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.

Tutte's 5-flow conjecture

The aim of this thesis is to show and put together the results, obtained so far, useful to tackle a conjecture of graph theory proposed in 1954 by William Thomas Tutte. The conjecture in question is Tutte's 5-flow conjecture, which states that every bridgeless graph admits a nowhere-zero 5-flow, namely a flow with non-zero integer values between -4 and 4. We will start by giving some basics on graph theory, useful for the followings, and proving some results about flows on oriented graphs and in particular about the flow polynomial. Next we will treat two cases: graphs embeddable in the plane $\mathbb{R}^2$ and graphs embeddable in the projective plane $\mathbb{P}^2$. In the first case we will see the correlation between flows and colorings and prove a theorem even stronger than Tutte's conjecture, using the 4-color theorem. In the second case we will see how in 1984 Richard Steinberg used Fleischner's Splitting Lemma to show that there can be no minimal counterexample of the conjecture in the case of graphs in the projective plane. In the fourth chapter we will look at the theorems of François Jaeger (1976) and Paul D. Seymour (1981). The former proved that every bridgeless graph admits a nowhere-zero 8-flow, the latter managed to go even further showing that every bridgeless graph admits a nowhere-zero 6-flow. In the fifth and final chapter there will be a short introduction to the Tutte polynomial and it will be shown how it is related to the flow polynomial via the Recipe Theorem. Finally we will see some applications of flows through the study of networks and their properties.

Philosophy of quantum field theory: an introduction with interviews and comments

In this thesis, I address quantum theories and specifically quantum field theories in their interpretive aspects, with the aim of capturing some of the most controversial and challenging issues, also in relation to possible future developments of physics. To do so, I rely on and review some of the discussions carried on in philosophy of physics, highlighting methodologies and goals. This makes the thesis an introduction to these discussions. Based on these arguments, I built and conducted 7 face-to-face interviews with physics professors and an online survey (which received 88 responses from master's and PhD students and postdoctoral researchers in physics), with the aim of understanding how physicists make sense of concepts related to quantum theories and to find out what they can add to the discussion. Of the data collected, I report a qualitative analysis through three constructed themes.