Two-dimensional traveling wave patterns in nonequilibrium systems

Traveling wave patterns formed at the oscillatory onset of convection in binary mixtures with free slip and permeable horizontal boundary conditions are theoretically derived by means of an order parameter equation for the case of large aspect ratio systems with circular and rectangular geometry. We obtain in addition to Zipper states the so called confined states, which so far has been observed only experimentally. Our present study of traveling wave patterns in circular systems, which are the first theoretical investigations in this respect, exhibit a characteristic change of behaviour. Close to onset the waves travel in radial direction towards the sidewalls. For higher Rayleigh-numbers the waves are confined to the circular boundary traveling in azimuthal direction. The occurrence of this transition should be confirmed experimentally.     

Identification of the principal high molecular weight fragments in the thermal degradation of poly(methyl acrylate)

The pyrolysis of poly(methyl acrylate) has been studied with identification of the major pyrolysis products. The degradation mechanism of Cameron and Kane involving random homolytic scission of the polymer chain followed by a series of intermolecular and intramolecular transfer reactions is extended and confirmed, and it is apparent that a series of saturated and unsaturated oligomers of methyl acrylate are produced.     

Quantities describing local properties of chaotic attractors

We numerically investigate the Local Divergence Rate (LDR) of the Hénon-map. We find that there exists a unique smooth LDR on the Hénon-attractor; locally expanding and contracting parts alternate regularly. Our concept leads to the definition of what we call fully developed chaos. Distribution functions (histograms) and auto-correlation functions for different dynamical behavior are computed. Our results indicate that the LDR may be a continuous function on the space in which the attractor is embedded.     

Studies in Transesterification. VII. Thermally Stable Surface Graft Catalysts

The preparation of methacrylate esters by transesterification with thermally stable surface or shell graft resins as acidic catalysts and n-butanol, n-hexanol, and n-tridecanol as the reactant alcohols is described. The performance of resins with a reactive shell graft polymerized to a solid polyethylene or polytrifluorochloroethylene nucleus has been compared with several conventional micro and macroporous cation exchangers. The graft polymers exhibit faster reaction rates than micro-and macroporous resins of significantly higher capacity. The graft polymer employing a polyethylene nucleus is of similar thermal stability to the conventional cation exchangers, while the second type of graft polymer exhibits increased thermal stability which allows repeated use at the operating temperatures experienced.     

Anisotropy in tendon investigated in vivo by a portable NMR scanner, the NMR-MOUSE

Ordered tissue like tendon is known to exhibit the magic-angle phenomenon in magnetic resonance investigations. Due to the anisotropic structure the transverse relaxation time T(2) depends on the orientation of the tendon in the magnetic field. In medical imaging, relaxation measurements of tendon orientation are restricted by the size of the object and the space available in the magnet. For humans, tendon orientation can only be varied within small limits. As a consequence, the magic-angle phenomenon may lead to a misjudgement of tendon condition. It is demonstrated that the NMR-MOUSE (mobile universal surface explorer), a hand-held NMR sensor, can be employed to investigate the anisotropy of T(2) in Achilles tendon in vivo. The NMR-MOUSE provides a convenient tool for analyzing the correlation of T(2) and the physical condition of tendon.     

The influence of noise on the logistic model

The behavior of the logistic system which is generated by the functionf(x =ax (1–x) changes in an interesting way if it is perturbed by external noise. It turns out that the chaotic behavior which was predicted by Li and Yorke for orbits of period 3, becomes visible and that a sequence of mergence transitions occurs at the critical parameter. The change of the invariant probability density and the Lyapunov exponents are examined numerically. The power spectrum for the period 3 orbit for different fluctuations is calculated and a recursion formula for the time evolution of the probability density is presented as a discrete-time analog of a Chapman-Kolmogorov equation.