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We demonstrate the adoption possibilities of the IDDES model in Nek5000 based on the spectral element method. The defined filter width for the LES mode, which considers the length of the element and the polynomial order, is implemented in Nek5000.
Delay-insensitive VLSI systems have a certain appeal on the ground due to difficulties with clocks; they are even more attractive in space. We answer the question, is it possible to control state explosion arising from various sources during automatic verification (model checking) of delay-insensitive systems? State explosion due to concurrency is handled by introducing a partial-order representation for systems, and defining system correctness as a simple relation between two partial orders on the same set of system events (a graph problem). State explosion due to nondeterminism (chiefly arbitration) is handled when the system to be verified has a clean, finite recurrence structure. Backwards branching is a further optimization. The heart of this approach is the ability, during model checking, to discover a compact finite presentation of the verified system without prior composition of system components. The fully-implemented POM verification system has polynomial space and time performance on traditional asynchronous-circuit benchmarks that are exponential in space and time for other verification systems. We also sketch the generalization of this approach to handle delay-constrained VLSI systems.
An analysis of the physical process for occurrence of flow stagnation in a space tube-radiator is performed and the mechanism and mathematic description for the flow stagnation are presented. Two causes for pressure drop unbalance between tubes of the radiator are identified: non-uniform cooling environment and different local flow resistances between the tubes. This analysis provides a theoretical basis for experimental simulations of the flow stagnation in a ground-based lab as well as two suggested methods to experimentally simulate flow stagnation. Criteria for the flow stagnation, depending on the viscosity data regressive polynomial, are derived from the extreme condition of the pressure drop in colder tubes. A preliminary numerical calculation is conducted for a space tube-radiator model which confirms the physical and mathematical analyses. The prediction by the criteria for flow stagnation in the tube-radiator model coincides with the numerical calculation result.
After 17 years, the NASA Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) mission ceased science operations in August 2023. For the final CALIPSO data products release (Version 5), the CALIPSO project seeks to improve the accuracy of its aerosol extinction by advancing knowledge of aerosol lidar ratios (i.e., extinction-to-backscatter ratios; LRs) for various aerosol types. The current algorithm assigns one LR value globally for each of the seven tropospheric aerosol types. The CALIPSO team aims to improve the retrieval algorithm through the development of regional and seasonal LR climatologies for the same aerosol types. In this study, aerosol LRs are inferred through Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) backscatter profiles constrained by collocated aerosol optical depth (AOD) from Aqua Moderate Resolution Imaging Spectroradiometer (MODIS) data over oceans during daytime. This analysis is subsampled for those profiles that are cloud-free and contain only one CALIOP-classified aerosol type. The CALIOP profiles are then collocated with aerosol volume fractions obtained through Goddard Chemistry Aerosol Radiation and Transport (GOCART) model simulations. This presentation will reveal findings that the 12-year (June 2006-August 2018) mean spatial distributions of inferred aerosol LRs for CALIOP-classified marine and dusty marine aerosols correspond inversely with patterns of GOCART sea salt volume fraction (SSVF). For example, smaller SSVFs (< 65%) and larger LRs (> 55 sr), are found near land masses (Fig. 1). This indicates the influence of advected anthropogenic aerosols (e.g., pollution and biomass burning smoke). In the remote oceans (i.e., regions likely less impacted by non-sea salt aerosols), the SSVFs are larger (> 95%) and the LRs are smaller (< 25 sr) (Fig. 1). A polynomial fit of the MODIS AOD constrained LRs to the corresponding GOCART SSVFs (intersect values of ~58 sr for SSVF of 0% and ~21 sr for SSVF of 100%) is further used to produce model-assisted climatological LR maps on seasonal scales. Additionally, we will show results of a LR validation analysis for which we compare the revised CALIPSO AODs obtained by applying the seasonal/regional constrained LRs against CALIPSO Version 4.51 Ocean Derived Column Optical Depth (ODCOD). While the majority of the presentation will focus on LRs for CALIOP-classified marine and dusty marine aerosols, an overview of LR results will show preliminary results for other aerosol types over ocean, such as dust and elevated smoke. The technique demon-strated in this study highlights the benefits not only to the final planned CALIPSO data release in 2025, but similar methods can be applied to future spaceborne elastic backscatter lidars with collocated passive sensors (e.g., such as those associated with NASA’s proposed Atmosphere Observing System).
