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At least 955 records · Page 53

Scattering from mirrors contaminated by particulates - A model

A model has been used to fit the bidirectional reflectance distribution function for a variety of samples with different angles of incidence and degrees of contamination and roughness by the proper adjustment of six parameters. Exponential and Gaussian composite surface height autocorrelation functions are used to simulate the data at the small and medium angles, and a perturbation of these functions with two additional parameters allows the fit of the upward and downward curve portions of the data at the large angles. Good agreement is found with previous results. The present approach is the same as the classical dispersion equation in treating the index of refraction of optical materials.

Wang, Yaujen↗

On hierarchical solutions to the BBGKY hierarchy

It is thought that the gravitational clustering of galaxies in the universe may approach a scale-invariant, hierarchical form in the small separation, large-clustering regime. Past attempts to solve the Born-Bogoliubov-Green-Kirkwood-Yvon (BBGKY) hierarchy in this regime have assumed a certain separable hierarchical form for the higher order correlation functions of galaxies in phase space. It is shown here that such separable solutions to the BBGKY equations must satisfy the condition that the clustered component of the solution has cluster-cluster correlations equal to galaxy-galaxy correlations to all orders. The solutions also admit the presence of an arbitrary unclustered component, which plays no dyamical role in the large-clustering regime. These results are a particular property of the specific separable model assumed for the correlation functions in phase space, not an intrinsic property of spatially hierarchical solutions to the BBGKY hierarchy. The observed distribution of galaxies does not satisfy the required conditions. The disagreement between theory and observation may be traced, at least in part, to initial conditions which, if Gaussian, already have cluster correlations greater than galaxy correlations.

Hamilton, A. J. S.↗

Calculation of the binomial survivor function

A method is presented for calculating the binomial SF (cumulative binomial distribution), binfc(k;p,n), especially for a large n, beyond the range of existing tables, where conventional computer programs fail because of underflow and overflow, and Gaussian or Poisson approximations yield insufficient accuracy for the purpose at hand. This method is used to calculate and sum the individual binomial terms while using multiplication factors to avoid underflow; the factors are then divided out of the partial sum whenever it has the potential to overflow. A computer program uses this technique to calculate the binomial SF for arbitrary inputs of k, p, and n. Two other algorithms are presented to determine the value of p needed to yield a specified SF for given values of k and n and calculate the value where p = SF for a given k and n. Reliability applications of each algorithm/program are given, e.g., the value of p needed to achieve a stated k-out-of-n:G system reliability and the value of p for which k-out-of-n:G system reliability equals p.

Bowerman, Paul N.↗

Adaptive methods of generating complex light arrays

Structured light arrays of various shapes have been a cornerstone in optical science, driven by the complexities of precise and adaptable generation. This study introduces an approach using a spatial light modulator (SLM) as a generator for these arrays. By projecting a holographic mask onto the SLM, it functions simultaneously as an optical convolution device, focusing mechanism, and structured light beam mask. Our approach offers unmatched versatility, allowing for the experimental fabrication of traditional beam arrays like azimuthal Laguerre–Gaussian (LG), Bessel–Gaussian (BG), and Hermite–Gauss (HG) in the far-field. Notably, it has enabled a method of generating Ince–Gauss (IG) and LG radial mode beam arrays using a convolution solution. Our system provides exceptional control over array periodicity and intensity distribution, bypassing the Talbot self-imaging phenomenon seen in traditional setups. We provide an in-depth theoretical discussion, supported by empirical evidence, of our far-field results. This method has vast potential for applications in optical communication, data processing, and multi-particle manipulation. It paves the way for rapid generation of structured light with high spatial frequencies and complex shapes, promising transformative advances in these domains.

