Invariant Measures for Dissipative Dynamical Systems: Abstract Results and Applications

In this work we study certain invariant measures that can be associated to the time averaged observation of a broad class of dissipative semigroups via the notion of a generalized Banach limit. Consider an arbitrary complete separable metric space $X$ which is acted on by any continuous semigroup $\{S(t)\}_{t \geq 0}$. Suppose that $\S(t)\}_{t \geq 0}$ possesses a global attractor $\mathcal{A}$. We show that, for any generalized Banach limit $\underset{T \rightarrow \infty}{\rm{LIM}}$ and any distribution of initial conditions $\mathfrak{m}_0$, that there exists an invariant probability measure $\mathfrak{m}$, whose support is contained in $\mathcal{A}$, such that $$\int_{X} \phi(x) d\mathfrak{m} (x) = \underset{T\to \infty}{\rm{LIM}} \frac{1}{T}\int_0^T \int_X \phi(S(t) x) d \mathfrak{m}_0(x) d t,$$ for all observables $\phi$ living in a suitable function space of continuous mappings on $X$. This work is based on a functional analytic framework simplifying and generalizing previous works in this direction. In particular our results rely on the novel use of a general but elementary topological observation, valid in any metric space, which concerns the growth of continuous functions in the neighborhood of compact sets. In the case when $\{S(t)\}_{t \geq 0}$ does not possess a compact absorbing set, this lemma allows us to sidestep the use of weak compactness arguments which require the imposition of cumbersome weak continuity conditions and limits the phase space $X$ to the case of a reflexive Banach space. Two examples of concrete dynamical systems where the semigroup is known to be non-compact are examined in detail.Comment: To appear in Communications in Mathematical Physic

Asymptotics of the Coleman-Gurtin model

This paper is concerned with the integrodifferential equation \partial_t u-\Delta u -\int_0^\infty \kappa(s)\Delta u(t-s)\,\d s + \varphi(u)=f arising in the Coleman-Gurtin's theory of heat conduction with hereditary memory, in presence of a nonlinearity $\varphi$ of critical growth. Rephrasing the equation within the history space framework, we prove the existence of global and exponential attractors of optimal regularity and finite fractal dimension for the related solution semigroup, acting both on the basic weak-energy space and on a more regular phase space.Comment: Accepted in Discrete and Continuous Dynamical Systems, Serie

Sulfotransferase-mediated chlorination of 1-hydroxymethylpyrene to a mutagen capable of penetrating indicator cells.

Methylated polycyclic aromatic hydrocarbons are common in the human environment. Many of them are stronger carcinogens than their purely aromatic congeners. They may be metabolized to benzylic alcohols. We report here on biochemical and toxicological characteristics of 1-hydroxymethylpyrene (HMP), a typical representative of this class of compounds. Rat liver cytosol, fortified with 3'-phosphoadenosine-5'-phosphosulfate, converted HMP into its sulfate ester (HMPS), HMPS bound covalently to isolated DNA. In physiological buffer at 37 degrees C, HMPS had a half-life of 2 min, the major decomposition product being HMP. Thus, cyclic activation is possible. When Cl- anions were present at physiological concentrations, an additional reaction product of HMPS, 1-chloromethylpyrene (ClMP), could be identified on the basis of its chromatographic properties and its mass spectrum, using the authentic standard for comparison. ClMP was shorter-lived in buffer than HMPS. ClMP reacted with DNA, the adduct pattern in the 32P-postlabeling analysis being similar, or identical, to that of HMPS. ClMP proved to be a very potent mutagen in Salmonella typhimurium, whereas HMPS, and HMP in the presence of a sulfate-conjugating system, showed strong mutagenicity only when Cl- or Br- ions were present in the exposure buffer. It is concluded that HMPS is capable of reacting with DNA, but is hampered in its distribution by membrane barriers.(ABSTRACT TRUNCATED AT 250 WORDS

Geometry Technology Module (GTM). Volume 1: Engineering description and utilization manual

The geometry technology module (GTM) is described as a system of computerized elements residing in the engineering design integration system library developed for the generation, manipulation, display, computation of mass properties, and data base management of panelled geometry. The GTM is composed of computer programs and associated data for performing configuration analysis on geometric shapes. The program can be operated in batch or demand mode and is designed for interactive use

Star Formation History in two fields of the Small Magellanic Cloud Bar

The Bar is the most productive region of the Small Magellanic Cloud in terms of star formation but also the least studied one. In this paper we investigate the star formation history of two fields located in the SW and in the NE portion of the Bar using two independent and well tested procedures applied to the color-magnitude diagrams of their stellar populations resolved by means of deep HST photometry. We find that the Bar experienced a negligible star formation activity in the first few Gyr, followed by a dramatic enhancement from 6 to 4 Gyr ago and a nearly constant activity since then. The two examined fields differ both in the rate of star formation and in the ratio of recent over past activity, but share the very low level of initial activity and its sudden increase around 5 Gyr ago. The striking similarity between the timing of the enhancement and the timing of the major episode in the Large Magellanic Cloud is suggestive of a close encounter triggering star formation.Comment: 30 pages, 22 figures, accepted for publication in Ap

Structure and pressure drop of real and virtual metal wire meshes

An efficient mathematical model to virtually generate woven metal wire meshes is presented. The accuracy of this model is verified by the comparison of virtual structures with three-dimensional images of real meshes, which are produced via computer tomography. Virtual structures are generated for three types of metal wire meshes using only easy to measure parameters. For these geometries the velocity-dependent pressure drop is simulated and compared with measurements performed by the GKD - Gebr. Kufferath AG. The simulation results lie within the tolerances of the measurements. The generation of the structures and the numerical simulations were done at GKD using the Fraunhofer GeoDict software