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.

Photovoltaic solar panels (PVP) are energy renewable systems capable of converting solar energy into electrical energy. These panels are formed by sets of photovoltaic (PV) cells that need sunlight to produce electrical energy.However, an excess of solar energy provides an increase in temperature on the cells surface, reducing the life and efficiency of these systems. The output power performance of a PV module decreases on average 0.5%/°C when it works above its ideal temperature, in most cases being 25°C [1]. Conventional cooling techniques, such as the use of natural air convection, are reaching their limits. Thus, it is essential to develop alternative cooling systems using liquids, to avoid overheating and possible failure of the devices. Single-phase flows, two-phase flows and nanofluids (NFs) are potential candidates to replace air-cooling techniques [2,3]. Generally, heat exchangers, serpentine type, are coupled to PV modules in order to reduce their operating temperature and consequently improving their power and efficiency. Despite the research efforts in developing new heat exchangers, still there is a need to improve their thermal performance. In addition, to the thermal efficiency, it essential to verify whether the energy expenses for pumping the fluids and the implementation costs with extra accessories is an efficient option for these systems. The main objective of this project is to develop an innovative heat exchanger for cooling a PVP through the flow of thermofluids by means of forced convection in order to prevent the nominal operating temperature of the PV cells from exceeding the maximum allowed and thus not losing efficiency. This proposal will first test pure water as a cooling fluid and in a second stage other alternative thermofluids will used such as glycol and NFs [3–6]. The main novelty and uniqueness of this project is the application of polydimethylsiloxane (PDMS) to fabricate the heat exchanger system. PDMS is a low cost, transparent and versatile material that allows the incorporation of materials with high thermal properties. Although the thermal conductivity (TC) of pure PDMS is low, it can be extremely increased by the incorporation of materials having high thermal properties [7-10]. Another important characteristic of PDMS, is its ability to mold itself to a specific surface and as a result increases the physical contact between the heat exchanger and the material to be cooled, unlike the conventional heat exchangers, such as those made of circular geometries [11]. For instance, a recent work has shown that a serpentine-type heat exchanger, made of stainless steel with a tubular geometry, did not show satisfactory performance when using pure water in forced flow to cool down a PV module [11]. By using the proposed PDMS heat exchanger this problem will be overcome and the cooling efficiency will be significantly increased. The preparation of the PDMS is a simple procedure that does not require clean rooms or specialized human technical skills and consists of a mixture of a pre-polymer plus a curing agent, where its mechanical properties can be changed according to the proportions adopted. As PDMS has a low TC, this project will incorporate high TC materials into the PDMS to increase its TC and consequently intensify the heat exchange when in contact with the PVP. The combination of the PDMS with materials having high thermal properties (such as carbon based nano/macro particles or industrial wastes from metallurgy plants) is extremely simple to be performed and can be added during the curing process [7-10,12,13].For the design and fabrication of the serpentine molds, numerical simulations and 3D printing will be used, allowing, in a simple way, to optimize the geometry and size of the flow channels. In summary, the main advantages of the proposed PDMS serpentine-type heat exchanger are as follows: low cost and simple fabrication; can be easily molded and attached to the PV system; the geometry can be easily modified; ability to have rectangular cross section that will increase the area available for exchanging heat with the thermofluid; easy to incorporate high TC materials into the PDMS that will significantly increase its TC; PDMS can be transparent and as result it will be possible to perform flow and thermal detailed studies improve the heat exchange efficiency. In this proposal there are many concepts and research fields involved and as a result it is essential to have a multidisciplinary research team (see Fig.1 in figures.pdf). Hence, this project team combines the expertise of the project leader in NFs and heat transfer [3, 6, A, B] with the knowledge of waste management [C], micro and nanofluidics [6, D], PDMS composites [E] and numerical simulation [A]. In addition, the center for waste valorisation (CVR) that is a technological interface center fully dedicated to the industrial waste selection and nanomaterials recovery will play an important role in this