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At least 739 records · Page 41
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Temperature Dependence of Band Gap Renormalization in High-T Sensor Materials via First-Principles and Experimental Corroboration

Understanding the temperature dependence of functional properties of high-T gas sensing materials is vital for their applications in combustion environments. The electron-phonon coupling that derives the electronic structure change with temperatures is a key property of interest as it affects other sensing responses. Herein, we assess the temperature dependence of band gap renormalization in metal oxides and perovskites by employing Allen-Heine-Cardona theory with first-principles simulations and corroborate with experimental observation. The calculated temperature-dependent band gap changes of these materials studied are in good agreement with in-house experimental data, proving that the theory can adequately predict renormalization on the band gap in the system of interest. The predicted and measured band gap variations are characterized using an analytical model, which can provide useful insights on the simulated zero-temperature band gaps. Based on the available data, a set of 53 metal oxides and perovskites were identified as potential high-T gas sensors. A machine learning model has been developed to predict the band-gap change by capturing the overall trend of the empirical parameters with respect to a reduced feature obtained by transforming the set of available physical features.

Park, Jongwoo↗
DOE OSTI2023

Additively Manufactured Strain Sensing for Nuclear Reactor Applications

Real-time monitoring of materials in harsh environments is a crucial technique towards reducing innovation time in nuclear systems. The successful measurement of real time, in-situ strain measurements during nuclear reactor operation requires innovative sensing solutions, including novel sensing strategies as well as advanced sensor design, manufacturing, and materials selection. In this paper, we will discuss two primary strategies for in-situ strain measurement strategies: additively manufactured (AM) capacitive strain gauges (CSGs) and digital image correlation (DIC). Current commercial strain gauges have limited applications in reactors due to the harsh operating conditions and non-trivial attachment strategies (i.e., welding, epoxy-adhesive) that can affect both the sensing performance and the underlying substrate under testing. AM CSGs are a viable solution as they have a low profile, low hysteresis, and wireless sensing integration capabilities that will enhance nuclear sensing technologies. In this work, the mechanical and thermal performance of the AM CSGs were tested up to 300 °C using ASTM standardized testing procedures to simulate the temperatures found in existing light water reactors. The AM CSGs had a similar performance across multiple samples which correlates to analytical models. This work leads towards the development of CSGs designed for higher temperatures and additional environmental factors found in Generation-IV reactors. Non-contact sensors, such as DIC, offer a less destructive way to measure deformation of materials when compared to alternative methods of in-situ strain determination, such as weldable strain gauges. However, DIC requires high contrast surfaces, which often relies on the implementation of artificial patterns. Using traditional splatter techniques to fabricate these patterns have limitations, including poor surface adhesion and reproducibility. In this work, AM fabrication techniques were implemented to avoid such limitations. Accordingly, aerosol jet printing (AJP) was used to print small scale periodic patterns of silver on stainless steel and aluminum tensile specimens. DIC was employed to monitor strain (up to 1100 µe) during temperature cycling from 23-600 °C. The results validated the use of AJP to better control pattern parameters for small fields of view applications at high temperatures.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Determining Compression Characteristics of Honeycomb Material - 19674

