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At least 1,189 records · Page 66

Page curves and typical entanglement in linear optics

Bosonic Gaussian states are a special class of quantum states in an infinite dimensional Hilbert space that are relevant to universal continuous-variable quantum computation as well as to near-term quantum sampling tasks such as Gaussian Boson Sampling. In this work, we study entanglement within a set of squeezed modes that have been evolved by a random linear optical unitary. We first derive formulas that are asymptotically exact in the number of modes for the Rényi-2 Page curve (the average Rényi-2 entropy of a subsystem of a pure bosonic Gaussian state) and the corresponding Page correction (the average information of the subsystem) in certain squeezing regimes. We then prove various results on the typicality of entanglement as measured by the Rényi-2 entropy by studying its variance. Using the aforementioned results for the Rényi-2 entropy, we upper and lower bound the von Neumann entropy Page curve and prove certain regimes of entanglement typicality as measured by the von Neumann entropy. Our main proofs make use of a symmetry property obeyed by the average and the variance of the entropy that dramatically simplifies the averaging over unitaries. In this light, we propose future research directions where this symmetry might also be exploited. We conclude by discussing potential applications of our results and their generalizations to Gaussian Boson Sampling and to illuminating the relationship between entanglement and computational complexity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Violation of light beam reversibility principle in optical media with a random quasi-zero refractive index

We report on experimental and theoretical evidence of the violation of one of the fundamental principles in the Fresnel optics, namely, light beam reversibility, in new nanostructured composite metamaterials with silver nanoparticle in a polymer matrix. It is shown that optical transmittance of (PMMA + Ag)/glass samples in counter directions is not the same. We propose a theoretical explanation of this phenomenon based on the effect of photon localization on the surface of the composite layer with a random quasizero refractive index.

36 MATERIALS SCIENCE↗

Evolution of Optical Diffraction Patterns on Disordered Woodpile Photonic Structures

Using three-dimensional direct laser writing, ordered and disordered photonic woodpile structures have been produced. An ideal woodpile is formed by layers of parallel “logs” turned through 90° with respect to logs of the previous layer. The disorder was specified by a random deviation in the angle with respect to their parallel arrangement in each layer of the woodpile. The quality of samples was tested by scanning electron microscopy. The optical diffraction patterns were studied experimentally on microsamples with different degrees of disorder and structure periods. With an increase in the degree of the disorder, the diffraction patterns changed qualitatively with the preservation of the zero diffraction order and formation of a speckle field pattern by higher diffraction orders.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Intrepid MCMC: Metropolis-Hastings with exploration

In engineering examples, one often encounters the need to sample from unnormalized distributions with complex shapes that may also be implicitly defined through a physical or numerical simulation model, making it computationally expensive to evaluate the associated density function. For such cases, MCMC has proven to be an invaluable tool. Random-walk Metropolis Methods (also known as Metropolis-Hastings (MH)), in particular, are highly popular for their simplicity, flexibility, and ease of implementation. However, most MH algorithms suffer from significant limitations when attempting to sample from distributions with multiple modes (particularly disconnected ones). Here, in this paper, we present Intrepid MCMC - a novel MH scheme that utilizes a simple coordinate transformation to significantly improve the mode-finding ability and convergence rate to the target distribution of random-walk Markov chains while retaining most of the simplicity of the vanilla MH paradigm. Through multiple examples, we showcase the improvement in the performance of Intrepid MCMC over vanilla MH for a wide variety of target distribution shapes. We also provide an analysis of the mixing behavior of the Intrepid Markov chain, as well as the efficiency of our algorithm for increasing dimensions. A thorough discussion is presented on the practical implementation of the Intrepid MCMC algorithm. Finally, its utility is highlighted through a Bayesian parameter inference problem for a two-degree-of-freedom oscillator under free vibration.

