Long range effect

3 Liquid-solid transitions of elastic flexible polymers 

Whereas the Mackay-anti-Mackay crossover is not recognizable in the specific heat curves, the probability of occurrence of specified numbers of icosahedral cells, reveals the transition temperature (Zf = 2.5a). From [53]. 

The second interesting result is the different ground states, zks in the case of unbormded clusters with untruncated LJ potential, the ground-state conformation is decahedral for N = 102 [Fig. 6.5(c)]. We can also identify the solid-solid transition toward Mackay structures The decahedral-icosahedral crossover occurs at the temperature T 0.02 (see Fig. 6.12), with a relatively prominent signal in the specific heat. 

To conclude, there is some evidence that during the change from atomic LJ clusters to polymers, Mackay-like stmctures are more favored independently of a truncation of the LJ 

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Volkov, S.N. Conformational transitions and the mechanism of transmission of long-range effects in DNA. Preprint ITP-88-12E, Kiev (1988) 22 Krumhansl, J.A., Alexander, D.M. Nonlinear dynamics and conformational exitations in biomolecular materials. In Structure and dynamics nucleic acids and proteins. (Clementi, E., Sarma, R.H., eds) Adenine Press, New York (1983) 61-80... 

There are a number of additional local structures and properties that appear even in elementary CA systems. Grassberger [grass84b, for example, has observed that rule R22 actually harbors very complex long-range effects, similar to a critical phenomenon (see section 3.1.4). Since the majority of these findings require the use of more general and sophisticated correlation measures than we have defined thus far, we will pick up our discussion of them in chapter 4. 

The boundary layers, or interphases as they are also called, form the mesophase with properties different from those of the bulk matrix and result from the long-range effects of the solid phase on the ambient matrix regions. Even for low-molecular liquids the effects of this kind spread to liquid layers as thick as tens or hundreds or Angstrom [57, 58], As a result the liquid layers at interphases acquire properties different from properties in the bulk, e.g., higher shear strength, modified thermophysical characteristics, etc. [58, 59], The transition from the properties prevalent in the boundary layers to those in the bulk may be sharp enough and very similar in a way to the first-order phase transition [59]. 

Lithium, promotion of carbon monoxide oxidation, 74, 293 Long range effects, 189... 

The van der Waals forces are present universally, regardless of the species and polarity of the interacting atoms or molecules. The forces can be attractive or repulsive, but mostly attractive and long-range, effective from a distance longer than 10 nm down to the equilibrium interatomic distance (about 0.2 nm). 

In the calculations presented here, the long-range effects present in a crystal were introduced explicitly for the SCF-MO treated cluster, by surrounding it with point-ions situated at the X-ray determined atomic positions of alpha-quartz. This method has been used for the more ionic systems of alpha-NaOH, and MgO with some success and the calculations described in this paper show that it is equally applicable for semi-covalent materials. 

We will not discuss the more obvious but very tedious and cumbersome task to improve force fields. Electrostatic interactions are the weakest parts of the force fields polarisability has to be introduced and dependable ways have to be found to include long range effects. 

There will be no long-range effects, due to resonant interactions, at high... 

The Flory principle, whose validity has been verified for a wide range of macromolecular reactions, is a good approximation for the description of the kinetics of many processes of polymer preparation. However, strong experimental evidence for the violation of this principle is currently available from the study of a number of macromolecular reactions. Possible reasons for such a violation may be connected with either short-range or long-range effects. 

Another kind of situation arises when it is necessary to take into account the long-range effects. Here, as a rule, attempts to obtain analytical results have not met with success. Unlike the case of the ideal model the equations for statistical moments of distribution of polymers for size and composition as well as for the fractions of the fragments of macromolecules turn out normally to be unclosed. Consequently, to determine the above statistical characteristics, the necessity arises for a numerical solution to the material balance equations for the concentration of molecules with a fixed number of monomeric units and reactive centers. The difficulties in solving the infinite set of ordinary differential equations emerging here can be obviated by switching from discrete variables, characterizing macromolecule size and composition, to continuous ones. In this case the mathematical problem may be reduced to the solution of one or several partial differential equations. 

A. Disentangling Resonance from Long-Range Effects... 

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