We develop new uncertainty propagation methods for feed-forward neural network architectures with leaky ReLU activation functions subject to random perturbations in the input vectors. In particular, we derive analytical expressions for the probability density function (PDF) of the neural network output and its statistical moments as a function of the input uncertainty and the parameters of the network, i.e., weights and biases. A key finding is that an appropriate linearization of the leaky ReLU activation function yields accurate statistical results even for large perturbations in the input vectors. This can be attributed to the way information propagates through the network. We also propose new analytically tractable Gaussian copula surrogate models to approximate the full joint PDF of the neural network output. To validate our theoretical results, we conduct Monte Carlo simulations and a thorough error analysis on a multi-layer neural network representing a nonlinear integro-differential operator between two polynomial function spaces. Our findings demonstrate excellent agreement between the theoretical predictions and Monte Carlo simulations.
The author has identified the following significant results. After parameter estimation, tests were conducted with variances from the fits, and on independent data. From these tests, it was generally concluded that exponential functions have little advantage over polynomials. Precipitation was not found to significantly affect the fits. The Robertson's triquadratic form, in general use for spring wheat, was found to show promise for winter wheat, but special techniques and care were required for its use. In most instances, equations with nonlinear effects were found to yield erratic results when utilized with daily environmental values as independent variables.
We extend a higher-order finite volume cell-centered hydrodynamic (CCH) formulation to include an interface-aware subscale closure model and a multi-material remap for simulating 3D compressible hydrodynamic problems within an arbitrary Lagrangian-Eulerian (ALE) framework. This CCH formulation involves a multidirectional approximate Riemann solution using quadratic polynomial reconstructions of the stress tensor and the velocity. At the subscale level, we determine pair-wise material interactions by solving a distinct approximate Riemann problem at the common interface, using the volume of fluids (VOF) method to find the interface. Material interactions are constrained to ensure smooth pressure equilibration among materials. The accuracy and robustness of the ALE method is demonstrated by simulating a suite of 3D Cartesian multi-material problems covering both gas and solid dynamics, where each test case has two or more materials.
The modeling of compressible multiphase flows is a decades-old area of study with many applications across various fields. Many of these application areas use stiff pressure relaxation. This process involves the solution of a nonlinear system with N + 1 equations and N + 1 unknowns, where N is the number of phases. The resolution of this system with general equations of state (EOSs) is difficult. Furthermore, nonlinear systems can admit multiple solutions, and current solution methods do not address this possibility. Very recently, a thermodynamic relaxation method was introduced, which effectively maps a relatively simple predictor equation of state onto a more complex target equation of state. In this context, the target EOSs are the chosen EOSs for the thermodynamic model. Furthermore, this thermodynamic relaxation has the benefit of simplifying the stiff pressure relaxation system of equations. In this article, we show this system reduces to a polynomial of degree N, which can be recast as an eigenvalue problem through the use of the associated companion matrix. We show that although this eigenvalue method is generally less efficient than Newton–Raphson iteration, it does not suffer from convergence issues and finds all N roots of the polynomial. Hence, the method provides a fail-safe for root-finding iterative methods and a way to address the issue of multiple solutions to the nonlinear system of equations in stiff pressure relaxation.
Asymptotic normalization coefficients (ANC) determine the overall normalization of cross sections of peripheral radiative capture reactions. In the present paper, we treat the ANC C for the virtual decay 16 O(0 + ; 6.05 MeV)→ α+ 12 C(g.s.), the known values of which are characterized by a large spread (0.29 - 1.65) × 10 3 fm -1/2 . The ANC C is found by analytic continuation in energy of the α 12 C s-wave scattering amplitude, known from the phase-shift analysis of experimental data, to the pole corresponding to the 16O bound state and lying in the unphysical region of negative energies. To determine C, two different methods of analytic continuation are used. In the first method, the scattering data are approximated by the sum of polynomials in energy in the physical region and then extrapolated to the pole. The best way of extrapolation is chosen on the basis of the exactly solvable model. Within the second approach, the ANC C is found by solving the Schrödinger equation for the two-body α 12 C potential, the parameters of which are selected from the requirement of the best description of the phase-shift analysis data at a fixed experimental binding energy of 16 O(0 + ; 6.05 MeV) in the α+ 12 C channel. The values of the ANC C obtained within these two methods lie in the interval (886–1139) fm -1/2 .
