Self-Organized Forest-Fires Near the Critical Time

We consider a forest-fire model which, somewhat informally, is described as follows: Each site (vertex) of the square lattice is either vacant or occupied by a tree. Vacant sites become occupied at rate 1. Further, each site is hit by lightning at rate λ. This lightning instantaneously destroys (makes vacant) the occupied cluster of the site.This model is closely related to the Drossel-Schwabl forest-fire model, which has received much attention in the physics literature. The most interesting behaviour seems to occur when the lightning rate goes to zero. In the physics literature it is believed that then the system has so-called self-organized critical behaviour.We let the system start with all sites vacant and study, for positive but small λ, the behaviour near the ‘critical time’ t _c , defined by the relation 1 − exp(− t _c ) = p _c , the critical probability for site percolation.Intuitively one might expect that if, for fixed t > t _c , we let simultaneously λ tend to 0 and m to ∞, the probability that some tree at distance smaller than m from O is burnt before time t goes to 1. However, we show that under a percolation-like assumption (which we can not prove but believe to be true) this intuition is false. We compare with the case where the square lattice is replaced by the directed binary tree, and pose some natural open problems.Part of vdB’s research is supported by BRICKS project AFM 2.2.     

N2O5 photolysis products investigated by fluorescence and optoacoustic techniques

Pulsed laser photolysis of N₂O₅ near 290 nm coupled with fluorescence detection (calibrated by NO₂ photolysis) showed that the O(³P) quantum yield is ≤0.1. A pulsed laser optoacoustic technique in a flow tube (ca. 6 torr of N₂) was tested by photolysis of NO₂ and then applied to N₂O₅. Nitric oxide was added to react with NO₃ free radical and the resulting increase in the optoacoustic signal confirmed the presence of NO₃ free radicals. Based on the relative optoacoustic signals observed for NO₂ and N₂O₅, the quantum yield for NO₃ production is 0.8 ± 0.2.     

Thermal isomerization of azulene to naphthalene in shock waves

The thermal isomerization of azulene was studied in shock waves over the range 1300–1900 K. Monitoring azulene and naphthalene light absorptions in the UV, a complete conversion azulene → naphthalene was observed. After correction for some falloff effects, a limiting high pressure rate constant k_x = 10^12.93 exp(?263 kJ mol^?1/RT) s^?1 was derived. Based on this k_x, specific rate constants k(E) for photoexcitation experiments were constructed.     

Geodetic graphs of diameter two

We survey what is known on geodetic graphs of diameter two and discuss the implications of a new strong necessary condition for the existence of such graphs.     

Resonance-enhanced multiphoton ionisation photoelectron spectroscopy of the ClO radical: the C 2 sigma- state

A (2 + 1) one-colour resonance-enhanced multiphoton ionisation study is carried out on the C 2 sigma- state of the ClO radical in the one-photon energy range 29,500-31,250 cm-1. The ClO radical is produced by one-photon photolysis of ClO2 employing 359.2 nm photons derived from a separate laser. In this way a significant concentration of vibrationally excited ClO in its spin-orbit split X 2 pi omega (omega = 3/2 or 1/2) electronic ground state is produced. In addition to mass-resolved excitation spectra, kinetic-energy resolved photoelectron spectra for the X 3 sigma-(v+)<--C 2 sigma-(v' = 3-5) transitions are measured. These transitions are not completely Frank-Condon diagonal, and indicate a decrease in bond length on removal of the Rydberg electron from the C 2 sigma- state. In addition to an unambiguous assignment of the C 2 sigma- state, valuable information is obtained on the degree of vibrational excitation with which the nascent ClO radical is formed in the photolysis of ClO2. Analysis of the photoelectron spectra is supported by Franck-Condon calculations based on potential energy curves either from experimental spectroscopic parameters, or obtained by theoretical ab initio methods.     

Electron delocalization in the radical cation of 1,3,6,8-tetraazatricyclo[4.4.1.1(3,8)]dodecane, a 4-nitrogen-7-electron system.

The radical cation of 1,3,6,8-tetraazatricyclo [4.4.1.1(3,8)]dodecane (TTD) has been studied using magnetic resonance and optical spectroscopic methods and computational techniques. With the help of deuterated isotopomers, assignments of EPR and resonance Raman spectra could be unequivocally established. The results demonstrate that the radical cation has D(2d) symmetry, and instantaneous electron delocalization over the four equivalent nitrogen atoms occurs. This extensive delocalization in a completely saturated system is a unique feature of the TTD radical cation. The spectroscopy of TTD, in contrast to that of simpler diamines such as 1,4-diaza[2.2.2]bicyclooctane, simultaneously reveals the consequences of orbital interactions through space and through bonds. The relationship between nitrogen pyramidalization and hyperfine coupling constants in nitrogen-centered radical cations with a number of different bonding arrangements is reviewed.     

On-line trace enrichment — column liquid chromatography of polar pollutants in surface water using bifunctional membrane-based extraction-disk cartridges

Summary An on-line trace-enrichment system, using a bifunctional membrane extraction-disk cartridge, has been combined with a column liquid chromatography separation for the simultaneous determination of basic, neutral and acidic pollutants in surface water. The enrichment device consisted of a specially constructed holder containing both C-18 and cation-exchange disks. The holder can contain up to 25 disks of 0.5 mm thickness and 4.6 mm diameter. Before trace enrichment of 20 ml of surface water (pH 3.0), calcium ions were removed from the sample by means of an oxalic acid precipitation. Desorption of the cartridge was at elevated temperature using reversed-phase gradient elution; detection was performed with a diode-array UV absorbance detector. The detection limits for the test compounds in surface water are typically 0.5–2 g/l; the calibration graphs are linear from the lower limit of determination up to 50 g/l.     

Trace enrichment of polar pollutants from water and the influence of humic substances

Summary A practical liquid chromatographic early-warning system for polar pollutants in water ought to have detection limits at a level below a microgram per litre. Using ultraviolet absorbance detection this normally necessitates trace enrichment of the samples. In this study ten different sorbents have been tested with respect to their enrichment capacity. The hydrophobic polymeric PLRP-S material, in combination with a C-18 modified analytical column, proved to be the best choice. The influence of humic substances, present in surface water, was also studied. Lowering of the sample pH, resulted in a significant increase in the interferences due to the humic substances.     

Expedient synthesis of a novel asymmetric selectively deprotectable derivative of the ATAC scaffold

An efficient multigram scale synthesis of a new asymmetric triazacyclophane scaffold, the ATAC (Asymmetric-TAC) scaffold, bearing three selectively removable groups is described. This scaffold is slightly more rigid than our frequently used TAC (TriAzaCyclophane) scaffold. The synthesis of the required triamine is very high yielding without difficult steps or purifications and was also applied to a much improved synthesis of our original TAC scaffold. Especially the tedious first reaction step, that is, mono-oNBS-protection of a triamine could be omitted. The rigidity of the triazacyclophane ring in both TAC- and ATAC scaffolds has also been investigated using variable temperature ¹H NMR experiments.