How to compute Green's Functions for entire Mass Trajectories within Krylov Solvers

The availability of efficient Krylov subspace solvers play a vital role for the solution of a variety of numerical problems in computational science. Here we consider lattice field theory. We present a new general numerical method to compute many Green's functions for complex non-singular matrices within one iteration process. Our procedure applies to matrices of structure $A=D-m$, with $m$ proportional to the unit matrix, and can be integrated within any Krylov subspace solver. We can compute the derivatives $x^{(n)}$ of the solution vector $x$ with respect to the parameter $m$ and construct the Taylor expansion of $x$ around $m$. We demonstrate the advantages of our method using a minimal residual solver. Here the procedure requires $1$ intermediate vector for each Green's function to compute. As real life example, we determine a mass trajectory of the Wilson fermion matrix for lattice QCD. Here we find that we can obtain Green's functions at all masses $\geq m$ at the price of one inversion at mass $m$.Comment: 11 pages, 2 eps-figures, needs epsf.st

Light Spectrum and Decay Constants in Full QCD with Wilson Fermions

We present results from an analysis of the light spectrum and the decay constants f_{\pi} and f_V^{-1} in Full QCD with n_f=2 Wilson fermions at a coupling of beta=5.6 on a 16^3x32 lattice.Comment: 3 pages, LaTeX with 4 eps figures, Talk presented at LATTICE96(spectrum

Animal Behavior Frozen in Time: Gregarious Behavior of Early Jurassic Lobsters within an Ammonoid Body Chamber

Direct animal behavior can be inferred from the fossil record only in exceptional circumstances. The exceptional mode of preservation of ammonoid shells in the Posidonia Shale (Lower Jurassic, lower Toarcian) of Dotternhausen in southern Germany, with only the organic periostracum preserved, provides an excellent opportunity to observe the contents of the ammonoid body chamber because this periostracum is translucent. Here, we report upon three delicate lobsters preserved within a compressed ammonoid specimen of Harpoceras falciferum. We attempt to explain this gregarious behavior. The three lobsters were studied using standard microscopy under low angle light. The lobsters belong to the extinct family of the Eryonidae; further identification was not possible. The organic material of the three small lobsters is preserved more than halfway into the ammonoid body chamber. The lobsters are closely spaced and are positioned with their tails oriented toward each other. The specimens are interpreted to represent corpses rather than molts. The lobsters probably sought shelter in preparation for molting or against predators such as fish that were present in Dotternhausen. Alternatively, the soft tissue of the ammonoid may have been a source of food that attracted the lobsters, or it may have served as a long-term residency for the lobsters (inquilinism). The lobsters represent the oldest known example of gregariousness amongst lobsters and decapods in the fossil record. Gregarious behavior in lobsters, also known for extant lobsters, thus developed earlier in earth's history than previously known. Moreover, this is one of the oldest known examples of decapod crustaceans preserved within cephalopod shells

24-th Order high temperature expansion for the 3-d Ising model

The authors present the series for the free energy and their estimate for the critical exponent {alpha}, as computed by a recursive bookkeeping algorithm on the CM5. They begin with a discussion of the algorithm to compute the High-Temperature expansion on finite 3-D Ising lattices