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At least 145 records · Page 8

Charged skyrmions and topological origin of superconductivity in magic-angle graphene

Topological solitons, a class of stable nonlinear excitations, appear in diverse domains as in the Skyrme model of nuclear forces. Here, we argue that similar excitations play an important role in a remarkable material obtained on stacking and twisting two sheets of graphene. Close to a magic twist angle, insulating behavior is observed, which gives way to superconductivity on doping. Here, we propose a unifying description of both observations. A symmetry breaking condensate leads to the ordered insulator, while topological solitons in the condensate—skyrmions—are shown to be charge 2 e bosons. Condensation of skyrmions leads to a superconductor, whose physical properties we calculate. More generally, we show how topological textures can mitigate Coulomb repulsion and provide a previously unexplored route to superconductivity. Our mechanism not only clarifies why several other moiré materials do not show superconductivity but also points to unexplored platforms where robust superconductivity is anticipated.

36 MATERIALS SCIENCE↗

Cherenkov-type three-dimensional breakdown behavior of the Bloch-point domain wall motion in the cylindrical nanowire

A three-dimensional breakdown behavior of the magnetic Bloch-point domain wall (BP-DW) propagation was investigated in a ferromagnetic nanowire with the variation of the external magnetic field by means of micromagnetic simulation. As magnetic field strength increases up to a threshold value, the BP-DW velocity approaches a critical phase velocity of the spontaneously emitting spin wave (SW), where a Cherenkov-type DW breakdown phenomenon is observed originating from an interaction between the spontaneously emitting SW and the BP-DW. It is found that the velocity of the BP-DW approaches a maximum value (~2000 m/s) due to the intrinsic reversal time of a BP spin texture. This suggests that although cylindrical ferromagnetic nanowires might be free from the two-dimensional Walker breakdown phenomenon, there exists a Cherenkov-type three-dimensional breakdown behavior.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Machine learning force field model for kinetic Monte Carlo simulations of itinerant Ising magnets

Here, we present a scalable machine learning (ML) framework for large-scale kinetic Monte Carlo (kMC) simulations of itinerant electron Ising systems. As the effective interactions between Ising spins in such itinerant magnets are mediated by conducting electrons, the calculation of energy change due to a local spin update requires solving an electronic structure problem. Such repeated electronic structure calculations could be overwhelmingly prohibitive for large systems. Assuming the locality principle, a convolutional neural network (CNN) model is developed to directly predict the effective local field and the corresponding energy change associated with a given spin update based on Ising configuration in a finite neighborhood. As the kernel size of the CNN is fixed at a constant, the model can be directly scalable to kMC simulations of large lattices. Our approach is reminiscent of the ML force field models widely used in first-principles molecular dynamics simulations. Applying our ML framework to a square-lattice double-exchange Ising model, we uncover unusual coarsening of ferromagnetic domains at low temperatures. Our work highlights the potential of ML methods for large-scale modeling of similar itinerant systems with discrete dynamical variables.

machine learning↗

Identifying insects, clouds, and precipitation using vertically pointing polarimetric radar Doppler velocity spectra

Abstract. This study presents a method to identify and distinguish insects, clouds, and precipitation in 35 GHz (Ka-band) vertically pointing polarimetric radar Doppler velocity power spectra and then produce masks indicating the occurrence of hydrometeors (i.e., clouds or precipitation) and insects at each range gate. The polarimetric radar used in this study transmits a linear polarized wave and receives signals in collinear (CoPol) and cross-linear (XPol) polarized channels. The measured CoPol and XPol Doppler velocity spectra are used to calculate linear depolarization ratio (LDR) spectra. The insect–hydrometeor discrimination method uses CoPol and XPol spectral information in two separate algorithms with their spectral results merged and then filtered into single value products at each range gate. The first algorithm discriminates between insects and clouds in the CoPol Doppler velocity power spectra based on the spectra texture, or spectra roughness, which varies due to the scattering characteristics of insects vs. cloud particles. The second algorithm distinguishes insects from raindrops and ice particles by exploiting the larger Doppler velocity spectra LDR produced by asymmetric insects. Since XPol power return is always less than CoPol power return for the same target (i.e., insect or hydrometeor), fewer insects and hydrometeors are detected in the LDR algorithm than the CoPol algorithm, which drives the need for a CoPol based algorithm. After performing both CoPol and LDR detection algorithms, regions of insect and hydrometeor scattering from both algorithms are combined in the Doppler velocity spectra domain and then filtered to produce a binary hydrometeor mask indicating the occurrence of cloud, raindrops, or ice particles at each range gate. Forty-seven summertime days were processed with the insect–hydrometeor discrimination method using US Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) program Ka-band zenith pointing radar observations in northern Oklahoma, USA. For these 47 d, over 70 % of the hydrometeor mask column bottoms were within ±100 m of simultaneous ceilometer cloud base heights. All datasets and images are available to the public on the DOE ARM repository.

