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At least 883 records · Page 49
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Computational tools and algorithms for ion mobility spectrometry-mass spectrometry

Ion mobility spectrometry-mass spectrometry (IMS-MS or IM-MS) is a powerful analytical technique that combines the gas-phase separation capabilities of IM with the identification and quantification capabilities of MS. IM-MS can differentiate molecules with indistinguishable masses but different structures (e.g., isomers, isobars, molecular classes, and contaminant ions). The importance of this analytical technique is reflected by a staged increase in the number of applications for molecular characterization across a variety of fields, from different MS-based omics (proteomics, metabolomics, lipidomics, etc.) to the structural characterization of glycans, organic matter, proteins, and macromolecular complexes. With the increasing application of IM-MS there is a pressing need for effective and accessible computational tools. This article presents an overview of the most recent free and open-source software tools specifically tailored for the analysis and interpretation of data derived from IM-MS instrumentation. This review enumerates these tools and outlines their main algorithmic approaches, while highlighting representative applications across different fields. Finally, a discussion of current limitations and expectable improvements is presented.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Design of an Online Electrochemical Mass Spectrometry System to Study Gas Evolution from Cells with Lean and Volatile Electrolytes

Gas evolution in high-energy Li-ion batteries remains a pervasive problem for a multitude of chemistries, jeopardizing the electrochemical performance and safety for consumers of electric vehicles. Many electrode–electrolyte degradation processes evolve gasses that may be detected in-situ with online electrochemical mass spectrometry (OEMS). In this work, details are provided for the setup and validation of an OEMS system that operates well under lean and volatile electrolyte conditions. Quite notably, the OEMS cells with only 40 µL of electrolyte and intermittent headspace sampling exhibit comparable electrochemical performance to flooded coin-cells. It is demonstrated that the onset time, shape, and magnitude of the gas evolution profiles calculated from mass spectrometer measurements match well to a known pressure reference through the use of an empirically determined fraction of removal. The off-gassing characteristics from a set of layered-oxide materials, NMC532, NMC811, and LNO, are used to further validate the OEMS setup against the literature. It is shown that many of the features present in the OEMS curves for equivalent systems from other groups are captured by this OEMS system. Finally, at an upper cut-off voltage of 4.4 V, LNO exhibits an intense release of CO 2 , O 2 , and CO gas relative to NMC532 and NMC811.

25 ENERGY STORAGE↗
DOE OSTI2020

An Experimental Method to Measure Gaseous Diffusivity in Tight and Partially Saturated Porous Media via Continuously Monitored Mass Spectrometry

Detection of radioxenon and radioargon produced by underground nuclear explosions is one of the primary methods by which the Comprehensive Nuclear-Test–Ban Treaty (CTBT) monitors for nuclear activities. However, transport of these noble gases to the surface via barometric pumping is a complex process relying on advective and diffusive processes in a fractured porous medium to bring detectable levels to the surface. To better understand this process, experimental measurements of noble gas and chemical surrogate diffusivity in relevant lithologies are necessary. However, measurement of noble gas diffusivity in tight or partially saturated porous media is challenging due to the transparent nature of noble gases, the lengthy diffusion times, and difficulty maintaining consistent water saturation. Here, the quasi-steady-state Ney–Armistead method is modified to accommodate continuous gas sampling via effusive flow to a mass spectrometer. An analytical solution accounting for the cumulative sampling losses and induced advective flow is then derived. Experimental results appear in good agreement with the proposed theory, suggesting the presence of retained groundwater reduces the effective diffusivity of the gas tracers by 10–1000 times. Finally, by using a mass spectrometer, the method described herein is applicable to a broad range of gas species and porous media.

