Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “reference models”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,657 records · Page 92
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Thermal Integration of Advanced Nuclear Reactors with a Reference Refinery, Methanol Synthesis, and a Wood Pulp Plant (Rev.1)

The present report is intended to provide process flow diagrams (PFDs) and energy and mass balance data sheets for a U.S. industrial sector subset with which nuclear heat and power could be integrated—a subset that includes the oil refining, methanol and pulp and paper industries. Coupling options for integrating nuclear energy into these industries are quantitatively outlined for reference systems, and future work will extend this analysis in greater detail. Opportunities for integrating small modular nuclear reactors (SMNRs) were investigated for each of the industrial process configurations. Aspen HYSYS and Cycle-Tempo models for a high-temperature gas-cooled reactor were developed to evaluate the proposed integration. This introductory evaluation provides a general description and assessment of the operating principles, reactor coolant core outlet temperature, and reactor size to be integrated with industry. The industrial processes of oil refining and the production of methanol, pulp and paper were simulated by using Aspen HYSYS, Aspen Plus, and the PRELIM (Petroleum Refinery Life Cycle Inventory Model) tool to develop process details. Cycle-Tempo models then extend the process modeling results to obtain net energy demands (e.g., heat, steam, and electricity) when accounting for process steam and waste heat recovery. This information is intended to foster the analysis of integrating an SMNR to decarbonize industrial facilities. The SMNR would provide reliable, competitive, and sustainable clean energy while reducing carbon emissions and other environmental impacts, such as water withdrawals, consumption, and contamination. The refining industry, exhibited in Figure ES1, is a leading consumer of fossil -fuel-based heat, power, and hydrogen in the U.S. industrial sector, generating over 164 million metric tons (MMT) of CO 2 emissions in 2023. The overall mass and energy pertaining to a generalized complex refinery in the United States is reflected in Figure ES1, along with energy metrics regarding integration with a nuclear power plant (NPP). Data sheets were developed to indicate the energy requirements for the overall refinery and each refinery process. The data sheet for the overall refinery is shown in Table ES2.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Sierra/SD – Theory Manual (V.5.24)

Sierra/SD provides a massively parallel implementation of structural dynamics finite element analysis, required for high fidelity, validated models used in modal, vibration, static and shock analysis of structural systems. This manual describes the theory behind many of the constructs in Sierra/SD. For a more detailed description of how to use Sierra/SD, we refer the reader to User’s Manual. Many of the constructs in Sierra/SD are pulled directly from published material. Where possible, these materials are referenced herein. However, certain functions in Sierra/SD are specific to our implementation. We try to be far more complete in those areas. The theory manual was developed from several sources including general notes, a programmer_notes manual, the user’s notes and of course the material in the open literature.

42 ENGINEERING↗
DOE OSTI2024

Thermal Analysis of the Sirius-3 Nuclear Propulsion Fuel Experiments

To support long space missions, NASA is designing and testing different fuels for nuclear thermal propulsion. These designs include a number ceramic metallic fuels which are to be irradiated in the Tranisent Test Reactor to test the fuel’s performance at protypical conditions. The irradiation campaign of these fuels is referred to as the Sirius experiments, and includes single and stacked experiment samples. In this paper we present the thermal analysis of the Sirius-3 experiment. For this analysis, temperatures from a Bison finite element model are compared to the temperatures obtained from an experiment thermocouple where good agreement between the two are found. Because agreement of the thermocouple and Bison finite element model, insight into the heat flow is provided to experimenters as they design future experiments. As an example of this insight, the rods through the fuel specimen as shown in Sirius A and B [1] were removed and replaced with hold down rings for the Sirius-2C

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2024

Development of a high current density, high temperature superconducting cable for pulsed magnets

