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At least 343 records · Page 19

Polyhalohydrins: Investigating Vicinal Functionalities by Ring-Opening of Epoxides on Polyolefins

Halohydrins are functional groups that are underexplored in polymer science. This study synthesized and examined structure–property relationships of halohydrin-functionalized polymers derived from polycyclooctene (PCOE), which was obtained via ring-opening metathesis polymerization (ROMP). The polyhalohydrins, including polychlorohydrin, polybromohydrin, and polyiodohydrin, were produced through a two-step process involving epoxidation of PCOE followed by epoxide ring-opening using hydrochloric, hydrobromic, or hydroiodic acid. These stereoirregular and regioirregular polymers are amorphous as measured by differential scanning calorimetry and X-ray scattering. Lap joint shear testing revealed an enhanced adhesive performance in polychlorohydrin and polybromohydrin, with the former demonstrating nearly three times the ultimate shear stress compared to a model polyethylene, hydrogenated PCOE. Additionally, contact angle measurements and surface free energy analysis showed an increase in hydrophilicity and polarity from iodine- to bromine- to chlorine-functionalized polyhalohydrins, aligning with trends in adhesion strength. Furthermore, these results underscore the potential of halohydrin functionalization as a versatile approach for tuning surface properties, offering new opportunities for polymer-to-polymer transformations.

Functional groups↗

In Cell Thermal Creep Frames for Demonstration Project Preparations

The thrust of advanced nuclear reactor demonstrations demands the accelerated qualification of in-core materials to enable licensing processes and developing the performance data. Due to the high-operating temperatures of such reactors, long-term mechanical behavior under constant load is essential to determine the geometrical and mechanical integrity of in-core components during operation and off-normal conditions. Therefore, the thermal creep behavior of neutron-irradiated advanced reactor materials must be determined. The feasibility of using subsize specimens for the irradiation campaigns and the limited available infrastructure challenge the assessment of thermal creep behavior of advanced reactor materials. Therefore, the U.S. Department of Energy Office of Nuclear Energy (DOE-NE) National Reactor Innovation Center (NRIC) prioritizes the development of a thermal creep testing infrastructure for multiple subsize specimens to accelerate the demonstration and deployment of advanced reactor concepts. This report describes the activities for the construction of a thermal creep testing capability at Idaho National Laboratory (INL). The overall project consists of conceptual design, out-of-cell demonstration, and in-cell demonstration phases. During fiscal year (FY)-2021, the team finished the conceptual design of a thermal creep test facility that can test multiple subsize specimens. This conceptual design consisted of the determination of technical and functional requirements, the determination of the design space, and the preparation of the technical drawings. Technical and functional requirements were categorized as required and desired capabilities and the conceptual design was performed to meet all the required capabilities with the flexibility to achieve the desired capabilities. The design space identified the operational capacity of the creep frame for different advanced reactor relevant materials with the consideration of the feasible operation in the hotcell at the Fuels and Applied Science Building (FASB) at INL. Based on the requirements and design space, the multiple specimen creep frame was designed. The official INL engineering drawing process was started and the procurement of materials for construction was initiated. For FY-2022, the out-of-cell demonstration and final installation of the multiple creep frame is planned.

36 MATERIALS SCIENCE↗

Facile Synthesis of Palladium-Based Nanocrystals with Different Crystal Phases and a Comparison of Their Catalytic Properties

A relatively unexplored aspect of noble-metal nanomaterials is polymorphism, or their ability to crystallize in different crystal phases. Here, in this work, a method is reported for the facile synthesis of Ru@Pd core–shell nanocrystals featuring polymorphism, with the core made of hexagonally close-packed (hcp)-Ru while the Pd shell takes either an hcp or face-centered cubic (fcc) phase. The polymorphism shows a dependence on the shell thickness, with shells thinner than ≈1.4 nm taking the hcp phase whereas the thicker ones revert to fcc. The injection rate provides an experimental knob for controlling the phase, with one-shot and drop-wise injection of the Pd precursor corresponding to fcc-Pd and hcp-Pd shells, respectively. When these nanocrystals are tested as catalysts toward formic acid oxidation, the Ru@Pd hcp nanocrystals outperform Ru@Pd fcc in terms of both specific activity and peak potential. Density functional theory calculations are also performed to elucidate the origin of this performance enhancement.

