Collective movement

Delarue, M. and Dumas, P. (2004) On the use of low-frequency normal modes to enforce collective movements in refining macromolecular structural models. Proc. Natl. Acad. Sci. USA 101, 6957-6962. 

In chemical reactions, orbits on stable and unstable manifolds of NHIMs describe movements of reaction coordinates. In some cases, these reaction coordinates are those degrees of freedom describing the behavior of individual nuclei such as a bond length between a pair of atoms. In other cases such as protein folding, reaction coordinates describe collective behavior where multiple nuclei participate. In either case, the processes of leaving a NHIM and approaching another one involve reformulation of reaction coordinates. In particular, when reaction coordinates are collective variables, reformulation processes themselves are of interest. We think that the study of intersections is crucial to understand how a certain collective movement is replaced by another one. 

If an incident laser light Eo interacts with the metal nanosphere, a collective movement of the electrons against the atomic cores of the metals - a so-called surface plasmon - is induced. The interaction of the surface plasmons and the incident laser light causes the so-called localized surface plasmon polaritons, resulting in an evanescent electromagnetic field E y, which is emitted fi-om the nanoparticle. The signal intensity achieved for SERS depends on the absolute square of the emitted field Egy, which can be simplified written as follows ... 

As the temperature is decreased below Tg, free rotation of the individual molecules decreases and molecular motions become restricted. In this temperature region, the collective movement of cooperatively rearranging regions (CRR) of the molecules dominates. Decrease of temperature leads to an increase in the size of the CRRs and hence to the decrease of configurational entropy below Tg (Metatla and Soldera 2007). Any description of relaxation time below Tg therefore has to consider the contribution of configurational entropy (Eq. 2.21) ... 

Plasmons Like phonons and excitons, plasmons represent the energy associated with the collective movement of particles. In this case, the particles are the free electrons present at and around the Fermi edge. 

Figure 2. Proton spin-lattice relaxation time T, obtained by field cycling as a function of the Larmor frequency CO/2n for the smectic C phase of a biforked liquid crystal. The solid line is the best fit of a model taking into account collective movements, self diffusion, and molecular rotation. Reprinted with permission from [41].

Previously, only mass transport due to diffusion was taken into account. Another influence on electrochemical process can be due to convection. Convection is the collective movement of ensembles of molecules within a fluid or a gas. To take into account convection. Equation 7.8 should be used for multidimensional processes or Equation 7.9 for a one-dimensional case. 

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