Integrated and holistic approach of water resources management is important for sustainability. Since the optimum use of water resources needs taking into account different environmental issues. Accordingly, the use of supportive models in decision making as an effective tool is significantly important. To addressing uncertainty in crop water allocation, several methodologies have been proposed. The most of these models consider rainfall as a stochastic variable affecting soil moisture. Applying a new methodology/model while considering the stochastic variable in nonnormal state and uncertainties for both irrigation depth and soil moisture looks more realistic. In this research, a mathematical model was developed based on Constraint-State equation optimization model and Beta function. The first and the second moments of soil moisture are used as constraints in optimization process. This model uses the soil moisture budget equation for a specific plant (winter wheat) on a weekly basis, considering the root depth, soil moisture, irrigation depth, rainfalls, evapotranspiration, leaching depth, soil physical properties and a stochastic variable. The model was written in MATLAB and was run for winter wheat in Badjgah, south of Iran. The results were compared with the results obtained from a simulation model. Based on the results, the optimum net irrigation depth of winter wheat including the rainfall was 306.2 mm. The insignificant difference of simulation and optimization results showed that, the optimization model works properly and is acceptable for optimization of irrigation depth, as its reliability index is 96.86 %.

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A 1D totally asymmetric exclusion process consisting of classical particles with next-nearestneighbor interactions has been considered on a discrete lattice with a ring geometry. Using large deviation techniques, we have investigated fluctuations of particle current in the system. In the twoparticle sector, we have obtained the large deviation function of the particle current. In this sector, we have also found the effective potential that the particles experience when an atypical particle current is generated. Numerical results in the three-particle sector have also been presented.

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In order to study the stochastic Markov processes conditioned on a specific value of a timeintegrated observable, the concept of ensembles of trajectories is recently used extensively. In this paper we consider a generic reaction-diffusion process consisting of classical particles with nearestneighbor interactions on a one-dimensional lattice with periodic boundary conditions. By introducing a time-integrated current as a physical observable, we have found certain constraints on the microscopic transition rates of the process under which the effective process contains local interactions; however, with rescaled transition rates comparing to the original process. A generalization of the linear Glauber model is then introduced and studied in detail as an example. Associated effective dynamics of this model is investigated and constants of motion are obtained.