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BCAMSevero Ochoa Award

basque center for applied mathematics

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Rusconi, Simone

Thesis

  • Probabilistic Modelling of Classical and Quantum Systems

    Date:
    14-06-2018
    University:
    UPV/EHU - University of the Basque Country
    Country:
    Spain
    File:
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    Comments:
    While probabilistic modelling has been widely used in the last decades, the quantitative prediction in stochastic modelling of real physical problems remains a great challenge and requires sophisticated mathematical models and advanced numerical algorithms.
    In this study, we developed the mathematical tools for solving three long-standing problems in Polymer Science and Quantum Measurement theory.
    The question, “Why kinetic models cannot reproduce experimental observations in Controlled Radical Polymerization (CRP)?” has been answered by introducing in the kinetic model a delay and treating CRP as a non-Markovian process. The efficient stochastic simulation (SS) approach allowing for an accurate description of CRP has been formulated, theoretically grounded and tested using experimental data and the less advanced SS algorithms.
    An accurate prediction of a morphology development in multi-phase polymers is vital for synthesis of new materials but still not feasible due to its complexity. We proposed a Population Balance Equations (PBE)-based model and derived a conceptually new and computationally tractable numerical approach for its solution in order to provide a systematic tool for a morphology prediction in composite polymers.
    Finally, we designed a stochastic simulation framework for continuous measurements performed on quantum systems of theoretical and experimental interest, which helped us to re-examine the “fuzzy continuous measurements” theory by Audretsch and Mensky (1997) and expose some of its deficiencies, while making amendments where necessary.
    All developed modelling approaches are general enough to be applied to the broad range of physical applications and thus ultimately to contribute to the understanding and prediction of complex chemical and physical processes.
  • Mathematical Modeling of Controlled Radical Polymerization

    Date:
    29-04-2014
    University:
    Politecnico di Milano
    Country:
    Italy
    File:
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    Comments:
    Controlled radical polymerization (CRP) is a process to form polymers by successive monomers additions. This growing process is mainly made by three events: propagation, if the next monomer is linearly added to the chain, backbiting, when the free radical changes its position and a new branch will start growing perpendicular to the previous one, and termination, if the chain stops to grow. We have proposed a model describing the CRP process and offered two different approaches for solving it: Partial Differential Equations solutions (PDE) and stochastic simulation algorithm based on Monte Carlo estimations (MC). In this work, the model and the two approaches are summarized and their benefits as well as drawbacks are discussed. Then, we realize that both the approaches can not explain some particular experimental results. MC method’s flexibility allows us to modify the model, varying the hypothesis on which it is built, in order to give an explanation to those experimental results.
Eusko Jaurlaritza - Gobierno Vasco ikerbasque - Basque Foundation for Science Bizkaia xede. Bizkaiko Foru Aldundia innobasque - Agencia vasca de la innovación Universidad del PaÃŒs Vasco (UPV/EHU)