Search NASA⌕ Search

SEARCH · Search NASA

Results for “diffusive transport”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Designing Multiscale Porous Metal by Simple Dealloying with 3D Morphological Evolution Mechanism Revealed via X-ray Nano-tomography

Designing materials with multiscale, hierarchical structure is critical to drive the advancement of new technology. Specifically, porous metals with multiscale porosity from nanometer to micrometer sizes would lead to enhanced physical and chemical properties—the micron-sized pores can increase the effective diffusivity of ion transport within the porous media, and the nano-sized pores provide high specific surface area, enabling functionalities that are unique to nanoporous metals. A new ternary precursor alloy selection concept utilizing the different mixing enthalpies is demonstrated in this work for the design of multiscale, bimodal porous copper from a simple, one-step dealloying of Cu–Fe–Al ternary alloy. The nanoporosity in the bimodal porous structure is formed from dealloying of the Cu-rich phase, whereas the microporosity is controlled by dissolving the Fe-rich phase, determined by both the initial Fe particle size and sintering profile. In addition to advancing the materials design method, the multiscale pore formation during dealloying was directly visualized and quantified via an interrupted in situ synchrotron X-ray nano-tomography. The 3D morphological analysis on tortuosity showed that the presence of the microporosity can compensate the increase of the diffusion path length due to nanoporosity, which facilitates diffusion within the porous structure. Altogether the focus of the work is to introduce a new strategy to design multiscale porous metals with enhanced transport properties, and sheds light on the fundamental mechanisms on the 3D morphological evolution of the system using advanced synchrotron X-ray nano-tomography for future materials development and applications.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Evaluation of a nonlinear variational multiscale method for fluid transport problems

Diverse transport problems, especially those based on fluid flow models, are intrinsically multiscale and nonlinear, characteristics that often lead to intricate dynamics such as the development of instabilities and turbulence. Computational simulations that resolve all scales in these problems are often unfeasible, prompting to coarse-grained simulation strategies in which small-scale features are modeled instead of resolved. Variational Multiscale (VMS) methods, and particularly residual-based Large-Eddy Simulation (LES) approaches, have proven effective and robust for the coarse-grained simulation of complex transport problems. VMS methods avoid the assumption of separable nonlinearity and the reliance on empirical small-scale models by using a variational decomposition of scales together with a residual-based approximation of the small-scales. Evaluation of a nonlinear VMS approach, denoted as VMS n , is presented for the coarse-grained simulation of transient-advective-diffusive-reactive (TADR) transport problems arising from fluid flow models. In contrast to classical VMS approaches that neglect the effect of the small scales on the transport operator, VMS n treats the inter-dependence between large- and small-scales upfront. The treatment of inter-scale coupling involves the solution of a local algebraic nonlinear system describing the evolution of the small-scales. The VMS n approach is complemented with two algebraic approximations of the small-scales: one based on the main diagonal of the transport matrices and another that preserves transport fluxes and is suitable for generic TADR systems. The suitability of the VMS n approach for handling general TADR problems and regimes is evaluated with benchmark incompressible, compressible, and magnetohydrodynamic laminar flow problems, the incompressible Taylor-Green vortex flow, the turbulent free jet, and the two-temperature arc in crossflow. Furthermore, simulation results show that VMS n leads to minor improvements in accuracy with respect to the classical VMS for the laminar flow problems, but to significantly greater accuracy for the turbulent flows and the unsteady plasma flow problems, while using the same cohesive numerical formulation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Remote Mesoscopic Signatures of Induced Magnetic Texture in Graphene

Mesoscopic conductance fluctuations are a ubiquitous signature of phase-coherent transport in small conductors, exhibiting universal character independent of system details. Here, however, we demonstrate a pronounced breakdown of this universality, due to the interplay of local and remote phenomena in transport. Our experiments are performed in a graphene-based interaction-detection geometry, in which an artificial magnetic texture is induced in the graphene layer by covering a portion of it with a micromagnet. When probing conduction at some distance from this region, the strong influence of remote factors is manifested through the appearance of giant conductance fluctuations, with amplitude much larger than e 2 / h . This violation of one of the fundamental tenets of mesoscopic physics dramatically demonstrates how local considerations can be overwhelmed by remote signatures in phase-coherent conductors.

