Mode-coupling model

Fig. 9. A correlation chart for the observed/predicted ripple characteristics for the reptation, Rouse and polymer mode coupling models. The restation model gives the best correlation ( 1) between theory and experiment.

FIG. 2.2 Rotation and inversion pathways of isomerization (A). Dynamic mode-coupling model of DMAAB in the excited state (B and C). 

Since there are very few dynamic experimental investigations of pretransitional effects [8], not much modeling has been reported to date either. Based on work for the macroscopic dynamics of the nematic-isotropic transition in sidechain polymers [27 -29], it has been suggested [28] that the non-meanfield exponent observed in dynamic stress-optical experiments [8] can be accounted for at least qualitatively by the mode-coupling model [28, 29]. Intuitively this qualitatively new dynamic behavior can be traced back to static nonlinear coupling terms between the nematic order parameter and the strain tensor. 

Schweizer and collaborators have elaborated an extensive mode-coupling model of polymer dynamics [52-54]. The model does not make obvious assumptions about the nature of polymer motion or the presence or absence of particular long-lived dynamic structures, e.g., tubes it yields a set of generalized Langevin equations and associated memory functions. Somewhat realistic assumptions are made for the equilibrium structure of the solutions. Extensive calculations were made of the molecular weight dependences for probe diffusion in melts, often leading by calculation rather than assumption to power-law behaviors for various transport coefficients. However, as presented in the papers noted here, the model is applicable to melts rather than solutions Momentum variables have been completely suppressed, so there are no hydrodynamic interactions. Readers should recall that hydrodynamic interactions usually refer to interactions that are solvent-mediated. 

Now the physical picture of multidimensional tunneling obtained from the above analysis is explained by taking a symmetric mode coupling model potential [30]. The Hamiltonian is given by... 

Finally, we touch upon the adiabatic and sudden approximations in the present model. In the same way as in the case of symmetric mode coupling model, the adiabatic approximation leads to the tunneling splitting independent of Hy. This does not exhibit any characteristic behavior discussed above and can never be reliable. If we apply the sudden approximation, we also encounter a problem since the potential curve in jc direction is not symmetric except when y is zero. Thus we cannot use Equation (4.12) directly anymore. 

PMMC polymer mode-mode coupling model... 

Rush M, Okuma M (2007) Effect of surface topography on mode-coupling model of dry contact sliding systems. J Sound Vib 308 721-734... 

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