Mathematics and Mars Exploration

In this study we consider modelization associated with study of solar radiation at the surface of Mars and the Martian atmosphere. In particular, we present elements concerning retrieval of the solar irradiance spectrum on the surface of Mars from data collected by arrays of photodiodes, such as those onboard the “Curiosity” MSL-rover and other missions currently under design. By using these techniques we are able to provide an approximate description of the expected measures. In this work we have also developed a new method of tomography-based signal analysis for detection of events in the Martian atmosphere boundary layer, such as dust devils. In general, this method enables detection of events that occur briefly in time and are localized in space. This tomographic method allows us to identify the presence of more dust devils than detected previously using the same data. Finally we show new scenarios of modelization through fractional differential equations associated with diffusion processes and nonlocal problems. Such approaches could be used to model complex Martian dynamics.