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DOE OSTI2026

Dependence of CCN closure relationship with organic fraction from two airborne field campaigns over mid-latitude land and ocean

This study investigates the relationship between measured and calculated cloud condensation nuclei (CCN) number concentration and its dependence with organic fraction utilizing aircraft observations from The Aerosol and Cloud Experiments in the Eastern North Atlantic (ACE-ENA, 2017–2018) and The Holistic Interactions of Shallow Clouds, Aerosols, and Land Ecosystems (HI-SCALE, 2016) campaigns, which represent midlatitude marine and continental environments, respectively. For the ACE-ENA marine region, aerosol and CCN concentrations were significantly higher in summer than in winter, whereas at continental site for HI-SCALE, aerosol and CCN concentrations showed no pronounced differences between spring and autumn. Using aerosol chemical composition and number size distribution data, CCN concentrations at various supersaturations are calculated based on Köhler theory and then compared with observations from CCN counter. The results show that CCN closure performs well at both sites with a slight overestimation, with mean closure ratio (CR) of 1.13 and 1.17, respectively. Further investigation reveals that CR at lower supersaturation perform better than that at higher supersaturation. The dependence of CR on organic mass fraction (MForg) varies by environment: for marine aerosols, CR decreases with increasing organic fraction at lower supersaturations, whereas continental aerosols exhibit a consistent overestimation, with CR decreasing as organic fraction increases at higher supersaturations. This study provides key insights into CCN characteristics over midlatitude marine and continental environments, emphasizing the necessity of incorporating size-resolved chemical composition and mixing states into future model parameterizations, and contributing to a better understanding of aerosol–cloud interactions.

ACE-ENA field campaign↗

DOE OSTI2025

Gaussian integral method for void fraction

Here, a novel method, the Gaussian Integral Method (GIM), is presented for calculating void fractions in Computational Fluid Dynamics–Discrete Element Method (CFD-DEM) simulations. GIM is versatile and applicable to various grid types, including structured and unstructured polyhedral meshes, without requiring special boundary treatments. An optimization technique is introduced to make GIM independent of grid resolution and type. The method is validated against experimental data from a fluidized bed, demonstrating that GIM produces realistic simulations closely resembling experimental observations. Additionally, unstructured polyhedral grids using GIM outperform structured grids of equivalent resolution, yielding results more aligned with experimental data. The gradient of the void fraction is computed in the CFD solver and utilized in the DEM solver for precise estimation at particle locations. Overall, GIM provides an effective solution for void fraction calculations in particulate media simulations with complex geometries, enhancing the accuracy and applicability of CFD-DEM simulations for industrial processes.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2025

Effect of particle size and moisture on flow performance of loblolly pine anatomical fractions: Experimental findings and model predictions

The rising energy demand has highlighted biomass as a promising next-generation energy source. However, commercializing biomass-derived energy faces challenges, particularly in handling biomass feedstock. Factors like particle size, shape, moisture content, and surface roughness significantly impact biomass flowability. This study addresses a crucial knowledge gap by examining the effects of particle size and moisture content on the flow behavior and shear properties of different anatomical fractions of loblolly pine (Pinus taeda). The bulk shear behavior was examined using a Schulze ring shear tester, while flow performance was tested through gravity-driven flow experiments in a variable wedge-shape hopper. Results were incorporated into empirical and machine learning-based flow prediction models to evaluate their accuracy and limitations. The study found that samples with higher moisture content show higher unconfined yield strength. The critical arching distance increased with particle size, e.g., from approximately 13 and 33 mm for 2- and 6-mm whole chips, respectively at a 32-degree inclination angle. Conversely, the flow rate decreased for a given hopper opening as particle size increased. For instance, at a 60-mm hopper opening and a 32-degree inclination angle, the mass flow rates for 2- and 6-mm whole chips were 7.83 and 6.42 tonne/h, respectively. The empirical model consistently overpredicted the mass flow rate for all anatomical fractions, while the machine learning model more accurately predicted the central tendency of flow rate but was insensitive to varying tissue proportions. These novel findings provide comprehensive characterization of anatomical fractions, reveal significant combined effects of particle size and moisture content on biomass flow behavior, and demonstrate a better predictive accuracy of a machine learning model, all of which are useful for optimizing material handling strategies and biomass utilization technologies in the industry.

