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At least 1,045 records · Page 58

Randomized measurement protocols for lattice gauge theories

Randomized measurement protocols, including classical shadows, entanglement tomography, and randomized benchmarking are powerful techniques to estimate observables, perform state tomography, or extract the entanglement properties of quantum states. While unraveling the intricate structure of quantum states is generally difficult and resource-intensive, quantum systems in nature are often tightly constrained by symmetries. Furthermore, this can be leveraged by the symmetry-conscious randomized measurement schemes we propose, yielding clear advantages over symmetry-blind randomization such as reducing measurement costs, enabling symmetry-based error mitigation in experiments, allowing differentiated measurement of (lattice) gauge theory entanglement structure, and, potentially, the verification of topologically ordered states in existing and near-term experiments. Crucially, unlike symmetry-blind randomized measurement protocols, these latter tasks can be performed without relearning symmetries via full reconstruction of the density matrix.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Polynomial chaos expansions on principal geodesic Grassmannian submanifolds for surrogate modeling and uncertainty quantification

In this work we introduce a manifold learning-based surrogate modeling framework for uncertainty quantification in high-dimensional stochastic systems. Our first goal is to perform data mining on the available simulation data to identify a set of low-dimensional (latent) descriptors that efficiently parameterize the response of the high-dimensional computational model. To this end, we employ Principal Geodesic Analysis on the Grassmann manifold of the response to identify a set of disjoint principal geodesic submanifolds, of possibly different dimension, that captures the variation in the data. Since operations on the Grassmann require the data to be concentrated, we propose an adaptive algorithm based on Riemannian K-means and the minimization of the sample Fréchet variance on the Grassmann manifold to identify “local” principal geodesic submanifolds that represent different system behavior across the parameter space. Polynomial chaos expansion is then used to construct a mapping between the random input parameters and the projection of the response on these local principal geodesic submanifolds. Here, the method is demonstrated on four test cases, a toy-example that involves points on a hypersphere, a Lotka-Volterra dynamical system, a continuous-flow stirred-tank chemical reactor system, and a two-dimensional Rayleigh-Bénard convection problem.

42 ENGINEERING↗

Redundancy: How Many Unreliable Spares are Needed for High Reliability and Confidence?

This paper investigates the number of redundant units needed to achieve high reliability with high confidence. The approach is developed for the case when the system failure rate is too high for a single unit to provide the required reliability over the mission duration. To achieve high reliability, N redundant units can be used, one operating unit and N – 1 spares. If the unit failure rate is f, the mission length is L, and f * L is small (not the case assumed here), the unit failure probability over the mission duration is F1 = f * L << 1. In this case, the probability that all N units will fail is Ffail = F1 N , and the needed redundancy N = LN(F)/LN(F1). For the case of large f * L assumed here, F1 = f * L > 1, and F1 is the expected number of failures during the mission. (When F1 = f * L << 1, F1 is the probability that a unit will fail during the mission. When F1 = f * L > 1, F1 is the expected number of failures during the mission.) The needed redundancy, N, to achieve the required N redundant unit reliability, FN, can be computed using the cumulative Poisson distribution with mean equal to F1. The number of spares, N - 1, is increased until the probability - that the total number of failures will be less than N -1 - is equal to the required reliability. The confidence that this reliability can be achieved can be computed using the cumulative Poisson distribution or the chi-square distribution. Since the measured unit failure rate, f, has some probabilistic uncertainty, the actual failure rate will be randomly higher or lower. This means that the reliability of the N redundant systems will be overestimated about half the time. Adding more redundant units increases the confidence that the required reliability will be achieved. For a fixed number of redundant units, the expected reliability and confidence can be traded off, since lower reliability goals will be achieved with higher confidence. Both the desired reliability and confidence can be specified as initial requirements and the needed number of redundant units estimated using the measured failure rate.

