The Fenchel-type inequality in the 3-dimensional Lorentz space and a Crofton formula

We generalize the Fenchel theorem to strong spacelike (which means that the tangent vector and the curvature vector span a spacelike 2-plane at each point) closed curves with index 1 in the 3-dimensional Lorentz space, showing that the total curvatures must be less than or equal to $2\pi$. A similar generalization of the Fary-Milnor theorem is also obtained. We establish the Crofton formula on the de Sitter 2-sphere which implies the above results.Comment: 9 pages, 4 figures. Comments are welcom

On the laboratory calibration of dielectric permittivity models for agricultural soils: Effect of systematic porosity variation

Dielectric techniques are fundamental methods for measuring soil water content, and they commonly rely on the conventional laboratory calibration of the dielectric permittivity models between a dielectric constant and water content. As a non-negligible factor, porosity has been constructed differently in some models as a calibration constant, but the systematic porosity variations during the laboratory model calibration and field applications are not yet well addressed. Based on time-domain reflectometer laboratory calibration experiments, this study investigated this issue using three preestablished dielectric permittivity models: the Purdue calibration equation (American Society for Testing and Materials model [ASTM]), the complex refractive index model (CRIM), and a piecewise CRIM model (CRIMP). Results demonstrate that a generalized porosity constant used in the calibration would bring in additional structural bias compared with the calibration using variable porosities, and its magnitude varies with the model structure. The deviation of the generalized porosity constant can further amplify the structural bias of ASTM and CRIM for soils with low clay content, but it is insensitive for the soils with high clay content due to the overwhelming role of model structure error. Only the model CRIMP with a “perfect” model structure can effectively cope with the systematic porosity variation and keep a stable built-in capability for estimating calibration constants from readily available soil data. These findings highlight ignoring porosity variation should not be taken for granted for calibrating and applying the preestablished models

Potential Root Foraging Strategy of Wheat (Triticum aestivum L.) for Potassium Heterogeneity

Potassium (K) distribution is horizontally heterogeneous under the conservation agriculture approach of no-till with strip fertilization. The root foraging strategy of wheat for K heterogeneity is poorly understood. In this study, WinRHIZO, microarray, Non-invasive Micro-test Technology (NMT) and a split-root system were performed to investigate root morphology, gene expression profiling and fluxes of K+ and O2 under K heterogeneity and homogeneity conditions. The split-root system was performed as follows: C. LK (both compartments had low K), C. NK (both compartments had normal K), Sp. LK (one compartment had low K) and Sp. NK (the other compartment had normal K). The ratio of total root length and root tips in Sp. NK was significantly higher than that in C. NK, while no significant differences were found between Sp. LK and C. LK. Differential expression genes in C. LK vs. C. NK had opposite responses in Sp. LK vs. C. LK and similar responses in Sp. NK vs. C. NK. Low-K responsive genes, such as peroxidases, mitochondrion, transcription factor activity, calcium ion binding, glutathione transferase and cellular respiration genes were found to be up-regulated in Sp. NK. However, methyltransferase activity, protein amino acid phosphorylation, potassium ion transport, and protein kinase activity genes were found to be down-regulated in Sp. LK. The up-regulated gene with function in respiration tended to increase K+ uptake through improving O2 influx on the root surface in Sp. NK, while the down-regulated genes with functions of K+ and O2 transport tended to reduce K+ uptake on the root surface in Sp. LK. To summarize, wheat roots tended to perform active-foraging strategies in Sp. NK and dormant-foraging strategies in Sp. LK through the following patterns: (1) root development in Sp. NK but not in Sp. LK; (2) low-K responsive genes, such as peroxidases, mitochondrion, transcription factor activity, calcium ion binding and respiration, were up-regulated in Sp. NK but not in Sp. LK; and (3) root K+ and O2 influxes increased in Sp. NK but not in Sp. LK. Our findings may better explain the optimal root foraging strategy for wheat grown with heterogeneous K distribution in the root zone

Organic amendments with high proportion of heterocyclic compounds promote soil microbiome shift and microbial use efficiency of straw-C

Soil microbial use efficiency of straw carbon (C), which is the proportion of straw-C microbes assimilate into new biosynthetic material relative to C lost out of the system as CO2, is critical in increasing soil organic C (SOC) content, and hence maintaining soil fertility and productivity. However, the effect of chemical structures of the organic amendments (OAs) on the microbial use efficiency of straw-C remains unclear. The effect of the chemical structure of the OAs on microbial use efficiency of straw-C was elucidated by a combination of 13C-straw labeling with high-throughput sequencing and pyrolysis-GC/MS. We found a strong positive correlation between the microbial use efficiency of straw-C and the proportion of heterocyclic compounds (Hete_C). The microbial use efficiency of straw-C was highest in soil supplemented with Hete_C-dominant OAs, which significantly shifted microbial community structure toward fungal dominance. Specifically, fungal-to-bacterial ratio, fungal richness, and the relative abundance of Ascomycota were higher in soil with a higher proportion of Hete_C-dominant OAs. Together, our study suggests that OAs with high proportion of Hete_C promote the microbial use efficiency of straw-C by increasing the dominance of fungi in the soil microbial community in agroecosystems

Estimation of Horton infiltration equation parameters and field-averaged roughness coefficient by surface irrigation advance

