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At least 73 records · Page 4

Effects of 9.5 years warming on SOC concentration and composition in bulk soil and density fractions

Original data of whole-soil warming experiment after 9.5 years at Blodgett Forest Research Station. The Blodgett Forest is a mixed coniferous temperate forest with Mediterranean climate. The annual air temperature is 12.5℃ and the annual precipitation is 1774 mm yr-1- The soil is mesic ultic Alfisol of granitic origin, equivalent to Dystric Cambisol according to The World Reference Base for Soil Resources (WRB) system. The soil is warmed down to 1 m at + 4℃ by vertically installed heating cables. At the time of soil sampling on 1 May 2023, the whole-soil warming experiment had been running for approximately 9.5 years, from January 2014 to May 2023. The dataset includes: - Bulk_EA: C, N content, δ13C, and CN ratio of bulk soil; - Density_fractionation: organic carbon concentration, δ13C, and C/N ratio of free light fraction (fLF), occluded ligh fraction (oLF), and heavy fraction (HF); - PCA_DRIFT_AUC: original data of area under the curve (AUC) values of eight carbon bond types integrated on diffuse reflectance infrared fourier transform spectroscopy for each soil sample and soil fraction, which are consequently used for principal component analysis (PCA); - DRIFTS_stability_index: the calculation of aliphatic C–H (3000–2800 cm-1) to aromatic C=C (1670–1600 cm-1) ratios for each bulk soil sample and soil fraction. All data are provided in CSV format and can be viewed using Microsoft Excel.

Climate change↗

Techno-Economic Case Study: Low-Temperature Conversion Performance Based on Isolated Anatomical Fractions of Corn Stover

This report summarizes analysis conducted to support a case study under the Feedstock-Conversion Interface Consortium (FCIC) focused on techno-economic analysis (TEA) modeling to quantify the yield and cost ramifications for processing isolated anatomical fractions of corn stover through a low-temperature conversion (biochemical pathway) biorefinery. It is hypothesized that different individual anatomical fractions of corn stover vary in composition and recalcitrance, such that processing each fraction on its own e.g. through dedicated campaigns may enable economic benefits relative to processing the whole stover material. To investigate this concept, we worked with FCIC researchers to obtain data on compositional analysis, as well as processing conditions and yields, for conversion of whole corn stover plus three individual anatomical fractions (cobs, husks, and stalks) across key steps of the biorefinery conversion process within FCIC research scope, namely pretreatment and enzymatic hydrolysis. After running the data through the TEA models, fractionated cobs and husks achieved higher fuel yields and lower minimum fuel selling prices than whole corn stover, but stalks fared worse than whole stover on both metrics. The most direct takeaway from this assessment is that a biorefinery would stand to benefit economically from maximizing the use of cob and husk fractions while avoiding or minimizing the use of stalks, though recognizing practical constraints with this approach in maintaining an equivalent processing capacity (fixed at 2,000 dry metric tonne per day in all cases).

09 BIOMASS FUELS↗

Potassium isotopic fractionation in a humid and an arid soil–plant system in Hawai‘i

