On entropy and Hausdorff dimension of measures defined through a non-homogeneous Markov process

In this work we study the Hausdorff dimension of measures whose weight distribution satisfies a markov non-homogeneous property. We prove, in particular, that the Hausdorff dimensions of this kind of measures coincide with their lower R\'enyi dimensions (entropy). Moreover, we show that the Tricot dimensions (packing dimension) equal the upper R\'enyi dimensions. As an application we get a continuity property of the Hausdorff dimension of the measures, when it is seen as a function of the distributed weights under the $\ell^{\infty}$ norm.Comment: 13 page

First exact Geon found is a non-singular monopole, propagating as a primordial gravitational pp-wave

Geons are particle-like electrovacua. The concept is well-defined, but it still lacks a proper first example. Emerging as such is a self-confined exact 2-parameter pp-wave non-Dirac monopole {\cal G} with primordial Q/r^2 (r\geq r_o) field plus higher moments. {\cal G} has effective mass, independently-scaled NUT-like charge \kappa|Q|=2r_o as diameter, and spin. {\cal G} {\em cannot} have actual {\sc em} charge $Q$ (by \partial{\cal G}=0), Ricci-flat limits, nor spacetime or Dirac-string singularities, but Dirac's quantization condition holds. {\cal G}/2, as an upgraded `Kerr-Newman' alternative or {\cal S}_Q geon, carries actual charge Q confined by topology on a round-S^2[r_o] physical singularity on \partial{\cal S}_Q\neq0. {\cal G} and {\cal S}_Q offer exact analytic models in particle physics and cosmology, notably for primordial gravitational waves, inflation, and pre-galactic dynamics.Comment: 13 page

A new class of spatially homogeneous 4D string backgrounds

A new class of spatially homogeneous 4D string backgrounds, the $X(d\rightarrow)$ according to a recent classification, is presented and shown to contain only five generic types. In contrast to the case of $X(d\uparrow)$ (which contains as a subclass all possible FRW backgrounds), exact $SO(3)$ isotropy is always broken in the $X(d\rightarrow)$ class. This is due to the $H$-field, whose dual is necessarily along a principal direction of anisotropy. Nevertheless, FRW symmetry can be attained asymptotically for Bianchi-types $I$ and $VII_0$ in a rather appealing physical context. Other aspects of the solutions found for types $X=I,II,III,VI_{-1}$, and of the $VII_0$ case are briefly discussed.Comment: LaTeX, 13 pages, no figures

Bianchi-type string cosmology

Bianchi-type string cosmology involves generalizations of the FRW backgrounds with three transitive spacelike Killing symmetries, but without any a priori assumption of isotropy in the 3D sections of homogeneity. With emphasis on those cases with diagonal metrics and vanishing cosmological constant which which have not been previously examined in the literature, the present findings allow an overview and the classification of all Bianchi-type backgrounds. These string solutions (at least to lowest order in alpha prime) offer prototypes for the study of spatial anisotropy and its impact on the dynamics of the early universe.Comment: 12 pages, latex, 1 table, no figure

A performance and reliability model for thermal barrier coatings

A modeling technique for predicting the performance and reliability of TBC's is being developed at Solar Turbines Incorporated. The concept combines experimental coating property data with finite element analyses to predict the thermal and mechanical behavior of coating systems in service. A key feature of Solar's approach is the use of a four point flexure test to estimate coating strength distributions and to predict coating failure probability. This model was used to evaluate the effect of physical variations on coating performance in high heat flux rocket engine applications for NASA. Current work, promoted by Caterpillar Tractor Company for diesel engine applications, is being conducted to measure coating strength as a function of temperature, and future work will document strength degradation with time at temperature. Solar's interest lies in the application of TBCs to gas turbine engine components