The two-neutron transfer reactions (O, O) with O, C and Mg targets

Excitation functions, angular distributions and differential ranges were measured for the ²⁶Mg(¹⁸O, ¹⁶O)²⁸Mg reaction at ¹⁸O beam energies of 20–45 MeV. Excitation functions only were measured for the reactions ¹⁴C(¹⁸O, ¹⁹O)¹³C, ¹⁴C(¹⁸O, ¹⁶O)¹⁶C, ¹⁴C(¹⁸O, ²⁰O)¹²C, ¹⁴C(¹⁸O, ¹⁵N)¹⁷N and ¹⁸O(¹⁸O, ¹⁹O)¹⁷O, ¹⁸O(¹⁸O, ¹⁶O)²⁰O, ¹⁸O(¹⁸O, ¹⁵N)²¹F at ¹⁸O beam energies of 13–41 MeV. We have identified these as direct reactions in which a single neutron, a two-neutron cluster, a deuteron and a triton are transferred between projectile and target.

The cross sections for two-neutron transfer reactions were found to be relatively high and those for the ¹⁸O+¹⁸O and the ¹⁴C+¹⁸O reactions were higher than the ones of single-neutron transfers over most of the energy range.

Attempts were made to apply the theory of Buttle and Goldfarb for single-neutron transfer to the case of two-neutron transfer in the ²⁶Mg(¹⁸O, ¹⁶O)²⁸Mg reaction below the Coulomb barrier. It is shown that for those reactions for which the assumptions, implicit in the model, are valid, good agreement is obtained with experiment. We also tried to apply the diffraction model of Dar and Kozlovsky to the calculation of the angular distribution of these reactions. A good fit to the experimental results could be obtained if quite different sets of parameters were used in the calculations for the two bombarding energies.     

Quasi‐polynomial mixing of critical two‐dimensional random cluster models

We study the Glauber dynamics for the random cluster (FK) model on the torus with parameters (p,q), for q ∈ (1,4] and p the critical point p_c. The dynamics is believed to undergo a critical slowdown, with its continuous‐time mixing time transitioning from for p ≠ p_c to a power‐law in n at p = p_c. This was verified at p ≠ p_c by Blanca and Sinclair, whereas at the critical p = p_c, with the exception of the special integer points q = 2,3,4 (where the model corresponds to the Ising/Potts models) the best‐known upper bound on mixing was exponential in n. Here we prove an upper bound of at p = p_c for all q ∈ (1,4], where a key ingredient is bounding the number of nested long‐range crossings at criticality.     

Cycle Factors and Renewal Theory

For which values of k does a uniformly chosen 3‐regular graph G on n vertices typically contain n/k vertex‐disjoint k ‐cycles (a k ‐cycle factor)? To date, this has been answered for k = n and for k ? log n ; the former, the Hamiltonicity problem, was finally answered in the affirmative by Robinson and Wormald in 1992, while the answer in the latter case is negative since with high probability (w.h.p.) most vertices do not lie on k ‐cycles. A major role in our study of this problem is played by renewal processes without replacement, where one wishes to estimate the probability that in a uniform permutation of a given set of positive integers, the partial sums hit a designated target integer. Using sharp tail estimates for these renewal processes, which may be of independent interest, we settle the cycle factor problem completely: the “threshold” for a k ‐cycle factor in G as above is κ ₀ log₂ n with . To be precise, G contains a k ‐cycle factor w.h.p. if and w.h.p. does not contain one if . Thus, for most values of n the threshold concentrates on the single integer K ₀(n ). As a byproduct, we confirm the “comb conjecture,” an old problem concerning the embedding of certain spanning trees in the random graph (n,p ).© 2015 Wiley Periodicals, Inc.     