Abstract A low AC loss Rare Earth Barium Copper Oxide (REBCO) cable, based on the VIPER cable technology has been developed by Commonwealth Fusion Systems for use in high field, REBCO based tokamaks. The new cable is composed of partitioned and transposed copper ‘petals’ shaped to fit together in a circular pattern with each petal containing a REBCO tape stack and insulated from each other to reduce AC losses. A stainless steel jacket adds mechanical robustness—also serving as a vessel for solder impregnation—while a tube runs through the middle for cooling purposes. Additionally, fiber optic sensors are placed under the tape stacks for quench detection. To qualify this design, a series of experiments were conducted as part of the SPARC tokamak Central Solenoid Model Coil program—to retire the risks associated with full scale, fast ramping, high flux HTS Central Solenoid (CS) and Poloidal Field (PF) coils for tokamak fusion power plants and net energy demonstrators. These risk study and risk reduction experiments include (1) AC loss measurement and model validation in the range of ~5 T/s, (2) an IxB electromagnetic loading of over 850 kN/m at the cable level and up to 300 kN/m at the stack level, (3) a transverse compression resilience of over 350 MPa, (4) manufacturability at tokamak relevant speeds and scales, (5) cable to cable joint performance, (6) fiber optic based quench detection speed, accuracy, and feasibility, and (7) overall winding pack integration and magnet assembly. The result is a cable technology, now referred to as PIT VIPER, with AC losses that measure fifteen times lower (at ~5 T/s) than its predecessor technology; a 2% or lower degradation of critical current (Ic) at high IxB electromagnetic loads; no detectable Ic degradation up to 570 MPa of transverse compression on the cable unit cell; end to end magnet manufacturing, consistently producing Ic values within 7% of the model prediction; cable to cable joint resistances at 20 K on the order of ~15 nΩ; and fast, functional quench detection capabilities that do not involve voltage taps. This cable technology will be tested comprehensively in a Central Solenoid Model Coil to prove its readiness for compact, high field tokamak operation.

Sanabria, Charlie (ORCID:0000000150175309)↗
DOE OSTI2022

Drying of tundra landscapes will limit subsidence-induced acceleration of permafrost thaw: Modeling Archive

This Modeling Archive is in support of a NGEE Arctic publication in review "Drying of tundra landscapes will limit subsidence-induced acceleration of permafrost thaw". The study used a cryohydrology model to assess the potential risk of abrupt permafrost thaw triggered by melting ground ice, a key open question associated with permafrost response to a warming Arctic. The spatially resolved simulations are for a small catchment 465 ice-wedge polygons in polygonal tundra near Utqiagvik, Alaska in the high-emissions RCP8.5 climate scenario. The simulations are compared to runoff, evapotranspiration and subsidence in the current climate and agree well. The study used the ATS code configured as an intermediate-scale cryohydrology model (Advanced Terrestrial Simulator, Version v2). The archive includes input files for spinup (1985 to 2005) and projections (2006 to 2100 - the manuscript reports 2006 to 2098). Three of the projections include the effects of subsidence and microtopography change with different depth profiles of ice content corresponding to the median, 20th percentile and 80th percentile. The fourth projection has subsidence turnoff and uses the reference case (median) ice content. Spatially averaged or aggregated output variables are included for the projections. Selected checkpoint files for the projections and postprocessing scripts are also included. Files included are *.xml; *.h5; *.exo; *.py; *.sh, *. nb, mesh files, and one file in the original Excel format plus *.csv and *.pdf to conserve formatting contained in the original file. The Next-Generation Ecosystem Experiments: Arctic (NGEE Arctic), was a research effort to reduce uncertainty in Earth System Models by developing a predictive understanding of carbon-rich Arctic ecosystems and feedbacks to climate. NGEE Arctic was supported by the Department of Energy's Office of Biological and Environmental Research. The NGEE Arctic project had two field research sites: 1) located within the Arctic polygonal tundra coastal region on the Barrow Environmental Observatory (BEO) and the North Slope near Utqiagvik (Barrow), Alaska and 2) multiple areas on the discontinuous permafrost region of the Seward Peninsula north of Nome, Alaska. Through observations, experiments, and synthesis with existing datasets, NGEE Arctic provided an enhanced knowledge base for multi-scale modeling and contributed to improved process representation at global pan-Arctic scales within the Department of Energy's Earth system Model (the Energy Exascale Earth System Model, or E3SM), and specifically within the E3SM Land Model component (ELM).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

