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At least 829 records · Page 46

Numerical approach based on fractional-order Lagrange polynomials for solving a class of fractional differential equations

In this study, we propose a new set of fractional functions based on the Lagrange polynomials to solve a class of fractional differential equations. Fractional differential equations are the best tools for modelling natural phenomenon that are elaborated by fractional calculus. Therefore, we need an accurate and efficient technique for solving them. The main purpose of this article is to generalize new functions based on Lagrange polynomials to the fractional calculus. At first, we present a new representation of Lagrange polynomials and in continue, we propose a new set of fractional-order functions which are called fractional-order Lagrange polynomials (FLPs). Besides, a general formulation for operational matrices of fractional integration and derivative of FLPs on arbitrary nodal points are extracted. These matrices are obtained using Laplace transform. The initial value problems is reduced to the system of algebraic equations using the operational matrix of fractional integration and collocation method. Also, we find the upper bound of error vector for the fractional integration operational matrix and we indicate convergence of approximations of FLPs. Illustrative examples are included to demonstrate the validity and applicability of the proposed technique.

97 MATHEMATICS AND COMPUTING↗

Reduction of baseplate distortion during directed energy deposition using compliant features

Distortion in additive manufacturing (AM) remains a barrier to its adoption in precision industries. Baseplate warpage is one such issue which compromises the feasibility of post-process precision machining. The restriction to thermal contraction of the deposited part, imposed by the baseplate, generates bending moments, that in turn causes warpage. A novel distortion mitigation strategy using baseplates with integrated compliant features, which enables thermal contraction of the build is presented. Six unique design concepts are evaluated, including a solid reference, using two deposition geometries. A laser, hot-wire, directed energy deposition (DED) process is used to deposit a symmetric cylindrical part (C-part) and a T-shaped asymmetric part (T-part). Flatness deviation of baseplates is measured using structured light 3D scanning. Measurements reveal a reduction in net flatness deviation of 58.8% for the C-part and 40.9% for the T-part, compared to the solid reference. While most designs yielded reductions exceeding 30% and 20% for the C- and T-parts, respectively, one configuration resulted in increased deviation. Finite element (FE) simulations are performed to elucidate the underlying mechanisms affecting distortion of compliant baseplates during DED. Despite variations between predictions and measurements, agreement in the general trend is observed. It also revealed that initial flatness errors in baseplates significantly affect its deviation during deposition. Predictions indicate that compliant features significantly affect the thermal distribution as well as the evolution of flatness deviation in the baseplate during deposition. Notably, one design exhibited a reduction in distortion during cooling, following its initial increase during deposition. FE predictions show a maximum reduction of 60.9% and 38.8% in net flatness deviation for the C- and T-parts, respectively. The performance of compliant baseplates is found to be governed by both its the thermal and mechanical characteristics, which are crucial factors to be considered during design.

Mathews, Ritin [ORNL] (ORCID:0000000301440828)↗

National soil organic carbon estimates can improve global estimates

Global inventories of spatial and vertical distribution of soil organic carbon (SOC) stocks are being used in national and global initiatives targeted to mitigate climate change and land degradation impacts. Yet, national level high-resolution estimates of SOC stocks can be useful for improving the accuracy of global SOC inventories. We estimated spatially resolved SOC stocks of surface 0–30 cm and subsurface 30–100 cm layers at a spatial resolution of 30m in tropical Island, Sri Lanka using a legacy harmonized soil database of 122 soil profiles. The national estimates were compared with two global estimates derived from WISE30sec and SoilGrids250m. The tropical Island (land area=64,610 km2) occupying 0.03% of global land area showed a considerable heterogeneity in SOC stocks ranging from 2.0-342.5 Mg ha -1 and 2.7-391.7 Mg ha -1 in the surface and subsurface soil layers, respectively. We found, elevation, precipitation and slope angle as main environmental controllers of the spatial distribution of SOC stocks under tropical climate. Incorporating the pedogenic information (derived from soil series level legacy map, soil orders and suborders) with environmental controllers resulted in better regression models of predicting surface (R 2 =0.61) and subsurface (R 2 =0.81) SOC stocks. Geographically weighted regression kriging derived maps of SOC stocks revealed that 0–100 cm soil layer of the tropical Island stored 500 Tg C contributing for 0.04% of the global SOC stocks. The validation results of our estimates showed low Mean Estimation Error (MEE: surface -1.6 and subsurface -1.6 Mg ha -1 ) and Root Mean Square Error (RMSE: surface 29.5 and subsurface 24.9 Mg ha -1 ) indicating a low bias and satisfactory predictions. The relative improvement of the prediction accuracy of the SOC stocks of our geospatial estimates in the 0–30 cm layer in comparison to SoilGrids250m and WISE30sec data derived SOC stocks were 51.7% and 35.2%, respectively. The SOC stocks predictions of the 30-100 cm soil layer showed even better relative improvement compared to SoilGrids250m (78.4%) and WISE30sec (57.4%) SOC estimates. Compared to estimates of total SOC stocks resulted in this study, WISE30sec data derived SOC stock maps showed 30% over estimation of the C stock in surface 0-30 cm (332 Tg C) and 41% overestimation in 30-100 cm layer (343 Tg C). The over estimation of total SOC stocks by the SoilGrids250 SOC stocks map for the surface 0-30 cm layer was 122% (567 Tg C) and for the 30-100 cm layer it was 209% (750 Tg C). We conclude that the fusion of legacy soil information of SOC stocks with appropriate environmental covariates and pedogenic information derived from legacy area-class soil maps at national level can produce more accurate inventories of spatial and vertical distribution of SOC stocks. As a result, these national inventories have a great potential of upgrading global inventories of SOC stocks.