36 MATERIALS SCIENCE↗

Electrical conductivities of (Mg,Fe)O at extreme pressures and implications for planetary magma oceans

During planet formation, planets undergo many impacts that can generate magma oceans. When these crystallize, part of the magma densifies via iron enrichment and migrates to the core–mantle boundary, forming an iron-rich basal magma ocean (BMO). The BMO could generate a dynamo in early Earth and super-Earths if the electrical conductivity of the BMO, which is thought to be sensitive to its Fe content, is sufficiently high. To test this hypothesis, here we conduct laser-driven shock experiments on ferropericlase (Mg x ,Fe 1−x )O (0.95 ≤ x ≤ 1) as an Fe-rich BMO analogue, perform density functional theory molecular dynamics simulations on MgO and calculate the long-term evolution of super-Earths. We find that the d.c. conductivities of MgO and (Mg,Fe)O are indistinguishable between 467 GPa and 1,400 GPa, despite previous predictions. Here, we predict that super-Earths larger than 3–6 Earth masses can produce BMO-driven dynamos that are almost one order of magnitude stronger than core-driven dynamos for several billion years.

Exoplanets↗

Evaluating the Effect of Electrolyte Additive Functionalities on NMC622/Si Cell Performance

Unstable electrode/electrolyte interface is the major cause of degradation for silicon (Si)-based anodes for lithium (Li)-ion batteries. Development of functional electrolyte additives can provide a viable path toward stabilizing the dynamic Si/electrolyte interface, which will benefit the development of high energy density Li-ion batteries. Here, we evaluate polymerizable electrolyte additives with varying functional groups (fluorocarbon, thiophosphate, and fluorophosphazene). The additives are examined using LiNi 0.6 Mn 0.2 Co 0.2 O 2 /Si full cells where the cycle performance and impedance are measured. Electrochemical tests show that the fluorine-containing additives provide better passivation at the Si electrode, leading to enhanced full cell performance. Here, among the three additives examined, best electrochemical performance is observed from the fluorocarbon-containing compound, followed by fluorophosphazene- and thiophosphate-containing compounds. Characterization of the solid electrolyte interphase (SEI) on cycled electrodes using Auger electron spectroscopy (AES), X-ray photoelectron spectroscopy (XPS), and attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FTIR) reveal that higher concentration of fluorine and lithium oxide, and lower concentration of carbonate and organic species correlate with enhanced electrochemical performance.

25 ENERGY STORAGE↗

Modeling Activities Related to Waste Form Degradation: Progress Report

This report represents the milestone deliverable M4SF-21SN010309021 “Modeling Activities Related to Waste Form Degradation: Progress Report” that describes the progress of R&D activities of ongoing modeling investigations specifically on nuclear waste glass degradation, Density Functional Theory (DFT) studies on clarkeite structure and stability, and electrochemical modeling of spent nuclear fuel (SNF). These activities are part of the newly-created Waste form Testing, Modeling, and Performance work package at Sandia National Laboratories (SNL). This work package is part of the “Inventory and Waste Form Characteristics and Performance” control account that includes various experimental and modeling activities on nuclear waste degradation conducted at Oak Ridge National Laboratory (ORNL), SNL, Argonne National Laboratory (ANL), and Pacific Northwest National Laboratory (PNNL).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

CalTestBed - Lucent Optics (CRADA Final Report)

The CRADA partner was developing a window film aimed at improving the control of the solar radiation that arrives at a building’s windows, ultimately reducing cooling loads and improving the distribution of daylight. The efforts under this CRADA were aimed at better understanding the performance of one or more prototypes of this film, with the aim of helping to narrow down the film design parameters to values more likely to achieve better performance. The technical means of achieving this project’s goals used LBNL’s world-class test facilities and expertise. These technical means included: (a) measurements of the bidirectional scattering distribution function (BSDF) of film samples, and (b) full-scale measurement of the energy (HVAC, lighting) and comfort (visual, thermal) impacts of at least one film prototype, for two solar angle “seasons” (“high” and “low” solar angle).

