different methods arising from scientific investigation for removing noise from chaotic signals have been introduced and one of their best is local projection approach. the local projection approach projects the chaotic data in the neighborhood onto the hyper-plane. selection of neighborhood radius has a direct impact on its performance. a noticeable feature associated with chaotic trajectories...

A new class of experiments that probe folding of individual protein domains uses mechanical stretching to cause the transition. We show how stretching forces can be incorporated in lattice models of folding. For fast folding proteins, the analysis suggests a complex relation between the force dependence and the reaction coordinate for folding.

We used force-clamp atomic force microscopy to measure the end-to-end length of the small protein ubiquitin during its folding reaction at the single-molecule level. Ubiquitin was first unfolded and extended at a high force, then the stretching force was quenched and protein folding was observed. The folding trajectories were continuous and marked by several distinct stages. The time taken to f...

Fluid mixing controls many natural and industrial processes, including the spread of air pollution1, mass transfer and reactions in microfluidic devices2,3 and the detection of odours or other chemical signals4. Strongly nonlinear flows enhance mixing by chaotic advection5,6, stretching and folding7,8 fluid volumes. Though these processes have been studied in simple models9,10, stretching and f...

Complex flows mix efficiently, and this process can be understood by considering the stretching and folding of material volumes. Although many metrics have been devised to characterize stretching, fewer are able to capture folding in a quantitative way in spatiotemporally variable flows. Here, we extend our previous methods based on the finite-time curving of fluid-element trajectories to nonze...