Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Classical mechanics”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Full Counting Statistics of Charge in Chaotic Many-Body Quantum Systems

We investigate the full counting statistics of charge transport in U(1)-symmetric random unitary circuits. We consider an initial mixed state prepared with a chemical potential imbalance between the left and right halves of the system and study the fluctuations of the charge transferred across the central bond in typical circuits. Using an effective replica statistical mechanics model and a mapping onto an emergent classical stochastic process valid at large on-site Hilbert space dimension, we show that charge transfer fluctuations approach those of the symmetric exclusion process at long times, with subleading t –1/2 quantum corrections. Here, we discuss our results in the context of fluctuating hydrodynamics and macroscopic fluctuation theory of classical nonequilibrium systems and check our predictions against direct matrix-product state calculations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Unconventional skyrmions in an interfacial frustrated triangular lattice

Magnetic skyrmions are spin topological textures of potential interest in spintronics-related data storage and processing devices. Here, in this work, we show the emergence of unconventional skyrmions in a geometrically frustrated triangular lattice on an inversion-symmetry-breaking two-dimensional electron gas substrate. Starting with a classical double-exchange mechanism, this generic interface induces exotic skyrmionic and unique noncoplanar magnetic states not observed in the equivalent square lattice interface. We study the model by deriving an effective spin Hamiltonian. Large scale classical Monte Carlo simulations provide a quantitative evidence for the emergence of these exotic magnetic states. We found that these chiral magnetic states exhibit a substantial and nonzero topological Hall conductivity. As potential material candidates, we propose Cr/MoS 2 , Fe/MoS 2 , and Fe/WSe 2 interfaces because they have the requisite underlying triangular lattice structures and large spin-orbit coupling.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Request for Information: Access to Quantum Systems

Quantum science and technology is a focal point of research at Lawrence Livermore National Laboratory (LLNL). Quantum-coherent devices offer the potential for unprecedented precision in sensing and the ability to directly simulate complex quantum phenomena that have no known efficient classical algorithms. Thus, development and implementation of quantum technologies is expected to have a significant impact on our ability to address some of the most complex national security problems. LLNL maintains projects involving a broad spectrum of Quantum Information Science (QIS) research activities including investigating sources of decoherence, the 3DQ microscope, studies into quantum interconnects, 3-D printed ion traps, fusion energy and nuclear physics simulations, modeling for data-starved environments, and quantum sensing, including accelerometry and timing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

On the effect of mixing-driven vaporization in a homogeneous relaxation modeling framework

The homogeneous relaxation model (HRM) is one of the most widely used models to describe the liquid–gas phase transition in multiphase flows due to the occurrence of cavitation. However, in its original formulation, the HRM does not account for the presence of ambient gas species, which generally limits its applicability to the injector's internal flow where ambient gases are negligible. In this work, a mixing-driven vaporization (MDV) model was developed to extend the capability of the HRM in handling the mixing effect in the regions external to the nozzle, where vapor–liquid equilibrium for multi-species mixtures of fuel and ambient gas is considered. Herein, to assess the model performance, simulations of the Engine Combustion Network's Spray G injector were performed with the HRM and the MDV model under both flash-boiling and evaporating conditions. It was found that the MDV model led to a better match against x-ray measurements of fuel density in the near-nozzle region. In contrast to the HRM, the MDV model was able to reproduce the vaporization process in the mixing zone at the edge of the fuel jet, which aligns with the expected physics. This resulted in substantial differences in the prediction of other flow characteristics such as mixture temperature and pressure. Furthermore, this work demonstrates that evaporation timescales have a considerable effect on the MDV model's predictions, as shown by a parametric study in which a time factor was introduced to mimic the effect of different timescales due to different phase change mechanisms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Unitary representation of the Poincaré group for classical relativistic dynamics

We give a unitary irreducible representation of the proper Poincaré group that leads to an operational version of the classical relativistic dynamics of a massive spinless particle. Unlike quantum mechanics, in this operational theory there is no uncertainty principle between position and momentum. It will be shown that the theory contains the Koopman–von Neumann formalism as a particular case, and an explicit connection with relativistic Hamiltonian mechanics will be given.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Photon pumping in a weakly-driven quantum cavity–spin system

