It is traditionally believed that the macroscopic randomness has nothing to do with the micro-level uncertainty. Besides, the sensitive dependence on initial condition (SDIC) of Lorenz chaos has never been considered togetherwith the so-called continuum-assumption of fluid (on which Lorenz equations are based), from physical and statistic viewpoints. A very fine numerical technique [6] with neg...

We analyze the convergence of compressive sensing based sampling techniques for the efficient evaluation of functionals of solutions for a class of high-dimensional, affine-parametric, linear operator equations which depend on possibly infinitely many parameters. The proposed algorithms are based on so-called “non-intrusive” sampling of the high-dimensional parameter space, reminiscent of Monte...

Mechanical systems operate under parametric and external excitation uncertainties. The polynomial chaos approach has been shown to be more efficient than Monte Carlo approaches for quantifying the effects of such uncertainties on the system response. This work uses the polynomial chaos framework to develop new methodologies for the simulation, parameter estimation, and control of mechanical sys...

Identifying the historical data that is the best analog with a pattern from which a forecast is sought allows time series data to be extrapolated. That technique of best analogs is most effective when the data contains underlying deterministic chaos. Here we apply similar techniques, modified to use two space dimensions instead of one time dimension, to fill-in and extrapolate missing image dat...

The development of the new information security systems based on chaos theory represents a new research field in communication and information technology domain. Cryptography is a permanent field of interest at all times. At present secret communication plays an increasing role in many fields of common life, like banking, industry, and telecommunication. In this paper we present some aspects re...

Pettersson, P. 2013. Uncertainty Quantification and Numerical Methods for Conservation Laws. Acta Universitatis Upsaliensis. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1008. 39 pp. Uppsala. ISBN 978-91-554-8569-6. Conservation laws with uncertain initial and boundary conditions are approximated using a generalized polynomial chaos expansi...

Chaos is a nonlinear behavior that shows chaotic and irregular responses to internal and external stimuli in dynamic systems. This behavior usually appears in systems that are highly sensitive to initial condition. In these systems, stabilization is a highly considerable tool for eliminating aberrant behaviors. In this paper, the problem of stabilization and tracking the chaos are investigated....

In this letter, a rigorous solution of the chaotic Lozi mapping is given for some regions of the bifurcation parameters. The relevance of this result is that while chaos has been proved for the Lozi mapping, there has not previously been discussion of the possibility of finding a rigorous formula for this solution. This important result is obtained using the Jordan normal form defined for matri...