Search Results (9)

In this paper, we derive sufficient conditions that guarantee an description of long-time asymptotic behavior of the solution to the Cauchy problem governed by a linear neutron transport equation with a partially elastic collision operator under periodic boundary conditions. Our strategy involves showing that the strongly continuous semigroups ${\left(e^{t(T+K_e)}\right)}_{t\ge 0}$ and ${\left(e^{t(T+K_c+K_e)}\right)}_{t\ge 0}$, generated by the operators $T+K_e$ and $T+K_c+K_e$, respectively, have the same essential type. According to Proposition 1, it is sufficient to show that remainder term in the Dyson–Philips expansion is compact. Our analysis focuses on the compactness properties of the second-order remainder term in the Dyson–Phillips expansion related to the problem. We first show that $R_2\left(t\right)$ is compact on $L^2(\mathsf{\Omega }\times V,dxdv)$, and, using an interpolation argument (see Proposition 2), we establish the compactness of $R_2\left(t\right)$ on $L^p(\mathsf{\Omega }\times V,dxdv)$-spaces for $1<p<+\infty$. To the best of our knowledge, outside the one-dimensional case, this result is known only for vaccum boundary conditions in the multidimensional setting. However, our result, Theorem 1, is new for periodic boundary conditions. Full article

In the design of furrow irrigation, and in general in surface irrigation, the reliable estimation of the advance time at the furrow end (t_L) is a key issue for improving the efficiency and uniformity of irrigation. In this study, three methods are used for estimating the t_L, and their results are compared with the experimental data of fifteen different furrows from the international literature. These methods are as follows: (a) the Valiantzas equation, (b) the method presented by Walker and Skogerboe, based on solving the volume balance equation by the Newton–Raphson iterative procedure and (c) the method of Philip and Farrell. The first two methods assume that the infiltration is described by the Lewis–Kostiakov equation and the extended Lewis–Kostiakov equation, respectively, while in the case of the Philip and Farrell method, the infiltration is described by the Philip equation and the Lewis-Kostiakov equation. The results showed that in most cases of the first two methods, the absolute relative error value of the predicted time t_L was less than 10%. The Philip and Farrell method using the Lewis–Kostiakov infiltration equation underestimates the time t_L and fails especially in the case where the volume of the surface water is not negligible compared to the total volume of water entering the system. The Valiantzas method is recommended because it was simpler and easier to use and showed greater prediction accuracy of t_L, resulting in better planning of irrigation systems and contributing to water saving, which is currently a big issue. Full article

The main aim of this paper was to analyze the sensitivity of the five infiltration equations (Kostiakov, Kostiakov–Lewis, Philip, Horton and SCS) and their coefficients to various ponding depths and initial soil moisture under different irrigation managements. The treatments included three qualities of water (electrical conductivity = 6, 3 and 0.6 dS/m), two managements of irrigation (intermittent irrigation and daily irrigation) and three irrigation periods (100, 45 and 8 days). The HYDRUS-1D model was calibrated to simulate infiltration in various initial soil moistures and ponding depths. Evaluating the performance of infiltration equations showed that the Horton and Kostiakov–Lewis had better accuracy and Kostiakov and SCS had less accuracy than the other equations. The empirical coefficients of SCS and Kostiakov had the most and least sensitivities, respectively. Furthermore, Horton was the most sensitive equation, while SCS was the least sensitive one. The output parameters under daily management were the most sensitive to variations in infiltration coefficients, especially when the salinity and sodium contents of water and soil were higher. The results also showed that the effect of the initial soil moisture on the infiltration coefficient in high permeable soil (arising from daily management) was greater; but in low permeable soil (arising from intermittent management), the ponding depth was more effective. It is concluded that the infiltration equations (specifically the SCS equation) and their coefficients (specifically coefficient c) should be calibrated relative to the initial soil moisture, ponding depth, soil solution and water irrigation quality. Particularly in areas with high permeable soil (in the daily management), the calibration of the infiltration equation should be conducted with the initial soil moisture. In these areas, the irrigation period should be controlled. In areas with low permeable soil (in intermittent management), calibration should be carried out relative to the ponding depth. In these areas, the inflow rate should be controlled. Full article

The process of how soil moisture profiles evolve into the soil and reach the root zone could be estimated by solving the appropriate strong nonlinear Richards’ equation. The nonlinearity of the equation occurs because diffusivity D is generally an exponential function of water content. In this work, the boundary conditions of the physical problem are considered fuzzy for various reasons (e.g., machine impression, human errors, etc.), and the overall problem is encountered with a new approximate fuzzy analytical solution, leading to a system of crisp boundary value problems. According to the results, the proposed fuzzy analytical solution is in close agreement with Philip’s semi-analytical method, which is used as a reference solution, after testing 12 different types of soils. Additionally, possibility theory is applied, enabling the decision-makers to take meaningful actions and gain knowledge of various soil and hydraulic properties (e.g., sorptivity, infiltration, etc.) for rational and productive engineering studies (e.g., irrigation systems). Full article

