We present channel length and stream order for possible fluvial channels present in Cassini Synthetic Aperture Radar (SAR) data from Ta to T19. These features are present at most latitudes observed, with the bulk of the channels located in near-equatorial latitudes. Many of them are also organized into four branching channel networks, three of third order and one of fourth order, similar to river systems on Earth and Mars. These networks appear well integrated, with few streams that are not incorporated into the higher order branches. The median channel length for all channels on Titan is 29 km, with the longest channels all being incorporated into the channel networks. Estimates of channel width and depth of 1 km and 100m respectively result in a channel volume of 1012 m3 which, when extrapolated to the entire surface of Titan results in 1013 m3 of sediment.

Two objectives are achieved in this thesis: (1) to develop a new method to measure the pH-dependent net surface charge of soils and (2) to determine if, by a combination of the surface charge evaluated by potentiometric titration and ion adsorption, we can separate the permanent charge, generated by the isomorphous substitution, from the variable charge. First, a laboratory procedure, using backtitration, was developed for the measurement of the pH-dependent net surface charge. This method was tested on ten soil horizons from Gleysols and Podzols. It appears that the pH-dependent net surface charge, measured by this technique, shows good agreement with that measured by ion adsorption. It is also possible, with this method, to identify some plateaus and inflection points in the backtitration curve associated with protonation/deprotonation reactions of specific soil components. Secondly, it was demonstrated that it is possible to increase the surface charge of montmorillonite with Al-oxide coatings under specific conditions.

In this thesis, we solve for (equivariant) Gromov-Witten theories of some important classes of surfaces and threefolds, and study their relationships to other brances of mathematics. The first object is the class of P2-bundles over a smooth curve C of genus g. Our bundles are of the form P(L0 + L1 +L2) for arbitrary line bundles L0, L1 and L2 over C. We compute the partition functions of these invariants for all classes of the form s + nf, where s is a section, f is a fiber and n is an integer. In the case where the class is Calabi-Yau, i.e., K • (s + nf) = 0,the partition function is given by 3g (2sin u/2) 2g-2 As an application, one can obtain a series of full predictions for the equivariant Donaldson Thomas invariants for this family of non-toric threefolds. Secondly, we compute the C-equivariant quantum cohomology ring of Y, the minimal resolution of the DuVal singularity C2 /G where G is a finite subgroup of SU(2). The quantum product is expressed in terms of an ADE root system canonically associated to G. We generalize the resulting Frobenius manifold to non-simply laced root systems to obtain an n parameter family of algebra structures on the affine root lattice of any root system. Using the Crepant Resolution Conjecture, we obtain a prediction for the orbifold Grornov-Witten potential of [C2 /G]. Thirdly, for a polyhedral group G, that is a finite subgroup of S0(3), we completely determine the Gromov-Witten theory of Nakamura's G- Hilbert scheme, which is a preferred Calabi-Yau resolution of the polyhedral singularity C3/G. The classical McKay correspondence determines the (classical) cohomology of this resolution in terms of the representation theory of G. We express the Cromov-Witten potential in terms of an ADE root system associated to G. As an application, we use the Crepant Resolution Conjecture to provide a full prediction for the orbifold Grornov-Witten invariants of [C3/G]. Finally, in the case that G is the group A4 or Z2 x Z2, we compute the integral of Ag on the Hurwitz locus HG C Mg of curves admitting a degree 4 cover of P1 having monodromy group G. We compute the generating functions for these integrals and write them as a trigonometric expression summed over the positive roots of the E6 and D4 root systems respectively. As an application, we prove the Crepaut Resolution Conjecture for the orbifolds [C3/A4] and [C3/(Z2 x Z2)].

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