Additive Schwarz methods for thep-version finite element method

Summary In this paper, we study some additive Schwarz methods (ASM) for thep-version finite element method. We consider linear, scalar, self adjoint, second order elliptic problems and quadrilateral elements in the finite element discretization. We prove a constant bound independent of the degreep and the number of subdomainsN, for the condition number of the ASM iteration operator. This optimal result is obtained first in dimension two. It is then generalized to dimensionn and to a variant of the method on the interface. Numerical experiments confirming these results are reported. As is the case for other additive Schwarz methods, our algorithms are highly parallel and scalable.This work was supported in part by the Applied Math. Sci. Program of the U.S. Department of Energy under contract DE-FG02-88ER25053 and, in part, by the National Science Foundation under Grant NSF-CCR-9204255     

Dense fluid displacement in wet porous media by spin relaxation selective contrast

Low field Magnetic Resonance Imaging is used to study oil diffusion in a wet soil model. A complete discrimination between oil and water has been obtained by using Inversion-Recovery pulse sequence. The time evolution of the oil image gives the parameters which describe the dense fluid diffusion rate in the whole space directions.     

Inter-cycle variation in whole-body vibration exposures of operators driving track-type loader machines

Whole-body vibration (WBV) measurements are an important aspect of performing risk assessments for those exposed to vibration. A large array of variables affect the outcome of a vibration measurement and its extrapolation to a daily dose measure: e.g. variability in driving style, road surface roughness, loading. The variability in vibration emission is an inherent property for most vibrating environments and there is a risk that a vibration measurement might not be representative of the long-term exposures. It is important to acknowledge the variation inherent to WBV exposure to help understand how this variation will affect health risk assessments. A field investigation was conducted in order to characterise the variation of WBV magnitudes between work cycles of track-type loaders. Six different track-type loaders were measured at four different work sites. The vibrations were measured at the operators seat in three translational axes (x-, y-, and z-axis) in accordance with ISO 2631-1 (1997). The findings indicate the worst axis of vibration for the track-type loaders was predominantly the fore-and-aft (x-axis), for most operations. The most severe emission values were measured for machine C at site 2 (1.12 ms⁻² rms) and machine D at site 2 (1.03 ms⁻² rms). These machines would exceed the action value of the Physical Agents (Vibration) Directive within 2 h of exposure. All of the machines measured would exceed the exposure action value of the Directive within an 8 h working period. The lateral (y-axis) produced the greatest amount of variability between work cycles (coefficient of variation up to 20%). It is concluded that the inherent variability between work cycles and tasks reinforces the requirement to perform a full task analysis prior to measuring WBV exposures to ensure that all tasks are measured and that adequate cycles are measured to obtain a reliable indication of the vibration emission.     

Do the molecules which form discotic liquid crystals have disc-like structures? The conformation of a simple model compound, 1,2-dihydroxydiacetylbenzene, determined from the NMR spectra of samples dissolved in liquid crystalline solvents

Many discotic mesogens are molecules with a central aromatic ring with adjacent alkylcarboxylate substituents. The simplest such molecule, 1,2-dihydroxydiacetylbenzene, which is not mesogenic, is studied by NMR spectroscopy as a solute in a nematic solvent. The spectra are analysed to give sets of residual dipolar couplings, D_ij , which are then used to test models for the conformation adopted by the acetate side groups. The conformations and geometry of an isolated molecule are calculated by the ab initio MP2/6-311G method and also by the DFT approach using the B3LYP functional with the 6-311++G** basis set. The quantum chemical calculations find that the minimum energy conformer has the acetate groups rotated in opposite directions out of the ring plane, and this kind of structure is also consistent with the NMR data.     

Neville elimination for rank-structured matrices

In this paper it is shown that Neville elimination is suited to exploit the rank structure of an order-r quasiseparable matrix A∈C^n×n by providing a condensed decomposition of A as product of unit bidiagonal matrices, all together specified by O(nr) parameters, at the cost of O(nr³) flops. An application of this result for eigenvalue computation of totally positive rank-structured matrices is also presented.     

Spectral measurement of the caesium D2 line with a tunable heterodyne interferometer

The optical properties of a caesium atomic beam driven on a resonant hyperfine transition in the D₂ line were studied as a function of the probe laser frequency. Using a third off-resonant laser system, a heterodyne interferometer allowed simultaneous absorption and phase shift measurements of either the probe or the coupling laser. The signal features of the probe and coupling laser transmitted intensities showed strong differences in the vicinity of the hyperfine transitions excited by the probe laser. Regular absorption signals and electromagnetically induced transparency were found in either transmitted intensities. Furthermore, light induced birefringence of the probe laser was measured.     

Uniform domains and quasiconformal mappings on the Heisenberg group

We prove that in the Heisenberg group the image of a uniform domain under a global quasiconformal homeomorphism is still a uniform domain. As a consequence, the class of NTA (non-tangentially accessible) domains in the Heisenberg group is also quasiconformally invariant. A large class of non-differentiable Lipschitz quasiconformal homeomorphisms is constructed. The images of smooth domains under these rough mappings give a class of non-smooth NTA domains in the Heisenberg group.     

Mean Field Dilute Ferromagnet: High Temperature and Zero Temperature Behavior

We study the mean field dilute model of a ferromagnet. We find and prove an expression for the free energy density at high temperature, and at temperature zero. We find the critical line of the model, separating the phase with zero magnetization from the phase with symmetry breaking. We also compute exactly the entropy at temperature zero, which is strictly positive. The physical behavior at temperature zero is very interesting and related to infinite dimensional percolation, and suggests possible behaviors at generic low temperatures. Lastly, we provide a complete solution for a (partially) annealed model. Our results hold both for the Poisson and the Bernoulli versions of the model.