Obidio Rubio Mercedes

By Alexis Rodriguez Carranza, Obidio Rubio Mercedes and Elder Joel Varas Peréz

The transfer of energy in turbulent flows occurs as a product of breaking of smaller and smaller eddies, this implies that in a spectral formulation, the transfer occurs from small wavenumbers to large wavenumbers. In order to observe the energy cascading, dissipation scales must be reached, which depend on the Reynolds number, this makes direct simulations of the Navier-Stokes equation impractical. Reduced models were investigated in recent years, such as shell models. Shell models are built by mimicking the spectral model respecting the mechanisms that are preserved, such as energy conservation, scaling and symmetries. In this paper, we will use the Sabra shell model for the study of the energy cascading in turbulent flows and we will show numerically that the energy dissipation is approximately −1/3 which is in agreement with the K41 theory.

Part of the book: Vortex Simulation and Identification

By Dennis Quispe and Obidio Rubio

In this chapter, we apply the exploration of the Euler–Maruyama, Milstein, and Runge–Kutta methods to solve systems of stochastic differential equations associated with the stochastic SIRD model. We simulate sample trajectories of each variable using Python and data collected in Peru during the years 2020 and 2021, marked by the onset of the COVID-19 pandemic. Our research involves comparing stochastic and deterministic systems obtained from the SIRD model in the Peruvian context. We use different values for the intensity of white noise to assess the impact of stochasticity on the dynamics of the SIRD model. Presenting random simulations alongside deterministic ones provides a comprehensive understanding of the effect of randomness in the context of infectious disease modeling.

Part of the book: Stochastic Processes - Theoretical Advances and Applications in Complex Systems [Working title]