Van Hove function

Figure 23 Isosurface of the intrachain distinct part of the van Hove function projected onto the time-distance plane. For t —> 0, one observes the intrachain pair correlation function along the radial axes. On the average time scale of a torsional transition, a bonded neighbor moves into the position that the center particle occupied at time zero i.e., the chain slithers along its contour.

Starting from Eq. (4.S) and projecting onto the states one obtains a(x, T/, 0 = Gj/(x, t), that is the projected Van Hove function. This fimction... 

Finally rototranslational coupling has been investigated in two recent papers by Wey and Patey [48,49], using the general approach of the Van Hove functions described within the Kerr approximation, which relates the rototranslational correlation function of the solute to the joint conditional probability in both the position and orientation of the molecule. This method is helpful in providing a physical and mathematical framework for rototranslational coupling in complex fluids. However, it requires as a starting point a well defined equation of motion for the conditional probability. Wey and Patey have tested only one-body stochastic equations (such as the Fick-Debye and the Berne-Pecora equations), which are necessarily restricted. 

Essentially all of the definitions given above carry over to this case if we simply replace / by /. The van Hove function is then obtained from the phase space correlation function... 

Yeomans-Reyna, L. and Medina-Noyola, M. 2000. Overdamped van Hove function of colloidal suspensions. Phys. Rev. E 62 3382. 

Chavez-Rojo, M. A. and Medina-Noyola, M. 2006. Van Hove function of colloidal mixtures Exact results. Physica A 366 55. 

It is well known that apart from dull factors the coherent scattering of neutrons from liquids and solids is determined by the Van Hove function (dynamical structure factor)... 

Cerda J, van Hove MA (1997) Efficient method for the simulation of STM images. I. Generalized green-function formalism. Phys Rev B 56 15885... 

Polymer Melts Coherent Scattering and van Hove Correlation Functions. Part I Dynamics in the p-Relaxation Regime. 

If (n — m( = 3q, where q is an integer, the SWNT is metallic, whereas for (n — m ( 3q, it is semiconducting with a bandgap in the density of states (DOS) whose size is inversely proportional to the diameter. As a consequence of the size-dependent quantization of electronic wave functions around the circumference of the SWNT, the DOS shows typical singularities, the so-called van Hove singularities, consisting of a... 

The correlation functions G are the same functions which Oppenheimer and Bloom introduced in their theory of nuclear spin relaxation [304], The function has been called the time-dependent pair distribution function it should not, however, be confused with the van Hove correlation function which is often referred to by the same name. The name time-dependent intermolecular correlation function (TDICF) has, therefore, been proposed for G [71]. 

Both Pecora (16) and Komarov and Fisher (17) adapted van Hove s space-time correlation function approach for neutron scattering (18) to the light-scattering problem to calculate the spectral distribution of the light scattered from a solution. Using a molecular analysis, Pecora assumed the scattering particles to be undergoing Brownian motion, and predicted a Lorentzian line shape for the spectral distribution of the... 

The most important experiment of this type is thermal neutron scattering A complete determination of the differential scattering cross section for the scattering of neutrons from liquids completely determines the Van Hove scattering function.18 This function is related through a space-time Fourier transform to the autocorrelation function of the number density at two... 

Spectral lineshapes were first expressed in terms of autocorrelation functions by Foley39 and Anderson.40 Van Kranendonk gave an extensive review of this and attempted to compute the dipolar correlation function for vibration-rotation spectra in the semi-classical approximation.2 The general formalism in its present form is due to Kubo.11 Van Hove related the cross section for thermal neutron scattering to a density autocorrelation function.18 Singwi et al.41 have applied this kind of formalism to the shape of Mossbauer lines, and recently Gordon15 has rederived the formula for the infrared bandshapes and has constructed a physical model for rotational diffusion. There also exists an extensive literature in magnetic resonance where time-correlation functions have been used for more than two decades.8... 

Gs(r, t) and Gd(r, t) are called the Van Hove self and distinct space-time correlation functions.18 It clearly follows that probability distribution describing the event that a molecule is at the origin at t = 0 and at the point r at the time t. Gs(r, t) is consequently the probability distribution characterizing the net displacement or diffusion of a particle in the time t. Gd(r, t) on the other hand is a probability distribution describing the event that a molecule is at the origin at t = 0 and a different molecule is at the point r at the time t. Gd(r, t) describes the correlated motion of two molecules. It should be noted that the initial value of Gs(r, t) is... 

G. Van Hove Self-Correlation Functions from Computer Experiments... 

We shall now discuss three Van Hove correlation functions 18,72 obtained from our CO simulations. These functions are defined as follows ... 

G. (x.) Van-Hove self space-time correlation function, (6.14). 

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