Introduction, Motivation

Polymers are typically not fuUy crystalline below the melting temperature, due to frustration effects. As a result, a significant fraction of the sample consists of non-crystalline material between lamellae. These frustration effects 

Hiitter et al. Monte Carlo Simulations of Semicrystalline Polyethylene Interlamellar Domain and Crystal-Melt Interface, Lect. Notes Phys. 714, 261-284 (2007) 

Since a substantial amount of material is contained in the interlamellar region, the properties of the latter give significant contributions to the overall material behavior. The properties of the interlamellar material he between those of the unconstrained amorphous melt and those of the crystalline phase [9-11], and the influence of the crystalline constraints can be addressed experimentally [12-14]. Furthermore, the properties of the crystal-melt interface have various ramifications that can be observed experimentally [15], e.g., interface stresses lead to distortion of the crystal lattice spacing [16-18], and they are possibly responsible for lamella twisting [19]. In addition, the surface tension enters in theoretical models for crystallization rates [20,21]. 

To characterize the structure and to quantify the mechanical and thermal properties of the interlamellar, non-crystalline material. Metropolis Monte Carlo simulations have been performed [22-26] on systems kept in metastable equilibrium [27,28]. Here, we give a summary of our most recent results for a realistic model for polyethylene including torsion interactions. For more details the reader is referred to the original publications [29,30], Throughout the manuscript, we concentrate our attention on the 201 crystal surface, because it was found to be energetically favored in simulations [25] and predominant 

In the remainder of this contribution we study, on one hand, the entire interlameUar domain as a whole, termed Study 1 [29]. On the other hand, the crj tal-melt interface specifically is examined in Study 2 [30]. hi the course of explaining the results, the benefits of both of these approaches will become evident. 

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Introductions Motivations Goals for Ex-core Analyses Modeling results... 

One approach to a mathematically well defined performance measure is to interpret the amplitude values of a processed signal as realizations of a stochastic variable x which can take a discrete number of values with probabilities P , n = 1,2,..., N. Briefly motivated in the introduction, then an interesting quality measure is the entropy H x) of the amplitude distribu-... 

A discussion of the motivation behind doing sputtered neutral analysis versus SIMS, plus a description of the first prototype SALI instrument. A well written introduction for someone without previous surface analysis experience it also includes an historical overview of the various post-ionization techniques. 

We will use Mathematica throughout the text. Most of what is necessary to know will be introduced at the time it is needed. Nonetheless, there is some motivation to begin with some very basic commands and structures so that the process is smooth. Therefore, this is the goal of this section—to make your introduction to Mathematica go smoothly. For more information of this type there are many texts that cover Mathematicam detail. 

Wave propagation in an inhomogeneous anisotropic material such as a fiber-reinforced composite material is a very complex subject. However, its study is motivated by many important applications such as the use of fiber-reinforced composites in reentry vehicle nosetips, heatshields, and other protective systems. Chou [6-56] gives an introduction to analysis of wave propagation in composite materials. Others have applied wave propagation theory to shell stress problems. 

In 1879 Lord Kelvin introduced the term nwtivity for the possession, the waste of which is called dissipation at constant temperature this is identical with Maxwell s available energy. He showed in a paper On Thermodynamics founded on Motivity and Energy Phil. Mag., 1898), that all the thermodynamic equations could be derived from the properties of motivity which follow directly from Carnot s theorem, without any explicit introduction of the entropy. 

In tfiis chapter we address first the electrochemical application of the more familiar method of molecular (or atom) dynamics, and later turn to consider Monte Carlo methods, in each case giving a short introduction that should motivate the reader to pursue reading more specific works. Although the present research field is relatively new, the investigations are already too extensive to review in detail in a single chapter. For this reason, we discuss here the more extended research branches in the field and present a few representative examples. The application of simulations applied to nanostructuring problems is discussed in Chapter 36 liquid-liquid interfaces have been addressed by I. Benjamin (1997). 

A recent and very promising application of the reachability analysis of TA is scheduling. This development, however, required the introduction of the notion of cost. In contrast to the verification of whether a behavior fulfills a specification or not, costs introduce a quantitative measure to evaluate the individual behaviors. Successful applications of priced TA [15, 16] by using the standard and a special version of Uppaal are documented in [17-19]. The first application to deterministic job-shop scheduling was published by Abdeddaim [20] and Abdeddaim and Maler [21], In order to further motivate the use of TA, the next section shows how the schedule in Figure 10.2 and the plant on which the operations are scheduled naturally translate into a set of timed automata. 

CSC should be very popular and many people believe that it is robust due to the Cooper instability even for small attractive quark-quark interaction in color 3 channel [1]. On the contrary, we are afraid that FM has not been so familiar yet. So, we d like to begin with a brief introduction about our motivation for the study of FM. 

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