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At least 1,747 records · Page 97

Theory of non-Gaussianity in warm inflation

The theory and methodology is developed to compute the bispectrum in warm inflation, leading to results for the non-linearity parameter and the shape of the bispectrum. Particular attention is paid to the study of the bispectrum in the regime of weak dissipation and how stochastic fluctuations affect the bispectrum. It is shown that, in contrast to the strong dissipative regime, the amplitude of non-Gaussianity is strongly dependent on the parameters governing the microscopic physics in the intermediate and weak dissipation warm inflation regimes. The most important results concern the shape of the bispectrum, which has two different, but distinct, forms in the weak and strong dissipative regimes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Investigation of Marangoni convection with high-fidelity simulations for metal melt pool dynamics

The goal of this research is to investigate and characterize the dynamics of a molten metal pool through modeling and simulation. Two manufacturing processes are of interest, laser spot welding and selective laser melting. These are laser-based techniques for joining parts together and for building up parts. The laser power impacts the melt pool temperature and therefore the dynamics. Moreover, the metals used are often alloys, containing impurities, where the concentration of these impurities can have a large effect on surface tension and therefore influence the melt pool dynamics. The application space considered in this project is for laser spot welding as a case study, and is also relevant to 3D metal printing. The thermal evolution and fluid dynamics in a 2D metal block exposed to a Gaussian distributed laser source is numerically simulated using a high-order, fully-implicit code. Results are compared to published experimental data and other published numerical simulations for laser spot welding. Results confirm that unstable structures appear at higher laser powers with higher impurity concentrations compared to simulations with no impurities and lower laser powers.

42 ENGINEERING↗

Lowest ionization potentials of Al2

Potential curves for the lowest two electronic states, X 2Sigma(+)g and A 2Pi(u), of Al2(+) were computed using complete active space SCF/multireference CI wave functions and large Gaussian basis sets. The lowest observable vertical ionization potential, to Al2(+) X 2Sigma(+)g, of the Al2 X 3 Pi(u) ground state is calculated to occur around 6.1 eV, in excellent agreement with the experimental range of 6.0 to 6.42 eV obtained in recent cluster ionization studies by Cox and co-workers. The second vertical ionization potential, to Al2(+) A 2Pi(u), occurs near 6.4 eV, also within the experimental range. The adiabatic IP of 5.90 eV is in good agreement with the value of 5.8 to 6.1 eV deduced by Hanley and co-workers from the difference in thresholds between collision induced dissociation processes of Al3(+). The computed IP values are somewhat larger than those deduced from branching ratios in cluster fragmentation experiments by Jarrold and co-workers. The observation of an ionization threshold below 6.42 eV is shown to be incompatible with an Al2 ground electronic state assignment of 3Sigma(-)g, but the separation between the two lowest states of Al2 is so small that it is likely that both are populated in the experiments, so that this does not provide unambiguous support for the recent theoretical assignment of the ground state as 3Pi(u).

Bauschlicher, Charles W., Jr.↗

SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrix is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of matrix operations on the Hankel matrix of moments. It can therefore be implemented without requiring prior knowledge about statistical data analysis or a detailed understanding of the mathematics of polynomial chaos expansions. The extension to more input variables suggested in this work, is an anisotropic and adaptive version of Smolyak's algorithm that is solely based on the moments of the input probability distributions. It is referred to as SAMBA (PC), which is short for Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos. It is illustrated that for moderately high-dimensional problems (up to 20 different input variables or histograms) SAMBA can significantly simplify the calculation of sparse Gaussian quadrature rules. SAMBA's efficiency for multivariate functions with regard to data availability is further demonstrated by analysing higher order convergence and accuracy for a set of nonlinear test functions with 2, 5 and 10 different input distributions or histograms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Necklace-structured high-harmonic generation for low-divergence, soft x-ray harmonic combs with tunable line spacing