Plants play a critical role in the cycling of potassium (K) and the fractionation of its isotopes. However, little is known about K stable isotopic compositions in natural soil–plant systems and possible fractionation during intra-plant transport and root-soil uptake of K. Herein this study focuses on K isotopic fractionation within a humid and an arid soil–plant system sampled on the windward and leeward sides of Kohala Mountain, Hawai‘i. We determined the K isotopic compositions of < 2-mm bulk soil, soil saturation extraction, and selected plant tissues by multi-collector inductively coupled plasma mass spectrometry and X-ray absorption spectroscopy. We studied soils and individual tissue samples such as roots, stems, barks, shoots (a sum of stems and fresh leaves), leaves (fresh and dead), seeds, and flowers of trees and grasses. The results demonstrated that: (i) tissue δ 41 K values ranged from –1.06 ± 0.06 to 1.15 ± 0.09‰; (ii) within the same plant, stems (barks), dead leaves, and reproductive tissues (flowers and seeds) were isotopically lighter compared to fresh leaves, and to a lesser extent, roots; (iii) δ 41 K values of the humid soil (-0.54 ± 0.07 to –0.49 ± 0.06‰) were lower than those of the arid soil (-0.24 ± 0.07 to –0.14 ± 0.06‰); and (iv) soil bioavailable pool δ 41 K (saturation extracts) ranged from –0.63 ± 0.08 to 0.34 ± 0.08‰ and 0.48 ± 0.08 to 0.54 ± 0.10‰ in the humid and arid soils, respectively. From synchrotron-based analysis of K atoms, we identified two major K-bearing phases co-existing as ionic K + and K-pectate association of different fractions. Based on K isotopic and synchrotron data, we conclude that two dominant processes are responsible for plant-mediated K isotopic fractionation, including (1) K redistribution during intra-plant circulation and (2) uptake at the root-soil interface. For intra-plant circulation of K, there is a high affinity of isotopically lighter K to organic complexes as K-pectate, and K-pectate is particularly enriched in roots and fresh leaves. For K uptake at root-soil interface, isotopically lighter K is preferentially taken by roots from soil bioavailable pools following a low-affinity (passive) transport path. Soil K budget in two sites reflects strong source mixing effects with limited plant imprints. This work provides exploratory data on the biogeochemical fractionation of K isotopes in the soil–plant system.

54 ENVIRONMENTAL SCIENCES↗

Upconversion of non-recycled MSW paper fractions into biochar via slow pyrolysis and life cycle analysis: Pathways to net negative GHG emission

This study presents an integrated and sustainable approach to valorizing non-recycled municipal solid waste (MSW), a heterogeneous and underutilized waste stream destined for landfilling, by converting it into valuable biochar resources. Specifically, we investigated the upcycling of nonrecycled paper waste based on compositional analysis into four major fractions: high cellulose, high lignin, high contamination, and high ash content papers. These fractions were then homogenized and subjected to slow pyrolysis. The high cellulose fraction (36.1 %) was the most abundant, and contained 66.7 % cellulose, while the high lignin fraction showed the highest lignin (12.1 %) and carbon content (44 %), resulting in highest energy value of 17.4 MJ kg −1 . Biochar yields ranged from 25.6 % to 35.6 %, with the high ash fraction producing the highest yield and alkalinity (pH ≈ 11.2) due to its higher mineral content. Elemental analysis revealed enhanced carbon content up to 76.9 % and reduced oxygen and hydrogen, confirming effective carbonization. The high lignin-derived biochar showed the highest aromatic carbon content (82.8 %) and greater structural stability, while contaminated and ash-rich fractions exhibited dense, low-porosity surfaces due to the presence of contaminants and minerals. Spectroscopic analysis revealed degradation of carbohydrates, disappearance of cellulose peaks and formation of aromatic and mineral derived phases. The scaled life cycle process yielded a global warming potential (GWP) of 119.3 kg CO 2 -eq per ton of dry paper waste, offset by soil carbon sequestration of − 556.41 kg CO 2 -eq, resulting in a net impact of − 427.36 kg CO 2 -eq. This represents a net carbon removal exceeding by ~186 % the emissions associated with landfilling paper waste with electricity generation.

09 BIOMASS FUELS↗

Radially resolved active charge exchange measurements of the hydrogenic isotope fraction on DIII-D

Radially resolved hydrogenic isotope fraction measurement capabilities have been developed for DIII-D using the main-ion charge exchange recombination (MICER) spectroscopy system in preparation for mixed hydrogen and deuterium experiments. Constraints on the hydrogenic ion temperatures and velocities based on measurements of the impurity ion properties are required to accurately fit the spectrum. Corrections for cross sectional distortions, spatial smearing due to the halo, and a neoclassical offset between the impurity and hydrogenic toroidal rotation are applied to the constraints prior to fitting the MICER spectrum. Extensive atomic physics calculations have been performed using the FIDASIM code, which has recently been improved to allow simulations using mixtures of hydrogenic species. Overall, these results demonstrate that for the same plasma parameters, the Dα emission is 20%–30% brighter than Hα due to differences in rate coefficients associated with the different ion thermal velocities for the same temperature and therefore must be taken into consideration when calculating absolute densities. However, despite these differences, the absolute error when estimating the hydrogen isotope fraction [n H /(n H + n D )] by using the Hα radiance fraction [L Hα /(L Hα + L Dα )] is typically less than 5% due to the way the fraction is formed, making the radiance fraction a reasonably accurate estimate of the isotope fraction for most cases.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Correlation between the relative blob fraction and plasma parameters in NSTX

