On the Fine Structure of Stationary Measures in Systems Which Contract-on-Average

Suppose {f ₁,...,f _m } is a set of Lipschitz maps of ^d . We form the iterated function system (IFS) by independently choosing the maps so that the map f _i is chosen with probability p _i ( ^m _i=1 p _i =1). We assume that the IFS contracts on average. We give an upper bound for the upper Hausdorff dimension of the invariant measure induced on ^d and as a corollary show that the measure will be singular if the modulus of the entropy _i p _i log p _i is less than d times the modulus of the Lyapunov exponent of the system. Using a version of Shannon's Theorem for random walks on semigroups we improve this estimate and show that it is actually attainable for certain cases of affine mappings of .     

Phase diagram of RDX (hexahydro-1,3,5-trinitro-s-triazine) at high pressures and temperatures

Abstract

The phase diagram of RDX-h₆ (hexahydro-1,3,5-trinito-s-triazine) and RDX-d₆ has been studied by Raman spectroscopy to more than 13 GPa at 295 K and 7.5 GPa between 150 and 450 K. Two stable high pressure phases have been found. γ-RDX or RDX-III forms from α-RDX above 3.8 GPa below 380 K. β-RDX forms when α- or γ-RDX are heated, can be retained metastably at low temperatues, and may be related to a very unstable form occasionally recovered at ambient pressure. Deuterium isotopic substitution and shear increase the temperature where β-RDX begins to form on heating.     

A Bernoulli toral linked twist map without positive Lyapunov exponents

The presence of positive Lyapunov exponents in a dynamical system is often taken to be equivalent to the chaotic behavior of that system. We construct a Bernoulli toral linked twist map which has positive Lyapunov exponents and local stable and unstable manifolds defined only on a set of measure zero. This is a deterministic dynamical system with the strongest stochastic property, yet it has positive Lyapunov exponents only on a set of measure zero. In fact we show that for any map in a certain class of piecewise linear Bernoulli toral linked twist maps, given any there is a Bernoulli toral linked twist map with positive Lyapunov exponents defined only on a set of measure zero such that is within of in the metric.

     

LIPS and linear correlation analysis applied to the classification of Roman pottery Terra Sigillata

Archaeological ceramics Terra Sigillata manufactured in different production centres have been studied by laser-induced plasma spectroscopy (LIPS). The aim of this work was to establish a procedure for the rapid classification of these archaeological ceramics in function of their provenance through combination of LIPS and statistical methodologies. Representative emission spectra of the Hispanic, Gaulish and African groups of pottery were selected as references. The use of linear correlation allowed one to cluster the samples by quantitative comparison of LIP spectra, leading to a reliable assignment of Terra Sigillata pieces to origin centres. PACS 42.62.Fi; 32.30.Jc; 02.50.-r; 81.05.Je     

NA48 results on neutral kaon and hyperon rare decays

The NA48 Collaboration has performed an extensive program of kaon and hyperon rare decays using the data collected during the period 1997–2001. This program includes new tests of chiral perturbation theory, new measurements of theη mass andK _s lifetime and the possibility to measure the Cabibbo angle using Ξ beta decays.     

Magnetfeldabhängige Mikrowellen-Absorption und -Dispersion zur Bestimmung von Stoßfrequenz und Stoßmodell bei Flammenplasmen

At atmospheric pressure acetylene-oxygen and acetylene-air flames were burning through anX-band waveguide resonator parallel to the microwave electric field vector and perpendicular to an external magnetic field in the Voigt-geometry commonly used to study electron cyclotron resonance. However, because the electron collision frequency is greater than the angular microwave frequency, absorption and dispersion are merely slowly decreasing functions of the magnetic field strength. They depend—besides on collision frequency—on the nature of the electron collisions. Both, absorption and dispersion were evaluated independently for different classical collision models. Taking into account the tensor-property of conductivity, closest agreement of the two results for the collision frequency and best coincidence of measurement and theory was obtained for the model of an electron-polarizable molecule collision, which corresponds to a collision frequency independent of electron velocity. The collision frequency amounts to 210±4 GHz for our acetylene-oxygen-flames and 249 ± 4 GHz for the acetylene-air-flames.     

Condensation of wet steam on a horizontal tube with additional droplet deposition

A theory is presented for condensation of downward flowing wet vapour on a horizontal tube. The vapour is assumed to consist of dry saturated vapour and uniformly distributed liquid droplets flowing independently of each other. In addition the droplets are assumed to be so large that they fall vertically on to the tube surface and are unaffected by the vapour flow around the cylinder. The results show that the heat transfer coefficients are extremely dependent on both the droplet mass flux and velocity as well as the steam velocity.