The objective is to determine compression test characteristics of stainless steel honeycomb material to be able to represent honeycomb structures accurately in analytical models used to simulate hypothetical accident scenarios of shipping packages. Honeycomb is a material used primary in the aerospace industry due to its high strength-to-weight ratio. Because it doesn't have a shelf life and can withstand high heats, it is an excellent candidate for a structural material in package designs. Honeycomb has orthotropic material properties. The honeycomb currently being evaluated is made of metal ribbons spot welded together to form hexagon pattern between metal plates. The hexagon ribbons are brazed to the metal plates. The complexity of the honeycomb significantly lengthens the simulation time, which is further complicated when the brazing, welding, and imperfections of the material is considered. This means to affectively represent the honeycomb in simulation programs, such as Abaqus, the material needs to be approximated as a uniform orthotropic material. This requires material properties in each of the three directions, T, W, and L. The T direction is defined as the 'strong' direction, perpendicular to the honeycomb sheet. The L direction is parallel the ribbon and the W direction is perpendicular to the ribbon. Honeycomb has 3 different compression stages. Stage 1 is the initial compression where the honeycomb maintains its structural integrity and does not permanently deform from loads from normal operations. Stage 2 is when the initial buckling causes irreversible damage to the honeycomb. Stage 2 is the one we are most interested in because it absorbs the most energy from a hypothetical accident scenario. During Stage 2, the honeycomb fails layer-by-layer, indicating that the more layers, the longer material crushing is sustained, and thus the more energy that is absorbed. Stage 3 is final compression, similar to compressing solid metal. During stage 3 the stress increases with a diminishing rate of elongation and the honeycomb is completely failed where the plates between the honeycomb core sandwich the crushed honeycomb ribbon. The stress-strain graph bellow shows compression test of 3 different samples in the T direction. The red lines divide the three stages. The far left is Stage 1, the middle stage 2, and the right stage 3. The data collected is displayed in the table below. The expressions in the table represent the regression formula that represents each stage of the compression on a stress-strain graph. Stage 1 is assumed to intersect with the origin; data for stage 3 for the crush in W and L directions where unable to be gathered due to the nature of failure for those directions. Stage 1 and 2 are linear regressions while stage 3 is a degree 2, to best match the curve. Linear regression is used on stage 2 because ultimately that represents the energy absorbed. With more data, a degree n x 2 regression would be a more appropriate regression for stage 2, where n is the number of layers. The table below is the approximation of each scenario and stage. Each stage starts and ends at the intersection of the next stage. There where two main objectives for these tests: firstly to understand how honeycomb performs under extreme compression, and secondly to be able to numerically represent the honeycomb structure. Both of these where completed to varying degrees. It is important understood how the honeycomb fails. If it is crushed in the T direction it retains its integrity even after being crushed, however when crushed in the L and W crush direction, if it fails, it disintegrates, and loses all integrity. Also, the more layers the more time the material spends in stage 2. Failure is started by buckling, thus if there is any imperfection, the stress will not spike but transition straight into stage 2. The data collected and aggregated can be used for initial simulation of honeycomb used in packages. The initial testing has set the ground work for more data to be collected in order to verify results and to allow more confidence in the simulation results. This is only the initial data collected. The next steps is to continue to collect more data to verify results and to test more variants of honeycomb, with different brazing, layers, and shape.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Dynamic Wind Loading on CSP Collectors Caused by Turbulent Wind Fluctuations: Insights from a 2-Year Field Campaign

Concentrating Solar Power (CSP) is a promising solar technology for electricity generation with thermal energy storage and with the additional benefit of industrial heat production. Wind loading on CSP collector structures, such as parabolic troughs or heliostats, is one of the primary drivers of their structural design costs. In particular, dynamic wind loading is a major source of uncertainty in the collector design process, which heavily relies on wind tunnel testing. In the field, the turbulent nature of the incoming wind creates fluctuating loads (support structure loads and resulting mirror deflections) on the collectors, with impacts on fatigue lifetime and optical performance. As is well known, wind tunnel tests cannot entirely reproduce the complex turbulent wind conditions typically observed at full-scale plants. To shed light on this topic, NREL initiated a field campaign at the operational Nevada Solar One (NSO) powerplant that uses parabolic troughs as solar collectors. The aim of the project is a detailed characterization of prevailing wind and turbulence conditions and resulting operational loads on parabolic troughs. We use the published 2-year dataset of high-resolution combined wind and structural loads measurements [1] to characterize the dynamic structural wind response. For quantifying dynamic wind loading, we apply the concept of admittance functions, which are spectral transfer functions that couple the turbulent wind to resulting structural loads (aerodynamic admittance), and to the structural response (mechanical admittance). In practice, aerodynamic admittance describes which turbulent eddy sizes are effective in creating structural loads. The mechanical admittance describes in which frequency ranges these loads are reinforced or dampened by the structure. While these functions are an established concept in civil engineering, their recent application to a single full-scale heliostat [2] proved their broader applicability to CSP collectors. Here, we present a characterization of admittance functions for full-scale parabolic trough collectors and show how wind characteristics (mean wind speed and direction, turbulent kinetic energy, turbulent length scales), the sun-tracking trough angle, and row position alter the admittance functions. Further, we study to which extent the admittance functions are universal for a specific trough geometry and how our findings compare to reported heliostat results. References [1] https://data.openei.org/submissions/5938. [2] Blume, K., Roger, M., and Pitz-Paal, R. 2023b. "Simplified analytical model to describe wind loads and wind-induced tracking deviations of heliostats." Solar Energy, 256, 96-109. https://doi.org/10.1016/j.solener.2023.03.055.