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

Hydrometallurgical Recycling of Black Mass of Spent Lithium-Ion Batteries Using Methanesulfonic Acid: Leaching, Kinetic Studies, and Potential for Total Recovery of Valuable Components

Methanesulfonic acid (MSA) exhibits several advantageous properties rendering it a promising candidate for circular hydrometallurgical processes. These properties include a high acidity (pKa = - 1.9) comparable to that of classical mineral acids as well as biodegradability, high stability, and high solubility of metal-MSA complexes in aqueous solutions. In this study, MSA was employed as a lixiviant for the leaching of metals (lithium, nickel, cobalt, and manganese) from the black mass of spent lithium-ion batteries (LIBs). The effect of various parameters, including MSA concentration, H 2 O 2 concentration, temperature, and pulp density, was systematically investigated. Under the optimized conditions (1.5 M MSA, 0.2 M H 2 O 2 , 60 °C, and 50 g/L pulp density), quantitative leaching of lithium was achieved within 30 min, while for nickel and cobalt it was after 2 h, and 4 h for manganese leaching. The leaching kinetics of Li, Ni, Co, and Mn were studies using the shrinking particle models (SPM) and the Avrami model. The results indicated that the Avrami model provided the best fit to the kinetic data, with apparent activation energies of 46.81 kJ/mol for Li, 58.61 kJ/mol for Ni, 59.69 kJ/mol for Co, and 58.86 kJ/mol for Mn, within the temperature range of 25-70 °C (except for Li, which was analyzed in the range of 25-60 °C), consistent with chemical reaction control. Subsequently, residual contaminants in the leaching residue were eliminated through pyrolysis. The quantitative leaching of metals in MSA solution (a green lixiviant), combined with the pyrolytic treatment of leaching residues, represents a circular strategy for the total recovery of valuable components from the black mass of spent LIBs.

25 ENERGY STORAGE↗
DOE OSTI2022

An approach to nearest neighbor analysis of pigment-protein complexes using chemical cross-linking in combination with mass spectrometry

Herein, protein cross-linking is the process of chemically joining two amino acids in a protein or protein complex by a covalent bond. When combined with mass spectrometry, it becomes one of the structural mass spectrometry techniques gaining in importance for deriving valuable three-dimensional structural information on proteins and protein complexes. This platform complements existing structural methods, such as NMR spectroscopy, X-ray crystallography, and cryo-EM. Photosynthetic pigment protein complexes serve as light-energy harvesting systems and perform photochemical conversion as part of the “early events” of photosynthesis. This chapter outlines how to prepare cross-linking pigment protein complex samples for LC-MS/MS analysis, including identification of the cross-linked species, network analysis in a protein complex, and structural modeling and justification.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

On the validity and limitations of 1D model for heat and mass transfer performance evaluation in a multilayer binder-free desiccant dehumidifier: isothermal dehumidification with internal cooling

Efficient humidity control is essential for maintaining indoor thermal comfort, yet conventional vapor-compression-based dehumidifiers are energy-intensive. Employing separate sensible and latent cooling through desiccant-coated heat exchangers (DCHEs) combined with evaporative coolers offers energy savings of up to 80 % compared to conventional systems. However, the dehumidification performance of DCHEs remains limited due to the use of polymer binders for coating desiccant materials onto heat exchange surfaces. In our previous study, we developed a multilayer fixed-bed binder-free desiccant dehumidifier (MFBDD) that demonstrated high dehumidification capacity and low pressure drop compared to rotary desiccant wheels. Nevertheless, its potential for further enhancement through internal cooling and the use of step-shaped adsorption isotherms has not been explored. In this study, a physics-based one-dimensional (1D) transient model is developed and validated to capture the coupled heat and mass transfer processes in the MFBDD and extended to simulate internal cooling using a high-capacity composite metal–organic framework, MIL-101/GO-6 (water uptake ≈1.6 g/g within 35–47 % RH). The model enables detailed analysis of local air and bed temperature dynamics and quantifies how internal cooling affects the dehumidification performance under a wide range of operating conditions. Results show that integrating internal cooling and using MIL-101/GO-6 enhance mass adsorbed, moisture removal capacity, and dehumidification effectiveness by 50 %–99 % compared with the M.S. Gel baseline. The study further reveals that achieving near-isothermal operation requires simultaneous enhancement of the convective heat transfer coefficient and heat exchange surface area. In conclusion, this work provides the first detailed physical insight into the interplay between internal cooling and step-shaped isotherms in a binder-free desiccant device and establishes a validated modeling framework for scaling up and system-level performance evaluation of next-generation energy-efficient dehumidification systems.