36 MATERIALS SCIENCE↗
DOE OSTI2020

High sensitivity pump–probe measurements of magnetic, thermal, and acoustic phenomena with a spectrally tunable oscillator

We describe an optical pump/probe system for sensitive measurements of time-resolved optical measurements of material dynamics. The instrument design is optimized for time-resolved magneto-optic Kerr effect (TR-MOKE) measurements of dynamics in magnetic materials. The system also allows for time-domain thermoreflectance (TDTR) measurements of thermal transport properties and picosecond acoustic measurements of film thickness and/or elastic constants. The system has several advantages over the conventional designs for TRMOKE and/or TDTR systems. Measurements of pump-induced changes to the probe beam intensity are shot-noise limited. The system’s design allows for MOKE and/or thermoreflectance measurements of both sides of a sample. Pumping and probing the sample on opposite sides allows nanoscale flash diffusivity measurements of transport properties. The wavelengths of the pump and probe beams are straightforward to tune between 350–525 nm and 690–1050 nm. A tunable wavelength allows for optical resonances in a wide array of materials to be excited and/or probed. Finally, the setup is calibrated to allow for the real and imaginary components of Kerr signals to be separately quantified.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Connecting Hindered Transport in Porous Media across Length Scales: From Single-Pore to Macroscopic

Hindered mass transport is widely observed in various porous media, including filtration membranes and porous rocks. However, there is no universal model capable of predicting transport in porous media due to the heterogeneity of porous structures and the complexity of the underlying microscopic mechanisms, including electrostatic and hydrodynamic effects. Here, we used a highly ordered porous medium (i.e. a silica inverse opal film) as a model system to directly explore the effects of geometric parameters (i.e. pore size, pore throat size and tracer particle size) and microscopic interaction parameters (e.g. controlled by ionic strength) on nanoparticle transport in porous environments using three-dimensional single-particle tracking. We found a linear scaling relation between the macroscopic diffusion coefficient and microscopic diffusion behaviors and a combination of parameters associated with microscopic features and phenomena, including both geometric effects and particle-level interactions. The proportionality coefficient relating micro and macro behaviors was complex and related to the connectivity of the matrix and pore-size variation, which could lead to tortuous diffusion pathways, hindering macroscopic transport. Furthermore, these findings provide important insights into nanoparticles and macromolecules transport in various porous media.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Diffusion and Solvation Dynamics of Ions in Water: Beyond the Brownian Approximation

The coupled dynamics of ions and water molecules in their first hydration shell impact a variety of processes including ion diffusion, selective ion transport in water-filled nanopores, and the kinetics of ion-pairing, ion adsorption, and metal-ligand binding reactions. In this work, we study these coupled dynamics for alkali metals (Li, Na, K, Rb, Cs), alkaline Earth metals (Mg, Ca, Sr, Ba), and chloride through the lens of their dependence on ion isotopic mass. Results are validated against previous measurements of the isotopic mass-dependence of ion diffusion coefficients in water and previous ab initio calculations of ion high-frequency dynamics in water. We find that the vibrational power spectra of ions in water consistently exhibit either two or three peaks, i.e., ions have several rattling frequencies within their solvations shells as previously reported for a subset of the species examined here. These frequencies have different sensititivies to isotopic mass that may serve as signatures of ion solvation processes (such as the tendency of ions to orient their first-shell water molecules) and that also may relate to Hofmeister-like effects including the relative affinity of different metals for ribonucleic acid (RNA).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Diffusion and Deformation Mechanism Maps in Li Metal from Atomistic Simulations

The rate of Li transport in the Li metal anode is important for the operation of Li metal-solid state batteries. Here, transport rates due to diffusion and creep are predicted in Li using atomistic simulations. First, molecular dynamics is used to estimate the rate of Li diffusion along dislocations and in grain boundary triple junctions. By combining this data with that from a prior study of grain boundary diffusion the dominant mechanisms and rates of self-diffusion in Li polycrystals are predicted as a function of grain size, grain shape, dislocation density, and temperature. Second, the dominant creep mechanisms are predicted and used to estimate critical current densities and void annihilation times. Grain boundary sliding and coble creep are the dominant mechanisms for micron-sized grains. Lastly, a continuum model for interfacial contact loss reveals that high dislocation densities of ∼10 12 /cm 2 enable achieving battery performance targets for Li grain sizes of ∼10 μm.

