Instantaneous structure

Crimaldi, J. P., M. B. Wiley, and J. R. Koseff. The relationship between mean and instantaneous structure in turbulent passive scalar plumes. J. Turbul. 3(14), 1-24... 

Hie instantaneous structure structure I) can be thought of as a snapshot of the network with an exposure time which is short compared with the molecular vibration times, that is, Ti = s (this is precisely the order of magnitude of the time s s used in computer simulation exf riments ). 

It is only on the basis of a correct knowledge of the most probable instantaneous structure that an accurate calculation of the static electric permittiwty can be made. It is indeed likdy that the comparison of experimental and calculated temperature variation of the static electric pmnitti-vity can serve as a test of the adequacy of the structural model proposed. 

Current Ideas on the Structure of Water Although the molecules in a liquid are in continual motion, there exists at any instant a configuration which can be regarded as the instantaneous structure. The time average of these configurations can still be regarded as... 

This term represents the creation of vibrations (phonons) of the instantaneous structure of the liquid. The second term is a slower, temperature dependent response caused by reorganization of the instantaneous structure. 

Suppose we have n data points associated with k variables—in our case, n instantaneous structures of 3N Cartesian coordinates of N particles along a molecular dynamics (MD) trajectory. Let D be a 3N x n matrix, whose elements Dim are defined as the deviation of the (mass-weighted) zth Cartesian coordinate qi(tm) at a time tm(l time average (qi), that is,... 

The model that we are going to consider in this section is given by two spherical rotators, simply called body 1 and body 2. Body 1 is the solute molecule, whereas body 2 is the instantaneous structure of solvent molecules in the immediate surroundings of the solute. The rest of the solvent is described as a homogeneous, isotropic and continuous viscous fluid. In the overdamped regime, the system is described by a Smoluchowski equation in the phase space where ft, and ftj... 

Considerable effort has been expended in characterizing the instantaneous structures of close-packed static amorphous assemblies of spherical particles, and this work has been extensively reviewed. High-density, simple model liquids also have been examined. Some attention has been directed toward dynamic structural properties, an area of great potential interest. 

The range of chemical shifts is much wider for O than for C and, as a result, provides a better opportunity for obtaining instantaneous structures for fluxional clusters than do - C NMR measurements. Although C O has been used for other clusters, there are no published reports of work on analogous rhodium-containing clusters. 

Fig. 8.1 An image of an odor plume taken using planar, laser-induced fluorescence. This image reveals the instantaneous scalar structure of the plume. The image was captured from the outer layer of the momentum boundary layer of the plume. It is a horizontal image spanning a lateral and streamwise range it reveals the spatial patterns at a given vertical location. The color scale indicates the concentration of the odor in the plume concentrations are normalized by the source concentration Co and color coded as shown in the legend. From Grimaldi et al.. Journal of Turbulence, 2002, The relationship between mean and instantaneous structure in turbulent passive scalar plumes, vol. 3, pp. 1-24. Reproduced with the permission of the authors and Taylor and Francis Ltd. (www.tandf.co.uk/ioumals).

Experimental evidence bearing on this point is, as we shall see, indirect and allows considerable latitude in building up a picture of the instantaneous structure of water. 

Fig. 4.1 Instantaneous vs. time average views of odor signal structure. Photograph is a series of laser-induced fluorescence images of dye concentration expressed as color (red is highest concentration, blue is lowest). The top 4 images are each taken on a rapid time scale (4 ns per frame, 30 ms per successive frame), and show the fine scale instantaneous structure. Note how coherent structures move downstream. The bottom panel is an average of 1,000 frames, and gives a result similar to employing a diffusion equation. This plume is approximately 1 x 0.15 m. Reproduced from Weissburg (2000) with permission from The Biological Bulletin...

A simulation for 1 fs after perturbation can cover only an infinitesimal area of the potential surfece, unlike simulations for a longer timescale, which can better explore the rugged potential surface. In this sense, our simulation of energy transfer during 1 fs after perturbation does not intend to analyze the kinetic process of energy transfer, but intends to study the shape of the local potential surface around an instantaneous structure formed at a finite temperature. Therefore, it is reasonable to analyze the results of such simulations from the viewpoint of series expansion of potential energy. 

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