Deterministic transport simulations for national-security and energy applications often operate in high-dimensional phase-space, where accuracy and cost both become major challenges. A common numerical artifact in such problems is the “ray-effect,” which appears as unphysical streaks. Beyond misinterpretation, these artifacts can contaminate tightly coupled physics, such as fluid dynamics, radiation-hydrodynamics, and laser-plasma interactions, eroding the predictive capability of entire multiphysics workflows. Our objective was to make high-dimension studies practical on modern hardware while mitigating the ray-effect without relying on prohibitively expensive sampling approaches such as Monte Carlo methods. We developed the Generic Discretization Library (GenDiL), a Graphics Processing Unit (GPU)-first framework that uses high-order Discontinuous Galerkin (DG) methods and matrix-free algorithms to reduce memory usage and improve computational efficiency, critical for phase-space simulations. GenDiL supports phase-space adaptivity in both mesh size and polynomial order (hp-adaptivity) to place resolution only where it is needed. A central capability is Local Dimensional Refinement (LDR), which couples lower-dimension continuum models to higher-dimension kinetic models through stable and conservative interfaces, so that high-fidelity physics is applied only in regions where it is essential. Building on the GenDiL framework, we developed the General SN (GSN) family of algorithms as a true generalization of the polar SN approach (discrete ordinates, often denoted SN). Rather than tying discrete ordinates to a specific polar change of coordinates, GSN formulates transport on an arbitrary change of coordinates chosen to reduce ray-effect. We studied two complementary variants: an analytic variant, where the coordinate map is prescribed in advance by a closed-form function; and a data-driven variant, where a quantity of interest, such as the net flux, guides the coordinate system. GenDiL provides the library infrastructure for efficient GPU execution, but the GSN concept is algorithmic and independent of any one library. Across representative high-dimension tests, including non-symmetric solutions, both variants delivered strong ray-effect mitigation at practical cost, moving four- to six-dimensional analysis toward repeatable, routine studies.
The paper compares recent center-limb studies of optical and IR continuum intensities (over the wavelength range 0.3-2.4 microns, with the data tabulated in the form of second- and fifth-order polynomial fits to empirical limb darkening curves) by Pierce and Slaughter (1977) and by Pierce et al. (1977) with predictions based on several current photospheric thermal structure models, using calibrated specific intensity measurements by Labs and Neckel (1968, 1970) to set an absolute temperature scale. The thermal structure in best quantitative agreement with the measurements of Pierce and Slaughter and Pierce et al. is the semiempirical model of Vernazza, Avrett and Loeser (1976). The temperatures in this model must be scaled upward, however, by a factor of 1.015 plus or minus 0.0005 to be consistent with the Labs and Neckel absolute calibration of continuum high points in the 0.40-0.65 micron region.
Expansions in Chebyshev polynomials are used to study the linear stability of one dimensional magnetohydrodynamic (MHD) quasi-equilibria, in the presence of finite resistivity and viscosity. The method is modeled on the one used by Orszag in accurate computation of solutions of the Orr-Sommerfeld equation. Two Reynolds like numbers involving Alfven speeds, length scales, kinematic viscosity, and magnetic diffusivity govern the stability boundaries, which are determined by the geometric mean of the two Reynolds like numbers. Marginal stability curves, growth rates versus Reynolds like numbers, and growth rates versus parallel wave numbers are exhibited. A numerical result which appears general is that instability was found to be associated with inflection points in the current profile, though no general analytical proof has emerged. It is possible that nonlinear subcritical three dimensional instabilities may exist, similar to those in Poiseuille and Couette flow.
Expansions in Chebyshev polynomials are used to study the linear stability of one-dimensional magnetohydrodynamic quasi-equilibria, in the presence of finite resistivity and viscosity. The method is modeled on the one used by Orszag in accurate computation of solutions of the Orr-Sommerfeld equation. Two Reynolds-like numbers involving Alfven speeds, length scales, kinematic viscosity, and magnetic diffusivity govern the stability boundaries, which are determined by the geometric mean of the two Reynolds-like numbers. Marginal stability curves, growth rates versus Reynolds-like numbers, and growth rates versus parallel wave numbers are exhibited. A numerical result that appears general is that instability has been found to be associated with inflection points in the current profile, though no general analytical proof has emerged. It is possible that nonlinear subcritical three-dimensional instabilities may exist, similar to those in Poiseuille and Couette flow.
