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Results for “CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS,MATHEMATICS AND COMPUTING”

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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8 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Theoretical guarantees for permutation-equivariant quantum neural networks

Despite the great promise of quantum machine learning models, there are several challenges one must overcome before unlocking their full potential. For instance, models based on quantum neural networks (QNNs) can suffer from excessive local minima and barren plateaus in their training landscapes. Recently, the nascent field of geometric quantum machine learning (GQML) has emerged as a potential solution to some of those issues. The key insight of GQML is that one should design architectures, such as equivariant QNNs, encoding the symmetries of the problem at hand. Here, we focus on problems with permutation symmetry (i.e., symmetry group $S_n$), and show how to build $S_n$-equivariant QNNs We provide an analytical study of their performance, proving that they do not suffer from barren plateaus, quickly reach overparametrization, and generalize well from small amounts of data. To verify our results, we perform numerical simulations for a graph state classification task. Our work provides theoretical guarantees for equivariant QNNs, thus indicating the power and potential of GQML.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Modeling Chemo-Mechanics with Electrolyte Infiltration to Quantify Degradation of Cathode Particles

One of the main goals in modeling lithium-ion batteries is to improve/predict longevity and resilience of new chemistries. To that end, this talk investigates the formation of stress-induced fracture within polycrystalline cathode particles and the impact on capacity loss. Physically based cathode aging dynamics is simulated in a 3D, continuum-level chemo-mechanical model. The model captures anisotropic Li diffusion within a single polycrystalline particle comprised of hundreds to thousands of randomly oriented grains. A recent addition to this model includes electrolyte infiltration, which occurs when the electrolyte seeps into surface cracks within the particle. The model predicts that particle fracture is primarily due to non-ideal grain interactions with slight dependence on high-rate charge demands. Essentially, when neighboring grains are misaligned, they expand a different rates relative to one another leading to high stresses and ultimately the formation of intraparticle cracks. The model predicts that small particles with large grains develop significantly less damage than larger particles with small grains. Finally, the model predicts most of the chemo-mechanical damage accumulates in the first charge after formation. This chemo-mechanical "damage saturation" effect indicates that initial particle fracture occurs within the first few cycles, while long-term cathode degradation is not solely chemo-mechanically induced. The principle contribution of this research is the use of an anisotropic chemo-mechanical model to test how particle geometry affect capacity fade, which predicts that particle size has a stronger effect on capacity fade than grain size and ultimately that small particles with large grains have the least capacity fade.

cathode↗
DOE OSTI2020

The paradox of the tight spiral pass in American football: A simple resolution

An American football is a rotationally symmetric object, which, when well-thrown, spins rapidly around its symmetry axis. In the absence of aerodynamic effects, the football would be a torque-free gyroscope and the symmetry/spin axis would remain pointing in a fixed direction in space as the football moved on its parabolic path. When a pass is well-thrown through the atmosphere, however, the symmetry axis remains—at least approximately—tangent to the path of motion. The rotation of the symmetry axis must be due to aerodynamic torque; yet, that torque, at first glance, would seem to have precisely the opposite effect. In this work, we explain the action of aerodynamics on the ball's orientation at second glance.

42 ENGINEERING↗
DOE OSTI2021

Transport barriers to self-propelled particles in fluid flows

Here, we present theory and experiments demonstrating the existence of invariant manifolds that impede the motion of microswimmers in two-dimensional fluid flows. One-way barriers are apparent in a hyperbolic fluid flow that block the swimming of both smooth-swimming and run-and-tumble Bacillus subtilis bacteria. We identify key phase-space structures, called swimming invariant manifolds (SwIMs), that serve as separatrices between different regions of long-time swimmer behavior. When projected into xy space, the edges of the SwIMs act as one-way barriers, consistent with the experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Random matrix theory of the isospectral twirling

We present a systematic construction of probes into the dynamics of isospectral ensembles of Hamiltonians by the notion of Isospectral twirling, expanding the scopes and methods of ref. [1]. The relevant ensembles of Hamiltonians are those defined by salient spectral probability distributions. The Gaussian Unitary Ensembles (GUE) describes a class of quantum chaotic Hamiltonians, while spectra corresponding to the Poisson and Gaussian Diagonal Ensemble (GDE) describe non chaotic, integrable dynamics. We compute the Isospectral twirling of several classes of important quantities in the analysis of quantum many-body systems: Frame potentials, Loschmidt Echos, OTOCs, Entanglement, Tripartite mutual information, coherence, distance to equilibrium states, work in quantum batteries and extension to CP-maps. Moreover, we perform averages in these ensembles by random matrix theory and show how these quantities clearly separate chaotic quantum dynamics from non chaotic ones.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Denoising and Extension of Response Functions in the Time Domain

Response functions of quantum systems, such as electron Green’s functions, magnetic, or charge susceptibilities, describe the response of a system to an external perturbation. They are the central objects of interest in field theories and quantum computing and measured directly in experiment. Further, response functions are intrinsically causal. In equilibrium and steady-state systems, they correspond to a positive spectral function in the frequency domain. Since response functions define an inner product on a Hilbert space and thereby induce a positive definite function, the properties of this function can be used to reduce noise in measured data and, in equilibrium and steady state, to construct positive definite extensions for data known on finite time intervals, which are then guaranteed to correspond to positive spectra.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Techniques for improved statistical convergence in quantification of eddy diffusivity moments

While recent approaches, such as the macroscopic forcing method (MFM) or Green's function-based approaches, can be used to compute Reynolds-averaged Navier-Stokes closure operators using forced direct numerical simulations, MFM can also be used to directly compute moments of the effective nonlocal and anisotropic eddy diffusivities. The low-order spatial and temporal moments contain limited information about the eddy diffusivity but are often sufficient for quantification and modeling of nonlocal and anisotropic effects. However, when using MFM to compute eddy diffusivity moments, the statistical convergence can be slow for higher-order moments. In this work, we demonstrate that using the same direct numerical simulation (DNS) for all forced MFM simulations improves statistical convergence of the eddy diffusivity moments. We present its implementation in conjunction with a decomposition method that handles the MFM forcing semianalytically and allows for consistent boundary condition treatment, which we develop for both scalar and momentum transport. We demonstrate that for a two-dimensional Rayleigh-Taylor instability case study, using the same DNS for all forced MFM simulations results in convergence with 𝒪⁡(100) simulations rather than 𝒪⁡(1000) simulations. In conclusion, we then demonstrate the impacts of improved convergence on the quantification of the eddy diffusivity.

general physics↗