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Module-Fluidics: Building Blocks for Spatio-Temporal Microenvironment Control

Generating the desired solute concentration signal in micro-environments is vital to many applications ranging from micromixing to analyzing cellular response to a dynamic microenvironment. We propose a new modular design to generate targeted temporally varying concentration signals in microfluidic systems while minimizing perturbations to the flow field. The modularized design, here referred to as module-fluidics, similar in principle to interlocking toy bricks, is constructed from a combination of two building blocks and allows one to achieve versatility and flexibility in dynamically controlling input concentration. The building blocks are an oscillator and an integrator, and their combination enables the creation of controlled and complex concentration signals, with different user-defined time-scales. We show two basic connection patterns, in-series and in-parallel, to test the generation, integration, sampling and superposition of temporally-varying signals. All such signals can be fully characterized by analytic functions, in analogy with electric circuits, and allow one to perform design and optimization before fabrication. Such modularization offers a versatile and promising platform that allows one to create highly customizable time-dependent concentration inputs which can be targeted to the specific application of interest.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The Dark Energy Camera Plane Survey 2 (DECaPS2): More Sky, Less Bias, and Better Uncertainties

Abstract Deep optical and near-infrared imaging of the entire Galactic plane is essential for understanding our Galaxy’s stars, gas, and dust. The second data release of the Dark Energy Camera (DECam) Plane Survey extends the five-band optical and near-infrared survey of the southern Galactic plane to cover 6.5% of the sky, ∣ b ∣ ≤ 10°, and 6° > ℓ > −124°, complementary to coverage by Pan-STARRS1. Typical single-exposure effective depths, including crowding effects and other complications, are 23.5, 22.6, 22.1, 21.6, and 20.8 mag in g , r , i , z , and Y bands, respectively, with around 1″ seeing. The survey comprises 3.32 billion objects built from 34 billion detections in 21,400 exposures, totaling 260 hr open shutter time on the DECam at Cerro Tololo. The data reduction pipeline features several improvements, including the addition of synthetic source injection tests to validate photometric solutions across the entire survey footprint. A convenient functional form for the detection bias in the faint limit was derived and leveraged to characterize the photometric pipeline performance. A new postprocessing technique was applied to every detection to debias and improve uncertainty estimates of the flux in the presence of structured backgrounds, specifically targeting nebulosity. The images and source catalogs are publicly available at http://decaps.skymaps.info/ .

79 ASTRONOMY AND ASTROPHYSICS↗

BSDF Data generation for daylight applications: A call for international standardization

Standardized methods for generating angle-dependent, bidirectional, solar-optical properties for complex fenestration systems do not exist, which means that energy and daylight evaluations in building performance simulations often suffer from major inaccuracies. This position paper provides an overview of state-of-the-art data-driven methods for characterizing light scattering properties of fenestration materials and blind systems (e.g. fabrics, metal slats, patterned glazing), validation via laboratory, simulation and field tests, and salient issues in support of standardization of such methods via the International Standardization Organization (ISO). The ISO standard is intended to provide the fundamental underpinnings for recently mandated daylight standards that rely on bidirectional scattering distribution function data for climate-based daylight modelling and building performance simulations.

Geisler-Moroder, D.↗

Reducing Mass of Steel Auto Bodies using Thin Advanced High Strength Steel with Carbon-Fiber Reinforced Epoxy

