The Renormalization Group According to Balaban - I. Small fields

This is an expository account of Balaban's approach to the renormalization group. The method is illustrated with a treatment of the the ultraviolet problem for the scalar phi^4 model on a toroidal lattice in dimension d=3. This yields another proof of the stability bound. In this first paper we analyze the small field contribution to the partition function.Comment: 52 pages. Some corrections, additions, reorganizatio

Super-Instantons and the Reliability of Perturbation Theory in Non-Abelian Models

In dimension $D\leq 2$ the low temperature behavior of systems enjoying a continuous symmetry is dominated by super-instantons: classical configurations of arbitrarily low energy. Perturbation theory in the background of a super-instanton produces thermodynamic answers for the invariant Green's functions that differ from the standard ones, but only in non-Abelian models and only starting at $O(1/\beta^2)$. This effect modifies the $\beta$-function of the $O(N)$ models and persists in the large $N$ limit of the $O(N)$ models.Comment: 8 pages, plain LaTeX, MPI-Ph/93-87 and AZPH-TH/93-3

Super-Instantons in Gauge Theories and Troubles with Perturbation Theory

In gauge theories with continuous groups there exist classical solutions whose energy vanishes in the thermodynamic limit (in any dimension). The existence of these super-instantons is intimately related to the fact that even at short distances perturbation theory can fail to produce unique results. This problem arises only in non-Abelian models and only starting at O(1/beta^2).Comment: 9 pages, 1 figure available on request from the author

Method for leakage testing of tanks Patent

Development of apparatus and method for testing leakage of large tank

Super-Instantons, Perfect Actions, Finite Size Scaling and the Continuum Limit

We discuss some aspects of the continuum limit of some lattice models, in particular the $2D$ $O(N)$ models. The continuum limit is taken either in an infinite volume or in a box whose size is a fixed fraction of the infinite volume correlation length. We point out that in this limit the fluctuations of the lattice variables must be $O(1)$ and thus restore the symmetry which may have been broken by the boundary conditions (b.c.). This is true in particular for the so-called super-instanton b.c. introduced earlier by us. This observation leads to a criterion to assess how close a certain lattice simulation is to the continuum limit and can be applied to uncover the true lattice artefacts, present even in the so-called 'perfect actions'. It also shows that David's recent claim that super-instanton b.c. require a different renormalization must either be incorrect or an artefact of perturbation theory.Comment: 14 pages, latex, no figure

Synthetic aperture radar signal processing on the MPP

Satellite-borne Synthetic Aperture Radars (SAR) sense areas of several thousand square kilometers in seconds and transmit phase history signal data several tens of megabits per second. The Shuttle Imaging Radar-B (SIR-B) has a variable swath of 20 to 50 km and acquired data over 100 kms along track in about 13 seconds. With the simplification of separability of the reference function, the processing still requires considerable resources; high speed I/O, large memory and fast computation. Processing systems with regular hardware take hours to process one Seasat image and about one hour for a SIR-B image. Bringing this processing time closer to acquisition times requires an end-to-end system solution. For the purpose of demonstration, software was implemented on the present Massively Parallel Processor (MPP) configuration for processing Seasat and SIR-B data. The software takes advantage of the high processing speed offered by the MPP, the large Staging Buffer, and the high speed I/O between the MPP array unit and the Staging Buffer. It was found that with unoptimized Parallel Pascal code, the processing time on the MPP for a 4096 x 4096 sample subset of signal data ranges between 18 and 30.2 seconds depending on options

Fermion Determinants: Some Recent Analytic Results

The use of known analytic results for the continuum fermion determinants in QCD and QED as benchmarks for zero lattice spacing extrapolations of lattice fermion determinants is proposed. Specifically, they can be used as a check on the universality hypothesis relating the continuum limits of the na\"{\i}ve, staggered and Wilson fermion determinants.Comment: 8th Workshop on Non-Perturbative QCD, 7-11 June 2004, Pari