Redundancy↗

A graph embedding‐based approach for automatic cyber‐physical power system risk assessment to prevent and mitigate threats at scale

Abstract Power systems are facing an increasing number of cyber incidents, potentially leading to damaging consequences to both physical and cyber aspects. However, the development of analytical methods for the study of large‐scale power infrastructures as cyber‐physical systems is still in its early stages. Drawing inspiration from machine‐learning techniques, the authors introduce a method inspired by the principles of graph embedding that is tailored for quantitative risk assessment and the exploration of possible mitigation strategies of large‐scale cyber‐physical power systems. The primary advantage of the graph embedding approach lies in its ability to generate numerous random walks on a graph, simulating potential access paths. Meanwhile, it enables capturing high‐dimensional structures in low‐dimensional spaces, facilitating advanced machine‐learning applications, and ensuring scalability and adaptability for comprehensive network analysis. By employing this graph embedding‐based approach, the authors present a structured and methodical framework for risk assessment in cyber‐physical systems. The proposed graph embedding‐based risk analysis framework aims to provide a more insightful perspective on cyber‐physical risk assessment and situation awareness for power systems. To validate and demonstrate its applicability, the method has been tested on two cyber‐physical power system models: the Western System Coordinating Council (WSCC) 9‐Bus System and the Illinois 200‐Bus System , thereby showing its advantages in enhancing the accuracy of risk analysis and comprehensiveness of situational awareness.

Sun, Shining↗

An introduction to chaotic and random time series analysis

The origin of chaotic behavior and the relation of chaos to randomness are explained. Two mathematical results are described: (1) a representation theorem guarantees the existence of a specific time-domain model for chaos and addresses the relation between chaotic, random, and strictly deterministic processes; (2) a theorem assures that information on the behavior of a physical system in its complete state space can be extracted from time-series data on a single observable. Focus is placed on an important connection between the dynamical state space and an observable time series. These two results lead to a practical deconvolution technique combining standard random process modeling methods with new embedded techniques.

Scargle, Jeffrey D.↗

Lifetime of binary asteroids versus gravitational encounters and collisions

We investigate the effect on the dynamics of a binary asteroid in the case of a near encounter with a third body. The dynamics of the binary is modeled as a two-body problem perturbed by an approaching body in the following ways: near encounters and collisions with a component of the system. In each case, the typical value of the two-body energy variation is estimated, and a random walk for the cumulative effect is assumed. Results are applied to some binary asteroid candidates. The main conclusion is that the collisional disruption is the dominant effect, giving lifetimes comparable to or larger than the age of the solar system.

Chauvineau, Bertrand↗

Techniques in Assessing Random Uncertainty of Wind Tunnel Replicate Test Data

The preferred method to determine the random uncertainty of variables of interest during wind tunnel tests is by direct analysis of replicate data. However, current information is limited to analysis of a single replicate set condition that does not consider data covariance. This paper provides additional information on considerations for quantifying random uncertainty including the evaluation and correction of replicate data covariance, the selection of replicate set conditions for the test, and the interpolation of random uncertainty at other than replicate set conditions. The analysis and techniques are supported by data from a conventional aircraft configuration test at the Oran Nicks Low-Speed Wind Tunnel and an ASME nozzle flow characterization at the Propulsion Systems Laboratory.

Uncertainty↗

Test procedures and performance measures sensitive to automobile steering dynamics

A maneuver complex and related performance measures used to evaluate driver/vehicle system responses as effected by variations in the directional response characteristics of passenger cars are described. The complex consists of normal and emergency maneuvers (including random and discrete disturbances) which, taken as a whole, represent all classes of steering functions and all modes of driver response behavior. Measures of driver/vehicle system response and performance in regulation tasks included direct describing function measurements and rms yaw velocity. In transient maneuvers, measures such as steering activity and cone strikes were used.

