Kranc: a Mathematica package to generate numerical codes for tensorial evolution equations

We present a suite of Mathematica-based computer-algebra packages, termed “Kranc”, which comprise a toolbox to convert certain (tensorial) systems of partial differential evolution equations to parallelized C or Fortran code for solving initial boundary value problems. Kranc can be used as a “rapid prototyping” system for physicists or mathematicians handling very complicated systems of partial differential equations, but through integration into the Cactus computational toolkit we can also produce efficient parallelized production codes. Our work is motivated by the field of numerical relativity, where Kranc is used as a research tool by the authors. In this paper we describe the design and implementation of both the Mathematica packages and the resulting code, we discuss some example applications, and provide results on the performance of an example numerical code for the Einstein equations.

Program summary

Title of program: KrancCatalogue identifier: ADXS_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXS_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandDistribution format: tar.gzComputer for which the program is designed and others on which it has been tested: General computers which run Mathematica (for code generation) and Cactus (for numerical simulations), tested under LinuxProgramming language used: Mathematica, C, Fortran 90Memory required to execute with typical data: This depends on the number of variables and gridsize, the included ADM example requires 4308 KBHas the code been vectorized or parallelized: The code is parallelized based on the Cactus framework.Number of bytes in distributed program, including test data, etc.: 1 578 142Number of lines in distributed program, including test data, etc.: 11 711Nature of physical problem: Solution of partial differential equations in three space dimensions, which are formulated as an initial value problem. In particular, the program is geared towards handling very complex tensorial equations as they appear, e.g., in numerical relativity. The worked out examples comprise the Klein-Gordon equations, the Maxwell equations, and the ADM formulation of the Einstein equations.Method of solution: The method of numerical solution is finite differencing and method of lines time integration, the numerical code is generated through a high level Mathematica interface.Restrictions on the complexity of the program: Typical numerical relativity applications will contain up to several dozen evolution variables and thousands of source terms, Cactus applications have shown scaling up to several thousand processors and grid sizes exceeding 500³.Typical running time: This depends on the number of variables and the grid size: the included ADM example takes approximately 100 seconds on a 1600 MHz Intel Pentium M processor.Unusual features of the program: based on Mathematica and Cactus     

Pulsed NMR of monolayer and near-monolayer films of 3He adsorbed on Grafoil at low temperatures

Pulsed NMR measurements at 30 MHz of near-monolayer coverages of ³He on Grafoil have been made between 4.2 and 0.1 K. The time constants of the free induction decay indicate that below 4.2 K the mobility of ³He in an exact monolayer is smaller than that at lower coverages or at coverages above one monolayer, in agreement with the results found by Hegde and Daunt, by Cowan and co-workers, and by Rollefson. Furthermore, in spite of rf heating of the sample, we were able to conclude that the mobility of ³He in nearmonolayers films decreases as the temperature is decreased below 4.2 K. At 4K and 30MHz our measurements give T₁ = 1 ± 0.3 sec for coverages between 0.6 and 1.35 monolayers. This is in agreement with previous work.Supported by the National Science Foundation.     

Particle emissions from diesel passenger cars equipped with a particle trap in comparison to other technologies

Tail pipe particle emissions of passenger cars, with different engine and aftertreatment technologies, were determined with special focus on diesel engines equipped with a particle filter. The particle number measurements were performed, during transient tests, using a condensation particle counter. The measurement procedure complied with the draft Swiss ordinance, which is based on the findings of the UN/ECE particulate measurement program. In addition, particle mass emissions were measured by the legislated and a modified filter method. The results demonstrate the high efficiency of diesel particle filters (DPFs) in curtailing nonvolatile particle emissions over the entire size range. Higher emissions were observed during short periods of DPF regeneration and immediately afterward, when a soot cake has not yet formed on the filter surface. The gasoline vehicles exhibited higher emissions than the DPF equipped diesel vehicles but with a large variation depending on the technology and driving conditions. Although particle measurements were carried out during DPF regeneration, it was impossible to quantify their contribution to the overall emissions, due to the wide variation in intensity and frequency of regeneration. The numbers counting method demonstrated its clear superiority in sensitivity to the mass measurement. The results strongly suggest the application of the particle number counting to quantify future low tailpipe emissions.     

Benzene: a secondary pollutant formed in the three-way catalyst

Benzene emissions from a relevant proportion of today's gasoline-driven passenger cars and light-duty vehicles can increase by up to 2 orders of magnitude when driving at high engine load (e.g., on highways). Under such conditions, post-catalyst benzene levels exceeded those found pre-catalyst. As a consequence, formation of benzene in the catalyst was postulated. To further reduce ambient air concentrations of benzene,these critical operating conditions must be carefully avoided. Here, we report in detail to what extent and at what operating conditions catalyst-induced benzene and toluene formation can occur. For that purpose, a EURO-1 passenger car (1.8 L, model year 1995)fulfilling the valid regulations, equipped with a new, two-layered, Pd-CeO2-Al2O3/Rh-ZrO2-Al2O3 three-way catalyst was operated at steady state on a chassis dynamometer at 100, 125, and 150 km/h at variable air to fuel ratios. Pre- and post-catalyst exhaust gas concentrations of benzene, toluene, C2-, and C3-benzenes were monitored at a time resolution of 0.5 Hz by means of chemical ionization mass spectrometry. A net benzene formation window, ranging from pre-catalyst exhaust gas temperatures of 600-730 degrees C and lambda-values of 0.83-0.95, with a pronounced minimum at 0.87, was observed. Dealkylation reactions of aromatic hydrocarbons are assumed to be the major pathway leading to benzene.     

Influence of in situ biofilm coverage on the radionuclide adsorption capacity of subsurface granite

Any migration of radionuclides from nuclear waste repositories is expected to be mitigated by adsorption to the host rocks surrounding hydraulically conductive fractures. Fluid rock interfaces are considered to be important barriers for nuclear waste disposal schemes but their adsorptive capacity can be affected by the growth of microbial biofilms. This study indicates that biofilms growing on fracture surfaces decrease the rocks adsorption capacity for migrating radionuclides except for trivalent species. Potential suppression of adsorption by biofilms should, therefore, be accounted for in performance safety assessment models. In this study, the adsorptive capacity of in situ anaerobic biofilms grown 450 m underground on either glass or granite slides was compared to the capacity of the same surfaces without biofilms. Surfaces were exposed to the radiotracers 60Co(II), 147Pm(III), 241Am(III), 234Th(IV), and 237Np(V) for a period of 660 h in a pH neutral anaerobic synthetic groundwater. Adsorption was investigated at multiple time points over the 660 h using liquid scintillation and ICP-MS. Results indicate that these surfaces adsorb between 0 and 85% of the added tracers under the conditions of the specific experiments. After 660 h, the distribution coefficients, R (ratio between what is sorbed and what is left in the aqueous phase), approached 3 x 10(4) m for 60Co, 3 x 10(5) m for 147Pm and 241Am, 1 x 10(6)m for 234Th, and 1 x 10(3) m for 237Np. The highest rate of adsorption was during the first 200 h of the adsorption experiments and started to approach equilibrium after 500 h. Adsorption to colloids and precipitates contributed to decreases of up to 20% in the available 60Co, 147Pm, 241Am, and 237Np in the adsorption systems. In the 234Th system 95% of the aqueous 234Th was removed by adsorbing to colloids. Although the range of Rvalues for each surface tested generally overlapped, the biofilms consistently demonstrated lower R values except for the trivalant 147Pm and 241Am adsorption systems.