09 - BIOMASS FUELS↗

DOE OSTI2026

A New Theoretical Framework for Parameterizing Nonequilibrium Fractionation During Evaporation From the Ocean

The evaporation model for water isotopes proposed by Craig and Gordon (1965, https://books.google.co.in/books?id=6wIKAQAAIAAJ) is used in most isotope-enabled atmospheric models for the parameterization of nonequilibrium fractionation during evaporation from the ocean. In this model, one of the most uncertain parameters is the nonequilibrium fractionation factor 𝛼 𝑘 . Many isotope models use the formulation of Merlivat and Jouzel (1979, https://doi.org/10.1029/jc084ic08p05029), which parameterizes 𝛼 𝑘 as a function of wind speed and distinguishes between a smooth and a rough regime to account for the effect of ocean waves. The resulting discontinuity in 𝛼 𝑘 between smooth and rough regimes has been disputed by several empirical studies. Here, we present a new approach to parameterizing 𝛼𝑘 by explicitly accounting for the influence of wave drag on the momentum flux near the surface. Following Cifuentes-Lorenzen et al. (2018, https://doi.org/10.1007/s10546-018-0376-0), we add a third wave-induced component to the total momentum flux, in addition to the viscous and turbulent components, and extend the definition of the eddy viscosity to account for the momentum flux due to waves and turbulent dissipation near the surface. The new scheme predicts a slight decrease of 𝛼 𝑘 with wind speed, similar to the smooth-regime parameterization of Merlivat and Jouzel (1979, https://doi.org/10.1029/jc084ic08p05029). This new parameterization is incorporated into the isotope-enabled Community Atmosphere Model, where it improves the correlation of simulated and measured vapor deuterium excess relative to the default version and a version with constant 𝛼 𝑘 , suggesting that it may be used as a valid representation of fractionation during evaporation from the ocean in future isotope models.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Phase-Selective Fractionation of Lignocellulosic Biomass Using a Lignin-Based Hydrophobic Deep Eutectic Solvent Biphasic System

Lignocellulose fractionation is a critical step in biomass valorization. Herein, we report a hydrophobic deep eutectic solvent (HDES)-mediated biphasic fractionation strategy that enables the simultaneous and selective separation of cellulose, hemicellulose, and lignin in a single process. Lignin-derived HDESs composed of thymol and 2,6-dimethoxyphenol (syringol) were combined with an acidic aqueous phase to create a water-HDES biphasic system, in which lignin was preferentially extracted into the HDES phase, hemicellulose-derived sugars were selectively solubilized in the aqueous phase, and cellulose was retained in the solid residue. Using wheat straw and poplar wood as representative herbaceous and woody biomass feedstocks, the HDES-acid system exhibited strong synergistic effects, achieving delignification up to 69.8% and xylan removal up to 93.6%. Structural characterization confirmed effective disruption of the lignocellulosic matrix and increased cellulose accessibility, resulting in markedly enhanced enzymatic saccharification, with glucose yields up to 96.2% for wheat straw. This work demonstrates a sustainable and efficient HDES-based biphasic fractionation platform that enables phase-selective separation of major lignocellulosic components and provides a foundation for further development of closed-loop biorefinery processes.

09 BIOMASS FUELS↗

DOE OSTI2025

Measurement of the branching fraction of Λ + 𝑐 →𝑝⁢𝐾 0 𝑆⁢ 𝜋 0 at Belle

We report a precise measurement of the ratio of branching fractions ℬ⁡(Λ$^+_𝑐$ → 𝑝⁢𝐾$^0_𝑆$⁢𝜋 0 )/ℬ⁡(Λ$^+_𝑐$ → 𝑝⁢𝐾 − ⁢𝜋 + ) using 980 fb −1 of 𝑒 + ⁢𝑒 − data from the Belle experiment. We obtain a value of ℬ⁡(Λ$^+_𝑐$ → 𝑝⁢𝐾$^0_𝑆$⁢𝜋 0 )/ℬ⁡(Λ$^+_𝑐$ → 𝑝⁢𝐾 − ⁢𝜋 + ) =0.339 ±0.002 ±0.009, where the first and second uncertainties are statistical and systematic, respectively. This Belle result is consistent with the previous measurement from the CLEO experiment but has a fivefold improvement in precision. By combining our result with the world average ℬ⁡(Λ$^+_𝑐$ → 𝑝⁢𝐾 − ⁢𝜋 + ), we obtain the absolute branching fraction ℬ⁡(Λ$^+_𝑐$ → 𝑝⁢𝐾$^0_𝑆$⁢𝜋 0 ) =(2.12 ± 0.01 ±0.05 ±0.10)%, where the uncertainties are statistical, systematic, and the uncertainty in the absolute branching fraction scale ℬ⁡(Λ$^+_𝑐$ → 𝑝⁢𝐾 − ⁢𝜋 + ), respectively. This measurement can shed light on hadronic decay mechanisms in charmed baryon decays.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Slow Quasiparticle Dynamics and Anyonic Statistics in a Fractional Quantum Hall Fabry-Pérot Interferometer