admittance functions↗
DOE OSTI2021

Agreement of Analytical and Simulation-Based Estimates of the Required Land Depth in Climate Models

Previous analytical and simulation-based analyses suggest that deeper land surface models are needed to realistically simulate the terrestrial thermal state in climate models, with implications for land-atmosphere interactions. Analytical approaches mainly focused on the subsurface propagation of harmonics such as the annual temperature signal, and a direct comparison with climate-change model output has been elusive. Here, this study addresses the propagation of a harmonic pulse fitted to represent the timescale and amplitude of anthropogenic warming. Its comparison to land model simulations with stepwise increased bottom boundary depth leads to an agreement between the simulation-based and analytical frameworks for long-term climate trends. Any depth increase gradually decreases the relative error in the subsurface thermodynamics, and a minimum depth of 170 m is recommended to simulate the ground climate adequately. The approach provides an accurate estimate of the required land-model depth for climate-change simulations and assesses the relative bias in insufficiently deep land models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

An analytic hybrid halo + perturbation theory model for small-scale correlators: baryons, halos, and galaxies

In this work, we update Halo Zeldovich Perturbation Theory (HZPT, [1]), an analytic model for the two-point statistics of dark matter, to describe halo and galaxy clustering, and galaxy-matter cross-correlation on nonlinear scales. The model correcting Zeldovich has an analytic Fourier transform, and therefore is valid in both configuration space and Fourier space. The model is accurate at the 2%-level or less for P_mm (k< 1 h/Mpc), P_hm (k< 1 h/Mpc), P_hh (k< 2 h/Mpc), P gm (k< 1 h/Mpc), P gg (k< 1 h/Mpc), ξ mm (r> 1 Mpc/h), ξ hm (r> 2 Mpc/h), ξ hh (r> 2 Mpc/h), ξ gm (r> 1 Mpc/h), ξ gg (r> 2 Mpc/h), for LRG-like mock galaxies. We show that the HZPT model for matter correlators can account for the effects of a wide range of baryonic feedback models and provide two extended dark matter models which are of 1% (3%) accuracy for k < 10 (8) h/Mpc. We explicitly model the non-perturbative features of halo exclusion for the halo-halo and galaxy-galaxy correlators, as well as the presence of satellites for galaxy-matter and galaxy-galaxy correlation functions. We perform density estimation using N-body simulations and a wide range of HOD galaxy mocks to obtain correlations of model parameters with the cosmological parameters Ω m and σ 8 . HZPT can provide a fast, interpretable, and analytic model for combined-probe analyses of redshift surveys using scales well into the non-linear regime.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Mesoscale modeling and semi-analytical approach for the microstructure-aware effective thermal conductivity of porous polygranular materials

Here we established a comprehensive modeling approach for investigating the microstructure-aware effective thermal conductivity ($κ_{eff}$) for porous microstructures containing solid particles and gaseous pores. Our approach combines the mesoscale computational modeling framework and the semi-analytical method, allowing for efficient prediction of $κ_{eff}$ for realistic porous microstructures, while considering complicated microstructural thermal conduction pathways effectively in the prediction. We used the diffuse-interface mesoscale computational model to generate extensive simulated $κ_{eff}$ data for realistic digital representations of microstructures with wide ranges of porosity ($f_p$), thermal conductivity of the gas phase ($κ_g$), and thermal conductivity of the solid phase ($κ_s$). From the simulated data, we identified two property variation regimes for $κ_{eff}$: (1) a slow $κ_{eff}$ increase for $κ_s ~ κ_g$; and (2) a faster $κ_{eff}$ increase for $κ_s \gg κ_g$. To capture the key features of the relationship between the microstructure and $κ_{eff}$, we derived a semi-analytical model by introducing structure and intensification factors. The two new factors incorporate the calibrated effective contribution of the solid volume with $κ_s$ and additional interfacial effects into the prediction of $κ_{eff}$, respectively, allowing for consideration of parallel, serial, and interfacial conduction mechanisms effectively. Using the selected simulation data, we quantified key model parameters within the semi-analytical model and verified that the parameterized model exhibits excellent agreement with simulated $κ_{eff}$ for the entire range of the parameter space.

