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DOE OSTI2021

Differentiable programming for online training of a neural artificial viscosity function within a staggered grid Lagrangian hydrodynamics scheme

Lagrangian methods to solve the inviscid Euler equations produce numerical oscillations near shock waves. A common approach to reducing these oscillations is to add artificial viscosity (AV) to the discrete equations. The AV term acts as a dissipative mechanism that attenuates oscillations by smearing the shock across a finite number of computational cells. However, AV introduces several control parameters that are not determined by the underlying physical model, and hence, in practice are tuned to the characteristics of a given problem. We seek to improve the standard quadratic-linear AV form by replacing it with a learned neural function that reduces oscillations relative to exact solutions of the Euler equations, resulting in a hybrid numerical-neural hydrodynamic solver. Because AV is an artificial construct that exists solely to improve the numerical properties of a hydrodynamic code, there is no offline ‘viscosity data’ against which a neural network can be trained before inserting into a numerical simulation, thus requiring online training. We achieve this via differentiable programming, i.e. end-to-end backpropagation or adjoint solution through both the neural and differential equation code, using automatic differentiation of the hybrid code in the Julia programming language to calculate the necessary loss function gradients. A novel offline pre-training step accelerates training by initializing the neural network to the default numerical AV scheme, which can be learned rapidly by space-filling sampling over the AV input space. We find that online training over early time steps of simulation is sufficient to learn a neural AV function that reduces numerical oscillations in long-term hydrodynamic shock simulations. These results offer an early proof-of-principle that online differentiable training of hybrid numerical schemes with novel neural network components can improve certain performance aspects existing in purely numerical schemes.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Validation and Evaluation Uses of Quasi-Differential High-Energy Scattering Data [Slides]

This presentation covers the validation and evaluation uses of quasi-differential high-energy scattering data. This lecture covers motivation behind this work. The lecture then touches on quasi-differential for evaluation, quasi-differential for covariance, and quasi-differential for validation. The presentation concludes with a summary.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Differential Privacy in Grid Kitchen: Implementation & Software Documentation

Sharing of power grid feeder models faces significant challenges due to the potential risk of exposing sensitive operational information. Traditional anonymization techniques have shown notable limitations in other sensitive domains, as evidenced by documented re-identification attacks that combine supposedly anonymized datasets with auxiliary information, raising concerns that similar vulnerabilities could affect power grid data. Consequently, there is a pressing need for a more rigorous privacy protection strategy that not only delivers formal mathematical guarantees but also preserves the analytical value of the shared models. To address this challenge, we have enhanced the Grid Kitchen framework by implementing differential privacy mechanisms within the distribution model dehydration pipeline. This implementation carefully calibrates and applies noise to sensitive attributes in feeder models according to configurable privacy levels—low, moderate, and high—each offering different balances between data utility and privacy protection. Our approach uses established noise functions (Gaussian for continuous data and Discrete Laplace for integer values) with parameters carefully calibrated so that the impact of individual data points is effectively masked in the final output. The integration leverages our Noise Catalog, which we developed to categorize feeder model properties by component type, data type, and sensitivity. This catalog guides the application of appropriate noise functions and privacy parameters ($\varepsilon$ and $\delta$) to each attribute, ensuring consistent privacy protection across the model while maintaining its structural integrity and analytical usefulness. This implementation also includes evaluation tools that allow model owners to assess the impact of privacy-preserving transformations before sharing data with external parties. This report provides documentation for the differential privacy capabilities added to the Grid Kitchen project. It includes a primer on differential privacy concepts and their importance in modern data sharing, details the architecture of our implementation, explains the privacy modes and parameter configurations, and offers practical guidance on using the code for applying differential privacy to grid feeder models. Through examples and code snippets, we demonstrate the effective application of these privacy-enhancing technologies, enabling utility operators and researchers to confidently share grid data while protecting sensitive information.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS2001

Erythroid cell growth and differentiation in vitro in the simulated microgravity environment of the NASA rotating wall vessel bioreactor

