Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields

In the present study we consider planar piecewise linear vector fields with two zones separated by the straight line $x=0$. Our goal is to study the existence of simultaneous crossing and sliding limit cycles for such a class of vector fields. First, we provide a canonical form for these systems assuming that each linear system has center, a real one for $y<0$ and a virtual one for $y>0$, and such that the real center is a global center. Then, working with a first order piecewise linear perturbation we obtain piecewise linear differential systems with three crossing limit cycles. Second, we see that a sliding cycle can be detected after a second order piecewise linear perturbation. Finally, imposing the existence of a sliding limit cycle we prove that only one adittional crossing limit cycle can appear. Furthermore, we also characterize the stability of the higher amplitude limit cycle and of the infinity. The main techniques used in our proofs are the Melnikov method, the Extended Chebyshev systems with positive accuracy, and the Bendixson transformation.Comment: 24 pages, 7 figure

Combustion instability research Summary report, 1970

Combustion instability in liquid rocket engine

Summary of combustion instability research at Princeton University, 1969

Control and causes of combustion instability in rocket engine

Norine, the knowledgebase dedicated to nonribosomal peptides, is now open to crowdsourcing

International audienceSince its creation in 2006, Norine remains the unique knowledgebase dedicated to non-ribosomal pep-tides (NRPs). These secondary metabolites, produced by bacteria and fungi, harbor diverse interesting biological activities (such as antibiotic, anti-tumor, siderophore or surfactant) directly related to the diversity of their structures. The Norine team goal is to collect the NRPs and provide tools to analyze them efficiently. We have developed a user-friendly interface and dedicated tools to provide a complete bioinformatics platform. The knowledgebase gathers abundant and valuable annotations on more than 1100 NRPs. To increase the quantity of described NRPs and improve the quality of associated annotations , we are now opening Norine to crowdsourc-ing. We believe that contributors from the scientific community are the best experts to annotate the NRPs they work on. We have developed MyNorine to facilitate the submission of new NRPs or modifications of stored ones. This article presents MyNorine and other novelties of Norine interface released since the first publication. Norine is freely accessible from the following URL: http://bioinfo.lifl.fr/NRP

Calibração de psicrômetros para avaliações de potencial hídrico foliar.

bitstream/item/71982/1/ID-30949.pd