Heat and mass transfer↗
DOE OSTI2021

Encapsulation of highly viscous CO 2 capture solvents for enhanced capture kinetics: Modeling investigation of mass transfer mechanisms

The encapsulation of highly viscous liquid-like Nanoparticle Organic Hybrid Materials (NOHMs) inside a gas permeable polymer to form SIPs (Solvent Impregnated Polymers) significantly enhanced the CO 2 capture kinetics of NOHMs, leading to a remarkable 50-fold increase in CO 2 flux compared to the neat NOHMs. To understand the mechanism for enhanced CO 2 mass transfer within these hybrid materials, kinetic modeling of CO 2 uptake into SIPs containing polyethylenimine functionalized NOHMs, denoted NPEI-SIP, was conducted. CO 2 mass transfer into NPEI-SIP films was found to conform, both qualitatively and quantitatively, with a diffusion-controlled moving front model. The diffusion-controlled model was also used to simulate CO 2 uptake within a fixed bed containing polydisperse NPEI-SIP particles, and this model accurately predicted experimentally measured breakthrough curves at 25 °C and 50 °C. The 50-fold increase in gas flux was shown to be a consequence of the very large CO 2 permeability within the polymer–solvent composite. Furthermore, the increase in gas flux is also dependent on the diffusion–reaction regime in which the chemical solvent operates, and the largest improvement will occur when immobilizing solvents, such as NOHMs, which operate in the instantaneous-reaction regime. The CO 2 capacity (~3 mol CO 2 /kg) and saturation time (~5 min) of 430 μm SIP particles were comparable to popular CO 2 chemisorption materials such as amine grafted silicates, in spite of the slow kinetics of NOHM-I-PEI in liquid form (CO 2 saturation time ~24 h for a 1 mm thin film).

36 MATERIALS SCIENCE↗
DOE OSTI2024

NO formation by N 2 /O 2 plasma catalysis: The impact of surface reactions, gas-phase reactions, and mass transport

Pathways and timescales relevant to facilitate plasma-assisted N 2 -O 2 reactions are assessed by measuring the consumption of plasma-derived N and the formation of NO in the gas phase and over Ag catalytic surfaces. These measurements are enabled by a setup that enables N 2 activation in an atmospheric pressure RF plasma jet, enables O 2 addition in the plasma afterglow, facilitates reactions over an Ag wire catalyst, and allows species density quantification by molecular beam mass spectrometry. Gas-phase reactions consume N but do not form NO with high selectivity. The presence of the non-porous Ag wire catalyst increases the rate of N conversion to NO, though mass transfer processes, not surface reactions, dictate the rate of N consumption. When O 2 concentrations and the ratio of the surface area of the catalyst to the void volume of the reactor are high (3–5 mol% O 2 , 10900 m –1 ), N conversion to NO reaches 100 % selectivity. When both N 2 and O 2 are fed through the plasma jet, gas-phase NO production increases 10×, although plasma and gas-phase processes do not exclusively produce NO. Above a threshold NO density, N cannot diffuse to the catalyst surface faster than it is consumed in the gas phase by reactions with NO. Furthermore, the use of heterogeneous catalysts to enhance plasma-driven N x O y formation and control N x O y product selectivity is limited to cases where diffusive transport of N from the gas phase to the catalyst surface is faster than consumption of N from gas-phase reactions with NO.

Engineering↗
DOE OSTI2025

A simplified CFD approach for modeling mass transport in catalytic open-cell foams

A simplified macroscopic CFD approach is presented to model mass transport including chemical reactions in washcoated open-cell foams. The foam is treated as a porous medium. Species conversion during chemical reactions is modeled using appropriate source terms based on reaction rate expressions and modified to account for the mass transport resistances occurring at the fluid-washcoat interfaces and within the washcoat layers. As example, the catalytic CO oxidation over platinum is studied. The simulation results show good agreement with experimental data from literature. A parametric study on washcoat parameters, such as thickness, tortuosity, porosity, and size, is carried out. Increasing the washcoat thickness from 5 to 100 µm or decreasing the tortuosity to porosity ratio from 5 to 20 decreases the CO conversion by 10 %. The proposed model is found to be reliable and has the advantage of lower computational cost, making it a suitable tool for foam-based catalytic reactor design.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

