Complete characterization of convergence to equilibrium for an inelastic Kac model

Pulvirenti and Toscani introduced an equation which extends the Kac caricature of a Maxwellian gas to inelastic particles. We show that the probability distribution, solution of the relative Cauchy problem, converges weakly to a probability distribution if and only if the symmetrized initial distribution belongs to the standard domain of attraction of a symmetric stable law, whose index $\alpha$ is determined by the so-called degree of inelasticity, $p>0$, of the particles: $\alpha=\frac{2}{1+p}$. This result is then used: (1) To state that the class of all stationary solutions coincides with that of all symmetric stable laws with index $\alpha$. (2) To determine the solution of a well-known stochastic functional equation in the absence of extra-conditions usually adopted

Probabilistic study of the speed of approach to equilibrium for an inelastic Kac model

This paper deals with a one--dimensional model for granular materials, which boils down to an inelastic version of the Kac kinetic equation, with inelasticity parameter $p>0$. In particular, the paper provides bounds for certain distances -- such as specific weighted $\chi$--distances and the Kolmogorov distance -- between the solution of that equation and the limit. It is assumed that the even part of the initial datum (which determines the asymptotic properties of the solution) belongs to the domain of normal attraction of a symmetric stable distribution with characteristic exponent \a=2/(1+p). With such initial data, it turns out that the limit exists and is just the aforementioned stable distribution. A necessary condition for the relaxation to equilibrium is also proved. Some bounds are obtained without introducing any extra--condition. Sharper bounds, of an exponential type, are exhibited in the presence of additional assumptions concerning either the behaviour, near to the origin, of the initial characteristic function, or the behaviour, at infinity, of the initial probability distribution function

Kinetic models with randomly perturbed binary collisions

We introduce a class of Kac-like kinetic equations on the real line, with general random collisional rules, which include as particular cases models for wealth redistribution in an agent-based market or models for granular gases with a background heat bath. Conditions on these collisional rules which guarantee both the existence and uniqueness of equilibrium profiles and their main properties are found. We show that the characterization of these stationary solutions is of independent interest, since the same profiles are shown to be solutions of different evolution problems, both in the econophysics context and in the kinetic theory of rarefied gases

An investigation on corrosion protection layers in pipelines transporting hydrocarbons

Chemical reactions between carbon steel, water and chemical species produce corrosion layers (scales) on the internal surface of pipelines transporting hydrocarbons. Scales act as a diffusion barrier and prevent the progress of corrosion, a dangerous failure initiator. The protective film (10-100 m thickness) can be removed locally by the action of the internal flow, or by other mechanisms. Adhesion with the substrate and the failure modes of the corrosion layer can be tested by indentation. Some results are presented of experiments performed on specimens with scales grown in a controlled environment

Optics and Quantum Electronics

Contains table of contents for Section 2 and reports on eleven research projects.Joint Services Electronics Program Contract DAAL03-89-C-0001National Science Foundation Grant EET 87-00474U.S. Air Force - Office of Scientific Research Contract F49620-88-C-0089Charles S. Draper Laboratory Contract DL-H-404179National Center for Integrated PhotonicsNational Science Foundation Grant ECS 87-18417NEC Research InstituteNational Science Foundation Grant ECS 85-52701Medical Free Electron Laser Program Contract N00014-86-K-0117National Institutes of Health Grant 5-RO1-GM35459Lawrence Livermore National Laboratory Contract B048704U.S. Department of Energy Grant DE-FG02-89-ER14012Columbia University Contract P016310

Optics and Quantum Electronics

Contains table of contents for Section 3 and reports on twenty-one research projects.Joint Services Electronics Program Contract DAAL03-89-C-0001Joint Services Electronics Program Contract DAAL03-92-C-0001U.S. Air Force - Office of Scientific Research Contract F49620-91-C-0091Charles S. Draper Laboratories Contract DL-H-441629MIT Lincoln LaboratoryCharles S. Draper Laboratories, Inc. Contract DL-H-418478Fujitsu LaboratoriesNational Science Foundation Grant ECS 90-12787National Center for Integrated PhotonicsNational Science Foundation Grant EET 88-15834National Science Foundation Grant ECS 85-52701U.S. Air Force - Office of Scientific Research Contract F49620-88-C-0089U.S. Navy - Office of Naval Research Contract N00014-91-C-0084U.S. Navy - Office of Naval Research Grant N00014-91-J-1956Johnson and Johnson Research GrantNational Institutes of Health Contract 2-R01-GM35459U.S. Department of Energy Grant DE-FG02-89 ER14012-A00

Integrity assessment of pipeline systems by an enhanced indentation technique

A non-destructive technique based on indentation and enhanced by the consideration of the imprint mapping is proposed for the diagnostic analysis of pipelines in oil transportation systems. The considered testing procedure can be applied in the field without the need of extracting spools and working out the specimens required by more traditional experimental approaches. The reliability of the presented methodology is verified by investigating a pipe segment with more than 25 years of service. The mechanical properties determined by indentation and imprint mapping compare well with the output of standard tensile tests in average terms while better insight on the spatial distribution of the material characteristics is achieved

SAPONINS FROM CROSSOPTERYX-FEBRIFUGA

Two bisdesmosidic saponins from the roots of Crossopteryx febrifuga were isolated by means of reversed phase HPLC. They were characterized on the basis of chemical and spectral data as 3-O-\u3b2-d-glucopyranosyl-2\u3b2,3\u3b2,6\u3b2,16\u3b1,23-pentahy droxyolean-12-en-28-oic acid 28-O-[\u3b1-l-rhamnopyranosyl(1\u21923)] [\u3b2-d-xylopyranosyl-(1\u21924)] [\u3b1-l-rhamnopyranosyl(1\u21922)]\u3b1-l-arabinopyranoside and 3-O-[\u3b2-d-apiofuranosyl(1\u21923)]\u3b2-d-glucopyrano-syl-2\u3b2,3 \u3b2,6\u3b2,16\u3b1,23-pentahydroxyolean-12-en-28-oic acid 28-O-[\u3b1-l-rhamnopyranosyl(1\u21923)] [\u3b2-d-xylopyranosyl-(1\u21924] [\u3b1-l-rhamnopyranosyl(1\u21922)]\u3b1-l-arabinopyranoside. 2D NMR experiments were useful in providing complete information on the structure and geometry of the new sapogenin present