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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 919 records · Page 51
All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

Prototype Vent Gas Heat Exchanger for Exploration EVA - Performance and Manufacturing Characteristics

NASA is developing new portable life support system (PLSS) technologies, which it is demonstrating in an unmanned ground based prototype unit called PLSS 2.0. One set of technologies within the PLSS provides suitable ventilation to an astronaut while on an EVA. A new component within the ventilation gas loop is a liquid-to-gas heat exchanger to transfer excess heat from the gas to the thermal control system's liquid coolant loop. A unique bench top prototype heat exchanger was built and tested for use in PLSS 2.0. The heat exchanger was designed as a counter-flow, compact plate fin type using stainless steel. Its design was based on previous compact heat exchangers manufactured by United Technologies Aerospace Systems, but was half the size of any previous heat exchanger model and one third the size of previous liquid-to-gas heat exchangers. The prototype heat exchanger was less than 40 cubic inches and weighed 2.6 lb. The water side and gas side pressure drops were 0.8 psid and 0.5 inches of water, respectively. Performance of the heat exchanger at the nominal pressure of 4.1 psia was measured at 94%, while a gas inlet pressure of 25 psia resulted in an effectiveness of 84%. These results compared well with the model, which was scaled for the small size. Modeling of certain phenomena that affect performance, such as flow distribution in the headers was particularly difficult due to the small size of the heat exchanger. Data from the tests has confirmed the correction factors that were used in these parts of the model.

Jennings, Mallory↗
NASA NTRS2019

Preliminary Computational Assessment of Disk Rotating Detonation Engine Configurations

The pressure gain combustion (PGC) community is currently investigating rotating detonation engine (RDE) configurations where the flow direction is predominantly radial while the detonation travels circumferentially. These configurations are sometimes referred to as disk rotating detonation engines (DRDE) due to their nominal appearance as two disks in parallel with a gap between them. Having radial flow between disks, as opposed to the conventional RDE with axial flow in an annulus, may have profound effects on both the flow field and the performance. It may also yield extraordinarily compact devices which are well suited to particular propulsion and power applications. This presentation describes a preliminary effort to model the DRDE using a modified computational fluid dynamics (CFD) code originally written for analyzing ordinary RDE's. The quasi-two-dimensional code modifications are described, and some simple test flows are analyzed to insure that the modifications are functioning as envisioned. The code is then used to examine several DRDE scenarios such as radially inward and radially outward devices to see if stable operation is possible and if so, to assess the performance in terms of pressure gain. It is found that several flow scenarios are not only stable, but show superior performance to the ordinary RDE.

Paxson, Daniel E.↗
DOE OSTI2024

Additive Manufacturing of Thermal Energy Storage Composites with Microencapsulated Phase Change Materials Supported in a Multi-Polymer Matrix

Advanced manufacturing techniques, such as additive manufacturing (AM), that can directly integrate phase change materials (PCMs) have garnered interest in recent years due to their potential for development of highly efficient thermal energy storage architectures. Complex, high surface area geometries embedded with PCMs that are only feasible with AM can improve thermal management with reduced material waste. Our work focuses on developing composite filaments with microencapsulated phase change materials (MEPCM) bound within a single or dual polymer matrix that can be processed through standard filament extruders and additively manufactured using off-the-shelf 3D printers. Polymer powders, rather than polymer pellets, were key to homogenously mixed filaments achieving high MEPCM loadings with no deterioration in thermal energy storage (TES) capability during extrusion. Composite filaments contain upwards of 60 wt% MEPCM and were printed without loss in feature resolution, print speed, or layer adhesion. Storage enthalpies of printed composites range from 100 - 130 kJ/kg, which were within 5% of the theoretical enthalpy based on weight fraction of MEPCM and maintained enthalpies within 1% over 500 thermal cycles. We can reliably manufacture low density, high surface area structures like 15% gyroid infill, along with dense, compact pucks at a 100% concentric infill. Prints were also scalable to a 900 cm3 honeycomb infill heat exchanger model that has an estimated energy storage capacity of 9 Wh.

