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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.

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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Pitfalls in the n -mode representation of vibrational potentials

Simulations of anharmonic vibrational motion rely on computationally expedient representations of the governing potential energy surface. The n-mode representation (n-MR)—effectively a many-body expansion in the space of molecular vibrations—is a general and efficient approach that is often used for this purpose in vibrational self-consistent field (VSCF) calculations and correlated analogues thereof. In the present analysis, a lack of convergence in many VSCF calculations is shown to originate from negative and unbound potentials at truncated orders of the n-MR expansion. For cases of strong anharmonic coupling between modes, the n-MR can both dip below the true global minimum of the potential surface and lead to effective single-mode potentials in VSCF that do not correspond to bound vibrational problems, even for bound total potentials. The present analysis serves mainly as a pathology report of this issue. Furthermore, this insight into the origin of VSCF non-convergence provides a simple, albeit ad hoc, route to correct the problem by “painting in” the full representation of groups of modes that exhibit these negative potentials at little additional computational cost. Somewhat surprisingly, this approach also reasonably approximates the results of the next-higher n-MR order and identifies groups of modes with particularly strong coupling. The method is shown to identify and correct problematic triples of modes—and restore SCF convergence—in two-mode representations of challenging test systems, including the water dimer and trimer, as well as protonated tropine.

Chemistry↗
NASA NTRS1991

NASA's Metrology and Calibration program

The success of the National Aeronautics and Space Administration's scientific and engineering projects is often based on the capability and quality of the metrology and calibration programs of its field centers and facilities. A Metrology and Calibration Working Group, having representation from each of the NASA field centers and facilities, was established to develop and implement a program to provide a centralized direction and agency wide focus. A brief history of the Group is presented. The development of the Group's operating philosophy, the long term objectives, the measurement research and development program, and review of accomplishments is discussed.

Kern, Frederick A.↗
DOE OSTI2017

Spin multiplicities

The number of times spin s appears in the Kronecker product of n spin j representations is computed, and the large n asymptotic behavior of the result is obtained. Applications are briefly sketched.

group representations↗
DOE OSTI2018

Supersymmetric symplectic quantum mechanics

Symplectic Quantum Mechanics SQM considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space H{sub Γ} to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville–von Neumann equation. In this article we extend the methods of supersymmetric quantum mechanics SUSYQM to SQM. With the purpose of applications in quantum systems, the factorization method of the quantum mechanical formalism is then set within supersymmetric SQM. A hierarchy of simpler hamiltonians is generated leading to new computation tools for solving the eigenvalue problem in SQM. We illustrate the results by computing the states and spectra of the problem of a charged particle in a homogeneous magnetic field as well as the corresponding Wigner function.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Quantum mechanics on phase space: The hydrogen atom and its Wigner functions

Symplectic quantum mechanics (SQM) considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space H{sub Γ}, to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville–von Neumann equation. In this article the Coulomb potential in three dimensions (3D) is resolved completely by using the phase space Schrödinger equation. The Kustaanheimo–Stiefel(KS) transformation is applied and the Coulomb and harmonic oscillator potentials are connected. In this context we determine the energy levels, the amplitude of probability in phase space and correspondent Wigner quasi-distribution functions of the 3D-hydrogen atom described by Schrödinger equation in phase space.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Self-Assembly and Critical Aggregation Concentration Measurements of ABA Triblock Copolymers with Varying B Block Types: Model Development, Prediction, and Validation

