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At least 1,207 records · Page 67

First-principles calculation of the configurational energy density of states for a solid-state ion conductor with a variant of the Wang and Landau algorithm

In this work, a variant of the Wang and Landau algorithm for calculation of the configurational energy density of states is proposed. The algorithm was developed for the purpose of using first-principles simulations, such as density functional theory, to calculate the partition function of disordered sublattices in crystal materials. The expensive calculations of first-principles methods make a parallel algorithm necessary for a practical computation of the configurational energy density of states within a supercell approximation of a solid-state material. The algorithm developed in this work is tested with the two-dimensional (2d) Ising model to bench mark the algorithm and to help provide insight for implementation to a materials science application. Tests with the 2d Ising model revealed that the algorithm has good performance compared to the original Wang and Landau algorithm and the 1/$\textit{t}$ algorithm, in particular the short iteration performance. Further, a proof of convergence is presented within an adiabatic assumption, and the analysis is able to correctly predict the time dependence of the modification factor to the density of states. The algorithm was then applied to the lithium and lanthanum sublattice of the solid-state lithium ion conductor Li 0.5 La 0.5 TiO 3 . This was done to help understand the disordered nature of the lithium and lanthanum. The results find, overall, that the algorithm performs very well for the 2d Ising model and that the results for Li 0.5 La 0.5 TiO 3 are consistent with experiment while providing additional insight into the lithium and lanthanum ordering in the material. The primary result is that the lithium and lanthanum become more mixed between layers along the c axis for increasing temperature. In part, the simulation of the disordered Li 0.5 La 0.5 TiO 3 system serves as a benchmark for what size systems are currently and in the near future practical to calculate with density functional theory methods.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Accelerated Distributed Energy Management for Microgrids

This paper considers the optimal energy management for a microgrid. The goal of optimal energy management is to minimize the total generation cost while meeting total demand and satisfying individual generator output limits. To achieve this goal, we develop a distributed algorithm based on the consensus theory and gradient estimation technique. Compared to the existing algorithms with diminishing step-sizes, the proposed algorithm enjoys a faster convergence speed due to the fixed step-size, and thus increases the computation speed, and reduces the computation and communication burden. The proposed distributed algorithm is applicable to both fixed and time-varying directed communication networks. We show that the convergence of the proposed distributed algorithm is achieved if the fixed communication network is strongly connected, or if the time-varying communication network is uniformly jointly strongly connected. Numerical simulation results are used to illustrate and demonstrate the effectiveness of the proposed algorithm.

Du, Wen↗

Landau discriminants

Scattering amplitudes in quantum field theories have intricate analytic properties as functions of the energies and momenta of the scattered particles. In perturbation theory, their singularities are governed by a set of nonlinear polynomial equations, known as Landau equations, for each individual Feynman diagram. The singularity locus of the associated Feynman integral is made precise with the notion of the Landau discriminant, which characterizes when the Landau equations admit a solution. In order to compute this discriminant, we present approaches from classical elimination theory, as well as a numerical algorithm based on homotopy continuation. These methods allow us to compute Landau discriminants of various Feynman diagrams up to 3 loops, which were previously out of reach. For instance, the Landau discriminant of the envelope diagram is a reducible surface of degree 45 in the three-dimensional space of kinematic invariants. We investigate geometric properties of the Landau discriminant, such as irreducibility, dimension and degree. In particular, we find simple examples in which the Landau discriminant has codimension greater than one. Furthermore, we describe a numerical procedure for determining which parts of the Landau discriminant lie in the physical regions. In order to study degenerate limits of Landau equations and bounds on the degree of the Landau discriminant, we introduce Landau polytopes and study their facet structure. Finally, we provide an efficient numerical algorithm for the computation of the number of master integrals based on the connection to algebraic statistics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Solving key challenges in collider physics with foundation models

Foundation models are neural networks that are capable of simultaneously solving many problems. Large language foundation models like ChatGPT have revolutionized many aspects of daily life, but their impact for science is not yet clear. In this paper, we use a new foundation model for hadronic jets to solve three key challenges in collider physics. In particular, we show how experiments can (1) save significant computing power when developing reconstruction algorithms, (2) perform a complete uncertainty quantification for high-dimensional measurements, and (3) search for new physics with model agnostic methods using low-level inputs. In each case, there are significant computational or methodological challenges with current methods that limit the science potential of deep learning algorithms. By solving each problem, we take jet foundation models beyond proof-of-principle studies and into the toolkit of practitioners.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Quantum embedding for material chemistry based on domain separation and open subsystems

