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Methods for calculating the statistical significance of excess events and the interpretation of the formally derived values are discussed. It is argued that a simple formula for a conservative estimate should generally be used in order to provide a common understanding of quoted values.
In the Probabilistic Finite Element Method (PFEM), finite element methods have been efficiently combined with second-order perturbation techniques to provide an effective method for informing the designer of the range of response which is likely in a given problem. The designer must provide as input the statistical character of the input variables, such as yield strength, load magnitude, and Young's modulus, by specifying their mean values and their variances. The output then consists of the mean response and the variance in the response. Thus the designer is given a much broader picture of the predicted performance than with simply a single response curve. These methods are applicable to a wide class of problems, provided that the scale of randomness is not too large and the probabilistic density functions possess decaying tails. By incorporating the computational techniques we have developed in the past 3 years for efficiency, the probabilistic finite element methods are capable of handling large systems with many sources of uncertainties. Sample results for an elastic-plastic ten-bar structure and an elastic-plastic plane continuum with a circular hole subject to cyclic loadings with the yield stress on the random field are given.
The recognition of material resources on a planetary surface requires exploration strategies not dissimilar to those employed by early field geologists who searched for ore deposits primarily from surface clues. In order to determine the location of mineral ores or other materials, it will be necessary to characterize host terranes at regional or subregional scales. This requires geographically broad surveys in which statistically significant numbers of samples are rapidly scanned from a roving platform. To enable broad-scale, yet power-conservative planetary-surface exploration, we are developing an instrument that combines x-ray diffractometry (XRD), x-ray fluorescence spectrometry (XRF), and optical capabilities; the instrument can be deployed at the end of a rover's robotic arm, without the need for sample capture or preparation. The instrument provides XRD data for identification of mineral species and lithological types; diffractometry of minerals is conducted by ascertaining the characteristic lattice parameters or "d-spacings" of mineral compounds. D-spacings of 1.4 to 25 angstroms can be determined to include the large molecular structures of hydrated minerals such as clays. The XRF data will identify elements ranging from carbon (Atomic Number = 6) to elements as heavy as barium (Atomic Number = 56).
The recognition of material resources on a planetary surface requires exploration strategies not dissimilar to those employed by early field geologists who searched for ore deposits primarily from surface clues. In order to determine the location of mineral ores or other materials, it will be necessary to characterize host terranes at regional or subregional scales. This requires geographically broad surveys in which statistically significant numbers of samples are rapidly scanned from a roving platform. To enable broad-scale, yet power-conservative planetary-surface exploration, we are developing an instrument that combines x-ray diffractometry (XRD), x-ray fluorescence spectrometry (XRF), and optical capabilities; the instrument can be deployed at the end of a rover's robotic arm, without the need for sample capture or preparation. The instrument provides XRD data for identification of mineral species and lithological types; diffractometry of minerals is conducted by ascertaining the characteristic lattice parameters or "d-spacings" of mineral compounds. D-spacings of 1.4 to 25 angstroms can be determined to include the large molecular structures of hydrated minerals such as clays. The XRF data will identify elements ranging from carbon (Atomic Number = 6) to elements as heavy as barium (Atomic Number = 56). While a sample is being x-rayed, the instrument simultaneously acquires an optical image of the sample surface at magnifications from lx to at least 50x (200x being feasible, depending on the sample surface). We believe that imaging the sample is extremely important as corroborative sample-identification data (the need for this capability having been illustrated by the experience of the Pathfinder rover). Very few geologists would rely on instrument data for sample identification without having seen the sample. Visual inspection provides critical recognition data such as texture, crystallinity, granularity, porosity, vesicularity, color, lustre, opacity, and so forth. These data can immediately distinguish