97 - MATHEMATICS AND COMPUTING↗

Visual signal detection in structured backgrounds. II. Effects of contrast gain control, background variations, and white noise

Studies of visual detection of a signal superimposed on one of two identical backgrounds show performance degradation when the background has high contrast and is similar in spatial frequency and/or orientation to the signal. To account for this finding, models include a contrast gain control mechanism that pools activity across spatial frequency, orientation and space to inhibit (divisively) the response of the receptor sensitive to the signal. In tasks in which the observer has to detect a known signal added to one of M different backgrounds grounds due to added visual noise, the main sources of degradation are the stochastic noise in the image and the suboptimal visual processing. We investigate how these two sources of degradation (contrast gain control and variations in the background) interact in a task in which the signal is embedded in one of M locations in a complex spatially varying background (structured background). We use backgrounds extracted from patient digital medical images. To isolate effects of the fixed deterministic background (the contrast gain control) from the effects of the background variations, we conduct detection experiments with three different background conditions: (1) uniform background, (2) a repeated sample of structured background, and (3) different samples of structured background. Results show that human visual detection degrades from the uniform background condition to the repeated background condition and degrades even further in the different backgrounds condition. These results suggest that both the contrast gain control mechanism and the background random variations degrade human performance in detection of a signal in a complex, spatially varying background. A filter model and added white noise are used to generate estimates of sampling efficiencies, an equivalent internal noise, an equivalent contrast-gain-control-induced noise, and an equivalent noise due to the variations in the structured background.

NASA Discipline Space Human Factors↗

Sample-efficient verification of continuously-parameterized quantum gates for small quantum processors

Most near-term quantum information processing devices will not be capable of implementing quantum error correction and the associated logical quantum gate set. Instead, quantum circuits will be implemented directly using the physical native gate set of the device. These native gates often have a parameterization (e.g., rotation angles) which provide the ability to perform a continuous range of operations. Verification of the correct operation of these gates across the allowable range of parameters is important for gaining confidence in the reliability of these devices. In this work, we demonstrate a procedure for sample-efficient verification of continuously-parameterized quantum gates for small quantum processors of up to approximately 10 qubits. This procedure involves generating random sequences of randomly-parameterized layers of gates chosen from the native gate set of the device, and then stochastically compiling an approximate inverse to this sequence such that executing the full sequence on the device should leave the system near its initial state. We show that fidelity estimates made via this technique have a lower variance than fidelity estimates made via cross-entropy benchmarking. This provides an experimentally-relevant advantage in sample efficiency when estimating the fidelity loss to some desired precision. We describe the experimental realization of this technique using continuously-parameterized quantum gate sets on a trapped-ion quantum processor from Sandia QSCOUT and a superconducting quantum processor from IBM Q, and we demonstrate the sample efficiency advantage of this technique both numerically and experimentally.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Polynomial Chaos Surrogate Construction for Random Fields with Parametric Uncertainty

Engineering and applied science rely on computational experiments to rigorously study physical systems. The mathematical models used to probe these systems are highly complex, and sampling-intensive studies often require prohibitively many simulations for acceptable accuracy. Surrogate models provide a means of circumventing the high computational expense of sampling such complex models. In particular, polynomial chaos expansions (PCEs) have been successfully used for uncertainty quantification studies of deterministic models where the dominant source of uncertainty is parametric. We discuss an extension to conventional PCE surrogate modeling to enable surrogate construction for stochastic computational models that have intrinsic noise in addition to parametric uncertainty. We develop a PCE surrogate on a joint space of intrinsic and parametric uncertainty, enabled by Rosenblatt transformations, which are evaluated via kernel density estimation of the associated conditional cumulative distributions. Furthermore, we extend the construction to random field data via the Karhunen–Loève expansion. We then take advantage of closed-form solutions for computing PCE Sobol indices to perform a global sensitivity analysis of the model which quantifies the intrinsic noise contribution to the overall model output variance. Additionally, the resulting joint PCE is generative in the sense that it allows generating random realizations at any input parameter setting that are statistically approximately equivalent to realizations from the underlying stochastic model. The method is demonstrated on a chemical catalysis example model and a synthetic example controlled by a parameter that enables a switch from unimodal to bimodal response distributions.