54 ENVIRONMENTAL SCIENCES↗

Electron‐Assisted Generation and Straight Movement of Skyrmion Bubble in Kagome TbMn 6 Sn 6

Abstract Topological magnetic textures are promising candidates as binary data units for the next‐generation memory device. The precise generation and convenient control of nontrivial spin topology at zero field near room temperature endows the critical advantages in skyrmionic devices but is not simultaneously integrated into one material. Here, in the Kagome plane of quantum TbMn 6 Sn 6 , the expedient generation of the skyrmion bubbles in versatile forms of lattice, chain, and isolated one by converging the electron beam, where the electron intensity gradient contributes to the dynamic generation from local anisotropy variation near spin reorientation transition (SRT) is reported. Encouragingly, by utilizing the dynamic shift of the SRT domain interface, the straight movement is actualized with the skyrmion bubble slave to the SRT domain interface forming an elastic composite object, avoiding the usual deflection from the skyrmion Hall effect. The critical contribution of the SRT domain interface via conveniently electron‐assisted heating is further theoretically validated in micromagnetic simulation, highlighting the compatible application possibility in advanced devices.

Li, Zhuolin↗

Spin orbit torque in ferromagnet/topological-quantum-material heterostructures

The main objective of this proposal was to investigate the spin-orbital driven phenomena in topological insulator (TI)/ferromagnet (FM) or transition metal (TM) heterostructures. In particularly, we tried to utilize the spin-momentum locking properties on the surface of TIs to achieve ideal spin-orbit torques (SOTs). In practice, we found that the surface properties have been greatly modified, resulting in much more complicated magneto-transport behaviors than what is expected in SOT-driven magnetotransport. Through systematic and extended investigations, we start to unravel that the nonlinear magnetotransport properties, which was, in the past, mainly attributed to SOT-driven phenomena, can be used to infer the modification of the electronic band structures of TIs and spin textures in FMs which are closely related with charge-spin interconversion phenomena. Regarding the band structures In TIs, we find under electrostatic perturbations imposed by deposition of nonmagnetic TMs, the quantum well states formed on the surface of TIs develop substantial Rashba spin-splitting, which is detected as a bilinear magnetoresistance (BMR). Under magnetic perturbations, the nonlinear planar Hall effect (NPHE) in the topological surface states is greatly enhanced, possibly reflecting the modified surface band structure due to time-reversal symmetry breaking. In a double HM/FM heterostructure where the magnetic anisotropy can be robustly tuned, we observed second-harmonic Hall voltage responses corresponding to domain wall structures with fixed chirality, stabilized by interfacial Dzyaloshinskii–Moriya interaction (DMI). In addition, in the linear transport regime, we utilized inverse-SHE-induced anomalous Hall effect in Pt to probe the exchange bias on the surface of a doped magnetic insulator Tm 3 Fe 5 O 12 .

36 MATERIALS SCIENCE↗

Machine learning-based multidomain processing for texture-based image segmentation and analysis

Atomic and molecular resolved atomic force microscopy (AFM) images offer unique insights into materials' properties such as local ordering, molecular orientation, and topological defects, which can be used to pinpoint physical and chemical interactions occurring at the surface. Utilizing machine learning for extracting underlying physical parameters increases the throughput of AFM data processing and eliminates inconsistencies intrinsic to manual image analysis, thus enabling the creation of reliable frameworks for qualitative and quantitative evaluation of experimental data. Here, we present a robust and scalable approach to the segmentation of AFM images based on flexible pre-selected classification criteria. The usage of supervised learning and feature extraction allows us to retain the consideration of specific problem-dependent features (such as types of periodical structures observed in the images and the associated numerical parameters: spacing, orientation, etc.). We highlight the applicability of this approach for the segmentation of molecular resolved AFM images based on the crystal orientation of the observed domains, automated selection of boundaries, and collection of relevant statistics. Finally, we outline a general strategy for machine learning-enabled analysis of nanoscale systems exhibiting periodic order that could be applied to any analytical imaging technique

