Cyril Fleurant

Dissolution on Titan and on Earth: Toward the age of Titan's karstic landscapes

Titans polar surface is dotted with hundreds of lacustrine depressions. Based on the hypothesis that they are karstic in origin, we aim at determining the efficiency of surface dissolution as a landshaping process on Titan, in a comparative planetology perspective with the Earth as reference. Our approach is based on the calculation of solutional denudation rates and allow inference of formation timescales for topographic depressions developed by chemical erosion on both planetary bodies. The model depends on the solubility of solids in liquids, the density of solids and liquids, and the average annual net rainfall rates. We compute and compare the denudation rates of pure solid organics in liquid hydrocarbons and of minerals in liquid water over Titan and Earth timescales. We then investigate the denudation rates of a superficial organic layer in liquid methane over one Titan year. At this timescale, such a layer on Titan would behave like salts or carbonates on Earth depending on its composition, which means that dissolution processes would likely occur but would be 30 times slower on Titan compared to the Earth due to the seasonality of precipitation. Assuming an average depth of 100 m for Titans lacustrine depressions, these could have developed in a few tens of millions of years at polar latitudes higher than 70°N and S, and a few hundreds of million years at lower polar latitudes. The ages determined are consistent with the youth of the surface (<1 Gyr) and the repartition of dissolution-related landforms on Titan.

Mathematics for Earth Science and Geography: Introductory Course with Practical Exercises and R/Xcas Resources

This undergraduate textbook presents a unique comprehensive overview on Mathematics in Earth Sciences and Geography. It deals with fundamental theoretical and applied mathematics, needed by bachelor students in a wide range of subjects. The book is illustrated with many examples and over a hundred practical exercises, with solutions included in the book. In addition, this textbook highlights numerical resources by using two free software packages (R and Xcas) and introducing their use.

Integration and Differential Equations

This chapter focuses on two fundamental function-related tools that are frequently used in Earth science and geography: integration and differential equations. Partial differential equations are presented very summarily to indicate to the reader their existence, but their study goes beyond the scope of this chapter and book.

Quantities and Measures

In geography as in Earth science, data are quantified, and numbers need to be manipulated constantly. This chapter deals with a base 10 system and a sexagesimal numeral system (for the use of time and angles). It deals with the concepts of measurement, unit, and approximate value (rounded, significant digits, uncertainties), as well as unit conversions, percentages, and rates. It also discusses scientific notation and the powers of ten. These notions are fundamental in applied science. The exercises show various contexts, for example, flow, planets, temperature, and albedo.

Trigonometry, Geometry of Plane and Space

In geography and Earth science, the use of geometric considerations is frequent, whether in a plane or in space. The use of angles is particularly important and leads to the introduction of notions of trigonometry as well as the functions cosine, sine, and tangent.

Variables and Functions

Geographers and Earth science specialists are confronted with phenomena that they try to apprehend and formalize by identifying the variables involved and the relations among them. This chapter introduces the notions of variables and functions (as a link between variables). These functions provide fundamental information to geographers and Earth science specialists, enabling them to study and conceptualize these phenomena.