Klein, R. H.↗

Remote Sensing/gis Integration for Site Planning and Resource Management

The development of an interactive/batch gridded information system (array of cells georeferenced to USGS quad sheets) and interfacing application programs (e.g., hydrologic models) is discussed. This system allows non-programer users to request any data set(s) stored in the data base by inputing any random polygon's (watershed, political zone) boundary points. The data base information contained within this polygon can be used to produce maps, statistics, and define model parameters for the area. Present/proposed conditions for the area may be compared by inputing future usage (land cover, soils, slope, etc.). This system, known as the Hydrologic Analysis Program (HAP), is especially effective in the real time analysis of proposed land cover changes on runoff hydrographs and graphics/statistics resource inventories of random study area/watersheds.

Fellows, J. D.↗

GRAM Series of Atmospheric Models for Aeroentry and Aeroassist

The eight destinations in the Solar System with sufficient atmosphere for either aeroentry or aeroassist, including aerocapture, are: Venus, Earth, Mars, Jupiter, Saturn; Uranus. and Neptune, and Saturn's moon Titan. Engineering-level atmospheric models for four of these (Earth, Mars, Titan, and Neptune) have been developed for use in NASA's systems analysis studies of aerocapture applications in potential future missions. Work has recently commenced on development of a similar atmospheric model for Venus. This series of MSFC-sponsored models is identified as the Global Reference Atmosphere Model (GRAM) series. An important capability of all of the models in the GRAM series is their ability to simulate quasi-random perturbations for Monte Carlo analyses in developing guidance, navigation and control algorithms, and for thermal systems design. Example applications for Earth aeroentry and Mars aerocapture systems analysis studies are presented and illustrated. Current and planned updates to the Earth and Mars atmospheric models, in support of NASA's new exploration vision, are also presented.

Duvall, Aleta↗

Exact spectral gaps of random one-dimensional quantum circuits

The spectral gap of local random quantum circuits is a fundamental property that determines how close the moments of the circuit's unitaries match those of a Haar random distribution. When studying spectral gaps, it is common to bound these quantities using tools from statistical mechanics or via quantum information-based inequalities. Here, by focusing on the second moment of one-dimensional unitary circuits where nearest-neighboring gates act on sets of qudits (with open and closed boundary conditions), we show that one can exactly compute the associated spectral gaps. Indeed, having access to their functional form allows us to prove several important results, such as the fact that the spectral gap for closed boundary condition is exactly the square of the gap for open boundaries, as well as improve on previously known bounds for approximate design convergence. Finally, we verify our theoretical results by numerically computing the spectral gap for systems of up to 70 qubits, as well as comparing them to gaps of random orthogonal and symplectic circuits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Single-shot imaging with randomized structured illumination at a free electron laser

Stroboscopic nanoscale imaging with free electron laser light is revolutionizing our understanding of fast dynamics in heterogeneous systems. The short wavelength of X-ray and extreme ultraviolet radiation makes it possible to achieve nanoscale resolution, while resonance with atomic transitions gives access to electronic and magnetic degrees of freedom. Here, we report on our implementation of a recently developed imaging method, randomized probe imaging, at a free electron laser. The advantage of randomized probe imaging over existing methods is its compatibility with extended and strongly scattering samples. Our implementation delivers robust single-shot reconstructions at up to a full-pitch resolution of 400 nm over a field of view with a 40 µm diameter. We also demonstrate single-shot imaging of magnetic domain structures using circular dichroism at resonance, paving the way to future time-resolved studies of magnetic dynamics, shock physics, and the dynamics of collective electronic phases.

47 OTHER INSTRUMENTATION↗

Non-Gaussian approach for parametric random vibration of non-linear structures

The dynamic response of a nonlinear, single degree of freedom structural system subjected to a physically white noise parametric excitation is investigated. The Ito stochastic calculus is employed to derive a general differential equation for the moments of the response coordinates. The differential equations of moments of any order are found to be coupled with higher order moments. A non-Gaussian closure scheme is developed to truncate the moment equations up to fourth order. The statistical of the stationary response are computed numerically and compared with analytical solutions predicted by a Gaussian closure scheme and the stochastic averaging method. It is found that the computed results exhibit the jump phenomenon which is typical of the characteristics of deterministic nonlinear systems. In addition, the numerical algorithm leads to multiple solutions all of which give positive mean squares. However, two of these solutions are found to violate the properties of high order moments. One solution preserves the moments properties and demonstrates that the system achieves a stationary response.

