Accelerated quasicontinuum: a practical perspective on hyper-QC with application to nanoindentation

Abstract

Hyper-QC is a multiscale method based on the quasicontinuum (QC) method in which time is accelerated using hyperdynamics through the addition of a suitable bias potential. This paper describes the practical details of implementing and carrying out hyper-QC simulations and introduces a novel mechanism-based bias potential for deformation processes in face-centred cubic (fcc) systems. The factors limiting the maximum achievable acceleration are discussed. The method is demonstrated for nanoindentation into a thin film of single crystal fcc nickel at near experimental loading rates. Speed up factors as high as 10,000 are achieved. The simulations reveal a thermally activated dislocation nucleation mechanism with a logarithmic dependence on temperature and indenter velocity in agreement with a theoretical model.     

Pattern dynamics in cellular perception

By using a giant amoeboid cell of the Physarum plasmodium, changes in the intracellular distribution of chemical components are studied in relation to information processing in cell behavior. Various kinds of metabolites oscillate, and so the protoplasm should be a collection of chemical oscillators. Spatially, characteristic chemical patterns are self-organized for different cell shapes, and hence cell behavior. New phase waves propagate throughout the cell upon local stimulation, their direction being opposite for attraction and repulsion. Locomotion is inhibited when the coherence of the oscillators breaks. Thus, pattern dynamics is correlated with information processing in the amoeboid cell.     

Large electro‐optic activity and enhanced temporal stability of methacrylate‐based crosslinking hyperbranched nonlinear optical polymer

A methacrylate‐based crosslinking hyperbranced polymers have been synthesized through initiator‐fragment incorporation radical polymerization and used for the temperature stable electro‐optic (EO) polymer application. This polymer consists of methyl methacrylate, 2‐metacryloxyethyl isocyanate, and ethylene glycol dimethacrylate (EGDMA) monomers. The use of EGDMA as a bifunctional unit resulted in the solvent‐soluble crosslinking hyperbranched chain, so that the EO polymer enhanced glass transition temperatures. A phenyl vinylene thiophene vinylene bridge nonlinear optical chromophore was attached to the polymer backbone as the side‐chain by a post‐functionalization reaction. The loading concentration of the chromophore was varied between 30 and 50 wt % by simply changing the mixing ratio of the precursor polymer to the chromophore. The synthesized EO polymers produced optical quality films with a light propagation loss of 0.61 dB/cm in a slab waveguide at 1.31 μm. The electrically poled film had an EO coefficient (r₃₃) of 139 pm/V at 1.31 μm. The EO crosslinking hyperbranced polymer had a high‐glass transition temperature of 170 °C, and exhibited excellent temporal stability of the EO activity at 85 °C for 500 h. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Addendum to “Spatiotemporal evolution in a (2+1) -dimensional chemotaxis model” [Physica A 391 (2012) 107–112]

After our article, Physica A 391 (2012) 107–112, had been published online, T. Hillen told us about a theorem by Osaki, relevant for our numerical simulations.     

Sharp oscillation and nonoscillation tests for delay dynamic equations

In this paper, we give new sufficient conditions for both oscillation and nonoscillation of the delay dynamic equation where and satisfy τ(t) ≤ σ(t) for all large t and . As an important corollary, we obtain the time scale invariant integral condition for nonoscillation: for all large t. Also, with some examples, we show that newly presented results are sharp.     

Mechanics of atoms interacting with a carbon nanotorus: optimal configuration and oscillation behaviour

In this paper, we investigate a carbon nanotorus as a caged molecular structure interacting with an atom. Assuming that the atom is located along the central axis perpendicular to the torus, the interaction energy of the system is determined using the continuum approximation together with the Lennard-Jones potential. This approach avoids the intensive computational calculations that are involved in other modelling approaches. Numerical results are presented in terms of dimensionless variables. The results show that the optimal major radius of the torus has a linear relationship with its minor radius when the atom is symmetrically situated along the torus axis. When the atom is offset from this axis, the minimum energy location shifts away from the centre as the ratio of the major and minor radii exceeds the value of 0.90. Finally, the oscillatory behaviour for the carbon atom is investigated. Our findings predict a novel nano-oscillator which can produce frequencies in the gigahertz range.     

Relaxation oscillations in a slow–fast modified Leslie–Gower model

In this paper, we prove the existence and uniqueness of relaxation oscillation cycle of a slow–fast modified Leslie–Gower model via the entry–exit function and geometric singular perturbation theory. Numerical simulations are also carried out to illustrate our theoretical result.