On the maximum number of edges in quasi-planar graphs

A topological graph is quasi-planar, if it does not contain three pairwise crossing edges. Agarwal et al. [P.K. Agarwal, B. Aronov, J. Pach, R. Pollack, M. Sharir, Quasi-planar graphs have a linear number of edges, Combinatorica 17 (1) (1997) 1-9] proved that these graphs have a linear number of edges. We give a simple proof for this fact that yields the better upper bound of 8n edges for n vertices. Our best construction with 7n−O(1) edges comes very close to this bound. Moreover, we show matching upper and lower bounds for several relaxations and restrictions of this problem. In particular, we show that the maximum number of edges of a simple quasi-planar topological graph (i.e., every pair of edges have at most one point in common) is 6.5n−O(1), thereby exhibiting that non-simple quasi-planar graphs may have many more edges than simple ones.     

Use of sol-gel entrapment techniques for the resolution of itaconic acid biosynthetic pathway in Aspergillus terreus

A new technique of investigation of labile metabolic pathways using immobilization of the pathway in sol-gel derived silicate matrices was demonstrated. The biosynthetic pathway of itaconic acid in Aspergillus terreus is believed to proceed through decarboxylation of cis-aconitate catalyzed by an unstable enzyme aconitate decarboxylase, E.C. 4.1.1.6. Stabilization of this pathway in sol-gel derived silicate matrix enabled the elucidation of the correct sequence of biosynthetic steps. The decarboxylation of cis-aconitate does not lead directly to itaconate, but rather to citraconate. The latter is then isomerized to itaconate by a previously unknown enzyme.     

Infrared laser enhancement of the reaction of sulfur hexafluoride with sodium vapor

The vibrational energy dependence of the rate of the gas phase reaction of Na with SF₆ has been determined in a diffusion cloud experiment using CO₂ laser excitation. The “conversion efficiency” of ca. 40% for vibrational energy suggests a preference for vibrational over the translational energy when compared with “prior” statistical expectation.     

Effect of the Solvent on the Conformation of Isolated MEH‐PPV Chains Intercalated Into SnS2

Photophysical processes in conjugated polymers are influenced by two competing effects: the extent of excited state delocalization along a chain, and the electronic interaction between chains. Experimentally, it is often difficult to separate the two because both are controlled by chain conformation. Here we demonstrate that it is possible to modify intra‐chain delocalization without inducing inter‐chain interactions by intercalating polymer monolayers between the sheets of an inorganic layered matrix. The red‐emitting conjugated polymer, MEH‐PPV, is confined to the interlayer space of layered SnS₂. The formation of isolated polymer monolayers between the SnS₂ sheets is confirmed by X‐ray diffraction measurements. Photoluminescence excitation (PLE) and photoluminescence (PL) spectra of the incorporated MEH‐PPV chains reveal that the morphology of the incorporated chains can be varied through the choice of solvent used for chain intercalation. Incorporation from chloroform results in more extended conformations compared to intercalation from xylene. Even highly twisted conformations can be achieved when the incorporation occurs from a methanol:chloroform mixture. The PL spectra of the MEH‐PPV incorporated SnS₂ nanocomposites using the different solvents are in good agreement with the PL spectra of the same solutions, indicating that the conformation of the polymer chains in the solutions is retained upon intercalation into the inorganic host. Therefore, intercalation of conjugated polymer chains into layered hosts enables the study of intra‐chain photophysical processes as a function of chain conformation.     

Synthesis and evaluation of a pseudocyclic tristhiourea-based anion host

A novel methodology for the evaluation of receptor arrangement in structurally flexible anion chemosensors was developed and applied to map the binding site of a new pseudocyclic tristhiourea chemosensor (6). The syntheses of 6 and related macrocyclic chemosensor 10 (a model of the folded monomeric structure of 6) are reported. Both chemosensors were evaluated by titration with a variety of structurally different anions in CH3Cl and DMSO, showing a common preference for F-, CH3CO2-, and H2PO4-. However, within this group of anions, the binding patterns of the chemosensors differed, indicating dissimilarity in the arrangement of the binding sites of 6 and 10.