A Phase-Disposition PWM Enabled Model Predictive Control for a Nine-Level Inner-Interleaved Hybrid Multilevel Converter

This article brings forward a phase-disposition pulse width modulation enabled model predictive control (PDPWM-MPC) for a nine-level inner-interleaved hybrid multilevel converter (9L-IHMC). Firstly, three layers of virtual space vector diagrams (VSVD) are established based on the sign patterns of the original and virtual reference vectors in the abcframe, respectively, to achieve the phase-disposition pulse width modulation (PD-PWM) in a non-independent three-phase way. Then, three adjacent virtual vectors in the third-layer VSVD, together with their optimized duty cycles, are applied to guarantee the optimal current tracking. Finally, through the use of the duty cycle alternation approach, dc-link and floating capacitors voltages are balanced and circulating currents are mitigated as well. The proposed PDPWM-MPC can not only enable the decoupling of the low-and high-frequency stages in the 9L-IHMC, but also reduce both output current ripples and computational burden. In addition, it can achieve a constant equivalent switching frequency and address the disproportion of power losses associated with the PD-PWM. Here, both simulations and experiments on a silicon carbide device-based prototype substantiate the effectiveness of the proposed control strategy.

42 ENGINEERING↗
DOE OSTI2020

Electron and proton conductivity of Fe-N-C cathodes for PEM fuel cells: A model-based electrochemical impedance spectroscopy measurement

Impedance spectra of a PEM fuel cell with three Fe-N-C cathodes have been measured under the H 2 /N 2 testing regime. The spectra have been fitted using a recently developed physics-based impedance model, which takes into account finite proton ($σ_p$) and electron ($σ_e$) conductivity of the oxygen-free cathode catalyst layer. Fitting allowed to extract numerical data for $σ_p$, $σ_e$, the double layer capacitance, and the inductance of cables used for measuring impedance spectra. The values of σp and σe are close to what previously found for standard Pt/C electrodes, which is found for the first time using PGM-free catalysts. The method enables simultaneous measurement of reference proton and electron conductivity of PEMFC cathode.

25 ENERGY STORAGE↗
DOE OSTI2020

ZAM Modeling Study to Support the Tank Closure Cesium Removal (TCCR) 1A Unit

Currently at the Savannah River Site (SRS), the Tank Closure Cesium Removal (TCCR) is an “at-tank” process designed to remove cesium from aqueous tank waste. Cesium will be removed by ion exchange using the engineered IONSIV® R9120 form of Crystalline Silicotitanate (CST) media. The current TCCR design has two columns online in a lead-lag configuration to optimize media usage and achieve the target decontamination. Once the lead column is saturated with cesium, it will be removed from service, the lag column will rotate into the lead position, and a new column with fresh ion-exchange media will be placed into the lag position. The TCCR process for cesium removal from Tank 10H is detailed in X-SOW-H- 00002. Demonstration of the system began in early calendar year 2019 with two batches of salt solution generated by dissolving saltcake in Tank 10H, followed by processing of these batches through the TCCR system. A third TCCR Tank 10H dissolved saltcake batch is scheduled for processing soon. Upon completion of the demonstration with Tank 10H dissolved saltcake, Tank 9H salt solution will be transferred to Tank 10H and subsequently processed through the TCCR unit with new CST media (referred to as R9120-B 30x60) added to new IX columns. The TCCR processing campaign of Tank 9H salt solution is referred to as TCCR-1A .

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

Simulation of natural circulation cartridge loop experiments and application to molten salt reactors