Here, we present a simple analysis of the fraction of blobs observed in the scrape-off layer of NSTX and calculates the correlation between this blob fraction and various plasma parameters. The measurements were made using the gas puff imaging (GPI) diagnostic on a database of 103 shots from 2010 with neutral beam power P NBI = 0–6 MW. The blob fraction ranged from f b = 0.1% to 4.8%, where f b is defined as the fraction of time the GPI signal was larger than three times its average value within 0–7.5 cm outside the separatrix. The blob fraction generally decreased with increasing neutral beam injection power and was lower on average in H-mode plasmas than Ohmic and L-mode plasmas. The blob fraction had its highest correlation with the measured poloidal turbulence velocity and its radial gradient just inside the separatrix. This is in part consistent with a model in which the blob generation rate increases with the poloidal velocity shear.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A fractional calculus framework for open quantum dynamics: From Liouville to Lindblad to memory kernels

Open quantum systems exhibit dynamics ranging from unitary evolution to irreversible dissipation. While the Gorini–Kossakowski–Sudarshan–Lindblad equation uniquely characterizes Markovian completely positive and trace-preserving (CPTP) evolution, many physical platforms display non-Markovian features such as algebraic relaxation and coherence backflow. Fractional calculus provides a natural way to model such long-memory behavior through power-law temporal kernels introduced by fractional time derivatives. Here, we develop a unified framework that embeds fractional master equations within the broader hierarchy of open-system formalisms. The fractional equation forms a structured subclass of memory-kernel models, reduces to the Lindblad form at unit order, and, through Bochner–Phillips subordination, admits a CPTP representation as an average over Lindblad semigroups. Its resolvent structure further connects fractional dynamics to established non-Markovian approaches, including Nakajima–Zwanzig kernels and hierarchical equations of motion, providing a compact surrogate for long-memory effects. This formulation positions fractional calculus as a rigorous and practical language for modeling non-Markovian quantum dynamics in chemical physics and physical chemistry, providing a CPTP-preserving, computationally efficient surrogate for structured condensed-phase environments where long-time memory and dissipation play a central role.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Mass dependence of halo baryon fractions from the kinetic Sunyaev–Zeldovich effect

ABSTRACT We detect the kinetic Sunyaev–Zeldovich imprint of peculiar motions of galaxy groups and clusters, using the photometric Dark Energy Spectroscopic Instrument Legacy Surveys together with cosmic microwave background (CMB) maps from the Atacama Cosmology Telescope (ACT). We develop a comprehensive forward model based on the AbacusSummit cosmological simulations: Mock galaxy group catalogues and synthetic kinetic Sunyaev–Zeldovich (kSZ) maps are generated, together with a reconstructed peculiar velocity field that allows for photo-z errors, redshift-space distortions, and survey masks. We investigate possible contamination from the cosmic infrared background (CIB), finding that CIB effects are subdominant to the kSZ signal in the relevant ACT frequency channel. We then predict the kSZ signal expected when stacking CMB temperature maps around groups, taking account of their estimated radial velocities. Comparing the model with observations, we are able to constrain the total baryon fraction within haloes, as well as their internal gas profiles. We find evidence for mass dependence of the halo baryon fraction within the virial radius. The gas fraction in massive groups is consistent with the universal baryon fraction, but low-mass groups ($10^{12.5} \lesssim M\, /\, h^{-1}\, \mathrm{M}_\odot \lesssim 10^{14}$) are depleted to $0.38 \pm 0.11$ times the universal baryon fraction. We find this low virial baryon fraction to be consistent with an extended gas profile, for which the total baryon content reaches the universal value well beyond the virial radius. This conclusion is consistent with previous analyses using X-ray, kSZ, and weak lensing, and plausibly reflects energetic feedback processes from the galaxies in these haloes.