36 MATERIALS SCIENCE↗

Nanoscale strain wave generation by a piezoelectric grating from polar vortices

Nanostructures formed by spontaneously broken symmetry have provided new ways to manipulate quantum states. Specifically, topological structures with periodic spatial ordering, such as polar vortices and skyrmions, can be ideal hosts for creating engineered responses in both spatial and frequency domains. So far, however, only a few examples of such hierarchical engineering have been reported in the literature. Here we demonstrate that the spatially modulated piezoelectric response of a polar vortex structure can create strain waves with a characteristic nanoscale wavefront. Using time-resolved pump–probe resonant X-ray scattering and diffraction measurements, coupled with dynamical phase-field simulations, we show that the piezoelectric modulation of the spontaneously formed polar vortex crystal functions as an acoustic diffraction grating. This system converts incoming laterally uniform strain waves into outgoing waves with a characteristic sub-terahertz frequency, driven by an intrinsic excitation of the polar vortex crystal. Moreover, our phase-field simulations suggest that the dynamic mechanical displacements exhibiting vortex textures are generated from both space- and time-varying piezoelectric responses. Our findings illustrate a new method for generating nanoscale strain waves with unique spatial textures by tuning the hierarchical order of polar topologies to engineer new collective modes, allowing for a wide range of control through the topological lattice.

ferroelectrics↗

Stabilization of magnetic bubbles in [Ni/Co]n multilayers on an oxygen-reconstructed Nb(110) surface via an ultra-thin Cu interlayer

Magnetic thin films hosting topological spin textures, such as magnetic skyrmions, hold high potential for breakthroughs in the field of spintronics, due to good scalability and energy efficiency. Novel computational architectures such as memory-in-logic devices rely on material platforms able to host those topological spin textures. Furthermore, recently proposed designs of novel quantum information technologies are based on heterostructures where topological spin textures are in direct proximity to a superconducting layer. Here, we demonstrate the stabilization of out-of-plane magnetic bubbles in highly ordered [Ni/Co]n multilayers on a Nb(110) single crystal. This is achieved without the need for the removal of the well-known Nb(110)-oxide surface reconstruction, due to the introduction of an ultra-thin Cu interlayer in between the Nb substrate and the magnetic multilayer. The Cu interlayer generates a well-ordered hexagonal surface, which is key for the epitaxial growth of the [Ni/Co]n multilayers hosting the desired out-of-plane anisotropy. The magnetic ground state of the prepared material stacks is directly imaged via spin-polarized low-energy electron microscopy, revealing the presence of magnetic bubble domains with lateral sizes as small as 450 nm.

Dibajeh, Ahmad↗

Criticality and Magnetic Phases of Ising Shastry–Sutherland Candidate Holmium Tetraboride

Frustrated magnetic systems arising in geometrically constrained lattices represent rich platforms for exploring unconventional phases of matter, including fractional magnetization plateaus, incommensurate orders and complex domain dynamics. However, determining the microscopic spin configurations that stabilize such phases is a key challenge, especially when in-plane and out-of-plane spin components coexist and compete. Here, we combine neutron scattering and magnetic susceptibility experiments with simulations to investigate the emergence of field-induced fractional plateaus and the related criticality in a frustrated magnet holmium tetraboride (HoB 4 ) that represents the family of rare earth tetraborides that crystalize in a Shastry–Sutherland lattice in the ab plane. We focus on the interplay between classical and quantum criticality near phase boundaries, as well as the role of material defects in the stabilization of the ordered phases. We find that simulations using classical annealing can explain certain observed features in the experimental Laue diffraction and the origin of multiple magnetization plateaus. Our results show that defects and out-of-plane interactions play an important role and can guide the route towards resolving microscopic spin textures in highly frustrated magnets.

