Nephrolithiasis (part 1): Epidemiology, causes and pathogenesis of recurrent nephrolithiasis

A recent increase in the incidence of recurrent renal calcium oxalate calculi has been demonstrated. Although a few advances have shown that the increase in incidence of these stones is due to genetic causes, it is mostly associated with a change in environmental factors. Global warming and weather changes, some medications administered to young children and eating habits play a pivotal role in increasing stone incidence. By far the most important single factor in stone incidence involves the increased ingestion of red meat and salt. So much so that it is anticipated that calcium oxalate stone occurrence will increase pari passu with dietary changes in the South African black community. The reasons for the difference in the incidence between males and females (12% v. 6%) remain controversial, and should be further studied

On the Numerical Dispersion of Electromagnetic Particle-In-Cell Code : Finite Grid Instability

The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation. For electromagnetic relativistic beam and plasma modeling, the most relevant numerical instabilities are the finite grid instability and the numerical Cherenkov instability. We review the numerical dispersion relation of the electromagnetic PIC algorithm to analyze the origin of these instabilities. We rigorously derive the faithful 3D numerical dispersion of the PIC algorithm, and then specialize to the Yee FDTD scheme. In particular, we account for the manner in which the PIC algorithm updates and samples the fields and distribution function. Temporal and spatial phase factors from solving Maxwell's equations on the Yee grid with the leapfrog scheme are also explicitly accounted for. Numerical solutions to the electrostatic-like modes in the 1D dispersion relation for a cold drifting plasma are obtained for parameters of interest. In the succeeding analysis, we investigate how the finite grid instability arises from the interaction of the numerical 1D modes admitted in the system and their aliases. The most significant interaction is due critically to the correct represenation of the operators in the dispersion relation. We obtain a simple analytic expression for the peak growth rate due to this interaction.Comment: 25 pages, 6 figure