Kinetic limit of a conservative lattice gas dynamics showing long-range correlations

An anisotropic lattice gas dynamics is investigated for which particles on ^d jump to empty nearest neighbor sites with (fast) rate ^–2 in a specified direction and some particular configuration-dependent rates in the other directions. The model is translation and reflection invariant and is particle conserving. The space coordinate in the fast-rate direction is rescaled by ^–1. It follows that the density field converges in probability, as 0, to the corresponding solution of a nonlinear diffusion-type equation. The microscopic fluctuations about the deterministic macroscopic evolution are determined explicitly and it is found that the stationary fluctuations decay via a power law (1/r ^d ) with the direction dependence of a quadrupole field.     

Statistical mechanics of probabilistic cellular automata

We investigate the behavior of discrete-time probabilistic cellular automata (PCA), which are Markov processes on spin configurations on ad-dimensional lattice, from a rigorous statistical mechanics point of view. In particular, we exploit, whenever possible, the correspondence between stationary measures on the space-time histories of PCAs on ^d and translation-invariant Gibbs states for a related Hamiltonian on ( ^d+1). This leads to a simple large-deviation formula for the space-time histories of the PCA and a proof that in a high-temperature regime the stationary states of the PCA are Gibbsian. We also obtain results about entropy, fluctuations, and correlation inequalities, and demonstrate uniqueness of the invariant state and exponential decay of correlations in a high-noise regime. We discuss phase transitions in the low-noise (or low-temperature) regime and review Toom's proof of nonergodicity of a certain class of PCAs.     

Spectral methods with sparse matrices

Summary Spectral methods employ global polynomials for approximation. Hence they give very accurate approximations for smooth solutions. Unfortunately, for Dirichlet problems the matrices involved are dense and have condition numbers growing asO(N ⁴) for polynomials of degree N in each variable. We propose a new spectral method for the Helmholtz equation with a symmetric and sparse matrix whose condition number grows only asO(N ²). Certain algebraic spectral multigrid methods can be efficiently used for solving the resulting system. Numerical results are presented which show that we have probably found the most effective solver for spectral systems.     

On the solution of singular linear systems of algebraic equations by semiiterative methods

Summary For a square matrixT ^n,n , where (I–T) is possibly singular, we investigate the solution of the linear fixed point problemx=T x+c by applying semiiterative methods (SIM's) to the basic iterationx ₀ ⁿ ,x _k T c _k–1+c(k1). Such problems arise if one splits the coefficient matrix of a linear systemA x=b of algebraic equations according toA=M–N (M nonsingular) which leads tox=M ^–1 N x+M ^–1 bT x+c. Even ifx=T x+c is consistent there are cases where the basic iteration fails to converge, namely ifT possesses eigenvalues 1 with ||1, or if =1 is an eigenvalue ofT with nonlinear elementary divisors. In these cases — and also ifx=T x+c is incompatible — we derive necessary and sufficient conditions implying that a SIM tends to a vector which can be described in terms of the Drazin inverse of (I–T). We further give conditions under which is a solution or a least squares solution of (I–T)x=c.Research supported in part by the Alexander von Humboldt-Stiftung     

N-(17-Phosphonooxylinolenoyl)glutamine and N-(17-phosphonooxylinoleoyl)glutamine from insect gut: the first backbone-phosphorylated fatty acid derivatives in nature

N-(17-Phosphonooxylinolenoyl)glutamine (1) and N-(17-phosphonooxylinoleoyl)glutamine (2) were isolated from the regurgitate of Spodoptora exigua and identified as the first natural alkyl chain-phosphorylated fatty acid derivatives. The compounds were characterized by HPLC-MS/MS and the assigned structures confirmed by synthesis via a dissymmetric bis-Wittig approach as the key reaction. Rearing of the larvae on a diet enriched with inorganic phosphate increased the amount of the phosphorylated N-acyl glutamines in the regurgitate.     

