Testing of subgrid scale (SGS) models for large-eddy simulation (LES) of turbulent channel flow

Sub-grid scale (SGS) models are required in order to model the influence of the unresolved small scales on the resolved scales in large-eddy simulations (LES), the flow at the smallest scales of turbulence. In the following work two SGS models are presented and deeply analyzed in terms of accuracy through several LESs with different spatial resolutions, i.e. grid spacings. The first part of this thesis focuses on the basic theory of turbulence, the governing equations of fluid dynamics and their adaptation to LES. Furthermore, two important SGS models are presented: one is the Dynamic eddy-viscosity model (DEVM), developed by \cite{germano1991dynamic}, while the other is the Explicit Algebraic SGS model (EASSM), by \cite{marstorp2009explicit}. In addition, some details about the implementation of the EASSM in a Pseudo-Spectral Navier-Stokes code \cite{chevalier2007simson} are presented. The performance of the two aforementioned models will be investigated in the following chapters, by means of LES of a channel flow, with friction Reynolds numbers $Re_\tau=590$ up to $Re_\tau=5200$, with relatively coarse resolutions. Data from each simulation will be compared to baseline DNS data. Results have shown that, in contrast to the DEVM, the EASSM has promising potentials for flow predictions at high friction Reynolds numbers: the higher the friction Reynolds number is the better the EASSM will behave and the worse the performances of the DEVM will be. The better performance of the EASSM is contributed to the ability to capture flow anisotropy at the small scales through a correct formulation for the SGS stresses. Moreover, a considerable reduction in the required computational resources can be achieved using the EASSM compared to DEVM. Therefore, the EASSM combines accuracy and computational efficiency, implying that it has a clear potential for industrial CFD usage.

Local and nonlocal integro-differential reaction-diffusion models for protein dynamics in Alzheimer's disease

In this work, integro-differential reaction-diffusion models are presented for the description of the temporal and spatial evolution of the concentrations of Abeta and tau proteins involved in Alzheimer's disease. Initially, a local model is analysed: this is obtained by coupling with an interaction term two heterodimer models, modified by adding diffusion and Holling functional terms of the second type. We then move on to the presentation of three nonlocal models, which differ according to the type of the growth (exponential, logistic or Gompertzian) considered for healthy proteins. In these models integral terms are introduced to consider the interaction between proteins that are located at different spatial points possibly far apart. For each of the models introduced, the determination of equilibrium points with their stability and a study of the clearance inequalities are carried out. In addition, since the integrals introduced imply a spatial nonlocality in the models exhibited, some general features of nonlocal models are presented. Afterwards, with the aim of developing simulations, it is decided to transfer the nonlocal models to a brain graph called connectome. Therefore, after setting out the construction of such a graph, we move on to the description of Laplacian and convolution operations on a graph. Taking advantage of all these elements, we finally move on to the translation of the continuous models described above into discrete models on the connectome. To conclude, the results of some simulations concerning the discrete models just derived are presented.

Machine Learning methods for hepatocellular malignancies segmentation and MVI prediction

The aim of this thesis project is to automatically localize HCC tumors in the human liver and subsequently predict if the tumor will undergo microvascular infiltration (MVI), the initial stage of metastasis development. The input data for the work have been partially supplied by Sant'Orsola Hospital and partially downloaded from online medical databases. Two Unet models have been implemented for the automatic segmentation of the livers and the HCC malignancies within it. The segmentation models have been evaluated with the Intersection-over-Union and the Dice Coefficient metrics. The outcomes obtained for the liver automatic segmentation are quite good (IOU = 0.82; DC = 0.35); the outcomes obtained for the tumor automatic segmentation (IOU = 0.35; DC = 0.46) are, instead, affected by some limitations: it can be state that the algorithm is almost always able to detect the location of the tumor, but it tends to underestimate its dimensions. The purpose is to achieve the CT images of the HCC tumors, necessary for features extraction. The 14 Haralick features calculated from the 3D-GLCM, the 120 Radiomic features and the patients' clinical information are collected to build a dataset of 153 features. Now, the goal is to build a model able to discriminate, based on the features given, the tumors that will undergo MVI and those that will not. This task can be seen as a classification problem: each tumor needs to be classified either as “MVI positive” or “MVI negative”. Techniques for features selection are implemented to identify the most descriptive features for the problem at hand and then, a set of classification models are trained and compared. Among all, the models with the best performances (around 80-84% ± 8-15%) result to be the XGBoost Classifier, the SDG Classifier and the Logist Regression models (without penalization and with Lasso, Ridge or Elastic Net penalization).

Anisotropic seismic tomography with the reversible jump Markov chain Monte Carlo

The established isotropic tomographic models show the features of subduction zones in terms of seismic velocity anomalies, but they are generally subjected to the generation of artifacts due to the lack of anisotropy in forward modelling. There is evidence for the significant influence of seismic anisotropy in the mid-upper mantle, especially for boundary layers like subducting slabs. As consequence, in isotropic models artifacts may be misinterpreted as compositional or thermal heterogeneities. In this thesis project the application of a trans-dimensional Metropolis-Hastings method is investigated in the context of anisotropic seismic tomography. This choice arises as a response to the important limitations introduced by traditional inversion methods which use iterative procedures of optimization of a function object of the inversion. On the basis of a first implementation of the Bayesian sampling algorithm, the code is tested with some cartesian two-dimensional models, and then extended to polar coordinates and dimensions typical of subduction zones, the main focus proposed for this method. Synthetic experiments with increasing complexity are realized to test the performance of the method and the precautions for multiple contexts, taking into account also the possibility to apply seismic ray-tracing iteratively. The code developed is tested mainly for 2D inversions, future extensions will allow the anisotropic inversion of seismological data to provide more realistic imaging of real subduction zones, less subjected to generation of artifacts.

ICE Emissions Estimation through Machine-learning techniques to support real-world R&D experiments

The emissions estimation, both during homologation and standard driving, is one of the new challenges that automotive industries have to face. The new European and American regulation will allow a lower and lower quantity of Carbon Monoxide emission and will require that all the vehicles have to be able to monitor their own pollutants production. Since numerical models are too computationally expensive and approximated, new solutions based on Machine Learning are replacing standard techniques. In this project we considered a real V12 Internal Combustion Engine to propose a novel approach pushing Random Forests to generate meaningful prediction also in extreme cases (extrapolation, very high frequency peaks, noisy instrumentation etc.). The present work proposes also a data preprocessing pipeline for strongly unbalanced datasets and a reinterpretation of the regression problem as a classification problem in a logarithmic quantized domain. Results have been evaluated for two different models representing a pure interpolation scenario (more standard) and an extrapolation scenario, to test the out of bounds robustness of the model. The employed metrics take into account different aspects which can affect the homologation procedure, so the final analysis will focus on combining all the specific performances together to obtain the overall conclusions.