3D printing↗
DOE OSTI2023

Advanced Modeling of Plasma-based Particle Accelerators

Plasma-based acceleration (PBA) driven by an intense laser (LWFA) or particle beam (PWFA) can produce ultra-high accelerating fields in excess of a GV/cm. PBA could substantially reduce the size and cost of future linear collider facilities if deployed successfully. PBA enables compact tabletop accelerators that can provide lower energy GeV-class beams in a laboratory setting. PBA enables high quality beam generation suitable for x-ray free electron lasers (XFEL) via controllable methods of self-injection. Challenges in modeling and optimization of multi-stage PBA motivate the need for exascale computing and state-of-the-art PIC codes.

43 PARTICLE ACCELERATORS↗
DOE OSTI2021

Deep Learning with Quantized Neural Networks for Gravitational-wave Forecasting of Eccentric Compact Binary Coalescence

We present the first application of deep learning forecasting for binary neutron stars, neutron star–black hole systems, and binary black hole mergers that span an eccentricity range e ≤ 0.9. In this work, we train neural networks that describe these astrophysical populations, and then test their performance by injecting simulated eccentric signals in advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) noise available at the Gravitational Wave Open Science Center to (1) quantify how fast neural networks identify these signals before the binary components merge; (2) quantify how accurately neural networks estimate the time to merger once gravitational waves are identified; and (3) estimate the time-dependent sky localization of these events from early detection to merger. Our findings show that deep learning can identify eccentric signals from a few seconds (for binary black holes) up to tens of seconds (for binary neutron stars) prior to merger. A quantized version of our neural networks achieves 4× reduction in model size, and up to 2.5× inference speedup. These novel algorithms may be used to facilitate time-sensitive multimessenger astrophysics observations of compact binaries in dense stellar environments.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Prediction of Long-Term Geochemical Change in Bentonite Based on the Interpretative THMC Model of the FEBEX In Situ Test

Since nuclear energy is crucial in the decarbonization of the energy supply, one hurdle to remove is the handling of high-level radioactive waste (HLW). Disposal of HLW in a deep geological repository has long been deemed a viable permanent option. In the design of a deep geological repository, compacted bentonite is the most commonly proposed buffer material. Predicting the long-term chemical evolution in bentonite, which is important for the safety assessment of a repository, has been challenging because of the complex coupled processes. Models for large-scale tests and predictions based on such models have been some of the best practices for such purposes. An 18-year-long in situ test with two dismantling events provided a unique set of chemical data that allowed for studying chemical changes in bentonite. In this paper, we first developed coupled thermal, hydrological, mechanical, and chemical (THMC) models to interpret the geochemical data collected in the in situ test and then extended the THMC model to 200 years to make long-term prediction of the geochemical evolution of bentonite. The interpretive coupled THMC model shows that the geochemical profiles were strongly affected by THM processes such as evaporation/condensation, porosity change caused by swelling, permeability change, and the shape of concentration profiles for major cations were largely controlled by transport processes, but concentration levels were regulated by chemical reactions, and the profiles of some species such as pH, bicarbonate, and sulfate were dominated by these reactions. The long-term THMC model showed that heating prolongs the time that bentonite becomes fully saturated in the area close to the heater/canister; however, once the bentonite becomes fully saturated, high concentrations of ions in bentonite near the heater, which was observed in the field test, will disappear; illitization continues for 50 years but will not proceed further.

Zheng, Liange↗
NASA NTRS2013

Electrical Capacitance Volume Tomography for the Packed Bed Reactor ISS Flight Experiment