sedimentary from igneous rocks, for example, and can thus eliminate geochemical or mineral ambiguities arising, say between arkose and granite. It would be important to know if the clay being analyzed was part of a uniform varve deposit laid down in a quiescent lake, or the matrix of a megabreccia diamictite deposited as a catastrophic impact ejecta blanket. The unique design of the instrument, which combines Debye-Scherrer geometry with elements of standard goniometry, negates the need for sample preparation of any kind, and thus negates the need for power-hungry and mechanically-complex sampling systems that would have to chip, crush, sieve, and mount the sample for x-ray analysis. Instead, the instrument is simply rested on the sample surface of interest (like a hand lens); the device can interrogate rough rock surfaces, coarse granular material, or fine rock flour. A breadboard version of the instrument has been deployed from the robotic arm of the Marsokhod rover in field trials at NASA Ames, where large vesicular boulders were x-rayed to demonstrate the functionality of the instrument design, and the ability of such a device to comply with constraints imposed by a roving platform. Currently under development is a flight prototype concept of this instrument that will weigh 0.3 kg, using about 4500 J of energy per sample analysis. It requires about 5 min. for XRD analysis, and about 30 min. for XRF interrogation. Its small mass and rugged design make it ideal for deployment on small rovers of the type currently envisaged for the exploration of Mars (e.g., Sojourner-scale platforms). The design utilizes a monolithic P-N junction photodiode pixel array for XRD, a Si PIN photodiode/avalanche photodiode system for XRF, and an endoscopic imaging camera system unobtrusively embedded between the detectors and the x-ray source (the endoscope with its board-mounted camera can be adapted for IR light in addition to visible wavelenths. A rugged, miniature (7 cu cm) x-ray source for the instrument has already been breadboarded.
In the year 2001, NASA will launch the satellite TRIANA that will be the first Earth observing mission to provide a continuous, full disk view of the sunlit Earth. As a part of the HPCC Program at NASA GSFC, we have started a project whose objectives are to develop and implement a 3D cloud data assimilation system, by combining TRIANA measurements with model simulation, and to produce accurate statistics of global cloud coverage as an important element of the Earth's climate. For simulation of the atmosphere within this project we are using the NCEP/NOAA operational Eta model. In order to compare TRIANA and the Eta model data on approximately the same grid without significant downscaling, the Eta model will be integrated at a resolution of about 15 km. The integration domain (from -70 to +70 deg in latitude and 150 deg in longitude) will cover most of the sunlit Earth disc and will continuously rotate around the globe following TRIANA. The cloud data assimilation is supposed to run and produce 3D clouds on a near real-time basis. Such a numerical setup and integration design is very ambitious and computationally demanding. Thus, though the Eta model code has been very carefully developed and its computational efficiency has been systematically polished during the years of operational implementation at NCEP, the current MPI version may still have problems with memory and efficiency for the TRIANA simulations. Within this work, we optimize a parallel version of the Eta model code on a Cray T3E and a network of PCs (theHIVE) in order to improve its overall efficiency. Our optimization procedure consists of introducing dynamically allocated arrays to reduce the size of static memory, and optimizing on a single processor by splitting loops to limit the number of streams. All the presented results are derived using an integration domain centered at the equator, with a size of 60 x 60 deg, and with horizontal resolutions of 1/2 and 1/3 deg, respectively. In accompanying charts we report the elapsed time, the speedup and the Mflops as a function of the number of processors for the non-optimized version of the code on the T3E and theHIVE. The large amount of communication required for model integration explains its poor performance on theHIVE. Our initial implementation of the dynamic memory allocation has contributed to about 12% reduction of memory but has introduced a 3% overhead in computing time. This overhead was removed by performing loop splitting in some of the high demanding subroutines. When the Eta code is fully optimized in order to meet the memory requirement for TRIANA simulations, a non-negligeable overhead may appear that may seriously affect the efficiency of the code. To alleviate this problem, we are considering implementation of a new algorithm for the horizontal advection that is computationally less expensive, and also a new approach for marching in time.