The dissipative particle dynamics (DPD) simulation technique is a coarse-grained (CG) molecular dynamics-based approach that can effectively capture the hydrodynamics of complex systems while retaining essential information about the structural properties of the molecular species. An advantageous feature of DPD is that it utilizes soft repulsive interactions between the beads, which are CG representation of groups of atoms or molecules. In this study, we used the DPD simulation technique to study the aggregation characteristics of ABA triblock copolymers in aqueous medium. Pluronic polymers (PEG-PPO-PEG) were modeled as two segments of hydrophilic beads and one segment of hydrophobic beads. Tyrosine-derived PEG 5K -b-oligo(desaminotyrosyl tyrosine octyl ester-suberate)-b-PEG 5K (PEG5K-oligo(DTO-SA)-PEG 5K ) block copolymers possess alternate rigid and flexible components along the hydrophobic oligo(DTO-SA) chain, and were modeled as two segments of hydrophilic beads and one segment of hydrophobic, alternate soft and hard beads. The formation, structure, and morphology of the initial aggregation of the polymer molecules in aqueous medium were investigated by following the aggregation dynamics. The dimensions of the aggregates predicted by the computational approach were in good agreement with corresponding results from experiments, for the Pluronic and PEG 5K -oligo(DTO-SA)-PEG 5K block copolymers. In addition, DPD simulations were utilized to determine the critical aggregation concentration (CAC), which was compared with corresponding results from an experimental approach. For Pluronic polymers F68, F88, F108, and F127, the computational results agreed well with experimental measurements of the CAC measurements. For PEG 5K -b-oligo(DTO-SA)-b-PEG 5K block polymers, the complexity in polymer structure made it difficult to directly determine their CAC values via the CG scheme. Therefore, we determined CAC values of a series of triblock copolymers with 3–8 DTO-SA units using DPD simulations, and used these results to predict the CAC values of triblock copolymers with higher molecular weights by extrapolation. In parallel, a PEG 5K -b-oligo(DTO-SA)-b-PEG 5K block copolymer was synthesized, and the CAC value was determined experimentally using the pyrene method. The experimental CAC value agreed well with the CAC value predicted by simulation. Furthermore, these results validate our CG models, and demonstrate an avenue to simulate and predict aggregation characteristics of ABA amphiphilic triblock copolymers with complex structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Construction of conformally invariant higher spin operators using transvector algebras

This paper deals with a systematic construction of higher spin operators, defined as conformally invariant differential operators acting on functions on flat space R{sup m} with values in an arbitrary half-integer irreducible representation for the spin group. To be more precise, the higher spin version of the Dirac operator and associated twistor operators will be constructed as generators of a transvector algebra, hereby generalising the well-known fact that the classical Dirac operator on R{sup m} and its symbol generate the orthosymplectic Lie superalgebra osp(1,2). To do so, we will use the extremal projection operator and its relation to transvector algebras. In the second part of the article, the conformal invariance of the constructed higher spin operators will be proven explicitly.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2003

Remote Instrumentation AMPATH Astronomy Working Group

This viewgraph representation presents an overview of the Telescience Resource Kit (TReK) and the Internet Voice Distribution System (IVoDS) applications which are being used to provide support for science experiments aboard the International Space Station (ISS). Operational logistics, structural design, technical capabilities for both systems are discussed. Additional topics covered include: general discussion of remote instrumentation and tools, and hypothetical examples where these tools are used.

Bradford, Robert N.↗
DOE OSTI2024

Hilbert series for covariants and their applications to minimal flavor violation

We elaborate how to apply the Hilbert series method to enumerating group covariants, which transform under any given representation, including but going beyond group invariants. Mathematically, group covariants form a module over the ring of the invariants. The number of independent covariants is given by the rank of the module, which can be computed by taking a ratio of two Hilbert series. In many cases, the rank equals the dimension of the group covariant representation. When this happens, we say that there is a rank saturation. We apply this technology to revisit the hypothesis of Minimal Flavor Violation in constructing Effective Field Theories beyond the Standard Model. We find that rank saturation is guaranteed in this case, leading to the important consequence that the MFV symmetry principle does not impose any restriction on the EFT, i.e. MFV SMEFT = SMEFT, in the absence of additional assumptions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Representations of relativistic particles of arbitrary spin in Poincaré, Lorentz, and Euclidean covariant formulations of relativistic quantum mechanics

