Coarse- grained interface

Moreover, both the technical as well as the homogenizing wrapper s interface can be further divided into (i) a coarse-grained interface to start/stop a wrapped tool or to load a document into a wrapped tool (black-box view) and (ii) a fine-grained interface to invoke tool specific operations, e.g. accessing the data maintained by the wrapped tool (white-box view). 

On short length scales the coarse-grained description breaks down, because the fluctuations which build up the (smooth) intrinsic profile and the fluctuations of the local interface position are strongly coupled and camiot be distinguished. The effective interface Flamiltonian can describe the properties only on length scales large compared with the width w of the intrinsic profile. The absolute value of the cut-off is difficult... 

Figure B3.6.3. Sketch of the coarse-grained description of a binary blend in contact with a wall, (a) Composition profile at the wall, (b) Effective interaction g(l) between the interface and the wall. The different potentials correspond to complete wettmg, a first-order wetting transition and the non-wet state (from above to below). In case of a second-order transition there is no double-well structure close to the transition, but g(l) exhibits a single minimum which moves to larger distances as the wetting transition temperature is approached from below, (c) Temperature dependence of the thickness / of the enriclnnent layer at the wall. The jump of the layer thickness indicates a first-order wetting transition. In the case of a conthuious transition the layer thickness would diverge continuously upon approaching from below.

These chain models are well suited to investigate the dependence of tire phase behaviour on the molecular architecture and to explore the local properties (e.g., enriclnnent of amphiphiles at interfaces, molecular confonnations at interfaces). In order to investigate the effect of fluctuations on large length scales or the shapes of vesicles, more coarse-grained descriptions have to be explored. 

By virtue of their simple stnicture, some properties of continuum models can be solved analytically in a mean field approxunation. The phase behaviour interfacial properties and the wetting properties have been explored. The effect of fluctuations is hrvestigated in Monte Carlo simulations as well as non-equilibrium phenomena (e.g., phase separation kinetics). Extensions of this one-order-parameter model are described in the review by Gompper and Schick [76]. A very interesting feature of tiiese models is that effective quantities of the interface—like the interfacial tension and the bending moduli—can be expressed as a fiinctional of the order parameter profiles across an interface [78]. These quantities can then be used as input for an even more coarse-grained description. 

Compared with the use of arbitrary grid interfaces in combination with reduced-order flow models, the porous medium approach allows one to deal with an even larger multitude of micro channels. Furthermore, for comparatively simple geometries with only a limited number of channels, it represents a simple way to provide qualitative estimates of the flow distribution. However, as a coarse-grained description it does not reach the level of accuracy as reduced-order models. Compared with the macromodel approach as propagated by Commenge et al, the porous medium approach has a broader scope of applicability and can also be applied when recirculation zones appear in the flow distribution chamber. However, the macromodel approach is computationally less expensive and can ideally be used for optimization studies. 

This type of functional, which we refer to as coarse-grained, can be used to calculate both surface tension and adsorption isotherms to quite good accuracy for many fluids and interfaces. It can also be used for screening problems in the theory of electrolytes. 

The next most important mechanism affecting the surface tension at a single component simple fluid gas-liquid interface is, we believe, associated with the nonlocality of the repulsive interaetions. To account for this mechanism, observe that it enters by way of the exeluded volume effeet. In the coarse-grained GvdW(S) theory above, the free volume faetor /(r) is given by... 

The structure of the liquid/vapour interface of ambient methanol obtained in the SS-LMBW/RISM-KHM approach is depicted in Figure 5.5. Compared to the non-polar n-hexane, the decay of the inhomogeneity away from the interface is noticeably quicker for the polar methanol 10 A to the gas and 30 A to the liquid phase. The coarse-grained... 

Interfacing atomistic with coarse grain models... 

Coarse grain models can be interfaced using a one-way, bottom-up scheme. In this scheme, an atomistic model of the system (be it MM or QM) is used to parameterize a coarse grain model of the system. This idea is not new, and was the parameterisa-... 

Continuum models can be directly interfaced with atomistic or coarse grain models using a two-way embedded interface. In this scheme, the atomistic or CG model is embedded within a continuum model. Implicit solvent methods, in which an atomistic or CG model of a solute is embedded within a continuum model of the solvent, are popular and well-established examples of this type of interface. Implicit solvent models represent the solvent as a dielectric continuum, and allow the electrostatics of the atomistic or CG solute to polarise the continuum, which then results in an electrostatic reaction field that returns to interact with the solute. Implicit solvent models have been reviewed in detail many times before, and enable the dynamic transfer of electrostatic information across the atomistic/ continuum or CG/continuum interfaces. Recently, new multiscale continuum methods have been developed that allow for the dynamic transfer of mechanical and hydrodynamic information across these interfaces. One example is the work by Villa... 

Unlike the density of bulk fluids, which is a function of pressure and temperature only (and composition for a mixture), the average density across the interface between a liquid and its vapor, as well as at the liquid/liquid interface, varies as a function of the distance along the interface normal p(z). Like other local thermodynamic quantities[30], it is defined by a coarse-graining procedure The volume of the system is divided into slabs perpendicular to the interface normal, and the density of each slab is computed in the usual way. The thickness of the slabs is chosen to be small enough so that the density does not vary much... 

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