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At least 1,027 records · Page 57

Toward perturbation theory methods on a quantum computer

Perturbation theory, used in a wide range of fields, is a powerful tool for approximate solutions to complex problems, starting from the exact solution of a related, simpler problem. Advances in quantum computing, especially over the past several years, provide opportunities for alternatives to classical methods. Here, we present a general quantum circuit estimating both the energy and eigenstates corrections that is far superior to the classical version when estimating second-order energy corrections. We demonstrate our approach as applied to the two-site extended Hubbard model. In addition to numerical simulations based on qiskit, results on IBM’s quantum hardware are also presented. Our work offers a general approach to studying complex systems with quantum devices, with no training or optimization process needed to obtain the perturbative terms, which can be generalized to other Hamiltonian systems both in chemistry and physics.

97 MATHEMATICS AND COMPUTING↗

Integrated Research Infrastructure Architecture Blueprint Activity (Final Report 2023)

The complexity of scientific pursuits is increasing rapidly with aspects that require dynamic integration of experiment, observation, theory, modeling, simulation, visualization, machine learning (ML), artificial intelligence (AI), and analysis. Research projects across the Department of Energy (DOE) are increasingly data and compute intensive. Innovative research teams are accelerating the pace of discovery by using high-performance computational and data tools in their research workflows and leveraging multiple research infrastructures. Additionally, several recent high-level U.S. government reports underscore the necessity of a new advanced computing ecosystem for international competitiveness and national security. International competitors are moving forward with major research infrastructure integration efforts that seek to capture a competitive advantage in the global innovation race. Owing to its unparalleled constellation of world-class experimental and observational facilities and high-performance and extreme-scale computational, data, and networking infrastructure, DOE is positioned to be a global leader in this new era of integrated science. However, this new integration paradigm will demand continuing evolution to ensure the U.S. remains a global leader in research and innovation. The DOE Office of Science (SC) has seized on the strategic importance of integration and has adopted a vision for Integrated Research Infrastructure (IRI): To empower researchers to meld DOE’s world-class research tools, infrastructure, and user facilities seamlessly and securely in novel ways to radically accelerate discovery and innovation. To respond to the evolving computational requirements of research and the competitive international innovation landscape, experimental facilities could be connected with high performance computing resources for near real-time analysis, and resources should be provided for merging enormous and diverse data for AI/ML techniques and analysis.

97 MATHEMATICS AND COMPUTING↗

Novel experimental probes of QCD in SIDIS and e + e - annihilation (Final Technical Report)

The research addressed with this award seeks to advance our understanding of the structure and dynamics underlying the properties of visible matter. In our current understanding the nucleons (protons and neutrons) are not fundamental but are comprised of quarks and gluons, which are collectively called partons. A static quark picture fails to explain the properties of the nucleons, such as their mass and intrinsic spin, which are thought to emerge dynamically from the quark-gluon interactions via the strong force. In this work, novel observables employing correlations of particles produced in the scattering of high energy electrons off protons at the CLAS12 experiment at Jefferson Lab were analyzed to probe quark-gluon interactions. The ultimate goal of this line of inquiry is to be able to describe the properties of protons and neutrons from first principles, similar to how studying the hydrogen atom has led to the formulation of the theory of Quantum Electrodynamics. Because quarks cannot be observed directly but only as part of more complex composite particles, a smaller, complimentary part of this work was the analysis of particle production in electron-positron annihilation at the Belle II experiment to understand the production of particles from initial quarks. This takes advantage of the fact that in e + e - annihilation the initial quark dynamics is known, unlike in the scattering of nucleons. Several new applications using Machine Learning algorithms for event tagging and reconstruction to support this program were developed as part of this award. In addition, we had a significant role in the development of the physics program for the future Electron-Ion Collider, which is a new collider to be build in the US within the next decade.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Phase operators and phase relations for photon states

For a quantized mode of the radiation field, the operator whose classical analog is the ordinary phase factor of the mode amplitudes has been shown to be nonunitary. A rigorous formulation of the phase P is given on the basis of the canonical factorization theorem. Many of the seemingly complex features of phase operators are found to be simple direct consequences of the general mathematical theory. It can be readily seen that P is a partial isometry but not a unitary operator. In contrast to the amplitude operator, it is found that P is not a spectral operator and that the set of phase eigenstates is not complete. Mathematically precise operator relations are developed, and a complete spectral analysis is given for each of the phase operators.-

