Mathematical modeling in the agro-industrial complex: basic problems and models construction

Currently, information technologies have been tightly integrated into agriculture. Since no computer calculations are possible without a powerful mathematical apparatus, the question arises about the possibility of modeling the processes occurring in agriculture with the help of modern achievements of science and technology. The present study is devoted to the existing methods of mathematical modeling in agriculture in relation to the applied aspects of agriculture. The aim of the research is to develop a critical approach to modern developments in the field of mathematical modeling and their place in agriculture. It is shown that the introduction of mathematical models based on modern scientific knowledge contributes to the optimization of agricultural processes and increasing the efficiency of any farm. Based on statistical studies, it is shown that among all branches of agriculture, mathematical methods are most often used in economic calculations, least of all, in calculations related to farm modeling. This is explained both by the complexity of modeling all processes occurring within a single farm, and by the loss of accuracy, which increases with the complexity of the system model

MODELING OF AGRICULTURAL SYSTEMS

The authors present an overview of agricultural systems models. Beginning with why systems are modeled and for what purposes, the paper examines types of agricultural systems and associated model types. The broad categories range from pictorial (iconic) models to descriptive analogue models to symbolic (usually mathematical) models. The uses of optimization versus non-optimizing mechanistic models are reviewed, as are the scale and aggregation challenges associated with scaling up from the plant cell to the landscape or from a farm enterprise to a world market supply-demand equilibrium Recent modeling developments include the integration of formerly stand-alone biophysical simulation models, increasingly with a unifying spatial database and often for the purpose of supporting management decisions. Current modeling innovations are estimating and incorporating environmental values and other system interactions. At the community and regional scale, sociological and economic models of rural community structure are being developed to evaluate long-term community viability. The information revolution is bringing new challenges in delivering agricultural systems models over the internet, as well as integrating decision support systems with the new precision agriculture technologies.Farm Management,

Modeling of the Labour Force Redistribution in Investment Projects with Account of their Delay

The mathematical model of the labour force redistribution in investment projects is presented in the article. The redistribution mode of funds, labour force in particular, according to the equal risk approach applied to the loss of some assets due to delay in all the investment projects is provided in the model. The sample of the developed model for three investment projects with the specified labour force volumes and their defined unit costs at the particular moment is given

Modeling deep-bed grain drying using Comsol Multiphysics

CFD simulations were carried out to predict the convective heat and mass transfer coefficients in the rice bed, and correlations were developed for the convective heat and mass transfer coefficients as a function of drying air flow rate. The developed correlations were used to extend the coupled CFD and diffusion model developed by ElGamal et al. (2013) for thinlayer rice drying to volumetric heat and mass transfer in a deep-bed of rice. All mathematical models were solved using the Comsol Multiphysics® simulation program v4.3 (Comsol Inc, Palo Alto), which uses the finite element method to solve the model equations. The model was used to predict the air temperature, as well as the grain moisture content and temperature at different locations of the dryer during the drying process. The theoretical predictions of moisture and temperature profiles inside a deep-bed of rice were verified by experimental data from literature

Multi-scale model for heat and mass transfer during rice drying

Grain drying is a simultaneous heat and moisture transfer problem. The modeling of such a problem is of significance in understanding and controlling the drying process. The main goal of this study was to predict the heat and mass transfer processes during deep-bed rice drying. To achieve this, first, CFD simulations were carried out to analyze the external flow and temperature fields at steady-state for a control volume of a stationary rice bed. The model was used to predict the convective heat and mass transfer coefficients in the rice bed, and correlations were developed for the convective heat and mass transfer coefficients as a function of drying air flow rate. Then, the coupled CFD and diffusion model developed by ElGamal, Ronsse, Radwan & Pieters (2013) to investigate the heat and mass transfer for thin-layer drying of rice was extended to volumetric heat and mass transfer in a deep-bed of rice using the predicted heat and mass transfer coefficients. All models were solved numerically using the finite element method. The model was used to predict the air temperature, as well as the grain moisture content and temperature at different locations of the dryer during the drying process. The theoretical predictions of moisture and temperature profiles inside a deep-bed of rice were verified by experimental data from literature. The average mean relative deviation values for the prediction of grain moisture content varied between 1.00 to 3.13%

ECONOMIC MODELING OF FARM PRODUCTION AND CONSERVATION DECISIONS IN RESPONSE TO ALTERNATIVE RESOURCE AND ENVIRONMENTAL POLICIES

Environmental Economics and Policy, Farm Management,

The influences of basic physical properties of clayey silt and silty sand on its laboratory electrical resistivity value in loose and dense conditions

Non-destructive test which refers to electrical resistivity method is recently popular in engineering, environmental, archaeological and mining studies. Based on the previous studies, the results on electrical resistivity interpretation were often debated due to lack of clarification and evidences in quantitative perspective. Traditionally, most of the previous result interpretations were depending on qualitative point of view which is risky to produce unreliable outcomes. In order to minimise those problems, this study has performed a laboratory experiment on soil box electrical resistivity test which was supported by an additional basic physical properties of soil test like particle size distribution test (d), moisture content test (w), density test (ρbulk) and Atterberg limit test (LL, PL and PI). The test was performed to establish a series of electrical resistivity value (ERV) with different quantity of water content for clayey silt and silty sand in loose and dense condition. Apparently, the soil resistivity value was different under loose (L) and dense (C) conditions with moisture content and density variations (silty SAND = ERVLoose: 600 - 7300 Ωm & ERVDense: 490 - 7900 Ωm while Clayey SILT = ERVLoose: 13 - 7700 Ωm & ERVDense: 14 - 8400 Ωm) due to several factors. Moreover, correlation of moisture content (w) and density (ρbulk) due to the ERV was established as follows; Silty SAND: w(L) = 638.8ρ-0.418, w(D) = 1397.1ρ-0.574, ρBulk(L) = 2.6188e-6E-05ρ, ρBulk(D) = 4.099ρ-0.07 while Clayey SILT: w(L) = 109.98ρ-0.268, w(D) = 121.88ρ-0.363, ρBulk(L) = -0.111ln(ρ) + 1.7605, ρBulk(D) = 2.5991ρ-0.037 with determination coefficients, R2 that varied from 0.5643 – 0.8927. This study was successfully demonstrated that the consistency of ERV was greatly influenced by the variation of soil basic physical properties (d, w, ρBulk, LL, PL and PI). Finally, the reliability of the ERV result interpretation can be enhanced due to its ability to produce a meaningful outcome based on supported data from basic geotechnical properties

Integrated approach for prediction of centrifugal fertilizer spread patterns

The present paper proposes a numerical approach for prediction of behavior of those fertilizers spreaders based on centrifugal disc functioning. In particular results from finite element multi-body simulations provided by commercial software are used in order to define boundary conditions of field tests carried out concurrently. Results are then integrated into a mathematical model to rapidly generate distribution charts and distribution diagrams. Such integrated approach can be implemented to effectively calibrate a theoretical model which provides simulations on different machine settings conditions: as a final point simulations allow fast testing of different distribution conditions, helping definition of those which minimize the variability of the distribution itself