Decay of confined,two-dimensional,spatially periodic arrays of vortices: A numerical investigation

The disarrangement of a perturbed lattice of vortices was studied numerically. The basic state is an exponentially decaying, exact solution of the Navier-Stokes equations. Square arrays of vortices with even numbers of vortex cells along each side were perturbed and their evolution was investigated. Whether the energy in the perturbation grows somewhat before it decays or decays monotonically depends on the initial strength of the vortices of the basic state, the extent of lateral confinement and the structure of the perturbation. The critical condition for temporally local instability, i.e. the critical amplitude of the basic state that must be exceeded to allow energy transfer from the basic state to the perturbation, is discussed. In the strongly confined case of a square lattice of four vortices the appearance of enchancement of global rotation is the result of energy transfer from the basic state to a temporally local unstable mode. Energy is transferred from the basic state to larger-scaled structures (inverse cascade) only if the scales of the larger structures are inherently contained in the initial structure of the perturbation. The initial structure of the double array of vortices is not maintained except for a very special form of perturbation. The facts that large scales decay more slowly than small scales and that, when non-linearities are sufficiently strong, energy is transferred from one scale to another explain the differences in the disarrangement process for different initial strengths of the vortices of the basic state. The stronger vortices, i.e. the vortices perturbed in a manner that increases their strength, tend to dominate the weaker vortices. The pairing and subsequent merging (or capture) of vortices of like sense into larger-scale vortices are described in terms of peaks in the evolution of the square root of the palinstrophy divided by the enstrophy.     

Effect of nanotube functionalization on the properties of single‐walled carbon nanotube/polyurethane composites

A commercially available aliphatic thermoplastic polyurethane formulated with a methylene bis(cyclohexyl) diisocyanate hard segment and a poly(tetramethylene oxide) soft segment and chain‐extended with 1,4‐butanediol was dissolved in dimethylformamide and mixed with dispersed single‐walled carbon nanotubes. The properties of composites made with unfunctionalized nanotubes were compared with the properties of composites made with nanotubes functionalized to contain hydroxyl groups. Functionalization almost eliminated the conductivity of the tubes according to the conductivity of the composites above the percolation threshold. In most cases, functionalized and unfunctionalized tubes yielded composites with statistically identical mechanical properties. However, composites made with functionalized tubes did have a slightly higher modulus in the rubbery plateau region at higher nanotube fractions. Small‐angle X‐ray scattering patterns indicated that the dispersion reached a plateau in the unfunctionalized composites that was consistent with the plateau in the rubbery plateau region. The room‐temperature modulus and tensile strength increase was proportionally higher than almost all increases seen previously in thermoplastic polyurethanes; however, the increase was still an order of magnitude below what has been reported for the best nanotube–polymer systems. Nanotube addition increased the hard‐segment glass transition temperature slightly, whereas the soft‐segment glass transition was so diffuse that no conclusions could be drawn. Unfunctionalized tubes suppressed the crystallization of the hard segment; whereas functionalized tubes had no effect. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 490–501, 2007     

Atomistic phenomena in dense fluid shock waves

The shock structure problem is one of the classical problems of fluid mechanics and at least for non-reacting dilute gases it has been considered essentially solved. Here we present a few recent findings, to show that this is not the case. There are still new physical effects to be discovered provided that the numerical technique is general enough to not rule them out a priori. While the results have been obtained for dense fluids, some of the effects might also be observable for shocks in dilute gases.     

Approximation of transient temperatures in complex geometries using fractional derivatives

It is shown that time-dependent temperatures in a transient, conductive system can be approximately modeled by a fractional-order differential equation, the order of which depends on the Biot number. This approximation is particularly suitable for complex shapes for which a first-principles approach is too difficult or computationally time-consuming. Analytical solutions of these equations can be written in terms of the Mittag-Leffler function. The approximation is especially useful if a suitable fractional-order controller is to be designed for the system.     

Damage and fracture evaluation of granular composite materials by digital image correlation method

This paper presents the applications of digital image correlation technique to the mesoscopic damage and fracture study of some granular based composite materials including steelfiber reinforced concrete, sandstone and crystal-polymer composite. The deformation fields of the composite materials resulted from stress localization were obtained by the correlation computation of the surface images with loading steps and thus the related damage prediction and fracture parameters were evaluated. The correlation searching could be performed either directly based on the gray levels of the digital images or from the wavelet transform (WT) coefficients of the transform spectrum. The latter was developed by the authors and showed higher resolution and sensitivity to the singularity detection. Because the displacement components came from the rough surfaces of the composite materials without any coats of gratings or fringes of optical interferometry, both surface profiles and the deformation fields of the composites were visualized which was helpful to compare each other to analyze the damage of those heterogeneous materials. The project supported by the National Natural Science Foundation of China (10125211 and 10072002), the Scientific Committee of Yunnan Province for the Program of Steel Fiber Reinforced Concrete, and the Institute of Chemical Materials, CAEP at Mianyang