Roper, Finn A [Institute for Astronomy, University↗

Measurement of 𝐵 meson production fraction ratios in proton-proton collisions at √𝑠 = 13 TeV using open-charm and charmonium decays

Production fraction ratios of 𝐵 + , 𝐵 0 , and 𝐵$^{0}_{𝑠}$ mesons are measured in proton-proton collisions at √𝑠 = 13 TeV using a special dataset recorded in 2018 with high-rate triggers designed to collect an unbiased sample of 1⁢010 𝑏 hadrons with the CMS experiment at the LHC. These data allow the study of the open-charm decays of 𝐵 mesons (𝐵 (𝑠) → 𝜋⁢𝐷 (𝑠) ) where the 𝐷 meson decays into fully hadronic final states. By utilizing known branching fractions and precise theoretical calculations, production fraction ratios as functions of 𝐵 meson transverse momentum (𝑝 T ) and rapidity (𝑦) are measured using open-charm decays in the kinematic range of 8 < 𝑝 T < 60 GeV and |𝑦| <2.25. In addition, the same dataset is used to measure the relative production fraction ratios with the charmonium decay channels [𝐵 (𝑠) →𝑋⁢𝐽/𝜓 with 𝑋 indicating a 𝐾 + , 𝐾*(892) 0 , or 𝜙⁡(1020) meson] where the 𝐽/𝜓 meson decays into a pair of muons. The open-charm results are used to normalize the relative production fraction ratios obtained from the charmonium samples. Measurements of the ratios of branching fractions of 𝐵 meson decays to charmonium and open-charm final states are also reported, which will improve the world-average values of these ratios. Finally, we test isospin invariance in 𝐵 meson production in proton-proton collisions and observe that it holds within the experimental precision.

Bottom mesons↗

Timescales of mafic magmatic fractionation documented by paleosecular variation in basaltic drill core, Snake River Plain volcanic province, Idaho, USA

Abstract The timescales over which fractional crystallization and recharge work in mafic volcano-plutonic provinces is subject to great uncertainty. Currently modeled processes are subject to the scale of measurement: monogenetic basaltic fields accumulate over hundreds of thousands of years, consistent with U-Th-Ra isotopic variations that imply 50% crystallization of basic magmas on timescales of 100,000 years or more, whereas crystal diffusion modeling implies phenocryst residence times of ~1–1000 years. Monogenetic basalts of the Snake River Plain in southern Idaho, USA, are up to 2 km thick and postdate passage over the Yellowstone–Snake River Plain hotspot. Detailed lithologic and geophysical logging of core from deep drill holes, along with chemical stratigraphy and high-resolution paleomagnetic inclination measurements, document individual eruptive units, compound lava flows, and basaltic flow groups that accumulated over 1–6 m.y. Hiatuses are commonly marked by loess or fluvial interbeds that vary from ~0.1 m thick to 20 m thick. Radiometric (40Ar-39Ar, detrital zircon U-Pb) and paleomagnetic timescale ages show that the deepest hole (Kimama drill hole, 1912 m total depth) accumulated over ~6 m.y. Cycles of fractional crystallization and recharge are recognized in the chemical stratigraphy as up-section shifts in major and trace elements; these fractionation cycles commonly represent 40%–50% fractionation. Individual fractionation cycles may comprise 20–40 eruptive units (8–17 lava flows) with little to no change in paleomagnetic inclination (0°–1°), whereas adjacent cycles may differ by several degrees from one another or reflect changes in polarity. Rates of paleosecular variation in Holocene lavas and sediments dated using 14C document significant shifts in magnetic inclination over short timescales, ranging from ~0.05° to 2°/decade, with an average of ~0.5°/decade and a minimum rate of 0.05°/decade. This implies that fractionation cycles with ≤1° variation in magnetic inclination formed on timescales of a few decades up to a few centuries (20–200 years). Thus, the lavas collectively represent only a few thousand years of eruptive activity, with major flow groups separated in time by tens to hundreds of thousands of years. We suggest that the rates defined by paleosecular variation capture the timescales of magmatic chamber evolution (fractionation/recharge) in the seismically imaged mid-crustal sill complex; in contrast, we suggest that crystal diffusion modeling captures the residence times in shallow subvolcanic magmatic chambers that underlie individual monogenetic volcanoes.