Diversitak, a company based in Detroit, MI, has developed a proprietary, low specific gravity, carbon fiber-reinforced epoxy (CFRE) under U.S. patent number 9,963,58832. Preliminary testing on this new material conducted in collaboration with ArcelorMittal Steel Company proved out the CFRE concept. A thin layer of this CFRE was applied to a stamped sheet of steel with residual stamping oils from a mill, in a time corresponding to automotive processing (e.g., ~15 seconds), and processed following automotive e-coat procedures (phosphating + 175–200°C heating), to complete the curing. No problems with adherence or performance were noted. While the CFRE does add weight to a thin gauge steel panel, it weighs much less than what is displaced by using thicker conventional mild steel gauges. The application of the coating showed a significant increased dent resistance, oil canning resistance, and part stiffness.This current two-year project was designed to mature this new technology to near manufacturing readiness to reduce the weight of a vehicle and lower the cost of weight reduction. The process involves the use of thinner gauge steels than are currently used. The collaborative development team included two industrial manufacturers: Diversitak and ArcelorMittal Steel Company; LightMAT; and two National Laboratories: Oak Ridge National Laboratory (ORNL) and Idaho National Laboratory (INL). The team developed a new manufacturing process to reduce the weight of a vehicle and lower the cost of weight reduction, as well as a better understanding of how to apply the coating so that it will perform to a high standard in-service. The team also performed an in-depth study to determine the long-term durability of the materials manufactured using this technology and well-known automotive industry standard tests.The overall process involved stiffening the thinner gauge steel by applying the CFRE on only one side. To accomplish this goal, the optimal reinforcement fiber length and fiber concentration was first determined. This was followed by measuring the coefficient of thermal expansion (CTE) in all three directions, so it could be fed into manufacturing models and methods for rapidly and inexpensively applying the coating. This was followed by panel level evaluations of the coating and steel combination, and then by full part demonstration of the technology on door panels. The final step was corrosion testing of the parts.ArcelorMittal characterized the advanced high strength steel (AHSS) (e.g., metallurgy-heat treatment for required AHSS properties as a function of the sheet thickness, state of internal stress) and quantified CFRE adhesion to the steel as a function of sheet preparation (e.g., rolling and stamping).ORNL optimized the fiber length, fiber concentration, and coating thickness for best vehicle function and performance at the least cost. Along with the suppliers, ORNL developed a durable CFRE application process (e.g., gun material, design, robotic dispensing process) and identified the adhesion stability of the CFRE during process holding. An approach to ensure that application/curing timing conforms to conventional assembly line speed and plant cycle times was determined. ORNL also determined the CTE of the material in all three directions and performed material scanning electron microscopy (SEM) analyses.INL characterized the corrosion properties of the steel panels coated with CFRE. The panels were investigated for corrosion resistance and stability as replacement materials used in automotive body panels to reduce mass. The coupons tested at INL were supplied by Diversitak after an optimized CFRE formulation was achieved in the already coated form for corrosion testing.

99 GENERAL AND MISCELLANEOUS↗

A novel active optimization approach for rapid and efficient design space exploration using ensemble machine learning

In this work, a novel design optimization technique based on active learning, which involves dynamic exploration and exploitation of the design space of interest using an ensemble of machine learning algorithms, is presented. In this approach, a hybrid methodology incorporating an explorative weak learner (regularized basis function model) which fits high-level information about the response surface, and an exploitative strong learner (based on committee machine) that fits finer details around promising regions identified by the weak learner, is employed. For each design iteration, an aristocratic approach is used to select a set of nominees, where points that meet a threshold merit value as predicted by the weak learner are selected to be evaluated using expensive function evaluation. In addition to these points, the global optimum as predicted by the strong learner is also evaluated to enable rapid convergence to the actual global optimum once the most promising region has been identified by the optimizer. This methodology is first tested by applying it to the optimization of a two-dimensional multi-modal surface. The performance of the new active learning approach is compared with traditional global optimization methods, namely micro-genetic algorithm (pGA) and particle swarm optimization (PSO). It is demonstrated that the new optimizer is able to reach the global optimum much faster with a significantly fewer number of function evaluations. Subsequently, the new optimizer is also applied to a complex internal combustion (IC) engine combustion optimization case with nine control parameters related to fuel injection, initial thermodynamic conditions, and in-cylinder flow. It is again found that the new approach significantly lowers the number of function evaluations that are needed to reach the optimum design configuration (by up to 80%) when compared to particle swarm and genetic algorithm-based optimization techniques.

Machine learning, active learning, design optimiza↗

Adaptive sampling quasi-Newton methods for zeroth-order stochastic optimization

Here, we consider unconstrained stochastic optimization problems with no available gradient information. Such problems arise in settings from derivative-free simulation optimization to reinforcement learning. We propose an adaptive sampling quasi-Newton method where we estimate the gradients using finite differences of stochastic function evaluations within a common random number framework. We develop modified versions of a norm test and an inner product quasi-Newton test to control the sample sizes used in the stochastic approximations and provide global convergence results to the neighborhood of a locally optimal solution. We present numerical experiments on simulation optimization problems to illustrate the performance of the proposed algorithm. When compared with classical zeroth-order stochastic gradient methods, we observe that our strategies of adapting the sample sizes significantly improve performance in terms of the number of stochastic function evaluations required.

