Banca de QUALIFICAÇÃO: LUCAS MONTE DE CASTRO ALENCAR

Uma banca de QUALIFICAÇÃO de DOUTORADO foi cadastrada pelo programa.
DISCENTE: LUCAS MONTE DE CASTRO ALENCAR
DATA: 14/07/2025
HORA: 08:30
LOCAL: Remota
TÍTULO: Kinetic Flat-Histogram Simulations of Non-Equilibrium Stochastic Processes with Continuous and Discontinuous Phase Transitions
PALAVRAS-CHAVES: ALGORITMO MONTE-CARLO CINÉTICO, SIMULAÇÃO ESTOCÁSTICA EXATA, ALGORITMO WANG-LANDAU, PROCESSOS ESTOCÁSTICOS, TRANSIÇÕES DE FASE FORA DO EQUILÍBRIO.
PÁGINAS: 11
GRANDE ÁREA: Ciências Exatas e da Terra
ÁREA: Física
RESUMO:

As far as we know, there is no flat-histogram algorithm to sample the stationary
distribution of non-equilibrium stochastic processes. The present work addresses this gap by
introducing a generalization of the Wang-Landau algorithm, applied to non-equilibrium
stochastic processes with local transitions. The main idea is to sample macroscopic states using a
kinetic Monte Carlo algorithm to generate trial moves, which are accepted or rejected with a
probability that depends inversely on the stationary distribution. The stationary distribution is
refined through the simulation by a modification factor, leading to convergence toward the true
stationary distribution. A visitation histogram is also accumulated, and the modification factor is
updated when the histogram satisfies a flatness condition. The stationary distribution is obtained
in the limit where the modification factor reaches a threshold value close to unity. To test the
algorithm, we compare simulation results for several stochastic processes with theoretically
known behavior. In addition, results from the kinetic flat-histogram algorithm are compared with
standard exact stochastic simulations. We show that the kinetic flat-histogram algorithm can be
applied to phase transitions in stochastic processes with bistability, which describe a wide range
of phenomena such as epidemic spreading, population growth, chemical reactions, and

consensus formation. With some adaptations, the kinetic flat-histogram algorithm can also be
applied to stochastic models on lattices and complex networks.

MEMBROS DA BANCA:
Interno - 1446938 - FRANCISCO WELINGTON DE SOUSA LIMA
Externo ao Programa - 936.***.***-06 - GLADSTONE DE ALENCAR ALVES - UESPI
Interno - 1654258 - PAULO RENATO SILVA DE CARVALHO
Presidente - 1650556 - TAYRONI FRANCISCO DE ALENCAR ALVES