On a certain non-split cubic surface

Science China Mathematics - This paper establishes an asymptotic formula with a power-saving error term for the number of rational points of bounded height on the singular cubic surface of...     

Visualisation of chemical processes during corrosion of zinc using magnetic resonance imaging

Compositional and structural changes within an electrolyte solution above an electrochemically active metal surface have been visualised using magnetic resonance imaging (MRI) for the first time. In these proof-of-concept experiments, zinc metal was galvanically corroded in a saturated lithium chloride solution. Magnetic resonance relaxation maps were taken during the corrosion process and spatial variations in both T₁ and T₂ relaxation times were observed to change with time. These changes were attributed to changes in the speciation of zinc ions in the electrolyte.     

Nuclear magnetic resonance studies of convection in the 1,4-cyclohexanedione-bromate-acid reaction

The manifestation and development of convection during pattern formation in the 1,4-cyclohexanedione-acid-bromate reaction was investigated using pulsed gradient spin-echo nuclear magnetic resonance (PGSE NMR) experiments. An apparatus was devised that enabled convection to be probed inside an NMR spectrometer and prevented hydrodynamic motion arising from extraneous sources, such as poor mixing or temperature gradients imposed by the experimental setup. PGSE experiments were performed concurrently with magnetic resonance imaging (MRI) experiments to show that convection arose spontaneously from inhomogeneities associated with the chemical patterns. Quantitative data on diffusion coefficients and hydrodynamic velocities are reported.     

Reduced density matrix quantum approach for particle trapping and sticking on corrugated moving surfaces

A short time propagation algorithm for the reduced density matrix is derived to model the interaction of a quantum particle with a moving corrugated surface. The algorithm includes dissipative terms, which can be derived directly from the full Hamiltonian. The scattering of He from a corrugated Cu surface is examined as a function of incident energy and angle and the temperature of the substrate, with a focus on the nature of trapping. It is found that corrugation can make a significant contribution to trapping, even on a metal surface. Energy exchange with the phonons is shown to significantly modify the nature of diffraction mediated selective adsorption.     

A <Emphasis Type="Italic">q</Emphasis>-player impartial avoidance game for generating finite groups

We study a q-player variation of the impartial avoidance game introduced by Anderson and Harary, where q is a prime. The game is played by the q players taking turns selecting previously-unselected elements of a finite group. The losing player is the one who selects an element that causes the set of jointly-selected elements to be a generating set for the group, with the previous player winning. We introduce a ranking system for the other players to prevent coalitions. We describe the winning strategy for these games on cyclic, nilpotent, dihedral, and dicyclic groups.     

Global potential energy minima of C60(H2O)n clusters

Likely candidates for the global potential energy minima of C60(H2O)n clusters with n < or = 21 are found using basin-hopping global optimization. The potential energy surfaces are constructed using the TIP4P intermolecular potential for the water molecules, a Lennard-Jones water-fullerene potential, and a water-fullerene polarization potential, which depends on the first few nonvanishing C60 multipole polarizabilities. This combination produces a rather hydrophobic water-fullerene interaction. As a consequence, the water component of the lowest C60(H2O)n minima is quite closely related to low-lying minima of the corresponding TIP4P (H2O)n clusters. In most cases, the geometrical substructure of the water molecules in the C60(H2O)n global minimum coincides with that of the corresponding free water cluster. Exceptions occur when the interaction with C60 induces a change in geometry. This qualitative picture does not change significantly if we use the TIP3P model for the water-water interaction. Structures such as C60@(H2O)60, in which the water molecules surround the C60 fullerene, correspond to local minima with much higher potential energies. For such a structure to become the global minimum, the magnitude of the water-fullerene interaction must be increased to an unphysical value.     

1,2,3,4,5,6,7,8-Octahydroanthracene-9,10- dicarbonitrile at 172, 216, 256, and 297 K

Octahydroanthracenedicarbonitrile is monoclinic, space group P2₁/c, at 172 K, a = 4.723(7), b = 8.254(3), c = 16.190(7) Å, = 91.76(8)°, Z = 2, V = 630.8(12) ų. The molecule, located on a center of symmetry, is disordered between the two senses of puckering in the aliphatic ring. The structure was also determined at 216, 256, and 297 K. The disorder increases with increasing temperature and can be described by a van't Hoff relationship with H = 5.2(3) kJ mol^–1 and S = 13.8(12) J K^–1 mol^–1.