Dynamical coupling

It is important to note that the non-adiabatic coupling terms have a direct effect on the momentum of the nuclei, which is the reason it is called a dynamic coupling. By substituting Eq. (B.13) in Eq. (B.9), we get... 

The vector potential-matrix A present in the Hamiltonian (or in the Lagrangean) arises from a dynamic coupling meaning, that it has the form... 

Although the concern is primarily for the response of the piping. system, the possibiliis of dynamic coupling with the containment structure should not be neglected. A concern is whether or not the secondary shield wall will withstand the dynamic interaction between the walls and the pump. This is answered by examining the mode shapes if there were no coupling between the walls and the pump. 

The natural frequency, co associated with the mode shape that exhibits a large displacement of the pump is compared with the fundamental frequency, of the wall. If co is much less than ru, then the dynamic interaction between the wall and the loop may be neglected, but the kinematic constraint on the pump imposed by the lateral bracing is retained. If nearly equals nr , the wall and steam supply systems are dynamically coupled. In which case it may be sufficient to model the wall as a one-mass system such that the fundamental frequency, Wo is retained. The mathematical model of the piping systems should be capable of revealing the response to the anticipated ground motion (dominantly translational). The mathematics necessary to analyze the damped spring mass. system become quite formidable, and the reader is referred to Berkowitz (1969),... 

In the above expressions, RT stands for restricted totalistic rules which maximally subdivide the local neighborhood. The inclusion of an ij in the expressions for tp assures that only those sites already linked can be decoupled and the 6 Dij,2) in the equations defining uj are put in to malce sure that only sites separated by distance=2 may be dynamically coupled. 

Mason SF (1980) The Ligand Polarization Model for the Spectra of Metal Complexes. The Dynamic Coupling Transition Probabilities. 39 43-81 Massey V, see Hemmerich P (1982) 48 93-124... 

The second category of DDT processes, which occur in smooth tubes, is considerably more complex, because it involves gas-dynamic coupling of turbulent flow with chemical reactions and a variety of instability processes. 

In this section, we switch gears slightly to address another contemporary topic, solvation dynamics coupled into the ESPT reaction. One relevant, important issue of current interest is the ESPT coupled excited-state charge transfer (ESCT) reaction. Seminal theoretical approaches applied by Hynes and coworkers revealed the key features, with descriptions of dynamics and electronic structures of non-adiabatic [119, 120] and adiabatic [121-123] proton transfer reactions. The most recent theoretical advancement has incorporated both solvent reorganization and proton tunneling and made the framework similar to electron transfer reaction, [119-126] such that the proton transfer rate kpt can be categorized into two regimes (a) For nonadiabatic limit [120] ... 

Stanton, R. V., D. S. Hartsough, and K. M. Merz Jr. 1993. Calculation of Solvation Free Energies Using a Density Functional/Molecular Dynamics Coupled Potential. J. Phys. Chem. 97, 11868. 

Sonnefeld, W. J., Zoller, W. H., May, W. E. (1983) Dynamic coupled-column liquid chromatographic determination of ambient temperature vapor pressures of polynuclear aromatic hydrocarbons. Anal. Chem. 55, 275-280. 

Yu, G., Xu, X. (1993) Investigation of aqueous solubility of nitro-PAH by dynamic coupled-column HPLC. Chemosphere 24,1699-1993. 

We shall consider here in more detail two models first a dynamic coupling approach, due to Weigang33, who considered optical activity deriving from the coupling of electric dipoles (the diene chromophore and the polarizable bonds around it) and second, a localized orbital investigation, which permits one to separate the contributions from the intrinsic diene optical activity and from the axial substituents. 

In this way, a As value of —0.57 is calculated at 250 nm, as compared with an experimental value of —0.63. This excellent agreement between the experimental and calculated values is a strong indication that a dynamic coupling mechanism is the major source of optical activity in these molecules. 

Both types of species adsorb competitively with CO, leading to a decrease in the amount of adsorbed CO and a shift of v(CO) to lower frequency. The latter effect is consistent with the decrease in dynamic coupling expected for a uniformly reduced CO coverage. 

The possibility even exists of including dynamical effects with time-dependent friction terms (plus random forces at finite temperatures).77-80 Flowever, it may not be advisable to take advantage of this possibility, as the simulation would become increasingly slow with increasing number of time steps. Moreover, the simulation will slow down considerably in higher dimensions because of the nonorthogonality of the dynamical coupling in reciprocal space. 

Regardless of the details of the dynamic coupling in the Q modes (eq 14), in all other modes the transition is between... 

Dynamic coupled-column liquid chromatographic method Calculation from evaporation rates and vapor pressures of reference compound... 

It is noteworthy that the phonon anomaly, due to the dynamical coupling between substrate Rayleigh wave and adlayer mode, is likewise present in the bi- and even the trilayer films. It is only the Q range of the anomaly which... 

The analysis shall be for the train as a whole unless the train includes a device that has weak dynamic coupling, for example, a hydraulic coupling or torqne converter. 

---