Calculation of the eigenfunctions of the two-group neutron diffusion equation and application to modal decomposition of BWR instabilities

In this thesis, numerical methods aiming at determining the eigenfunctions, their adjoint and the corresponding eigenvalues of the two-group neutron diffusion equations representing any heterogeneous system are investigated. First, the classical power iteration method is modified so that the calculation of modes higher than the fundamental mode is possible. Thereafter, the Explicitly-Restarted Arnoldi method, belonging to the class of Krylov subspace methods, is touched upon. Although the modified power iteration method is a computationally-expensive algorithm, its main advantage is its robustness, i.e. the method always converges to the desired eigenfunctions without any need from the user to set up any parameter in the algorithm. On the other hand, the Arnoldi method, which requires some parameters to be defined by the user, is a very efficient method for calculating eigenfunctions of large sparse system of equations with a minimum computational effort. These methods are thereafter used for off-line analysis of the stability of Boiling Water Reactors. Since several oscillation modes are usually excited (global and regional oscillations) when unstable conditions are encountered, the characterization of the stability of the reactor using for instance the Decay Ratio as a stability indicator might be difficult if the contribution from each of the modes are not separated from each other. Such a modal decomposition is applied to a stability test performed at the Swedish Ringhals-1 unit in September 2002, after the use of the Arnoldi method for pre-calculating the different eigenmodes of the neutron flux throughout the reactor. The modal decomposition clearly demonstrates the excitation of both the global and regional oscillations. Furthermore, such oscillations are found to be intermittent with a time-varying phase shift between the first and second azimuthal modes.

Excited state energy surfaces of flexible emitters for thermally activated delayed fluorescence

Organic Light-Emitting Diodes (OLEDs) technology has matured over recent years, reaching the commercialization level and being used in various applications. The required efficiency can be achieved by transforming triplet excitons into singlet states via Reverse InterSystem Crossing (RISC), which a general mechanism called thermally activated delayed fluorescence (TADF). Two prototypical molecules in the field, 2CzBN and 4CzBN, Carbazole Benzonitrile (donor-acceptor) derivatives, possess similar energy gap between singlet and triplet (∆EST, a key parameter in the RISC rate), but different TADF performance. In this sense, other parameter must be considered to explain these different behaviors. In this work, we theoretically investigate 2CzBN and 4CzBN and address the problem of how flexible donor-acceptor (D-A) or donor-acceptor-donor (D-A-D) molecular architectures affect the nature of excited state, and the oscillator strength. Furthermore, we analyze the RISC rates as a function of the conformation of the carbazole side groups, considering the S0, S1, T1 and T2 states. The oscillator strength of 4CzBN is higher than of 2CzBN, which, in turn, is almost vanishing, resulting in only 4CzBN being a TADF active molecule. We also note the presence of a second triplet state T2 lower in energy than S1, and that the reorganization energies, associated to the RISC processes involving T1 and T2, are both important factor in differentiating the rates in 2CzBN and 4CzBN. However, the 4CzBN RISC rate from T2 to S1 is surprisingly high with respect to the one from T1 to S1, although, according to EL-Sayed rules, since T2 (CT/LE) is more similar to S1 (CT) than in 2CzBN (LE, CT), this transition should be less favored. These insights are important to understand the photophysics of the TADF process and to design novel TADF emitters based on the benzo-carbazole architecture.