This work uses the TRAC/RELAP Advanced Computational Engine (TRACE) thermal hydraulics (TH) code to model natural circulation cartridge loop experiments previously conducted at Oak Ridge National Laboratory (ORNL) using water and compares the simulated and experimental results. TRACE is also used to characterize natural circulation in the cartridge loop vehicle using FLiNaK as the working fluid. The experimental vehicle is a buoyancy-aided, annular cartridge loop, referred to as a thermosyphon, and is designed to aid in qualifying liquid–fueled and/or liquid–cooled irradiation experiments for the Versatile Test Reactor (VTR), which is currently being designed in the United States. Out-of-pile water experiments have been conducted using the cartridge and the Thermosyphon Test Loop facility at ORNL, and future experiments are anticipated that would use other molten salt surrogates as the working fluid, followed by eventual insertion of a similar cartridge into VTR. Additionally, this work aims to determine how well TRACE can replicate the natural convection conditions that were observed experimentally; this serves as an initial step for validating the modeling tool for design and safety calculations to support future irradiation experiments in VTR. Initial predictions of potential experiments were made using FLiNaK as the natural circulation fluid to demonstrate the relevance of the cartridge design to molten salt reactors (MSRs). Results from this study indicate that TRACE can accurately capture natural convection phenomena in the thermosyphon and that several design changes to the current cartridge vehicle are necessary to achieve hydraulic conditions similar to those expected in MSRs.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

HT Model Dataset

This website contains the dataset that was used for writing the manuscript "HT Model: Using the Molecular Transformer for predicting hydrotreating reactions" (PNNL-SA-186589) The dataset includes a collection of hydrotreating reactions compiled from 41 peer-reviewed literature sources. These sources contain experimental data related to hydrotreating reactions. These reactions involve the reaction of chemical compounds with hydrogen gas in the presence of a catalyst to remove heteroatoms or to convert specific functional groups. The dataset contains reactions both with and without reaction conditions. Reaction conditions refer to the specific parameters under which the reaction takes place, such as temperature and pressure. For each reaction, the dataset includes both SMILES and SELFIES representations. SMILES (Simplified Molecular Input Line Entry System) and SELFIES (SELF-referencIng Embedded Strings) are two popular notations used to represent chemical structures in a compact and standardized format. The dataset was created with the aim of training a predictive model, specifically using the Molecular Transformer architecture.

bioprocessing, hydrotreating, deep learning algori↗
DOE OSTI2020

Performance and wake flow characterization of a 1:8.7-scale reference USDOE MHKF1 hydrokinetic turbine to establish a verification and validation test database

As hydrokinetic turbine technologies continue to advance towards commercialization, public datasets on the performance characteristics for these devices and their flow field effects are invaluable to advance our understanding of these technologies and to validate analytical and numerical models. The Applied Research Laboratory at The Pennsylvania State University (ARL Penn State) collaborated with Sandia National Laboratories and the University of California at Davis to design, fabricate (at a 1:8.7 scale), and experimentally test a novel hydrokinetic turbine rotor design to provide an open platform and dataset for further study and development. The water tunnel test of this three-bladed, horizontal-axis rotor recorded power production, blade loading, the near-wake flow, cavitation effects, and noise generation. These state-of-the-art measurements demonstrate much of the complex physics associated with the flow through an unducted, horizontal-axis turbine, and they elucidate the performance characteristics and flow field effects at an unprecedented fidelity, accuracy and resolution. Measurements of powering coefficients (power, torque and thrust) as a function of tip-speed-ratio were performed. The dataset also includes unsteady measurements of driveshaft loading, blade strain, tower pressures, and radiated noise. Detailed flow mapping using laser Doppler velocimetry, and planar and stereo particle image velocimetry includes measurements of mean velocity and Reynolds stresses. Although the wake measurements are limited to less than half a diameter, they reveal the complex flow patterns in the near-wake structure of the rotor. The full database, available at the United States Department of Energy’s marine and hydrokinetic data repository, includes tunnel and model Computer Aided Design geometry files and inflow data sufficient for a “Model-the-Test” computational Verification and Validation study.

13 HYDRO ENERGY↗
DOE OSTI2026

An Optimized Parameterization of Sub‐Grid Scale Advection for Convection Permitting Models