The use of gas chromatography – high resolution mass spectrometry for suspect screening and non-targeted analysis of per- and polyfluoroalkyl substances

This study is a workflow development for the analysis, identification, and categorization of per- and polyfluoroalkyl substances (PFAS) using gas chromatography-high resolution mass spectrometry (GC-HRMS) with non-targeted analysis (NTA) and suspect screening techniques. The behavior of various PFAS in a GC-HRMS was studied with regards to retention indices, ionization susceptibility, fragmentation patterns, etc. A custom PFAS database was constructed from 141 diverse PFAS. The database contains mass spectra from electron ionization (EI) mode, as well as MS and MS/MS spectra from positive and negative chemical ionization (PCI and NCI, respectively) modes. Common fragments of PFAS were identified across a diverse set of 141 PFAS analyzed. A workflow for suspect screening of PFAS and partially fluorinated products of incomplete combustion/destruction (PICs/PIDs) was developed which utilized both the custom PFAS database and external databases. PFAS and other fluorinated compounds were identified in both a challenge sample (designed to test the identification workflow) and incineration samples suspected to contain PFAS and fluorinated PICs/PIDs. The challenge sample resulted in a 100% true positive rate (TPR) for PFAS which were present in the custom PFAS database. In conclusion, several fluorinated species were tentatively identified in the incineration samples using the developed workflow.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Reactions of Propyl Radicals: A Shock Tube - VUV Photoionization Mass Spectrometry Study

The pyrolytic reactions of n-propyl and i-propyl radicals and their precursors have been investigated at elevated temperatures and pressures (600 – 900 K and 5 – 8 bar). The studies were performed in a miniature high repetition rate shock tube with synchrotron vacuum ultraviolet photoionization mass spectrometry yielding comprehensive datasets of temporal and photoionization energy dependencies of reagents and products. The propyl radicals were generated by pyrolysis of alkyl nitrites. In addition to the main decomposition path, NO elimination, the mass spectra allowed an alternative minor path via HNO elimination to be identified and quantified. For the n-propyl precursor the HNO elimination route accounted for 9% of the alkyl nitrite while for the i-propyl precursor it was 2.5%. These values are in good agreement with a recent study on i-butyl radicals in the same apparatus at similar conditions. The ratio of disproportionation/recombination was obtained for n- propyl from the relative concentrations of n-hexane and propene and for i-propyl from 2,3-dimethyl butane and propene. For n-propyl the ratio is 0.3 and 1.2 for i-propyl, both are independent of temperature and pressure over the experimental range. The disproportionation/recombination ratios are about a factor of 2 higher than prior evaluations that are based mainly on room temperature data. The experimental results are some of the first from the apparatus used and comments are made about the technique, challenges encountered, and suggestions for future developments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

A mass–momentum consistent coupling for mesh-adaptive two-phase flow simulations

Here, we present a novel mass-momentum consistent coupling between a geometric volume-of-fluid scheme and an incompressible flow solver with differing directional-splitting approaches. The advection of the volume fraction is performed using a direction-split algorithm, whereas the momentum advection algorithm uses a traditional unsplit, fractional-step approach. Both algorithms employ finite-volume discretizations based on Cartesian meshes. In solving the mass-momentum consistency problem, momentum fluxes at the cell faces are weighted by the density fluxes based on the already advected volume fraction. The success of our approach lies on introducing a Favre-averaged velocity interpolation at the liquid/gas interface along with a minmod slope limiter. Mesh-convergence studies show that when the minmod slope limiter is used, the two-phase solver retains an accuracy between first and second order, but when a purely upwind scheme is considered, its accuracy drops to first order. Finally, after considering several validation problems, the solver is shown to agree well with reference numerical and experimental data while retaining its robustness and efficiency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Model-based compositional predictions for a differential scanning calorimetry/thermogravimetric analysis-mass spectrometry system used for heat of vaporization measurements