Frustration↗

Prediction of hemiwicking dynamics in micropillar arrays

Dynamic hemiwicking behavior is observable in both nature and a wide range of industrial applications ranging from biomedical devices to thermal management. We present a semi-analytical modeling framework (without empirical fitting coefficients) to predict transient capillary-driven hemiwicking behavior of a liquid through a nano/microstructured surface, specifically a micropillar array. In our model framework, the liquid domain is discretized into micropillar unit cells to enable the time marching of the hemiwicking front. A simplified linear pressure drop is assumed along the hemiwicking length such that the local meniscus curvature, contact angle, and effective liquid height are determined at each time step in our transient model. This semi-analytical model is validated with experimental data from our own experiments and from published literature for different fluids. Our model predicts hemiwicking dynamics with <20% error over a broad range of micropillar geometries with height-to-pitch ratio ranging between ≈0.34 and 6.7 and diameter-to-pitch ratio in the range of ≈0.25–0.7 and without any fitting parameters. For lower diameter-to-pitch ratio data points related to sparse micropillar array arrangements, we suggest modifications to the semi-analytical model. This work sheds light on complex and dynamic solid–liquid–vapor interfacial interactions which could serve as a guide for the design of textured surfaces for wicking enhancement in multi-phase thermal and mass transport technologies and applications.

Mechanics↗

Magnetic Texture in Insulating Single Crystal High Entropy Oxide Spinel Films

Magnetic insulators are important materials for a range of next-generation memory and spintronic applications. Structural constraints in this class of devices generally require a clean heterointerface that allows effective magnetic coupling between the insulating layer and the conducting layer. However, there are relatively few examples of magnetic insulators that can be synthesized with surface qualities that would allow these smooth interfaces and precisely tuned interfacial magnetic exchange coupling, which might be applicable at room temperature. In this work, we demonstrate an example of how the configurational complexity in the magnetic insulator layer can be used to realize these properties. The entropy-assisted synthesis is used to create single-crystal (Mg 0.2 Ni 0.2 Fe 0.2 Co 0.2 Cu 0.2 )Fe 2 O 4 films on substrates spanning a range of strain states. These films show smooth surfaces, high resistivity, and strong magnetic responses at room temperature. Furthermore, local and global magnetic measurements further demonstrate how strain can be used to manipulate the magnetic texture and anisotropy. These findings provide insight into how precise magnetic responses can be designed using compositionally complex materials that may find application in next-generation magnetic devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Calibration, measurement, and characterization of soil moisture dynamics in a central Amazonian tropical forest

Soil moisture plays a key role in hydrological, biogeochemical, and energy budgets of terrestrial ecosystems. Accurate soil moisture measurements in remote ecosystems such as the Amazon are difficult and limited because of logistical constraints. Time domain reflectometry (TDR) sensors are widely used to monitor soil moisture and require calibration to convert the TDR's dielectric permittivity measurement (K a ) to volumetric water content (θ v ). In this study, our objectives were to develop a field-based calibration of TDR sensors in an old-growth upland forest in the central Amazon, to evaluate the performance of the calibration, and then to apply the calibration to determine the dynamics of soil moisture content within a 14.2 -m-deep vertical soil profile. Depth-specific TDR calibration using local soils in a controlled laboratory setting yielded a novel K a –θ v third-degree polynomial calibration. The sensors were later installed to their specific calibration depth in a 14.2-m pit. The widely used K a –θ v relationship (Topp model) underestimated the site-specific θ v by 22–42%, indicating significant error in the model when applied to these well-structured, clay-rich tropical forest soils. The calibrated wet- and dry-season θ v data showed a variety of depth and temporal variations highlighting the importance of soil textural differentiation, root uptake depths, as well as event to seasonal precipitation effects. Data such as these are greatly needed for improving our understanding of ecohydrological processes within tropical forests and for improving models of these systems in the face of changing environmental conditions.