36 MATERIALS SCIENCE↗
DOE OSTI2020

What can we learn from N 2 O isotope data? – Analytics, processes and modelling

The isotopic composition of nitrous oxide (N 2 O) provides useful information for evaluating N 2 O sources and budgets. Due to the co–occurrence of multiple N 2 O transformation pathways, it is, however, challenging to use isotopic information to quantify the contribution of distinct processes across variable spatiotemporal scales. Here, we present an overview of recent progress in N 2 O isotopic studies and provide suggestions for future research, mainly focusing on: analytical techniques; production and consumption processes; and interpretation and modelling approaches. Comparing isotope–ratio mass spectrometry (IRMS) with laser absorption spectroscopy (LAS), we conclude that IRMS is a precise technique for laboratory analysis of N 2 O isotopes, while LAS is more suitable for in situ/inline studies and offers advantages for site–specific analyses. When reviewing the link between the N 2 O isotopic composition and underlying mechanisms/processes, we find that, at the molecular scale, the specific enzymes and mechanisms involved determine isotopic fractionation effects. In contrast, at plot–to–global scales, mixing of N 2 O derived from different processes and their isotopic variability must be considered. We also find that dual isotope plots are effective for semi–quantitative attribution of co–occurring N 2 O production and reduction processes. More recently, process–based N 2 O isotopic models have been developed for natural abundance and 15 N–tracing studies, and have been shown to be effective, particularly for data with adequate temporal resolution. Here, despite the significant progress made over the last decade, there is still great need and potential for future work, including development of analytical techniques, reference materials and inter–laboratory comparisons, further exploration of N 2 O formation and destruction mechanisms, more observations across scales, and design and validation of interpretation and modelling approaches. Synthesizing all these efforts, we are confident that the N 2 O isotope community will continue to advance our understanding of N 2 O transformation processes in all spheres of the Earth, and in turn to gain improved constraints on regional and global budgets.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Solar Performance Insight (Final Report)

The PV Operations and Maintenance (O&M) service industry lacks an affordable, well-documented, intuitive PV modeling and analytics tool to calculate modeled performance from actual data from multiple data acquisition systems (DAS). We envision a performance modeling and analytics platform built on open-source, extensible, community-maintained code. The key innovation is the community-driven development of pvlib python delivered through a lightweight web service to provide configurable, consistent and reproducible PV modeling for O&M providers.

14 SOLAR ENERGY↗
DOE OSTI2020

Modeling thin layers of analytes on substrates for spectral analysis: use of solid/liquid n and k values to model reflectance spectra

Since solids are only sometimes seen en masse in a pure bulk form, and for liquids other than water almost never, a capability to model reflectance spectra from analytes deposited on various substrates would be highly advantageous. If available, the real, n ( ν ) , and imaginary, k ( ν ) , components of the complex refractive index, n n + i k , can be used to simulate infrared spectra, accounting for reflection, refraction, and absorption phenomena as a function of wavelength. We focus on using the Pacific Northwest National Laboratory (PNNL) derived n / k vectors for solid and liquid analytes deposited as thin layers on different types of substrates including conductors, such as aluminum, and inorganic dielectrics, such as glass. The model is an adaptation of the Monte Carlo ray trace modeling program, TracePro, extended through the use of its macrolanguage. The model is tested using thin films of organic liquids including silicone oil and no. 2 diesel fuel, as well as organic solids such as caffeine and acetaminophen on aluminum and glass. The predicted spectra for the solid films were compared to experimental hemispherical reflectance data measured using a Fourier transform spectrometer with an integrating sphere. The thickness of the calculated layer is a parameter for predicting the (transflectance) spectra and is obtained using the areal density measured from gravimetric methods to generate the thin-layer samples. Comparison of the calculated spectra with experimental hemispherical reflectance data shows excellent agreement, indicating promise for the use of measured n / k data to synthesize reference spectral data. In particular, accounting for the inhomogeneity of the deposits greatly improved the match with experimental data. Finally, the theoretical modeling shows that for thicker layers (ca. 20 to 100 μm) of typical organics possessing moderately strong k values, the longwave infrared features are often saturated and better spectral contrast is obtained from the overtone/combination bands in the shortwave infrared.

