Mesoscopic analysis

Shenoy V. B., Kukta R. and Phhlips R., Mesoscopic Analysis of Structure and Strength of Dislocation Junctions in fee Metals, Phys. Rev. Lett., 84, 1491 (2000). 

Using the calculational method based on DDFT, deviations from the cylinder bulk morphology have been identified as surface reconstructions [58, 62], The constructed structure or phase diagrams allowed surface field and confinement effects to be distinguished [57-59, 107, 145, 186], The comparative analysis of defect types and dynamics disclosed annihilation pathways via temporal phase transitions [36, 111]. Further, a quantitative analysis of defect motion led to an estimate of the interfacial energy between the cylinder and the PL phases [117]. A DDFT-based model was effectively used to simulate a block copolymer film with a free surface and to study the dynamics of terrace development [41,42], We showed how our computational method and an advanced dynamic SFM can be exploited in a synergetic fashion to extend the information about the elementary steps in structural transitions at the mesoscopic level. In particular, the experiments validate the dynamic DDFT method, and the DDFT calculations rationalize the characterization of the film surface in the interior of the film [187],... 

During the past few decades, various theoretical models have been developed to explain the physical properties and to find key parameters for the prediction of the system behaviors. Recent technological trends focus toward integration of subsystem models in various scales, which entails examining the nanophysical properties, subsystem size, and scale-specified numerical analysis methods on system level performance. Multi-scale modeling components including quantum mechanical (i.e., density functional theory (DFT) and ab initio simulation), atom-istic/molecular (i.e., Monte Carlo (MC) and molecular dynamics (MD)), mesoscopic (i.e., dissipative particle dynamics (DPD) and lattice Boltzmann method (LBM)), and macroscopic (i.e., LBM, computational... 

A convincing demonstration of the anisotropic organization of these hybrid xerogels is their birefringence when observed in polarized light. This analysis is usually performed on liquid crystal compounds in order to determine their mesoscopic anisotropic organization. 

The review is organized as follows In Section 2 we present the multiscale equilibrium thermodynamics in the setting of contact geometry. The time evolution (multiscale nonequilibrium thermodynamics) representing approach of a mesoscopic level LmeSoi to the level of equilibrium thermodynamics Leth is discussed in Section 3. A generalization in which the level Leth is replaced by another mesoscopic level LmesoZ is considered in Section 4. The notion of multiscale thermodynamics of systems arises in the analysis of this type of time evolution. 

In this section we limit ourselves to equilibrium. The time evolution that is absent in this section will be taken into consideration in the next two sections. We begin the equilibrium analysis with classical equilibrium thermodynamics of a one-component system. The classical Gibbs formulation is then put into the setting of contact geometry. In Section 2.2 we extend the set of state variables used in the classical theory and introduce a mesoscopic equilibrium thermodynamics. 

Many systems exhibit nonlinear behavior. This is another systems-level task that is computationally very demanding. Application of bifurcation analysis to simple and complex chemistry hybrid stochastic (KMC)-deterministic (ODE) models has been presented by our group (Raimondeau and Vlachos, 2002b, 2003 Vlachos et al., 1990) for various catalytic surface reactions. Prototype hybrid continuum-stochastic models that exhibit bifurcations were recently explored by Katsoulakis et al. (2004). It was found that mesoscopic... 

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