Deflated Iterative Methods for Linear Equations with Multiple Right-Hand Sides

A new approach is discussed for solving large nonsymmetric systems of linear equations with multiple right-hand sides. The first system is solved with a deflated GMRES method that generates eigenvector information at the same time that the linear equations are solved. Subsequent systems are solved by combining restarted GMRES with a projection over the previously determined eigenvectors. This approach offers an alternative to block methods, and it can also be combined with a block method. It is useful when there are a limited number of small eigenvalues that slow the convergence. An example is given showing significant improvement for a problem from quantum chromodynamics. The second and subsequent right-hand sides are solved much quicker than without the deflation. This new approach is relatively simple to implement and is very efficient compared to other deflation methods.Comment: 13 pages, 5 figure

Bulk fields in the Randall-Sundrum compactification scenario

Recently, Randall and Sundrum proposed a solution to the hierarchy problem where the background spacetime is five dimensional. There are two 3-branes, and the mass scale for fields that propagate on one of the 3-branes is exponentially suppressed relative to the fundamental scale of the theory, which is taken to be the Planck mass MPl. In this Brief Report we show that bulk fields with a five dimensional mass term of order MPl have, after integrating over the extra dimension, modes with four-dimensional masses that are exponentially suppressed as well. This opens the possibility that in this scenario the standard model matter fields may correspond to degrees of freedom that are not confined to a 3-brane

Dynamic Hardness Tester and Cure Meter

The Shore hardness tester is used extensively throughout industry to determine the static modulus of materials. The new apparatus described here extends the capability of an indentor-type tester into the dynamic regime, and provides a measurement of the dynamic shear or Young's modulus and loss factor as a function of frequency. The instrument, model and data of typical rubber samples are given and compared to other dynamic measurements