42 ENGINEERING↗
DOE OSTI2020

Analytical formula for pellet fuel source density in toroidal plasma configurations based on an areal deposition model

An analytical formula for the fuel source density η F (&Psi;) over a magnetic flux surface &Psi; following pellet injection is derived. During pellet motion the ablated and ionized fuel will be initially deposited nearby the pellet, prior to subsequent homogenization within the magnetic flux surfaces. Here in our research, it is assumed that the deposition area projected normal to the magnetic field is on the order of the cross-sectional area of the ionized ablation column whose axis is aligned with the magnetic field. Previous pellet deposition codes [1] employed a point source deposition approximation, which overpredicts the surface-averaged density, particularly when the obliquity between the pellet trajectory and the flux surface normal approaches 90 degrees. A key finding of this study is that as the obliquity approaches 90 degrees, grazing trajectory, the areal model predicts a well behaved η F and removes the unphysical divergence stemming from the point model. To illustrate the difference exhibited between areal and point models for near grazing trajectories, we considered vertical pellet injection into a CFETR-like tokamak with a negative triangularity plasma cross section using a pellet ablation/deposition module.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Generalized analytical and numerical modeling of optical second harmonic generation in anisotropic crystals and complex heterostructures using #SHAARP package

Optical second harmonic generation (SHG) is a nonlinear optical effect widely used for nonlinear optical microscopy and laser frequency conversion. The closed-form analytical solution of the nonlinear optical responses is essential for evaluating the optical responses of new materials whose optical properties are unknown a priori. Many approximations have therefore been employed in the existing analytical approaches, such as slowly varying approximation, weak reflection of the nonlinear polarization, transparent medium, high crystallographic symmetry, Kleinman symmetry, easy crystal orientation along a high-symmetry direction, phase matching conditions and negligible interference among nonlinear waves, which may lead to large errors in the reported material properties. To avoid these approximations, here we have developed an open-source package named Second Harmonic Analysis of Anisotropic Rotational Polarimetry (#SHAARP) for single interface (si) and in multilayers (ml) for homogeneous crystals. The reliability and accuracy are established by experimentally benchmarking with both the SHG polarimetry and Maker fringes predicted from the package using standard materials. SHAARP.si and SHAARP.ml are available through GitHub https://github.com/Rui-Zu/SHAARP and https://github.com/bzw133/SHAARP.ml, respectively.

complex systems↗
DOE OSTI2021

Visual HPC Workflows for the Analysis of System Dynamics Models

Visual analytics supported by high performance computing (HPC) accelerates and enhances the discovery, exploration, and analysis of causal patterns in complex system dynamics (SD) models. We present a suite of visualization-assisted ensemble-based techniques for hypothesis generation and testing, and for sensitivity analysis. By employing HPC to provide parallel, on-demand simulation of SD models, one can “steer” an ensemble of simulated scenarios in real time as one first formulates and then informally tests those hypotheses: this provides rapid feedback for analysts to refine their understanding of the causal relationships emergent from a model. Such understandings can be followed and augmented by rigorous application of statistical methods, namely global variance-based sensitivity analysis, Monte-Carlo filtering, adaptive regional sensitivity analysis, and self-organized maps: here timely computation relies on HPC, while effective presentation emphasizes high-dimensional multivariate data visualization. Immersive visualization in virtual 3D environments provides an excellent adjunct to the traditional 2D graphics typically used for SD models, as it generates an embodied understanding of model behavior and facilitates an active, collaborative critique of model structure and output. Finally, we summarize prospects for HPC-enabled visual analytics applied to SD modeling.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2021