Our perspective considers two theories we recently proposed to perform quantum embedding calculations for chemical systems: domain-separated density functional theory (DSDFT) and locally coupled open subsystems (LCOS). The development includes both the fundamentals of each theory as well as potential applications, some technical aspects, and related challenges. DS-DFT is suited to study intramolecular effects, where one can apply a high level of theory (based on DFT or wave function theory) to a region of interest inside a molecule or solid, and lower level theory elsewhere, with smooth switching between the regions. LCOS, in contrast, is a fragment-based embedding which offers computational advantages to study intermolecular behavior such as electron hopping, spin-environment interaction, and charge transfer excitations. Yet, both theories can exchange roles when appropriate. In addition, these theories allow for control of computational scaling of their algorithms. We investigate paths to determine the charge-transfer operator used in LCOS, and suggest an auxiliary energy minimization that can provide a practical estimate to this operator. We also briefly discuss how to implement density fitting techniques in domain separation, and how domain separation can be used for pure wavefunction-based embedding.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Characterization of Quantum States Based on Creation Complexity

Abstract The creation complexity of a quantum state is the minimum number of elementary gates required to create it from a basic initial state. The creation complexity of quantum states is closely related to the complexity of quantum circuits, which is crucial in developing efficient quantum algorithms that can outperform classical algorithms. A major question unanswered so far is what quantum states can be created with a number of elementary gates that scales polynomially with the number of qubits. In this work, it is first shown that for an entirely general quantum state it is exponentially hard (requires a number of steps that scales exponentially with the number of qubits) to determine if the creation complexity is polynomial. Then, it is shown that it is possible for a large class of quantum states with polynomial creation complexity to have common coefficient features such that, given any candidate quantum state, an efficient coefficient sampling procedure can be designed to determine if the state belongs to the class or not with arbitrarily high success probability. Consequently, partial knowledge of a quantum state's creation complexity is obtained, which can be useful for designing quantum circuits and algorithms involving such a state.

74 ATOMIC AND MOLECULAR PHYSICS↗

Finite Combinatorial Generation of Metabelian T-Ideal

In this work, we develop our idea on the construction of a system of combinatorial generators in a T-ideal of a free associative algebra, which is a full analogy of a Gröbner–Shirshov basis in a polynomial ideal. We prove a theorem on multilinear monomials that enables us to establish the existence of a finite set of combinatorial generators in a metabelian T-ideal.

97 MATHEMATICS AND COMPUTING↗

Effect of Yagi–Uda nano-antenna element shape on the directivity and radiation efficiency

In this paper, different optimal designs of Yagi–Uda nano-antennas (NAs) are introduced and analyzed based on different element shapes to maximize the directivity and radiation efficiency. The studied element shapes include triangular, hexagonal, cube, square, rotated square, rectangular, ellipsoid, and elliptical cylinder shapes. The NAs parameters for each design are optimized using particle swarm optimization algorithm to achieve high directivity at a wavelength of 500 nm for wireless point-to-point applications. The designs are numerically analysed using 3-D finite difference time domain method (3-D FDTD) via Lumerical software package. To illustrate the performance of the proposed antennas, different radiation parameters such as radiation pattern, directivity, and radiation efficiency have been studied. Moreover, a tolerance of ± 5% is calculated to consider the imperfections that may appear in the fabrication process at a nanoscale. The optimized rectangular prism NA achieves the highest directivity of 24.21 with an efficiency of 50.74%. However, the optimized triangular prism NA has the highest efficiency of 73% with a directivity of 20.89. This enhancement is mainly attributed to the efficient coupling between array elements along with low side lobe level. However, a trade-off between directivity and radiation efficiency is obtained by the hexagonal prism NA with directivity of 21.9 and radiation efficiency of 69.1%.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

The origin of CEMA and its relation to CSP

Currently, there exist two methods for analysing an explosive mode introduced by chemical kinetics in a reacting process: the Computational Singular Perturbation (CSP) algorithm and the Chemical Explosive Mode Analysis (CEMA). CSP was introduced in 1989 and addressed both dissipative and explosive modes encountered in the multi-scale dynamics that characterize the process, while CEMA was introduced in 2009 and addressed only the explosive modes. It is shown that (i) the algorithmic tools incorporated in CEMA were developed previously on the basis of CSP and (ii) the examination of explosive modes has been the subject of CSP-based works, reported before the introduction of CEMA.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Hybridizable Discontinuous Galerkin solver for the Grad–Shafranov equation