The primary goal of this project was to continue populating the currently existing web site developed in 1998 in conjunction with the NASA Dryden Flight Research Center and California Polytechnic State University, with more mathematics lesson plans and activities that K-12 teachers, students, home-schoolers, and parents could access. All of the activities, while demonstrating some mathematical topic, also showcase the research endeavors of the NASA Dryden Flight Research Center. The website is located at: http://daniel.calpoly.edu/~dfrc/Robin. The secondary goal of this project was to share the web-based activities with educators at various conferences and workshops. To address the primary goal of this project, over the past year, several new activities were posted on the web site and some of the existing activities were enhanced to contain more video clips, photos, and materials for teachers. To address the project's secondary goal, the web-based activities were showcased at several conferences and workshops. Additionally, in order to measure and assess the outreach impact of the web site, a link to the web site hitbox.com was established in April 2001, which allowed for the collection of traffic statistics against the web site (such as the domains of visitors, the frequency of visitors to this web site, etc.) Provided is a description of some of the newly created activities posted on the web site during the project period of 2001-2002, followed by a description of the conferences and workshops at which some of the web-based activities were showcased. Next is a brief summary of the web site's traffic statistics demonstrating its worldwide educational impact, followed by a listing of some of the awards and accolades the web site has received.
The expansion of a coronal hole filled with a discrete number of higher density coronal plumes is simulated using a time-dependent two-dimensional code. A solar wind model including an exponential coronal heating function and a flux of Alfven waves propagating both inside and outside the structures is taken as a basic state. Different plasma plume profiles are obtained by using different scale heights for the heating rates. Remote sensing and solar wind in situ observations are used to constrain the parameter range of the study. Time dependence due to plume ignition and disappearance is also discussed. Velocity differences of the order of approximately 50 km/s, such as those found in microstreams in the high-speed solar wind, may be easily explained by slightly different heat deposition profiles in different plumes. Statistical pressure balance in the fast wind data may be masked by the large variety of body and surface waves which the higher density filaments may carry, so the absence of pressure balance in the microstreams should not rule out their interpretation as the extension of coronal plumes into interplanetary space. Mixing of plume-interplume material via the Kelvin-Helmholtz instability seems to be possible within the parameter ranges of the models defined here, only at large di stances from the Sun, beyond 0.2-0.3 AU. Plasma and composition measurements in the inner heliosphere, such as those which will become available with Solar Orbiter and Solar Probe Plus, should therefore definitely be able to identify plume remnants in the solar wind.
Introduction: An intranasal gel dosage formulation of scopolamine (INSCOP) was developed for the treatment of Space Motion Sickness (SMS).The bioavailability and pharmacokinetics (PK) was evaluated using data collected in Phase II IND protocols. We reported earlier statistically significant gender differences in PK parameters of INSCOP at a dose level of 0.4 mg. To identify covariates that influence PK parameters of INSCOP, we examined population covariates of INSCOP PK model for 0.4 mg dose. Methods: Plasma scopolamine concentrations versus time data were collected from 20 normal healthy human subjects (11 male/9 female) after a 0.4 mg dose. Phoenix NLME was employed for PK analysis of these data using gender, body weight and age as covariates for model selection. Model selection was based on a likelihood ratio test on the difference of criteria (-2LL). Statistical significance for base model building and individual covariate analysis was set at P less than 0.05{delta(-2LL)=3.84}. Results: A one-compartment pharmacokinetic model with first-order elimination best described INSCOP concentration ]time profiles. Inclusion of gender, body weight and age as covariates individually significantly reduced -2LL by the cut-off value of 3.84(P less than 0.05) when tested against the base model. After the forward stepwise selection and backward elimination steps, gender was selected to add to the final model which had significant influence on absorption rate constant (ka) and the volume of distribution (V) of INSCOP. Conclusion: A population pharmacokinetic model for INSCOP has been identified and gender was a significant contributing covariate for the final model. The volume of distribution and Ka were significantly higher in males than in females which confirm gender-dependent pharmacokinetics of scopolamine after administration of a 0.4 mg dose.
