Fully rotating model

A suitable approach to the equilibration of an amorphous polymer system at bulk density becomes much more likely when the fully atomistic model in continuous space is replaced by an equivalent coarse-grained model on a lattice with sufficient conformational flexibility. Different strategies, which seek results at different levels of detail, can be employed to create an appropriate coarse-grained model. Section 4 (Doruker, Mattice) describes an approach which attempts to retain a connection with the covalent bonds in the polymer. The rotational isomeric state (RIS) [35,36] model for the chain is mapped into... 

Not only are steric interferences intolerably severe in the fully extended configuration XI it is usually impossible to eliminate them altogether through bond rotation, as may be seen from models. Even when the substituents are no larger than methyl, as in polyisobutylene (X = Y=CH3), steric interferences are so great as to preclude construction of a scale model for any configuration of the chain if the normal C—C and C—H distances and the usually accepted van der Waals radii are used. If Stuart models are used, in which the van der Waals... 

Of considerable interest is the use of small isolated electrodes, in the form of strips or disks embedded in the wall, to measure local mass-transfer rates or rate fluctuations. Mass-transfer to spot electrodes on a rotating disk is represented by Eqs. (lOg-i) of Table VII. Analytical solutions in this case have to take account of curved streamlines. Despic et al. (Dlld) have proposed twin spot electrodes as a tool for kinetic studies, similar to the ring-disk electrode applications of disk and ring-disk electrodes for kinetic studies are discussed in several monographs (A3b, P4b). In fully developed channel or pipe flow, mass transfer to such electrodes is given by the following equation based on the Leveque model ... 

Massive stars play an important role in numerous astrophysical contexts that range from the understanding of starburst environments to the chemical evolution in the early Universe. It is therefore crucial that their evolution be fully and consistently understood. A variety of observations of hot stars reveal discrepancies with the standard evolutionary models (see [1] for review) He and N excesses have been observed in O and B main sequence stars and large depletions of B accompanied by N enhancements are seen in B stars and A-F supergiants [2,3,4,5], All of these suggest the presence of excess-mixing, and have led to the development of a new generation of evolutionary models which incorporate rotation (full reviews in [1], [6], [7]). 

Recent research now concentrates on the more physical models involving theories of rotation. The long-term aim of these attempts are to provide fully self-consistent models which include stellar evolution, rotation, transport of angular momentum and of chemical species. The key players in this field are P. Denis-senkov [11,12] and C. Charbonnel and coworkers (for their approach, see the contributions by Charbonnel and Palacios in this volume). Both groups employ the theoretical description of rotation by Zahn and Maeder [27,19]. 

Red giant stars, both in the field and in globular clusters, present abundance anomalies that can not be explained by standard stellar evolution models. Some of these peculiarities, such as the decline of 12C/13C, and that of Li and 12C surface abundances for stars more luminous than the bump, clearly point towards the existence of extra-mixing processes at play inside the stars, the nature of which remains unclear. Rotation has often been invoked as a possible source for mixing inside Red Giant Branch (RGB) stars ([8], [1], [2]). In this framework, we present the first fully consistent computations of rotating low mass and low metallicity stars from the Zero Age Main Sequence (ZAMS) to the upper RGB. 

In sharp contrast to the large number of experimental and computer simulation studies reported in literature, there have been relatively few analytical or model dependent studies on the dynamics of protein hydration layer. A simple phenomenological model, proposed earlier by Nandi and Bagchi [4] explains the observed slow relaxation in the hydration layer in terms of a dynamic equilibrium between the bound and the free states of water molecules within the layer. The slow time scale is the inverse of the rate of bound to free transition. In this model, the transition between the free and bound states occurs by rotation. Recently Mukherjee and Bagchi [14] have numerically solved the space dependent reaction-diffusion model to obtain the probability distribution and the time dependent mean-square displacement (MSD). The model predicts a transition from sub-diffusive to super-diffusive translational behaviour, before it attains a diffusive nature in the long time. However, a microscopic theory of hydration layer dynamics is yet to be fully developed. 

The book Gas Turbine Performance by Walsh and Fletcher [10] has excellent treatment on turbomachineiy maps. An example of a compressor map is shown in Figure 8.10. This map fully defines the pressure-flow-efficiency-rotational speed relationship of the compressor. Employing the Beta-line or R-line method, maps can be digitized into tabular form as described by Walsh and Fletcher [10], The Betaline method is helpful to ensure numeric stability with such maps that would be otherwise problematic because of the near zero and infinite slope at the ends of the constant speed lines. Note that the compressor model can either be a flow element or a pressure element. That is, from speed and pressure it is possible to obtain flow and efficiency from the map, or from speed and flow it is possible to obtain pressure and efficiency from the map. The choice depends on what is more convenient, that is, what type of elements are modeled upstream and downstream. 

---