Based on the analyses of water stream and irrigation advance, two functions were given to describe irrigation advance and water depth profile. A method for estimation of Manning roughness coefficient was developed through adopting Manning equation for water flow. Combining with Horton infiltration equation, the solution for estimation of infiltration properties was established based on the water volume balance. The method was evaluated by the field experimental data, and the results indicate that the predicted irrigation advance and recession of SRFR4.06 with the parameters obtained by the new method go well with the observed

A Simple Method for Estimating Field Crop Evapotranspiration from Pot Experiments

Pot experiments are a low-cost and easy-to-use technique for studies of soil evaporation and plant transpiration in controlled environments. However, little attention has been paid to the applicability of evapotranspiration (ET) measured in pot experiments to the field. The objective of this study was to determine whether a pot experiment can be used for measuring field ET. Evapotranspiration experiments with winter wheat and summer maize were conducted in pots and lysimeters under various water-deficit conditions. The measured ET values in the pot experiments under different water conditions were considerably different from those of the lysimeters. Causes of such differences in ET were analyzed, and a series of corrections were proposed to eliminate the effects of different crop densities, representative areas per plant, and soil moisture conditions on pot experiment results. After these corrections, the discrepancy in the total ET of wheat-maize seasons between pots and lysimeters was greatly reduced from a maximum of 117% to only approximately 10%. The relative mean square errors (RMSEs) for daily ET values also decreased from a maximum value of 4.56 mm to less than 1.5 mm for the wheat season and from a maximum value of 6.02 mm to approximately 2 mm for the maize season. Possible measures were proposed to further improve the accuracy of the corrected ET obtained from pot experiments. In sum, pot experiments can serve as a feasible tool for estimating ET in the field just with a few routine measurements at regions where large-scale weighing lysimeters, an eddy covariance device, and even meteorological data are not available. The proposed corrections can also be used for upscaling small-scale ET measurements to a large scale

Analytical Method for Estimating Soil Hydraulic Parameters from Horizontal Absorption

Soil hydraulic properties are required to quantitatively simulate water and chemical transport processes in the vadose zone and groundwater with various numerical models. Most methods for determination of soil hydraulic properties are time consuming and expensive, which limits the application of the methods. The objective of this study was to develop an analytical method based on an assumption of exponential flux distribution to determine soil hydraulic parameters. Using this method, parameters of the Brooks-Corey model and exponential water diffusivity can be easily estimated from cumulative infiltration and wetting length vs. time in horizontal absorption experiments. The analytical method was tested and improved using 19 numerical soils in a wide range of textures. The results indicated that all the Brooks-Corey model parameters estimated by the improved method were very close to the simulated values. In addition, the water content, soil tension, and water flux distributions of three typical soils (clay, loam, and sand soils) estimated by the approximate solution of the improved method agreed well with those calculated by the HYDRUS-1D software as well as cumulative infiltration data. Therefore, although a large number of experiments are still required to test the method, it provides a simple approach to determine the hydraulic parameters of soils in a wide range of textures, providing a very good approximate solution to the problem of horizontal absorption

Simulating infiltration into stony soils with a dual-porosity model

Soils containing rock fragments are widely distributed in the world. However, literature on the dynamic simulation of water movement in stony soils is scarce. In this paper, a dual-porosity model was used to simulate water infiltration into soils containing rock fragments. Sensitivity analysis of the dual-porosity model parameters demonstrates that the increase of rock fragment content clearly decreased infiltration into stony soils. Big stones hampered infiltration more than small stones. Spherical stones accelerated infiltration compared with solid, cylindrical stones and rectangular, slab-like stones. Numerical analysis was also performed to test and compare a non-equilibrium dual-porosity model (NDPM) with an equilibrium dual-porosity model (EDPM) and an equilibrium single-pore model (ESPM). Infiltration experiments on disturbed soils were carried out to verify the ability of the NDPM to simulate infiltration into stony soils. Based on hydraulic parameters of soils without rock fragments and mass transfer coefficients obtained independently, the extrapolated cumulative infiltrations calculated by the NDPM were in good agreement with the observed data. Fitted model parameters of the NDPM indicate that rock fragments not only act as a source or sink to affect infiltration but also change the pore structure of the fine earth, apart from reducing the cross-sectional area for water flow. Though further studies are required to improve the dual-porosity model, it already describes more characteristics of infiltration into stony soils and explains more phenomena than does the single-porosity model

Fatigue Fracture Analysis on 2524 Aluminum Alloy with the Influence of Creep-Aging Forming Processes

The different creep-aging forming processes of 2524 aluminum alloy were taken as the research object, and the effects of creep-aging temperature and creep stress on the fatigue-crack propagation properties of the alloy were studied. The research results showed the following under the same sintering time of 9 h, at creep-aging temperatures of 100 °C, 130 °C, 160 °C, and 180 °C, respectively, with an increase in creep-aging temperature: the fatigue-crack propagation rate was promoted, the spacing of fatigue striations increased, and the sizes of dimples decreased while the number was enlarged; this proves that the fatigue property of the alloy was weakened. Compared with the specimens with creep deformation radii of 1000 mm and 1500 mm, the creep deformation stress was the smallest when the forming radius was 1800 mm, with a higher threshold value of fatigue-crack growth in the near-threshold region of fatigue-crack propagation (ΔK ≤ 8 MPa·m1/2). Under the same fatigue cycle, the specimens under the action of larger creep stress endured a longer fatigue stable-propagation time and a faster fracture speed. Comparing the effect of creep-aging temperature and creep stress, the creep-aging temperature plays a dominant role in the fatigue-crack propagation of creep-aged 2524 aluminum alloy