Sequence order parameter

This means that distortions do not modify significantly the phase sequences, order parameter, etc. 

This is achieved by coupling the system to a suitably defined order parameter that is sensitive to the crystal order (the stacking sequence of 111 planes in this case), and doing umbrella sampling with this quantity. The result of the simulation is the free energy difference between both candidate structures—and the winner is fed... 

Figure 2 Time sequence of th< spin configuration on a (100) plane at 50% when the system at T=2.5 (snapshot a) is quenched down to T—1.7 and is subject to an isothermal aging. Snapshots demonstrated in figs, b, c and d correspond to time t=20,000, 43,000 and 50,000. The long range and short range order parameters input from the PPM calculations and resultant ones in the simulated lattice are also demonstrated [22, 24, 28]. ...

Alternatively, proton double quantum (DQ) NMR, based on a combined DQ excitation and a reconversion block of the pulse sequence, has been utilized to gain direct access to residual DCCs for cross-linked systems.69,83-89 For this purpose, double-quantum buildup curves are obtained with use of a well-defined double-quantum Hamiltonian along with a specific normalization approach. Residual interactions are directly proportional to a dynamic order parameter Sb of the polymer backbone,87... 

Fig. 1 Solid-state NMR structure analysis relies on the 19F-labelled peptides being uniformly embedded in a macroscopically oriented membrane sample, (a) The angle (0) of the 19F-labelled group (e.g. a CF3-moiety) on the peptide backbone (shown here as a cylinder) relative to the static magnetic field is directly reflected in the NMR parameter measured (e.g. DD, see Fig. 2c). (b) The value of the experimental NMR parameter varies along the peptide sequence with a periodicity that is characteristic for distinct peptide conformations, (c) From such wave plot the alignment of the peptide with respect to the lipid bilayer normal (n) can then be evaluated in terms of its tilt angle (x) and azimuthal rotation (p). Whole-body wobbling can be described by an order parameter, S rtlo. (d) The combined data from several individual 19F-labelled peptide analogues thus yields a 3D structural model of the peptide and how it is oriented in the lipid bilayer...

Fig. 16 (a) 2D-SAXS images of a 32.5 wt% solution of SI in toluene under an electric field of 3 kV/mm at different temperatures. The arrow in the first image indicates the direction of the electric field vector, (b) Azimuthal scattering intensity after background subtraction and normalization. The curves correspond to the sequence of images in (a), (c) Order parameter P% (filled circles) and temperature (solid line) as functions of time. Numbers 1-4 correspond to scattering patterns shown in (a) and (b). Adapted with permission from Macromolecules [72]. Copyright 2009 American Chemical Society... 

The basic approach adopted is derived from lattice model studies of protein folding. For bead sequences confined to a lattice, the following order parameter can be defined[27,28]... 

Fig. 13. In an umbrella sampling simulation for pathways configuration space is covered with a sequence of overlapping windows W[i]. For each window a separate transition path sampling simulation for paths with starting points in A and endpoints in >V[ ] is carried out. From the order parameter distributions matched where the windows overlap the distribution PA X,t) can be calculated...

Molecular simulations result in sequences of configurations of the protein. These configurations consists of many atoms, beads, particles or lattice sites. One might inspect these trajectories visually, but in general, it is desirable to analyze the data more quantitatively. To do so, one has to reduce a 3N-dimensional configuration to a number of low dimensional order parameters that contain physical information on the state of the system. For proteins many such order parameters exist. In this section I will discuss a few. 

The ability to retain anisotropic spin interactions and the power to selectively suppress unwanted interactions using pulse sequences such as PISEMA in aligned solids have played a significant role in the applications of solid-state NMR spectroscopy. In addition, the excellent control over the order parameter (ranging from isotropic to rigid solids) of a system and creation of model biological systems obviously invited, simplified, created, and amplified the applications of solid-state NMR techniques. Although solid-state NMR... 

As discussed in Section 1.5, the characterization of observables as random variables is ubiquitous in descriptions of physical phenomena. This is not immediately obvious in view of the fact that the physical equations of motion are deterministic and this issue was discussed in Section 1.5.1. Random functions, ordered sequences of random variable, were discussed in Section 1.5.3. The focus of this chapter is a particular class of random functions, stochastic processes, for which the ordering parameter is time. Time is a continuous ordering parameter, however in many practical situations observations of the random function z(Z) are made at discrete time 0 < Zi < t2, , < tn < T. In this case the sequence z(iz) is a discrete sample of the stochastic process z(i). 

Fig. 12.5. Illustration of the spatio-temporal evolution of the order parameter field for a system described by the Allen-Cahn equation (courtesy of W. Craig Carter). The temporal sequence runs from left to right starting with the first row.

A series of articles by Brandolini, Dybowski and co-workers [25-29] reported the use of NMR for static samples of PTFE to obtain information on orientation distribution of crystallites following deformation by tensile stress. The spectra were obtained using the MREV8 pulse sequence to remove homonuclear dipolar coupling so as to observe chemical shift dispersion as a function both of the draw ratio and of the angle between the draw direction and applied magnetic field (Fig. 18.5). The moments of the spectra were used [25-28] to determine the order parameters of the samples up to (Pg(cos 0)). The orientation distribution functions were then calculated... 

Figure 9.20 Dependence of the order parameter s on the average length fj of rigid sequences in the PLC chain for selected values of the concentration 0 of rigid segments. (According to [58] with permission of The American Chemical Society.)...

As noted before, MLCs and PLCs share essentially the same kinds of phases these are nematic, cholesteric, and a variety of smectic phases. These three names have been proposed by Friedel [1] in 1922 who imagined that such phases should exist—long before his concepts were confirmed by diffiractometric experiments. In all these phases the entire molecules (in MLCs) or the LC sequences in the chains (in PLCs) are oriented approximately— but not quite—perpendicularly to a preferred axis in space called director. The degree of alignment is characterized by the order parameter (also called the anisotropy factor) defined in 1946 by Hermans [36] as... 

Fig 6.2 Sequence of the phase transitions with decreasing temperature and lowering the phase symmetry. A new order parameter r i, r 2, etc. is introduced for each new phase with lower symmetry... 

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