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Predicting geomechanical properties of rock and other types of porous media is essential to accurate modeling of many important processes, such as wave propagations, seismic events, and underground gas storage, and CO₂sequestration, all of which involve deformation of the pore space. We propose a model to predict the porosity dependence of the Young's and bulk moduli in heterogeneous porous media by combining the universal power law, predicted by percolation theory that describes the behavior of elastic moduli near the percolation threshold of the solid skeletons, and the effective‐medium approximation (EMA) for elastic materials that is accurate away from the threshold. The parameters of the model have unambiguous physical meanings, and can, in principle, be measured. We estimate the parameters ‐ the percolation threshold , crossover point between the EMA and percolation power law, the average particle coordination number , and the elastic moduli of the solid skeleton by using experimental data or numerical simulations for a wide variety of porous media in both two and three dimensions. Whenever data are available, the predictions are consistent with them. We then predict the elastic moduli for another 10 porous media using the proposed model and the estimated parameters without adjusting any new parameter. The predictions are in most cases in agreement with the data, hence indicating the accuracy of the approach. 

Sap flow measurement is one of the most effective methods for quantifying plant water use.A better understanding of sap flow dynamics can aid in more efficient water and crop management, particularly under unpredictable rainfall patterns and water scarcity resulting from climate change. In addition to detecting infected plants, sap flow measurement helps select plant species that could better cope with hotter and drier conditions. There exist multiple methods to measure sap flow including heat balance, dyes and radiolabeled tracers. Heat sensor-based techniques are the most popular and commercially available to study plant hydraulics, even though most of them are invasive and associated with multiple kinds of errors. Heat-based methods are prone to errors due to misalignment of probes and wounding, despite all the advances in this technology. Among existing methods for measuring sap flow, nuclear magnetic resonance (NMR) is an appropriate non-invasive approach. However, there are challenges associated with applications of NMR to measure sap flow in trees or field crops, such as producing homogeneous magnetic field, bulkiness and poor portable nature of the instruments, and operational complexity. Nonetheless, various advances have been recently made that allow the manufacture of portable NMR tools for measuring sap flow in plants. The basic concept of the portal NMR tool is based on an external magnetic field to measure the sap flow and hence advances in magnet types and magnet arrangements (e.g., C-type, U-type, and Halbach magnets) are critical components of NMR-based sap flow measuring tools. Developing a non-invasive, portable and inexpensive NMR tool that can be easily used under field conditions would significantly improve our ability to monitor vegetation responses to environmental change. 

Abstract The heat transfer and water retention in soils, governed by soil thermal conductivity (λ) and soil water retention curve (SWRC), are coupled. Soil water content (θ) significantly affects λ. Several models have been developed to describe λ(θ) relationships for unsaturated soils. Ghanbarian and Daigle presented a percolation‐based effective‐medium approximation (P‐EMA) for λ(θ) with two parameters: scaling exponent (t_s) and critical water content (θ_c). In this study, we explored the new insights into the correlation between soil thermal conductivity and water retention using the P‐EMA and van Genuchten models. The θ_cwas strongly correlated to selected soil hydraulic and physical properties, such as water contents at wilting point (θ_pwp), inflection point (θ_i), and hydraulic continuity (θ_hc) determined from measured SWRCs for a 23‐soil calibration dataset. The established relationships were then evaluated on a seven‐soil validation dataset to estimate θ_c. Results confirmed their robustness with root mean square error ranging from 0.011 to 0.015 cm³cm⁻³, MAE ranging from 0.008 to 0.013 cm³cm⁻³, andR²of 0.98. Further discussion investigated the underlying mechanism for the correlation between θ_cwith θ_hcwhich dominate both heat transfer and water flow. More importantly, this study revealed the possibility to further investigate the general relationship between λ(θ) and SWRC data in the future.