Highlights: • We study photon frequency conversion in a driven spin coupled to a cavity mode. • Quantized frequency conversion is excpected in the strong-drive adiabatic limit. • A new photon pumping effect is established in the accessible weak drive regime. • Pumping is linked to the delocalization of the corresponding Floquet states. • Quantum coherence is preserved in both the strong and ultraweak-drive limits. We investigate the photon pumping effect in a topological model consisting of a periodically driven spin-1/2 coupled to a quantum cavity mode out of the adiabatic limit. In the strong-drive adiabatic limit, a quantized frequency conversion of photons is expected as the temporal analog of the Hall current. We numerically establish a novel photon pumping phenomenon in the experimentally accessible nonadiabatic driving regime for a broad region of the parameter space. The photon frequency conversion efficiency exhibits strong fluctuations and high efficiency that can reach up 80% of the quantized value for commensurate frequency combinations. We link the pumping properties to the delocalization of the corresponding Floquet states which display multifractal behavior as the result of hybridization between localized and delocalized sectors. Finally we demonstrate that the quantum coherence properties of the initial state are preserved during the frequency conversion process in both the strong and ultra-weak-drive limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Statistical mechanical model for crack growth

Analytic relations that describe crack growth are vital for modeling experiments and building a theoretical understanding of fracture. Upon constructing an idealized model system for the crack and applying the principles of statistical thermodynamics, it is possible to formulate the rate of thermally activated crack growth as a function of load, but the result is analytically intractable. In this report an asymptotically correct theory is used to obtain analytic approximations of the crack growth rate from the fundamental theoretical formulation. These crack growth rate relations are compared to those that exist in the literature and are validated with respect to Monte Carlo calculations and experiments. The success of this approach is encouraging for future modeling endeavors that might consider more complicated fracture mechanisms, such as inhomogeneity or a reactive environment.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Fracture mechanisms of sodium silicate glasses

Reactive classical molecular dynamics simulations of sodium silicate glasses, xNa 2 O–(100 – x)SiO 2 (x = 10–30), under quasi-static loading, were performed for the analysis of molecular scale fracture mechanisms. Mechanical properties of the sodium silicate glasses were consistent with experimentally reported values, and the amount of crack propagation varied with reported fracture toughness values. The most crack propagation occurred in NS20 systems (20-mol% Na 2 O) compared with the other simulated compositions. Dissipation via two mechanisms, the first through sodium migration as a lower activation energy process and the second through structural rearrangement as a higher activation energy process, was calculated and accounted for the energy that was not stored elastically or associated with the formation of new fracture surfaces. Here, a correlation between crack propagation and energy dissipation was identified, with systems with higher crack propagation exhibiting less energy dissipation. Sodium silicate glass compositions with lower energy dissipation also exhibited the most sodium movement and structural rearrangement within 10 Å of the crack tip during loading. Therefore, high sodium mobility near the crack tip may enable energy dissipation without requiring formation of structural defects. Therefore, the varying mobilities of the network modifiers near crack tips influence the brittleness and the crack growth rate of modified amorphous oxide systems.

36 MATERIALS SCIENCE↗
DOE OSTI2023

An analytic approach to quasinormal modes for coupled linear systems

Quasinormal modes describe the ringdown of compact objects deformed by small perturbations. In generic theories of gravity that extend General Relativity, the linearized dynamics of these perturbations is described by a system of coupled linear differential equations of second order. We first show, under general assumptions, that such a system can be brought to a Schrödinger-like form. We then devise an analytic approximation scheme to compute the spectrum of quasinormal modes. We validate our approach using a toy model with a controllable mixing parameter ε and showing that the analytic approximation for the fundamental mode agrees with the numerical computation when the approximation is justified. The accuracy of the analytic approximation is at the (sub-) percent level for the real part and at the level of a few percent for the imaginary part, even when ε is of order one. Our approximation scheme can be seen as an extension of the approach of Schutz and Will [1] to the case of coupled systems of equations, although our approach is not phrased in terms of a WKB analysis, and offers a new viewpoint even in the case of a single equation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Searching for Kerr in the 2PM amplitude

The classical scattering of spinning objects is well described by the spinor-helicity formalism for heavy particles. Using these variables, we derive spurious-pole-free, all-spin opposite-helicity Compton amplitudes (factorizing on physical poles to the minimal, all-spin three-point amplitudes) in the classical limit for QED, QCD, and gravity. The cured amplitudes are subject to deformations by contact terms, the vast majority of whose contributions we can fix by imposing a relation between spin structures — motivated by lower spin multipoles of black hole scattering — at the second post-Minkowskian (2PM) order. For QED and gravity, this leaves a modest number of unfixed coefficients parametrizing contact-term deformations, while the QCD amplitude is uniquely determined. Our gravitational Compton amplitude allows us to push the state-of-the-art of spinning-2PM scattering to any order in the spin vectors of both objects; we present results here and in the supplementary material file 2PMSpin8Aux.nb up to eighth order in the spin vectors. Interestingly, despite leftover coefficients in the Compton amplitude, imposing the aforementioned relation between spin structures uniquely fixes some higher-spin parts of the 2PM amplitude.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Radiative classical gravitational observables at $ \mathcal{O} $(G 3 ) from scattering amplitudes