Prolonged exposure of humans and experimental animals to the altered gravitational conditions of space flight has adverse effects on the lymphoid and erythroid hematopoietic systems. Although some information is available regarding the cellular and molecular changes in lymphocytes exposed to microgravity, little is known about the erythroid cellular changes that may underlie the reduction in erythropoiesis and resultant anemia. We now report a reduction in erythroid growth and a profound inhibition of erythropoietin (Epo)-induced differentiation in a ground-based simulated microgravity model system. Rauscher murine erythroleukemia cells were grown either in tissue culture vessels at 1 x g or in the simulated microgravity environment of the NASA-designed rotating wall vessel (RWV) bioreactor. Logarithmic growth was observed under both conditions; however, the doubling time in simulated microgravity was only one-half of that seen at 1 x g. No difference in apoptosis was detected. Induction with Epo at the initiation of the culture resulted in differentiation of approximately 25% of the cells at 1 x g, consistent with our previous observations. In contrast, induction with Epo at the initiation of simulated microgravity resulted in only one-half of this degree of differentiation. Significantly, the growth of cells in simulated microgravity for 24 h prior to Epo induction inhibited the differentiation almost completely. The results suggest that the NASA RWV bioreactor may serve as a suitable ground-based microgravity simulator to model the cellular and molecular changes in erythroid cells observed in true microgravity.

NASA Discipline Cell Biology↗

NASA NTRS1996

Cyclooxygenases in human and mouse skin and cultured human keratinocytes: association of COX-2 expression with human keratinocyte differentiation

Epidermal expression of the two isoforms of the prostaglandin H-generating cyclooxygenase (COX-1 and COX-2) was evaluated both by immunohistochemistry performed on human and mouse skin biopsy sections and by Western blotting of protein extracts from cultured human neonatal foreskin keratinocytes. In normal human skin, COX-1 immunostaining is observed throughout the epidermis whereas COX-2 immunostaining increases in the more differentiated, suprabasilar keratinocytes. Basal cell carcinomas express little if any COX-1 or COX-2 immunostaining whereas both isozymes are strongly expressed in squamous cell carcinomas deriving from a more differentiated layer of the epidermis. In human keratinocyte cultures, raising the extracellular calcium concentration, a recognized stimulus for keratinocyte differentiation, leads to an increased expression of both COX-2 protein and mRNA; expression of COX-1 protein, however, shows no significant alteration in response to calcium. Because of a recent report that failed to show COX-2 in normal mouse epidermis, we also looked for COX-1 and COX-2 immunostaining in sections of normal and acetone-treated mouse skin. In agreement with a previous report, some COX-1, but no COX-2, immunostaining is seen in normal murine epidermis. However, following acetone treatment, there is a marked increase in COX-1 expression as well as the appearance of significant COX-2 immunostaining in the basal layer. These data suggest that in human epidermis as well as in human keratinocyte cultures, the expression of COX-2 occurs as a part of normal keratinocyte differentiation whereas in murine epidermis, its constitutive expression is absent, but inducible as previously published.

NASA Discipline Cell Biology↗

NASA NTRS1995

In vitro chick pre-cardiac explant tissue differentiation during spaceflight on SpaceHab-02

Chick precardiac tissue explants were cultured on the 8-day mission of STS-60, space shuttle Discovery. Development of in vitro cultures of precardiac chick tissue from embryo stages 5 though 8 (H-H) were initiated during orbit and were terminated after approximately fifteen hours of 37 degree C culture. Transmission electron microscopy and tritiated thymidine studies were performed postflight. No significant differences in cell proliferation were observed between flight and ground controls. Electron-microscopic studies revealed stage 8 explants were capable of differentiation during flight in a pattern which matched ground control tissues. As anticipated, stage 7 explant tissues had differentiated to a lesser extent compared to stage 8 tissues. Interestingly, stage 7 precardiac explant flight tissue differentiation was less than ground control tissue. This difference in differentiation between flight and ground cultures was enhanced in stage 6 tissues, as high levels of myofibril organization were only seen in ground controls. Other cellular components such as Golgi apparatus, junctional complexes, and mitochondria were present and appeared normal and healthy.