54 ENVIRONMENTAL SCIENCES↗

Topological Defect Mediated Helical Phase Reorientation by Uniaxial Stress

Strain engineering enables precise, energy-efficient control of nanoscale magnetism. However, unlike well-studied strain-dislocation interactions in mechanical deformation, the spatial evolution of strain-induced spin rearrangement remains poorly understood. Using Lorentz transmission electron microscopy, we manipulate and observe helical domain reorientation under quantitatively applied uniaxial tensile stress. Our findings reveal striking similarity to plastic deformation in metals, where the critical stress for propagation vector ( Q ) reorientation depends on its angle with the stress direction. Magnetic defects mediate reorientation via “break-and-reconnect” or “dislocation gliding–annihilation” processes. Simulations confirm that strain-induced anisotropic Dzyaloshinskii-Moriya interaction may play a key role. These insights advance strain-driven magnetism and offer a promising route for energy-efficient magnetic nanophase control in next-generation information technology. Published by the American Physical Society 2025

36 MATERIALS SCIENCE↗

Emergence of a Spin Microemulsion in Spin-Orbit Coupled Bose-Einstein Condensates

We report the first numerical prediction of a “spin microemulsion”—a phase with undulating spin domains resembling classical bicontinuous oil-water-surfactant emulsions—in two-dimensional systems of spinor Bose-Einstein condensates with isotropic Rashba spin-orbit coupling. Using field-theoretic numerical simulations, we investigated the melting of a low-temperature stripe phase with supersolid character and find that the stripes lose their superfluidity at elevated temperature and undergo a Kosterlitz-Thouless-like transition into a spin microemulsion. Momentum distribution calculations highlight a thermally broadened occupation of the Rashba circle of low-energy states with macroscopic and isotropic occupation around the ring. Here, we provide a finite-temperature phase diagram that positions the emulsion as an intermediate, structured isotropic phase with residual quantum character before transitioning at higher temperature into a structureless normal fluid.

Finite temperature field theory↗

Anomalies in the electromagnetic response and peculiarities of the domain structure in the magnetic Weyl semimetal Co 3⁢ Sn 2 ⁢S 2

In this paper, we present a comprehensive study of magnetic properties of Co 3 ⁢Sn 2 ⁢S 2 (CoSnS) crystals using macroscopic characterization and observations of the domain structure (DS) in a wide range of easy- and hard-axis fields (𝐻) and temperatures (𝑇). From macroscopic measurements, we derive temperature dependences of the basic magnetic parameters of the material [saturation magnetization 𝑀 𝑠 ⁡(𝑇), uniaxial anisotropy constant 𝐾⁡(𝑇), and exchange stiffness 𝐴⁡(𝑇)] and, based on them, calculate the thermodynamic magnetization 𝑀⁡(𝐻,𝑇) curves and DS parameters for pinning-free samples. We find important qualitative and quantitative differences between the theory and experiment defined by the efficient pinning of domain walls (DWs) in our samples. It turns out that, already at temperatures close to the ferromagnetic transition 𝑇 𝑐 , the DW dynamics falls into the heavy creep regime, resulting in a strong deferral of the DS adjustment into the equilibrium state. Here, we suggest that specific magnetic defects, responsible for pinning and causing field-tuned reproducible domain nucleation patterns observed in our high-quality samples, are pointlike. Recently found magnetic polarons formed around vacancies and impurities, which carry strong diamagnetic moments of spin-orbit nature and are intrinsic for CoSnS and expected in other Weyl semimetals, are a possible source of pinning yielding peculiar 𝑀⁡(𝐻,𝑇) response of CoSnS.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Coal to Carbon Fiber (C2CF) Continuous Processing for High Value Composites (Final Report)