Anyons are two-dimensional particles with fractional exchange statistics that emerge as elementary excitations of fractional quantum Hall phases. Experimentally, their exchange statistics can be measured in the edge-state Fabry-Pérot interferometer, wherein the presence of 𝑁 𝑞⁢𝑝 localized anyons contributes a phase 𝑁 𝑞⁢𝑝⁢ 𝜃 𝑎 to the interference pattern where 𝜃 𝑎 is twice the exchange phase. Here we report the observation of large, hysteretic phase jumps in a monolayer graphene Fabry-Pérot interferometer at 𝜈 = 1/3. When the filling factor is increased from 𝜈 < 1/3 toward the center of the plateau, we observe phase slips with magnitude Δ⁢𝜃 ≈ 2⁢𝜋/3, consistent with the addition of individual quasiparticles to the interferometer bulk. These phase slips occur as instantaneous jumps in the interference signal, with intervals between the jumps indicating quasiparticle equilibration times exceeding 20 min. We use this long timescale to investigate the effect of changes in interferometer area 𝐴 𝐼 and 𝑁 𝑞⁢𝑝 independently at fixed magnetic field, revealing a striking memory effect in the phase slip magnitude. In particular, as the 𝜈 =1/3 plateau is approached from higher filling, we observed phase slips with Δ⁢𝜃 significantly larger than 2⁢𝜋/3 over the same range of gate voltage where quantized jumps are seen for increasing 𝜈. We discuss this asymmetry in terms of bulk-edge coupling of quasiparticles localized near the edge or in the bulk, and argue that this effect can be qualitatively reconciled with theoretical expectations for strongly interacting quasiparticles in the presence of weak disorder and strongly nonequilibrium charge dynamics. Besides providing a replication of interferometric measurements sensitive to 𝜃 𝑎 , our results highlight the key role played by charge dynamics on signatures of the anyon phase, and demonstrate that fractional quasiparticles can be indefinitely localized in nonequilibrium configurations.

anyons↗

DOE OSTI2025

Measurement of the 𝐷 0 →𝐾 − ⁢𝜋 + ⁢𝑒 + ⁢𝑒 − branching fraction and search for 𝐷 0 → 𝜋 + ⁢𝜋 − ⁢𝑒 + ⁢𝑒 − and 𝐷 0 →𝐾 + ⁢𝐾 − ⁢𝑒 + ⁢𝑒 − decays at Belle

We present a study of the rare charm meson decays 𝐷 0 →𝐾 + ⁢𝐾 − ⁢𝑒 + ⁢𝑒 − , 𝜋 + ⁢𝜋 − ⁢𝑒 + ⁢𝑒 − , and 𝐾 − ⁢𝜋 + ⁢𝑒 + ⁢𝑒 − using a 942 fb −1 dataset collected by the Belle detector at the KEKB asymmetric-energy 𝑒 + ⁢𝑒 − collider. We identify 𝐷 0 candidates via the charge of the pion from 𝐷* + →𝐷 0 ⁢𝜋 + decays and normalize the branching fractions to 𝐷 0 → 𝐾 − ⁢𝜋 + ⁢𝜋 − ⁢𝜋 + decays. The branching fraction for decay 𝐷 0 → 𝐾 − ⁢𝜋 + ⁢𝑒 + ⁢𝑒 − is measured to be (39.6 ± 4.5 (stat) ± 2.9 (syst)) × 10 −7 , with the dielectron mass in the 𝜌/𝜔 mass region 675 < 𝑚 𝑒⁢𝑒 < 875 MeV/⁢𝑐 2 . We also search for 𝐷 0 → ℎ − ⁡ℎ (′)+ ⁡𝑒 + ⁢𝑒 − (ℎ (′) = 𝐾, 𝜋) decays with the dielectron mass near the 𝜂 and 𝜙 resonances, and away from these resonances for the 𝐾 + ⁢𝐾 − ⁢𝑒 + ⁢𝑒 − and 𝜋 + ⁢𝜋 − ⁢𝑒 + ⁢𝑒 − modes. For these modes, we find no significant signals and set 90% confidence level upper limits on their branching fractions at the 𝒪⁡(10 −7 ) level.

