This article gives a short and elementary presentation of random evolutions toward applications in reliability and quality engineering. At first, the following two examples are presented: dynamical stochastic systems and increment processes both in Markov media. A dynamical system in continuous time is presented since nowadays they are widely used in dynamic reliability modeling. Limit theorems...

We consider the gradient flow associated to the following functionals Fm(φ) = ∫ M 1 + |∇ν| dμ . The functionals are defined on hypersurfaces immersed in R via a map φ : M → R, where M is a smooth closed and connected n–dimensional manifold without boundary. Here μ and ∇ are respectively the canonical measure and the Levi–Civita connection on the Riemannian manifold (M, g), where the metric g is...

Motivated by the physics of quark-gluon plasma created in heavy-ion collision experiments, we use holography to study regime applicability various theories relativistic viscous hydrodynamics. Using microscopic description provided a system that relaxes equilibrium, obtain initial data with which perform real-time evolutions 2+1 dimensional conformal fluids using first-order hydrodynamics theory...