Geology↗

Fractional Quantum Anomalous Hall Effect

The realization of the fractional quantum anomalous Hall effect (FQAHE) in a zero-field fractional Chern insulator is a new advancement in condensed matter physics, resulting from the interplay among strong correlations, topology, and spontaneous time-reversal symmetry breaking in lattice systems. In this review, we highlight the experimental and theoretical progress toward achieving FQAHE in two material platforms: twisted bilayer MoTe 2 and rhombohedral-stacked multilayer graphene. These systems host narrow topological bands with nontrivial Chern numbers, enabling interaction-driven fractionalized states analogous to the fractional quantum Hall effect, but without external magnetic fields. We discuss how spontaneous ferromagnetism, moiré lattice reconstruction, and band topological effects underpin the emergence of FQAHE in twisted MoTe 2 . We describe experimental discoveries of zero-field fractional Chern insulators in both transport and optical experiments, as well as signatures of composite Fermi liquids and higher-energy Chern band, which may shed light on engineering nonabelian states. In rhombohedral graphene/hexagonal boron nitride moiré superlattices, we review the recent observations of fractionally quantized Hall resistance, connections between FQAHE and extended quantum anomalous Hall phases, and the coexistence of superconductivity and FQAHE. Furthermore, these discoveries not only deepen our understanding of strongly correlated topological matter but also open new frontiers for exploring nonabelian anyons, fault-tolerant quantum computation, and topological opto-spintronics free of magnetic fields.

bilayer↗

The extended auxiliary equation mapping method to determine novel exact solitary wave solutions of the nonlinear fractional PDEs

Abstract In this paper, some new nonlinear fractional partial differential equations (PDEs) have been considered.Three models are including the space-time fractional-order Boussinesq equation, space-time (2 + 1)-dimensional breaking soliton equations, and space-time fractional-order SRLW equation describe the behavior of these equations in the diverse applications. Meanwhile, the fractional derivatives in the sense of β -derivative are defined. Some fractional PDEs will convert to the considered ordinary differential equations by the help of transformation of β -derivative. These equations are analyzed utilizing an integration scheme, namely, the extended auxiliary equation mapping method. The different kinds of traveling wave solutions, solitary, topological, dark soliton, periodic, kink, and rational, fall out as a by-product of this scheme. Finally, the existence of the solutions for the constraint conditions is also shown. The outcome indicates that some fractional PDEs are used as a growing finding in the engineering sciences, mathematical physics, and so forth.

Engineering↗

Physico-chemical properties of lignin fractions from acid pretreated corn stover and their effects on enzymatic hydrolysis of microcrystalline cellulose

Lignin has been shown to be a recalcitrance factor in many biomass conversion studies. To better understand the effects of lignin on cellulose conversion, different lignin fractions were extracted from the same dilute acid pretreated corn stover by three sequential isolation methods, namely ethanol extraction, dioxane extraction, and enzyme purification. The physicochemical properties of each lignin fraction including molecular weight distribution, surface area, surface charge, and other structural features varied, depending on the isolation methods. All three lignin fractions had negative surface charges, and ethanol-extracted lignin carried the highest surface charges, followed by dioxane-extracted lignin and cellulase-purified residual lignin. These physicochemical properties of lignin fractions also resulted in different extent of inhibitory effects on enzymatic hydrolysis of microcrystalline cellulose (MCC). Dioxane-extracted lignin exhibited the highest inhibitory effect on glucose release from MCC, followed by the cellulase-purified residual lignin fraction and ethanol-extracted lignin. Furthermore, lignin fractions with higher contents of syringyl (S) substructure and β-O-4 aryl ether interunit linkages showed a stronger negative effect on cellulase hydrolysis of MCC.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Theoretical Analysis of Fractional Viscoelastic Flow in Circular Pipes: General Solutions

Fractional calculus is a relatively old yet emerging field of mathematics with the widest range of engineering and biomedical applications. Despite being an incredibly powerful tool, it, however, requires promotion in the engineering community. Rheology is undoubtedly one of the fields where fractional calculus has become an integral part of cutting-edge research. There exists extensive literature on the theoretical, experimental, and numerical treatment of various fractional viscoelastic flows in constraint geometries. However, the general theoretical approach that unites several most commonly used models is missing. Here we present exact analytical solutions for fractional viscoelastic flow in a circular pipe. We find velocity profiles and shear stresses for fractional Maxwell, Kelvin–Voigt, Zener, Poynting–Thomson, and Burgers models. The dynamics of these quantities are studied with respect to normalized pipe radius, fractional orders, and elastic moduli ratio. Three different types of behavior are identified: monotonic increase, resonant, and aperiodic oscillations. The models developed are applicable in the widest material range and allow for the alteration of the balance between viscous and elastic properties of the materials.

