Geometric properties of Poisson matchings

Suppose that red and blue points occur as independent Poisson processes of equal intensity in ${\mathbb {R}^d}$ , and that the red points are matched to the blue points via straight edges in a translation-invariant way. We address several closely related properties of such matchings. We prove that there exist matchings that locally minimize total edge length in d?=?1 and d??? 3, but not in the strip ${\mathbb {R}\times[0,1]}$ . We prove that there exist matchings in which every bounded set intersects only finitely many edges in d ?? 2, but not in d = 1 or in the strip. It is unknown whether there exists a matching with no crossings in d = 2, but we prove positive answers to various relaxations of this question. Several open problems are presented.     

Determining exchange splitting in a magnetic semiconductor by spin-filter tunneling

A large exchange splitting of the conduction band in ultrathin films of the ferromagnetic semiconductor EuO was determined quantitatively, by using EuO as a tunnel barrier and fitting the current-voltage characteristics and temperature dependence to tunneling theory. This exchange splitting leads to different tunnel barrier heights for spin-up and spin-down electrons and is large enough to produce a near-fully spin-polarized current. Moreover, the magnetic properties of these ultrathin films (<6 nm) show a reduction in Curie temperature with decreasing thickness, in agreement with theoretical calculation [R. Schiller, Phys. Rev. Lett. 86, 3847 (2001)10.1103/Phys. Rev. Lett.86.3847].     

Inequalities in Entanglement Percolation

We present proofs of two results concerning entanglement in three-dimensional bond percolation. Firstly, the critical probability for entanglement with free boundary conditions is strictly less than the critical probability for connectivity percolation. (The proof presented here is a detailed justification of the ideas sketched in Aizenman and Grimmett.) Secondly, under the hypothesis that the critical probabilities for entanglement with free and wired boundary conditions are different, for p between the two critical probabilities, the size of the entangled cluster at the origin with free boundary conditions does not have exponentially decaying tails.     

Lattice distortion around the F+ center in MgO

Nuclear quadrupole couplings have been measured for Mg²⁵ nuclei in the third and fifth ion shells around the F⁺ center in MgO. These couplings are used to determine the lattice relaxations and polarizations in the neighbourhood of the defect.     

Energetics and volume changes in electron attachment to pyrazine in supercritical xenon

The attachment of electrons to pyrazine occurs reversibly over a wide range of pressures at and above room temperature in supercritical xenon. The rate constant for attachment increases with pressure at low pressures, passes through a maximum, and levels off at values of 1-3x10(12) m(-1) s(-1) at high pressure. The activation volumes for attachment (DeltaVa*) are quite small but show maxima near the compressibility maxima. In contrast, DeltaVa* is always negative for this reaction in sc-ethane and exhibits minima near the compressibility maxima. The rate constants for electron detachment change little with pressure but increase with temperature. Activation volumes for detachment are small. To explain the small volume change observed for this reaction, it is proposed that at the higher pressures clustering around the neutral pyrazine is comparable to that around the ion; i.e., the partial molar volumes are comparable. The free energy change (DeltaGr) of this reaction decreases between 40 and 60 bar and then is fairly constant at higher pressures. The dependence of DeltaGr on pressure is consistent with clustering around the neutral pyrazine at higher pressure. Also, the electron affinity of the clusters, pyrazineXen, increases with n to a few tenths of an eV.     

Sharp metastability threshold for two-dimensional bootstrap percolation

 In the bootstrap percolation model, sites in an L by L square are initially independently declared active with probability p. At each time step, an inactive site becomes active if at least two of its four neighbours are active. We study the behaviour as p→0 and L→∞ simultaneously of the probability I(L,p) that the entire square is eventually active. We prove that I(L,p)→1 if , and I(L,p)→0 if , where λ=π²/18. We prove the same behaviour, with the same threshold λ, for the probability J(L,p) that a site is active by time L in the process on the infinite lattice. The same results hold for the so-called modified bootstrap percolation model, but with threshold λ^′=π²/6. The existence of the thresholds λ,λ^′ settles a conjecture of Aizenman and Lebowitz [3], while the determination of their values corrects numerical predictions of Adler, Stauffer and Aharony [2]. Received: 12 May 2002 / Revised version: 12 August 2002 / Published online: 14 November 2002 Research funded in part by NSF Grant DMS-0072398 Mathematics Subject Classification (2000): Primary 60K35; Secondary 82B43 Key words or phrases: Bootstrap percolation – Cellular automaton – Metastability – Finite-size scaling     

Computational Investigation of the Substituent Effect on the Intramolecular Proton Transfer Reaction of 3-Hydroxytropolone

The effects of substituent type and position on the proton transfer reaction of 3-hydroxytropolone(3-OHTRN) have been investigated theoretically by using density functional theory at the level of B3LYP/ 6-31+G** method. The influence of solvent on the proton transfer reactions of substituted 3-OHTRN has been examined using the self-consistent isodensity polarized continuum model(SCI-PCM) in water. As a result, while the proton transfer reaction is kinetically the easiest by substitution on position 3 of-NH2 group in the gas phase, it is kinetically the easiest by substitution on position 5 of the same group in water. In addition, these reactions are either kinetically or thermodynamically easier in the gas phase than that in water, except the reaction of structure with-NH2 group at position 6.     

Molecular beam studies of ethanol oxidation on Pd(110)

The adsorption and decomposition of ethanol on Pd(110) has been studied by use of a molecular beam reactor and temperature programmed desorption. It is found that the major pathway for ethanol decomposition occurs via a surface ethoxy to a methyl group, carbon monoxide and hydrogen adatoms. The methyl groups can either produce methane (which they do with a high selectivity for adsorption below 250 K) or can further decompose (which they do with a high selectivity for adsorption above 350 K) resulting in surface carbon. If adsorption occurs above 250 K a high temperature (450 K) hydrogen peak is observed in TPD, resulting from the decomposition of stable hydrocarbon fragments. A competing pathway also exists which involves C---O bond scission of the ethoxy, probably caused by a critical ensemble of palladium atoms at steps, defects or due to a local surface reconstruction. The presence of oxygen does not significantly alter the decomposition pathway above 250 K except that water and, above 380 K, carbon dioxide are produced by reaction of the oxygen adatoms with hydrogen adatoms and adsorbed carbon monoxide respectively. Below 250 K, some ethanol can form acetate which decomposes around 400 K to produce carbon dioxide and hydrogen.