Short-term effects of human urine fertiliser and wood ash on soil pH and electrical conductivity

The fertiliser value of human urine has been examined on several crops, yet little is known about its effects on key soil properties of agronomic significance. This study investigated temporal soil salinization potential of human urine fertiliser (HUF). It further looked at combined effects of human urine and wood ash (WA) on soil pH, urine-NH_3 volatilisation, soil electrical conductivity (EC), and basic cation contents of two Acrisols (Adenta and Toje series) from the coastal savannah zone of Ghana. The experiment was a factorial design conducted in the laboratory for 12 weeks. The results indicated an increase in soil pH by 1.2 units for Adenta series and 1 unit for Toje series after one week of HUF application followed by a decline by about 2 pH units for both soil types after twelve weeks. This was attributed to nitrification of ammonium to nitrate leading to acidification. The EC otherwise increased with HUF application creating slightly saline conditions in Toje series and non-saline conditions in Adenta series. When WA was applied with HUF, both soil pH and EC increased. In contrast, the HUF alone slightly salinized Toje series, but both soils remained non-saline whenWA and HUF were applied together. The application ofWA resulted in two-fold increase in Ca, Mg, K, and Na content compared to HUF alone. Hence, WA is a promising amendment of acid soils and could reduce the effect of soluble salts in human urine fertilizer, which is likely to cause soil salinity.

Time Discretization of the SST-generalized Navier-Stokes Equations: Positive and Negative Results

In the theory of the Navier-Stokes equations, the proofs of some basic known results, like for example the uniqueness of solutions to the stationary Navier-Stokes equations under smallness assumptions on the data or the stability of certain time discretization schemes, actually only use a small range of properties and are therefore valid in a more general context. This observation leads us to introduce the concept of SST spaces, a generalization of the functional setting for the Navier-Stokes equations. It allows us to prove (by means of counterexamples) that several uniqueness and stability conjectures that are still open in the case of the Navier-Stokes equations have a negative answer in the larger class of SST spaces, thereby showing that proof strategies used for a number of classical results are not sufficient to affirmatively answer these open questions. More precisely, in the larger class of SST spaces, non-uniqueness phenomena can be observed for the implicit Euler scheme, for two nonlinear versions of the Crank-Nicolson scheme, for the fractional step theta scheme, and for the SST-generalized stationary Navier-Stokes equations. As far as stability is concerned, a linear version of the Euler scheme, a nonlinear version of the Crank-Nicolson scheme, and the fractional step theta scheme turn out to be non-stable in the class of SST spaces. The positive results established in this thesis include the generalization of classical uniqueness and stability results to SST spaces, the uniqueness of solutions (under smallness assumptions) to two nonlinear versions of the Euler scheme, two nonlinear versions of the Crank-Nicolson scheme, and the fractional step theta scheme for general SST spaces, the second order convergence of a version of the Crank-Nicolson scheme, and a new proof of the first order convergence of the implicit Euler scheme for the Navier-Stokes equations. For each convergence result, we provide conditions on the data that guarantee the existence of nonstationary solutions satisfying the regularity assumptions needed for the corresponding convergence theorem. In the case of the Crank-Nicolson scheme, this involves a compatibility condition at the corner of the space-time cylinder, which can be satisfied via a suitable prescription of the initial acceleration.