Batteries↗
DOE OSTI2026

Robustness of Kardar-Parisi-Zhang-like transport in long-range interacting quantum spin chains

Isotropic integrable spin chains such as the Heisenberg model feature superdiffusive spin transport belonging to an as-yet-unidentified dynamical universality class closely related to that of Kardar, Parisi, and Zhang (KPZ). To determine whether these results extend to more generic one-dimensional models, particularly those realizable in quantum simulators, we investigate spin and energy transport in non-integrable, long-range Heisenberg models using state-of-the-art tensor network methods. Despite the lack of integrability and the asymptotic expectation of diffusion, for power-law models (with exponent 2<α<∞) we observe long-lived z=3/2 superdiffusive spin transport and two-point correlators consistent with KPZ scaling functions, up to times t∼103/J. We conjecture that this KPZ-like transport is due to the proximity of such power-law-interacting models to the integrable family of Inozemtsev models, which we show to also exhibit KPZ-like spin transport across all interaction ranges. Finally, we consider anisotropic spin models naturally realized in Rydberg atom arrays and ultracold polar molecules, demonstrating that a wide range of long-lived, non-diffusive transport can be observed in experimental settings.

Anand↗
DOE OSTI2025

Complex Dependence of Calcite Crack Kinetics on Salinity: The Role of DLVO and Hydration Forces

Abstract Subcritical crack growth (SCG) plays an important role in many geological processes such as delayed earth rupture and rock weathering. The complex dependency of SCG on the in‐crack fluid chemistry, however, is still poorly understood. In this study, we utilize the newly developed surface force‐based fracture theory (SFFT) to elucidate the relative contributions of surface forces and solute transport to the crack growth kinetics of calcite in NaCl solutions. Expanding on Barenblatt's cohesive crack model, SFFT introduces an effective stress intensity at the crack tip that encompasses all the relevant intermolecular forces across the crack in addition to the external far‐field stresses. The nonlinear system of equations portraying the crack opening profile, the solute distribution in a propagating crack, and the crack growth velocity are numerically solved via an implicit scheme. After carefully calibrating the model for calcite‐water systems, the SFFT is used to predict the SCG response of calcite at different NaCl concentrations, based on various hypotheses. These predictions are then compared to existing SCG data from the literature. We demonstrate that the experimentally observed variation of SCG rate with NaCl concentration cannot be explained solely by DLVO forces (electrostatic and Van der Waals interactions). This can be remediated by introducing an exponentially decaying hydration force with a nonlinear, nonmonotonic dependence on NaCl concentration. Furthermore, we demonstrate that accounting for both diffusive and advective transport of ions is important in explaining the absence of a stage‐II SCG response for calcite in electrolyte solutions. Plain Language Summary Subcritical crack growth (SCG) refers to the slow propagation of cracks in materials under a stress below the threshold for catastrophic failure. SCG is a key process in many geological events, for example, delayed earth ruptures and rock weathering. New initiatives such as underground CO 2 and H 2 storage in carbonate reservoirs further call for better understanding of SCG in carbonate minerals subjected to varying fluid chemistry. This study examines the SCG of calcite, a key mineral found in carbonate rocks, intergranular cement in sandstones, and filling material in mineral veins and faults, determining their deformation and strength. A mathematical model is developed to describe how the crack opens and propagates, how solutes (like salts) distribute within the crack, and how the crack surfaces interact with each other. We used the model to predict calcite SCG in water at different salt concentrations and compared it with experimental data. Our results revealed that the hydration force is the dominating factor in determining the complex, non‐linear dependency of SCG on salinity. We also found that both the movement of ions by diffusion and by bulk water flow are crucial for explaining the SCG rates, especially when the cracks grow quickly. Key Points Surface Force‐Based Fracture Theory predicts the complex subcritical crack growth patterns of calcite crystals immersed in NaCl solutions Results highlight the dominant role of hydration forces in altering the fracture behavior of calcite compared to VdW and electric double‐layer forces Advective solute transport explains the absence of stages‐II and ‐III subcritical crack growth responses in solid‐liquid systems