54 ENVIRONMENTAL SCIENCES↗

Compressed baryon acoustic oscillation analysis is robust to modified-gravity models

Abstract We study the robustness of the baryon acoustic oscillation (BAO) analysis to the underlying cosmological model. We focus on testing the standard BAO analysis that relies on the use of a template. These templates are constructed assuming a fixed fiducial cosmological model and used to extract the location of the acoustic peaks. Such “compressed analysis” had been shown to be unbiased when applied to the ΛCDM model and some of its extensions. However, it has not been known whether this type of analysis introduces biases in a wider range of cosmological models where the template may not fully capture relevant features in the BAO signal. In this study, we apply the compressed analysis to noiseless mock power spectra that are based on Horndeski models, a broad class of modified-gravity theories specified with eight additional free parameters. We study the precision and accuracy of the BAO peak-location extraction assuming DESI, DESI II, and MegaMapper survey specifications. We find that the bias in the extracted peak locations is negligible; for example, it is less than 10% of the statistical error for even the proposed future MegaMapper survey. Our findings indicate that the compressed BAO analysis is remarkably robust to the underlying cosmological model.

Astronomy & Astrophysics↗

Private Tabular Survey Data Products through Synthetic Microdata Generation

We propose two synthetic microdata approaches to generate private tabular survey data products for public release. We adapt a pseudo posterior mechanism that downweights by-record likelihood contributions with weights ∈[0,1] based on their identification disclosure risks to producing tabular products for survey data. Our method applied to an observed survey database achieves an asymptotic global probabilistic differential privacy guarantee. Our two approaches synthesize the observed sample distribution of the outcome and survey weights, jointly, such that both quantities together possess a privacy guarantee. The privacy-protected outcome and survey weights are used to construct tabular cell estimates (where the cell inclusion indicators are treated as known and public) and associated standard errors to correct for survey sampling bias. Through a real data application to the Survey of Doctorate Recipients public use file and simulation studies motivated by the application, we demonstrate that our two microdata synthesis approaches to construct tabular products provide superior utility preservation as compared to the additive noise approach of the Laplace Mechanism. Moreover, our approaches allow the release of microdata to the public, enabling additional analyses at no extra privacy cost.

Mathematical Methods In Social Sciences↗

Quasisymmetric Optimization of Nonaxisymmetry in Tokamaks

Predictive 3D optimization reveals a novel approach to modify a nonaxisymmetric magnetic perturbation to be entirely harmless for tokamaks, by essentially restoring quasisymmetry in perturbed particle orbits as much as possible. Such a quasisymmetric magnetic perturbation (QSMP) has been designed and successfully tested in the KSTAR and DIII-D tokamaks, demonstrating no performance degradation despite the large overall amplitudes of nonaxisymmetric fields and strong response otherwise expected in the tested plasmas. The results indicate that a quasisymmetric optimization is a robust path of error field correction across the resonant and nonresonant field spectrum in a tokamak, leveraging the prevailing concept of quasisymmetry for general 3D plasma confinement systems such as stellarators. Finally, the optimization becomes, in fact, a simple eigenvalue problem to the so-called torque response matrices if a perturbed equilibrium is calculated consistent with nonaxisymmetric neoclassical transport.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Predictive Model for Starlink Maritime Performance Using Multi-Horizon RandomForest