NASA Program NSCORT↗

NASA NTRS2017

Differential Drag Demonstration: A Post-Mission Experiment with the EO-1 Spacecraft

Differential drag is a technique for altering the semi-major axis, velocity, and along-track position of a spacecraft in low Earth orbit. It involves varying the spacecrafts cross-sectional area relative to its velocity direction by temporarily changing attitude and solar array angles, thus varying the amount of atmospheric drag on the spacecraft. The technique has recently been proposed and used by at least three satellite systems for initial separation of constellation spacecraft after launch, stationkeeping during the mission, and potentially for conjunction avoidance. Similarly, differential drag has been proposed as a control strategy for rendezvous, removing the need for active propulsion. In theory, some operational missions that lack propulsion capability could use this approach for conjunction avoidance, though options are typically constrained for spacecraft that are already in orbit. Shortly before the spacecraft was decommissioned, an experiment was performed using NASAs EO-1 spacecraft in order to demonstrate differential drag on an operational spacecraft in orbit, and discover some of the effects differential drag might manifest. EO-1 was not designed to maintain off-nominal orientations for long periods, and as a result the team experienced unanticipated challenges during the experiment. This paper will discuss operations limitations identified before the experiment, as well as those discovered during the experiment. The effective displacement that resulted from increasing the drag area for 39 hours will be compared to predictions as well as the expected position if the spacecraft maintained nominal operations. A hypothetical scenario will also be examined, studying the relative risks of maintaining an operational spacecraft bus in order to maintain the near-maximum drag area orientation and hasten reentry.

differential drag↗

NASA NTRS2017

Differential Drag Demonstration: A Post-Mission Experiment with the EO-1 Spacecraft

Differential drag is a technique for altering the semimajor axis, velocity, and along-track position of a spacecraft in low Earth orbit. It involves varying the spacecraft's cross-sectional area relative to its velocity direction by temporarily changing attitude and solar array angles, thus varying the amount of atmospheric drag on the spacecraft. The technique has recently been proposed and used by at least three satellite systems for initial separation of constellation spacecraft after launch, stationkeeping during the mission, and potentially for conjunction avoidance. Similarly, differential drag has been proposed as a control strategy for rendezvous, removing the need for active propulsion. In theory, some operational missions that lack propulsion capability could use this approach for conjunction avoidance, though options are typically constrained for spacecraft that are already in orbit. Shortly before the spacecraft was decommissioned, an experiment was performed using NASA's EO-1 spacecraft in order to demonstrate differential drag on an operational spacecraft in orbit, and discover some of the effects differential drag might manifest. EO-1 was not designed to maintain off-nominal orientations for long periods, and as a result the team experienced unanticipated challenges during the experiment. This paper will discuss operations limitations identified before the experiment, as well as those discovered during the experiment. The effective displacement that resulted from increasing the drag area for 39 hours will be compared to predictions as well as the expected position if the spacecraft maintained nominal operations. A hypothetical scenario will also be examined, studying the relative risks of maintaining an operational spacecraft bus in order to maintain the near-maximum drag area orientation and hasten reentry.

orbital lifetim↗

NASA NTRSDate not supplied

Multi-Anvil Experimentation Applied to Planetary Differentiation

Planets undergo differentiation that includes segregation of metal from silicate at high temperatures and pressures ranging from deep planetary core pressures (>300 GPa for Earth)to very shallow conditions of asteroids (<100 MPa).The multi-anvil solid media apparatus accesses the middle part of this range from 3 to 30 GPa –pressure relevant to the interior of Mercury, Venus, Earth, Earth’s Moon, and Mars. Early planets are thought to have experienced high temperatures from a combination of heat sources including radioactive decay, gravitational and accretional heating, and impact processes. These heating events led to melting of mantles and cores, thus requiring an understanding of solid-liquid equilibria in metal-silicate systems. In 2006 we established a multi-anvil facility at NASA-JSC combining an 880 ton press and a Kawai/Walker type module from Rockland Research. Our high PT work has been greatly facilitated by use of the COMPRES multi-anvil assemblies (1). Our recent work has included studies of element partitioning between liquid metal and liquid silicate(e.g., 2), as well as between minerals and melts(e.g., 3), both of which have led to better constraints on the timing and conditions of planetary differentiation(e.g. 4). Several examples involving sustained efforts will be summarized below and for the presentation. The distribution of siderophile (iron-loving) elements between core and mantle is controlled by metal-silicate equilibrium across a wide range of pressures. Therefore, experimentation across this pressure range helps to calibrate elemental partitioning models that can be applied to planets, and used to predict mantle chemistry and composition during planetary differentiation. Our studies have focused on a wide range of siderophile elements (refractory Ni, Co, W, Mo; volatile P, Ga, Cu, Sn, Sb; highly siderophile Au, Pd) that have constrained partitioning, valence, and isotopic fractionation, and applied to Earth, Moon, and Mars. When molten mantles (magma oceans) cool enough to initiate crystallization, the solids precipitate at depth and in large planets this involves high pressure phases like garnet, majorite, akimotoite, and ringwoodite. As these solids precipitate they can segregate from liquid by density contrasts, thus causing elemental fractionation which can be used to decipher timing of differentiation. Mineral/melt and metal/silicate equilibria in our lab have helped to better understand high pressure fractionation of isotopic parent/daughter pairs Hf/W, Mn/Cr, Pd/Ag, Pt/Os, Re/Os, and U/Pb, and their application to Earth, Moon and Mars. There remains great potential for multi-anvil experimentation to shed light on many pressure–dependent aspects of planetary evolution such as core formation, high pressure phase equilibria, redox equilibria, and volatile evolution and storage. References1. Leinenweber, K., et al.(2012) American Mineralogist,97, 353–368. 2.Righter, K., et al.(2020) Geochem. Persp. Lett.15, 1-6.3. Righter, K., et al.(2020) Met. Planet. Sci 55, 2741-2757.4. Righter, K., et al.(2020)Earth and Planetary Science Letters,552, 116590.