Fixed packed bed reactors are compact, require minimum power and maintenance to operate, and are highly reliable. These features make this technology a highly desirable unit operation for long duration life support systems in space. NASA is developing an ISS experiment to address this technology with particular focus on water reclamation and air revitalization. Earlier research and development efforts funded by NASA have resulted in two hydrodynamic models which require validation with appropriate instrumentation in an extended microgravity environment. To validate these models, the instantaneous distribution of the gas and liquid phases must be measured.Electrical Capacitance Volume Tomography (ECVT) is a non-invasive imaging technology recently developed for multi-phase flow applications. It is based on distributing flexible capacitance plates on the peripheral of a flow column and collecting real-time measurements of inter-electrode capacitances. Capacitance measurements here are directly related to dielectric constant distribution, a physical property that is also related to material distribution in the imaging domain. Reconstruction algorithms are employed to map volume images of dielectric distribution in the imaging domain, which is in turn related to phase distribution. ECVT is suitable for imaging interacting materials of different dielectric constants, typical in multi-phase flow systems. ECVT is being used extensively for measuring flow variables in various gas-liquid and gas-solid flow systems. Recent application of ECVT include flows in risers and exit regions of circulating fluidized beds, gas-liquid and gas-solid bubble columns, trickle beds, and slurry bubble columns. ECVT is also used to validate flow models and CFD simulations. The technology is uniquely qualified for imaging phase concentrations in packed bed reactors for the ISS flight experiments as it exhibits favorable features of compact size, low profile sensors, high imaging speed, and flexibility to fit around columns of various shapes and sizes. ECVT is also safer than other commonly used imaging modalities as it operates in the range of low frequencies (1 MHz) and does not radiate radioactive energy. In this effort, ECVT is being used to image flow parameters in a packed bed reactor for an ISS flight experiment.

Tomography↗
NASA NTRS1981

The design of a wind tunnel VSTOL fighter model incorporating turbine powered engine simulators

A wind-tunnel model of a supersonic VSTOL fighter aircraft configuration has been developed for use in the evaluation of airframe-propulsion system aerodynamic interactions. The model may be employed with conventional test techniques, where configuration aerodynamics are measured in a flow-through mode and incremental nozzle-airframe interactions are measured in a jet-effects mode, and with the Compact Multimission Aircraft Propulsion Simulator which is capable of the simultaneous simulation of inlet and exhaust nozzle flow fields so as to allow the evaluation of the extent of inlet and nozzle flow field coupling. The basic configuration of the twin-engine model has a geometrically close-coupled canard and wing, and a moderately short nacelle with nonaxisymmetric vectorable exhaust nozzles near the wing trailing edge, and may be converted to a canardless configuration with an extremely short nacelle. Testing is planned to begin in the summer of 1982.

Bailey, R. O.↗
DOE OSTI2022

Development of an ammonia pretreatment that creates synergies between biorefineries and advanced biomass logistics models

In this study, a novel ammonia-based pretreatment for densified lignocellulosic biomass was developed to reduce ammonia usage and integrate with viable biomass logistics scenarios. The COmpacted Biomass with Recycled Ammonia (COBRA) pretreatment performed at 100 °C allows >95% conversion of sugarcane bagasse (SCB) carbohydrates into soluble monomeric and oligomeric sugars (glucose and xylose) using industrially relevant 6% glucan loading (~21% solids loading) enzymatic hydrolysis conditions at reduced enzyme loadings. Pretreatment via COBRA with simultaneous lignin extraction (COBRA-LE) improved Saccharomyces cerevisiae 424A(LNH-ST) metabolic yield from 89% to 97.5% relative to COBRA without delignification, allowing a process ethanol yield of 71.6%. A technoeconomic analysis on SCB biorefining to ethanol in the state of São Paulo, Brazil, compared COBRA to other mature technologies, such as AFEX and steam-explosion. Amongst all scenarios studied, biorefineries based on COBRA-LE pretreatment offered the lowest average minimum ethanol selling price of US$1.45 per gallon ethanol. COBRA pretreatment was subsequently tested on perennial grasses and hardwoods, and >80% total sugar yields were achieved for all cases.

09 BIOMASS FUELS↗
NASA NTRS1985

Autoclave processing for composite material fabrication. 1: An analysis of resin flows and fiber compactions for thin laminate

High quality long fiber reinforced composites, such as those used in aerospace and industrial applications, are commonly processed in autoclaves. An adequate resin flow model for the entire system (laminate/bleeder/breather), which provides a description of the time-dependent laminate consolidation process, is useful in predicting the loss of resin, heat transfer characteristics, fiber volume fraction and part dimension, etc., under a specified set of processing conditions. This could be accomplished by properly analyzing the flow patterns and pressure profiles inside the laminate during processing. A newly formulated resin flow model for composite prepreg lamination process is reported. This model considers viscous resin flows in both directions perpendicular and parallel to the composite plane. In the horizontal direction, a squeezing flow between two nonporous parallel plates is analyzed, while in the vertical direction, a poiseuille type pressure flow through porous media is assumed. Proper force and mass balances have been made and solved for the whole system. The effects of fiber-fiber interactions during lamination are included as well. The unique features of this analysis are: (1) the pressure gradient inside the laminate is assumed to be generated from squeezing action between two adjacent approaching fiber layers, and (2) the behavior of fiber bundles is simulated by a Finitely Extendable Nonlinear Elastic (FENE) spring.