Convection‐permitting models (CPMs) explicitly resolve deep convection yet under‐resolve the organized lateral exchanges among drafts and their environment that control entrainment/detrainment, precipitation efficiency, and mesoscale structure. In this work, we introduce the Optimized Advection Scheme (OAS), which introduces a small rotation of the Cartesian frame of reference for the horizontal winds relative to other variables used in advection that induces cross‐gradient transport to mimic under‐resolved convective mixing. The rotation angle is selected to minimize the Kullback–Leibler divergence between the simulated and satellite observed precipitation intensity distributions, yielding a physically consistent perturbation that is computationally inexpensive and portable. Optimized Advection Scheme is implemented in WRF and evaluated over Amazon (April 2014). It shifts precipitation–precipitable‐water joint distributions toward lighter rain, reduces overly intense rates, and improves mesoscale convective system (MCS) lifetime and propagation. Mechanistically, the added cross‐gradient transport promotes convective detrainment and environmental mixing, which cools and moistens the mid‐troposphere, weakens downward momentum transport, alleviates excessive downwelling shortwave biases, and warms the surface temperature. The optimized rotation angle yields comparable improvements at 4‐km and 1‐km grid spacing, demonstrating resolution‐independent benefits across the CPM gray zone. By targeting the dynamical root of under‐mixed convective circulations, rather than tuning model microphysics or closures, OAS delivers robust, scale‐aware improvements in precipitation statistics, cloud vertical structure, and characteristics of MCS (MCSs), offering a practical pathway to more reliable CPM simulations for weather and climate applications.

CPM↗
DOE OSTI2020

Chromatographic Modeling of 1-Foot Detritiation Test Column Results for the Optimization of Regeneration Time

This report documents the methods and results of a modeling study on a series of data generated by 1-foot test columns for the Water Detritiation project. In order to compliment modeling work already in progress on this project, a purely empirical curve-fitting approach is used in this study to determine chromatographic performance indicators such as retention time, curve width, and the number of chromatographic stages. The data used in this study comes from four sets of chromatographic test separations performed in March through May of 2017 using 1-foot columns. All are using the same flow rates and temperature (room temperature, nominally 25 C°). The first set of data (referred to in this report as the Column 1 data) is a series of twelve breakthrough curve measurements. Prior to each of these twelve runs, the column was regenerated by flowing hydrogen gas through the column, for increasing amounts of time, ranging from 2 hours to 25 hours. The second set of data (referred to as the Column 2 data) is comprised of five measurements of breakthrough curves measured in similar fashion as the Column 1 data, across a range of regeneration times from 2 to 21 hours. The third set of data (referred to as the Purge data) is of three breakthrough curves, measured after a regeneration time of 8 hours, which takes place after a nitrogen purge of 15, 30, or 45 minutes. The fourth data set is a series of five breakthrough curve measurements using a 2 nd batch of stationary phase, taken after regeneration times ranging from 2 to 20 hours. The overall modeling approach is as follows. First, the data is pre-processed for formatting, artifact removal, and is normalized. The data is then fit by integrated versions of four common chromatographic models. The best model is chosen based on the predictive performance of the model, and chromatographic performance values are calculated based on the best model’s fit parameters. Each of these processes are detailed below.

42 ENGINEERING↗
DOE OSTI2026

Idealized Offshore Low‐Level Jets for Turbine Structural Impact Considerations

Low-level jets (LLJs) describe conditions in which the wind speed reaches a local maximum with respect to altitude near the surface; they have been observed intermittently in the US mid-Atlantic offshore environment. LLJs pose unique operating conditions for future wind turbines operating in the region, such as negative shear and locally strong veer, but they are not typically considered in existing turbine standards. This work builds upon recent research that explains the formation and evolution of the US mid-Atlantic LLJs through a simple analytical governing equation. We generate several LLJ inflow conditions with varying jet characteristics based on this analytical model and create monotonically sheared (MS) analogues with matched veer to assess the impacts of the LLJ on turbine performance and loading. Using aeroelastic simulations with these inflow conditions on the International Energy Agency 15-MW reference turbine, we find that the LLJ leads to a greater range of tower-top pitching and yawing moments, which could contribute to larger accumulated structural fatigue in components compared to MS inflow. These preliminary results demonstrate a path toward a unified set of test cases for low-level wind maxima that can inform the International Electrotechnical Commission standards related to offshore wind turbine design.

