Artículos con la etiqueta ‘Dinámica y caos’

Frontiers of chaotic advection

Por • 13 mar, 2014 • Category: Leyes

We review the present position of and survey future perspectives in the physics of chaotic advection; the field that emerged three decades ago at the intersection of fluid mechanics and nonlinear dynamics, which encompasses a range of applications with length scales ranging from micrometers to hundreds of kilometers, including systems as diverse as mixing and thermal processing of viscous fluids, micro-fluidics, biological flows, and large-scale dispersion of pollutants in oceanographic and atmospheric flows.

Symbolic Toolkit for Chaos Explorations

Por • 27 oct, 2013 • Category: Ciencia y tecnología

New computational technique based on the symbolic description utilizing kneading invariants is used for explorations of parametric chaos in a two exemplary systems with the Lorenz attractor: a normal model from mathematics, and a laser model from nonlinear optics. The technique allows for uncovering the stunning complexity and universality of the patterns discovered in the bi-parametric scans of the given models and detects their organizing centers — codimension-two T-points and separating saddles.

Production and Transfer of Energy and Information in Hamiltonian Systems

Por • 9 oct, 2013 • Category: Ambiente

We present novel results that relate energy and information transfer with sensitivity to initial conditions in chaotic multidimensional Hamiltonian systems. We show the relation among Kolmogorov – Sinai entropy, Lyapunov exponents, and upper bounds for the Mutual Information Rate calculated in the Hamiltonian phase space and on bi-dimensional subspaces. Our main result is that the net amount of transfer from kinetic to potential energy per unit of time is a power-law of the upper bound for the Mutual Information Rate between kinetic and potential energies, and also a power-law of the Kolmogorov – Sinai entropy. Therefore, transfer of energy is related with both transfer and production of information. However, the power-law nature of this relation means that a small increment of energy transferred leads to a relatively much larger increase of the information exchanged. Finally, a relation between our results and important quantities of Thermodynamics is presented.

What Are the New Implications of Chaos for Unpredictability?

Por • 9 oct, 2013 • Category: Ciencia y tecnología

From the beginning of chaos research until today, the unpredictability of chaos has been a central theme. It is widely believed and claimed by philosophers, mathematicians and physicists alike that chaos has a new implication for unpredictability, meaning that chaotic systems are unpredictable in a way that other deterministic systems are not. Hence one might expect that the question ‘What are the new implications of chaos for unpredictability?’ has already been answered in a satisfactory way. However, this is not the case. I will critically evaluate the existing answers and argue that they do not fit the bill. Then I will approach this question by showing that chaos can be defined via mixing, which has not been explicitly argued for. Based on this insight, I will propose that the sought-after new implication of chaos for unpredictability is the following: for predicting any event all sufficiently past events are approximately probabilistically irrelevant.