Hou, T. H.↗
DOE OSTI2021

A Massively Parallel Implementation of the CCSD(T) Method Using the Resolution-of-the-Identity Approximation and a Hybrid Distributed/Shared Memory Parallelization Model

In this work, a parallel algorithm is described for the coupled-cluster singles and doubles method augmented with a perturbative correction for triple excitations [CCSD(T)] using the resolution-of-the-identity (RI) approximation for two-electron repulsion integrals (ERIs). The algorithm bypasses the storage of four-center ERIs by adopting an integral-direct strategy. The CCSD amplitude equations are given in a compact quasi-linear form by factorizing them in terms of amplitude-dressed three-center intermediates. A hybrid MPI/OpenMP parallelization scheme is employed, which uses the OpenMP-based shared memory model for intranode parallelization and the MPI-based distributed memory model for internode parallelization. Parallel efficiency has been optimized for all terms in the CCSD amplitude equations. Two different algorithms have been implemented for the rate-limiting terms in the CCSD amplitude equations that entail and -scaling computational costs, where N O and N V denote the number of correlated occupied and virtual orbitals, respectively. One of the algorithms assembles the four-center ERIs requiring N V 4 and N O 2 N V 2 -scaling memory costs in a distributed manner on a number of MPI ranks, while the other algorithm completely bypasses the assembling of quartic memory-scaling ERIs and thus largely reduces the memory demand. It is demonstrated that the former memory-expensive algorithm is faster on a few hundred cores, while the latter memory-economic algorithm shows a better strong scaling in the limit of a few thousand cores. The program is shown to exhibit a near-linear scaling, in particular for the compute-intensive triples correction step, on up to 8000 cores. The performance of the program is demonstrated via calculations involving molecules with 24–51 atoms and up to 1624 atomic basis functions. As the first application, the complete basis set (CBS) limit for the interaction energy of the π-stacked uracil dimer from the S66 data set has been investigated. This work reports the first calculation of the interaction energy at the CCSD(T)/aug-cc-pVQZ level without local orbital approximation. The CBS limit for the CCSD correlation contribution to the interaction energy was found to be -8.01 kcal/mol, which agrees very well with the value -7.99 kcal/mol reported by Schmitz, Hättig, and Tew [ Phys. Chem. Chem. Phys. 2014 , 16 , 22167-22178]. The CBS limit for the total interaction energy was estimated to be -9.64 kcal/mol.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2019

Thermochemical Modelling of Fluid-Rock Reactions in Vera Rubin Ridge, Galecrater, Mars

Vera Rubin Ridge (VRR) in Gale Crater, Mars, is a ~200 m wide ~6.5 km long northeast- southwest resistant geomorphological feature on the northern slopes of Aeolis Mons (Mt. Sharp). Analysis of Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) orbital data showed that VRR has strong hematite spectral signatures. Hematite was confirmed in-situ at VRR with the Curiosity rover and has been shown to be present throughout the Mur- ray formation. VRR is stratigraphically continu-ous with the underlying Murray formation. Previous thermochemical modelling showed how hematite at VRR could have formed as the result of open-system weathering at high water/rock ratios. Here we use thermochemical modelling to investigate possible reaction pathways for the hematite-clay- bearing assemblage observed at VRR, starting from an identified least-altered (minimum clay content) Murray composition, and a Mars basal brine.