97 MATHEMATICS AND COMPUTING↗

Solidification pattern, microstructure and texture development in Laser Powder Bed Fusion (LPBF) of Al10SiMg alloy

Highlights: • The complex solidification pattern during Laser Powder Bed Fusion of Al10SiMg alloy is explained. • The evolution of α-Al cellular network, grain structure and texture development is characterized. • The grain structure is shown to be columnar throughout the printed sample • The grains’ orientation align with that of the α-Al cells. • The size evolution of α-Al cells and grains within the scan tracks follow opposite patterns. • Utilizing of a 67° hatch angle enhances densification and promotes a more isotropically developed texture across the build. - Abstract: A comprehensive analysis of solidification patterns and microstructural development is presented for an Al10SiMg sample produced by Laser Powder Bed Fusion (LPBF). Utilizing a novel scanning strategy that involves counter-clockwise rotation of the scan vector by 67° upon completion of each layer, a relatively randomized cusp-like pattern of protruding/overlapping scan tracks has been produced along the build direction. We show that such a distribution of scan tracks, as well as enhancing densification during LPBF, reduces the overall crystallographic texture in the sample, as opposed to those normally achieved by commonly-used bidirectional or island-based scanning regimes with 90° rotation. It is shown that, under directional solidification conditions present in LPBF, the grain structure is strictly columnar throughout the sample and that the grains' orientation aligns well with that of the α-Al cells. The size evolution of cells and grains within the melt pools, however, is shown to follow opposite patterns. The cells'/grains' size distribution and texture in the sample are explained via use of analytical models of cellular solidification as well as the overall heat flow direction and local solidification conditions in relation to the LPBF processing conditions. Such a knowledge of the mechanisms upon which microstructural features evolve throughout a complex solidification process is critical for process optimization and control of mechanical properties in LPBF.

36 MATERIALS SCIENCE↗

Optical Variability of Narrow-line and Broad-line Seyfert 1 Galaxies

We studied the optical variability (OV) of a large sample of narrow-line Seyfert 1 (NLSy1) and broad-line Seyfert 1 (BLSy1) galaxies with z < 0.8 to investigate any differences in their OV properties. Using archival optical V -band light curves from the Catalina Real Time Transient Survey that span 5–9 years and modeling them using damped random walk, we estimated the amplitude of variability. We found that NLSy1 galaxies as a class show lower amplitude of variability than their broad-line counterparts. In the sample of both NLSy1 and BLSy1 galaxies, radio-loud sources are found to have higher variability amplitude than radio-quiet sources. Considering only sources that are detected in the X-ray band, NLSy1 galaxies are less optically variable than BLSy1 galaxies. The amplitude of variability in the sample of both NLSy1 and BLSy1 galaxies is found to be anti-correlated with Fe ii strength but correlated with the width of the H β line. The well-known anti-correlation of variability–luminosity and the variability–Eddington ratio is present in our data. Among the radio-loud sample, variability amplitude is found to be correlated with radio-loudness and radio-power, suggesting that jets also play an important role in the OV in radio-loud objects, in addition to the Eddington ratio, which is the main driving factor of OV in radio-quiet sources.

79 ASTRONOMY AND ASTROPHYSICS↗

Model reduction for fractured porous media: a machine learning approach for identifying main flow pathways

Discrete fracture networks (DFN) are often used to model flow and transport in fractured porous media. The accurate resolution of flow and transport behavior on a large DFN involving thousands of fractures is computationally expensive. This makes uncertainty quantification studies of quantities of interest such as travel time through the network computationally intractable, since hundreds to thousands of runs of the DFN model are required to get bounds on the uncertainty of the predictions. Prior works on the subject demonstrated that the complexity of a DFN could be reduced by considering a sub-network of it (often termed a “backbone” sub-network), one whose flow and transport properties were then shown to be similar to that of the full network. The technique is tantamount to partitioning the complete set of fractures of a network into two disjoint sets, one of which is the backbone sub-network while the other its complement. It is in this context that we present a system-reduction technique for DFNs using supervised machine learning via a Random Forest Classifier that selects a backbone sub-network from the full set of fractures. The in-sample errors (in terms of precision and recall scores) of the trained classifier are found to be very accurate indicators of the out-of-sample errors, thus exhibiting that the classifier generalizes well to test data. Moreover, this system-reduction technique yields sub-networks as small as 12% of the full DFN that still recover transport characteristics of the full network such as the peak dosage and tailing behavior for late times. Most importantly, the sub-networks remain connected, and their size can be controlled by a single dimensionless parameter. Furthermore, measures of KL-divergence and KS-statistic for the breakthrough curves of the sub-networks with respect to the full network show physically realistic trends in that the measures decrease monotonically as the size of the sub-networks increase. In conclusion, the computational efficiency gained by this technique depends on the size of the sub-network, but large reductions in computational time can be expected for small sub-networks, yielding as much as 90% computational savings for sub-networks that are as small as 10-12% of the full network.