pressure↗

NASA NTRSDate not supplied

Differential Drag Efficacy for Close Approach Remediation

Differential drag has become a viable alternative to propulsion for satellites to avoid collisions, but there is little guidance in the literature to aid mission designers in developing a differential drag capability that verifiably meets collision avoidance efficacy standards or requirements, if such requirements were to exist. This paper proposes a differential drag efficacy determination approach based on empirical conjunctions from the NASA Conjunction Assessment Risk Analysis historical database, focusing on energy dissipation rate and change in ballistic coefficient as the key satellite parameters correlated to efficacy. The data analysis informs the discussion toward adoption of recommended differential drag requirements. A case study is presented to walk through the process to determine efficacy of a proposed mission assuming several potential requirements.

conjunction remediation↗

DOE OSTI2022

Reverse-mode differentiation in arbitrary tensor network format: with application to supervised learning.

This paper describes an efficient reverse-mode differentiation algorithm for contraction operations of tensor networks that may have arbitrary and unconventional network topologies. The approach leverages the tensor contraction tree of Evenbly and Pfeifer (2014), which provides an instruction set for the contraction sequence of a network. We show that this tree can be efficiently leveraged for differentiation of a full tensor network contraction using a recursive scheme that exploits (1) the bilinear property of contraction and (2) the property that trees have single path from root to leaves. While differentiation of tensor-tensor contraction is already possible in most automatic differentiation packages, we show that exploiting these two additional properties in the specific context of contraction sequences can improve efficiency. Following a description of the algorithm and computational complexity analysis, we investigate its utility for gradient-based supervised learning for low-rank function recovery and for fitting real-world unstructured datasets. We demonstrate improved performance over alternating least-squares optimization approaches and the capability to handle heterogeneous and arbitrary tensor network formats. When compared to alternating minimization algorithms, we find that the gradient-based approach requires a smaller oversampling ratio (number of samples compared to number model parameters) for recovery. This increased efficiency extends to fitting unstructured data of varying dimensionality and when employing a variety of tensor network formats. Here, we show improved learning using the hierarchical Tucker method over the tensor-train in high-dimensional settings on a number of benchmark problems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Combination and interpretation of differential Higgs boson production cross sections in proton-proton collisions at $ \sqrt{s}=13 $ TeV

Precision measurements of Higgs boson differential production cross sections are a key tool to probe the properties of the Higgs boson and test the standard model. New physics can affect both Higgs boson production and decay, leading to deviations from the distributions that are expected in the standard model. In this paper, combined measurements of differential spectra in a fiducial region matching the experimental selections are performed, based on analyses of four Higgs boson decay channels (γγ, ZZ$^{(*)}$, WW$^{(*)}$, and ττ) using proton-proton collision data recorded with the CMS detector at $ \sqrt{s}=13 $ TeV, corresponding to an integrated luminosity of 138 fb$^{−1}$. The differential measurements are extrapolated to the full phase space and combined to provide the differential spectra. A measurement of the total Higgs boson production cross section is also performed using the γγ and ZZ decay channels, with a result of $ {53.4}_{-2.9}^{+2.9}{\left(\textrm{stat}\right)}_{-1.8}^{+1.9}\left(\textrm{syst}\right) $ pb, consistent with the standard model prediction of 55.6 ± 2.5 pb. The fiducial measurements are used to compute limits on Higgs boson couplings using the κ-framework and the SM effective field theory.[graphic not available: see fulltext]

