NEW METHODS IN THE STUDY OF PROBLEMS IN STATISTICAL MECHANICS AND STOCHASTIC PROCESSES
This thesis is focused on the development of advanced computational tools for prediction and control of scientific phenomena. The work is divided into two well defined parts. In the first part, our aim is to control the phase diagram of the ternary system composed of water, gelatin and maltodextrin, which is a water in water emulsion of great importance in food production. We develop a numerical approach, based on the Flory-Huggins (FH) theory, with an application of a Neural Network (NN) non-linear regression. The result of this part is to provide the FH-parameters that best describe the ternary system of interest. In the second part, we focus on Random differential Equations (RDE). These type of RDE turn to be equivalent to the very well known and very old (RVT) problem of the transformation of a Random Variable (RV) into another RV under the action of a given mapping function g. Our contribution provides a new mathematical description of functions that allows to easily find all the pre-images of a given function g in the case of non-invertible g. With this mathematical tool, we can easily solve the RVT problem for the general case. Then, our theoretical contribution can be implemented to produce a very effective and precise algorithm to solve the above mentioned RDE with a very low computational cost.
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