Numerical stability of high-order filter schemes developed by Yee & Sjogreen is tested on three-dimensional turbulence simulations with stochastic forcing and their performance is compared with that of TVD and WENO schemes. The best performing filter method employs an eighth-order central base scheme with the Kennedy & Gruber skew-symmetric splitting of the inviscid flux derivative, a wavelet-based local flow sensor, a nonlinear filter utilizing the dissipative portion of seventh-order \VENO scheme, and an explicit third - or fourth-order Runge-Kutta time integration. We show that the filter scheme is more computational]y efficient and provides a wider spectral bandwidth compared to the seventh-order WENO scheme. The method also demonstrates robust long-time integration for moderately compressible turbulence. In contrast, the fifth- and seventh order WENO schemes show non-trivial evolution of the velocity and density power spectra. over a. few dozen dynamical times, where both TVD and filter schemes recover a so lid statistically stationary turbulent state
We analyze new aerosol products from NASA satellite retrievals over the western U.S. during August 2013, with special attention to locally generated wildfire smoke and downwind plume structures. Aerosol optical depth (AOD) at 550 nm from MODIS (Terra and Aqua Collections 6 and 6.1) and VIIRS Deep Blue (DB) and MODIS (Terra and Aqua) Multi‐Angle Implementation of Atmospheric Correction (MAIAC) retrievals are evaluated against ground‐based AErosol RObotic NETwork (AERONET) observations. We find a significant improvement in correlation with AERONET and other metrics in the latest DB AOD (MODIS C6.1 r^2=0.75, VIIRS r^2=0.79) compared to MODIS C6 (r2=0.62). In general, MAIAC (r^2=0.84) and DB (MODIS C6.1 and VIIRS) present similar statistical evaluation metrics for the western U.S. and are useful tools to characterize aerosol loading associated with wildfire smoke. We also evaluate three novel NASA MODIS plume injection height (PIH) products, one from MAIAC and two from the Aerosol Single scattering albedo and layer Height Estimation (ASHE) (MODIS and VIIRS) algorithm. Both Terra and Aqua MAIAC PIHs statistically agree with ground‐based and satellite lidar observations near the fire source, as do ASHE, although the latter is sensitive to assumptions about aerosol absorption properties. We introduce a first‐order approximation Smoke Height Boundary Layer Ratio (SHBLR) to qualitatively distinguish between aerosol pollution within the planetary boundary layer and the free troposphere. We summarize the scope, limitations, and suggestions for scientific applications of surface level aerosol concentrations specific to wildfire emissions and smoke plumes using these novel NASA MODIS and VIIRS aerosol products.
The small fluctuations of the neutron flux caused by small perturbations of the macroscopic cross-sections take the name of neutron noise. Advanced Monte Carlo methods have been recently proposed in order to solve the neutron noise equations in the frequency domain, which allows establishing reference solutions to validate faster but approximate deterministic solvers. Due to the presence of particles carrying two statistical weights (for the real and imaginary components of the noise field), both of which may be positive or negative, Monte-Carlo simulations of neutron noise pose distinct challenges in terms of variance reduction. In this work we investigate two variance-reduction techniques, namely branchless collisions and weight cancellation, and probe their effectiveness for a benchmark con- figuration concerning the noise field induced by a pin with oscillating cross sections in a fuel assembly.
A major limitation of transient optical spectroscopy is that relatively high laser fluences are required to enable broadband, multichannel detection with acceptable signal-to-noise levels. Under typical experimental conditions, many condensed phase and nanoscale materials exhibit fluence-dependent dynamics, including higher order effects such as carrier–carrier annihilation. With the proliferation of commercial laser systems, offering both high repetition rates and high pulse energies, have come new opportunities for high sensitivity pump-probe measurements at low pump fluences. However, experimental considerations needed to fully leverage the statistical advantage of these laser systems have not been fully described. Here, we demonstrate a high repetition rate, broadband transient spectrometer capable of multichannel shot-to-shot detection at 90 kHz. Importantly, we find that several high-speed cameras exhibit a time-domain fixed pattern noise resulting from interleaved analog-to-digital converters, which is particularly detrimental to the conventional “ON/OFF” modulation scheme used in pump-probe spectroscopy. Using a modified modulation and data processing scheme, we achieve a noise level of 10−5 in 4 s for differential transmission, an order of magnitude lower than for commercial 1 kHz transient spectrometers for the same acquisition time. We leverage the high sensitivity of this system to measure the differential transmission of monolayer graphene at low pump fluence. We show that signals on the order of 10−6 OD can be measured, enabling a new data acquisition regime for low-dimensional materials.
