Selection-mutation balance models with epistatic selection

We present an application of birth-and-death processes on configuration spaces to a generalized mutation4 selection balance model. The model describes the aging of population as a process of accumulation of mu5 tations in a genotype. A rigorous treatment demands that mutations correspond to points in abstract spaces. 6 Our model describes an infinite-population, infinite-sites model in continuum. The dynamical equation which 7 describes the system, is of Kimura-Maruyama type. The problem can be posed in terms of evolution of states 8 (differential equation) or, equivalently, represented in terms of Feynman-Kac formula. The questions of interest 9 are the existence of a solution, its asymptotic behavior, and properties of the limiting state. In the non-epistatic 10 case the problem was posed and solved in [Steinsaltz D., Evans S.N., Wachter K.W., Adv. Appl. Math., 2005, 11 35(1)]. In our model we consider a topological space X as the space of positions of mutations and the influence of epistatic potentials

Extension of explicit formulas in Poissonian white noise analysis using harmonic analysis on configuration spaces

Harmonic analysis on configuration spaces is used in order to extend explicit expressions for the images of creation, annihilation, and second quantization operators in L2-spaces with respect to Poisson point processes to a set of functions larger than the space obtained by directly using chaos expansion. This permits, in particular, to derive an explicit expression for the generator of the second quantization of a sub-Markovian contraction semigroup on a set of functions which forms a core of the generator.

The role of Ti3+ interstitials in TiO2(110) reduction and oxidation

Here we describe results which teach us much about the mechanism of the reduction and oxidation of TiO2(110) by the application of scanning tunnelling microscopy imaging at high temperatures. Titania reduces at high temperature by thermal oxygen loss to leave localized (i.e. Ti3+) and delocalized electrons on the lattice Ti, and a reduced titania interstitial that diffuses into the bulk of the crystal. The interstitial titania can be recalled to the surface by treatment in very low pressures of oxygen, occurring at a significant rate even at 573 K. This re-oxidation occurs by re-growth of titania layers in a Volmer-Weber manner, by a repeating sequence in which in-growth of extra titania within the cross-linked (1 x 2) structure completes the (1 x 1) bulk termination. The next layer then initiates with the nucleation of points and strings which extend to form islands of cross-linked (1 x 2), which once again grow and fill in to reform the (1 x 1). This process continues in a cyclical manner to form many new layers of well-ordered titania. The details of the mechanism and kinetics of the process are considered.

Adsorption and dissociation of benzene on bimetallic surfaces - the influence of surface geometry and electronic structure

This topical review discusses the influence of the surface geometry (e.g. lattice parameters and termination) and electronic structure of well-defined bimetallic surfaces on the adsorption and dissociation of benzene. The available data can be divided into two categories with combinations of non-transition metals and transition metals on the one side and combinations of two transition metals on the other. The main effect of non-transition metals in surface alloys is site blocking which can suppress chemisorption and dissociation of the molecules completely. When two transition metals are combined, the effects are less dramatic. They mainly affect the strength of the chemisorption bond and the degree of dissociation due to electronic and template effects.

The influence of carbon surface oxygen groups on Dubinin–Astakhov equation parameters calculated from CO2 adsorption isotherm

We present the results of a systematic study of the influence of carbon surface oxidation on Dubinin–Astakhov isotherm parameters obtained from the fitting of CO2 adsorption data. Using GCMC simulations of adsorption on realistic VPC models differing in porosity and containing the most frequently occurring carbon surface functionalities (carboxyls, hydroxyls and carbonyls) and their mixtures, it is concluded that the maximum adsorption calculated from the DA model is not strongly affected by the presence of oxygen groups. Unfortunately, the same cannot be said of the remaining two parameters of this model i.e. the heterogeneity parameter (n) and the characteristic energy of adsorption (E0). Since from the latter the pore diameters of carbons are usually calculated, by inverse-type relationships, it is concluded that they are questionable for carbons containing surface oxides, especially carboxyls.

The influence of the carbon surface chemical composition on Dubinin-Astakhov equation parameters calculated from SF(6) adsorption data-grand canonical Monte Carlo simulation

Using grand canonical Monte Carlo simulation we show, for the first time, the influence of the carbon porosity and surface oxidation on the parameters of the Dubinin-Astakhov (DA) adsorption isotherm equation. We conclude that upon carbon surface oxidation, the adsorption decreases for all carbons studied. Moreover, the parameters of the DA model depend on the number of surface oxygen groups. That is why in the case of carbons containing surface polar groups, SF(6) adsorption isotherm data cannot be used for characterization of the porosity.

Ultrathin graphitic structures and carbon nanotubes in a purified synthetic graphite

A new class of carbon structure is reported, which consists of microscale graphitic shells bounded by curved and faceted planes containing two to five layers. These structures were originally found in a commercial graphite produced by the Acheson process, followed by a purification treatment. The particles, which could be several hundreds of nanometres in size, were frequently decorated with nanoscale carbon particles, or short nanotubes. In some cases, nanotubes were found to be seamlessly connected to the thin shells, indicating that the formation of the shells and that of the nanotubes are intimately connected. The structures are believed to form during a purification process which involves passing an electric current through the graphite in the presence of a reactive gas. In support of this, it is shown that similar particles can be produced in a standard carbon arc apparatus. With their extremely thin graphene walls and high surface areas, the new structures may have a range of useful properties.