branching fraction↗

DOE OSTI2025

Composition and Plume Gas Interaction Control Iron Fractional Solubility More Than Particle Size in Volcanic Ash: Implications for Fertilization of the North Atlantic

Deposition of volcanic ash is thought to impact marine biogeochemical cycling by adding soluble iron (Fe) to the surface ocean. The magnitude of this input is a function of the amount of ash deposited, the total Fe content in the ash, and ash‐derived Fe's fractional solubility. However, the relative importance of chemical composition, acidic processing by the volcanic plume, and ash particle size in determining solubility is unclear. We paired an aerosol leach meant to provide an upper limit for fractional Fe solubility with chemical analyses of ash from the Cumbre Vieja (CV) and La Soufrière eruptions, which both impacted the North Atlantic in 2021. Fe in the ash samples is <6% soluble, but Fe fractional solubility in CV ash is approximately triple that of La Soufrière ash. Compared to La Soufrière, a larger proportion of the Fe in CV ash is in silicate rather than oxide minerals, which release more soluble Fe. Elevated levels of surficial fluorine (F) also suggest that CV ash was subjected to a more fluorine‐rich eruption plume and underwent more acidic processing. Particle size does not appear to be a primary control on Fe release. We estimate that the CV eruption had a much larger impact on dissolved Fe (DFe) concentration in the surface ocean than the La Soufrière eruption because of differences in soluble Fe content and particle deposition velocity. These differences may help explain why some eruptions elicit a biological response in the ocean while others do not.

Elliott, Hope E. [Univ. of Miami, FL (United State↗

DOE OSTI2025

Fractional quantization in insulators from Hall to Chern

The discovery of the integer and fractional quantum Hall effects naturally prompted the question of whether these effects can be realized without a magnetic field. Answering this is fundamentally important and requires a synthesis of the concepts of band topology, quantum geometry and electronic correlations. Here we summarize the basic concepts of both fractional Chern and fractional topological insulators and illustrate them with the theoretical lattice models that support the flat Chern bands in which the states were first predicted. We then examine their experimental realizations in twisted bilayer transition metal dichalcogenides and moiré rhombohedral few-layer graphene. Here, we also discuss the future challenges and opportunities in this research field.

Quantum Hall↗

DOE OSTI2026

Optical control of integer and fractional Chern insulators

Optical control of topology, particularly in the presence of electron correlations, is an interesting topic with broad scientific and technological impact. Twisted MoTe 2 bilayer (tMoTe 2 ) is a zero-field fractional Chern insulator (FCI), exhibiting the fractionally quantized anomalous Hall effect. As the chirality of the edge states and sign of the Chern number are determined by the underlying ferromagnetic polarization, manipulation of ferromagnetism would realize control of the Chern insulator (CI)/FCI states. Here, in this work, we demonstrate control of ferromagnetic polarization, and thus the CI and FCI states, by circularly polarized optical pumping in tMoTe 2 . At low excitation power, we achieve on-demand preparation of ferromagnetic polarization by optical training, that is, electrically tuning the system from non-ferromagnetic to desirable ferromagnetic states under helicity-selective optical pumping. With increased excitation power, we further realize direct optical switching of ferromagnetic polarization at a temperature far below the Curie temperature. Both optical training and direct switching are most effective near CI and FCI states, which we attribute to a gap-enhanced valley polarization of optically pumped holes. The magnetization can be dynamically switched by modulating the helicity of optical excitation. Spatially resolved measurements further demonstrate optical writing of ferromagnetic, and thus CI (or FCI) domains. Our work realizes precise optical control of a topological quantum many-body system with potential applications in topological spintronics, quantum memories and creation of exotic edge states by programmable patterning of integer and fractionally quantized anomalous Hall domains.