The extreme nonlinear optical process of high-harmonic generation (HHG) makes it possible to map the properties of a laser beam onto a radiating electron wave function and, in turn, onto the emitted x-ray light. Bright HHG beams typically emerge from a longitudinal phased distribution of atomic-scale quantum antennae. Here, we form a transverse necklace-shaped phased array of linearly polarized HHG emitters, where orbital angular momentum conservation allows us to tune the line spacing and divergence properties of extreme ultraviolet and soft x-ray high-harmonic combs. The on-axis HHG emission has extremely low divergence, well below that obtained when using Gaussian driving beams, which further decreases with harmonic order. This work provides a new degree of freedom for the design of harmonic combs—particularly in the soft x-ray regime, where very limited options are available. Such harmonic beams can enable more sensitive probes of the fastest correlated charge and spin dynamics in molecules, nanoparticles, and materials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Image gathering and digital restoration for fidelity and visual quality

The fidelity and resolution of the traditional Wiener restorations given in the prevalent digital processing literature can be significantly improved when the transformations between the continuous and discrete representations in image gathering and display are accounted for. However, the visual quality of these improved restorations also is more sensitive to the defects caused by aliasing artifacts, colored noise, and ringing near sharp edges. In this paper, these visual defects are characterized, and methods for suppressing them are presented. It is demonstrated how the visual quality of fidelity-maximized images can be improved when (1) the image-gathering system is specifically designed to enhance the performance of the image-restoration algorithm, and (2) the Wiener filter is combined with interactive Gaussian smoothing, synthetic high edge enhancement, and nonlinear tone-scale transformation. The nonlinear transformation is used primarily to enhance the spatial details that are often obscurred when the normally wide dynamic range of natural radiance fields is compressed into the relatively narrow dynamic range of film and other displays.

Huck, Friedrich O.↗

Classifying Agnostic Biosignatures using Raman, VNIR, and Elemental Data

How can we use our current wealth of terrestrial data, encompassing biogenic and abiogenic systems, to determine the distinguishing properties of life? SCOBI (Statistical Classification of Biosignature Information) uses machine learning techniques to algorithmically identify combinations of measurements that are “indicative of life”. A set of ~1000 observations, comprising elemental abundance, isotopic fractionation, VNIR reflectance, and (in progress) Raman spectra, have been assembled from existing literature and databases. The observations cover systems classified as “indicative alive” (e.g., cells, vegetation), “indicative non-alive” (e.g., fossils, teeth), “mixed indicative” (e.g., soil, pond water), or “non-indicative” (e.g., rocks, meteorites). VNIR data was preprocessed by linear interpolation from 400-2100 nm and smoothed with a Savitzky-Golay filter. To limit the amount of Earth-biochemistry-specific (non-agnostic) information included, the first five spectral features extracted were number of peaks, number of troughs, mean reflectance, mean peak width, and broadest peak width. To help further emphasize agnostic biosignatures, Earth-specific features such as chlorophylls have been manually flagged so that feature importance with and without them can be compared. Classifiers including k-nearest neighbors (KNN), Gaussian Naïve Bayes (GNB), logistic regression (LR), random forest (RF), and support vector machine (SVM) were implemented, as was a combination voting classifier. Performance metrics included false positive rates, false negative rates, and AUC with 50-50 test/train splits (Monte Carlo simulations). Key takeaways from this stage, prior to the inclusion of Raman spectra, are (1) the overall success rate of 0.933 AUC was most heavily influenced by the elemental abundance data; and (2) VNIR reflectance had the lowest classification performance with 0.52 AUC (58% of objects correctly classified). The next steps are to complete integration of Raman spectral data and to improve the approach to pre-processing and feature extraction for both types of spectral data, such as automated baseline removal, whole spectrum matching, and dimensionality reduction.

Biosignatures↗

Explicit Backscattering Coefficient for Ultrasonic Wave Propagating in Hexagonal Polycrystals with Fiber Texture

