High-Tc superconductivity and electronic band structure

We review the main results of the van Hove scenario applied to superconducting cuprates. It is based on the assumption that in these materials, the Fermi level lies near a singularity in the density of states (DOS). This hypothesis has recently been confirmed experimentally. We show that this model explains many properties of the high-T _c superconductors. We show that an anaogous model with a peak in the DOS may also be applied to the superconducting doped fullerenes. A general feature of the model is a very short coherence length.     

Modeling frequency- and temperature-invariant dissipative behaviors of randomly entangled carbon nanotube networks under cyclic loading

Recent experiments have shown that entangled networks of carbon nanotubes exhibit temperature- and frequency-invariant dissipative behaviors under cyclic loading. We have performed coarse-grained molecular dynamics simulations which show that these intriguing phenomena can be attributed to the unstable attachments/detachments between individual carbon nanotubes induced by van der Waals interactions. We show that this behavior can be described by a triboelastic constitutive model. This study highlights the promise of carbon nanomaterials for energy absorption and dissipation under extreme conditions.      

Behavior of a nonconformal mixture via computer simulation

A binary 50% mixture of soft spheres is studied via nonequilibrium molecular dynamics, and the equilibrium and nonequilibrium radial distribution functions for a nonconformal mixture with a mass ratio of 10 and a size ratio of about 2 are examined. This model system is related to the real methane/decane mixture, and it is shown that apparently anomalous properties of this mixture, especially the viscosity, could perhaps be understood in terms of the local or ambient mole fraction. In addition, the postulates of the Van der Waals one fluid conformal solution theory are discussed, and a mixing rule for the mass is derived.     

Fourier methods for quasi‐periodic oscillations

Quasi‐periodic oscillations and invariant tori play an important role in the study of forced or coupled oscillators. This paper presents two new numerical methods for the investigation of quasi‐periodic oscillations. Both algorithms can be regarded as generalizations of the averaging and the harmonic (spectral) balance methods. The algorithms are easy to implement and require only minimal a priori knowledge of the system. Most importantly, the methods do not depend on an a priori co‐ordinate transformation. The methods are applied to a number of illustrative examples from non‐linear electrical engineering and the results show that the methods are efficient and reliable. In addition, these examples show that the presented algorithms can also continue through regions of sub‐harmonic (phase‐locked) resonance even though they are designed only for the quasi‐periodic case. Copyright © 2006 John Wiley & Sons, Ltd.     

Numerical simulation of the head-on collision of two equal-sized drops with van der Waals forces

The head-on collision of two equal-sized drops in a hyperbolic flow is investigated numerically. An axisymmetric volume-of-fluid (VOF) method is used to simulate the motion of each drop toward a symmetry plane where it interacts and possibly coalesces with its mirror image. The volume-fraction boundary condition on the symmetry plane is manipulated to numerically control coalescence. Two new numerical methods have been developed to incorporate the van der Waals forces in the Navier–Stokes equations. One method employs a body force computed as the negative gradient of the van der Waals potential. The second method employs the van der Waals forces in terms of a disjoining pressure in the film depending on the film thickness. Results are compared to theory of thin-film rupture. Comparisons of the results obtained by the two methods at various values of the Hamaker constant show that the van der Waals forces calculated from the two methods have qualitatively similar effects on coalescence. A study of the influence of the van der Waals forces on the evolution and rupture of the film separating the drops reveals that the film thins faster under stronger van der Waals forces. Strong van der Waals forces lead to nose rupture, and small van der Waals forces lead to rim rupture. Increasing the Reynolds number causes a greater drop deformation and faster film drainage. Increasing the viscosity ratio slows film drainage, although the effect is small for small viscosity ratio.