Conselho Nacional de Desenvolvimento Científico e Tecnológico / This study employed different autocorrelation functions and Maclaurin series expansions in the derivation of expressions describing the dissipation rate of turbulent kinetic energy. These expressions have the same functional form, but are described in terms of different numerical coefficients. The values obtained for the numerical coefficients were used in a Lagrangian stochastic dispersion model to simulate the dispersion of contaminants in the Planetary Boundary Layer (PBL). The simulation results were compared with concentration data observed in the Copenhagen experiment. The good performance of the parameterization and analysis through statistical indices showed that the mathematical relationships that describe the turbulent dissipation rate present an uncertainty. The analysis developed in this study indicates that there is no a universal functional form describing the dissipation rate of turbulent energy. / Neste estudo foram empregadas diferentes funções de autocorrelação e expansões em série de Maclaurin na derivação de expressões que descrevem a taxa de dissipação da energia cinética turbulenta. Estas expressões apresentam a mesma forma funcional, porém são descritas em termos de diferentes coeficientes numéricos. Os valores obtidos para os coeficientes numéricos foram empregados em um modelo de dispersão estocástico Lagrangiano para simular a dispersão de contaminantes na Camada Limite Planetária (CLP). Os resultados das simulações foram comparados com dados de concentração do experimento de Copenhagen. O bom desempenho da parametrização e a análise através de índices estatísticos permitiram concluir que as relações matemáticas que descrevem a taxa de dissipação da turbulenta, apresentam uma incerteza. A análise desenvolvida nesse estudo permite concluir que não existe uma forma funcional universal descrevendo a taxa de dissipação de energia turbulenta.

Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits non-trivial temporal decay of velocity autocorrelation functions. This means that the corresponding dynamics is characterized by memory effects that slowly decay in time. Motivated by this we construct non-Markovian lattice-gas cellular automata models for moving agents with memory. For this purpose the reorientation probabilities are derived from velocity autocorrelation functions that are given a priori; in that respect our approach is “data-driven”. Particular examples we consider are velocity correlations that decay exponentially or as power laws, where the latter functions generate anomalous diffusion. The computational efficiency of cellular automata combined with our analytical results paves the way to explore the relevance of memory and anomalous diffusion for the dynamics of interacting cell populations, like confluent cell monolayers and cell clustering.

Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits non-trivial temporal decay of velocity autocorrelation functions. This means that the corresponding dynamics is characterized by memory effects that slowly decay in time. Motivated by this we construct non-Markovian lattice-gas cellular automata models for moving agents with memory. For this purpose the reorientation probabilities are derived from velocity autocorrelation functions that are given a priori; in that respect our approach is “data-driven”. Particular examples we consider are velocity correlations that decay exponentially or as power laws, where the latter functions generate anomalous diffusion. The computational efficiency of cellular automata combined with our analytical results paves the way to explore the relevance of memory and anomalous diffusion for the dynamics of interacting cell populations, like confluent cell monolayers and cell clustering.