A Differential Scanning Calorimetry/Thermogravimetric Analysis (DSC/TGA) procedure for determination of Heat of Vaporization (HOV) of fuel and surrogate fuel mixtures has been previously utilized for evaluation of oxygenate impacts on spark ignition fuels. This analysis has been further leveraged with mass spectrometry (MS) to elucidate vapor phase compositional changes during evaporation. In this study we focus on a simple system of three compounds (ethanol, n-hexane, and n-octane) to provide a model-based understanding of the evaporation process under these experimental conditions. An Aspen Plus model was set up to provide liquid and vapor phase concentration predictions during mixture evaporation using the initial mixture composition, and measured temperature and mass loss profiles from DSC/TGA experiments. Agreements between the trends of the MS ion count profiles and model composition predictions provide a degree of validation of this modeling approach that can allow the interpretation and extrapolation of DSC/TGA measurements for more complex fuel mixtures.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2023

Investigation of methane mass transfer and sorption in Marcellus shale under variable net-stress

Natural gas in shale exists as free and adsorbed gas, subject to prevailing pore pressures and stress conditions. Accordingly, to accurately estimate/predict the shale gas recovery potential, a central requirement is to represent gas transport and sorption behavior under varying stress conditions. The objective of this work is to facilitate the interpretation of laboratory-scale experiments, at relevant conditions, in an attempt to bridge the gap in scales between laboratory- and field-scale observations. We have conducted a series of high-pressure experiments on a full-diameter core sample from the Marcellus shale. These include gas loading (pressure-decay) and depletion (production) experiments with pure methane (CH 4 ) at variable stress conditions to characterize transport and sorption behavior under reservoir-relevant conditions. Here we have formulated and applied a novel integral model for mass transfer and storage in multi-porosity shale systems that allows us to effectively investigate transport and sorption phenomena: We delineate gas transport by interpreting helium (He) pressure-decay experiments and demonstrate how to use the information gained to calculate the relevant transport coefficients of CH 4 and other gases. A separate measurement of the CH 4 sorption isotherm on a smaller sample (a shale cube) was interpreted and combined with the transport description to predict the production behavior of CH 4 from the experiments with the full-diameter core. Our experiments demonstrate that the representation of sorption hysteresis is crucial for predicting and guiding shale gas production: At the end of both gas production experiments, approximately 20% of the initial gas in place remained in the core. Without accounting for sorption hysteresis, our modeling demonstrates that the CH 4 production could be overestimated by 10%. We demonstrate that our integral, triple-porosity model provides an effective approach for the interpretation and prediction of gas transport and sorption behavior during loading and production experiments on shale cores under variable net-stress conditions. In summary, our work combines measurements and modeling of mass transfer and sorption in shales at different scales to validate a characterization approach that facilitates an improved understanding of shale gas production. Furthermore, the triple-porosity model utilized in our work defines a potential pathway for the translation of laboratory-scale experimentation to larger-scale applications.

58 GEOSCIENCES↗
DOE OSTI2022

A modified model parametrization algorithm for solving a special type of heat and mass transfer systems

A new method for solving nonlinear heat and mass transfer design tasks was considered. Systems using the Number of Transfer Units (NTU) method are a special type of mathematical model of heat and mass exchangers. It was observed, that the NTU models in a form of differential-algebraic equations (DAEs) cannot be directly solved with higher values of NTU. The requirements for consistent initial conditions, as well as numerical limitations of DAEs solvers, result, that the solution to the considered design problems that cannot be obtained by a classical direct shooting procedure. To overcome the presented difficulties, the αDAE model optimization algorithm was adjusted for solving NTU-based models. The new approach consists of 3 main steps: 1) task discretization by a multiple-shooting approach, 2) design an appropriate function $f_{NTU}$(α) to effectively influence the variability of the state variables described by dynamical relations, 3) the iterative numerical optimization algorithm for the new parametrized system. Moreover, computations can be performed by a chosen numerical optimization approach, which can be communicated with an available outer procedure for solving differential-algebraic equations. The presented algorithm was implemented and applied to solve the design task with the NTU model of a counter-flow exchanger. Here, the new approach was used to modify the system dynamics to influence the difficulty of the considered problem. Finally, the presented method enabled failure-free numerical computations for the higher values of the NTU parameter.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Coupled heat and mass transfer in internally cooled silica gel-coated aluminum foam heat exchangers for dehumidification