97 MATHEMATICS AND COMPUTING↗

Illuminating the pathways to carbon liberation: a systems approach to characterizing the consequential unknowns of carbon transformation and loss from thawing permafrost peatlands (Final Report)

The IsoGenie3 Project delivered new systems-level insights into carbon cycling in thawing permafrost landscapes, with an emphasis on methane and carbon dioxide emissions. From >200 samples from the site collected over a decade, co-analyzed for geochemistry and microbiology, the team recovered ~1,500 assembled microbial genomes and ~1,900 viral population genomes, revealing appreciable genetic novelty - from a new highly abundant bacterial phylum, to novel methane consumers and their activities, to rampant viral novelty. IsoGenie3 linked these organisms to carbon compound transformations (which define the cycling of organic matter in soils, and the loss of the greenhouse gases carbon dioxide and methane), and saw that the microbes at each stage of permafrost thaw had different genetic potential to degrade categories of compounds, expressed that genetic potential differently, and actually transformed carbon compounds into greenhouse gases in different ways. IsoGenie 3 identified that some of the thaw-stage differences were due to plant-microbiome relationships; the plant species across the thaw gradient contributed different carbon compounds into the soil, and hosted distinct microbiota (differing among parts of plants as well as species). Lastly, microbes in the saturated post-thaw conditions appeared likely to contribute to the mobilization and toxification of mercury released during thaw. In parallel with ongoing field sampling and analysis, hypotheses arising from field observations were tested via lab incubation experiments. When communities are taken out of their native habitats, they behave differently, and the team first rigorously quantified the magnitude of this effect on microbiome composition and functional capacity, organic matter composition, and gas production; overall the main system processes were maintained in the lab incubations under the conditions tested. Further, the microbial data could inform geochemical reaction network models of those processes. Then, the team ran experiments with additions of compounds, varying temperature, and “live” vs. “dead” peat (the latter having been gamma irradiated, with a few additional variants to control for methodological artifacts). From these, we (a) determined the importance of plant-derived soluble phenolic compounds in bogs’ extraordinary recalcitrance of organic matter, and carbon gas emissions skewed to carbon dioxide; (b) proposed an abiotic ‘tanning’ mechanism, which could contribute to Sphagnum’s inhibitory effect on anaerobic decomposition through alteration of N availability. IsoGenie3 illuminated longer-term and landscape-scale interactions of permafrost thaw and carbon cycling, advancing knowledge of the drivers of methane dynamics not only across in the permafrost-associated peatland (where hydrology and plant communities dictate microbiomes) but also their interconnected lakes (where sediment carbon quality and resident microbiota are determined by position within lake, and lake features). By leveraging observations of site methane dynamics extending well before this project, the team was able to construct a 44-year portrait of the interplay of permafrost thaw, hydrology, vegetation dynamics, and carbon gas emissions, and the doubling of the fully-thawed fens over this time. From the detailed study of this focal site, IsoGenie3 also aimed to improve model representation of these kinds of sites and processes. To improve predictions of methane transformations, we incorporated acetate and isotope dynamics into the ‘DNDC’ biogeochemistry model. In addition, recovered genomes were grouped into ‘functional groups’, i.e. the genomes that perform a specific function of interest, then used to parameterize maximum growth rate and optimum growth temperature (via signatures in their sequence composition) for the BioCrunch model. The BioCrunch model was then in turn used to test the impact of increasing functional resolution of the microbes, on the carbon gas emissions. Lastly for modeling, the ecosys model was parameterized from the microbial and other data, and used to evaluate drivers of e.g. change in methane emissions. Finally, this project also led to the development of a range of new methods and tools, a new metric of organic matter decomposability, as well as a graph-database solution to multidisciplinary data storage and querying. This project’s ongoing analyses at our focal site also contributed to broader advancements in understanding elements of genetic plasticity and methane metabolism, climate change microbiology and community assembly, global peatland geochemistry and Arctic lakes’ roles in climate feedbacks.

54 ENVIRONMENTAL SCIENCES↗

Molecular fingerprint and machine learning to accelerate design of high-performance homochiral metal–organic frameworks

In this report computational screening was employed to calculate the enantioseparation capabilities of 45 functionalized homochiral metal–organic frameworks (FHMOFs), and machine learning (ML) and molecular fingerprint (MF) techniques were used to find new FHMOFs with high performance. With increasing temperature, the enantioselectivities for (R,S)-1,3-dimethyl-1,2-propadiene are improved. The “glove effect” in the chiral pockets was proposed to explain the correlations between the steric effect of functional groups and performance of FHMOFs. Moreover, the neighborhood component analysis and RDKit/MACCS MFs show the highest predictive effect on enantioselectivities among the four ML classification algorithms with nine MFs that were tested. Based on the importance of MF, 85 new FHMOFs were designed, and a newly designed FHMOF, NO 2 -NHOH-FHMOF, with high similarity to the optimal MFs achieved improved chiral separation performance, with enantioselectivities of 85%. The design principles and new chiral pockets obtained by ML and MFs could facilitate the development of new materials for chiral separation.