The motion of domain walls is crucial for ferroelectric switching. Conventionally, the switching dynamics is believed to be determined by the motion of one or a few low-energy domain wall types of dominant population. Here, we challenge this conventional idea in multiple-order-parameter ferroelectrics. Using hafnia as example, we show that the multiple-order-parameter nature not only provides various mobile domain walls and defectlike immobile domain walls, but also enables the domain wall reactions. In analogy with chemical reactions where substances react to form new substances, domain walls could also react to form other domain walls during switching. We identify several elementary domain wall reaction types including synthesis, decomposition, and exchange reactions. Domain walls are continually changed by these reactions during switching so that the switching behavior reflects the statistical average of many domain wall types with distinct mobility and stability. These reactions also lead to phenomenon like remanent nuclei and defect-site nucleation that facilitate switching and lower coercive field. Finally, the concept of domain wall reaction is not limited to hafnia but can be generalized to any multiple-order-parameter ferroelectric. As a result, this Letter conceptualizes domain wall reaction, expands the theory of ferroelectric switching, and suggests a practical way for defect engineering to control switching behavior.
ABSTRACT We present, for the first time, an observational test of the consistency relation for the large-scale structure (LSS) of the Universe through a joint analysis of the anisotropic two- and three-point correlation functions (2PCF and 3PCF) of galaxies. We parameterize the breakdown of the LSS consistency relation in the squeezed limit by Es, which represents the ratio of the coefficients of the shift terms in the second-order density and velocity fluctuations. Es ≠ 1 is a sufficient condition under which the LSS consistency relation is violated. A novel aspect of this work is that we constrain Es by obtaining information about the non-linear velocity field from the quadrupole component of the 3PCF without taking the squeezed limit. Using the galaxy catalogues in the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12, we obtain $E_{\rm s} = -0.92_{-3.26}^{+3.13}$, indicating that there is no violation of the LSS consistency relation in our analysis within the statistical errors. Our parameterization is general enough that our constraint can be applied to a wide range of theories, such as multicomponent fluids, modified gravity theories, and their associated galaxy bias effects. Our analysis opens a new observational window to test the fundamental physics using the anisotropic higher-order correlation functions of galaxy clustering.
Thermodynamics is a science concerning the state of a system, whether it is stable, metastable or un- stable, when interacting with the surroundings. In this overview, fundamentals of thermodynamics are briefly reviewed through the combination of first and second laws of thermodynamics for open and nonequilibrium systems to demonstrate that the reversible equilibrium and irreversible nonequilibrium thermodynamics can be integrated to enhance the power and utilities of thermodynamics. The recent progresses in computational thermodynamics, the remaining challenges, and potential impacts in broad scientific fields are discussed here. It is shown that computational thermodynamics enables the modeling of thermodynamics of a state as a function of both external and internal variables and quantitative calculations of a broad range of properties of a multicomponent system in terms of first and second derivatives of energy, including not only equilibrium states when there are no driving forces for any internal processes and but also non-equilibrium states with driving forces for internal processes. Consequently, external constraints such as fixed strain and internal degree of freedoms such as ordering and defects can be described in a coherent framework and applied to materials design. Furthermore, two important but largely overlooked aspects in thermodynamics will be discussed, i.e. the rigorous application of statistical thermodynamics with the probability of configurations and their contributions to system properties, and the applications of second derivatives of energy with respect to either two extensive variables or two potentials or a mixture of them in terms of understanding and predicting emergent behaviors, critical phenomena, kinetic coefficients, and mechanical properties.