DLVO↗
DOE OSTI2023

Coupled Lattice Boltzmann Modeling Framework for Pore-Scale Fluid Flow and Reactive Transport

In this paper, we propose a modeling framework for pore-scale fluid flow and reactive transport based on a coupled lattice Boltzmann model (LBM). We develop a modeling interface to integrate the LBM modeling code parallel lattice Boltzmann solver and the PHREEQC reaction solver using multiple flow and reaction cell mapping schemes. The major advantage of the proposed workflow is the high modeling flexibility obtained by coupling the geochemical model with the LBM fluid flow model. Consequently, the model is capable of executing one or more complex reactions within desired cells while preserving the high data communication efficiency between the two codes. Meanwhile, the developed mapping mechanism enables the flow, diffusion, and reactions in complex pore-scale geometries. We validate the coupled code in a series of benchmark numerical experiments, including 2D single-phase Poiseuille flow and diffusion, 2D reactive transport with calcite dissolution, as well as surface complexation reactions. The simulation results show good agreement with analytical solutions, experimental data, and multiple other simulation codes. In addition, we design an AI-based optimization workflow and implement it on the surface complexation model to enable increased capacity of the coupled modeling framework. Compared to the manual tuning results proposed in the literature, our workflow demonstrates fast and reliable model optimization results without incorporating pre-existing domain knowledge.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Modeled production, oxidation, and transport processes of wetland methane emissions in temperate, boreal, and Arctic regions

Abstract Wetlands are the largest natural source of methane (CH 4 ) to the atmosphere. The eddy covariance method provides robust measurements of net ecosystem exchange of CH 4 , but interpreting its spatiotemporal variations is challenging due to the co‐occurrence of CH 4 production, oxidation, and transport dynamics. Here, we estimate these three processes using a data‐model fusion approach across 25 wetlands in temperate, boreal, and Arctic regions. Our data‐constrained model—iPEACE—reasonably reproduced CH 4 emissions at 19 of the 25 sites with normalized root mean square error of 0.59, correlation coefficient of 0.82, and normalized standard deviation of 0.87. Among the three processes, CH 4 production appeared to be the most important process, followed by oxidation in explaining inter‐site variations in CH 4 emissions. Based on a sensitivity analysis, CH 4 emissions were generally more sensitive to decreased water table than to increased gross primary productivity or soil temperature. For periods with leaf area index (LAI) of ≥20% of its annual peak, plant‐mediated transport appeared to be the major pathway for CH 4 transport. Contributions from ebullition and diffusion were relatively high during low LAI (<20%) periods. The lag time between CH 4 production and CH 4 emissions tended to be short in fen sites (3 ± 2 days) and long in bog sites (13 ± 10 days). Based on a principal component analysis, we found that parameters for CH 4 production, plant‐mediated transport, and diffusion through water explained 77% of the variance in the parameters across the 19 sites, highlighting the importance of these parameters for predicting wetland CH 4 emissions across biomes. These processes and associated parameters for CH 4 emissions among and within the wetlands provide useful insights for interpreting observed net CH 4 fluxes, estimating sensitivities to biophysical variables, and modeling global CH 4 fluxes.