Optics↗

Bayesian model updating with finite element vs surrogate models: Application to a miter gate structural system

Bayesian finite element (FE) model updating using direct model evaluations of large-scale high-fidelity FE models is extremely computationally expensive. Surrogate models can be used as fast emulators of FE models to accelerate the model calibration process. The physics/mechanics-based FE models are still the underpinning behind the surrogate models. Here, this paper evaluates the loss in accuracy and the gain in computational time while performing Bayesian model updating by using surrogate model evaluations compared to using direct FE model evaluations. This evaluation is crucial before entirely relying on surrogate models in model updating for structural health monitoring (SHM) and damage prognosis (DP) purposes. This paper also demonstrates Bayesian updating and surrogate model construction of large-scale high-fidelity FE models of infrastructure systems. In this regard, the miter gate structural system is considered as the testbed structure. Three predominant damage modes (loss of contact between gate and wall, loss of thickness due to corrosion, and loss of tension in the diagonal rods) are considered for model updating purposes. Bayesian model updating is performed using direct FE evaluations by leveraging parallel computing. Two types of surrogates, namely polynomial chaos expansion (PCE) and Gaussian process regression (GPR), are developed for the miter gate. Model updating is performed again using the trained surrogate models, and the updating results are compared with their counterparts obtained using the direct FE evaluation results. The posterior distribution of the FE model parameters obtained using the trained surrogates are sufficiently accurate with respect to the posterior obtained utilizing the direct FE evaluations. In addition, an approximate 4-fold decrease in the computational time was observed when using surrogate model evaluations instead of direct FE evaluations for model updating.

42 ENGINEERING↗

Dark energy survey year 3 results: likelihood-free, simulation-based w CDM inference with neural compression of weak-lensing map statistics

We present simulation-based cosmological wcold dark matter (wCDM) inference using dark energy survey year 3 weak-lensing maps, via neural data compression of weak-lensing map summary statistics: power spectra, peak counts, and direct map-level compression/inference with convolutional neural networks (CNN). Using simulation-based inference, also known as likelihood-free or implicit inference, we use forward-modelled mock data to estimate posterior probability distributions of unknown parameters. This approach allows all statistical assumptions and uncertainties to be propagated through the forward-modelled mock data; these include sky masks, non-Gaussian shape noise, shape measurement bias, source galaxy clustering, photometric redshift uncertainty, intrinsic galaxy alignments, non-Gaussian density fields, neutrinos, and non-linear summary statistics. We include a series of tests to validate our inference results. This paper also describes the Gower Street simulation suite: 791 full-sky pkdgrav3 dark matter simulations, with cosmological model parameters sampled with a mixed active-learning strategy, from which we construct over 3000 mock dark energy survey lensing data sets. For wCDM inference, for which we allow –1 < w < –$\frac{1}{3}$⁠, our most constraining result uses power spectra combined with map-level (CNN) inference. Using gravitational lensing data only, this map-level combination gives Ω m = 0.283$^{+0.020}_{–0.027}$⁠, S 8 = 0.804$^{+0.025}_{–0.017⁠}$, and w < –0.80 (with a 68 per cent credible interval); compared to the power spectrum inference, this is more than a factor of two improvement in dark energy parameter (Ω⁠ DE , w⁠) precision.

79 ASTRONOMY AND ASTROPHYSICS↗

Probabilistic Data Association for Orbital-Element Estimation Using Multistage Expectation–Maximization

Tracking space objects is important for managing space traffic and predicting collisions, but is difficult in part due to data association and orbit model uncertainty. Expectation–maximization (EM) is a commonly used tracking method that has not been widely considered for tracking space objects. The technique consists of iteratively computing data association probabilities with a set of current element estimates, and updating estimates of the elements by solving a nonlinear weighted least-squares regression problem where the weights are the data association probabilities. In this paper, we demonstrate the use of EM for probabilistic data association and orbital-element estimation by applying the technique to simulated data from two angles-only tracking scenarios. In both scenarios, EM provides correct data associations and accurate maximum likelihood estimates of orbital elements. One scenario considers tracking a single object in clutter and quantifies the improvement of the orbital-element estimates and data associations as the detection probability increases. However, standard application of EM requires knowing the number of objects or may fail when a large number of objects are present. To address these issues, this paper employs a multistage version of EM that is applicable when there are a large and possibly unknown number of objects.