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Measurement of the total and differential cross-sections of $t\bar{t}$$W$ production in pp collisions at $\sqrt{s}$ = 13 TeV with the ATLAS detector

Measurements of inclusive and differential production cross-sections of a top-quark-top-antiquark pair in association with a W boson ($t\bar{t}$$W$) are presented. They are performed by targeting final states with two same-sign or three isolated leptons (electrons or muons) and are based on $\sqrt{s}$ = 13 TeV proton-proton collision data with an integrated luminosity of 140 fb −1 , recorded from 2015 to 2018 with the ATLAS detector at the Large Hadron Collider. The inclusive $t\bar{t}$$W$ production cross-section is measured to be 880 ± 80 fb, compared to a reference theoretical prediction of 745 ± 50 (scale) ± 13 (2-loop approx.) ± 19 (PDF, α s ) fb. Differential cross-section measurements characterise this process in detail for the first time. Several particle-level observables are compared with a variety of theoretical predictions, which generally agree well with the normalised differential cross-section results. Additionally, the relative charge asymmetry of $t\bar{t}$$W$ + and $t\bar{t}$$W$ – is measured inclusively to be $A$$^{rel}_{C}$ = 0.33 ± 0.05, in very good agreement with the theoretical prediction of 0.322 ± 0.003 (scale) ± 0.007 (PDF), as well as differentially.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Estrogen depletion alters osteogenic differentiation and matrix production by osteoblasts in vitro

Highlights: • Estrogen depletion accelerates osteoblast differentiation in static culture. • Mechanical stimulation exacerbated the effects of estrogen depletion on osteoblast differentiation. • Estrogen depletion alters osteoblasts capacity to produce a good quality matrix. Recent studies have revealed that the effects of estrogen deficiency are not restricted to osteoclasts and bone resorption, but that bone matrix composition is altered and osteoblasts exhibit an impaired response to mechanical stimulation. In this study, we test the hypothesis that estrogen depletion alters osteogenic differentiation and matrix production by mechanically stimulated osteoblasts in vitro. MC3T3-E1 cells were pre-treated with estrogen for 14 days, after which estrogen was withdrawn or inhibited with Fulvestrant up to 14 days. Fluid shear stress (FSS) was applied using an orbital shaker. Under estrogen depletion in static culture, osteogenic marker (ALP) and gene expression (Runx2) were decreased at 2 and after 7 days of estrogen depletion, respectively. In addition, up to 7 day the inhibition of the estrogen receptor significantly decreased fibronectin expression (FN1) under static conditions. Under estrogen depletion and daily mechanical stimulation, changes in expression of Runx2 occurred earlier (4 days) and by 14 days, changes in matrix production (Col1a1) were reported. We propose that changes in osteoblast differentiation and impaired matrix production during estrogen depletion may contribute to the altered quality of the bone and act as a contributing factor to increased bone fragility in postmenopausal osteoporosis.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2021

Electron emission from fluorene (C 13 H 10 ) upon 3.5 MeV/u Si 8+ ion impact: double differential distributions

In this work, we have studied the electron emission from one of the polycyclic aromatic hydrocarbon (PAH) molecules namely, fluorene (C13H10), upon 3.5 MeV/u Si8+ ion impact. The experimentally measured absolute double differential cross sections (DDCS) are compared with the continuum distorted wave-eikonal initial state (CDW-EIS) model and the first Born approximation including correct boundary conditions (CB1). The measurements are carried out in the ejected e⁻-energy range of 1 eV–400 eV and in the angular range of 20°–160°. We have obtained the single differential and the total cross sections (TCSs) of e⁻-emission as well. The CB1 calculation largely underestimates the data. The CDW-EIS model, which is applied for the PAH molecule for the first time, provides an overall better agreement with the double differential, single differential and TCS data. The DDCS data for fluorene has also been compared with that for CH4 molecule, at a few angles. The forward–backward angular asymmetry shows a relatively flatter distribution compared to the theoretical predictions. The contribution due to the giant plasmon resonance could not be clearly observed except a mild indication in the asymmetry parameter. The angular distribution of the carbon KLL Auger electron cross section shows certain variations. The study of the KLL hyper-satellite component indicates the double K-ionization cross section is about 8.6% of the single K-ionization one.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2024