Solid desiccant dehumidifiers offer significant potential to improve humidity control in buildings due to their ability to independently regulate latent (humidity) and sensible (temperature) loads. However, adsorption of water vapor by desiccants is an exothermic process; the resulting heat of adsorption increases both the desiccant bed temperature and the temperature of the air flowing over the bed, thereby limiting the performance of desiccant dehumidifiers. To address this problem, desiccant-coated heat exchanger prototypes were developed by coating silica gel onto aluminum foam substrates and integrated with chilled water circulation for effective removal of the heat of adsorption. Prototype heat exchangers with two different pore densities (10 and 20 pores per inch (PPI)) and two different desiccant loadings (∼10.36% and ∼17.80%) were fabricated. Experiments were conducted by varying the inlet air face velocity, chilled water inlet temperature, and chilled water flow rate to investigate the coupled heat and mass transfer characteristics of the prototype heat exchangers over a wide range of operating conditions. The underlying transport mechanisms were analyzed using transient desiccant bed temperature, outlet air temperature, and outlet humidity profiles. The results demonstrate that internal cooling significantly enhances dehumidification performance by maintaining more favorable thermodynamic conditions for water vapor adsorption. Under identical operating conditions, a 20 PPI heat exchanger coated with 25.05 g of silica gel achieved 98.98% higher cumulative water uptake and 97.75% higher moisture removal capacity than the corresponding non-cooled case after 5 min of adsorption. This substantial enhancement was further supported by a validated one-dimensional coupled heat and mass transfer model developed in the present study. To date, this is one of the first experimental studies to systematically investigate the combined effects of internal cooling, foam pore density, and desiccant loading on the performance of silica-gel-coated metal foam heat exchangers under HVAC-relevant operating conditions.

42 ENGINEERING↗
DOE OSTI2023

Resolving metal binding properties within subunits of a multimeric enzyme Mnx by surface induced dissociation and native ion mobility mass spectrometry

Multi-subunit enzymes function as coordinated assemblies. Yet most enzymatic assays measure the summed output of all populations in solution and cannot easily differentiate contributions of individual subunits. Native mass spectrometry detects intact protein complexes in the gas phase. Surface induced dissociation further releases subunits from protein complexes while retaining compact conformations and bound ligands. Combined with ion mobility, the released subunits can then be carefully monitored for more in-depth structural analysis. Mnx is a unique bacterial multicopper oxidase complex that oxidizes Mn(II) to form MnO 2 minerals, and is composed of three subunits: MnxG, a multicopper oxidase containing the active site, and two accessory proteins, MnxE and MnxF which also bind copper ions. Other known multicopper oxidases do not require accessory proteins, therefore the functions of MnxE and MnxF are not well understood. Here, we use native mass spectrometry with surface induced dissociation and ion mobility to characterize the metal binding properties of Mnx with two metals, catalytic Cu(II) and Mn(II) substrate. We demonstrate our assay can detect subtle structural changes within each subunit, which are presumably related to the allosteric mechanism. We also noticed that ionic strength and solution composition can impact metal binding and must be carefully investigated for such experiments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

A mass conservative, well balanced, tangency preserving and energy decaying method for the shallow water equations on a sphere

Here a fully discrete surface finite element method is proposed for solving the viscous shallow water equations in a bounded Lipschitz domain on the sphere based on a general triangular mesh. The method consists of a modified Crank–Nicolson method in time and a Galerkin surface finite element method in space for the fluid thickness H and the fluid velocity u. A finite element space tangential to the sphere at all finite element nodes is proposed to approximate the fluid velocity u. The proposed method has second-order accuracy in time and first-order accuracy in space, and preserves mass conservation, well balancedness, tangency of velocity to the sphere, and energy decay. Numerical experiments are presented to illustrate the accuracy of the proposed method and the preservation of the physical properties, including mass conservation, well balancedness, and energy decay. A numerical simulation of ocean mesoscale activity on a circular basin with a continental shelf is provided.

97 MATHEMATICS AND COMPUTING↗