Turner, S. M. R.↗
DOE OSTI2025

Effects of Subhalos on Interpreting Highly Magnified Sources Near Lensing Caustics

Large magnification factors near gravitational lensing caustics of galaxy-cluster lenses allow the study of individual stars or compact stellar associations at cosmological distances. We study how the presence of sub-galactic subhalos, an inevitable consequence of cold dark matter, can alter the property of caustics and hence change the interpretation of highly magnified sources that lie atop them. First, we consider a galaxy-cluster halo populated with subhalos sampled from a realistic subhalo mass function calibrated to N-body simulations. Then, we compare a semianalytical approximation and an adaptive ray-shooting method that we employ to quantify the property of the caustics. As a case study, we investigate Earendel, a z = 6.2 candidate of magnified single- or multiple-star system with a lone lensed image atop the critical curve in the Sunrise Arc. We find that the source size constraint (≲0.3 pc) previously derived from macrolens models should be relaxed by a factor of a few to 10 when subhalos are accounted for, therefore allowing the possibility of a compact star cluster. The subhalos could introduce an astrometric perturbation that is ≲0$^{"}_{.}$5, which does not contradict observation. These conclusions are largely robust to changes in the subhalo population. Subhalos therefore should be seriously accounted for when interpreting the astrophysical nature of similar highly magnified sources uncovered in recent high-z observations.

Caustic curve↗
DOE OSTI2022

Comparison of AGR-3/4 Fission Product Transport Model to Measurements and Extraction of Diffusivities via Analytical Fits

A one-dimensional finite-element model based on the MOOSE framework has been constructed, and overall transport estimates are predicted based on available diffusivities and sorption isotherms in the extant literature. The predicted transport profiles are compared to experimental results, where such results are available, including total inventory analysis of gamma emitters, liquid scintillation results for Sr-90 concentrations, radial deconsolidation leach-burn-leach within compacts, tomographic reconstructions based on detailed gamma scanning and destructive physical sampling of several rings. The magnitude of expected transport to the sink ring is generally predicted by the model for silver and cesium, however, modeled detailed concentration profiles are not consistent with experimental results. Strontium and europium transport is not well characterized by model results.

07 ISOTOPE AND RADIATION SOURCES↗
NASA NTRS2004

Spectral Index and Quasi-Periodic Oscillation Frequency Correlation in Black Hole Sources: Observational Evidence of Two Phases and Phase Transition in Black Holes

Recent studies have shown that strong correlations are observed between the low frequencies (1-10 Hz) of quasi-periodic oscillations (QPOs) and the spectral power law index of several black hole (BH) candidate sources, in low (hard) states, steep power law (soft) states, and transitions between these states. The observations indicate that the X-ray spectra of such state (phases) show the presence of a power-law component and are sometimes related to simultaneous radio emission, indicating the probable presence of a jet. Strong QPOs (>20% rms) are present in the power density spectrum in the spectral range where the power-law component is dominant (i.e., 60%90%). This evidence contradicts the dominant, long-standing interpretation of QPOs as a signature of the thermal accretion disk. We present the data from the literature and our own data to illustrate the dominance of power-law index-QPO frequency correlations. We provide a model that identifies and explains the origin of the QPOs and how they are imprinted on the properties of the power-law flux component. We argue for the existence of a bounded compact coronal region that is a natural consequence of the adjustment of the Keplerian disk flow to the innermost sub-Keplerian boundary conditions near the central object and that ultimately leads to the formation of a transition layer (TL) between the adjustment radius and the innermost boundary. The model predicts two phases or states dictated by the photon upscattering produced in the TL: (1) a hard state, in which the TL is optically thin and very hot (kT approximately greater than 50 keV), producing photon upscattering via thermal Comptonization (the photon spectrum index Gamma approximates 1.7 for this state is dictated by gravitational energy release and Compton cooling in an optically thin shock near the adjustment radius), and (2) a soft state that is optically thick and relatively cold (kT approximately less than 5 keV the index for this state, Gamma approximates 2.8, is determined by soft-photon upscattering and photon trapping in a converging flow into the BH). In the TL model for the corona, the QPO frequency V(sub high) is related to the gravitational (close to Keplerian) frequency V(sub K) at the outer (adjustment) radius and v(sub low) is related to the TL's normal mode (magnetoacoustic) oscillation frequency v(sub MA) . The observed correlations between index and low and high QPO frequencies are readily explained in terms of this model. We also suggest a new method for evaluation of the BH mass using the index-frequency correlation.