Background: Relativistic treatments of quantum mechanical systems are important for understanding hadronic structure and dynamics at subnucleon scales. Relativistic invariance of a quantum system means that there is an underlying unitary representation of the Poincaré group. This is equivalent to the requirement that the quantum observables (probabilities, expectation values, and ensemble averages) for equivalent measurements performed in different inertial reference frames are identical. Different representations are used in practice, including Poincaré covariant forms of dynamics, representations based on Lorentz covariant wave functions, Euclidean covariant representations, and representations generated by Lorentz covariant fields. Purpose: The purpose of this work is to illustrate the relation between the different equivalent representations of states in relativistic quantum mechanics. Method: The starting point is a description of a particle of mass m and spin j using irreducible representations of the Poincaré group. Since any unitary representation of the Poincaré group can be decomposed into a direct integral of irreducible representations, these are the basic building blocks of any relativistically invariant quantum theory. The equivalence is established by constructing equivalent Lorentz covariant irreducible representations from Poincaré covariant irreducible representations and constructing equivalent Euclidean covariant irreducible representations from Lorentz covariant irreducible representations. Results: Equivalent descriptions for positive mass representations of arbitrary spin are presented in each of these frameworks. Dynamical realizations of the different representations are briefly discussed. Conclusion: Poincaré covariant, Lorentz covariant, and Euclidean covariant realizations of relativistic dynamics are shown to be equivalent by explicitly relating the positive-mass positive-energy irreducible representations of the Poincaré group that appear in the direct integral.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

Elementary results for the fundamental representation of SU(3)

A general group element for the fundamental representation of SU(3) can always be expressed as a second order polynomial in a Hermitian generating matrix H, with coefficients consisting of elementary trigonometric functions dependent on the sole invariant det(H), in addition to the group parameter.

Cayley↗
DOE OSTI2025

Unification of finite symmetries in the simulation of many-body systems on quantum computers

Symmetry is fundamental in the description and simulation of quantum systems. Leveraging symmetries in classical simulations of many-body quantum systems can result in significant overhead due to the exponentially growing size of some symmetry groups as the number of particles increases. Quantum computers hold the promise of achieving exponential speedup in simulating quantum many-body systems; however, a general method for utilizing symmetries in quantum simulations has not yet been established. In this work, we present a unified framework for incorporating symmetry group transforms on quantum computers to simulate many-body systems. The core of our approach lies in the development of efficient quantum circuits for symmetry-adapted projection onto irreducible representations of a group or pairs of commuting groups. We provide resource estimations for common groups, including the cyclic and permutation groups. Our algorithms demonstrate the capability to prepare coherent superpositions of symmetry-adapted states and to perform quantum evolution across a wide range of models in condensed-matter physics and ab initio electronic structure in quantum chemistry. Specifically, we execute a symmetry-adapted quantum subroutine for small molecules in first-quantization on noisy hardware and demonstrate the emulation of symmetry-adapted quantum phase estimation for preparing coherent superpositions of quantum states in various irreducible representations of a symmetry group. In addition, we present a discussion of open problems regarding treating symmetries in digital quantum simulations of many-body systems, paving the way for future systematic investigations into leveraging symmetries quantumly for practical quantum advantage. The broad applicability and rigorous resource estimation for symmetry transformations make our framework appealing for achieving provable quantum advantage on fault-tolerant quantum computers, especially for symmetry-related properties.

quantum algorithms↗
DOE OSTI2023

Loop-level double-copy for massive fermions in the fundamental

We find that unitarity cuts and the duality between color and kinematics are sufficient constraints to bootstrap D-dimensional QCD scattering amplitudes starting from three-particle tree-level. Specifically, we calculate tree level amplitudes through six-points, as well as the four-point one-loop correction for massive fermions in the fundamental representation of the gauge group — constructing a color-dual representation of the latter for the first time. To do so we clarify a prescription for functional kinematic ansatze involving fermionic matter. The advantages of color-dual calculation, familiar from particles in the adjoint, also apply here: only a small number of basis topologies must be constrained via physical information of the theory, and algebraic relations propagate this to a full solution. As all the QCD amplitudes we construct here are color-dual, they trivially generate D-dimensional amplitudes in gravitational theories via double-copy construction.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Symmetry-Based Structured Matrices for Efficient Approximately Equivariant Networks