Hexagonal polycrystalline materials such as titanium, zirconium and magnesium are common in engineering structures like car bodies and airplane engines. These components are usually specially designed in microstructure level to guarantee desired mechanical properties, so microstructure characterization is of great importance to the optimization of manufacturing processes. Compared with traditional destructive characterization methods like scanning electron microscopy (SEM), the ultrasonic approach is nondestructive and cost-effective. Although some progress has been made in ultrasonic microstructure characterization of polycrystal aggregates of hexagonal grains, some factors like macro texture and grain size distribution associated with realistic microstructures were not accounted for yet. Targeting one common texture component for hexagonal polycrystalline materials, {0001} basal fiber texture, this paper derived the explicit backscattering coefficient for aggregates of ellipsoidal grains through one texture parameter and obtained an analytical backscattering coefficient for microstructures with various grain size distributions. In this study, the basal fiber texture was quantified by the 1D Gaussian orientation distribution function (ODF), which merely includes one texture parameter, and its relationship with generalized spherical harmonics ODF was also addressed. Moreover, explicit expressions for effective elastic moduli and elastic constant covariances were derived. Furthermore, some computational examples were given to demonstrate the impacts of texture, frequency, grain geometry and grain size distribution on backscattering behavior. The theoretical results in this study will greatly benefit the later ultrasonic microstructure characterization of hexagonal polycrystalline materials.

42 ENGINEERING↗

The lowest ionization potentials of Al2

Potential curves for the lowest two electronic states (X 2 sigma g + and A 2 pi u) of Al2(+) were computed using complete active space SCF/multireference CI wave functions and large Gaussian basis sets. The lowest observable vertical ionization potential (to Al2(+) X 2 sigma g +) of the Al2 X 3 pi u ground state is calculated to occur around 6.1 eV, in excellent agreement with the experimental range of 6.0 to 6.42 eV obtained in recent cluster ionization studies by Cox and co-workers. The second vertical ionization potential (to Al2(+) A 2 pi u) occurs near 6.4 eV, also within the experimental range. The adiabatic IP of 5.90 eV is in good agreement with the value of 5.8 to 6.1 eV deduced by Hanley and co-workers from the difference in thresholds between collision induced dissociation processes of Al3(+). The computed IP values are somewhat larger than those deduced from branching ratios in cluster fragmentation experiments by Jarrold and co-workers. The observation of an ionization threshold below 6.42 eV is shown to be incompatible with an Al2 ground electronic state assignment of 3 sigma g -, but the separation between the two lowest states of Al2 is so small that it is likely that both are populated in the experiments, so that this does not provide unambiguous support for the recent theoretical assignment of the ground state as 3 pi u.

Bauschlicher, Charles W., Jr.↗

Dimension-independent likelihood-informed MCMC

Many Bayesian inference problems require exploring the posterior distribution of high-dimensional parameters that represent the discretization of an underlying function. This work introduces a family of Markov chain Monte Carlo (MCMC) samplers that can adapt to the particular structure of a posterior distribution over functions. Two distinct lines of research intersect in the methods developed here. First, we introduce a general class of operator-weighted proposal distributions that are well defined on function space, such that the performance of the resulting MCMC samplers is independent of the discretization of the function. Second, by exploiting local Hessian information and any associated low-dimensional structure in the change from prior to posterior distributions, we develop an inhomogeneous discretization scheme for the Langevin stochastic differential equation that yields operator-weighted proposals adapted to the non-Gaussian structure of the posterior. The resulting dimension-independent and likelihood-informed (DILI) MCMC samplers may be useful for a large class of high-dimensional problems where the target probability measure has a density with respect to a Gaussian reference measure. Two nonlinear inverse problems are used to demonstrate the efficiency of these DILI samplers: an elliptic PDE coefficient inverse problem and path reconstruction in a conditioned diffusion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Evolution of the proton velocity distribution due to stochastic heating in the near-sun solar wind

We investigate how the proton distribution function evolves when the protons undergo stochastic heating by strong, low-frequency, Alfvén-wave turbulence under the assumption that β is small. We apply our analysis to protons undergoing stochastic heating in the supersonic fast solar wind and obtain proton distributions at heliocentric distances ranging from 4 to 30 solar radii. We find that the proton distribution develops non-Gaussian structure with a flat core and steep tail. For r>5 R{sub S}, the proton distribution is well approximated by a modified Moyal distribution. Comparisons with future measurements from Solar Probe Plus could be used to test whether stochastic heating is occurring in the solar-wind acceleration region.