97 MATHEMATICS AND COMPUTING↗

The reflection of impulses from a nonlinear random sea

A model of the reflection of radar impulses from the sea at near-vertical incidence is used to account for non-Gaussian ocean waves statistics. The joint probability density function (pdf), of wave height and slope, is calculated according to the theory of Longuet-Higgins (1963) on the distribution of variables in a 'weakly nonlinear' random era. The long-crested approximation is made, a Phillips wave spectrum is assumed, and the Gram-Charlier series is truncated after skewness terms. It is found that the height and height-slope skewness coefficients bear the ratio 1:2 and that the derived impulse response and conditional cross section versus wave height are in excellent agreement with previous observations. Finally, it is suggested that the empirically determined and theoretically predicted sea state bias be corrected for in the routine processing of satellite radar altimeter data.

Jackson, F. C.↗

A hill-sliding strategy for initialization of Gaussian clusters in the multidimensional space

A hill sliding technique was devised to extract Gaussian clusters from the multivariate probability density estimate of sample data for the first step of iterative unsupervised classification. Each cluster was assumed to posses a unimodal normal distribution. A clustering function proposed distinguished elements of a cluster under formation from the rest in the feature space. Initial clusters were extracted one by one according to the hill sliding tactics. A dimensionless cluster compactness parameter was proposed as a universal measure of cluster goodness and used satisfactorily in test runs with LANDSAT multispectral scanner data. The normalized divergence, defined by the cluster divergence divided by the entropy of the entire sample data, was utilized as a general separability measure between clusters. An overall clustering objective function was set forth in terms of cluster covariance matrices, from which the cluster compactness measure could be deduced. Minimal improvement of initial data partitioning was evaluated by this objective function in eliminating scattered sparse data points. The hill sliding clustering technique developed herein has the potential applicability to decomposition any multivariate mixture distribution into a number of unimodal distributions when an appropriate distribution function to the data set is employed.

Park, J. K.↗

Preliminary fatigue tests on short-crack specimens

The objective of the preliminary fatigue tests was to determine the stress levels to be used by the participants in the Cooperative Test Program. As previously mentioned, the United States Air Force Wright-Patterson Aeronautical Laboratory machined about 700 single-edge-notched tension (SENT) specimens from material supplied by the NASA Langley Research Center. In addition, NASA Langley machined about 50 SENT specimens from the same material. Comparison of fatigue tests conducted on the two sets of specimens indicated a large difference in fatigue behavior under constant-amplitude loading. A recovery program was initiated to resolve this difference before the specimens were distributed to participants. The following sections describe the recovery program and the preliminary fatigue tests and analyses conducted to determine stress levels for constant-amplitude, FALSTAFF, and Gaussian loading.

Newman, J. C., Jr.↗

Transient cooling of a square region of radiating medium

A time-accurate numerical solution was carried out for transient radiative cooling of a gray emitting and absorbing medium in a square two-dimensional region. The integro-differential energy equation for transient temperature distributions was solved in two stages. At each time increment, the local radiative source term was obtained by numerical integration of the temperature field using two-dimensional Gaussian integration over rectangular subregions. Then the differential portion of the equation was integrated forward in time by use of the local first and second time derivatives. The results were compared with available limiting case, and excellent agreement was obtained. Transient results are given for a wide range of optical thicknesses of the region. Optimum transient cooling is obtained when the optical side length is about 4.

Siegel, Robert↗

Control Law Synthesis for Vertical Fin Buffeting Alleviation Using Strain Actuation

In the present investigation, the results obtained during the ground test of a closed-loop control system conducted on a full-scale fighter to attenuate vertical fin buffeting response using strain actuation are presented. Two groups of actuators consisting of piezoelectric elements distributed over the structure were designed to achieve authority over the first and second modes of the vertical fin. The control laws were synthesized using the Linear Quadratic Gaussian (LQG) method for a time-invariant control system. Three different pairs of sensors including strain gauges and accelerometers at different locations were used to close the feedback loop. The results demonstrated that measurable reductions in the root-mean-square (RMS) values of the fin dynamic response identified by the strain transducer at the critical point for fatigue at the root were achieved under the most severe buffet condition. For less severe buffet conditions, reductions of up to 58% were achieved.