ferromagnetism↗

DOE OSTI2025

Viroid-like “obelisk” agents are widespread in the ocean and exceed the abundance of RNA viruses in the prokaryotic fraction

Abstract “Obelisks” are recently discovered ribonucleic acid (RNA) viroid-like elements present in diverse environments with no phylogenetic similarity to any known biological agent. obelisks were first identified in the human gut and in a commensal bacterium acting as a replicative host. They have a circular ∼1 kb RNA genome, rod-like secondary structures, and the encoding of a protein superfamily called “Oblins”. We performed a large-scale search of obelisks in the ocean using the Pebblescout program and the transcriptomic Sequence Archive Read databases, revealing the biogeography and abundance of these viroid-like RNA elements. We detected 55 obelisk genomes resulting in 35 marine clusters at the species level. These obelisks were detected in the prokaryotic fraction and to a lesser extent in the eukaryotic fraction, and distributed across all the oceans from surface to mesopelagic including the Arctic, and even in the coldest seawater of Earth beneath the Antarctic Ross Ice Shelf. The obelisk hallmark protein Oblin-1 confirmed by 3D models was found in various marine samples. Some of the detected marine obelisks harbor hammerhead self-cleaving ribozymes in both polarities. In the prokaryotic, but not the eukaryotic, fraction of the Tara Ocean dataset, relative abundance of obelisks calculated by transcriptomic fragment recruitment indicated that they are abundant in marine samples, reaching or even exceeding the relative abundance of the previously discovered uncultured RNA viruses. In conclusion, obelisks are abundant and widespread viroid-like elements that should be included in ocean biogeochemical models.

Environmental Sciences & Ecology↗

DOE OSTI2026

Accessing the gluon momentum fraction of nucleons through the gradient flow

We calculate the gluon momentum fraction of the nucleon using lattice QCD, with a nonperturbative renormalization technique based on the gradient flow. The gluon momentum fraction is determined on a single Wilson-clover ensemble using 𝑁 𝑓 =2 +1 flavors with pion mass 358 MeV and lattice spacing 0.094 fm. We employ the variational method to reduce excited-state contamination and apply the distillation framework to ensure a large operator basis. To reduce systematic uncertainties, we apply Bayesian model averaging to all fit procedures. We apply matching coefficients to the flow-time dependent lattice results to recover the gluon momentum fraction in the $\overline{MS}$-scheme at 2 GeV. Our final result is ⟨𝑥⟩ 𝑔 ⁢(𝜇 =2 GeV) =0.482⁢(35), where we quote only statistical uncertainties.

Lattice QCD↗

DOE OSTI2026

Unified Description of Cuprate Superconductors by Fractionalized Electrons Emerging from Integrated Analyses of Photoemission Spectra and Quasiparticle Interference

Electronic structure of high-temperature superconducting cuprates is studied by analyzing experimental data independently obtained from two complementary spectroscopies: one, quasiparticle interference (QPI) measured by scanning-tunneling microscopy, and the other, angle-resolved photoemission spectroscopy (ARPES). We combine these two sets of data in a unified theoretical analysis. Through explicit calculations of experimentally measurable quantities, we show that a simple two-component fermion model (TCFM) representing electron fractionalization succeeds in reproducing various detailed features of these experimental data: ARPES and QPI data are concomitantly reproduced by the TCFM in full energy and momentum spaces. The measured QPI pattern reveals a signature characteristic of the TCFM, distinct from the conventional single-component prediction, supporting the validity of the electron fractionalization in the cuprates. The integrated analysis also solves the puzzles of ARPES and QPI data that are seemingly inconsistent with each other. The overall success of the TCFM offers a comprehensive understanding of the electronic structure of the cuprates, in particular, the unoccupied side of the spectra, of which momentum-resolved structure has long been unexplored experimentally. We further predict that a characteristic QPI pattern should appear in the unoccupied high-energy part if the fractionalization is at work. We propose that integrated-spectroscopy analyses offer a promising way to explore challenging issues of strongly correlated electron systems.

