Order parameter microscopic

Principal Orientational Order Parameter (Microscopic Approach)... 

The function / incorporates the screening effect of the surfactant, and is the surfactant density. The exponent x can be derived from the observation that the total interface area at late times should be proportional to p. In two dimensions, this implies R t) oc 1/ps and hence x = /n. The scaling form (20) was found to describe consistently data from Langevin simulations of systems with conserved order parameter (with n = 1/3) [217], systems which evolve according to hydrodynamic equations (with n = 1/2) [218], and also data from molecular dynamics of a microscopic off-lattice model (with n= 1/2) [155]. The data collapse has not been quite as good in Langevin simulations which include thermal noise [218]. 

I think Dr. Williams avowed pessimism is inevitable if one is trying to explain all biological phenomena in terms of molecular, microscopic concepts. But molecular description can be a Procrustean bed when dealing with complex, intrinsically macroscopic phenomena, because simple interpretability may not be feasible. In fact, the selection of a few essential macroscopic variables from a vast number of microscopic variables (or their combinations) is crucial not only for understanding via simplification, but also because collective variables (order parameters) tend to obey qualitatively different rules or laws that are not obvious in,... 

As it is known [5], the intensity of the scattered light gives us an information about the system s disorder, e.g., presence therein of pores, impurities etc. Since macroscopically liquid is homogeneous, critical opalescence arises due to local microscopic inhomogeneities - an appearance of small domains with different local densities. In other words, liquid is ordered inside these domains but still disorded on the whole since domains are randomly distributed in size and space, they appear and disappear by chance. Fluctuations of the order parameter have large amplitude and involve a wide spectrum of the wavelengths (which results in the milk colour of the scattered light). 

Theory for block copolymer rheology is still in its infancy. There are no models that can predict the rheological behaviour of a block copolymer from microscopic parameters. Fredrickson and Helfand (1988) considered fluctuation effects on the low frequency linear viscoelastic properties of block copolymers in the disordered melt near the ODT. They found that long-wavelength transverse momentum fluctuations couple only to compositional order parameter fluctua-... 

In this section we derive the effective Hamiltonian which will be the starting point for our further treatment. The strategy of the calculation is therefore separated into two steps. In the first step the system is treated in a mean-field-(MF) type approximation applied to a microscopic Hamiltonian. This leaves us with a slowly varying complex order parameter field for which we derive an effective Hamiltonian. The second step involves the consideration of the fluctuations of this order parameter. 

The hypothesis that the constituents of the mixture have a Lagrangian microstructure (in the sense of Capriz [3]) means that each material element of a single body reveals a microscopic geometric order at a closer look then it is there assigned a measure Vi(x) of the peculiar microstructure, read on a manifold Mi of finite dimension rnp e.g., the space of symmetric tensor in the theory of solids with large pores or the interval [0, v) of real number, with v immiscible mixture (see [5, 9]). We do not fix the rank of the tensor order parameter u%. 

Although we expect for dimensional reasons that the average magnitude of h, and hence the magnitude of ([nh]), will be proportional to pv, the tensorial form of ([nh]) is unknown. To obtain ([nh]), without having to revert back to (an almost impossible) microscopic calculation of the director field, Larson and Doi (1991 Kawaguchi 1996) assumed Aat ([nh]) is a function of the mesoscopic order parameter S— that is, that ([nh]) = Ka f(S). Dimensional reasoning then leads to the ansatz that... 

The abscissas of the correlation diagrams can be quantified. The quantification is thus far only an ex post facto device with power to classify but not yet to predict. It does not yet have a microscopic interpretation. Nevertheless it satisfies the needs of a theory of the equilibrium behavior of melting and freezing of clusters. Only the existence and not the definition of the nonrigidity parameter or the details of its origins is used in stage 2. However, we make a brief aside here to explain the definition in order to clarify just what information it carries. To understand the order parameter y (not to be confused with the surface tension), it is useful to examine how nonrigidity is traditionally characterized in diatomic and linear, particularly triatomic molecules. For... 

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