Titarchuk, Lev↗
NASA NTRS2020

The Variable and Non-Variable X-Ray Absorbers in Compton-Thin Type II Active Galactic Nuclei

We have conducted an extensive X-ray spectral variability study of a sample of 20 Compton-thin type II galaxies using broadband spectra from XMM-Newton, Chandra, and Suzaku. The aim is to study the variability of the neutral intrinsic X-ray obscuration along the line of sight and investigate the properties and location of the dominant component of the X-ray-obscuring gas. The observations are sensitive to absorption columns of N(sub H) ∼ 10(exp 20.5–24) cm(exp -2) of fully and partially covering neutral and/or lowly ionized gas on timescales spanning days to well over a decade. We detected variability in the column density of the full-covering absorber in 7/20 sources, on timescales of months to years, indicating a component of compact-scale X-ray-obscuring gas lying along the line of sight of each of these objects. Our results imply that torus models incorporating clouds or over-dense regions should account for line-of-sight column densities as low as ∼a few ×10(exp 21) cm(exp -2). However, 13/20 sources yielded no detection of significant variability in the full-covering obscurer, with upper limits of ΔN(sub H) spanning 10(exp 21–23) cm(exp -2). The dominant absorbing media in these systems could be distant, such as kiloparsec-scale dusty structures associated with the host galaxy, or a homogeneous medium along the line of sight. Thus, we find that overall, strong variability in full-covering obscurers is not highly prevalent in Compton-thin type IIs, at least for our sample, in contrast to previous results in the literature. Finally, 11/20 sources required a partial-covering, obscuring component in all or some of their observations, consistent with clumpy near-Compton-thick compact-scale gas.

Active galaxies↗
NASA NTRS2004

Future Probes of the Neutron Star Equation of State Using X-ray Bursts

Observations with NASA s Rossi X-ray Timing Explorer (RXTE) have resulted in the discovery of fast (200 - 600 Hz), coherent X-ray intensity oscillations (hereafter, %urstoscillations ) during thermonuclear X-ray bursts from 12 low mass X-ray binaries (LMXBs). Although many of their detailed properties remain to be fully understood, it is now beyond doubt that these oscillations result from spin modulation of the thermonuclear burst flux from the neutron star surface. Among the new timing phenomena revealed by RXTE the burst oscillations are perhaps the best understood, in the sense that many of their properties can be explained in the framework of this relatively simple model. Because of this, detailed modelling of burst oscillations can be an extremely powerful probe of neutron star structure, and thus the equation of state (EOS) of supra-nuclear density matter. Both the compactness parameter beta = GM/c(sup 2)R, and the surface velocity, nu(sub rot) = Omega(sub spin)R, are encoded in the energy-dependent amplitude and shape of the modulation pulses. The new discoveries have spurred much new theoretical work on thermonuclear burning and propagation on neutron stars, so that in the near future it is not unreasonable to think that detailed physical models of the time dependent flux from burning neutron stars will be available for comparison with the observed pulse profiles from a future, large collecting area X-ray timing observatory. In addition, recent high resolution burst spectroscopy with XMM/Newton suggests the presence of redshifted absorption lines from the neutron star surface during bursts. This leads to the possibility of using large area, high spectral resolution measurements of X-ray bursts as a precise probe of neutron star structure. In this work I will explore the precision with which constraints on neutron star structure, and hence the dense matter EOS, can be made with the implementation of such programs.

Strohmayer, Tod E.↗
DOE OSTI2026

Deep learning for time series forecasting: a survey of recent advances

Time series forecasting plays a critical role in numerous real-world applications, such as finance, healthcare, transportation, and scientific computing. In recent years, deep learning has become a powerful tool for modeling complex temporal patterns and improving forecasting accuracy. This survey provides an overview of recent deep learning approaches for time series forecasting, involving various architectures including RNNs, CNNs, GNNs, transformers, large language models, MLP-based models, and diffusion models. We first identify key challenges in the field, such as temporal dependency, efficiency, and cross-variable dependency, which drive the development of forecasting techniques. Then, the general advantages and limitations of each architecture are discussed to contextualize their adaptation in time series forecasting. Furthermore, we highlight promising design trends like multi-scale modeling, decomposition, and frequency-domain techniques, which are shaping the future of the field. This paper serves as a compact reference for researchers and practitioners seeking to understand the current landscape and future trajectory of deep learning in time series forecasting.

97 MATHEMATICS AND COMPUTING↗