17 WIND ENERGY↗
DOE OSTI2021

Prospects for Surrogate Neutron Capture Measurements with Radioactive Ion Beams and GODDESS

Neutron capture reactions are responsible for the synthesis of almost all of the elements heavier than iron through the slow s-process, that proceeds close to the line of stability, and the rapid r-process, with very neutron-rich waiting points. Uncertainties in (n,γ) rates in neutron rich nuclei, especially near closed neu- tron shells, can have significant impact [1] on the predictions of final abundances for different astrophysical scenarios for the r process. Understanding (n,γ) rates on neutron-rich fission fragments is also important for nuclear forensics and stockpile stewardship science. Ratkiewicz et al. [2 and references therein] has recently demonstrated that the (d,pγ) reaction is a valid surrogate for (n,γ), where the formation of the compound nucleus from the breakup of the deuteron has been calculated in a reaction model and the subsequent measured gamma-decay probabilities are reproduced with standard level density and strength functions in a Bayesian approach. In parallel to the surrogate validation efforts, we have demonstrated that the (d,pγ) reaction can be measured in inverse kinematics with Gammasphere ORRUBA: Dual Detectors for Experimental Structure Studies (GODDESS) [3] where the Gammasphere array of Compton-suppressed HPGe detectors is coupled to the Oak Ridge Rutgers University Barrel Array of position-sensitive silicon strip detectors. During the commissioning campaign we measured the (d,pγ) reaction with 134 Xe and 95 Mo beams, the latter to demonstrate the surrogate method in inverse kinematics. The present talk will present preliminary results from this campaign including γ-decay probabilities and prospects for surrogate (n,γ) measurements with 143 Ba fission-fragment beams.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Modeling lattice rotation fields from discrete crystallographic slip bands in superalloys

Here in this work, we investigate the relationship between an intense slip band (ISB) and the zone of large lattice rotations that forms ahead of the tip of the ISB. We develop a crystal plasticity finite element model of a discrete ISB lying within an oligocrystalline assembly and calculate the local crystalline stress and lattice rotation fields generated by the ISB. The calculations demonstrate that, first, a region of severe lattice rotations, commonly referred to as a microvolume, does not form without the ISB, and second, large amounts of accumulated slip in the ISB are required to enlarge the microvolume to sizes and rotation magnitudes observed experimentally. Ahead of the ISB tip, the quintessential plastic zone always forms, but the atypical microvolume forms when non-concentrated and spatially diffuse slip is activated by the ISB-induced stress field. This result suggests that the detrimental ISB/microvolume pair will likely appear in pairs of crystals in which transmission of the slip from the ISB is severely blocked by the grain boundary, a hypothesis that we verify with a few target cases.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Model calibration of the liquid mercury spallation target using evolutionary neural networks and sparse polynomial expansions

The mercury constitutive model predicting the strain and stress in the target vessel plays a central role in improving the lifetime prediction and future target designs of the mercury targets at the Spallation Neutron Source. We leverage the experiment strain data collected over multiple years to improve the mercury constitutive model through a combination of large scale simulations of the target behavior and the use of machine learning tools for parameter estimation. We present two interdisciplinary approaches for surrogate-based model calibration of expensive simulations using evolutionary neural networks and sparse polynomial expansions. The newly calibrated simulations achieve 7% average improvement on the prediction accuracy and 8% reduction in mean absolute error compared to previously reported reference parameters, with some individual sensors experiencing up to 30% improvement. The calibrated simulations can aid in fatigue analysis to estimate the mercury target lifetime, which reduces abrupt failure and saves tremendous amount of costs.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

Correlating AGP on a quantum computer

For variational algorithms on the near term quantum computing hardware, it is highly desirable to use very accurate ansatze with low implementation cost. Recent studies have shown that the antisymmetrized geminal power (AGP) wavefunction can be an excellent starting point for ansatze describing systems with strong pairing correlations, as those occurring in superconductors. In this work, we show how AGP can be efficiently implemented on a quantum computer with circuit depth, number of CNOTs, and number of measurements being linear in system size. Using AGP as the initial reference, we propose and implement a unitary correlator on AGP and benchmark it on the ground state of the pairing Hamiltonian. Furthermore, the results show highly accurate ground state energies in all correlation regimes of this model Hamiltonian.

97 MATHEMATICS AND COMPUTING↗