We compute classical gravitational observables for the scattering of two spinless black holes in general relativity and N =8 supergravity in the formalism of Kosower, Maybee, and O’Connell (KMOC). We focus on the gravitational impulse with radiation reaction and the radiated momentum in black hole scattering at $ \mathcal{O} $(G 3 ) to all orders in the velocity. These classical observables require the construction and evaluation of certain loop-level quantities which are greatly simplified by harnessing recent advances from scattering amplitudes and collider physics. In particular, we make use of generalized unitarity to construct the relevant loop integrands, employ reverse unitarity, the method of regions, integration-by-parts (IBP), and (canonical) differential equations to simplify and evaluate all loop and phase-space integrals to obtain the classical gravitational observables of interest to two-loop order. The KMOC formalism naturally incorporates radiation effects which enables us to explore these classical quantities beyond the conservative two-body dynamics. From the impulse and the radiated momentum, we extract the scattering angle and the radiated energy. Finally, we discuss universality of the impulse in the high-energy limit and the relation to the eikonal phase.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Bulk entropy is crucial to validate the second law of the extended black hole thermodynamics

The extended black hole thermodynamics in which the cosmological constant plays the role of pressure significantly enriches the phase structure of the theory. In order to understand the extended black hole thermodynamics more precisely, we let the value of the cosmological constant vary dynamically via tunneling from one vacuum to another in a black hole induced vacuum decay. In this process, entropy of the matter/energy released by a black hole is crucial to validate the second law of thermodynamics. In other words, without taking this bulk entropy into account, entropy associated with the black hole and cosmological horizons may not always increase. Since the bulk entropy is not represented by the black hole and the cosmological horizons, this result calls for a more careful interpretation of the holographic principle in which environmental effects are taken into account.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

On the Approximability of Random-Hypergraph MAX-3-XORSAT Problems with Quantum Algorithms

Constraint satisfaction problems are an important area of computer science. Many of these problems are in the complexity class NP which is exponentially hard for all known methods, both for worst cases and often typical. Fundamentally, the lack of any guided local minimum escape method ensures the hardness of both exact and approximate optimization classically, but the intuitive mechanism for approximation hardness in quantum algorithms based on Hamiltonian time evolution is poorly understood. We explore this question using the prototypically hard MAX-3-XORSAT problem class. We conclude that the mechanisms for quantum exact and approximation hardness are fundamentally distinct. We qualitatively identify why traditional methods such as quantum adiabatic optimization are not good approximation algorithms. We propose a new spectral folding optimization method that does not suffer from these issues and study it analytically and numerically. We consider random rank-3 hypergraphs including extremal planted solution instances, where the ground state satisfies an anomalously high fraction of constraints compared to truly random problems. We show that, if we define the energy to be $E = N_{unsat}-N_{sat}$, then spectrally folded quantum optimization will return states with energy $E \leq A E_{GS}$ (where $E_{GS}$ is the ground state energy) in polynomial time, where conservatively, $A \simeq 0.6$. We thoroughly benchmark variations of spectrally folded quantum optimization for random classically approximation-hard (planted solution) instances in simulation, and find performance consistent with this prediction. We do not claim that this approximation guarantee holds for all possible hypergraphs, though our algorithm's mechanism can likely generalize widely. These results suggest that quantum computers are more powerful for approximate optimization than had been previously assumed.

Kapit, Eliot↗
DOE OSTI2021

Beyond the universal Dyson singularity for 1-D chains with hopping disorder

We study a simple non-interacting nearest neighbor tight-binding model in one dimension with disorder, where the hopping terms are chosen randomly. This model exhibits a well-known singularity at the band center both in the density of states and localization length. If the probability distribution of the hopping terms is well-behaved, then the singularities exhibit universal behavior, the functional form of which was first discovered by Freeman Dyson in the context of a chain of classical harmonic oscillators. We show here that this universal form can be violated in a tunable manner if the hopping elements are chosen from a divergent probability distribution. We also demonstrate a connection between a breakdown of universality in this quantum problem and an analogous scenario in the classical domain — that of random walks and diffusion with anomalous exponents.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Turbulence theories and statistical closure approaches