97 MATHEMATICS AND COMPUTING↗

Estimating posterior quantity of interest expectations in a multilevel scalable framework

Scalable approaches for uncertainty quantification are necessary for characterizing prediction confidence in large-scale subsurface flow simulations with uncertain permeability. To this end we explore a multilevel Monte Carlo approach for estimating posterior moments of a particular quantity of interest, where we employ an element-agglomerated algebraic multigrid (AMG) technique to generate the hierarchy of coarse spaces with guaranteed approximation properties for both the generation of spatially correlated random fields and the forward simulation of Darcy's law to model subsurface flow. In both these components (sampling and forward solves), we exploit solvers that rely on state-of-the-art scalable AMG. To illustrate the applicability of this approach, numerical tests are performed on two 3D examples-a unit cube and an egg-shaped domain with an irregular boundary-where the scalability of each simulation as well as the scalability of the overall algorithm are demonstrated.

97 MATHEMATICS AND COMPUTING↗

Analysis of stress corrosion cracking in alloy 718 following commercial reactor exposure

Alloy 718 is generally considered a highly corrosion-resistant material but can still be susceptible to stress corrosion cracking (SCC). The combination of factors leading to SCC susceptibility in the alloy is not always clear enough. In this paper, alloy 718 leaf spring (LS) materials that suffered stress corrosion damage during two 24-month cycles in pressurized water reactor service, operated to >45 MWd/mtU burn-up, was investigated. Compared to archival samples fabricated through the same processing conditions, little microstructural and property changes occurred in the material with in-service irradiation, contrary to high dose rate laboratory-based experiments reported in literature. Though the lack of delta phase formation along grain boundaries would suggest a more SCC resistant microstructure, grain boundary cracking in the material was extensive. Crack propagation routes were explored through focused ion beam milling of specimens near the crack tip for transmission electron microscopy as well as in polished plan view and cross-sectional samples for electron backscatter diffraction analysis. It has been shown in this study that cracks propagated mainly along random high-angle grain boundaries, with the material around cracks displaying a high local density of dislocations. The slip lines were produced through the local deformation of the leaf spring material above their yield strength. Also, the cause for local SCC appears to be related to oxidation of both slip lines and grain boundaries, which under the high in-service stresses resulted in crack development in the material.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Slate – A new record for crystal preferred orientation

This report describes microstructures and preferred orientation of a Devonian slate from the Belgian Ardennes (La Fortelle quarry). The sample, composed largely of muscovite, chlorite, and quartz, displays extraordinary texture strength of muscovite, exceeding 100 multiples of random distribution (m.r.d.) for (001) pole figures and thus setting a new record for preferred orientation in rocks. Quantitative texture analysis was performed with the Rietveld method on synchrotron X-ray diffraction images. Interestingly, quartz also displays strong shape preferred orientation (SPO) as revealed by X-ray microtomography and SEM imaging but largely random crystallographic preferred orientation (CPO). In conclusion, microstructural evidence suggests that this fine-grained rock formed by recrystallization of shale under stress, with growth of phyllosilicates and dissolution and growth of quartz.

58 GEOSCIENCES↗

Strong Correspondence in Evapotranspiration and Carbon Dioxide Fluxes Between Different Eddy Covariance Systems Enables Quantification of Landscape Heterogeneity in Dryland Fluxes

Abstract The eddy covariance method is widely used to investigate fluxes of energy, water, and carbon dioxide at landscape scales, providing important information on how ecological systems function. Flux measurements quantify ecosystem responses to environmental perturbations and management strategies, including nature‐based climate‐change mitigation measures. However, due to the high cost of conventional instrumentation, most eddy covariance studies employ a single system, limiting spatial representation to the flux footprint. Insufficient replication may be limiting our understanding of ecosystem behavior. To address this limitation, we deployed eight lower‐cost eddy covariance systems in two clusters around two conventional eddy covariance systems in the Chihuahuan Desert of North America for a period of 2 years. These dryland settings characterized by large temperature variations and relatively low carbon dioxide fluxes represented a challenging setting for eddy covariance. We found very good closure of energy and water balance across all systems (within ±9% of unity). We found very good correspondence between the lower‐cost and conventional systems' fluxes of sensible heat (with concordance correlation coefficient (CCC) of ≥0.87), latent energy (evapotranspiration; CCC ≥ 0.89), and useful correspondence in the net ecosystem exchange ((NEE); with CCC ≥ 0.4) at the daily temporal resolution. Relative to the conventional systems, the low‐frequency systems were characterized by a higher level of random error, particularly in the NEE fluxes. Lower‐cost systems can enable wider deployment affording better replication and sampling of spatiotemporal variability at the expense of greater measurement noise that might be limiting for certain applications. Replicated eddy covariance observations may be useful when addressing gaps in the existing monitoring of critical and underrepresented ecosystems and for measuring areas larger than a single flux footprint.