Volkin, H. C.↗

Mixed boundary-value problems in mechanics

Definitions in the case of multiple series equations and multiple integral equations are examined. In considering the solution of a given mixed boundary value problem perhaps the simplest technique is the direct application of the method of complex potentials provided the problem admits such potentials and the domain and the boundary conditions are suitable for such an application. The direct application of complex potentials is described with the aid of examples, taking into account a problem in potential theory, the case of periodic cuts, and an elasticity problem for a nonhomogeneous plane. The reduction to singular integral equations is discussed along with the numerical solution of singular integral equations of the first kind, integral equations with generalized Cauchy kernels, and singular integral equations of the second kind.

Erdogan, F.↗

Dynamic response of a viscoelastic Timoshenko beam

The analysis presented in this study deals with the vibratory response of viscoelastic Timoshenko (1955) beams under the assumption of small material loss tangents. The appropriate method of analysis employed here may be applied to more complex structures. This study compares the damping ratios obtained from the Timoshenko and Euler-Bernoulli theories for a given viscoelastic material system. From this study the effect of shear deformation and rotary inertia on damping ratios can be identified.

Kalyanasundaram, S.↗

Filling the expertise gap

Aeroelasticity, structures, and stability-and-control specialists can work in concerted fashion during the early design phases of future aircraft to achieve active control of naturally unstable configurations. In order to take full advantage of active control, attention must be given by designers to control-law synthesis, and to tools for the efficient synthesis and analysis of complex flexible-aircraft control systems. Analysts must consider interfaces among unsteady aerodynamics, structures, and control theory, as explored by the theory of analytic continuation for unsteady aerodynamics.

Abel, Irving↗

The Interactions Between Nitrogen and Oxygen Molecules

Lippincott's delta-function model for atomic interactions is analyzed, both physically and mathematically, and extended, by differentiation between K- and L-shell electrons and the introduction of a variable parameter in the expression for the delta-function strength, to cover homonuclear molecules more complex than hydrogen. In addition, modifications are made which allow treatments of diatomic, heteronuclear molecules. This theory, in conjunction with a reasonably extensive study of resonance, dispersion, and configuration interaction phenomena, as well as the use of simple quantum mechanical arguments, is then applied to the N2-N2, N2-O2, and O2-O2 interactions.

Meador, Willard E., Jr.↗

Applying STAMP in Accident Analysis

Accident models play a critical role in accident investigation and analysis. Most traditional models are based on an underlying chain of events. These models, however, have serious limitations when used for complex, socio-technical systems. Previously, Leveson proposed a new accident model (STAMP) based on system theory. In STAMP, the basic concept is not an event but a constraint. This paper shows how STAMP can be applied to accident analysis using three different views or models of the accident process and proposes a notation for describing this process.

Leveson, Nancy↗

Spectroscopic and computational investigations of organometallic complexation of group 12 transition metals by methanobactins from Methylocystis sp. SB2

Methanotrophic bacteria catalyze the aerobic oxidation of methane to methanol using Cu-containing enzymes, thereby exerting a modulating influence on the global methane cycle. To facilitate the acquisition of Cu ions, some methanotrophic bacteria secrete small modified peptides known as “methanobactins,” which strongly bind Cu and function as an extracellular Cu recruitment relay, analogous to siderophores and Fe. In addition to Cu, methanobactins form complexes with other late transition metals, including the Group 12 transition metals Zn, Cd, and Hg, although the interplay among solution-phase configurations, metal interactions, and the spectroscopic signatures of methanobactin-metal complexes remains ambiguous. In this study, the complexation of Zn, Cd, and Hg by methanobactin from Methylocystis sp. strain SB2 was studied using a combination of absorbance, fluorescence, extended x-ray absorption fine structure (EXAFS) spectroscopy, and time-dependent density functional theory (TD-DFT) calculations. We report changes in sample absorbance and fluorescence spectral dynamics, which occur on a wide range of experimental timescales and characterize a clear stoichiometric complexation dependence. Mercury L3-edge EXAFS and TD-DFT calculations suggest a linear model for Hg--S coordination, and TD-DFT suggests a tetrahedral model for Zn 2+ and Cd 2+ . We observed an enhancement in the fluorescence of methanobactin upon interaction with transition metals and propose a mechanism of complexation-hindered isomerization drawing inspiration from the wild-type Green Fluorescent Protein active site. Collectively, our results represent the first combined computational and experimental spectroscopy study of methanobactins and shed new light on molecular interactions and dynamics that characterize complexes of methanobactins with Group 12 transition metals.

