In this study, by Laplace transform method, the analytical solution of the pollution TRANSPORT EQUATION in the limited domain for the river network to the upstream and downstream Dirichlet boundary conditions, and the initial condition of zero was extracted, and simulation was performed for two branch and loop networks with fixed and variable boundary conditions. After naming the nodes, by forming matrices of how to connect, flow characteristics and geometry of the river for each network as input to the problem, the diffusion matrix is created based on a function of the Laplace variable, which The value of the concentration in each node is calculated by solving the complex device created and using the inverse Laplace transform. Then, using the analytical solution extracted in a branch of the river for the pollution transfer EQUATION, the analytical solution can calculate the value of pollution concentration at any desired location and time along with the river network. Finally, for validation, the analytical solution was compared with the numerical solution, and then the statistical error indices were calculated. The results indicate the optimal performance and high ability of analytical solution in modeling the two networks and its good adaptation to the numerical solution, which can replace numerical solution due to high accuracy and speed of calculations. Generally, due to common errors in numerical solutions such as numerical dispersion error, Round-off error, Truncation error of Taylor expansion mathematical sentences, analytical solutions, if any, for the river network are recommended over numerical solutions. Also, in the performed simulations, due to the change of the inlet flow and the flow cross-section to each, changes in the pollution concentration occur in the areas where the branches connect to each other, increasing or decreasing. The proposed analytical solution for river networks can model more complex river networks and can be considered a criterion for the validation of numerical solutions. Also, the existing analytical solution can be used as a tool to validate other analytical solutions in the river network.

For preventing groundwater and soil from heavy metal contamination and/or to decrease contamination, and to clean up the former disposal sites from these metals, one must be beforehand able to predict the movement of these pollutants in soils. In this research in order to describe Cadmium [Cd (II)] TRANSPORT in soils, we incorporated an equilibrium-kinetic two-site model into the convection-dispersion EQUATION for reactive solutes under steady state water flow conditions in uniform soils. Also the irreversible retention of Cd (II) was described as a first-order kinetic process. For an assessment of Cd (II) movement in soils, five samples with different physical and chemical properties were collected and taken to the laboratory. Miscible displacement experiments were conducted with disturbed soil columns. Model parameters were obtained by fitting model to the experimental data resulting from miscible displacement experiments using a nonlinear least squares (best fit) parameter optimization scheme. The model was applicable in predicting Cd (II) BTCs for different soils representing a broad array of soil properties. By putting these parameters into the model, concentration and retention of Cd (II) with time and depth were calculated for different soils.

Air TRANSPORT system has always been involved in all aspects of life because of its high potential in TRANSPORTing passengers and goods. In this research we surveys the effects of travel variables on demand of domestic air TRANSPORT, and for gathering required information from passengers, a questionnaire was designed including 20 effective parameters on air TRANSPORT demand with questions These parameters were investigated based on their importance using “ Factor Analysis” and finally proved that the factors “ price paid by passengers” , ” services offered by air TRANSPORT system” and “ time” has had the greatest impact on air TRANSPORT demand with more than 20 % influence. “ Structural EQUATION Modeling” has been used for checking the “ Factor Analysis” results. The results of the model proved the correctness of factor analysis. Furthermore, the result of factor analysis has showed that the most important parameter has been “ low cost travel” with the factor load of 0. 9-1 in all case studies. Results show that both groups with factor load of more than 0. 5 in the obtained factors have identified the factor “ services” as the important and effective factor with the influence value of more than 20%.

Today, most of the surface water and groundwater resources are exposed to contamination by different materials sewage. because most of the methods have been used to restore the pollution intensity function for groundwater, representing a method to restore pollution intensity function in rivers with more complex flow conditions is considerable. this research aim is to calculate the intensity function of the contamination source, by the numerical solution of group preserving scheme, which has not been observed in other researches done so far. Group preserving scheme is an accurate method to solve ill-posed problems. By implementing this method the one-dimensional advection-dispersion EQUATION with variable coefficients has been solved. The principle of the introduced backward solution method is that by solving the dynamic systems in negative time steps, a general EQUATION will be obtained, which can solve ordinary differential EQUATIONs. The responses of this EQUATION will lead to convergence of the EQUATION and prevent the divergence of the data. three examples have been presented to show the accuracy of the forward and backward group preserving scheme, Firstly, using direct solutions of the river, the intensity of pollution concentration in the river is calculated, and the implicit finite difference method is applied to verify the accuracy of the direct solutions. In the direct method, the results of the two models were compared with statistical indexes in order to demonstrate the conformity of the two models. In the next step, by solving the backward group preserving scheme in two different examples, the concentration of pollutants upstream is simulated. Following the simulation and verification of the inverse model by direct solution, statistical indexes are used to evaluate the effectiveness of this method.

