Parametric coupling

Melnikov, A. V., Radu, I., Bovensiepen, U., Krupin, O., Starke, K., Matthias, F. and Wolf M. (2003) Coherent optical phonons and parametrically coupled magnons induced by femtosecond laser excitation of the Gd(OOOl) surface. Phys. Rev. Lett., 91, 227403. 

Thus, In the vicinity of a shape resonance, the electronic transition moment varies rapidly with R. This parametric coupling was estimated In the adlabatlc-nuclel approximation by computing the net transition moment for a particular vibrational channel as an average of the R-dependent dipole amplitude, weighted by the product of the Initial- and final-state vibrational wavefunctlons at each R (40.43). 

The Insulation In the BNL solar collector design uses rigid Insulation as a structural member. This member Is presently made from glass reinforced polylsocyanurate with a aluminum foil facer (Thermax, Celotex). The sheet metal frame Is parametrically coupled to the rigid Insulation and Is under compression when the... 

The level of excitation in Ty is indicated by the subscript, e, and the order is defined by the superscript, /. For example, second-order, triple excitations are represented by Coupled-cluster parametrizations of this metric [19] suggest an alternative form ... 

These compounds have been the subject of several theoretical [7,11,13,20)] and experimental[21] studies. Ward and Elliott [20] measured the dynamic y hyperpolarizability of butadiene and hexatriene in the vapour phase by means of the dc-SHG technique. Waite and Papadopoulos[7,ll] computed static y values, using a Mac Weeny type Coupled Hartree-Fock Perturbation Theory (CHFPT) in the CNDO approximation, and an extended basis set. Kurtz [15] evaluated by means of a finite perturbation technique at the MNDO level [17] and using the AMI [22] and PM3[23] parametrizations, the mean y values of a series of polyenes containing from 2 to 11 unit cells. At the ab initio level, Hurst et al. [13] and Chopra et al. [20] studied basis sets effects on and y. It appeared that diffuse orbitals must be included in the basis set in order to describe correctly the external part of the molecules which is the most sensitive to the electrical perturbation and to ensure the obtention of accurate values of the calculated properties. 

However, due to the availability of numerous techniques, it is important to point out here the differences and equivalence between schemes. To summarize, two EDA families can be applied to force field parametrization. The first EDA type of approach is labelled SAPT (Symmetry Adapted Perturbation Theory). It uses non orthogonal orbitals and recomputes the total interaction upon perturbation theory. As computations can be performed up to the Coupled-Cluster Singles Doubles (CCSD) level, SAPT can be seen as a reference method. However, due to the cost of the use of non-orthogonal molecular orbitals, pure SAPT approaches remain limited... 

Dynamic interaction effects are commonly neglected. Under certain circumstances, unconscrvalivc answers could result from neglecting the effects of coupling. Though some simple parametric studies can be made to evaluate these effects, coupling is normally expected to be negligible if the natural frequencies of... 

After the separation of the kinetic energy operator due to the center-of-mass motion from the Hamiltonian, the Hamiltonian describes the internal motions of electrons and nuclei in the system. These in the BO approximation can be separated into the vibrational and rotational motions of the nuclear frame of the molecule and the electronic motion that only parametrically depends on the instantenous positions of the nuclei. When the BO approximation is removed, the electronic and nuclear motions become coupled and the only good quantum numbers, which can be used to quantize the stationary states of the system, are the principle quantum number, the quantum number quantizing the square of the total (nuclear and electronic) squared angular momentum, and the quantum number quantizing the projection of the total angular momentum vector on a selected direction (usually the z axis). The separation of different rotational states is an important feamre that can considerably simplify the calculations. 

The first observation of the stimulated Raman effect was reported by Woodbury and Ng 215) j e effect was then thoroughly studied by several authors 216-218) and its theoretical background developed 219.220) (see also the review articles by Zubov et a/.22D). The stimulated Raman effect can be described as a parametric process where the coupling between a light wave at the Stokes frequency (Os and an optical phonon (vibrational wave) at cOy is produced by a pump field at col = (Oj + ojy. 

The use of feedback-control techniques to modulate combustion processes in propulsion systems has recently received extensive attention [1-3]. Most of the previous studies involved direct implementation of existing control methods designed for mechanical devices, with very limited effort devoted to the treatment of model and parametric uncertainties commonly associated with practical combustion problems. It is well established that the intrinsic coupling between flow oscillations and transient combustion responses prohibits detailed and precise modeling of the various phenomena in a combustion chamber, and, as such, the model may not accommodate all the essential processes involved due to the physical assumptions and mathematical approximations employed. The present effort attempts to develop a robust feedback controller for suppressing combustion instabilities in propulsion systems. Special attention is given to the treatment of model uncertainties. Various issues related to plant... 

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