Internal atomic oscillator

All atomic clocks are based on the same servo-loop scheme (Figure 11.1). An internal atomic oscillator at cOai is used to lock an external or local atomic oscillator at frequency (Dq- The local oscillator is used to probe the atomic transition at (0, and... 

Atomic Clock Clock that either contains an internal atomic oscillator or uses an external atomic oscillator as a reference. 

In this expression, s is the number of internal harmonic oscillators, which is 3N — 5 for linear molecules and 3N—6 for nonlinear molecules, and N is the number of atoms in the species. These are the precise conditions under which the high-pressure rate parameters discussed in the previous sections are applicable. 

An ideal glass is a solid in internal equilibrium in which there exists a definite set of equilibrium positions about which each atom oscillates. 

Minimized structures gained from MD simulations are also often basis of normal mode analysis (NMA) [41-43]. NMA assumes that all atoms harmonically oscillate around their equilibrium points. The oscillations deflned by frequency and amplitude (normal mode) are extracted and reflect directions of internal protein motions. Given all its normal modes, the entire protein motion can be expressed as a superposition of modes. The modes vith lo vest frequency correspond to rather delocalized motions in proteins in vhich a large number of atoms oscillate in coordinated motion vith considerable amplitude. Modes vith higher frequency represent more localized motions. Linear combinations of the most relevant normal modes can be employed to depict essential protein motions. Stepwise displacement of atoms of the original structure along the modes can be applied to build up an ensemble of relevant protein conformations [44, 45]. 

Fig. 5.2 A schematic energy diagram J2(K) of the internal and the external molecular vibrations in molecular crystals. Q is the frequency, hS2 the energy and K is the magnitude of the wavevector in a particular direction, e.g. in the direction a. (C = 0 is the centre and K = itja the boundary of the Brillouin zone, with the lattice constant a. P is the usual notation for the centre of the Brillouin zone. MSi is a low-frequency internal molecular oscillation with a small or vanishing dispersion const.). MSi is a high-frequency internal molecular oscillation. All together, there are 3N-6 internal modes N is the number of atoms per molecule. OP is an optical phonon in which whole molecules are excited to carry out translational or libration oscillations whose frequencies are...

Most of the molecules we shall be interested in are polyatomic. In polyatomic molecules, each atom is held in place by one or more chemical bonds. Each chemical bond may be modeled as a harmonic oscillator in a space defined by its potential energy as a function of the degree of stretching or compression of the bond along its axis (Fig. 4-3). The potential energy function V = kx j2 from Eq. (4-8), or W = ki/2) ri — riof in temis of internal coordinates, is a parabola open upward in the V vs. r plane, where r replaces x as the extension of the rth chemical bond. The force constant ki and the equilibrium bond distance riQ, unique to each chemical bond, are typical force field parameters. Because there are many bonds, the potential energy-bond axis space is a many-dimensional space. 

This energy increase can take different forms. It can be added as translational kinetic energy to speed up the movement to and fro of the molecules it can be added to the rotations of the molecules to get them to spin faster it can be added to increase the amplitude of the vibrational oscillations of the molecules and it can be added to excite electrons to higher energy states in the atoms or molecules. Other forms of internal energy are also possible, but the above are the most common. 

Taking advantage of advances in computational atomic and plasma physics and of the availability of powerful supercomputers, a collaborative effort - the international Opacity Project - has been made to compute accurate atomic data required for opacity calculations. The work includes computation of energy levels, oscillator strengths, photoionization cross-sections and parameters for pressure broadening of spectral lines. Several... 

D. S. Leckrone and J. Sugar (eds). The 4th International Colloquium on Atomic Spectra and Oscillator Strengths for Astrophysical and Laboratory Plasmas, Gaithersburg, MD, USA, September 14-17, 1992 (Invited Papers), Physica Scripta, T47 (1993). 

Partitioning of the various modes of reorientation—even for the simplest member of this class, a disaccharide molecule—is not an easy task. For instance, separation of rotatory diffusion from internal oscillations around the glycosidic bonds is not feasible because no ring carbon atom in the disaccharide moiety relaxes exclusively via the overall molecular motion. This problem becomes more serious if the internal motion of exocyclic substituents, such as a hydroxymethyl group, is considered in the process of dynamic modeling. 

Another study used H T, T2 and 13C T, T p measurements to assess the molecular dynamics in dry and wet solid proteins bacterial RNAase, lysozyme and bovine serum albumin.115 All relaxation time data were analysed assuming three components for the molecular motion methyl group rotation and slow and fast oscillations of all atoms. An inhomogeneous distribution of correlation times was found for all samples, not surprisingly given the inhomogeneous nature of the samples. Interestingly, it was found that dehydration affected only the slow internal motions of the proteins and that the fast ones remained unaltered. 

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