In axisymmetric fusion reactors, the equilibrium magnetic configuration can be expressed in terms of the solution to a semi-linear elliptic equation known as the Grad–Shafranov equation, the solution of which determines the poloidal component of the magnetic field. When the geometry of the confinement region is known, the problem becomes an interior Dirichlet boundary value problem. We propose a high order solver based on the Hybridizable Discontinuous Galerkin method. The resulting algorithm (1) provides high order of convergence for the flux function and its gradient, (2) incorporates a novel method for handling piecewise smooth geometries by extension from polygonal meshes, (3) can handle geometries with non-smooth boundaries and x-points, and (4) deals with the semi-linearity through an accelerated two-grid fixed-point iteration. The effectiveness of the algorithm is verified with computations for cases where analytic solutions are known on configurations similar to those of actual devices (ITER with single null and double null divertor, NSTX, ASDEX upgrade, and Field Reversed Configurations).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Assessing and advancing the potential of quantum computing: A NASA case study

Quantum computing is one of the most enticing computational paradigms with the potential to revolutionize diverse areas of future-generation computational systems. While quantum computing hardware has advanced rapidly, from tiny laboratory experiments to quantum chips that can outperform even the largest supercomputers on specialized computational tasks, these noisy-intermediate scale quantum (NISQ) processors are still too small and non-robust to be directly useful for any real-world applications. In this paper, we describe NASA’s work in assessing and advancing the potential of quantum computing. We discuss advances in algorithms, both near- and longer-term, and the results of our explorations on current hardware as well as with simulations, including illustrating the benefits of algorithm-hardware co-design in the NISQ era. This work also includes physics-inspired classical algorithms that can be used at application scale today. We discuss innovative tools supporting the assessment and advancement of quantum computing and describe improved methods for simulating quantum systems of various types on high-performance computing systems that incorporate realistic error models. We provide an overview of recent methods for benchmarking, evaluating, and characterizing quantum hardware for error mitigation, as well as insights into fundamental quantum physics that can be harnessed for computational purposes.

Rieffel, Eleanor G.↗

A dynamic control approach for energy-efficient production scheduling on a single machine under time-varying electricity pricing

This paper proposes a dynamic control algorithm to enable an energy-aware single machine scheduling under the time-varying electricity pricing policy, in which price rates remain fixed day-to-day over the season. The key issue is to assign a set of jobs to available time periods where different electricity prices are assigned, while considering requested due dates of jobs so as to minimize total penalty costs for earliness and tardiness of jobs and total energy consumption costs, simultaneously. As the first contribution of this study, we develop a new mixed integer nonlinear programming (MINLP) model that aims at determining job arrival times and resulting earliness and tardiness of jobs and energy consumption costs for machine idle and normal processing. Second, an efficient heuristic approach based on continuous-time variable control models and algorithm is developed. The proposed heuristic adaptively changes job arrival times and due dates, which finally determine production sequence over the time periods of different electricity prices, machine turn-off, and machine idle with minimum energy consumption costs and just-in-time (JIT) penalty. Energy and JIT performance of the proposed approach is examined using real energy and machining parameters of a HAAS machine and compared to those of the metaheuristic approach. For relatively large size data groups, the proposed approach incurs about higher energy consumption costs on average, which are offset by up to lower JIT costs, resulting in lower total costs on average compared to the metaheuristic approach. Further, the proposed time-scaled heuristic algorithm yields extremely short computational time, which enables production managers to flexibly select proper production strategies and to implement them for different production environments.

42 ENGINEERING↗

Boundary-consistent B-spline filtering schemes and application to high-fidelity simulations of turbulence

A filtering operation, based on B-spline discretizations, is introduced to target weakly growing mesh-scale oscillations that can arise in high-fidelity turbulence simulations. This is a spectral regularization that can be described using the singular values of a banded matrix operator, with the filtering strength set by a scalar- or vector-valued penalty parameter. The penalty parameter can be specified though it can also be advantageously selected to minimize the generalized cross validation (GCV) measure of distance between the pre- and post-filtered solutions. Efficient algorithms are developed to compute both the scalar and vector penalty parameters. The B-spline filter has a sharper localization to high-wavenumber than compact or explicit filters of the same stencil width and is demonstrated for solutions of the Burgers' equation, decaying Burgers' turbulence, and compressible Navier–Stokes turbulent channel flow. Furthermore, these simulations confirm the scheme's numerical stability and ability to narrowly target the high wavenumber components of numerical solutions. An advantage over finite-difference filters is that these B-spline filters are stable on bounded domains and even preserve formal order of accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A conservative Galerkin solver for the quasilinear diffusion model in magnetized plasmas

