One Spin Trace Formalism for BK B_K

It has been known for some time that there are two methods to calculate $B_K$ with staggered fermions: one is the two spin trace formalism and the other is the one spin trace formalism. Until now, the two spin trace formalism has been exclusively used for weak matrix element calculations with staggered fermions. Here, the one spin trace formalism to calculate $B_K$ with staggered fermions is explained. It is shown that the one spin trace operators require additional chiral partner operators in order to keep the continuum chiral behavior. The renormalization of the one spin trace operators is described and compared with the two spin trace formalism.Comment: 47 pages, latex, 4 figures are available on reques

New extended high temperature series for the N-vector spin models on three-dimensional bipartite lattices

High temperature expansions for the susceptibility and the second correlation moment of the classical N-vector model (O(N) symmetric Heisenberg model) on the sc and the bcc lattices are extended to order $\beta^{19}$ for arbitrary N. For N= 2,3,4.. we present revised estimates of the critical parameters from the newly computed coefficients.Comment: 11 pages, latex, no figures, to appear in Phys. Rev.

N-vector spin models on the sc and the bcc lattices: a study of the critical behavior of the susceptibility and of the correlation length by high temperature series extended to order beta^{21}

High temperature expansions for the free energy, the susceptibility and the second correlation moment of the classical N-vector model [also known as the O(N) symmetric classical spin Heisenberg model or as the lattice O(N) nonlinear sigma model] on the sc and the bcc lattices are extended to order beta^{21} for arbitrary N. The series for the second field derivative of the susceptibility is extended to order beta^{17}. An analysis of the newly computed series for the susceptibility and the (second moment) correlation length yields updated estimates of the critical parameters for various values of the spin dimensionality N, including N=0 [the self-avoiding walk model], N=1 [the Ising spin 1/2 model], N=2 [the XY model], N=3 [the Heisenberg model]. For all values of N, we confirm a good agreement with the present renormalization group estimates. A study of the series for the other observables will appear in a forthcoming paper.Comment: Revised version to appear in Phys. Rev. B Sept. 1997. Revisions include an improved series analysis biased with perturbative values of the scaling correction exponents computed by A. I. Sokolov. Added a reference to estimates of exponents for the Ising Model. Abridged text of 19 pages, latex, no figures, no tables of series coefficient

A new AMR-solver for precise and fast simulations of blast events in urban scenarios

There is a demand for reliable, fast and easy-to-use simulation tools for the analysis of blast effects in urban environments. Most existing easy-to-use tools for this purpose are based on simplified calculation models, which limit their accuracy and/or their flexibility. General-purpose hydrocodes offer both accuracy and flexibility in application, they are however difficult to use and require long calculation times. Given this situation we have developed a fast and precise solver specifically for the simulation of blast propagation in urban scenarios. The method allows the simulation of blast propagation outside and inside of one or more buildings and can be coupled to damage models for the assessment of blast effects. An automated calculation setup makes the tool easy to use. The solver implements a first principles calculation, using an explicit finite volume scheme with Cartesian grids and automatic mesh refinement (AMR). The tool includes a 1D multi-fluid method for the calculation of the initially spherical detonation, which provides the initial blast wave for the subsequent three-dimensional simulation phase. The computational domain is set up automatically based on the scenario information. The first version of this tool has been introduced in a previous contribution [1]. The current paper focuses on a new AMR-concept, which as recently been implemented in the solver. The new concept led to a significant speedup and increase in modeling flexibility. Details of the new method are presented together we new experimental data used for the validation

A comparative study of Navier-Stokes and Viscous Shock Layer Solutions for a wide range of Reynolds and Mach numbers

A parametric comparison of solutions of the full Navier-Stokes equations and the full viscous shock layer (FVSL) equations is presented. These equations are both widely used for modelling of steady supersonic viscous gas flows. The time dependent 2D NavierStokes equations are solved with a second order explicit shock-capturing ENO scheme with a finite volume approach. To solve 2D FVSL equations the method of global iterations with respect to the streamwise pressure gradient and the shock standoff distance is used. Computed results are compared for a broad range of Reynolds (10 3 Re1 10 5 ) and Mach (5 M1 15) numbers. Key Words: Full Navier-Stokes Equations, Full Viscous Shock Layer Equations, Finite Volume Method, Method of Global Iterations AMS Subject Classification: 76M25, 35Q30 * Supported by the DAAD, grant no. K A95 07202-113, Ref. 325 y Supported by the Graduiertenkolleg Transport Phenomena in Hypersonic Flows List of symbols ae mass density p pressure T temper..

Mesoscale Analysis of Sintered Metals Fragmentation under Explosive and Subsequent Impact Loading

Sintered metal compositions are used in many applications, including shells of explosive warheads. The properties of the compositions depend on both the base materials and the fabrication process. In order to achieve specific strength and fragmentation properties under dynamic loading, these parameters need to be optimized. We present a strategy to facilitate this process by numerical analyses on the meso scale for the case of the fragmentation of sintered metal cubes that shall survive an explosive launch and fragment into fine particles after perforation of a plate. This is an extension of work presented in [1], where only plate impact and different materials were regarded. The results are computed fragment size distributions for different base materials, grain size distributions, porosities and mesoscale material parameters like intergranular cohesive strength. The analysis is based on Hydrocode simulations with different numerical approaches and models for the launch and the impact phase. The transient pressures acting on the cube during the explosive launch from the warhead are evaluated from fluid-structure coupled computations on the macro scale. These transient pressures are then used as boundary conditions for a single cubic Representative Volume Element (RVE) in the mesoscale analysis of the launch phase. After the acceleration the same RVE impacts an aluminum plate at velocities of approx. 1100 m/s. In order to keep the computational effort feasible, scaling needs to be used. The validity of the scaling is checked by numerical simulations with different RVE sizes. Quantitative analyses of fragment size distributions are carried out