project. Os painéis solares fotovoltaicos (PVP) são sistemas de energia renovável capazes de converter a energia solar em energia elétrica. Eles são formados por conjuntos de células fotovoltaicas (PV) que precisam da luz solar para produzir energia elétrica. No entanto, um excesso de energia solar proporciona um aumento de temperatura na superfície das células, reduzindo a vida útil e a eficiência desses sistemas. O desempenho da potência de saída de um módulo fotovoltaico diminui em média 0,5%/°C quando trabalha acima de sua temperatura ideal [1]. As técnicas convencionais de arrefecimento, como o uso da convecção natural a ar, estão atingindo seus limites. Assim, é fundamental desenvolver sistemas alternativos de refrigeração utilizando líquidos, para evitar superaquecimento e possível falha dos dispositivos. Escoamentos monofásicos e bifásicos e nanofluidos (NFs) são potenciais candidatos a substituir as técnicas de arrefecimento a ar [2,3]. Geralmente, os trocadores de calor (TC) do tipo serpentina são acoplados aos módulos fotovoltaicos com o objetivo de reduzir sua temperatura de operação e consequentemente melhorar sua potência e eficiência. Apesar dos esforços das pesquisas no desenvolvimento de novos TC, ainda há necessidade de melhorar seu desempenho térmico. Além da eficiência térmica, é fundamental verificar se os gastos com energia para bombeamento dos fluidos e os custos de implantação com acessórios extras é uma opção eficiente para esses sistemas. O principal objetivo deste projeto é desenvolver um TC inovador para resfriamento de um PVP através do fluxo de termofluidos por meio de convecção forçada, a fim de evitar que a temperatura nominal de operação das células fotovoltaicas ultrapasse a máxima permitida e, assim, não perca eficiência. Esta proposta testará primeiro a água pura como fluido de arrefecimento e, em uma segunda etapa, outros termofluidos alternativos serão usados, como glicol e NFs [3-6]. A principal novidade deste projeto é a aplicação do polidimetilsiloxano (PDMS) para fabricar o sistema trocador de calor. O PDMS é um material de baixo custo, transparente e versátil que permite a incorporação de materiais com altas propriedades térmicas. Embora a condutividade térmica (CT) do PDMS puro seja baixa, ela pode ser extremamente aumentada pela incorporação de materiais com altas propriedades térmicas [7-10]. Outra característica importante do PDMS, é sua capacidade de se moldar a uma superfície específica e com isso aumentar o contato físico entre o TC e o material a ser arrefecido, diferentemente dos TC convencionais, como os de geometrias circulares [11]. Por exemplo, um trabalho recente mostrou que um TC do tipo serpentina, feito de aço inoxidável com geometria tubular, não apresentou desempenho satisfatório ao usar água em fluxo forçado para resfriar um módulo fotovoltaico [11]. Ao usar o trocador de calor PDMS proposto, este problema será superado e a eficiência de arrefecimento será significativamente aumentada. A preparação do PDMS é um procedimento simples que não requer salas limpas ou habilidades técnicas especializadas e consiste em uma mistura de um pré-polímero mais um agente de cura, onde suas propriedades mecânicas podem ser alteradas de acordo com as proporções adotadas. Como o PDMS possui baixa CT, este projeto irá incorporar materiais de alta CT no PDMS para aumentar seu CT e consequentemente intensificar a troca de calor quando em contato com o PVP. A combinação do PDMS com materiais com altas propriedades térmicas é extremamente simples de ser realizada e pode ser adicionada durante o processo de cura [7–10,12,13]. Para o projeto e fabricação dos moldes em serpentina, serão utilizadas simulações numéricas e impressão 3D, permitindo, de forma simples, otimizar a geometria e o tamanho dos canais de escoamento. Assim, as principais vantagens do trocador de calor tipo serpentina PDMS proposto são: baixo custo e fabricação simples; pode ser facilmente moldado e fixado ao sistema fotovoltaico; a geometria pode ser facilmente modificada; capacidade de ter seção transversal retangular que aumentará a área disponível para troca de calor com o termofluido; fácil de incorporar materiais de alto CT no PDMS; o PDMS pode ser transparente e, como resultado, será possível realizar estudos detalhados de escoamento e térmicos para melhorar a eficiência da troca de calor. Nesta proposta há muitos conceitos e campos de pesquisa envolvidos e como resultado é essencial ter uma equipe de pesquisa multidisciplinar (ver Fig.1 em figures.pdf). Assim, esta equipe combina a experiência do líder do projeto em NFs e transferência de calor [3, 6, A, B] com o conhecimento de gerenciamento de resíduos [C], micro e nanofluídica [6, D], compósitos PDMS [E] e simulação numérica [A]. Além disso, o centro de valorização de resíduos (CVR) que é um centro de interface tecnológica totalmente dedicado à seleção de resíduos industriais e recuperação de nanomateriais terá um papel importante neste projeto.

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