Mesoscopic Model

The predicted critical sizes agree with measurement as derived from Fig. 28.3 unless with given references. Changing the f value only affects the c (= 2ilcd) of a material with below 1,000 K [75] 

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Continuum models go one step frirtlier and drop the notion of particles altogether. Two classes of models shall be discussed field theoretical models that describe the equilibrium properties in temis of spatially varying fields of mesoscopic quantities (e.g., density or composition of a mixture) and effective interface models that describe the state of the system only in temis of the position of mterfaces. Sometimes these models can be derived from a mesoscopic model (e.g., the Edwards Hamiltonian for polymeric systems) but often the Hamiltonians are based on general symmetry considerations (e.g., Landau-Ginzburg models). These models are well suited to examine the generic universal features of mesoscopic behaviour. 

The hierarchy of models is complemented by a variety of methods and tecluiiques. Mesoscopic models tliat incorporate some fluid-like packing (e.g., spring-bead models for polymer solutions) are investigated by Monte Carlo... 

Mesoscopic models can often be treated by molecnlar dynamics simnlations. This method generates a realistic... 

From this short discussion, it is clear that atomistically detailed molecular dynamics or Monte Carlo simulations can provide a wealth of information on systems on a local molecular atomistic level. They can, in particular, address problems where small changes in chemical composition have a drastic effect. Since chemical detail is avoided in mesoscopic models, these can often capture such effects only indirectly. 

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. 

A. Malevanets and R. Kapral, Mesoscopic model for solvent dynamics, J. Chem. Phys. 110, 8605 (1999). 

T. Ihle and D. M. Kroll, Stochastic rotation dynamics a Galilean-invariant mesoscopic model for fluid flow, Phys. Rev. E 63, 020201(R) (2001). 

James M. Briggs and Jan Antosiewicz, Simulation of pH-dependent Properties of Proteins Using Mesoscopic Models. 

Note here that the relation between mesoscopic and microscopic approaches is not trivial. In fact, the former is closer to the macroscopic treatment (Section 2.1.1) which neglects the structural characteristics of a system. Passing from the micro- to meso- and, finally, to macroscopic level we loose also the initial statement of a stochastic model of the Markov process. Indeed, the disadvantages of deterministic equations used for rather simplified treatment of bimolecular kinetics (Section 2.1) lead to the macro- and mesoscopic models (Section 2.2) where the stochasticity is kept either by adding the stochastic external forces (Section 2.2.1) or by postulating the master equation itself for the relevant Markov process (Section 2.2.2). In the former case the fluctuation source is assumed to be external, whereas in the latter kinetics of bimolecular reaction and fluctuations are coupled and mutually related. Section 2.3.1.2 is aimed to consider the relation between these three levels as well as to discuss problem of how determinicity and stochasticity can coexist. 

Mesoscopic Modeling of Two-Phase Transport in Polymer Electrolyte Fuel Cells... 

In this chapter, the development of a mesoscopic modeling formalism is presented in order to gain fundamental insight into the structure-wettability influence on the underlying liquid water transport and interfacial dynamics in the PEFC CL and GDL. 

The mesoscopic modeling approach consists of a stochastic reconstruction method for the generation of the CL and GDL microstructures, and a two-phase lattice Boltzmann method for studying liquid water transport and flooding phenomena in the reconstructed microstructures. 

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