We find a solution of an unknown time-dependent DIFFUSIVITY a(t) in a linear inverse parabolic problem by a modified genetic algorithm. At first, it is shown that under certain conditions of data, there exists at least one solution for unknown a(t) in (a(t), T (x, t)), which is a solution to the corresponding problem. Then, an optimal estimation for unknown a(t) is found by applying the least-squares method and a modified genetic algo rithm. Results show that an excellent estimation can be obtained by the implementation of a modified real-valued genetic algorithm within an Intel Pentium (R) dual-core CPU with a clock speed of 2.4 GHz.

In this paper, a nonlinear inverse problem of parabolic type, is considered. By reducing this inverse problem to a system of Volterra integral EQUATIONs the existence, uniqueness, and stability of the solution will be shown.

Introduction: Theoretical calculations of DIFFUSIVITY into the solids are subjected to a lot of limitations. Consequently in most researches related to the molecular diffusion into the solids and foods, the effective diffusivities are measured by laboratory methods. In this research the effective DIFFUSIVITY of salt into the potato tissues was measured experimentally applying analytical solution of Fick's EQUATIONs in mass transfer.Materials and Methods: The cylindrical samples of potato with 3 cm diameter and 3.5 cm height were immersed into the brine. The surrounding surfaces of the samples were covered by a suitable sealant in order to consider one dimensional mass transfer. Variations in brine concentration and consequently the rate of salt diffusion into the potatoes were calculated by measuring the electrical conductivity of brine.Results: The DIFFUSIVITY of salt into the potato tissues is increased by increase in brine concentrations, but it won’t be remarkable increase at high brine concentrations. The salt concentration in potato tissues reaches to equilibrium in 300 min and then no more diffusion will be occurred. Using the results of experiments and analytical solution of Fick’s law EQUATIONs the DIFFUSIVITY of salt into the potato tissues at 24°C were measured to be (3.45- 4.39) 10-9×m2/s for 1-3% (w/v) brine solutions.Conclusion: According to the results of this research, Fick’s law EQUATIONs in mass transfer and their analytical solutions represented by Crank give a precise explanation of mass transfer in solids. Furthermore, the DIFFUSIVITY of salt in the potato is independent of the variety of potato and consequently different researches have concluded similar results.

Thin layer drying behavior of sweet lemon slice was experimentally investigated in a convective type dryer and the mathematical modeling performed, using thin layer drying models given in literature. Drying experiments were conducted at inlet drying air temperatures of 40, 50, 60, 70 and 80oC; two slice thicknesses of 3 and 6 mm, and, at one drying air velocity of 0.5 m/s with three replications in each treatment. Page model was employed (according to their coefficients of correlation) to estimate the drying curves. The effects of drying air temperature on the model constants and coefficients were evaluated through a non-linear regression technique. The accuracy of the model was estimated according to three statistical parameters of: coefficient of determination (R2), Chi-square (X2) and Root Mean Square Error (RMSE). Results indicated that Page model could satisfactorily describe the drying curve of sweet lemon slices with R2=0.99812, (X2)=0.0000518 and RMSE=0.003912 for a thickness of 3 mm while R2=0.997776, (X2)=0.0000715 and RMSE=0.0082232 for a thickness of 6 mm. Moisture transfer from the slices was described by applying Fick's diffusion model. The effective DIFFUSIVITY coefficient values changed from 8.04x10-9 to 7.63x10-8 m2/s for the range of temperatures considered. An Arrhenius relation with an activation energy value of 28.53 kJ/mol and the DIFFUSIVITY constant of 5.01x 10-4 m2/s for a thickness of 3 mm, while 39.46 kJ/mol along with a DIFFUSIVITY constant of 9.37x10-4 m2/s for a slice thickness of 6 mm, were obtained, indicating the effect of drying air temperature and slice thickness on the DIFFUSIVITY parameter.

An improved model of mud dispersion has been introduced in this work. The advantages of this model consist of a new analytical correlation for dispersivity by using resistivity log data and using a new aspect of capacitance dispersion model. Mathematical formulations were expressed, solved by numerical model taking advantage of actual log and formation data. Achieved results yielded reasonable values and trends which can be used to predict the drilling fluid concentration near wellbore region and interpret the well log data. In comparison with the previous models (Civan and Engler, 1994; Donaldson and Chernoglazov, 1987), this model uses more reasonable data and assumptions making it closer to real conditions.

Reactive barriers are one of the most promising and novel environmental noise barriers. In this case using Schroeder diffusers (e.g. quadratic residue diffusers) on the top surface of the T-shape barrier was shown to significantly improve the performance of absorbent T-shape barriers. The reasons behind the high performance of diffuser barriers are considered in this investigation. A question about the DIFFUSIVITY behavior of Schroeder diffusers when they are utilized on the top of barrier was raised. Diffusion coefficients of a diffuser in different conditions at some receiver locations were predicted by using a 2D boundary element method. It was found that the diffusion coefficient of diffuser at the top of barrier is so small that the DIFFUSIVITY of the structure is almost the same as rigid T-shape barrier. To find the barrier’s cap behavior, the total field above the top surface of profile barriers was also predicted. It was found that the lowest total energy is at the receiver side of the cap very close to the top surface, which could demonstrate the effect of top surface on absorbing the energy as wave transfers from source edge toward the receiver side of the cap. In this case the amount of minimum total energy depends on the frequency and the configuration of the top surface. A comparison between the reductions of total field at the source side of the cap with the improvements of barrier's performance was also done. It was shown that the amount of decrease in total field compared to that of an absorbent barrier "Ref" is directly associated to the amount of improvement in the insertion loss made by the diffuser barrier compared to the "Ref" barrier in the wide area on the ground at the shadow zone. Finally it was concluded that the diffuser on the top of barrier does not act as a diffuser and a kind of similarity between the contribution of diffuser and absorbent material on the top of T-profile barrier is seen.