Periodicity mesoscopic

The period of the lamellar structures or the size of the cubic cell can be as large as 1000 A and much larger than the molecular size of the surfactant (25 A). Therefore mesoscopic models like a Landau-Ginzburg model are suitable for their study. In particular, one can address the question whether the bicontinuous microemulsion can undergo a transition to ordered bicontinuous phases. 

The mesoscopic domain of real catalysts is mostly covered by the typical catalysis periodicals, such as Applied Catalysis, the Journal of Catalysis, Catalysis Letters, Topics in Catalysis, Catalysis Today, Microporous Materials and Zeolites, although occasionally articles also appear in Journal of Physical Chemistry and Physical Chemistry-Chemical Physics, and many others. 

In what follows we will discuss systems with internal surfaces, ordered surfaces, topological transformations, and dynamical scaling. In Section II we shall show specific examples of mesoscopic systems with special attention devoted to the surfaces in the system—that is, periodic surfaces in surfactant systems, periodic surfaces in diblock copolymers, bicontinuous disordered interfaces in spinodally decomposing blends, ordered charge density wave patterns in electron liquids, and dissipative structures in reaction-diffusion systems. In Section III we will present the detailed theory of morphological measures the Euler characteristic, the Gaussian and mean curvatures, and so on. In fact, Sections II and III can be read independently because Section II shows specific models while Section III is devoted to the numerical and analytical computations of the surface characteristics. In a sense, Section III is robust that is, the methods presented in Section III apply to a variety of systems, not only the systems shown as examples in Section II. Brief conclusions are presented in Section IV. 

Placing a QD on one path, and changing its plunger gate voltage V, would vary the corresponding phase ol = olqd- If the 2-slit formula were valid, it would allow the determination of the dependence of olqd on V. This was the motivation of Yacoby et al. [6], who placed a QD on one path of a closed mesoscopic ABI. Indeed, the measured conductance was periodic in cj>, and the detailed dependence of Q on varied with V. However, close to a resonance the data did not fit the simple 2-slit formula they required more harmonics in 4>, e.g. of the form... 

Weissman JM, Sunkara HB, Tse AS, Asher SA. Thermally switchable periodicities and diffraction from mesoscopically ordered materials. Science 1996, 274, 959-960. 

Liu L, Li PS, Asher SA (1999) Entropic trapping of macromolecules by mesoscopic periodic voids in a polymer hydrogel. Nature 397(6715) 141-144... 

Figure 29. a) Conductivity variation in the system /J-Agl-AgCl (volume fraction) for different temperatures."8 b) Conductivity variation in CaFi-BaF heterolayers as a function of temperature for different periods (spacings)."9 (Reprinted from N. Sata, K. Eberman, K. Eberl and J. Maier, Mesoscopic fast ion conduction in nanometre-scale planar heterostructures. Nature. 408, 946-949. Copyright 2000 with permission from Macmillan Magazines Ltd.)... 

Asher, S., Holtz, J., Weissman, J. et ah, Mesoscopically periodic photonic crystal materials for linear and nonhnear optics and chemical sensing, MRS Bull., 23, 44, 1998. 

The mesoscaled structural regularity causes various features that are observed for mesoporous materials, such as crystal-like particle morphologies and the existence of sharp XRD peaks. Although no atomic-scaled structural ordering is observed in the mesoporous crystal , these particles can be described as being artificial single-crystalline with a mesoscopic periodic structure. 

The current control at the one-by-one electron accuracy level is feasible in mesoscopic devices due to quantum interference. Though the electric charge is quantized in units of e, the current is not quantized, but behaves as a continuous fluid according to the jellium electron model of metals. The prediction of the current quantization dates back to 1983 when D. Thouless [Thouless 1983] found a direct current induced by slowly-traveling periodic potential in a ID gas model of non-interacting electrons. The adiabatic current is the charge... 

Larson and Doi introduced a mesoscopic polydomain model based on LE theory. This model includes a domain orientation distribution function and incorporates director tumbling, distortional elasticity, and texture size. Larson-Doi model can qualitatively predict the steady flow behavior and transient behavior. However, discrepancies between the theoretical predictions and the experiments of model systems were observed, especially when the shear history includes rest periods. ° This model is restricted to low shear rates without perturbing the molecular orientation distribution function in each domain.f ... 

The complex rotational behavior of interacting molecules in the liquid state has been studied by a number of authors using MD methods. In particular we consider here the work of Lynden-Bell and co-workers [60-62] on the reorientational relaxation of tetrahedral molecules [60] and cylindrical top molecules [61]. In [60], both rotational and angular velocity correlation functions were computed for a system of 32 molecules of CX (i.e., tetrahedral objects resembling substituted methanes, like CBt4 or C(CH3)4) subjected to periodic boundary conditions and interacting via a simple Lennard-Jones potential, at different temperatures. They observe substantial departures of both Gj 2O) and Gj(() from predictions based on simple theoretical models, such as small-step diffusion or 7-diffusion [58]. Although we have not attempted to quantitatively reproduce their results with our mesoscopic models, we have found a close resemblance to our 2BK-SRLS calculations. Compare for instance our Fig. 13 with their Fig. 1 in [60]. 

Brenner (1980) has explored the subject of solute dispersion in spatially periodic porous media in considerable detail. Brenner s analysis makes use of the method of moments developed by Aris (1956) and later extended by Horn (1971). Carbonell and Whitaker (1983) and Koch et al. (1989) have addressed the same problem using the method of volume averaging, whereby mesoscopic transport coefficients are derived by averaging the basic conservation equations over a single unit cell. Numerical simulations of solute dispersion, based on lattice scale calculations of the Navier-Stokes velocity fields in spatially periodic structures, have also been performed (Eidsath et al., 1983 Edwards et al., 1991 Salles et al., 1993). These simulations are discussed in detail in the Emerging Areas section. 

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