Order parameter radial

While order parameters, radial distributions and thermodynamic quantities have been calculated for GB discotics, very few other observables have been determined until now. An excq>tion is the determination of elastic constants, via the direct pair correlation functitm route [50], where an ordo ing < K i < K 2was found, in agreement with experimoit. 

In order to determine the thickness of each layer for the concentric cylinder barrel structure, the radial order parameter, = ([Pg.187]

The push to highlight performance on GPUs has meant that not one of the currently published papers on GPU implementations of MD actually provide any validation of the approximations made in terms of statistical mechanical properties. For example, one could include showing that converged simulations run on a GPU and CPU give identical radial distribution functions, order parameters, and residue dipolar couples to name but a few possible tests. 

Fig. 10. Structural evolution of an a -Si 11 film during its deposition by MD simulation (from Ramalingam, 2000). (a) Profile evolution ot the order parameter, f, in the direction of growth, profiles are shown after 1,2. and 5 ns. respectively, (b) Si-Si radial distribution function. g(r), after 2 and 5 ns. (c) a-Si H/c-Si film/substrate conhguration after 5 ns of film growth simulation.

Fig. 35. (a) Order parameter profile 0(z) across an interface between two coexisting phases the interface being oriented perpendicular to the z-direclion. (b) The radial order parameter profile for a marginally stable critical droplet in a metastable state which is close to the coexistence curve, (c) Same as (b) but for a state close to the spinodal curve, 0sp. In (a) and (b) the intrinsic thickness of the interface is of the order of the correlation length ifeoex whereas in (c) it is of the order of the critical droplet radius / . From Binder (1984b). 

Figure 26. Characterization of the inherent structures for the model calamitic system GB(3,5,2, 1) ( = 256). (a) Parallel radial distribution function g (/ ) for the inherent structures at all temperatures considered along the isochor at density p = 0.32. Note that the curves for the highest five temperatures are nearly superposed on each other. For others, the amplitude of the peaks gradually increases as the temperature drops, (b) Evolution of the 6-fold bond orientational order parameter 4>6 for the inherent stmctures with temperature at three densities. (Reproduced from Ref. 144.)...

Radial density profiles perpendicular to the fiber axis can be fitted to a hyperbolic tangent function. Equation (1). For fibers with diameters in the range 5-8 nm, the correlation lengths, are about 0.6 nm, which is close to the value obtained with the models of the free-standing thin films. The end beads are enriched in the surface region, as was also the case with the free-standing thin films. The anisotropy of the chord vectors, as assessed by the order parameter, S, is also similar to the result obtained with the free-standing thin films. 

These concepts also lead naturally to an interpretation of the triple point and sublimation. This random gel model is seen to be consistent with most of the known properties of liquid water, in particular the radial distribution function, infrared and Raman spectra, dielectric properties, density maximum, and anomalous properties in the supercooled region. The difficulty of such analogies is the quantification, as the order parameters are all collective many-body quantities which are not always easy to measure, even in simulations. 

Demixing, Fig. 3 (a) Order parameter profile V (z) across an interface between two coexisting bulk phases with order parameters i fcoex. the interface being oriented perpendicular to the z-direction and centered at z = 0. (b) Radial order parameter profile for a marginally stable droplet of radius R. In the center of the droplet, the order parameter takes the value of the stable phase at coexistence, — i coex, while for radial distances p oo, ij/ip) — ij/jas< the order parameter of the considered metastable state, f(OT ij/jos close to t coex- (e) Same as (b), but for < ms close to the spinodal, ij/sp. Then, ij/(j> = 0) does not reach — i coex. but rather stays close to the unstable extremum of the free energy/(ij/), ij/ ... 

This expression has the same form as the modified embedded atom model. Taylor represented the local atomic density by bond-order parameters and different radial functions as discussed in Sect. 2.3.1 in Chap. 2. By choosing appropriate radial functions, he obtained the original modified embedded-atom formula, but systematic improvement of the formula is also possible in his framework. 

Figure 3. Nematic order parameter P2) versus temperature for the radial, toroidal and bipolar boundary conditions (J = 1) and for the bulk. All the results have been obtained from simulations of a droplet carved from a 10 x 10 x 10 lattice. 

Figure 4- Radial order parameter P2)r for a nematic droplet with radial boundary conditions plotted agcunst the distamce, in lattice units, from the center of the sphere. Results for 3L N = 5832 particle droplet at some scaled temperatures left) and for different system sizes at temperature T = 0.2 right). 

Figure 1. Order parameters calculated for the radial droplet at T = 0.8 (nematic phase). Local nematic (5, le/t) and external field right) order parameter...

We have described lattice spin models for the simulation of polymer-dispersed liquid crystals. The biggest advantage of Monte Carlo simulations is the possibility of investigating the system at a microscopic level, and to calculate thermodynamic properties and their specific order parameters suitable for different types of PDLC. Molecular organizations can be investigated by calculating the order parameters point by point across the droplet. Moreover, it is possible to calculate experimental observables like optical textures and, as discussed here, NMR line shapes. We have given an overview of the method and some applications to models of PDLC with radial and bipolar boundary conditions, and considered the effect of orientational and translational diffusion on the spectra. We have examined in particular under what conditions the NMR spectra of the deuterated nematic can provide reliable information on the actual boundaries present in these submicron size droplets. 

Fig. 4. (a) Translational order parameter for rigid dumbbells with interatomic separation A/rr = 0.50 as a function of density for temperatures T = 0.30, 0.40, 0.42, 0.44, 0.46, 0.48, 0.50 and 0.60 (from top to bottom) (b) radial distribution functions (g (r)) for a fixed temperature T = 0.30 and several densities. The colors correspond to the densities where the translational order parameter increases (red), decreases (black) or increases (blue) under increasing density, as in (a). 

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