Ibrahim, R. A.↗

Active phase compensation system for fiber optic holography

Fiber optic delivery systems promise to extend the application of holography to severe environments by simplifying test configurations and permitting the laser to be remotely placed in a more benign location. However, the introduction of optical fiber leads to phase stability problems. Environmental effects cause the pathlengths of the fibers to change randomly, preventing the formation of stationary interference patterns which are required for holography. An active phase control system has been designed and used with an all-fiber optical system to stabilize the phase difference between light emitted from two fibers, and to step the phase difference by 90 deg without applying any constraints on the placement of the fibers. The accuracy of the phase steps is shown to be better than 0.02 deg., and a stable phase difference can be maintained for 30 min. This system can be applied to both conventional and electro-optic holography, as well as to any system where the maintenance of an accurate phase difference between two coherent beams is required.

Mercer, Carolyn R.↗

Active phase compensation system for fiber optic holography

Fiber optic delivery systems promise to extend the application of holography to severe environments by simplifying test configurations and permitting the laser to be remotely placed in a more benign location. However, the introduction of optical fiber leads to phase stability problems. Environmental effects cause the pathlengths of the fibers to change randomly, preventing the formation of stationary interference patterns which are required for holography. An active phase control system has been designed and used with an all-fiber optical system to stabilize the phase difference between light emitted from two fibers, and to step the phase difference by 90 deg without applying any constraints on the placement of the fibers. The accuracy of the phase steps is shown to be better than 0.02 deg., and a stable phase difference can be maintained for 30 min. This system can be applied to both conventional and electro-optic holography, as well as to any system where the maintenance of an accurate phase difference between two coherent beams is required.

Mercer, Carolyn R.↗

Subexponential Decay of Local Correlations from Diffusion-Limited Dephasing

Chaotic quantum systems at finite entropy density are expected to act as their own heat baths, rapidly dephasing local quantum superpositions. Here, we argue that in fact this dephasing is generically subexponential in one-dimensional systems with conservation laws: all local correlation functions decay as exp⁡[−𝒪⁡(𝑡 𝛼 )] with 0 ≤ 𝛼 ≤ 2/3, even when the operators are orthogonal to all hydrodynamic modes. The mechanism is diffusion-limited dephasing, in which rare low-entropy regions (“voids”) protect quantum coherences. This intrinsically quantum effect lies beyond standard hydrodynamics and disappears under extrinsic dephasing. In random charge-conserving circuits we find 𝛼 = 1/2, while in generic translation-invariant Floquet systems we bound 𝛼 ≤ 2/3. Our arguments are general, subject principally to the assumption that thermal fluctuations can create regions of zero entropy density. In systems with energy conservation, this assumption is automatically satisfied because of the third law of thermodynamics.

information scrambling↗

Robust Bonding Through Process Control

Process control has been proven to be the most reliable means of safeguarding the quality of adhesive bonds according to Federal Aviation Administration (FAA). A method for implementing process control for reduction in risk in a bonded joint fabrication process is demonstrated in this study using a selected bonding system. The stepwise method included risk analysis to identify defects with the highest impact and likelihood to occur, evaluation of various pre-bond surface analysis tools to monitor for the selected defects, and demonstration of the benefits of in-process monitoring utilizing threshold limits determined from bond performance tests. The bonded system selected for investigation was an aerospace carbon fiber epoxy composite substrate surface prepared with random orbital sanding using 180 grit aluminum oxide sand paper. A series of portable, pre-bond surface analysis tools were investigated for their ability to be used for in-line bond process control. Results and threshold limits are presented from roughness, ballistic water contact angle (WCA), color, gloss, and Fourier transform infrared spectroscopy (FTIR) surface analysis tools. Results demonstrated how in-process inspection methods can be used to ensure quality of a surface preparation for a selected bonding system. A framework is provided for implementation of bond process control for robust bonding.

Kutscha, Eileen O.↗