This paper deals with methods for obtaining near-optimum step sizes for finite difference approximations to first derivatives with particular application to sensitivity analysis. A technique denoted the finite difference (FD) algorithm, previously described in the literature and applicable to one derivative at a time, is extended to the calculation of several simultaneously. Both the original and extended FD algorithms are applied to sensitivity analysis for a data-fitting problem in which derivatives of the coefficients of an interpolation polynomial are calculated with respect to uncertainties in the data. The methods are also applied to sensitivity analysis of the structural response of a finite-element-modeled swept wing. In a previous study, this sensitivity analysis of the swept wing required a time-consuming trial-and-error effort to obtain a suitable step size, but it proved to be a routine application for the extended FD algorithm herein.
Basic aerodynamic coefficients are modeled as functions of angles of attack and sideslip with vehicle lateral symmetry and compressibility effects. Most of the aerodynamic parameters can be well-fitted using polynomial functions. In this paper a fast, reliable way of predicting aerodynamic coefficients is produced using a neural network. The training data for the neural network is derived from wind tunnel test and numerical simulations. The coefficients of lift, drag, pitching moment are expressed as a function of alpha (angle of attack) and Mach number. The results produced from preliminary neural network analysis are very good.
In a computational fluid model of the atmosphere, the advective transport of trace species, or tracers, can be computationally expensive. For efficiency, models often use semi-Lagrangian advection methods. High-order interpolation semi-Lagrangian (ISL) methods, in particular, can be extremely efficient, if the problem of property preservation specific to them can be addressed. Atmosphere models often use geometrically and logically nonuniform grids for efficiency and, as a result, element-based discretizations. Such grids and discretizations make stability a particular problem for ISL methods. Generally, high-order, element-based ISL methods that use the natural polynomial interpolant associated with a nodal finite-element discretization are unstable. Here, we derive new bases having order of accuracy up to nine, with positive nodal weights, that stabilize the element-based ISL method. We use these bases to construct the linear advection operator in the property-preserving Interpolation Semi-Lagrangian Element-based Transport (Islet) method. Then we discuss key software implementation details. Finally, we show performance results for the Energy Exascale Earth System Model's atmosphere dynamical core, comparing the original and new transport methods. These simulations used up to 27,600 Graphical Processing Units (GPU) on the Oak Ridge Leadership Computing Facility's Summit supercomputer.
The effect of nonlinearity on the higher harmonic control (HHC) of helicopter vibration is investigated using a nonlinear aeroelastic simulation. A nonlinear solution is proposed which relates the HHC inputs to vibration outputs on the basis of a Volterra functional series. The Volterra series solution is shown to reduce to a vector polynomial equation relating HHC inputs to vibration outputs at any harmonic frequency. The nonlinear transfer relationship is identified from a nonlinear vibration analysis computer program, and the identification model is examined in detail. Improvements to current HHC algorithms are presented, and several Kalman filter divergence problems are quantified.
The current status of the Deep Space Network advanced systems research into ionospheric calibration techniques, based on Global Positioning System (GPS) data is described. A GPS-based calibration system is planned to replace the currently used Faraday rotation method by 1989. The SERIES receiver system determines the differential group delay of signals transmitted at two different carrier frequencies. This differential delay includes an ionospheric component and a GPS transmitter offset. The transmitter offsets are different for each GPS satellite. Tests were conducted to assess the effect of the offsets on the ionospheric calibration accuracy. From the obtained data, the total electron content and GPS transmitter offsets are calculated by a least squares estimation method employing a local model of total ionospheric electron content. The end product is an estimation of the total ionospheric content for an arbitrary line-of-sight direction. For the presented polynomial fitting technique, the systematic error due to mismodeling is estimated to be approximately 6 x 10 to the 16th power el/sq m, while the formal error is approximately 2 x 10 to the 16th power el/sq m. The final goal is an error of 3 x 10 to the 16th power el/sq m (approximately 0.7 ns at 2.3 GHz).