Fe(CO)5 thin films adsorbed on Au(111) and on self-assembled organic monolayers: I. Structure

The adsorption of Fe(CO)(5) onto Au(111)/mica and C(4), C(8), C(12), and C(16) SAMs/Au(111)/mica surfaces has been studied using infrared spectroscopy to elucidate the coverage-dependent structures of these films and the intermolecular couplings that determine the form of the spectra. For all substrates, the first layer is composed of molecules physisorbed with one axial and two equatorial carbonyl groups directed toward the substrate; subsequent layers are preferentially oriented with the C(3) molecular axis aligned perpendicular to the substrate (i.e., one axial carbonyl group directed toward the substrate). The axial vibrational band systematically shifts to higher frequencies with increasing surface coverage because of the effects of intermolecular coupling of the quasiparallel transition dipole moments. The strong effects of dipolar coupling are also witnessed by the trends of the band positions when the distance to the image plane is systematically varied using highly organized self-assembled organic substrates; no band shifts are observed when dilute Fe(CO)(5) is embedded in Xe matrixes under identical experimental conditions. The as-deposited films are structurally stable below 125 K on Au(111)/mica surfaces and below 100 K on the organic self-assembled monolayers. The instability of the films above these temperatures demonstrates that the as-adsorbed films do not form thermodynamically well-defined phases but are structurally metastable. The results presented herein and in the companion paper provide a consistent framework to interpret the spectroscopy of these systems that resolves outstanding issues concerning these films and provides a structural model that explains the dynamic properties of these films during exposure to low-energy electron beams.     

Synthesis of some substituted 3-alkenyl-1-phenylpyrazoles

The regioselective synthesis of new 3-alkenyl-1-phenylpyrazoles 4 from the reaction of phenylhydrazine with 2,3-dihydro-4H-pyran-4-ones 1 is described.     

Synthetic applications of 2-chlorooxiranes: preparation of thiazoles,dihydrothiazoles and selenazoles

The reaction of 2-chlorooxiranes 1 with thioamides and thioureas provides access to thiazoles, 4-hydroxy-4,5-dihydrothiazoles and 2-imino-2,3-dihydrothiazoles under mild conditions and with excellent yields. With 1 and selenourea, near quantitative yields of selenazoles are obtained.     

Determination of zearalenone and ochratoxin A in soil

Mycotoxins are secondary metabolites, formed by the action of fungi on agricultural crops in the field or during storage. These metabolites are highly toxic to animals and humans and high levels have been measured in agricultural crops. In order to evaluate human risks due to ingestion of mycotoxin-contaminated food different methods have been developed for analysis of mycotoxins in cereals and maize. In this project the focus was on mycotoxins in agricultural soil and the fate of these toxins in the soil-water-plant system. Two different mycotoxins were selected in the study: zearalenone (ZON) produced by species of Fusariumor Aspergillusand ochratoxin A (OTA) produced by species of Penicillium. We developed a method for analysis of these toxins in soil. Soil samples were extracted with methanol-water (9:1) and purified by solid-phase extraction (SPE, C8-columns). The final extract was analysed using high-pressure liquid chromatography (HPLC) with fluorescence detection. A Phenyl Hexyl column was used to separate the toxins. The detection limits obtained were 0.1 and 1.0 microg kg(-1) dry weight (dw) for OTA and ZON, respectively. The developed method has been used for analysis of different soils in connection with growth chamber experiments. The soil types used in the growth chamber experiments were a sandy soil, a sandy clay soil, and a soil with high content of organic matter. The recovery was determined as 85.8 and 93.4% and the repeatability to 5.1 and 12.8% for OTA and ZON, respectively. The reproducibility obtained was 8.5 and 15.0% for soil samples, representing concentration levels from 0.2-30 microg kg(-1) dw (OTA) and from 1.0-100 microg kg(-1) dw (ZON).