molecular fingerprint↗

Unconventional desalination: The use of cyclone separators in HDH desalination to achieve zero liquid discharge

Research in water desalination technologies is constantly growing to meet global demands for freshwater. Though acting to meet these demands, the rapid growth and spread of desalination technologies poses environmental issues due to the increasing brine concentrates that are ultimately discharged back to nature. This article presents a cyclone separator to transform a humidification-dehumidification (HDH) cycle to a dual-product cycle to produce freshwater and solid salt crystals for highly saline streams. A desalination cycle equipped with a cyclone separator is used to treat water with 3.5%–81% salinity. The separation efficiency is well above 99% and can produce potable water from hyper saline feed in a once-through process. Further, the cyclone separator performance was tested under different conditions including humidity ratios, relative humidities, and feed stream's salinities. The cyclone separator is self-cleaning and overcomes salt scaling. This behavior is a direct function of the walls' temperature and the carrier air dew point. Self-cleaning capability allows the cyclone separator to treat feed water of extreme salinities (up to 810,000ppm) down to freshwater salinity with zero liquid discharge. The cyclone separator was utilized in a novel HDH desalination technology to treat different salinities. The product was freshwater of salinity <500ppm.

42 ENGINEERING↗

Too big, too small, or just right? A benchmark assessment of density functional theory for predicting the spatial extent of the electron density of small chemical systems

Multipole moments are the first-order responses of the energy to spatial derivatives of the electric field strength. The quality of density functional theory prediction of molecular multipole moments thus characterizes errors in modeling the electron density itself, as well as the performance in describing molecules interacting with external electric fields. However, only the lowest non-zero moment is translationally invariant, making the higher-order moments origin-dependent. Therefore, instead of using the 3 × 3 quadrupole moment matrix, we utilize the translationally invariant 3 × 3 matrix of second cumulants (or spatial variances) of the electron density as the quantity of interest (denoted by K). The principal components of K are the square of the spatial extent of the electron density along each axis. A benchmark dataset of the principal components of K for 100 small molecules at the coupled cluster singles and doubles with perturbative triples at the complete basis set limit is developed, resulting in 213 independent K components. The performance of 47 popular and recent density functionals is assessed against this Var213 dataset. Several functionals, especially double hybrids, and also SCAN and SCAN0 predict reliable second cumulants, although some modern, empirically parameterized functionals yield more disappointing performance. The H, Li, and Be atoms, in particular, are challenging for nearly all methods, indicating that future functional development could benefit from the inclusion of their density information in training or testing protocols.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Numerical methods and hypoexponential approximations for gamma distributed delay differential equations

Abstract Gamma distributed delay differential equations (DDEs) arise naturally in many modelling applications. However, appropriate numerical methods for generic gamma distributed DDEs have not previously been implemented. Modellers have therefore resorted to approximating the gamma distribution with an Erlang distribution and using the linear chain technique to derive an equivalent system of ordinary differential equations (ODEs). In this work, we address the lack of appropriate numerical tools for gamma distributed DDEs in two ways. First, we develop a functional continuous Runge–Kutta (FCRK) method to numerically integrate the gamma distributed DDE without resorting to Erlang approximation. We prove the fourth-order convergence of the FCRK method and perform numerical tests to demonstrate the accuracy of the new numerical method. Nevertheless, FCRK methods for infinite delay DDEs are not widely available in existing scientific software packages. As an alternative approach to solving gamma distributed DDEs, we also derive a hypoexponential approximation of the gamma distributed DDE. This hypoexponential approach is a more accurate approximation of the true gamma distributed DDE than the common Erlang approximation but, like the Erlang approximation, can be formulated as a system of ODEs and solved numerically using standard ODE software. Using our FCRK method to provide reference solutions, we show that the common Erlang approximation may produce solutions that are qualitatively different from the underlying gamma distributed DDE. However, the proposed hypoexponential approximations do not have this limitation. Finally, we apply our hypoexponential approximations to perform statistical inference on synthetic epidemiological data to illustrate the utility of the hypoexponential approximation.

97 MATHEMATICS AND COMPUTING↗