We present in this paper a useful strategy to solve stochastic partial differential equations (SPDEs) involving stochastic coefficients. Using the Wick-product of higher order and the Wiener-Itô chaos expansion, the SPDEs is reformulated as a large system of deterministic partial differential equations. To reduce the computational complexity of this system, we shall use a decomposition-coordina...

Ant colony optimization algorithm (ACO) is a heuristic bionic evolutionary system based on the population. The positive feedback of ACO helps to search the approximate optimal solution, however, it also makes it easier to get trapped in local optimal solution. In order to avoid prematurity and enhance its adaptability, this paper introduces chaos principle in ACO and proposes an adaptive chaoti...

“Plus que jamais, la recherche me paraissait s’identifier à la nature humaine. En exprimer l’appétit, le désir de vivre. C’était bien le meilleur moyen trouvé par l’homme de braver le chaos de l’univers. De dominer la mort.” (More than ever, scientific research seemed to me to be intrinsic to human nature. It expressed the hunger, the desire to live. It has, in fact, been the best means found b...

Congenital High Airways Obstruction Syndrome (CHAOS) is a rare condition associated with high fetal or neonatal mortality. Prenatal diagnosis in the second trimester is made by the typical ultrasound features of large echogenic lungs, a flattened or inverted diaphragm, and fetal ascites or hydrops. We present two cases diagnosed at our institution; one in the second trimester, and a first trime...

A new concept, namely the critical predictable time Tc, is introduced to give a more precise description of computed chaotic solutions of non-linear differential equations: it is suggested that computed chaotic solutions are unreliable and doubtable when t > Tc. This provides us a strategy to detect reliable solution from a given computed result. In this way, the computational phenomena, such a...

In this paper a new concept, namely the critical predictable time Tc, is introduced to give a more precise description of computed chaotic solutions of nonlinear differential equations: it is suggested that computed chaotic solutions are unreliable and doubtable when t > Tc. This provides us a strategy to detect reliable solution from a given computed result. In this way, the computational phen...

We show that initial data near an unperturbed stable plane wave can evolve into a regime of spatiotemporal chaos in the slightly forced conservative periodic one-dimensional nonlinear Schrödinger equation. Statistical measures are employed to demonstrate that this spatiotemporal chaos is intermittent: there are windows in time for which the solution gains spatial coherence. The parameters and i...

The occurrence of chaos in basic Lotka-Volterra models of four competing species is studied. A brute-force numerical search conditioned on the largest Lyapunov exponent indicates that chaos occurs in a narrow region of parameter space but is robust to perturbations. The dynamics of the attractor are studied using symbolic dynamics, and the question of self-organized critical behavior (scale-inv...

In this paper, we propose a numerical method based on Wiener Chaos expansion and apply it to solve the stochastic Burgers and Navier–Stokes equations driven by Brownian motion. The main advantage of the Wiener Chaos approach is that it allows for the separation of random and deterministic effects in a rigorous and effective manner. The separation principle effectively reduces a stochastic equat...