Fullerene Black: Relationship between Catalytic Activity in n-alkanes Dehydrocyclization and Reactivity in Oxidation, Bromination and Hydrogenolysis

The reactivity of fullerene black in oxidation (by air oxygen or ions MnO4–or Cr2O7 2– in solution), bromination (by Br2 or (C4H9)4NBr3) and hydrogenolysis (without hydrogenation catalyst) are studied. The dehydrocyclization of n-alkanes over fullerene black is realized via the monofunctional mechanism, i.e. the dehydrogenation and cyclization stages proceed on the same catalytic center. The addition of alumina to the catalyst transforms dehydrocyclization mechanism to bifunctional one, when fullerene black acts as dehydrogenation agent. Reactivity studies and ESR spectroscopy data for initial and annealed fullerene black show the presence in fullerene black structure of both non-conjugated multiple and dangling bonds. Nonconjugated bonds determine catalytic activity and reactivity of fullerene black. They are localized in amorphous part of fullerene black. Technological aspects of fullerene black as alkanes dehydrocyclization catalyst are discussed

Controllability of 2D Euler and Navier-Stokes equations by degenerate forcing

We study controllability issues for the 2D Euler and Navier- Stokes (NS) systems under periodic boundary conditions. These systems describe motion of homogeneous ideal or viscous incompressible fluid on a two-dimensional torus T^2. We assume the system to be controlled by a degenerate forcing applied to fixed number of modes. In our previous work [3, 5, 4] we studied global controllability by means of degenerate forcing for Navier-Stokes (NS) systems with nonvanishing viscosity (\nu > 0). Methods of dfferential geometric/Lie algebraic control theory have been used for that study. In [3] criteria for global controllability of nite-dimensional Galerkin approximations of 2D and 3D NS systems have been established. It is almost immediate to see that these criteria are also valid for the Galerkin approximations of the Euler systems. In [5, 4] we established a much more intricate suf- cient criteria for global controllability in finite-dimensional observed component and for L2-approximate controllability for 2D NS system. The justication of these criteria was based on a Lyapunov-Schmidt reduction to a finite-dimensional system. Possibility of such a reduction rested upon the dissipativity of NS system, and hence the previous approach can not be adapted for Euler system. In the present contribution we improve and extend the controllability results in several aspects: 1) we obtain a stronger sufficient condition for controllability of 2D NS system in an observed component and for L2- approximate controllability; 2) we prove that these criteria are valid for the case of ideal incompressible uid (\nu = 0); 3) we study solid controllability in projection on any finite-dimensional subspace and establish a sufficient criterion for such controllability

Methane Pyrolysis over Carbon Catalysts

Methane pyrolysis at the temperature range of 550-1000 °C in gas flow reactor with fixed bed of mixed  catalysts based on carbon materials of various structure (fullerene cocoons, fullerene black, vacuum black, cathode deposit, onion-like carbon, glassy carbon, carbon fibers, mineral shungite and graphite) has been studied. Methane pyrolysis products, including stoichiometric amount of hydrogen are C3-C4 alkanes, C2-C4 alkenes, aromatics and pyrolytic carbon. Methane pyrolysis is carried out both on a catalytic surface and in a volume and contribution of the surface is determined by pyrolysis temperature. Materials with curved carbon surface show an activity in methane dehydrogenation at lower temperatures, than materials with planar basic structure elements. Materials with a small specific surface area favor methane aromatization at 950–1000 °C with formation of mainly benzene, toluene and naphthalene. The primary activation of C–H bond in methane at temperatures of lower than 850 °C, as well as the multiple dehydrogenation conversions resulting in the formation of pyrolytic carbon and its precursors (aromatics), are, probably, heterogeneous reactions

A Priori Error Estimate of Stochastic Galerkin Method for Optimal Control Problem Governed by Random Parabolic PDE with Constrained Control

A stochastic Galerkin approximation scheme is proposed for an optimal control problem governed by a parabolic PDE with random perturbation in its coefficients. The objective functional is to minimize the expectation of a cost functional, and the deterministic control is of the obstacle constrained type. We obtain the necessary and sufficient optimality conditions and establish a scheme to approximate the optimality system through the discretization with respect to both the spatial space and the probability space by Galerkin method and with respect to time by the backward Euler scheme. A priori error estimates are derived for the state, the co-state and the control variables. Numerical examples are presented to illustrate our theoretical results

Quantitative estimates of unique continuation for parabolic equations, determination of unknown time-varying boundaries and optimal stability estimates

In this paper we will review the main results concerning the issue of stability for the determination unknown boundary portion of a thermic conducting body from Cauchy data for parabolic equations. We give detailed and selfcontained proofs. We prove that such problems are severely ill-posed in the sense that under a priori regularity assumptions on the unknown boundaries, up to any finite order of differentiability, the continuous dependence of unknown boundary from the measured data is, at best, of logarithmic type

Metal hydride hydrogen storage and compression systems for energy storage technologies

Along with a brief overview of literature data on energy storage technologies utilising hydrogen and metal hydrides, this article presents results of the related R&D activities carried out by the authors. The focus is put on proper selection of metal hydride materials on the basis of AB5- and AB2-type intermetallic compounds for hydrogen storage and compression applications, based on the analysis of PCT properties of the materials in systems with H2 gas. The article also presents features of integrated energy storage systems utilising metal hydride hydrogen storage and compression, as well as their metal hydride based components developed at IPCP and HySA Systems