54 ENVIRONMENTAL SCIENCES↗

Simultaneous quantification of uranium( VI ), samarium, nitric acid, and temperature with combined ensemble learning, laser fluorescence, and Raman scattering for real-time monitoring

In this work, laser-induced fluorescence spectroscopy (LIFS), Raman spectroscopy, and a stacked regression ensemble was developed for near real-time quantification of uranium(VI) (1–100 μg mL –1 ), samarium (0–200 μg mL –1 ) and nitric acid (0.1–4 M) with varying temperature (20 °C–45 °C). LIFS applications range from fundamental lab-scale studies to real-time process monitoring at industrial levels, such as nuclear reprocessing applications, provided the phenomena affecting the fluorescence spectrum are accounted for (e.g., absorption, quenching, complexation). Multiple chemometric models were examined and compared to a more traditional multivariate regression approach called partial least squares (PLS). Results obtained on synthetic samples selected using D-optimal experimental design indicated that a stacked regression method, which included ridge regression, random forest, PLS, and an eXtreme gradient boost algorithm, successfully measured uranium(VI) concentrations directly in nitric acid without measuring luminescence lifetimes or standard addition. The top model resulted in percent root-mean-square error of prediction values of 5.2, 1.9, 3.0, and 2.3% for U(VI), Sm 3+ , HNO 3 , and temperature, respectively. The approach may be useful for quantifying fluorescent fission products (e.g., Sm 3+ ) to provide information on burnup of irradiated nuclear fuel. This novel framework reinforces the applicability of LIFS for real-time applications in nuclear fuel cycle applications.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Effects of mold geometry on fiber orientation of powder injection molded metal matrix composites

Fiber orientations in metal matrix composites have significant effect on improving tensile properties. Control of fiber orientations in metal injection molded metal composites is a difficult task. In this study, two mold cavities of dimensions 6x6x90 mm and 10x20x180 mm were used for comparison of fiber orientation in injection molded metal composites test parts. In both mold cavities, convergent and divergent flows were developed by modifying the sprue dimensions. Scanning electron microscope (SEM) was used to examine the fiber orientations within the test samples. The results showed highly aligned fiber in injection molded test bars developed from the convergent melt flow. Random orientation of fibers was noted in the composites test bars produced from divergent melt flow.

36 MATERIALS SCIENCE↗

Global sensitivity analysis in stochastic simulators of uncertain reaction networks

Stochastic models of chemical systems are often subjected to uncertainties in kinetic parameters in addition to the inherent random nature of their dynamics. Uncertainty quantification in such systems is generally achieved by means of sensitivity analyses in which one characterizes the variability with the uncertain kinetic parameters of the first statistical moments of model predictions. In this work, we propose an original global sensitivity analysis method where the parametric and inherent variability sources are both treated through Sobol’s decomposition of the variance into contributions from arbitrary subset of uncertain parameters and stochastic reaction channels. The conceptual development only assumes that the inherent and parametric sources are independent, and considers the Poisson processes in the random-time-change representation of the state dynamics as the fundamental objects governing the inherent stochasticity. Here, a sampling algorithm is proposed to perform the global sensitivity analysis, and to estimate the partial variances and sensitivity indices characterizing the importance of the various sources of variability and their interactions. The birth-death and Schlögl models are used to illustrate both the implementation of the algorithm and the richness of the proposed analysis method. The output of the proposed sensitivity analysis is also contrasted with a local derivative-based sensitivity analysis method classically used for this type of systems.

97 MATHEMATICS AND COMPUTING↗