Low Earth orbit (LEO) satellite systems have become a crucial enabler of broadband access for maritime industries, where traditional networks are unavailable. However, the high mobility of LEO constellations and constantly changing weather conditions result in unpredictable link fluctuations, limiting the ability of maritime platforms to plan bandwidth usage proactively. To the best of our knowledge, no prior work has developed a short-term predictive model for maritime LEO connectivity using real experimental field measurements. This paper proposes a data-driven forecasting model that predicts future downlink throughput using multi-horizon RandomForest regression. The model is trained using real experimental coastal measurement data incorporating recent throughput history, network-layer indicators, and environmental variables. The proposed approach reduces mean absolute error by approximately 31% compared to a persistence baseline for 15-minute horizons. It maintains a measurable improvement at 30 minutes, despite increased stochasticity. These findings confirm that proactive bandwidth awareness is feasible on maritime platforms and can effectively support operational decisions such as adaptive streaming, routing, and resource scheduling. The performance gap between forecasting horizons also highlights the need for expanded offshore datasets to improve prediction robustness under harsher maritime environments.

97 MATHEMATICS AND COMPUTING↗

Estimating Fine-Resolution Shortwave Broadband Albedo of Croplands from Harmonized Landsat and Sentinel-2 Data

Altered surface albedo due to land-cover conversions and management is a significant driver of global climate change. Albedo can be directly measured at ground stations, and remote sensing data can be used to scale-up albedo values to regional and global levels. Some previous studies have retrieved fine-resolution (10–30 m) instantaneous albedo and coarse-resolution (500–1000 m) daily mean albedo from remote sensing data, but they all required the input of Moderate Resolution Imaging Spectroradiometer (MODIS) albedo information at 500-m resolution, and none have assembled both instantaneous and daily albedo based exclusively on fine-resolution satellite data. Here, to address this issue, we compiled 387 instantaneous and 346 daily albedo records using field net radiometer measurements from the bioenergy croplands at the W. K. Kellogg Biological Station in southwest Michigan. We then connected these albedo records with a suite of variables derived from harmonized Landsat and Sentinel-2 data through two machine learning algorithms (random forest regression and extreme gradient boosting) to retrieve clear-sky instantaneous and daily shortwave broadband albedo. The performance statistics indicate reasonable accuracy of model results [root-mean-square error (RMSE)] around or below 0.03 except for snow-covered surfaces), suggesting that the retrieval of both instantaneous and daily albedo based exclusively on fine-resolution satellite data is promising. To facilitate the use of fine-resolution albedo products at the global level, future efforts need to include more albedo records of diverse surface cover types, as well as to accurately model daily albedo for cloudy days to address the “clear-sky bias.”

Harmonized Landsat and Sentinel-2↗

Testing of an Iodine and Tritium Capture System for an NO₂-Based Tritium Pretreatment Process