79 ASTRONOMY AND ASTROPHYSICS↗

The Dynamic of Complex Two-Phase Mixtures During Coarsening: From Dendritic to Bicontinuous Mixtures

Dendrites are tree-like crystals that frequently form during the solidification of castings. In systems with nearly isotropic interfacial energy, these dendrites possess secondary and sometimes even tertiary arms, and lead to morphologically complex two-phase mixtures. Dealloying, in which one component is selectively leached, leads to nanoporous structures that have proven useful for many technological applications. These bicontinuous two-phase mixtures are topologically and morphologically complex with spatially varying mean and Gaussian curvatures. The evolution of these structures during coarsening is of considerable technological importance since the morphology of the dendrites and nanoporous structure sets the properties of the resulting material. During coarsening, the total surface area per volume of the mixture decreases, thus resulting in an increase in the size-scale of the two-phase mixture. The evolution of interfacial morphology of these interconnected two-phase mixtures is being studied using large-scale computer simulations. The simulations are used to develop a theory of coarsening in these systems that will elucidate the impact of the complicated morphology found in dendritic and nanoporous systems on the coarsening process. The experiments employ four-dimensional X-ray microtomography, which enables the morphology of the two-phase mixture to be followed in three dimensions and time (an additional dimension). The experiments also serve as a test of simulations and theory of the coarsening process, as well as to provide initial conditions for the simulations. Through these experiments and theory, we aim to develop a comprehensive description of coarsening in these complex and technologically important two-phase mixtures.

36 MATERIALS SCIENCE↗

Improved renormalization group computation of likelihood functions for cosmological data sets

Evaluation of likelihood functions for cosmological large scale structure data sets (including CMB, galaxy redshift surveys, etc.) naturally involves marginalization, i.e., integration, over an unknown underlying random signal field. Recently, I showed how a renormalization group method can be used to carry out this integration efficiently by first integrating out the smallest scale structure, i.e., localized structure on the scale of differences between nearby data cells, then combining adjacent cells in a coarse graining step, then repeating this process over and over until all scales have been integrated. Here I extend the formulation in several ways in order to reduce the prefactor on the method's linear scaling with data set size. The key improvement is showing how to integrate out the difference between specific adjacent cells before summing them in the coarse graining step, compared to the original formulation in which small-scale fluctuations were integrated more generally. I suggest some other improvements in details of the scheme, including showing how to perform the integration around a maximum likelihood estimate for the underlying random field. In the end, an accurate likelihood computation for a million-cell Gaussian test data set runs in two minutes on my laptop, with room for further optimization and straightforward parallelization.

79 ASTRONOMY AND ASTROPHYSICS↗

Causality constraints on corrections to the graviton three-point coupling

In this paper, we consider higher derivative corrections to the graviton three-point coupling within a weakly coupled theory of gravity. Lorentz invariance allows further structures beyond the one present in the Einstein theory. We argue that these are constrained by causality. We devise a thought experiment involving a high energy scattering process which leads to causality violation if the graviton three-point vertex contains the additional structures. This violation cannot be fixed by adding conventional particles with spins J ≤ 2. But, it can be fixed by adding an in finite tower of extra massive particles with higher spins, J > 2. In AdS theories this implies a constraint on the conformal anomaly coefficients |$\frac{a-c}{c}$|≲ $\frac{1}{2}$ ${^Δ}_{gap}$ in terms of Δgap, the dimension of the lightest single trace operator with spin J > 2. Lastly, for inflation, or de Sitter-like solutions, it indicates the existence of massive higher spin particles if the gravity wave non-gaussianity deviates significantly from the one computed in the Einstein theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Intensity Conserving Spectral Fitting

The detailed shapes of spectral line profiles provide valuable information about the emitting plasma, especially when the plasma contains an unresolved mixture of velocities, temperatures, and densities. As a result of finite spectral resolution, the intensity measured by a spectrometer is the average intensity across a wavelength bin of non-zero size. It is assigned to the wavelength position at the center of the bin. However, the actual intensity at that discrete position will be different if the profile is curved, as it invariably is. Standard fitting routines (spline, Gaussian, etc.) do not account for this difference, and this can result in significant errors when making sensitive measurements. Detection of asymmetries in solar coronal emission lines is one example. Removal of line blends is another. We have developed an iterative procedure that corrects for this effect. It can be used with any fitting function, but we employ a cubic spline in a new analysis routine called Intensity Conserving Spline Interpolation (ICSI). As the name implies, it conserves the observed intensity within each wavelength bin, which ordinary fits do not. Given the rapid convergence, speed of computation, and ease of use, we suggest that ICSI be made a standard component of the processing pipeline for spectroscopic data.

