DEFESA DE TESE DE DOUTORADO #455 – GUILHERME EDUARDO FREIRE OLIVEIRA – 03/02/2026

We investigate nonequilibrium pattern formation in a binary driven diffusive system composed of repulsive A and B particles. We first propose a hybrid model that combines elements of the driven Widom–Rowlinson lattice gas (DWRLG) and its associated statistical field theory, introduced by Dickman and Zia (2018), and Lavrentovich, Dickman and Zia (2021). Using Monte Carlo simulations, we show that the resulting driven Widom–Rowlinson field-based lattice model(DWRFLM) successfully captures most of the phenomenology previously reported: For zero external drive, the system undergoes a transition from a fully disordered to a fully ordered phase, whereas for nonzero external drive, it displays a structured disordered phase (microemulsion) at low densities and stripes perpendicular to the drive at high densities. In addition, we identify an intermediate-density regime characterized by irregular stripes, which was not reported in earlier studies. A continuum description of the DWRFLM is constructed byapplying a gradient expansion to the mean mass-transfer equations and supplementing the resulting dynamics with additive noise. The corresponding field theory is expressed in terms of the charge and density, defined as the difference and sum of the densities of A and B particles, respectively. While consistent with the field theory developed by Lavrentovich, Dickman and Zia (2021) for the low-density phase, the present formulation includes additional terms that are necessary at high densities. To study the resulting stochastic partial differential equations, we develop a numerical pseudospectral solver, the PyPSpecBR Python library, that is first validated in well-established models from the literature, including Model B and Active Model B. The PyPSpecBR library constitutes an original by-productof this thesis. We find remarkable agreement between the phenomenology of the continuum field theory and the behavior previously observed in the lattice models. In particular, we highlight the central role played by the velocity difference between the charge and density fields in generating the periodic structures observed in both the low- and high-density regimes. This work demonstrates how the interplay between external drive, repulsive interactions, and noise gives rise to a rich phenomenology in strongly driven binary mixtures.