Wake steering of multirotor wind turbines

Abstract In this paper, wake steering is applied to multirotor turbines to determine whether it has the potential to reduce wind plant wake losses. Through application of rotor yaw to multirotor turbines, a new degree of freedom is introduced to wind farm control such that wakes can be expanded, channelled or redirected to improve inflow conditions for downstream turbines. Five different yaw configurations are investigated (including a baseline case) by employing large‐eddy simulations (LES) to generate a detailed representation of the velocity field downwind of a multirotor wind turbine. Two lower‐fidelity models from single‐rotor yaw studies (curled‐wake model and analytical Gaussian wake model) are extended to the multirotor case, and their results are compared with the LES data. For each model, the wake is analysed primarily by examining wake cross‐sections at different downwind distances. Further quantitative analysis is carried out through characterisations of wake centroids and widths over a range of streamwise locations and through a brief analysis of power production. Most significantly, it is shown that rotor yaw can have a considerable impact on both the distribution and magnitude of the wake velocity deficit, leading to power gains for downstream turbines. The lower‐fidelity models show small deviation from the LES results for specific configurations; however, both are able to reasonably capture the wake trends over a large streamwise range.

17 WIND ENERGY↗
DOE OSTI2026

AI-Based Analytics and Energy Modeling Framework for Characterizing Urban Energy Systems

Developing location-specific district energy models is essential for understanding energy patterns and supporting efficient management and planning decisions. However, accurately characterizing these models remains challenging due to gaps in building characteristics and labor-intensive traditional modeling workflows. To address these challenges, we develop an AI-based framework that integrates top-down and bottom-up building energy data to automate urban energy model characterization. The framework trains multimodal deep learning models using heterogeneous ResStockTM datasets to infer missing building characteristics from varying levels of known information and generate simulation-ready inputs for district-scale energy modeling. It also employs a conditioning-based injection approach to generate ”what-if” scenarios, enabling users to explore retrofit, efficiency, and technology-upgrade pathways. Integrated within URBANoptTM, a bottom-up district energy modeling platform for simulating co-located buildings, the framework infers detailed building-level inputs required for bottom-up simulations. Both localized and generalized AI models are developed to learn relationships across categorical, numerical, and time-series data, enabling reconstruction of missing attributes and generation of targeted upgrade scenarios. We demonstrate this methodology on a residential neighborhood in Baltimore, MD, assessing internal consistency against ResStock reference data and URBANopt simulation, and comparing selected attributes against real-world building characteristics. Results show strong overall predictive accuracy in data completion and scenario generation, with localized and generalized models offering complementary trade-offs between precision and scalability. Overall, our automated framework streamlines energy modeling and provides a reliable framework for urban building energy characterization.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

Frequency-dependent sensitivity of AC elastocaloric effect measurements explored through analytical and numerical models

We present a comprehensive study of the frequency-dependent sensitivity for measurements of the AC elastocaloric effect by applying both exactly soluble models and numerical methods to the oscillating heat flow problem. These models reproduce the finer details of the thermal transfer functions observed in experiments, considering here representative data for single-crystal Ba(Fe1−xCox)2As2. Based on our results, we propose a set of practical guidelines for experimentalists using this technique. This work establishes a baseline against which the frequency response of the AC elastocaloric technique can be compared and provides intuitive explanations of the detailed structure observed in experiments.

Straquadine, J. A. W. (ORCID:0000000165309541)↗
DOE OSTI2023

A differentiable model of the evolution of dark matter halo concentration

ABSTRACT We introduce a new model of the evolution of the concentration of dark matter haloes, c(t). For individual haloes, our model approximates c(t) as a power law with a time-dependent index, such that at early times, concentration has a nearly constant value of c ≈ 3–4, and as cosmic time progresses, c(t) smoothly increases. Using large samples of halo merger trees taken from the Bolshoi–Planck and MultiDark Planck 2 cosmological simulations, we demonstrate that our three-parameter model can approximate the evolution of the concentration of individual haloes with a typical accuracy of 0.1 dex for $t\gtrsim 2\, {\rm Gyr}$ for all Bolshoi–Planck and MultiDark Planck 2 haloes of present-day peak mass $M_{0}\gtrsim 10^{11.5}\, {\rm M}_{\odot }$. We additionally present a new model of the evolution of the concentration of halo populations, which we show faithfully reproduces both average concentration growth and the diversity of smooth trajectories of c(t), including capturing correlations with halo mass and halo assembly history. Our publicly available source code, diffprof, can be used to generate Monte Carlo realizations of the concentration histories of cosmologically representative halo populations. diffprof is differentiable due to its implementation in the jax autodiff library, which facilitates the incorporation of our model into existing analytical halo model frameworks.

Stevanovich, Dash↗