Klimchuk, J. A.↗

ENTROPY VS. ENERGY WAVEFORM PROCESSING: A COMPARISON ON THE HEAT EQUATION

Virtually all modern imaging devices function by collecting either electromagnetic or acoustic backscattered waves and using the energy carried by these waves to determine pixel values that build up what is basically an ”energy” picture. However, waves also carry ”informa- tion” that also may be used to compute the pixel values in an image. We have employed several measures of information, all of which are based on different forms of entropy. Numerous published studies have demonstrated the advantages of entropy, or “information imaging”, over conventional methods for materials characterization and medical imaging. Similar results also have been obtained with microwaves. The most sensitive information measure appears to be the joint entropy of the backscattered wave and a reference signal. A typical study is comprised of repeated acquisition of backscattered waves from a specimen that is changing slowing with acquisition time or location. The sensitivity of repeated experimental observations of such a slowly changing quantity may be defined as the mean variation (i.e., observed change) divided by mean variance (i.e., observed noise). We compute the sensitivity for joint entropy and signal energy measurements assuming that noise is Gaussian and using Wiener integration to compute the required mean values and variances. These can be written as solutions to the Heat equation, which permits estimation of their magnitudes. There always exists a reference such that joint entropy has larger variation and smaller variance than the corresponding quantities for signal energy, matching observations of several studies. Moreover, a general prescription for finding an “optimal” reference for the joint entropy emerges, which also has been validated in several studies.

Entropy↗

Fourth-order partial differential equation noise removal on welding images

Partial differential equation (PDE) has become one of the important topics in mathematics and is widely used in various fields. It can be used for image denoising in the image analysis field. In this paper, a fourth-order PDE is discussed and implemented as a denoising method on digital images. The fourth-order PDE is solved computationally using finite difference approach and then implemented on a set of digital radiographic images with welding defects. The performance of the discretized model is evaluated using Peak Signal to Noise Ratio (PSNR). Simulation is carried out on the discretized model on different level of Gaussian noise in order to get the maximum PSNR value. The convergence criteria chosen to determine the number of iterations required is measured based on the highest PSNR value. Results obtained show that the fourth-order PDE model produced promising results as an image denoising tool compared with median filter.

42 ENGINEERING↗

A New Criterion to Improve Operational Drizzle Detection with Ground-Based Remote Sensing

Light shallow precipitation in the form of drizzle is one of the mechanisms for liquid water removal, affecting cloud lifetime and boundary layer dynamics and thermodynamics. The early formation of drizzle drops is of particular interest for quantifying aerosol–cloud–precipitation interactions. In models, drizzle initiation is represented by the autoconversion, that is, the conversion of liquid water from a cloud liquid water category (where particle sedimentation is ignored) into a precipitating liquid water category. Various autoconversion parameterizations have been proposed in recent years, but their evaluation is challenging due to the lack of proper observations of drizzle development in the cloud. This work presents a new algorithm for Classification of Drizzle Stages (CLADS). CLADS is based on the skewness of the Ka-band radar Doppler spectrum. Skewness is sensitive to the drizzle growth in the cloud: the observed Gaussian Doppler spectrum has skewness zero when only cloud droplets are present without any significant fall velocity. Defining downward velocities positive, skewness turns positive when embryonic drizzle forms and becomes negative when drizzle starts to dominate the spectrum. CLADS identifies spatially coherent structures of positive, zero, and negative skewness in space and time corresponding to drizzle seeding, drizzle growth/nondrizzle, and drizzle mature, respectively. We test CLADS on case studies from the Jülich Observatory for Cloud Evolution Core Facility (JOYCE-CF) and the Barbados Cloud Observatory (BCO) to quantitatively estimate the benefits of CLADS compared to the standard Cloudnet target categorization algorithm. We suggest that CLADS can provide additional observational constraints for understanding the processes related to drizzle formation better.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