The kinetics of prompt dissociation involves rovibrationally excited species (generally formed by exothermic reactions) which may dissociate or isomerize prior to thermalization via collisions with the bath gas. Treating such rovibrationally excited species (so-called "hot" species) with standard kinetic phenomenology may result in incorrect macroscopic representation of their reactivity. Here this work presents the first fully automated methodology for the calculation of prompt effects of a chosen species in a kinetic mechanism, including (i) reaction selection; (ii) theoretical calculation of rate constants and prompt branching fractions; and (iii) final rate constant fitting. The energy partition between hot fragments is estimated using a variety of statistical models, including a new physically sound microcanonical statistical model based on the rovibrational density of states of the fragments. The methodology is validated against literature data for the prompt dissociations of HCO and C 3 H 7 radicals. The microcanonical statistical model is in better agreement with trajectory simulations for larger species and is thus applicable for practical systems that typically involve large molecules, for which direct dynamics calculations are impractical. The automated workflow is applied to the evaluation of the effects of prompt dissociation for two isomeric radicals C 4 H 7 1-3 (1-methylallyl) and C 4 H 7 1-4 (3-buten-1-yl). Twelve H-atom abstraction reactions are selected and the corresponding rate constants are computed with first principles theory. The microcanonical statistical model predicts that prompt dissociations of C 4 H 7 1-3 and C 4 H 7 1-4 are already significant at 1000K, resulting in differences of up to an order of magnitude at 2000K with respect to the phenomenological thermal rate constants. To illustrate the effects of prompt dissociation on simulations of experimental data, the calculated prompt rate constants are implemented in both CRECK and C3MechV3.3 kinetic mechanisms. Simulations of experimental flame data illustrate the noticeable impact of prompt dissociation kinetics on the high-temperature combustion reactivity of C 4 H 8 -1 and C 4 H 8 -2.
We introduce a scale-aware, data-driven deep learning modeling framework for accurately predicting the time evolution of multi-scale turbulent plasma and liquid flows. The approach is motivated by the idea of scale separation. Structures of vastly different length scales emerge in these systems, and interactions between these structures occur only locally. To exploit this structure, the flow state is transformed by a hierarchical, fully convolutional autoencoder, not into a single embedding layer as in conventional convolutional surrogate models, but into a series of embedding layers. A stepwise training strategy ensures that fine-scale features are encoded on a high-resolution grid, while larger structures are represented on progressively coarser layers. The time evolution predictor advances all embedding layers in sync, capturing local interactions between features at the same scale as well as between all scales. This approach enables efficient modeling of multi-scale systems since negligible interactions between distant, small-scale structures do not need to be directly modeled. Our hierarchical-embedding autoencoder with a predictor framework is evaluated on canonical examples of multi-scale turbulence: two-dimensional Kolmogorov flow and Hasegawa–Wakatani plasma turbulence. In both cases, the proposed framework significantly improves predictive accuracy relative to conventional convolutional network architectures. A significant improvement in prediction accuracy was observed for crucial statistical characteristics of the Hasegawa–Wakatani plasma as well as for individual trajectories of the Kolmogorov flow turbulence. Importantly, the model's rollout for the Hasegawa–Wakatani problem demonstrates a four-order-of-magnitude speedup compared to traditional numerical solvers.
We investigate how confinement geometry leads to the emergence of a Generalized Gibbs Ensemble (GGE) in classical systems. Unlike the standard Gibbs ensemble, the GGE includes additional conserved quantities, such as angular momentum, that arise from boundary-induced symmetries. Using analytical arguments based on the maximum entropy principle, we show that circular boundaries preserve angular momentum and drive the system toward a chiral, non-ergodic GGE that violates time-reversal symmetry. This ensemble differs fundamentally from the Gibbs case, producing near-boundary condensation and revealing how geometry alone can alter thermal equilibration. To quantify these effects, we introduce an order parameter measuring deviations from Gibbs behavior and demonstrate that conventional Monte Carlo methods must incorporate angular momentum conservation under such conditions. Our study highlights how geometric constraints shape non-equilibrium statistical ensembles and lead to subtle departures from the Bohr-van Leeuwen theorem. These predictions are validated through detailed simulations of confined classical hard-disk gases.