Rivers are one of the most important natural water resources in the world. Pollution TRANSPORT modeling in rivers is performed by the partial advection-dispersion-reaction EQUATION (ADRE). In the present study, using the Laplace transform, which is a powerful and useful tool in solving differential EQUATIONs, the analytical solution of the ADRE EQUATION was obtained in a finite domain with variable coefficients for the upstream and downstream Dirichlet boundary conditions and the initial zero condition in the river. To use the analytical solution in this study, three examples are presented, each of which, the river are divided into two, four, and eight parts, which, while the parameters of flow, pollution, and river geometry are variable in all three examples, for each of the examples, the accuracy of the analytical solution available when the segmentation of the intervals increases as compared to the numerical solution. By specifying the matrices of velocity, dispersion coefficient, cross-section, etc. as input to the problem, the diffusion matrix is calculated and, consequently, a complex system of EQUATIONs is created that doubles the complexity of the work. The amount of pollutant concentration is calculated by solving the system of the above EQUATIONs. The numerical solution is used to validate the existing analytical solution, the results showed that the greater the number of river divisions, the higher the accuracy of the solution, and the two analytical and numerical solutions will be well compatible with each other. Given the ability and performance of the existing analytical solution, it can be acknowledged that the analytical solution in this study can be used as a tool to validate and verification numerical solutions and other analytical solutions for the coefficients of the EQUATION.

In this research, the analytical solution to bi-dimensional Advection-Dispersion-EQUATION was obtained in the finite domain at the open channels using Generalized Integral Transform Technique (GITT). The upstream boundary condition was considered Dirichlet type with arbitrary and irregular time pattern of the entrance concentration. The downstream, right and left bank boundary condition was considered zero gradient. The initial condition function was assumed in the general form. The Evaluation of the derived solution was performed using two hypothetical examples and by comparing the results with the analytical solution resulting from the Green’ s Function Method (GFM). In this way, in the first example, the entrance concentration from the upstream boundary was assumed zero and the initial condition function was considered impulsive at the specific point at the domain. At the second example, the irregular time pattern function of the entrance concentration from the upstream boundary and impulsive initial condition function was considered simultaneously. The results of both examples were compared with the results of GFM and the concentration contours at different times were presented. The results show good agreement between the proposed solution and the GFM solution and report the performance of the proposed solutions is satisfactory and accurate. The proposed analytical solution has high flexibility in adopting the various functions as the initial and boundary conditions. So it is very applicable and useful for verification of the two-dimensional complex numerical models.

In this research, a model is developed for the optimal design of storm water networks.The model uses the powerful genetic algorithm as the search engine. The "TRANSPORT" module of "SWMM 4.4h" is used as the hydraulic analyzer of the model. Two different approach are used to formulate the problem with varying degrees of success in reaching a "near optimal" solution. The proposed model is applied to some benchmark examples in the literature leading to achieve good solution compared to previous results.

Contamination TRANSPORT in the river is expressed using advection-dispersion-reaction partial differential EQUATION (ADRE). There are a variety of analytical and numerical methods for solving the aforementioned EQUATION. Analytical solutions such integral transforms are very powerful and useful tools in solving ADRE. In the present study, one-dimensional ADRE with space-dependent coefficients in river has been solved using generalized integral transform technique (GITT). Forward and inverse transformations are defined in GITT technique which using them in problem solving leads to generating time-dependent system of ordinary differential EQUATIONs. Analytical solution verification was accomplished using the comparison of the results of mathematical models with analytical solutions and also numerically model based on finite differences method. To inspect the accuracy of models’ results, statistical indicators were calculated. Comparison of GITTs’ result with analytical solutions that used in verification and numerical solution implied high accuracy of the proposed solution. Also to show the importance of the application of variable coefficients in ADRE in river, the results of solving EQUATION with constant and variable coefficients were compared.