Sakai, Shiro [Sophia University; RIKEN Center for ↗

DOE OSTI2024

Signatures of fractionalization in the optical phonons of the hyperhoneycomb Kitaev magnet 𝛽−Li 2 ⁢IrO 3

Here, in this study, we propose that the signatures of spin fractionalization in quantum magnets can be identified through a detailed analysis of the temperature dependence of the asymmetric Fano lineshape of optical phonons overlapping with a continuum of spin excitations. We focus on the hyperhoneycomb magnet 𝛽−Li 2 ⁢IrO 3 , a promising candidate for being in proximity to a three-dimensional Kitaev quantum spin liquid. The Raman response in 𝛽−Li 2 ⁢IrO 3 notably displays a distinctive asymmetric Fano lineshape in the 24 meV Raman-active optical phonon. This asymmetry arises from the interaction between the discrete phonon mode and the spin excitation continuum, which could be fractionalized if the material is indeed near a quantum spin-liquid phase. Our theoretical model considers the coupling of this optical phonon to Majorana fermions in the Kitaev model on the hyperhoneycomb lattice. Our findings reveal that the temperature-dependent Fano lineshape is consistent with the fractionalization of spins into Majorana fermions and ℤ ⁢2 fluxes.

Kitaev model↗

DOE OSTI2024

Measurement of the branching fraction of ψ ( 2 S ) → γ π 0

Based on ( 2712.4 ± 14.1 ) × 10 6 ψ ( 2 S ) events, 7.9 fb − 1 ψ ( 3773 ) data, and 0.8 fb − 1 off-resonance data samples collected with the BESIII detector, we measure the branching fraction of ψ ( 2 S ) → γ π 0 and e + e − → γ π 0 form factor at momentum transfers Q 2 ∼ 13 GeV 2 . The e + e − → γ π 0 cross section is fitted with considering the interference between the ψ ( 2 S ) and continuum amplitudes and two solutions are found, B = 3.74 × 10 − 7 with ϕ = 3.93 rad and B = 7.87 × 10 − 7 with ϕ = 2.08 rad . Here, B is the branching fraction of ψ ( 2 S ) → γ π 0 and ϕ is the relative phase angle between the ψ ( 2 S ) and continuum amplitudes. Due to insufficient off-resonance data, the branching fraction B ( ψ ( 2 S ) → γ π 0 ) is determined to be in the range [ 2.7 , 9.7 ] × 10 − 7 within 1 standard deviation of the contour region. Published by the American Physical Society 2024

Astronomy & Astrophysics↗

DOE OSTI2024

Anomalous Hall Crystals in Rhombohedral Multilayer Graphene. I. Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field

Recent experiments on rhombohedral pentalayer graphene with a substrate-induced moiré potential have identified both Chern insulators and fractional quantum Hall states at zero magnetic field. Surprisingly, these states are observed in strong displacement fields where the effects of the moiré lattice are weak, and seem to be readily accessed without fine-tuning. To address these experimental puzzles, we study a model of interacting electrons in this geometry. Within self-consistent Hartree-Fock (SCHF) calculations, we find an isolated Chern band with small bandwidth and good quantum geometry. Exact diagonalization and density-matrix renormalization group calculations both confirm the band hosts fractional quantum Hall states without a magnetic field. Remarkably, the Chern band is stable at a wide range of angles, at four through six rhombohedral layers, at varying rhombohedral hopping parameters, and—most strikingly—survives in SCHF calculations when the moiré potential vanishes. In this limit, the state spontaneously breaks time-reversal and translation symmetry simultaneously, giving a topological crystalline state that we term the “anomalous Hall crystal.” We argue this is a general mechanism to create stable Chern bands in rhombohedral multilayer graphene, opening the door to studying the interplay between electronic topology, fractionalization, and spontaneous translation symmetry breaking.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Virtual element approximations of the time-fractional nonlinear convection-diffusion equation on polygonal meshes

We extend the Virtual Element Method to a two-dimensional unsteady nonlinear convection-diffusion equation characterized by a fractional-order derivative with respect to the time variable. Our methodology is based on three fundamental technical components: a fractional version of the Grunwald-Letnikov approximation, discrete maximal regularity, and the regularity theory associated with non-linearity. We prove the method's well-posedness, i.e., the approximate solution's existence and uniqueness to the time-fractional convection-diffusion equation with a Lipschitz nonlinear source term. The fully discrete scheme inherently maintains stability and consistency by leveraging the discrete maximal regularity and the energy projection operator. The convergence in the L 2 -norm and H 1 -norm to various mesh configurations is validated by numerical results, underlining the practical effectiveness of the proposed method.

97 MATHEMATICS AND COMPUTING↗