The reprocessing of used nuclear fuel would release volatile radionuclides into the off-gas streams of a processing plant, including ³H, ¹⁴C, ⁸⁵Kr, and ¹²⁹I. One potential simplification to the management of the off-gas streams could be achieved through an efficient tritium pretreatment (TPT) step in which the UO₂ fuel is oxidized by either air or NO₂ before dissolution. The oxidation of the UO₂ fuel matrix will result in the release of tritium from the fuel. Upfront release of tritium from the fuel in a pretreatment step with subsequent tritium abatement can minimize or eliminate the distribution of tritium throughout a plant. This can decrease or eliminate the need for tritium capture on multiple off-gas streams and prevent distribution to the aqueous inventory. The use of NO₂ as the oxidant in an advanced tritium pretreatment (ATPT) allows for the oxidation to be performed at lower temperatures and may also result in the quantitative release of iodine from the fuel. The ATPT off-gas will contain up to 75 vol% NO₂ gas. Spencer et al. identified the most promising iodine sorbent as silver nitrate-impregnated alumina (AgA) and the most promising tritium sorbents as 3Å molecular sieve (3Å MS) and silica gel for radionuclide capture from ATPT off-gas streams. An initial series of tests were conducted in fiscal years 2017–2018 with the intent of demonstrating the recovery of iodine and tritium using these sorbents from a recirculating gas stream that simulated the NO₂ recycle loop envisioned for the ATPT system. These initial tests showed low tritium recoveries and significant variations in the iodine recovery on the AgA. Ultimately it was concluded, following disassembly of the system, that corrosion within the system was partially the cause of the poor recovery of both species. All components of that system were disposed of at the end of the analysis. One of the conclusions drawn from the initial tests pointed to the reconsideration of the materials of construction. Based on that recommendation a new test bed for the advanced TPT off-gas system, that addresses the issues identified in the fiscal years 2017 and 2018 scoping tests, was designed and constructed. The test bed used high nickel alloys wherever possible to address the previously observed corrosion issues, a redesigned surge tank to permit ease of purging, an improved feed injection system and a more modular system design that allowed testing of incremental increases in system complexity to allow the isolation of any element that results in changes to recovery of target species. Accompanying that design, a multifaceted test plan was completed. The overarching goals of this test series were two-fold. The first goal was to demonstrate the ability to recover both the iodine and tritium that would be released during TPT in a manner that the releases from the fuel can be quantified. The second goal was to demonstrate that the combined recovery system could operate in any of the three proposed TPT modes (once-through air or O₂, recirculating air or O₂, or recirculating NO x ). A total of 22 tests were completed. Ten tests examined tritium behavior under varying operating parameters, 8 tests examined iodine behavior under varying operating parameters, and 4 tests examined both tritium and iodine behavior. Silica gel was used for the tritium sorbent, and AgA or Ag-mordenite (AgZ) was used as the iodine sorbent. The following conclusions were drawn: Full recovery is achieved for both sorbates when no sorbent is in place indicating no accumulation within the test system. In even the simplest of the configurations (i.e., no sorbents in the columns), iodine is more difficult to transport and recover from the system than tritium. Analysis of the AgA iodine sorbent beds from the integrated tritium and iodine tests indicate quantitative iodine recovery can be achieved (within anticipated experimental errors). This system may provide a means for the quantification of the iodine released by the ATPT process within the experimental uncertainties. This would support 0.33 to 1.00 kg demonstrations of the ATPT process with actual used nuclear fuel. Iodine penetrated further into AgZ than into AgA when operated in gas recirculation mode. Tritium adsorbs to and cannot be fully recovered from the 10-cm column of silica gel at regeneration temperatures up to 140 °C.; Tritium adsorbs to and cannot be recovered from the 10-cm column of AgA at desorption temperatures up to 200 °C. Co-adsorbed tritium was recovered to a greater extent from AgZ than from AgA, but recovery was not complete. No visible corrosion was observed in the test system.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Overlay board for control consoles

Board that fits over the control panel decreases errors and time loss. Device has cutouts for controls and indicators, bears all appropriate labeling information, can be removed with the changing computer assignments, and guards against accidental changes in control settings.

Jackson, C. T.↗

Attitude stability and performance of a dual-spin satellite with nutation damping.

Previous work of Anand and al. (1969) on the effect of aerodynamic torques on the steady-state behavior of a slowly spinning satellite without damping is extended to consideration of the effects of external torques and of a nutational damper on the transient and state motions of a satellite. Both the transient and steady-state behaviors are analyzed, and the attitude errors relative to a fixed star are established. The results indicate that, in the case of a particular satellite to be used for charting X-ray emitting sources in the celestial sphere, the effect of a nutational damper on the accuracy of the charting computations is significant.

Anand, D. K.↗

An extension to the Chahine method of inverting the radiative transfer equation

An extension of the Chahine relaxation method (1970) for inverting the radiative transfer equation is presented. This method is superior to the original method in that it takes into account in a realistic manner the shape of the kernel function, and its extension to nonlinear systems is much more straightforward. A comparison of the new method with a matrix method due to Twomey (1965), in a problem involving inference of vertical distribution of ozone from spectroscopic measurements in the near ultraviolet, indicates that in this situation this method is stable with errors in the input data up to 4%, whereas the matrix method breaks down at these levels. The problem of non-uniqueness of the solution, which is a property of the system of equations rather than of any particular algorithm for solving them, remains, although it takes on slightly different forms for the two algorithms.

Twomey, S.↗

Possible measurement of the coefficient of the second zonal harmonic of the sun's gravitational field with a solar probe

The use of radio tracking of a solar probe to estimate accurately the coefficient of the second zonal harmonic of the sun's gravitational field was examined. Preliminary results indicate that the coefficient can be estimated with a standard error of 10 to the minus 8th power or less, provided that the probe is equipped with a suitable drag-free system to compensate for the effects of non-gravitational accelerations. For signal paths that pass near the sun, dual-band ranging to the probe can provide the tracking accuracy needed to insure that the standard of error is equal to or less than 10 to minus 8th power. The possibility of achieving such accuracy with a single-band radio uplink and a dual-band downlink is discussed.