Ueyama, Masahito↗
DOE OSTI2025

The rigorous upscaling of advection-dominated transport in heterogeneous porous media via the Method of Finite Averages

Systems involving advection-dominated transport through heterogeneous porous and fractured media are ubiquitous in subsurface engineering applications. However, upscaling such systems continues to challenge rigorous modeling efforts, particularly when advection is stronger than diffusion at fine spatial scales (i.e., when the Péclet number is greater than one at length scales that characterize a system’s unit-cells, representative elementary volumes, or averaging regions). Here, in this work, we propose and validate a strategy for extending the Method of Finite Averages (MoFA), a rigorous upscaling methodology for heterogeneous porous media, to upscale transport systems experiencing stronger advection than diffusion at fine scales (i.e., fine-scale Péclet numbers greater than one). We detail the strategy, the physical conditions under which it can be applied while retaining a priori modeling error guarantees, and implement the strategy to obtain a MoFA model for advective-diffusive transport that accommodates advective physics at fine spatial scales. We then perform two numerical experiments considering systems with system-scale Péclet numbers of 300 and 1000 — which correspond to fine-scale Péclet numbers of 30 and 100, respectively — to verify that the error guarantees are met under the strategy. After, we conduct a numerical study to demonstrate the strategy’s advantages over the original MoFA methodology. The results suggest that rigorously-upscaled transport models for heterogeneous porous media experiencing advective physics at finer spatial scales can be derived through MoFA and resolved orders of magnitude faster than their pore-scale counterparts. The results also suggest that the presented strategy is limited to modeling shallow concentration gradients when there are large differences between the time scales related to advection and a system’s temporally-varying boundary conditions. This limitation hinders the strategy’s practicality in modeling more advective systems, and as such, opportunity exists for developing additional strategies that accommodate rapidly-varying boundary conditions — and consequentially, steeper concentration gradients — while modeling advective systems with MoFA.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Modeling glass degradation and release of radionuclides from vitrified waste for performance assessment simulations

The release of radionuclides initially encapsulated in a slowly degrading solid waste form and contained in an eventually corroding canister defines the source term for numerical simulations for the assessment of a geologic repository for high-level radioactive waste. While the details of waste degradation, canister corrosion, and dissolution and mobilization of the radionuclides in pore water include complex chemical reaction and transport processes that are coupled to the thermal, hydrological, microbiological, and mechanical conditions in the repository, the source-term model suitable for use in a numerical performance assessment model should be a defensible abstraction of these mechanisms. We developed a radiological source-term model and implemented it into a non-isothermal flow and transport simulator. While the proposed source-term model is applicable to various waste forms, canister systems, and disposal concepts, we specifically considered radionuclide releases from vitrified high-level waste placed in a cylindrical canister disposed in a deep vertical borehole repository. In this model, waste degradation is a function of temperature, and it can be adjusted to evaluate the influence of and propagate uncertainties in pH, passivation reactions, and chemical conditions as well as geometrical factors. The time-dependent, congruent release of safety-relevant radionuclides present in the decaying inventory is then calculated. Finally, the radionuclides are mobilized by diffusive and advective transport according to the thermo-hydraulic conditions prevailing in the near field of the repository, from where they migrate through the geosphere to the accessible environment. We examine the influence of the source-term model’s parameters on performance assessment calculations through sensitivity and uncertainty propagation analyses, identifying influential factors and confirming the upper bound of their impact. These considerations align with the overarching goal of repository design, which is to demonstrate that engineered and natural barriers can collectively delay radionuclide migration for timescales far exceeding human planning, thereby providing multiple, redundant barriers against environmental contamination.

iTOUGH2↗
DOE OSTI2020

Quantum prediction of ultra-low thermal conductivity in lithium intercalation materials

Lithium-intercalated layered transition-metal oxides, Li x TMO 2, brought about a paradigm change in rechargeable batteries in recent decades and show promise for use in memristors, a type of device for future neural computing and on-chip storage. Thermal transport properties, although being a crucial element in limiting the charging/discharging rate, package density, energy efficiency, and safety of batteries as well as the controllability and energy consumption of memristors, are poorly managed or even understood yet. Here, for the first time, we employ quantum calculations including high-order lattice anharmonicity and find that the thermal conductivity κ of Li x TMO 2 materials is significantly lower than hitherto believed. More specifically, the theoretical upper limit of κ of LiCoO 2 is 6 W/m-K, 2–6 times lower than the prior theoretical predictions. Delithiation further reduces κ by 40–70% for LiCoO 2 and LiNbO 2 . Grain boundaries, strain, and porosity are yet additional causes of thermal-conductivity reduction, while Li-ion diffusion and electrical transport are found to have only a minor effect on phonon thermal transport. The results elucidate several long-standing issues regarding the thermal transport in lithium-intercalated materials and provide guidance toward designing high-energy-density batteries and controllable memristors.