We propose a conservative Galerkin scheme for the quasilinear model in three-dimensional momentum space and three-dimensional spectral space, with cylindrical symmetry. We construct an unconditionally conservative weak form and use a discretization that preserves conservation properties independent of the wave emission probability. The discrete operators, combined with a consistent quadrature rule, preserve all the conservation laws rigorously. The proposed scheme is quite general: it works for both relativistic and non-relativistic systems, for both magnetized and unmagnetized plasmas, and even for problems with time-dependent dispersion relations. We represent the particle distribution by continuous basis functions and use discontinuous basis functions for the wave spectral energy density, which enables the application of a positivity-preserving technique. We adopt the marching simplex algorithm, designed initially for computer graphics, for numerical integration on the resonance manifold. Furthermore, the numerical examples with a bump-on-tail initial configuration show how the unstable waves produce strong momentum space diffusion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

PDB-IHM: A System for Deposition, Curation, Validation, and Dissemination of Integrative Structures

Structures of many large biomolecular assemblies are now being determined using integrative approaches. In these approaches, information derived from multiple experimental and computational methods is combined to compute three-dimensional structures of multi-protein complexes and other macromolecular machines. A standalone prototype data resource for integrative structures called PDB-Dev was built, based on recommendations of the Integrative and Hybrid Methods (IHM) Task Force of the Worldwide Protein Data Bank (wwPDB). This effort included developing data standards and software tools for collecting, curating, validating, visualizing, archiving, and disseminating integrative structures that span diverse spatiotemporal scales and conformational states. Mechanisms have been created to validate integrative structures based on the experimental data underpinning them. Building upon this foundational framework, PDB-Dev has been further expanded to handle large dynamic macromolecular systems and integrative structures that combine, for example, experimental restraints with atomic coordinates computed by machine learning algorithms. Data standards and supporting tools have also been extended to capture information about biomolecular dynamics, such as conformational transitions and related kinetic data derived from biophysical methods. Recently, PDB-Dev was unified with the PDB archive and rebranded as PDB-IHM (pdb-ihm.org), further promoting FAIR (Findable, Accessible, Interoperable, and Reusable) principles of data stewardship for integrative structural biology.

IHMCIF↗

Metal-embedded fiber optic sensor packaging and signal demodulation scheme towards high-frequency dynamic measurements in harsh environments

Optical fiber-based sensors are commonly used for industrial monitoring and control processes due to their small size, resistance to electromagnetic interference, and ability to perform a wide variety of high-precision measurements. However, implementing optical fiber sensors in harsh environments is challenging because they are small and fragile. Proper packaging of fiber-optic sensors could extend their use to harsh environments, including at high temperature and under high radiation. Furthermore, conventional fiber optic-based measurement systems often use computationally expensive signal processing algorithms which hinder their use in high-frequency dynamic applications. This work reports on the design of an optical fiber-pressure sensor system based on low-coherence interferometry that uses a metal-embedded optical fiber to provide a robust sensor package. Additionally, a novel phase demodulation scheme is proposed to extract length changes from the deformation of a thin diaphragm within a Fabry–Pérot cavity to measure pressure. The sensor has been tested to ±100 kPa, has a theoretical linear response over a 270 kPa dynamic range (24 dB maximum signal-to-noise ratio), and can resolve pressure transients up to 3910 kPa/s. Sampling at 100 kHz, the present sensor can resolve 2 kPa dynamic pressures at frequencies up to 2 kHz. Faster transients on the order of tens to hundreds of kHz can theoretically be resolved at the expense of decreasing the maximum resolvable amplitude. A methodology for designing a LCI pressure sensor for a given application is outlined based on the limitations imposed by the Nyquist criterion, the diaphragm's resonant frequency, the LCI optoelectronics, and the phase demodulation scheme. The sensor is the first to implement a low-coherence light source and a Fabry–Pérot interferometer designed to provide real-time high-fidelity pressure measurements using a metal-embedded optical fiber. The demonstrated sensor provides a platform for sensing in harsh conditions such as in nuclear and energy applications.

47 OTHER INSTRUMENTATION↗