Molecular dynamics simulation of observed c(4x4) and c(4x3) C60 alignments on the Si(100) reconstructed surface.

We have implemented a large-scale classical molecular dynamics simulation at constant temperature to provide a theoretical insight into the results of a recently performed experiment on the monolayer and multi-layer formations of molecular films on the Si(100) reconstructed dimerized surface. Our simulation has successfully reproduced all of the morphologies observed on the monolayer film by this experiment. We have obtained the formation of both c(4 4) and c(4 3) structures of the molecules and have also obtained phase transitions of the former into the latter.

A multi-scale atomistic-continuum modelling of crack propagation in a two-dimensional macroscopic plate

A novel multi-scale seamless model of brittle-crack propagation is proposed and applied to the simulation of fracture growth in a two-dimensional Ag plate with macroscopic dimensions. The model represents the crack propagation at the macroscopic scale as the drift-diffusion motion of the crack tip alone. The diffusive motion is associated with the crack-tip coordinates in the position space, and reflects the oscillations observed in the crack velocity following its critical value. The model couples the crack dynamics at the macroscales and nanoscales via an intermediate mesoscale continuum. The finite-element method is employed to make the transition from the macroscale to the nanoscale by computing the continuum-based displacements of the atoms at the boundary of an atomic lattice embedded within the plate and surrounding the tip. Molecular dynamics (MD) simulation then drives the crack tip forward, producing the tip critical velocity and its diffusion constant. These are then used in the Ito stochastic calculus to make the reverse transition from the nanoscale back to the macroscale. The MD-level modelling is based on the use of a many-body potential. The model successfully reproduces the crack-velocity oscillations, roughening transitions of the crack surfaces, as well as the macroscopic crack trajectory. The implications for a 3-D modelling are discussed.

Neutron quasi-elastic scattering in disordered solids: a Monte Carlo study of metal-hydrogen systems

The dynamic structure factor of neutron quasi-elastic scattering has been calculated by Monte Carlo methods for atoms diffusing on a disordered lattice. The disorder includes not only variation in the distances between neighbouring atomic sites but also variation in the hopping rate associated with each site. The presence of the disorder, particularly the hopping rate disorder, causes changes in the time-dependent intermediate scattering function which translate into a significant increase in the intensity in the wings of the quasi-elastic spectrum as compared with the Lorentzian form. The effect is particularly marked at high values of the momentum transfer and at site occupancies of the order of unity. The MC calculations demonstrate how the degree of disorder may be derived from experimental measurements of the quasi-elastic scattering. The model structure factors are compared with the experimental quasi-elastic spectrum of an amorphous metal-hydrogen alloy.

Rotating-frame nuclear magnetic relaxation of spins diffusing on a disordered lattice: a Monte Carlo model

The rotating-frame nuclear magnetic relaxation rate of spins diffusing on a disordered lattice has been calculated by Monte Carlo methods. The disorder includes not only variation in the distances between neighbouring spin sites but also variation in the hopping rate associated with each site. The presence of the disorder, particularly the hopping rate disorder, causes changes in the time-dependent spin correlation functions which translate into asymmetry in the characteristic peak in the temperature dependence of the dipolar relaxation rate. The results may be used to deduce the average hopping rate from the relaxation but the effect is not sufficiently marked to enable the distribution of the hopping rates to be evaluated. The distribution, which is a measure of the degree of disorder, is the more interesting feature and it has been possible to show from the calculation that measurements of the relaxation rate as a function of the strength of the radiofrequency spin-locking magnetic field can lead to an evaluation of its width. Some experimental data on an amorphous metal - hydrogen alloy are reported which demonstrate the feasibility of this novel approach to rotating-frame relaxation in disordered materials.

Maximum curves and isolated points of entire functions

Given M(r; f) =maxjzj=r (jf(z)j) , curves belonging to the set of points M = fz : jf(z)j = M(jzj; f)g were de�ned by Hardy to be maximum curves. Clunie asked the question as to whether the set M could also contain isolated points. This paper shows that maximum curves consist of analytic arcs and determines a necessary condition for such curves to intersect. Given two entire functions f1(z) and f2(z), if the maximum curve of f1(z) is the real axis, conditions are found so that the real axis is also a maximum curve for the product function f1(z)f2(z). By means of these results an entire function of in�nite order is constructed for which the set M has an in�nite number of isolated points. A polynomial is also constructed with an isolated point.

