Cycles in bipartite tournaments

It is shown that if an oriented complete bipartite graph has a directed cycle of length 2n, then it has directed cycles of all smaller even lengths unless n is even and the 2n-cycle induces one special digraph.     

Symmetric space scalar field theory

Some quantum field theories, such as the chiral SU(2) ? SU(2) theory, can have a dynamics invariant under a group $\text{G}$ that is realized on a vacuum which is invariant only under a subgroup $\text{H}$ of $\text{G}$. These theories may be defined by scalar fields which are coordinates for the coset manifold $\text{G}$/$\text{H}$. They are thus non-polynomial theories on a symmetric space, with the group motions in this space described by a set of Killing vectors. We show how the Lagrange function may be constructed entirely from the Killing vectors. In particular, all physical quantities may be expressed in terms of the currents formed out of the Killing vectors. The current correlation functions do not exhibit the spurious wave function renormalizations which are encountered if ordinary Green's functions are computed. We illustrate the general method by calculating one-loop counter terms in a completely invariant fashion. An Appendix describes in simple terms the general theory of symmetric spaces, which should prove useful in other contexts.     

Diffusion mechanisms in solid and molten polyethylene

The diffusion coefficient D and solubility coefficient k of small molecules [C₃H₆, C₄H₁₀, (CH₃)₄C] are determined at very low solute concentrations in annealed linear polyethylene over a wide range of temperature above and below the melting point T_m. For measurements above T_m the specimen was lightly crosslinked by irradiation from a ⁶⁰Co source. The diffusion data fit equations of the form D = D₀ exp {–ΔH_D/RT}. An abrupt change in ΔH_D occurs at T_m: representative values (for C₄H₁₀) are 4.53 and 14.9 kcal/mole above and below T_m. At T_m, D₀ also changes abruptly: representative values (for C₄H₁₀) are log D₀ = ?2.65 above T_m and log D₀ = +2.70 below T_m. The mechanism of diffusion therefore changes at the melting point. The melt exhibits typical liquidlike characteristics (negative values of activation entropy ΔS_D). The ratio ΔS_D/ΔH_D = 4β (β denoting the isobaric coefficient of volume expansion) holds below but not above T_m. Equations of the form k = k₀ exp {–ΔH_k/RT} fit the solubility data. The log k versus T^?1 plots above and below T_m are parallel but separated by a step at T_m. If crystallization followed by annealing is assumed to leave a weight fraction of polymer α_k (the amorphous fraction) in which the solute can absorb and if the specific solubility coefficient of the amorphous fraction is identical to that of the melt, then log α_k Equals the magnitude of the step at T_m. Values of α_k determined from the observed step are very close to values of amorphous fraction determined by measurement of density. The solubility experiments support the concept of polyethylene as a two-phase solid with the amorphous fraction of specific volume equal to the extrapholated specific volume of the melt. The passage of a solute molecule from one potential well to another, however, occurs by processes in the melt and the amorphous fraction which are entirely different.     

Contact electrification

If two materials are brought into contact and then separated they are found to be charged; this is the phenomenon of ‘contact electrification’. The subject falls naturally into three divisions—electrification of metals by metals; of insulators by metals; and of insulators by insulators. The first of these is well understood; charge transfer between metals is such as to bring the two Fermi levels into coincidence. The second division, electrification of insulators by metals, has been much studied recently and takes up the main part of our review; our understanding remains imperfect, chiefly because of lack of knowledge about the relevant electron states in insulators. Electrification of insulators by insulators has not been studied so extensively, but there is evidence that an understanding of the metal/insulator case will lead to an understanding of the insulator/insulator case as well.     

An Epr Study of Alkali-Metal-Doped Poly(P-Phenylene) and P-Phenylene Oligomers

Poly(p-phenylene), PPP, and fully-deuterated poly(p-phenylene), DPPP, were heavily doped with lithium, sodium, potassium, rubidium, cesium, and successively with potassium then lithium. Inert atmosphere conditions using alkali naphthalides in THF were used. The spin susceptibility of each of these samples was not Curie-Weiss over the entire temperature range 7 to 300 K. The EPR linewidths at 300 K of donor-doped PPP were dependent on spinorbit coupling with the alkali metal, varying from a peak-to-peak width at 300 K of 0.5 G for the lithium-doped sample to 5.5 G for the cesium-doped sample. A small decrease in linewidths was noted upon doping of DPPP, these same linewidths equaling 0.35 and 4.5 G. In contrast, the linewidths of Li, K. and Rb graphite complexes are much larger. The linewidth for potassium-doped PPP decreased from 1.9 G at 300 K to 0.45 G at 7 K while the linewidth for potassium-doped p-terphenyl, p-quaterphenyl, and p-sexiphenyl increased. The concentration of unpaired spins at 3W K was approximately 10% of the potassium concentration. These observations suggest that the equilibrium between the radical anion and the dianion (paramagnetic diamagnetic) may he important and that alkali metal orbitals and hydrogens do interact with the unpaired electrons on the polymer chain.     

Measurement of atomic lifetimes with a mode-locked laser

We present a new technique for measuring atomic lifetimes with a mode-locked laser. A single laser pulse excites the atoms and a subsequent frequency-doubled pulse ionizes the excited-state atoms. The ions are collected and counted. The measurement is repeated using excitation and detection pulses with different time separations, which determines the excited-state decay rate. We demonstrated this technique for the 6P(3/2) state of cesium. The measured lifetime was 30.5 ns and had a statistical uncertainty of 0.1 ns. Systematic effects limited the overall experimental uncertainty to approximately 0.6 ns in this initial experiment.     

Crystal and molecular structure of dichlorofluoroacetamide

The crystal structure of dichlorofluoroacetamide has been determined from three-dimensional counter data, and refined by full-matrix least-squares techniques. The crystals belong to the monoclinic space groupP2₁ /c and have the unit-cell parametersa = 10.207(4),b = 5.729(2),c = 9.971(4) Å, = 105.21(8) °, andD _x = 1.72 g cm^-3. The structural refinement gave a finalR factor of 0.067 from 440 observed reflections. The compound has nearly equal disorder of the -Cl₂F moiety about the C-C bond axis with occupancy factors of the two fragments being 0.48 and 0.52.     

Low-density polyethylene: Variation of branching frequency with molecular weight and its influence on molecular weight as determined by gel-permeation chromatography

A method for determining long-chain branching frequency and molecular weight averages for unfractionated low-density polyethylene (LDPE) by the combined use of gel-permeation chromatography (GPC) and intrinsic viscosity data has been reported (GPC–IV method). The method assumes that the number of long branches λ per unit molecular weight is a constant independent of molecular weight. Recent data reported on λ as a function of molecular weight M in commercial LDPE indicate that this assumption is not generally valid, and concern has been expressed as to the size of the errors in molecular weights calculated using this assumption. The errors associated with assuming that λ is constant were evaluated in this study by first determining the way in which λ varies with M for two typical commerical LDPE resins by fractionation and application of the GPC–IV method to representative fractions. The experimentally determined relations between λ and M were then employed in the calculation of molecular weight and molecular size averages from GPC–IV data on the original unfractonated samples. Although it was found that λ increases with molecular weight for both samples, the results indicate that the error involved in assuming that λ is a constant is no greater than the precision with which molecular weight averages can be evaluated by GPC.