Generalized hydrodynamics of a (1+1)-dimensional integrable scattering theory with roaming trajectories

The emergence of hydrodynamic features in off-equilibrium (1 + 1)-dimensional integrable quantum systems has been the object of increasing attention in recent years. In this Master Thesis, we combine Thermodynamic Bethe Ansatz (TBA) techniques for finite-temperature quantum field theories with the Generalized Hydrodynamics (GHD) picture to provide a theoretical and numerical analysis of Zamolodchikov’s staircase model both at thermal equilibrium and in inhomogeneous generalized Gibbs ensembles. The staircase model is a diagonal (1 + 1)-dimensional integrable scattering theory with the remarkable property of roaming between infinitely many critical points when moving along a renormalization group trajectory. Namely, the finite-temperature dimensionless ground-state energy of the system approaches the central charges of all the minimal unitary conformal field theories (CFTs) M_p as the temperature varies. Within the GHD framework we develop a detailed study of the staircase model’s hydrodynamics and compare its quite surprising features to those displayed by a class of non-diagonal massless models flowing between adjacent points in the M_p series. Finally, employing both TBA and GHD techniques, we generalize to higher-spin local and quasi-local conserved charges the results obtained by B. Doyon and D. Bernard [1] for the steady-state energy current in off-equilibrium conformal field theories.

The Libor Market Model: from theory to calibration

This thesis is focused on the financial model for interest rates called the LIBOR Market Model. In the appendixes, we provide the necessary mathematical theory. In the inner chapters, firstly, we define the main interest rates and financial instruments concerning with the interest rate models, then, we set the LIBOR market model, demonstrate its existence, derive the dynamics of forward LIBOR rates and justify the pricing of caps according to the Black’s formula. Then, we also present the Swap Market Model, which models the forward swap rates instead of the LIBOR ones. Even this model is justified by a theoretical demonstration and the resulting formula to price the swaptions coincides with the Black’s one. However, the two models are not compatible from a theoretical point. Therefore, we derive various analytical approximating formulae to price the swaptions in the LIBOR market model and we explain how to perform a Monte Carlo simulation. Finally, we present the calibration of the LIBOR market model to the markets of both caps and swaptions, together with various examples of application to the historical correlation matrix and the cascade calibration of the forward volatilities to the matrix of implied swaption volatilities provided by the market.

Numerical study on viscoelastic behavior of polypropylene fiber reinforced concrete subjected to temperature variations using LDPM theory

This thesis is focused on the viscoelastic behavior of macro-synthetic fiber-reinforced concrete (MSFRC) with polypropylene studied numerically when subjected to temperature variations (-30 oC to +60 oC). LDPM (lattice discrete particle model), a meso-scale model for heterogeneous composites, is used. To reproduce the MSFRC structural behavior, an extended version of LDPM that includes fiber effects through fiber-concrete interface micromechanics, called LDPM-F, is applied. Model calibration is performed based on three-point bending, cube, and cylinder test for plain concrete and MSFRC. This is followed by a comprehensive literature study on the variation of mechanical properties with temperature for individual fibers and plain concrete. This literature study and past experimental test results constitute inputs for final numerical simulations. The numerical response of MSFRC three-point bending test is replicated and compared with the previously conducted experimental test results; finally, the conclusions were drawn. LDPM numerical model is successfully calibrated using experimental responses on plain concrete. Fiber-concrete interface micro-mechanical parameters are subsequently fixed and LDPM-F models are calibrated based on MSFRC three-point bending test at room temperature. Number of fibers contributing crack bridging mechanism is computed and found to be in good agreement with experimental counts. Temperature variations model for individual constituents of MSFRC, fibers and plain concrete, are implemented in LDPM-F. The model is validated for MSFRC three-point bending stress-CMOD (crack mouth opening) response reproduced at -30 oC, -15 oC, 0 oC, +20 oC, +40 oC and +60 oC. It is found that the model can well describe the temperature variation behavior of MSFRC. At positive temperatures, simulated responses are in good agreement. Slight disagreement in negative regimes suggests an in-depth study on fiber-matrix interface bond behavior with varying temperatures.