Gritsenko, Dmitry (ORCID:0000000248181512)↗

Techno-Economic Case Study: Low-Temperature Conversion Performance Based on Isolated Anatomical Fractions of Corn Stover

This report summarizes analysis conducted to support a case study under the Feedstock Conversion Interface Consortium (FCIC) focused on techno-economic analysis (TEA) modeling to quantify the process yield and resulting process cost impacts for processing isolated anatomical fractions of corn stover through a low-temperature conversion (biochemical) pathway. It is hypothesized that different individual anatomical fractions of corn stover vary in both composition and recalcitrance, giving biorefineries options in whether and how to deal with fractionated or whole biomass feedstock. By quantifying the techno-economic impacts of this variability, we provide actionable information for end users to understand tradeoffs in conversion system yields and economics in considering feedstock processing decisions at the biorefinery gate. For this study, we worked with FCIC researchers to obtain data on the compositional analysis and conversion performance of whole corn stover alongside three individual anatomical fractions (cobs, husks, and stalks) across key steps of the biorefinery conversion process within FCIC’s research scope—pretreatment and enzymatic hydrolysis. This TEA screening assessment highlighted biorefinery economic trade-offs observed through this approach. Namely, relative to processing whole stover biomass, two of the three anatomical fractions for which composition/conversion data were available (cobs and husks) demonstrated the ability to achieve higher fuel yields and lower minimum fuel selling prices (MFSPs), while the third fraction (stalks) led to the opposite result, as a composite reflection of compositional differences and process convertibility.

cost impacts↗

A fractional model for anomalous diffusion with increased variability: Analysis, algorithms and applications to interface problems

Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. Here, we introduce a new fractional operator characterized by a doubly-variable fractional order and possibly truncated interactions. Under certain conditions on the model parameters and on the regularity of the fractional order we show that the corresponding Poisson problem is well-posed. Additionally, we introduce a finite element discretization and describe an efficient implementation of the finite-element matrix assembly in the case of piecewise constant fractional order. Through several numerical tests, we illustrate the improved descriptive power of this new operator across media interfaces. Furthermore, we present one-dimensional and two-dimensional h-convergence results that show that the variable-order model has the same convergence behavior as the constant-order model.

97 MATHEMATICS AND COMPUTING↗

Normal Tissue Response of Combined Temporal and Spatial Fractionation in Proton Minibeam Radiation Therapy

Proton minibeam radiation therapy, a spatial fractionation concept, widens the therapeutic window. By reducing normal tissue toxicities, it allows a temporally fractionated regime with high daily doses. However, an array shift between daily fractions can affect the tissue-sparing effect by decreasing the total peak-to-valley dose ratio. Therefore, combining temporal fractions with spatial fractionation raises questions about the impact of daily applied dose modulations, reirradiation accuracies, and total dose modulations.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Rheological effects of moisture content on the anatomical fractions of loblolly pine (Pinus taeda)

Here, this study focused on assessing the influence of moisture content on the rheological properties of different anatomical fractions of pine residue using the FT4 powder rheometer. Moisture content exhibited some influence on the 2 mm bark and needle fractions, increasing their cohesion, angle of internal friction, unconfined yield strength, and major principal stress. Stem and whole, on the other hand, presented minimal changes upon moisture introduction. All 4 mm fractions did not show many changes in their rheological properties with moisture introduction, which can be due to less particle-particle interactions and consequently reducing any liquid bridging the particles might undergo; however, they were shown to have a more unpredictable behavior compared to the 2 mm analogues (i.e., higher standard deviation) which can be due to a higher degree of particle-interlocking. Out of the three fractions, needle presented the poorest rheological properties for flowability in addition to being susceptible by moisture, unlike other fractions.

36 MATERIALS SCIENCE↗