Production of dimuons from high-energy polarized proton-proton collisions

The high-energy process p+p→μ⁺+μ^?+X for dimuons with large invariant mass is studied in the case that the protons are polarized. In general, the cross section $\text{d}\text{σ/}\text{d}\text{Q}{}^2\text{d}\text{y}\text{d}\text{Ω}$ is determined by nine structure functions, and several interesting correlations between the polarization direction and the observed cross section are possible. In the Drell-Yan parton model for the process, the structure of the cross section is much simpler: there are six linear relations among the structure functions. An experimental test of these relations would provide a stringent test of the Drell-Yan model.     

Contact angle relaxation on low energy surfaces

The spontaneous relaxation of the water—vapour interface, in contact with the “low energy” solids poly(ethylene terephthalate) (PET) and poly(methyl methacrylate) (PMMA), has been investigated after forced advancing and receding movement. A tensiometric apparatus has been used to probe the three-phase contact zone during relaxation for periods of up to 24 h. The measured force—time trace differs from that which might be anticipated, due to extraneous phenomena such as bulk evaporation/condensation/absorption. It is clear that even for a pure low viscosity liquid such as water, an imbalance in interfacial energies in the neighbourhood of the three-phase contact line (TPCL) exists for extended periods. Measurements have been made at both high and low water vapour pressures. In the advancing case, the TPCL is pinned and equilibration occurs via an essentially evaporative mechanism. In the receding case, the TPCL is mobile and the approach to equilibrium, which also occurs by an evaporative mechanism, is much slower. Indeed our results lead us to question whether equilibrium in the receding case is experimentally accessible. Contact angle hysteresis was found to be significantly smaller in magnitude than that typically measured within seconds or a few minutes of the cessation of forced TPCL movement.     

Semi-classical asymptotics in solid state physics

This article studies the Schrödinger equation for an electron in a lattice of ions with an external magnetic field. In a suitable physical scaling the ionic potential becomes rapidly oscillating, and one can build asymptotic solutions for the limit of zero magnetic field by multiple scale methods from homogenization. For the time-dependent Schrödinger equation this construction yields wave packets which follow the trajectories of the semiclassical model. For the time-independent equation one gets asymptotic eigenfunctions (or quasimodes) for the energy levels predicted by Onsager's relation.     

On the distribution of squares in a finite field

Given the Galois field GF(n) where n is odd we may partition the pairs (g, g+1) where g, g+1 GF(n), g(g+1) 0 into four classes as follows: RR denotes the class of such pairs for which both g and g+1 are squares in GF(n), RN the pairs for which g is a square and g+1 a nonsquare, NR the pairs for which g is a nonsquare and g+1 a square, and NN the pairs for which both g and g+1 are nonsquares. Raber [6] has recently applied geometric arguments to show that each class contains [(n–1)/4]+ elements, where || 1. The exact size of these classes is also known (see, for example, L. E. Dickson's book, Linear Groups, Dover, 1958, p. 48). In this paper we use arguments similar to those used by Raber to obtain the exact size of each class.The author acknowledges financial support by the NRC.     

Water and ice in contact with octadecyl-trichlorosilane functionalized surfaces: a high resolution x-ray reflectivity study

We present a high energy x-ray reflectivity study of the density profiles of water and ice at hydrophobic and hydrophilic substrates. At the hydrophobic water/octadecyl-trichlorosilane (water-OTS) interface, we find clear evidence for a thin density depletion layer with an integrated density deficit corresponding to approximately 40% of a monolayer of water molecules. We discuss the experimental results in terms of a simple model of hydrophobic/hydrophilic solid-liquid interfaces. Our results also exclude the presence of nanobubbles. A detailed study of possible radiation damage induced by the intense x-ray beam at the dry OTS surface and at the ice-OTS, as well as at water-OTS interfaces, discloses that noticeable damage is only induced at the water-OTS interface, and thus points to the dominant role of highly mobile radicals formed in bulk water close to the interface.