Robust Preconditioners for Incompressible MHD Models

In this paper, we develop two classes of robust preconditioners for the structure-preserving discretization of the incompressible magnetohydrodynamics (MHD) system. By studying the well-posedness of the discrete system, we design block preconditioners for them and carry out rigorous analysis on their performance. We prove that such preconditioners are robust with respect to most physical and discretization parameters. In our proof, we improve the existing estimates of the block triangular preconditioners for saddle point problems by removing the scaling parameters, which are usually difficult to choose in practice. This new technique is not only applicable to the MHD system, but also to other problems. Moreover, we prove that Krylov iterative methods with our preconditioners preserve the divergence-free condition exactly, which complements the structure-preserving discretization. Another feature is that we can directly generalize this technique to other discretizations of the MHD system. We also present preliminary numerical results to support the theoretical results and demonstrate the robustness of the proposed preconditioners

Suppression of methane uptake by precipitation pulses and long-term nitrogen addition in a semi-arid meadow steppe in northeast China

In the context of global change, the frequency of precipitation pulses is expected to decrease while nitrogen (N) addition is expected to increase, which will have a crucial effect on soil C cycling processes as well as methane (CH4) fluxes. The interactive effects of precipitation pulses and N addition on ecosystem CH4 fluxes, however, remain largely unknown in grassland. In this study, a series of precipitation pulses (0, 5, 10, 20, and 50 mm) and long-term N addition (0 and 10 g N m-2 yr-1, 10 years) was simulated to investigate their effects on CH4 fluxes in a semi-arid grassland. The results showed that large precipitation pulses (10 mm, 20 mm, and 50 mm) had a negative pulsing effect on CH4 fluxes and relatively decreased the peak CH4 fluxes by 203-362% compared with 0 mm precipitation pulse. The large precipitation pulses significantly inhibited CH4 absorption and decreased the cumulative CH4 fluxes by 68-88%, but small precipitation pulses (5 mm) did not significantly alter it. For the first time, we found that precipitation pulse size increased cumulative CH4 fluxes quadratically in both control and N addition treatments. The increased soil moisture caused by precipitation pulses inhibited CH4 absorption by suppressing CH4 uptake and promoting CH4 release. Nitrogen addition significantly decreased the absorption of CH4 by increasing NH4+-N content and NO3–-N content and increased the production of CH4 by increasing aboveground biomass, ultimately suppressing CH4 uptake. Surprisingly, precipitation pulses and N addition did not interact to affect CH4 uptake because precipitation pulses and N addition had an offset effect on pH and affected CH4 fluxes through different pathways. In summary, precipitation pulses and N addition were able to suppress the absorption of CH4 from the atmosphere by soil, reducing the CH4 sink capacity of grassland ecosystems

Structural Studies of Ternary Mixture Lipid Multilayer Systems and the Effect of High Hydration with X-ray Diffraction

Phase separated lipid mixtures systems have been of vast interest due to their possible relationship with lipid raft formation which is believed to facilitate certain protein activities and is associated with important biological processes. While a lipid multilayer system serve as an ideal system for high resolution structural studies with X-ray scattering techniques and has mostly been used to obtain an averaged result for pure or mixed systems (e.g., proteins, peptides in membrane), we have found that multilayer systems of phase separated lipid mixtures are actually able to give independent information regarding the coexisting phases due to the demonstrated columnar order of each of the two phases arising from the selective coupling in the third dimension. This finding opens up another dimension of studies for phase separated lipid mixture systems. In the first part of the dissertation, we describe a quantitative study of cholesterol partition and its condensing effect in phase separated ternary lipid mixtures using X-ray diffraction. The electron density profiles (EDP) of both phases were constructed and a newly invented EDP baseline-scaling model was used to extract the quantitative information of the cholesterol composition and lipid packing. Next, the effect of close to 100% hydration on the different phases in the phase separated lipid mixture multilayer was studied. Firstly, we developed a high precision method for achieving and controlling hydration close to 100%, and an accurate method for calibrating the relative humidity using a 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) multilayer. With this setup, we discovered the novel phenomenon of anomalous swelling type II in the liquid disordered (Ld) phase of the phase separated mixed multilayer. This anomalous swelling is most likely due to the hydrophobic mismatch energy at the phase boundaries

Structural Studies of Ternary Mixture Lipid Multilayer Systems and the Effect of High Hydration with X-ray Diffraction

Phase separated lipid mixtures systems have been of vast interest due to their possible relationship with lipid raft formation which is believed to facilitate certain protein activities and is associated with important biological processes. While a lipid multilayer system serve as an ideal system for high resolution structural studies with X-ray scattering techniques and has mostly been used to obtain an averaged result for pure or mixed systems (e.g., proteins, peptides in membrane), we have found that multilayer systems of phase separated lipid mixtures are actually able to give independent information regarding the coexisting phases due to the demonstrated columnar order of each of the two phases arising from the selective coupling in the third dimension. This finding opens up another dimension of studies for phase separated lipid mixture systems. In the first part of the dissertation, we describe a quantitative study of cholesterol partition and its condensing effect in phase separated ternary lipid mixtures using X-ray diffraction. The electron density profiles (EDP) of both phases were constructed and a newly invented EDP baseline-scaling model was used to extract the quantitative information of the cholesterol composition and lipid packing. Next, the effect of close to 100% hydration on the different phases in the phase separated lipid mixture multilayer was studied. Firstly, we developed a high precision method for achieving and controlling hydration close to 100%, and an accurate method for calibrating the relative humidity using a 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) multilayer. With this setup, we discovered the novel phenomenon of anomalous swelling type II in the liquid disordered (Ld) phase of the phase separated mixed multilayer. This anomalous swelling is most likely due to the hydrophobic mismatch energy at the phase boundaries