Interfacial, stochastic model

Stochastic variation may be introduced in other models as well. In this context, Lansky and Weiss [130] have also considered random variation for the parameter k of the interfacial barrier model (5.20). 

The stochastic model of ion transport in liquids emphasizes the role of fast-fluctuating forces arising from short (compared to the ion transition time), random interactions with many neighboring particles. Langevin s analysis of this model was reviewed by Buck [126] with a focus on aspects important for macroscopic transport theories, namely those based on the Nernst-Planck equation. However, from a microscopic point of view, application of the Fokker-Planck equation is more fruitful [127]. In particular, only the latter equation can account for local friction anisotropy in the interfacial region, and thereby provide a better understanding of the difference between the solution and interfacial ion transport. 

A Stochastic Model for Interfacial Temperature Generated at Discrete Sites... 

Although this treatment does not explicitly involve interactions at a solid-liquid interface, the application of Green s function to find the stochastic friction force may be an excellent opportunity for modeling interfacial friction and coupling, in the presence of liquid. An interesting note made by the authors is that the stochastic friction mechanism is proportional to the square of the frequency. This will likely be the case for interfacial friction as well. 

Inner slip, between the solid wall and an adsorbed film, will also influence the surface-liquid boundary conditions and have important effects on stress propagation from the liquid to the solid substrate. Linked to this concept, especially on a biomolecular level, is the concept of stochastic coupling. At the molecular level, small fluctuations about the ensemble average could affect the interfacial dynamics and lead to large shifts in the detectable boundary condition. One of our main interests in this area is to study the relaxation time of interfacial bonds using slip models. Stochastic boundary conditions could also prove to be all but necessary in modeling the behavior and interactions of biomolecules at surfaces, especially with the proliferation of microfluidic chemical devices and the importance of studying small scales. 

Bascom and Jensen [67], used an approach similar to that of Drzal and coworkers. Wimolkiatisak et al. [70] found that the fragmentation length data fitted both the Gaussian and Weibull distributions equally well. Fraser et al. [71 ] developed a computer model to simulate the stochastic fracture process and, together with the shear-lag analysis, described the shear transmission across the interface. Netravali et al. [72], used a Monte Carlo simulation of a Poisson-Weibull model for the fiber strength and flaw occurrence to calculate an effective interfacial shear strength X using the relationship ... 

Random disturbance interfacial model, in which the disturbed points are stochastic. 

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