Reasenberg, R. D.↗

Use of global atmospheric data sets to test quasi-geostrophic eddy momentum flux convergence

The quasi-geostrophic relation between the fluxes of momentum, potential vorticity, and potential temperature is tested with global sets of atmospheric wind and temperature data by computing the convergence of momentum flux as a residual of the potential temperature and potential vorticity flux and comparing it to the momentum flux convergence computed directly. It is shown that in the troposphere between 18 N and 74 N the observed momentum flux convergence differs from the quasi-geostrophic convergence by 25%-60%, with the larger errors only occurring where the convergence is small. These results indicate that momentum flux convergence obtained from quasi-geostrophic theory is adequate for qualitative studies of the general circulation, and is comparable in accuracy to values obtained in general circulation models. For simple climate models and qualitative process studies, it can thus provide a useful approach.

Heck, W. J.↗

Radiative and free convective heat transfer from a containerless sphere

A mathematical model is derived for heat loss due to radiation and free convection for a small copper sphere (approximately 0.3 to 0.4 cm diameter) cooled by a helium-argon gas mixture. A FORTRAN program written to simplify calculations and extend the range of applicability to experimentation is presented. Pressures used were less than 400 torr, and resulting temperatures ranged from 500 to 4600 K. Comparison of results for initial cooling by the gas mixture with experimental data showed a 5 percent error for temperature values and a 2.7 percent error for the temperature difference caused by the cooling. Results indicate that the accuracy could be increased significantly by using better estimates for thermal conductivities.

Johnson, K.↗

Multiple spacecraft observations of interplanetary shocks: Characteristics of the upstream ULF turbulence

All interplanetary shocks observed by ISEE-3 and either ISEE-1 or ISEE-2 or both in 1978 and 1979 are examined for evidence of upstream waves. In order to characterize the properties of these shocks it is necessary to determine accurate shock normals. An overdetermined set of equations were inverted to obtain shock normals, velocities and error estimates for all these shocks. Tests of the method indicate it is quite reliable. Using these normals the Mach number and angle were between the interplanetary magnetic field and the shock normal for each shock. The upstream waves were separated into two classes: whistler mode precursors which occur at low Mach numbers and upstream turbulence whose amplitude at Mach numbers greater than 1.5 is controlled by the angle of the field to the shock normal. The former waves are right hand circularly polarized and quite monochromatic. The latter waves are more linearly polarized and have a broadband featureless spectrum.

Russell, C. T.↗

Timing performance of phased-locked loops in optical pulse position modulation communication systems

An optical digital communication system requires that an accurate clock signal be available at the receiver for proper synchronization with the transmitted signal. Phase synchronization is especially critical in M-ary pulse position modulation (PPM) systems where the optimum decision scheme is an energy detector which compares the energy in each of M time slots to decide which of M possible words was sent. Timing errors cause energy spillover into adjacent time slots (a form of intersymbol interference) so that only a portion of the signal energy may be attributed to the correct time slot. This effect decreases the effective signal, increases the effective noise, and increases the probability of error. A timing subsystem for a satellite-to-satellite optical PPM communication link is simulated. The receiver employs direct photodetection, preprocessing of the detected signal, and a phase-locked loop for timing synchronization. The variance of the relative phase error is examined under varying signal strength conditions as an indication of loop performance, and simulation results are compared to theoretical calculations.

Lafaw, D. A.↗

Pointing and control system design study for the space infrared telescope facility (SIRTF)

The design and performance of pointing and control systems for two space infrared telescope facility vehicles were examined. The need for active compensation of image jitter using the secondary mirror or other optical elements was determined. In addition, a control system to allow the telescope to perform small angle slews, and to accomplish large angle slews at the rate of 15 deg per minute was designed. Both the 98 deg and the 28 deg inclination orbits were examined, and spacecraft designs were developed for each. The results indicate that active optical compensation of line-of-sight errors is not necessary if the system is allowed to settle for roughly ten seconds after a slew maneuver. The results are contingent on the assumption of rigid body dynamics, and a single structural mode between spacecraft and telescope. Helium slosh for a half full 4000 liter tank was analyzed, and did not represent a major control problem.

Lorell, K. R.↗