emsam also inhibited MAO-A (33.2 ± 28.9 (range 9-68%) the difference did not reach significance (p=0.10)) presumably because of the small sample size. Our results provide the first direct evidence of brain MAO-A inhibition in humans by formulations of selegiline, which are currently postulated but not verified to target brain MAO-A in addition to MAO-B.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

DOE OSTI2021

Introduction of Chalcogenide Glasses to Additive Manufacturing: Nanoparticle Ink Formulation, Inkjet Printing, and Phase Change Devices Fabrication

Abstract Chalcogenide glasses are one of the most versatile materials that have been widely researched because of their flexible optical, chemical, electronic, and phase change properties. Their application is usually in the form of thin films, which work as active layers in sensors and memory devices. In this work, we investigate the formulation of nanoparticle ink of Ge–Se chalcogenide glasses and its potential applications. The process steps reported in this work describe nanoparticle ink formulation from chalcogenide glasses, its application via inkjet printing and dip-coating methods and sintering to manufacture phase change devices. We report data regarding nanoparticle production by ball milling and ultrasonication along with the essential characteristics of the formed inks, like contact angle and viscosity. The printed chalcogenide glass films were characterized by Raman spectroscopy, X-ray diffraction, energy dispersive spectroscopy and atomic force microscopy. The printed films exhibited similar compositional, structural, electronic and optical properties as the thermally evaporated thin films. The crystallization processes of the printed films are discussed compared to those obtained by vacuum thermal deposition. We demonstrate the formation of printed thin films using nanoparticle inks, low-temperature sintering and proof for the first time, their application in electronic and photonic temperature sensors utilizing their phase change property. This work adds chalcogenide glasses to the list of inkjet printable materials, thus offering an easy way to form arbitrary device structures for optical and electronic applications.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2012

A new, analytic, non-perturbative, gauge-invariant formulation of realistic QCD

This Formulation [1], [2], [3] is New, in the sense that it is less than 3 years old. But it could have been done decades ago, since the input information existed, but was overlooked. It is Analytic in the sense that physically-reasonable approximations can be estimated with paper and pencil; and exact amplitudes can be calculated as Meijer G-functions of various orders. It is Non-Perturbative in the sense that sums over all possible gluon exchanges between any pair of quarks and/or antiquarks, including cubic and quartic gluon interactions, are exactly performed. These multiple gluon exchanges combine into 'Gluon Bundles' (GBs), as sums over Feynman graphs with finite numbers of exchanged gluons are replaced by {sup B}undle Graphs{sup .} In effect, gluons disappear from the formalism, and GBs remain as the effective carrier of all interactions between quark lines. A simple re-arrangement of the Schwinger/Symanzik functional solution for the Generating Functional of QCD - a rearrangement possible in QCD but not in QED - produces a formal statement of Gauge-Invariance, even though the formulation contains gauge-dependent gluon propagators. After the non-perturbative sums produce GBs, one sees explicit cancelation of all gauge-dependent gluon propagators; gauge-invariance is achieved as gauge-independence. A new insight into Realistic QCD appears in the non-perturbative domain, because quarks do not have individual asymptotic states; they are always asymptotically bound, and their transverse coordinates cannot, in principle, be measured exactly. 'Transverse Imprecision' is introduced into the basic Lagrangian, and quark-binding potentials for the construction of mesons and nucleons can then be defined and evaluated. And the greatest surprise of all: A new, non-perturbative property appears, called Effective Locality, with the result that all functional integrals reduce to (a few) sets of ordinary integrals, easy to estimate approximately, or calculate on a desk-top computer. A fantastic simplification{exclamation_point} With the aid of the above techniques, this presentation will describe each of the above paragraphs, with explicit descriptions of gauge-invariance, of the summation of all relevant Feynman graphs, of quark-binding into hadrons, and of nucleon-nucleon binding to form a deuteron. To our knowledge, the latter calculation is the first analytic example of Nuclear Physics obtained directly from basic QCD.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2014

Coherent states formulation of polymer field theory

We introduce a stable and efficient complex Langevin (CL) scheme to enable the first direct numerical simulations of the coherent-states (CS) formulation of polymer field theory. In contrast with Edwards’ well-known auxiliary-field (AF) framework, the CS formulation does not contain an embedded nonlinear, non-local, implicit functional of the auxiliary fields, and the action of the field theory has a fully explicit, semi-local, and finite-order polynomial character. In the context of a polymer solution model, we demonstrate that the new CS-CL dynamical scheme for sampling fluctuations in the space of coherent states yields results in good agreement with now-standard AF-CL simulations. The formalism is potentially applicable to a broad range of polymer architectures and may facilitate systematic generation of trial actions for use in coarse-graining and numerical renormalization-group studies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2014

Differentiable but exact formulation of density-functional theory

The universal density functional F of density-functional theory is a complicated and ill-behaved function of the density—in particular, F is not differentiable, making many formal manipulations more complicated. While F has been well characterized in terms of convex analysis as forming a conjugate pair (E, F) with the ground-state energy E via the Hohenberg–Kohn and Lieb variation principles, F is nondifferentiable and subdifferentiable only on a small (but dense) subset of its domain. In this article, we apply a tool from convex analysis, Moreau–Yosida regularization, to construct, for any ε > 0, pairs of conjugate functionals ({sup ε}E, {sup ε}F) that converge to (E, F) pointwise everywhere as ε → 0{sup +}, and such that {sup ε}F is (Fréchet) differentiable. For technical reasons, we limit our attention to molecular electronic systems in a finite but large box. It is noteworthy that no information is lost in the Moreau–Yosida regularization: the physical ground-state energy E(v) is exactly recoverable from the regularized ground-state energy {sup ε}E(v) in a simple way. All concepts and results pertaining to the original (E, F) pair have direct counterparts in results for ({sup ε}E, {sup ε}F). The Moreau–Yosida regularization therefore allows for an exact, differentiable formulation of density-functional theory. In particular, taking advantage of the differentiability of {sup ε}F, a rigorous formulation of Kohn–Sham theory is presented that does not suffer from the noninteracting representability problem in standard Kohn–Sham theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

The Lagrangian formulation of strong-field quantum electrodynamics in a plasma

The Lagrangian formulation of the scalar and spinor quantum electrodynamics in the presence of strong laser fields in a plasma medium is considered. We include the plasma influence in the free Lagrangian analogously to the “Furry picture” and obtain coupled equations of motion for the plasma particles and for the laser propagation. We demonstrate that the strong-field wave (i.e., the laser) satisfies a massive dispersion relation and obtain self-consistently the effective mass of the laser photons. The Lagrangian formulation derived in this paper is the basis for the cross sections calculation of quantum processes taking place in the presence of a plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