This paper investigates the possibility of using the global VAR (GVAR) model to estimate a simple New Keynesian DSGE-type multi-country model. The long-run forecasts from an estimated GVAR model were used to calculate the steady-states of macro variables as differences. The deviations from the long-run forecasts were taken as the deviation from the steady-states and were used to estimate a simple NK open economy model with an IS curve, Philips curve, Taylor rule, and an exchange rate equation. The shocks to these equations were taken as the demand shock, supply shock, monetary shock, and exchange rate shock, respectively. An alternative model was constructed to compare the results from GVAR long-run forecasts. The alternative model used a Hodrick–Prescott (HP) filter to derive deviations from the steady-states. The impulsive response functions from the shocks were then compared to results from other DSGE models in the literature. Both GVAR and HP estimates produced dissimilar results, although the GVAR managed to capture more from the data, given the explicit co-integration relationships. For the IRFs, both GVAR and HP estimated DSGE models appeared to be as expected before the pandemic; however, if we include the pandemic data, i.e., 2020, the IRFs are very different, due to the nature of the policy actions. In general, DSGE–GVAR models appear to be much more versatile, and are able to capture dynamics that HP filters are not. Full article

Residue cover is widely used for soil conservation after crop harvesting in the black soil region of the Northeastern China, which influences infiltration. It is necessary to optimize infiltration models for accurate predictions under bare and residue cover slope conditions. Rainfall simulation experiments were conducted to quantify the infiltration for the black soil under four rainfall intensities (30, 60, 90, and 120 mm/h), five residue coverage controls (15%, 35%, 55%, 75%, and bare slope), and two soil moisture (8% and approximately 30%) conditions. The observed data were used to fit and compare four infiltration models by Kostiakov, Mein and Larson (short for GAML, a modification of GreenAmpt model made by Mein and Larson), Horton, and Philip under the bare slope conditions. The residue cover infiltration factor (RCF_i) was derived to predict the infiltration under the residue cover slopes, which was defined as the ratio of infiltration from residue-covered soil to that from bare soil. The results showed that the newly derived equation coupling the Philip model with the RCF_i was the most accurate way of predicting the cumulative infiltration of black soil under various residue covers, and could be applied to the black soil region for residue cover infiltration predictions. Full article

The removal of nutrients by overland flow remains a major source of non-point pollution in agricultural land. In this study, a mathematical model of ammonium nitrogen transport from soil solution to overland flow was established. The model treated the mass transfer coefficient (k_m) as a time-dependent parameter, which was not a constant value as in previous studies, and it was evaluated with a four-slope gradient and three rainfall intensities. The kinematic-wave equation for overland flow was solved by an approximately semi-analytical solution based on Philip’s infiltration model, while the diffusion-based mass conversation equation for overland nutrient transport was solved numerically. The results showed that the simulated runoff processes and ammonium nitrogen concentration transport to the overland flow agreed well with the experimental data. Further correlation analyses were made to determine the relationships between the slope gradient, rainfall intensity and the hydraulic and nutrient transport parameters. It turned out that these parameters could be described as a product of exponential functions of slope gradient and rainfall intensity. Finally, a diffusion-based model with a time-dependent mass transfer coefficient was established to predict the ammonium nitrogen transport processes at the experimental site under different slope gradients and rainfall intensities. Full article

The uncertainty in a hydrological model, due to its structure or implemented input parameters, affects the accuracy of simulations that are usually used for important applications such as drought predictions, flood risk assessment, irrigation scheduling, ground water recharge and contamination. Several models describing soil infiltration processes have been developed. Some are analytical, while others implement numerical solutions of the Richards’ equation. The objective of this work was to assess the impact of infiltration process modeling on soil water content simulations. For this study, different infiltration models were included within FEST-WB (Flash Flood Event-based Spatially-distributed rainfall-runoff Transformations-Water Balance) distributed hydrological model (SCS-CN, Green and Ampt, Philip and Ross solution). Performances of implemented infiltration models in simulating soil water content were evaluated against observations acquired in the experimental site located in a maize field in northern Italy. Soil water content was monitored together with continuous measurements of meteorological data. A sensitivity analysis was performed to assess the most important parameters governing infiltration process in the different models tested. A comparison of soil water content simulations show that Ross solution allowed the description of soil moisture variation along the vertical, but simpler lumped models provide sufficient accuracy when properly calibrated. Full article

The rainfall-runoff process (RRP) is an important part of hydrologic process. There is an effective measure to study RRP through artificial rainfall simulation. This paper describes a study on three growing stages (jointing stage, tasseling stage, and mature stage) of spring maize in which simulated rainfall events were used to study the effects of various factors (rainfall intensity and slope gradient) on the RRP. The RRP was tested with three different rainfall intensities (0.67, 1.00, and 1.67 mm/min) and subjected to three different slopes (5°, 15°, and 20°) so as to study RRP characteristics in semiarid regions. Regression analysis was used to study the results of this test. The following key results were obtained: (1) With the increase in rainfall intensity and slope, the increasing relationship with rainfall duration, overland flow, and cumulative runoff, respectively, complied with logarithmic and quadratic functions before reaching stable runoff in each growing stage of spring maize; (2) The runoff coefficient increased with the increase in rainfall intensity and slope in each growing stages of spring maize. The relationship between runoff coefficient, slope, rainfall intensity, rainfall duration, antecedent soil moisture, and vegetation coverage was multivariate and nonlinear; (3) The runoff lag time decreased with the increase in rainfall intensity and slope within the same growing stage. In addition, the relationship between runoff lag time, slope, rainfall intensity, antecedent soil moisture, and vegetation coverage could also be expressed by a multivariate nonlinear equation; (4) The descent rate of soil infiltration rate curve increased with the increased rainfall intensity and slope in the same growing stage. Furthermore, by comparing the Kostiakov, Horton, and Philip models, it was found that the Horton infiltration model was the best for estimating soil infiltration rate and cumulative infiltration under the condition of test. Full article