25 ENERGY STORAGE↗
DOE OSTI2023

Parametric Study of the Vacuum Permeator for the Tritium Extraction eXperiment

Tritium breeding is a critical component of any self-sustaining future fusion reactor. The liquid metal eutectic, PbLi, is of particular interest as a tritium breeder material due to its favorable thermophysical and neutronic properties. One of the several remaining challenges facing PbLi breeder blankets is the need to design and validate a highly efficient tritium extraction system. The vacuum permeator is a promising extraction concept that utilizes tritium permeation through a highly permeable metal membrane. The Tritium Extraction eXperiment (TEX) is a forced-convection PbLi loop constructed to investigate tritium extraction from PbLi with vacuum permeators. Accurate thermal-hydraulic and tritium transport models are required to establish appropriate test matrices, predict experiment outcomes, and analyze data. However, the hydrogen transport properties of PbLi and permeator materials have large uncertainties. A database is collected, and a parametric analysis is conducted on the effect of hydrogen transport material properties: diffusivity of H in PbLi and permeator, solubility of H in PbLi and permeator, and permeator surface recombination constant on the expected tritium extraction efficiency for a vacuum permeator installed in TEX. As a result, we observe solubility of H in PbLi and the permeator and the recombination constant of the permeator have the largest effect on the extraction efficiency.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

A pseudo-two-dimensional (P2D) model for FeS 2 conversion cathode batteries

Conversion cathode materials are gaining interest for secondary batteries due to their high theoretical energy and power density. However, practical application as a secondary battery material is currently limited by practical issues such as poor cyclability. To better understand these materials, we have, for this study, developed a pseudo-two-dimensional model for conversion cathodes. We apply this model to FeS 2 – a material that undergoes intercalation followed by conversion during discharge. The model is derived from the half-cell Doyle–Fuller–Newman model with additional loss terms added to reflect the converted shell resistance as the reaction progresses. We also account for polydisperse active material particles by incorporating a variable active surface area and effective particle radius. Using the model, we show that the leading loss mechanisms for FeS 2 are associated with solid-state diffusion and electrical transport limitations through the converted shell material. The polydisperse simulations are also compared to a monodisperse system, and we show that polydispersity has very little effect on the intercalation behavior yet leads to capacity loss during the conversion reaction. Finally, we provide the code as an open-source Python Battery Mathematical Modeling (PyBaMM) model that can be used to identify performance limitations for other conversion cathode materials.

25 ENERGY STORAGE↗
DOE OSTI2022

Deterministic modelling of the SPERT IV reactor transients using the multi-physics capability of WIMS

The ANSWERS WIMS reactor physics code is being developed for whole core multi-physics modelling. The established neutronics capability for lattice calculations has recently been extended to be suitable for whole core modelling of Small Modular Reactors (SMRs). A whole core transport, SP3 or diffusion flux solution is combined with fuel assembly resonance shielding. An integrated thermal hydraulic solver permits temperature and density variations to feedback to the neutronics calculation. This capability can be applied to both steady state and time dependent transient problems. Nuclear reactor design and safety case development requires assessment of a range of reactor transients, to inform both normal operation limitations and accident scenario analysis. This paper presents new methodology developed in WIMS to couple the core neutronics to the integrated core thermal hydraulics solver for the simulation of reactor transients in whole core models. To support the validation of the multi-physics capability of WIMS, this capability has been applied to the reactivity insertion transient experiments performed in the plate fuelled SPERT-IV reactor. This study employs WIMS using the whole core solver MERLIN, which calculates the time-dependent flux distribution and magnitude, coupled to ARTHUR, which solves for the time-dependent thermal hydraulics solution, and provides thermal feedback via the cross sections generated by GEOM, which performs resonance shielding calculations and generates cross section data for the plate geometry. This spatial kinetics model, with dynamic cross section generation, allows for variations in the temperature and neutron flux profile with time.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