Modelling meso-scale diffusion processes in stochastic fluid bio-membranes

The space–time dynamics of rigid inhomogeneities (inclusions) free to move in a randomly fluctuating fluid bio-membrane is derived and numerically simulated as a function of the membrane shape changes. Both vertically placed (embedded) inclusions and horizontally placed (surface) inclusions are considered. The energetics of the membrane, as a two-dimensional (2D) meso-scale continuum sheet, is described by the Canham–Helfrich Hamiltonian, with the membrane height function treated as a stochastic process. The diffusion parameter of this process acts as the link coupling the membrane shape fluctuations to the kinematics of the inclusions. The latter is described via Ito stochastic differential equation. In addition to stochastic forces, the inclusions also experience membrane-induced deterministic forces. Our aim is to simulate the diffusion-driven aggregation of inclusions and show how the external inclusions arrive at the sites of the embedded inclusions. The model has potential use in such emerging fields as designing a targeted drug delivery system.

Multiscale numerical modelling of crack propagation in two-dimensional metal plate

A novel multiscale model of brittle crack propagation in an Ag plate with macroscopic dimensions has been developed. The model represents crack propagation as stochastic drift-diffusion motion of the crack tip atom through the material, and couples the dynamics across three different length scales. It integrates the nanomechanics of bond rupture at the crack tip with the displacement and stress field equations of continuum based fracture theories. The finite element method is employed to obtain the continuum based displacement and stress fields over the macroscopic plate, and these are then used to drive the crack tip forward at the atomic level using the molecular dynamics simulation method based on many-body interatomic potentials. The linkage from the nanoscopic scale back to the macroscopic scale is established via the Ito stochastic calculus, the stochastic differential equation of which advances the tip to a new position on the macroscopic scale using the crack velocity and diffusion constant obtained on the nanoscale. Well known crack characteristics, such as the roughening transitions of the crack surfaces, crack velocity oscillations, as well as the macroscopic crack trajectories, are obtained.

A multi-scale numerical modelling of crack propagation in a 2D metallic plate

A new multi-scale model of brittle fracture growth in an Ag plate with macroscopic dimensions is proposed in which the crack propagation is identified with the stochastic drift-diffusion motion of the crack-tip atom through the material. The model couples molecular dynamics simulations, based on many-body interatomic potentials, with the continuum-based theories of fracture mechanics. The Ito stochastic differential equation is used to advance the tip position on a macroscopic scale before each nano-scale simulation is performed. Well-known crack characteristics, such as the roughening transitions of the crack surfaces, as well as the macroscopic crack trajectories are obtained.

Water transport in resin-modified glass-ionomer dental cement

Water uptake and water loss have been studied in a commercial resin-modified glass-ionomer cement, Fuji II LC, under a variety of conditions. Uptake was generally non-Fickian, but affected by temperature. At room temperature, the equilibrium water uptake values varied from 2.47 to 2.78% whereas at low temperature (12 degrees C), it varied from 0.85 to 1.18%. Cure time affected uptake values significantly. Water uptake was much lower than in conventional glass-ionomer restorative cements exposed to water vapor. Loss of water under desiccating conditions was found to be Fickian for the first 5 h loss at both 22 and 12 degrees C. Diffusion coefficients were between 0.45 and 0.76 x 10( -7) cm(2)/s, with low temperature diffusion coefficients slightly greater than those at room temperature. Plotting water loss as percentage versus s(-(1/2)) allowed activation energies to be determined from the Arrhenius equation and these were found to be 65.6, 79.8, and 7.7 kJ/mol respectively for 30, 20, and 10 s cure times. The overall conclusion is that the main advantage of incorporating HEMA into resin-modified-glass-ionomers is to alter water loss behavior. Rate of water loss and total amount lost are both reduced. Hence, resin-modified glass-ionomers are less sensitive to water loss than conventional glass-ionomers.