A majority of methods from dynamical system analysis, especially those in applied settings, rely on Poincare's geometric picture that focuses on "dynamics of states." While this picture has fueled our field for a century, it has shown difficulties in handling high-dimensional, ill-described, and uncertain systems, which are more and more common in engineered systems design and analysis of "big data" measurements. This overview article presents an alternative framework for dynamical systems, based on the "dynamics of observables" picture. The central object is the Koopman operator: an infinite-dimensional, linear operator that is nonetheless capable of capturing the full nonlinear dynamics. The first goal of this paper is to make it clear how methods that appeared in different papers and contexts all relate to each other through spectral properties of the Koopman operator. The second goal is to present these methods in a concise manner in an effort to make the framework accessible to researchers who would like to apply them, but also, expand and improve them. Finally, we aim to provide a road map through the literature where each of the topics was described in detail. We describe three main concepts: Koopman mode analysis, Koopman eigenquotients, and continuous indicators of ergodicity. For each concept, we provide a summary of theoretical concepts required to define and study them, numerical methods that have been developed for their analysis, and, when possible, applications that made use of them. The Koopman framework is showing potential for crossing over from academic and theoretical use to industrial practice. Therefore, the paper highlights its strengths in applied and numerical contexts. Additionally, we point out areas where an additional research push is needed before the approach is adopted as an off-the-shelf framework for analysis and design. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4772195
An emerging field of plasma medicine is discussed, where non-equilibrium plasmas are shown to be able to initiate, promote, control, and catalyze various complex behaviors and responses in biological systems. More importantly, it will be shown that plasma can be tuned to achieve the desired medical effect, especially in medical sterilization and treatment of different kind of skin diseases. Wound healing and tissue regeneration can be achieved following various types of plasma treatment in a multitude of wound pathologies. Non-equilibrium plasmas will be shown to be non-destructive to tissue, safe, and effective in inactivation of various parasites and foreign organisms.
Plant response to drought is complex, so that traits adapted to a specific drought type can confer disadvantage in another drought type. Understanding which type(s) of drought to target is of prime importance for crop improvement. Modelling was used to quantify seasonal drought patterns for a check variety across the Australian wheatbelt, using 123 yr of weather data for representative locations and managements. Two other genotypes were used to simulate the impact of maturity on drought pattern. Four major environment types summarized the variability in drought pattern over time and space. Severe stress beginning before flowering was common (44% of occurrences), with (24%) or without (20%) relief during grain filling. High variability occurred from year to year, differing with geographical region. With few exceptions, all four environment types occurred in most seasons, for each location, management system and genotype. Applications of such environment characterization are proposed to assist breeding and research to focus on germplasm, traits and genes of interest for target environments. The method was applied at a continental scale to highly variable environments and could be extended to other crops, to other drought-prone regions around the world, and to quantify potential changes in drought patterns under future climates.
An integrated, selective interlayer structure is developed to further mitigate the diffusion of polysulfides, simply by coating the surface of a C–S cathode with a graphene/TiO 2 film. It is found that the application of the graphene/TiO 2 film as an interlayer enables the porous carbon nanotubes–S cathode to exhibit a high reversible specific capacity and extraordinarily excellent cycling stability.