Non-smooth dynamical systems arise in many applications, in particular to model mechanical systems subjected to impact or electrical systems with switches. The main goal of the subject is to develop a qualitative theory similar to the one existing for smooth systems. A natural approach to study such systems is the regularization, which produces a family of smooth dynamical systems converging to the initial system in some suitable topology. One of the delicate issues is to establish under which conditions the dynamics of this regularizing family allows to deduce information about the dynamics in the limit non-smooth case. In 2006, Buzzi, Teixeira and da Silva proposed a geometric framework to study such regularization through blowings-up. This framework naturally relates the regularizing families mentioned above to singular perturbation systems defined on manifolds with corners; thus establishing a strong bridge between these two subjects. There is now a large literature on this subject, but mainly limited to the so-called systems of regular type, where the non-smoothness locus is a smooth hypersurface and a single blowing-up suffices. However, there are several cases of interest (such as systems with multiple switches) where such regularity condition fails. In a joint paper from 2018, Panazzolo and da Silva proposed a general theory of geometric regularization for systems of non-regular type. Many basic problems are still open, such as a complete qualitative study of germs of planar vector fields possessing a discontinuity locus of cross type. The main goal of this project is to further explore these subjects, by enhancing the collaboration between the Brazilian team (da Silva and Buzzi) and the French team (Panazzolo, Fruchard). One of our priorities will be to recruit and form a PhD student to work in this subject. We expect to supervise this student in a collaborative way, allowing him/her to make long stays on both universities during the project.

NERC-FAPESP Seedcorn Fund Collaboration Project "Fire-adapted seed traits in Cerrado species" between RHUL (UK) and UNESP (Brazil) Fire is a global phenomenon which together with climate shapes the vegetation of natural and agricultural land. Our interaction with fire is characterised by both positive and negative aspects for mankind. Humans have long used fire including for landscape and weed management, and as tool to improve crop growth on arable land. Controlled fire is necessary to preserve the health and stimulate rejuvenation of wildland ecosystems such as the Brazilian Cerrado, the Mediterranean, as well as UK peatland and moorland. In these fire-prone regions plant regeneration is achieved to a large extent from soil-stored plant seeds. Depending on the species, environment, season and seed properties, the germination of the soil-stored seeds may be stimulated by compounds derived from the smoke or by the fire-generated heat-shock. The aim of the project is to comparatively investigate seeds from species adapted to fire-prone regions to identify novel mechanisms underpinning fire-generated heat-shock and smoke as germination cues. The derived mechanisms will be tested as tools for weed management and crop seed enhancement. Treatment with smoke and various smoke-derived compounds can stimulate the germination of certain weed seeds. This can be used as a weed management tool to deprive the soil from weeds prior to crop seed sowing. We however do not know why this does not work with all weed species, at all ambient conditions (temperature, seasons), and what seed structures and seed coat properties determine the effectiveness of the treatment. Smoke, various smoke-derived compounds, as well as heat-shock treatment can also improve the seed quality and performance of seedling establishment of certain vegetable crops. Again, we do not know what seed structures, seed coat properties and genes are responsible for these effects and why it only works with certain crop species. To advance our knowledge in this topic the leading seed science lab of Royal Holloway University of London (RHUK, United Kingdom) will collaborate with experts for fire vegetation management and Brazilian Cerrado species properties of Sao Paulo State University (UNESP, Brazil). The FAPESP-NERC programme is especially suited to support this collaboration based on the agreement of the two funding agencies. In the project we will investigate seeds of different fire-adapted species to identify novel mechanisms controlling how fire-derived smoke and heat-shock affect their germination, storability, and seedling establishment. This work will be conducted using methods from different science and engineering fields (including molecular biology, microscopy/imaging, biomechanical engineering, physiology) through interdisciplinary collaboration in a comparative approach with many fire-adapted species. This approach will for example identify certain seed coat properties or certain genes associated with the adaptation to fire-derived cues. Seeds of weed and crop species with similar properties/genes will then be used to test if the identified novel mechanism has potential for weed control or improving crop seed quality. The consortium has solid fire vegetation management and agri-technological expertise in these applications to provide solutions for this global challenge in climate change, healthy environment and food security.

Atmospheric CO2 has risen from 280 micro-atmospheres during preindustrial times to 370 micro-atmospheres today. This is predicted to double over the next 100 years if anthropogenic emissions of CO2 continue at their current rate. The microscopic marine algae (the phytoplankton), are able to fix CO2 through photosynthesis and can therefore reduce atmospheric CO2 by drawing it down into the ocean. Photosynthesis involves a series of enzymatic controlled reactions that start with capturing light energy and finish with fixing CO2 to build phytoplankton cells. Some of the fixed carbon is lost through respiration. Marine bacteria, the microscopic animals known as the zooplankton and phytoplankton themselves during the night time respire. The extent to which phytoplankton photosynthesize and fix carbon and the bacteria-zoophytoplankton (or marine plankton) community respires carbon controls whether CO2 is drawn down from the atmosphere to the ocean or is released to the atmosphere from the ocean. The overall objective of this proposal is to improve our understanding of how the marine plankton community in the South Atlantic and the coast of Brazil potentially regulate the atmospheric CO2 concentration. Phytoplankton carbon fixation can be monitored from space using satellite sensors. A new satellite sensor, that has the capability to do this, will be launched by the European Space Agency in autumn 2015. We will use data from this new satellite to study this phenomena in collaboration with a Brazilian Research Institute. The results will benefit both UK and Brazilian research on climate change. The RCUK-FAPESP Lead Agency Agreement is being applied by the applicants

This proposed partnership addresses key challenges in planning for sustainable urban environments. The themes of water and energy are of strategic relevance to development goals in Brazil. The proposed partnership activities will build on an established collaborative knowledge base, bringing together social scientists and engineers with substantial track records in relation to sustainable urban development. In Brazil, the water/energy nexus is a research theme of major importance, due to water scarcity, and since >70% of Brazilian electricity comes from hydroelectricity. Evidence suggests that interventions at different spatio-temporal scales are required to reduce significant impacts-for-development resulting from mismanagement of water/energy resources. The inter-disciplinary project team and proposed activities shall afford innovative forms of dissemination and knowledge exchange between diverse academics, professionals and publics. Planned activities will include publicly-available research summaries, an online research network, the development of an existing app for the Brazilian context, a summer school and theory/practice workshops, and collaborative skills development/sharing. These activities will ensure that the project has extensive impact in Brazil, with potential to deliver long-term benefits in areas of strategic relevance to this call (water/energy), for the welfare of society in diverse developing contexts. Specifically, building upon the project team's existing links, the project will produce impacts in collaboration with NGOs focused upon sustainable development in Latin America and national/regional partners directly involved in the Brazilian water/energy nexus. Finally, the project will support the research team as it develops larger, related collaborative research projects on the crucial theme of water/energy in sustainable urban development.