When discussing research in physics and in science more generally, it is common to ascribe equal importance to the three components of the scientific trinity: theoretical, experimental, and computational studies. This review will explore the future of modern turbulence theory by tracing its history, which began in earnest with Kolmogorov’s 1941 analysis of turbulence cascade and inertial range [A.N. Kolmogorov, Dokl. Akad. Nauk SSSR, 30, 299, (1941); 32, 19, (1941)]. The 80th Anniversary of Kolmogorov’s landmark study is a welcome opportunity to survey the achievements and evaluate the future of the theoretical approach of turbulence research. Over the years, turbulence theories have been critically important in laying the foundation of our understanding of the nature of turbulent flows. In particular, the Direct Interaction Approximation (DIA) [R.H. Kraichnan, J. Fluid Mech., 5, 497 (1959)] and its subsequent development, known as the statistical closure approach, can be identified as perhaps the most profound single advancement. The remarkable success of the statistical closure has furnished a platform to study such essential concepts as the energy transfer process and interacting scales, and the roles of the straining and sweeping motions. More recently, the quasi-Lagrangian formulation of V. L’vov & I. Procaccia and Kraichnan’s solvable passive scalar model provided powerful ways to explore another fundamental aspect of turbulent flows, the phenomena of intermittency, and the associated anomalous scaling exponents. In the meantime, the theory of fluid equilibria has been developed to describe the large-scale structures that can emerge from turbulent cascades of two-dimensional and geophysical flows at a later time. And yet, despite all these successes, analytical treatments suffer from mathematical complexities. As a result, the utility of theoretical approaches has been limited to relatively idealized flows. On the other hand, in recent decades, computational abilities and experimental facilities have reached an unprecedented scale. Looking beyond the horizon, the imminent deployment of exascale supercomputers will generate complete datasets of the entire flow field of key benchmark flows, allowing researchers to extract additional measurements concerning fully developed, complex turbulent flow fields far beyond those available from the statistical closure theories. Some other developments that could potentially influence the future course of turbulence theories include the advancement of machine learning, artificial intelligence, and data science; likely disruptions arising from the advent of quantum computation; and the increasingly prominent role of turbulence research in providing more accurate climate scientific data. Finally, turbulence theorists can leverage these developments by asking the right questions and developing advanced, sophisticated frameworks that will be able to predict and correlate vast amounts of data from the other two components of the trinity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Extending C++ for Heterogeneous Quantum-Classical Computing

In this report we present qcor - a language extension to C++ and compiler implementation that enables heterogeneous quantum-classical programming, compilation, and execution in a single-source context. Our work provides a first-of-its-kind C++ compiler enabling high-level quantum kernel (function) expression in a quantum-language agnostic manner, as well as a hardware-agnostic, retargetable compiler workflow targeting a number of physical and virtual quantum computing backends. qcor leverages novel Clang plugin interfaces and builds upon the XACC system-level quantum programming framework to provide a state-of-the-art integration mechanism for quantum-classical compilation that leverages the best from the community at-large. qcor translates quantum kernels ultimately to the XACC intermediate representation, and provides user-extensible hooks for quantum compilation routines like circuit optimization, analysis, and placement. This work details the overall architecture and compiler workflow for qcor, and provides a number of illuminating programming examples demonstrating its utility for near-term variational tasks, quantum algorithm expression, and feed-forward error correction schemes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Deformation of Lie–Poisson algebras and chirality

Linearization of a Hamiltonian system around an equilibrium point yields a set of Hamiltonian symmetric spectra: If λ is an eigenvalue of the linearized generator, -λ and $\barλ$ (hence, -$\barλ$) are also eigenvalues—the former implies a time-reversal symmetry, while the latter guarantees the reality of the solution. However, linearization around a singular equilibrium point (which commonly exists in noncanonical Hamiltonian systems) works out differently, resulting in breaking of the Hamiltonian symmetry of spectra; time-reversal asymmetry causes chirality. This interesting phenomenon was first found in analyzing the chiral motion of the rattleback, a boat-shaped top having misaligned axes of inertia and geometry [Z. Yoshida et al., Phys. Lett. A 381, 2772–2777 (2017)]. To elucidate how chiral spectra are generated, we study the three-dimensional Lie–Poisson systems and classify the prototypes of singularities that cause symmetry breaking. The central idea is the deformation of the underlying Lie algebra; invoking Bianchi’s list of all three-dimensional Lie algebras, we show that the so-called class-B algebras, which are produced by asymmetric deformations of the simple algebra s o ( 3 ) , yield chiral spectra when linearized around their singularities. The theory of deformation is generalized to higher dimensions, including the infinite-dimensional Poisson manifolds relevant to fluid mechanics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