59 BASIC BIOLOGICAL SCIENCES↗

Exact solutions of burst pressure for thick-walled cylinders in power-law strain hardening steels

Exact solutions of burst pressure for defect-free, thick-walled cylindrical pressure vessels with capped ends are developed using the flow theory of plasticity in terms of the Tresca, von Mises, and Zhu-Leis yield criteria. The material is assumed to obey a power-law strain hardening rule, and the finite strain theory is adopted to describe large plastic deformation. On this basis, internal pressure is obtained as a complex polynomial function of effective strains on the inside and outside surfaces of the pressure vessel with the use of the Bernoulli numbers. At burst failure, the effective strains and stresses on the inside and outside surfaces are first determined, and then three flow solutions of burst pressure are obtained as a power series function of the diameter ratio (D o /D i ), strain hardening exponent (n), and ultimate tensile strength (UTS). The power series solution is confirmed to agree well with the exact flow solution of burst pressure in a closed-form for each yield criterion, and the results show that the von Mises flow solution is an upper bound prediction, the Tresca flow solution is a lower bound prediction, and the Zhu-Leis flow solution is an intermediate prediction of burst pressure. In conclusion, two sets of full-scale burst test data are then utilized to evaluate and validate the proposed flow solutions of burst pressure for both thin-walled pipes and thick-walled cylindrical pressure vessels.

36 MATERIALS SCIENCE↗

Structural and compositional complexities of hierarchical self-assembly: A hypergraph approach

Programmable self-assembly enables the construction of complex molecular, supramolecular, and crystalline architectures from well-designed building blocks. In this work, we introduce a hypergraph-based formalism, Blocks & Bonds (B&B), which generalizes classical chemical graph theory by incorporating directed and multicolored interactions, internal symmetries, and hierarchical organization. Within this framework, we develop the Structure Code (SC), a compact and versatile language for describing self-assembled architectures. We define a Kolmogorov-style structural complexity as the total information content of SC, obtained through its tokenization and Shannon information assignment. Complementing this encoding-based measure, we introduce a much simpler quantity, the compositional complexity, which depends only on the number and cumulative usage of block and bond types in the construction set. A central result of this work is a strong empirical correlation between the token-based structural complexity and the compositional complexity across all examined systems. Owing to this agreement, the compositional complexity emerges as the most practical and broadly applicable measure: it is easy to compute, requires no explicit encoding, and yet closely tracks the actual information content of structurally diverse architectures. Applications to molecular systems (ethylene glycol and glucose), DNA-origami lattices, and crystalline assemblies show that B&B hypergraphs provide a unified, scalable, and information-efficient representation of structural organization, naturally capturing symmetry, modularity, and stereochemistry. This framework establishes a quantitative foundation for complexity-aware classification and inverse design of programmable matter.

36 MATERIALS SCIENCE↗

Shadow poles in the alternative parametrization of R-matrix theory

In this work, we discover new, hitherto unknown, shadow poles in Brune’s alternative parametrization of R-matrix theory [C. R. Brune, Phys. Rev. C 66, 044611 (2002)]. Where these poles are, and how many, depends on how one continues R-matrix operators to complex wavenumbers (specially the shift S and penetration P functions). This has little consequence for the exact R-matrix formalism (past the last energy threshold), as we show one can still always fully reconstruct the scattering matrix with only the previously known alternative parameters (poles and corresponding resonance widths), for which there were as many poles as the number of levels Nλ. However, we generalize the alternative parametrization to the Reich-Moore formalism, and show that the choice of continuation is now critical as it changes the alternative parameters values (poles and residue widths are now complex). In order to establish nuclear libraries with alternative parameters, the nuclear community will thus have to decide what convention to adopt. We argue in favor of analytical continuation (against the legacy Lane and Thomas approach) in a follow-up article [P. Ducru, Phys. Rev. C, submitted (2020)]. We observe the first evidence of shadow poles in the alternative parametrization of R-matrix theory in isotope xenon 134 Xe spin-parity group J π = 1=2 (–) , and show how they indeed depend on the choice of continuation to complex wavenumbers.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