Use of differential plasma rotation to prevent disruptive tearing mode onset from 3-wave coupling

Abstract Plasma differential rotation is found to be capable of preventing disruptive neoclassical tearing modes (NTMs) seeded by nonlinear three-wave coupling. As tearing modes degrade confinement and can lead to disruptions, stabilization strategies are crucial to the successful operation of future devices. In ITER-relevant scenarios on DIII-D, rotationally coupled m / n = 1/1 and 3/2 modes have been observed to drive 2/1 islands through three-wave coupling. The frequency of the driven 2/1 mode is set by matching conditions and the frequencies of the driving modes. When the driven mode frequency matches the local plasma rotation frequency, e.g. at low differential rotation, the driven 2/1 island can grow into a disruptive NTM. Using neutral beam torque as an actuator to scan the differential rotation, these experiments demonstrate that a sufficiently large frequency mismatch prevents destabilization of disruptive 2/1 NTMs by three-wave coupling. This work indicates that differential rotation can be used as an actuator to prevent NTMs seeded by three-wave coupling.

Richner, N. J. (ORCID:0000000155443915)↗

DOE OSTI2023

Differentiable Earth mover’s distance for data compression at the high-luminosity LHC

Abstract The Earth mover’s distance (EMD) is a useful metric for image recognition and classification, but its usual implementations are not differentiable or too slow to be used as a loss function for training other algorithms via gradient descent. In this paper, we train a convolutional neural network (CNN) to learn a differentiable, fast approximation of the EMD and demonstrate that it can be used as a substitute for computing-intensive EMD implementations. We apply this differentiable approximation in the training of an autoencoder-inspired neural network (encoder NN) for data compression at the high-luminosity LHC at CERN The goal of this encoder NN is to compress the data while preserving the information related to the distribution of energy deposits in particle detectors. We demonstrate that the performance of our encoder NN trained using the differentiable EMD CNN surpasses that of training with loss functions based on mean squared error.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2023

Divergent selection and climate adaptation fuel genomic differentiation between sister species of Sphagnum (peat moss)

Abstract Background and Aims New plant species can evolve through the reinforcement of reproductive isolation via local adaptation along habitat gradients. Peat mosses (Sphagnaceae) are an emerging model system for the study of evolutionary genomics and have well-documented niche differentiation among species. Recent molecular studies have demonstrated that the globally distributed species Sphagnum magellanicum is a complex of morphologically cryptic lineages that are phylogenetically and ecologically distinct. Here, we describe the architecture of genomic differentiation between two sister species in this complex known from eastern North America: the northern S. diabolicum and the largely southern S. magniae. Methods We sampled plant populations from across a latitudinal gradient in eastern North America and performed whole genome and restriction-site associated DNA sequencing. These sequencing data were then analyzed computationally. Key Results Using sliding-window population genetic analyses we find that differentiation is concentrated within ‘islands’ of the genome spanning up to 400 kb that are characterized by elevated genetic divergence, suppressed recombination, reduced nucleotide diversity and increased rates of non-synonymous substitution. Sequence variants that are significantly associated with genetic structure and bioclimatic variables occur within genes that have functional enrichment for biological processes including abiotic stress response, photoperiodism and hormone-mediated signalling. Demographic modelling demonstrates that these two species diverged no more than 225 000 generations ago with secondary contact occurring where their ranges overlap. Conclusions We suggest that this heterogeneity of genomic differentiation is a result of linked selection and reflects the role of local adaptation to contrasting climatic zones in driving speciation. This research provides insight into the process of speciation in a group of ecologically important plants and strengthens our predictive understanding of how plant populations will respond as Earth’s climate rapidly changes.

58 GEOSCIENCES↗