Counting reducible, powerful, and relatively irreducible multivariate polynomials over finite fields

We present counting methods for some special classes of multivariate polynomials over a finite field, namely the reducible ones, the s-powerful ones (divisible by the s-th power of a nonconstant polynomial), and the relatively irreducible ones (irreducible but reducible over an extension field). One approach employs generating functions, another one uses a combinatorial method. They yield exact formulas and approximations with relative errors that essentially decrease exponentially in the input size.Comment: to appear in SIAM Journal on Discrete Mathematic

Benchmarking computer platforms for lattice QCD applications

We define a benchmark suite for lattice QCD and report on benchmark results from several computer platforms. The platforms considered are apeNEXT, CRAY T3E, Hitachi SR8000, IBM p690, PC-Clusters, and QCDOC.Comment: 3 pages, Lattice03, machines and algorithm

A study of subsonic transport aircraft configurations using hydrogen (H2) and methane (CH4) as fuel

The acceptability of alternate fuels for future commercial transport aircraft are discussed. Using both liquid hydrogen and methane, several aircraft configurations are developed and energy consumption, aircraft weights, range and payload are determined and compared to a conventional Boeing 747-100 aircraft. The results show that liquid hydrogen can be used to reduce aircraft energy consumption and that methane offers no advantage over JP or hydrogen fuel

Better than $1/Mflops sustained: a scalable PC-based parallel computer for lattice QCD

We study the feasibility of a PC-based parallel computer for medium to large scale lattice QCD simulations. The E\"otv\"os Univ., Inst. Theor. Phys. cluster consists of 137 Intel P4-1.7GHz nodes with 512 MB RDRAM. The 32-bit, single precision sustained performance for dynamical QCD without communication is 1510 Mflops/node with Wilson and 970 Mflops/node with staggered fermions. This gives a total performance of 208 Gflops for Wilson and 133 Gflops for staggered QCD, respectively (for 64-bit applications the performance is approximately halved). The novel feature of our system is its communication architecture. In order to have a scalable, cost-effective machine we use Gigabit Ethernet cards for nearest-neighbor communications in a two-dimensional mesh. This type of communication is cost effective (only 30% of the hardware costs is spent on the communication). According to our benchmark measurements this type of communication results in around 40% communication time fraction for lattices upto 48^3\cdot96 in full QCD simulations. The price/sustained-performance ratio for full QCD is better than $1/Mflops for Wilson (and around$1.5/Mflops for staggered) quarks for practically any lattice size, which can fit in our parallel computer. The communication software is freely available upon request for non-profit organizations.Comment: 14 pages, 3 figures, final version to appear in Comp.Phys.Com