mathematical modeling

Piezoelectric materials are a type of smart materials that are of interest to many researchers in various engineering sciences due to their extraordinary properties such as converting mechanical energy into electrical energy and vice versa. In this article, the determination and control of the dynamic deformation of a one-span concrete frame with a piezoelectric layer coating on beams and columns under seismic load is discussed. In order to control the dynamic deformation of the concrete frame, a proportional-derivative controller has been used in such a way that a piezoelectric layer is considered as an actuator and a layer as a sensor. The governing equations for the beam and column components of concrete frame are obtained by using high-order shear theory, calculating energy relations, applying Hamilton's principle and considering the applied voltage on piezoelectric materials. In order to solve the dynamic coupled equations, the numerical method of differential quadrature method has been used and finally, with the help of Newmark method, the dynamic deformation of the concrete frame is calculated. After validating the results, the effect of various parameters such as voltage applied to the piezoelectric layer, piezoelectric type controller, thickness of the piezoelectric layer on dynamic deformation were investigated. Here, the optimal values of controller parameters, including proportionality coefficient and derivative coefficient, were obtained as 3.824 and 5.812, respectively. The results show that the use of the controller leads to a reduction of 72 and 65 percent of the lateral and vertical dynamic deflection of the frame, respectively.

The population is growing at an unprecedented rate, leading to a surge in food demand. This surge is coinciding with scarcity of water resources and intensifying competition among various sectors for water consumption and therefore there is an urgent need to precisely assess the water requirements of crops. Numerous studies have been conducted so far to determine water demand by considering various factors. Among these approaches, the FAO-Penman-Monteith equation has emerged as a widely recognized method. However, this equation entails extensive data requirements and involves lengthy calculations. The objective of this study was to develop a model for estimating the cumulative water requirement of common crops (wheat, barley, corn, and forage corn) on various latitudes within a specific region (the western vertical strip of Iran). Remarkably, the model only considers time as the input variable (growth period duration). Since the relationship between the cumulative water requirement of various crops and the length of the growth period follows a sigmoidal pattern, three mathematical models were employed to capture this trend; three-parameter logistic models, Gaussian functions, and third-order polynomials, all used for the purpose of modeling. The findings indicated that all three models exhibited high accuracy in estimating the cumulative water requirement for the crops during the growth period. The logistic model, in particular, demonstrated superior performance when evaluated using R2, RMSE, and NSE indices. Unlike the Gaussian and polynomial models, the logistic model preserved its original shape within the range of the growth period length, making it more appropriate for modeling the cumulative water demand from physical and biological standpoints. By utilizing this model, the water requirement for the intended product can be effortlessly estimated at any given point and within any desired time interval throughout the growth period, spanning from seconds and minutes to days, weeks, months, and beyond. As per the findings of this study, an equation with exceptional precision was introduced for each product in a homogeneous region, where the length of the growth period is consistent. This equation allows for the straightforward and precise estimation of crop water requirements.

The increasing population of the world, the change of style and the limited number of natural resources and energy all make freshwater industrial productions the main contenders for the cost-effective production of freshwater. In this research, the combination of combined cycle power plant (CCPP) using multiple effect distillation (MED) and reverse osmosis (RO) desiccation techniques is investigated through normal and advanced exergy, exergy-economic and exergy-environmental comprehensive analysis. First, CCPP thermodynamic modeling is done using mathematical programming method. Then, a mathematical model is presented to integrate the existing CCPP with MED and RO desalination plants. Finally, the aforementioned normal and advanced analyzes are performed to evaluate the main performance parameters of the integrated CCPP system and MED-RO desalination system, and to identify potential technical, economic, and environmental improvements. A case study is also presented about the Shahid Salimi Neka power plant located in the north of Iran along the Caspian Sea.The mathematical modeling method for this integrated system is solved in "MATLAB" program and its results are validated by "Thermoflex" software. The results show a 3.79% increase in fuel consumption after combining CCPP and water desalination facilities. The exergy efficiency of the advanced system is 42.7% and the highest combustion chamber exergy destruction cost is $1.09 per second. Economic and environmental analyzes of the integrated system also show that gas turbines have the highest investment cost ($0.047 per second). At the same time, the MED system has the highest environmental impact rate, i.e. 0.025 points per second.

This article studies an issue in the fish farming industry in which the goal is to find the best multi-period planning for handling various chains, including ordering, breeding, and selling of trout over a time horizon.

In this study, a new formulation is presented as a mixed integer linear programming model that could find the optimum solution quickly. In the new proposed formulation, some intermediate stages of the breeding chain that do not affect decisions are ignored, and therefore, the size and complexity of the proposed model reduce without compromising the optimality of the answers.

After implementing the proposed model, using different data samples, it can be seen that this model achieves the optimal solution in a short time, including volume and time of spawning in each breeding chain and different periods, harvesting time, and accepting or rejecting the main demands.

Originality/Value:

 In this paper, the issue of scheduling of fish farming chains and sales management, which there are a few studies in this field, has been studied and a new mixed integer linear programming model is presented. Compared to the previous model, this model has more realistic assumptions and less complexity and execution time.

Recently, supply chains and supply networks are developing towards intertwined supply networks. These new, dynamic structures are different from linear supply chains with static structures and require a revision of some traditional concepts. The aim of this research is mathematical modeling of the three-level supply network (including suppliers, firms, customers) based on resilience. Its approach is quantitative and mathematical modeling. In this research, first the problem is modeled and solved using real data in GAMS software, and after determining the optimal values of the decision variables, the results are analyzed. Also, a sensitivity analysis has been performed on the effective parameter (production capacity). The analysis of the results showed that increase of the capacity parameter did not affect the total cost of the network due to the constant demand. The proposed model, while optimizing the intertwined supply networks, is able to strengthen the resilience of the network in the face of disruption. On the other hand, the effectiveness of the proposed approach has been shown by using it in a case study of the intertwined supply network of tiles and ceramics.