Coal tar is a condensed and recovered by-product of the coking of metallurgical coal for steel production. The heaviest fraction of distilled coal tar is an isotropic pitch largely used as a binder in the manufacturing of carbonaceous electrodes for primary aluminum smelting and in electric arc furnaces. Coal tar pitch offers high carbon yield upon carbonization. In this project, a process to convert the domestically sourced isotropic coal tar pitch, containing very low particulates (QI = 0.32 wt.%), to form flow-domain mesophase pitch amenable for melt spinning into precursor (green) fibers for carbon fiber, was developed and optimized. The final reproducible processing developed is reviewed in this report, along with several characterizations of the mesophase pitch. A final definition of the characteristics of a ‘spinnable’ mesophase pitch is presented. With this mesophase pitch, reproducible and stable multifilament melt spinning was developed, producing green fiber tows with filament diameters of approximately 20 m. The multifilament melt spinning was the most challenging aspect of the project and required the most effort. The best practices learned from this project for melt spinning are reviewed in this report. Once spun, the green fibers were oxidatively stabilized, carbonized and graphitized under inert gas atmosphere to form the final carbon fibers. Given the relatively high softening point of the mesophase pitch, no issues of interfilament fusion were observed during batch oxidation, and subsequent batch carbonization and graphitization went smoothly in all cases. An ~ 80 wt.% conversion of the green fiber mass to final carbon fiber was achieved. After graphitization, the carbon fibers showed high tensile moduli (most were ~ 600 GPa, or 87 Msi) consistent with commercially-available high-performance pitch-based carbon fiber. However, tensile strength and strain to failure were comparatively low. Further work to reduce defects in and on the fiber surfaces would increase these properties. SEM imaging of the graphitic fiber textures is presented herein. Rudimentary composites were fabricated from the carbon fibers and characterized showing similar modulus to baseline composites fabricated with commercial carbon fiber. Finally, a basic economic analysis was done showing the potential to increase the value of the isotropic coal tar pitch by up to 13.6 to 136 times based on a carbon fiber value of $\$$5/lb to $\$$50/lb, respectively. Moreover, the site case study suggests that the coal tar from the single integrated steel mill could supply production of up to 16 kt/yr of carbon fiber. Finally, a technological gap analysis was done which shed light on remaining technical challenges. These challenges included: recovery and utilization of condensates from the mesophase pitch processing, further advancing and increasing stability of the multifilament melt spinning processing, optimization of the oxidation processing, defect reduction for increased carbon fiber strength, and the development of a weaving process towards carbon fiber fabrics. To maximize the coal value chain, the primary objectives of this project were to (a) develop and scale efficient processing technology for producing melt-spinnable mesophase pitch from isotropic coal tar pitch, (b) clarify and simplify tedious continuous fiber processing technologies (particularly multifilament melt spinning of mesophase pitch) towards the efficient production of high performance carbon fiber, and (c) demonstrate and characterize representative composite parts derived from the final carbon fiber. Immense progress was made on all 3 objectives and is detailed in this report.

01 COAL, LIGNITE, AND PEAT↗

Relating flow resistance to equivalent roughness

Describing flow resistance using the physical properties of an underlying surface is a recalcitrant problem in overland flow models. If discharge measurements are available, an equivalent roughness (e.g., Manning’s n) can be calibrated to represent the effects of surface properties within the domain with a single numerical value. Alternatively, the flow resistance can be estimated from discharge and velocity measured at a point, typically a runoff plot outlet. However, such experimental estimates are often inconsistent with the equivalent roughness determined from calibration to discharge, even if both derive from the same dataset. For example, if Manning’s equation is used to parameterize flow resistance, the Manning’s n obtained by calibrating a model to discharge differs from the value of n calculated from measured flow and velocity at the hillslope outlet. Here, this discrepancy is resolved by deriving a correction factor relating experimentally-determined flow resistance to the equivalent roughness. The derived correction factor is tested for four commonly-used resistance formulations using 129 rainfall simulator experiments. The correction factor is necessary to reproduce measured velocities, and yields minor improvements in discharge prediction. Plain Language Summary: Accurate runoff prediction is needed for land and water management in dryland regions, where sporadic and limited rainfall necessitate efficient water use and drought mitigation strategies. The skill of runoff models is known to be hindered by out ability to estimate flow resistance, which is the quantity that describes how energy is lost from flowing water to the underlying surface. Typically, models represent flow resistance with an equivalent roughness, e.g., Manning’s n, that is adjusted until the model can reproduce available discharge observations at watershed scale. However, the flow resistance measured in plot-scale experiments (1–10 m) often exceeds equivalent roughness coefficients by a factor of 10. This means that the direct use of plot-scale experimental data to parameterize runoff models could cause errors in discharge and runoff velocity predictions. Here, we resolve these differences by deriving an analytic correction factor that relates flow resistance to the equivalent roughness required for models to reproduce experimental velocity and discharge data. This correction factor is tested using rainfall simulator data from 129 experiments performed in the US Southwest covering a wide range of precipitation intensities, soil textures and vegetation types. Use of the correction factor substantially improves model prediction of flow velocity, which is needed for reproducing the timing of flood events and the estimation of erosion.

54 ENVIRONMENTAL SCIENCES↗