CpFe(CO) 2 Radical Generated from Dinuclear [CpFe(CO) 2 ] 2 and Mononuclear (Cp)(CO) 2 Fe(H): Density Functional Theory Is Accurate for One, But Not Both

Density functional theory (DFT) methods remain the most practical approach to calculating properties and reaction mechanisms of transition metal complexes. While the accuracy of DFT methods has been evaluated for some properties of mononuclear organometallic complexes there has been a general lack of evaluation for dinuclear organometallic complexes, in particular bonding changes related to reaction mechanisms. Here, this work evaluated DFT and coupled cluster methods for the accuracy of calculating the CpFe(CO) 2 radical (Fp•) generated from dinuclear [CpFe(CO) 2 ] 2 (Fp 2 ) and mononuclear [(Cp)(CO) 2 Fe(H)] (Fp-H). This transition metal radical fragment was evaluated because dinuclear complexes built with it have recently shown a variety of unique reactions but has proven challenging to accurately calculate with DFT methods. Here we show that DFT methods provide a surprising wide range of fragmentation energies for Fp 2 and lower and mid rung DFT methods as well as DLPNO–CCSD(T) perform well for this dissociation energy. The highest rung double-hybrid methods have a large range in the Fp 2 dissociation energy, and the energy greatly depends on the amount of MP2 correlation energy included. For generating Fp• from Fp-H the lower and mid rung methods that worked well for Fp 2 showed significant error. Double-hybrid methods unfortunately are only accurate for the Fe–H bond if they are very inaccurate for the Fp 2 dissociation energy. While DLPNO–CCSD(T) is not perfect, and not close to chemically accurate for the Fe–H bond, it does provide reasonable accuracy for both Fp 2 and Fp-H dissociation energies.

density functional theory↗

Determining Concentration of Nanoparticles from Ellipsometry

A method of using ellipsometry or polarization analysis of light in total internal reflection of a surface to determine the number density of gold nanoparticles on a smooth substrate has been developed. The method can be modified to enable determination of densities of sparse distributions of nanoparticles in general, and is expected to be especially useful for measuring gold-nanoparticle-labeled biomolecules on microarrays. The method is based on theoretical calculations of the ellipsometric responses of gold nanoparticles. Elements of the calculations include the following: For simplicity, the gold nanoparticles are assumed to be spherical and to have the same radius. The distribution of gold nanoparticles is assumed to be a sub-monolayer (that is, sparser than a monolayer). The optical response of the sub-monolayer is modeled by use of a thin-island-film theory, according to which the polarizabilities parallel and perpendicular to the substrate are functions of the wavelength of light, the dielectric functions (permittivities expressed as complex functions of frequency or wavelength) of the gold and the suspending medium (in this case, the suspending medium is air), the fraction of the substrate area covered by the nanoparticles, and the radius of the nanoparticles. For the purpose of the thin-island-film theory, the dielectric function of the gold nanoparticles is modeled as the known dielectric function of bulk gold plus a correction term that is necessitated by the fact that the mean free path length for electrons in gold decreases with decreasing radius, in such a manner as to cause the imaginary part of the dielectric function to increase with decreasing radius (see figure). The correction term is a function of the nanoparticle radius, the wavelength of light, the mean free path and the Fermi speed of electrons in bulk gold, the plasma frequency of gold, and the speed of light in a vacuum. These models are used to calculate ellipsometric responses for various concentrations of gold nanoparticles having an assumed radius. The modeled data indicates distinct spectral features for both the real and the imaginary part of the dielectric function. An ellipsometric measurement would determine this distinct feature and thus can be used to measure nanoparticle concentration. By "ellipsometric responses" is meant the intensities of light measured in various polarization states as functions of the angle of incidence and the polarization states of the incident light. These calculated ellipsometric responses are used as calibration curves: Data from subsequent ellipsometric measurements on real specimens are compared with the calibration curves. The concentration of the nanoparticles on a specimen is assumed to be that of the calibration curve that most closely matches the data pertaining to that specimen.

Venkatasubbarao, Srivatsa↗