We report on the experimental observation of the Fermi–Pasta–Ulam (FPU) recurrence in an experimental bi-modal nonlinear transmission line. The FPU recurrence is observed in the two transmission modes known as the low frequency mode and the high frequency mode. In each case, a spectrum analysis is performed in order to study the waves along the line.

After a few years of calm, the investigations on the dynamic, especially nonlinear, systems returned to the front of the research in non-linear physics. We propose, in this chapter, a study of an electrical nonlinear transmission line, realized in a previous work, to use the latter to highlight certain properties (modulation instability-MI, Fermi-Pasta-Ulam (FPU) recurrence, fragmentation of solitons in wave trains, multiplication(increase) and division of frequencies, etc.), which are observed in several domains in applied physics: hydraulic, artificial neuronal, network physical appearance (physics) of the plasma, and the circulation.

The rapid evolution of technology in the field of wireless telecommunications and micro components using MEMS technologies (Micro-electromechanical systems) has contributed to the expansion and rapid development of wireless sensor networks (WSN). This rapid development has contributed to the appearance of sensor and actuator networks (WSAN) or even to the Internet of Things with DL-IoT (Device Layer-Internet of Things). This rapid evolution of WSN is due to the enthusiasm generated by this last in industry and research. This new technology is used in several applications, particularly in the outdoor location of communicating nodes. The process of distance calculation between nodes (ranging) is a primordial phase for a precise location of these nodes. This paper presents the result of measurements does with three ranging protocols (TWR, TWR_Skew and SDS-TWR) implemented on De-caWiNo nodes. DecaWiNo nodes use the Ultra-Wide Band (UWB) radio links, proposed by the IEEE 802.15.4 standard amendment of the year 2007, which provides a high-performance ranging by ToF (Time of Flight) [1] [2]. The results are very promising with precision errors of the order of 50 cm over 20 meters.

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Senegal is a country of the Sahel. In this region, most of the populations live from agro-pastoral activities. The northern zone of Senegal is strongly influenced by river cultures. And the dynamics of the Senegal River are dependent on rainfall. The rainfall in the area is very closely linked to the dynamics of the atmosphere. The study of the spatio-temporal variability of rainfall in the northern region of Senegal requires quality rainfall observation data. It includes the Ferlo and the Senegal River valley, in particular the regions of Louga (department of Linguère included), Saint-Louis (departments of Dagana and Podor included) and Matam. These stations have been defined since Le Borgne (1988). The difficulty of having quality rain observation data can be resolved by using more accessible and good quality satellite data. Using satellite data, namely MSWEP, CRU, TAMSAT, ARC and PERSIANN, we showed the return of precipitation that appeared in 2000 and the unimodal cycle of precipitation in our study area. These data were validated using the correlation coefficient, the bias, the RMSE and the Nash index with observation data from the Regional Study Center for the Improvement of Adaptation to Drought (CERASS). The CRU data is then retained. Thus, this study made it possible to show the zonal distribution of rainfall in the northern zone of Senegal.