There has been much recent interest in designing symmetry-aware neural networks (NNs) exhibiting relaxed equivariance. Such NNs aim to interpolate between being exactly equivariant and being fully flexible, affording consistent performance benefits. In a separate line of work, certain structured parameter matrices -- those with displacement structure, characterized by low displacement rank (LDR) -- have been used to design small-footprint NNs. Displacement structure enables fast function and gradient evaluation, but permits accurate approximations via compression primarily to classical convolutional neural networks (CNNs). In this work, we propose a general framework -- based on a novel construction of symmetry-based structured matrices -- to build approximately equivariant NNs with significantly reduced parameter counts. Our framework integrates the two aforementioned lines of work via the use of so-called Group Matrices (GMs), a forgotten precursor to the modern notion of regular representations of finite groups. GMs allow the design of structured matrices -- resembling LDR matrices -- which generalize the linear operations of a classical CNN from cyclic groups to general finite groups and their homogeneous spaces. We show that GMs can be employed to extend all the elementary operations of CNNs to general discrete groups. Further, the theory of structured matrices based on GMs provides a generalization of LDR theory focussed on matrices with cyclic structure, providing a tool for implementing approximate equivariance for discrete groups. We test GM-based architectures on a variety of tasks in the presence of relaxed symmetry. We report that our framework consistently performs competitively compared to approximately equivariant NNs, and other structured matrix-based compression frameworks, sometimes with a one or two orders of magnitude lower parameter count.

Samudre, Ashwin↗
DOE OSTI2019

Generic matter representations in 6D supergravity theories

In six-dimensional supergravity, there is a natural sense in which matter lying in certain representations of the gauge group is “generic,” in that other “exotic” matter representations require more fine tuning. From considerations of the dimensionality of the moduli space and anomaly cancellation conditions, we find that the generic sets of matter representations are well-defined for 6D supergravity theories with gauge groups containing arbitrary numbers of nonabelian factors and U(1) factors. These generic matter representations also match with those that arise in the most generic F-theory constructions, both in 6D and in 4D, with non-generic matter representations requiring more exotic singularity types. The analysis of generic versus exotic matter illuminates long-standing puzzles regarding F-theory models with multiple U(1) factors and provides a useful framework for analyzing the 6D “swampland” of apparently consistent low-energy theories that cannot be realized through known string constructions. We note also that the matter content of the standard model is generic by the criteria used here only if the global structure is SU(3) c × SU(2) L × U(1) Y / Z 6 .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Lorentz group equivariant autoencoders

Abstract There has been significant work recently in developing machine learning (ML) models in high energy physics (HEP) for tasks such as classification, simulation, and anomaly detection. Often these models are adapted from those designed for datasets in computer vision or natural language processing, which lack inductive biases suited to HEP data, such as equivariance to its inherent symmetries. Such biases have been shown to make models more performant and interpretable, and reduce the amount of training data needed. To that end, we develop the Lorentz group autoencoder (LGAE), an autoencoder model equivariant with respect to the proper, orthochronous Lorentz group $$\textrm{SO}^+(3,1)$$ SO + ( 3 , 1 ) , with a latent space living in the representations of the group. We present our architecture and several experimental results on jets at the LHC and find it outperforms graph and convolutional neural network baseline models on several compression, reconstruction, and anomaly detection metrics. We also demonstrate the advantage of such an equivariant model in analyzing the latent space of the autoencoder, which can improve the explainability of potential anomalies discovered by such ML models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Decomposition of the polynomial kernel of arbitrary higher spin Dirac operators

In a series of recent papers, we have introduced higher spin Dirac operators, which are generalisations of the classical Dirac operator. Whereas the latter acts on spinor-valued functions, the former acts on functions taking values in arbitrary irreducible half-integer highest weight representations for the spin group. In this paper, we describe how the polynomial kernel spaces of such operators decompose in irreducible representations of the spin group. We will hereby make use of results from representation theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

BMS symmetry, soft particles and memory

Here, in this work, we revisit unitary irreducible representations of the Bondi–Metzner–Sachs (BMS) group discovered by McCarthy. Representations are labelled by an infinite number of supermomenta in addition to 4-momentum. Tensor products of these irreducible representations lead to particle-like states dressed by soft gravitational modes. Conservation of 4-momentum and supermomentum in the scattering of such states leads to a memory effect encoded in the outgoing soft modes. We note there exist irreducible representations corresponding to soft states with strictly vanishing 4-momentum, which may nevertheless be produced by scattering of particle-like states. This fact has interesting implications for the S-matrix in gravitational theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