Nitzsche, F.↗

Guidance and Control System for a Satellite Constellation

A distributed guidance and control algorithm was developed for a constellation of satellites. The system repositions satellites as required, regulates satellites to desired orbits, and prevents collisions. 1. Optimal methods are used to compute nominal transfers from orbit to orbit. 2. Satellites are regulated to maintain the desired orbits once the transfers are complete. 3. A simulator is used to predict potential collisions or near-misses. 4. Each satellite computes perturbations to its controls so as to increase any unacceptable distances of nearest approach to other objects. a. The avoidance problem is recast in a distributed and locally-linear form to arrive at a tractable solution. b. Plant matrix values are approximated via simulation at each time step. c. The Linear Quadratic Gaussian (LQG) method is used to compute perturbations to the controls that will result in increased miss distances. 5. Once all danger is passed, the satellites return to their original orbits, all the while avoiding each other as above. 6. The delta-Vs are reasonable. The controller begins maneuvers as soon as practical to minimize delta-V. 7. Despite the inclusion of trajectory simulations within the control loop, the algorithm is sufficiently fast for available satellite computer hardware. 8. The required measurement accuracies are within the capabilities of modern inertial measurement devices and modern positioning devices.

Bryson, Jonathan Lamar↗

Large-Eddy Simulation of Flow Over Boeing Gaussian Bump Using Multiagent Reinforcement Learning Wall Model: Preprint

We develop a wall model for large-eddy simulation (LES) that takes into account various pressure-gradient effects using multi-agent reinforcement learning. The model is trained using low-Reynolds-number flow over periodic hills with agents distributed on the wall at various computational grid points. It utilizes a wall eddy-viscosity formulation as the boundary condition to apply the modeled wall shear stress. Each agent receives states based on local instantaneous flow quantities at an off-wall location, computes a reward based on the estimated wall-shear stress, and provides an action to update the wall eddy viscosity at each time step. The trained wall model is validated in wall-modeled LES of flow over periodic hills at higher Reynolds numbers, and the results show the effectiveness of the model on flow with pressure gradients. The analysis of the trained model indicates that the model is capable of distinguishing between the various pressure gradient regimes present in the flow. To further assess the robustness of the developed wall model, simulations of flow over the Boeing Gaussian bump are conducted at a Reynolds number of 2 x 10^6, based on the free-stream velocity and the bump width. The results of mean skin friction and pressure on the bump surface, as well as the velocity statistics of the flow field, are compared to those obtained from equilibrium wall model (EQWM) simulations and published experimental data sets. The developed wall model is found to successfully capture the acceleration and deceleration of the turbulent boundary layer on the bump surface, providing better predictions of skin friction near the bump peak and exhibiting comparable performance to the EQWM with respect to the wall pressure and velocity field. We also conclude that the subgrid-scale model is crucial to the accurate prediction of the flow field, in particular the prediction of separation.

boundary layer↗

Stochastic Inflation at NNLO

Stochastic Inflation is an important framework for understanding the physics of de Sitter space and the phenomenology of inflation. In the leading approximation, this approach results in a Fokker-Planck equation that calculates the probability distribution for a light scalar field as a function of time. Despite its successes, the quantum field theoretic origins and the range of validity for this equation have remained elusive, and establishing a formalism to systematically incorporate higher order effects has been an area of active study. In this paper, we calculate the next-to-next-to-leading order (NNLO) corrections to Stochastic Inflation using Soft de Sitter Effective Theory (SdSET). In this effective description, Stochastic Inflation manifests as the renormalization group evolution of composite operators. The leading impact of non-Gaussian quantum fluctuations appears at NNLO, which is presented here for the first time; we derive the coefficient of this term from a two-loop anomalous dimension calculation within SdSET. We solve the resulting equation to determine the NNLO equilibrium distribution and the low-lying relaxation eigenvalues. In the process, we must match the UV theory onto SdSET at one-loop order, which provides a non-trivial confirmation that the separation into Wilson-coefficient corrections and contributions to initial conditions persists beyond tree level. Furthermore, these results illustrate how the naive factorization of time and momentum integrals in SdSET no longer holds in the presence of logarithmic divergences. It is these effects that ultimately give rise to the renormalization group flow that yields Stochastic Inflation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

