Pattern formation in diffusion-limited reactions

The conditions for macroscopic segregation ofA andB in a steady-stateA+B 0 reaction are studied in infinite systems. Segregation occurs in one and two dimensions and is marginal ford=3. We note the dependence of these results on the precise experimental conditions assumed in the theory. We also note the difference between these results and our earlier ones for finite systems where the critical dimension isd=2.     

Networks and chain coverings in partial orders and their products

For an arbitrary poset P, subposets {P _i : 1ik} form a transitive basis of P if P is the transitive closure of their union. Let u be the minimum size of a covering of P by chains within posets of the basis, s the maximum size of a family of elements with no pair comparable in any basis poset, and a the maximum size of an antichain in P. Define a dense covering to be a collection D of chains within basis posets such that each element belongs to a chain in D within each basis poset and is the top of at least k-1 chains and the bottom of at least k-1 chains in D. Dense coverings generalize ordinary chain coverings of poset. Let d=min {|D|–(k–1)|P|}. For an arbitrary poset and transitive basis, a convenient network model for dense coverings yields the following: Theorem 1: da, with equality iff P has a minimum chain decomposition in which every pair of consecutive elements on each chain are comparable in some basis poset. Theorem 2: usda. Theorem 3: s=d iff s=a. The most interesting special case is where the transitive basis expresses P as the product of two posets, in which case u and s measure the minimum and maximum sizes of unichain coverings and semiantichains.     

Some spectrofluorimetric applications of the cerium(IV)-cerium(III) system

Cerium(III) ions in dilute sulphuric acid medium exhibit a characteristic fluorescence which has its excitation maximum at 260 nm and its fluorescence emission maximum at 350 nm. By utilising the osmium-catalysed redox reaction between cerium(IV) and arsenic(III), microgram amounts of arsenic (7.5–37.5 μg) may be determined by spectrofluorimetric measurement of the ceriurm(III) produced. The principle may be applied to the determination of several other ions which cannot yet be determined by direct spectrofluorimetry, e.g.. Fe(II) (5.6–28 μg), oxalate (8.8–44μg). Osmium(VIII) (0.05–0.2 μg) and iodide (0.6–2.5 μg) may be determined by their catalytic action.     

Regressions and monotone chains II: The poset of integer intervals

A regressive function (also called a regression or contractive mapping) on a partial order P is a function mapping P to itself such that (x)x. A monotone k-chain for is a k-chain on which is order-preserving; i.e., a chain x ₁<...ksuch that (x ₁)...(x_k). Let P _nbe the poset of integer intervals {i, i+1, ..., m} contained in {1, 2, ..., n}, ordered by inclusion. Let f(k) be the least value of n such that every regression on P _nhas a monotone k+1-chain, let t(x,j) be defined by t(x, 0)=1 and t(x,j)=x ^t(x,j–1). Then f(k) exists for all k (originally proved by D. White), and t(2,k) < f(K) <t( + _k, k) , where _k 0 as k. Alternatively, the largest k such that every regression on P _nis guaranteed to have a monotone k-chain lies between lg^*(n) and lg^*(n)–2, inclusive, where lg^*(n) is the number of appliations of logarithm base 2 required to reduce n to a negative number. Analogous results hold for choice functions, which are regressions in which every element is mapped to a minimal element.     

Analogy between the Lorenz strange attractor and a bistable stochastic oscillator

The relation between the aperiodic solution of the Lorenz model and that of a stochastic anharmonic oscillator is explored. The stochastic oscillator is constructed by replacing (t) in the Lorenz model by a stochastic variable(t) of specified statistics. The resulting system is of course not isomorphic to the Lorenz model, but does share with it a number of statistical properties. Thus, within the confines of these measures the two systems are physically very similar.     

Statistical replacement for systems with delta-correlated fluctuations

Nonlinear systems with stochastic parameters are approximated by simpler systems using a method that we call statistical replacement. This method is an extension of the previously developed AGREE which was restricted to systems with additive fluctuations. Statistical replacement incorporates the distinctions between globally stable thermodynamically closed systems and thermodynamically open systems that can be unstable.     

Preparation and Characterization of Compositions Based on PbO-MgO-Nb2O5 Using the Sol-Gel Method

Lead Magnesium Niobate, Pb(Mg_1/3Nb_2/3)O₃ (PMN), is an important relaxor ferroelectric material. A significant problem exists, however, in the preparation of this material: it is very difficult to prepare pure phase, without the presence of a pyrochlore impurity phase which degrades the dielectric properties. Depending on the processing conditions, the amount of pyrochlore phase varies.Considering the ternary diagram PbO-MgO-Nb₂O₅, different compositions have been prepared by a simple sol-gel method at room temperature using Pb(CH₃COO)₂, Mg(CH₃COO)₂, Nb(OC₂H₅)₅ as precursors. After the heat treatment, the samples obtained were analyzed by XRD and EPMA with the purpose of studying the compositions formed.From the analysis of these results, it seems to be that the appearance of pyrochlore can be related to the reactivity of the MgO and/or the presence of other phases of the binary system PbO-Nb₂O₅. An excess of Pb and Mg is necessary for compositions to be formed near the PMN. The control of the amount of these two elements is very important because an excess of MgO would lead to rich compositions in Mg as a secondary phase.     

Atomic emission spectrometry with an induction-coupled high-frequency plasma source: The determination of iodine,mercury, arsenic and selenium

The application of an inductively coupled high-frequency plasma source to the determination of iodine, mercury, arsenic and selenium by atomic emission spectrometry at wavelengths less than 200 nm is described. Optimal conditions have been established, and the spectral interference effects at different atomic lines for each element have been investigated. With the type of instrumentation employed, the determination of iodine at 183.04 nm, mercury at 184.96 nm, arsenic at 189.0 nm and selenium at 196.09 nm is recommended to minimize spectral interferences. No chemical or physical interferences resulting from the influence of foreign ions on the solute vaporization process have been noted.