Semi-Lagrange time integration for PDE models of asian options

Semi-Lagrange time integration is used with the finite difference method to provide accurate stable prices for Asian options, with or without early exercise. These are combined with coordinate transformations for computational efficiency and compared with published results

Low temperature crystal structures of two rhodanine derivatives, 3-amino rhodanine and 3-methyl rhodanine: geometry of the rhodanine ring

Rhodanines (2-thio-4-oxothiazolidines) are synthetic small molecular weight organic molecules with diverse applications in biochemistry, medicinal chemistry, photochemistry, coordination chemistry and industry. The X-ray crystal structure determination of two rhodanine derivatives, namely (I), 3-aminorhodanine [3-amino-2-thio-4-oxothiazolidine], C3H4N2OS2, and (II) 3-methylrhodanine [3-methyl-2-thio-4-oxothiazolidine], C4H5NOS2, have been conducted at 100 K. I crystallizes in the monoclinic space group P2(1)/n with unit cell parameters a = 9.662(2), b = 9.234(2), c = 13.384(2) angstrom, beta = 105.425(3)degrees, V = 1151.1(3) angstrom(3), Z = 8 (2 independent molecules per asymmetric unit), density (calculated) = 1.710 mg/m(3), absorption coefficient = 0.815 mm(-1). II crystallizes in the orthorhombic space group Iba2 with unit cell a = 20.117(4), b = 23.449(5), c = 7.852(2) angstrom, V = 3703.9(12) angstrom(3), Z = 24 (three independent molecules per asymmetric unit), density (calculated) = 1.584 mg/m(3), absorption coefficient 0.755 mm(-1). For I in the final refinement cycle the data/restraints/parameter ratios were 2639/0/161, goodness-of-fit on F-2 = 0.934, final R indices [I > 2sigma(I)] were R1 = 0.0299, wR2 = 0.0545 and R indices (all data) R1 = 0.0399, wR2 = 0.0568. The largest difference peak and hole were 0.402 and -0.259 e angstrom(-3). For II in the final refinement cycle the data/restraints/parameter ratios were 3372/1/221, goodness-of-fit on F(2) = 0.950, final R indices [I > 2sigma(I)] were R1 = 0.0407, wR2 = 0.1048 and R indices (all data) R1 = 0.0450, wR2 = 0.1088. The absolute structure parameter = 0.19(9) and largest difference peak and hole 0.934 and -0.301 e angstrom(-3). Details of the geometry of the five molecules (two for I and three for II) and the crystal structures are fully discussed. Corresponding features of the molecular geometry are highly consistent and firmly establish the geometry of the rhodanine

Velocity measurement of pneumatically conveyed solids using electrodynamic sensors

Theoretical and experimental studies of cross correlation techniques applied to non-restrictive velocity measurement of pneumatically conveyed solids using ring-shaped electrodynamic flow sensors are presented. In-depth studies of the electrodynamic sensing mechanism, and also of the spatial sensitivity and spatial filtering properties of the sensor are included, together with their relationships to measurement accuracy and the effects of solids' velocity profiles. The experimental evaluation of a 53 mm bore sensing head is described, including trials using a calibrated pneumatic conveyor circulating pulverized fuel and cement. Comparisons of test results with the mathematical models of the sensor are used to identify important aspects of the instrument design. Off-line test results obtained using gravity-fed solids flow show that the system repeatability is within +/-0.5% over the velocity range of 2-4 m s(-1) for volumetric concentrations of solids no greater than 0.2%. Results obtained in the pilot-plant trials demonstrate that the system is capable of achieving repeatability better than +/-2% and linearity within +/-2% over the velocity range 20-40 m s(-1) for volumetric concentrations of solids in the range 0.01-0.44%.