From Femtoseconds to Gigaseconds: The SolDeg Platform for the Performance Degradation Analysis of Silicon Heterojunction Solar Cells

Heterojunction Si solar cells exhibit notable performance degradation. Here, we modeled this degradation by electronic defects getting generated by thermal activation across energy barriers over time. To analyze the physics of this degradation, we developed the SolDeg platform to simulate the dynamics of electronic defect generation. First, femtosecond molecular dynamics simulations were performed to create a-Si/c-Si stacks, using the machine learning-based Gaussian approximation potential. Second, we created shocked clusters by a cluster blaster method. Third, the shocked clusters were analyzed to identify which of them supported electronic defects. Fourth, the distribution of energy barriers that control the generation of these electronic defects was determined. Fifth, an accelerated Monte Carlo method was developed to simulate the thermally activated time-dependent defect generation across the barriers. Our main conclusions are as follows. (1) The degradation of a-Si/c-Si heterojunction solar cells via defect generation is controlled by a broad distribution of energy barriers. (2) We developed the SolDeg platform to track the microscopic dynamics of defect generation across this wide barrier distribution and determined the time-dependent defect density N(t) from femtoseconds to gigaseconds, over 24 orders of magnitude in time. (3) We have shown that a stretched exponential analytical form can successfully describe the defect generation N(t) over at least 10 orders of magnitude in time. (4) We found that in relative terms, Voc degrades at a rate of 0.2%/year over the first year, slowing with advancing time. (5) We developed the time correspondence curve to calibrate and validate the accelerated testing of solar cells. We found a compellingly simple scaling relationship between accelerated and normal times t normal ∝ t accel T(accel)/T(normal) . (6) We also carried out experimental studies of defect generation in a-Si:H/c-Si stacks. We found a relatively high degradation rate at early times that slowed considerably at longer time scales.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Strong-field QED limitations on TeV-class plasma wakefield accelerators

We demonstrate that quantum and classical radiation effects can become non-negligible for TeV-class beams propagating through plasma channels typical of staged plasma accelerators. Although the quantum nonlinearity parameter χ e remains small under currently envisioned experimental conditions, the cumulative influence of radiation over long acceleration distances can lead to significant modifications to the beam’s energy spread, emittance, and polarization. Our analytic models, validated by particle-in-cell simulations, highlight that for standard Gaussian beams, the orbit-induced energy spread dominates over quantum stochastic effects but can be mitigated by tailoring the beam profile, for example, through ring-shaped transverse distributions. In regimes where the radiation reaction approaches the accelerating force, the emittance may be cooled, forming distinctive ring-shaped phase-space structures. Finally, we analyze the influence of the radiation effect on spin transport inside the wakefield. These findings underscore the importance of considering both classical and quantum radiation dynamics in the design and optimization of future high-intensity plasma accelerators.

accelerator↗

Hydrodynamic fluctuations near a Hopf bifurcation: Stochastic onset of vortex shedding behind a circular cylinder

Here, we investigate hydrodynamic fluctuations in the flow past a circular cylinder near the critical Reynolds number Re c for the onset of vortex shedding. Starting from the fluctuating Navier-Stokes equations, we perform a perturbation expansion around Re c to derive analytical expressions for the statistics of the fluctuating lift force. Molecular-level simulations using the direct simulation Monte Carlo method support the theoretical predictions of the lift power spectrum and amplitude distribution. Notably, we have been able to collect sufficient statistics at distances Re ⁡/ Re c – 1 = O ⁡(10 –3 ) from the instability that confirm the appearance of non-Gaussian fluctuations, and we observe that they are associated with intermittent vortex shedding. These results emphasize how unavoidable thermal-noise-induced fluctuations become dramatically amplified in the vicinity of oscillatory flow instabilities and that their onset is fundamentally stochastic.

42 ENGINEERING↗