Stochastic scattering

Stochastic scattering refers to the random electron-electron interactions that result from when an electron beam is focused into a small volume, where the individual electrons experience the electric fields of the other electrons. For electrons traveling with a velocity v, given by... 

To visualize the effects induced by paramagnetic relaxation, the time-dependent forward-scattering intensity has been calculated by implementing the stochastic relaxation between spin states i ) and j ) into the SYNFOS program package [30]. The transition rates from i) to j ) with , > Ej are described by [53]... 

Scalar equations, transition state trajectory deterministically moving manifolds, 224—228 stochastically moving manifolds, 214—222 Scattering theory, two-pathway excitation,... 

Introduction. After we have discussed examples of uncorrelated but polydisperse particle systems we now turn to materials in which there is more structure - discrete scattering indicates correlation among the domains. In order to establish such correlation, various structure evolution mechanisms are possible. They range from a stochastic volume-filling mechanism over spinodal decomposition, nucleation-and-growth mechanisms to more complex interplays that may become palpable as experimental and evaluation technique is advancing. 

Scattering Data of the Iterated Stochastic Structure. The computer simulation of the pure stochastic structure evolution process even yields the respective IDF and the scattering data [184], Here it becomes clear that a standard concept of arranged but distorted structure, the convolution polynomial, is not applicable to... 

In Sect. 7.4.6, we discussed various stochastic simulation techniques that include the kinetics of recombination and free-ion yield in multiple ion-pair spurs. No further details will be presented here, but the results will be compared with available experiments. In so doing, we should remember that in the more comprehensive Monte Carlo simulations of Bartczak and Hummel (1986,1987, 1993,1997) Hummel and Bartczak, (1988) the recombination reaction is taken to be fully diffusion-controlled and that the diffusive free path distribution is frequently assumed to be rectangular, consistent with the diffusion coefficient, instead of a more realistic distribution. While the latter assumption can be justified on the basis of the central limit theorem, which guarantees a gaussian distribution for a large number of scatterings, the first assumption is only valid for low-mobility liquids. 

More informative are the stochastic trajectory simulations run by Muhl-hausen et al. (M WT), on empirical interaction potential surfaces for scattering and desorption Although the major thrust was to understand the direct beam scattering results of NO/Ag(l 11), extension of these calculations allows for comparison to the desorption of NO from Pt(lll) Important insights derived from the NO/Ag(lll) calculations were ... 

A STOCHASTIC MODEL FOR NEUTRON SCATTERING BY SIMPLE LIQUIDS... 

Neutron Scattering, A Stochastic Model for, by Simple Liquids... 

The interest in fluctuations and in the stochastic methods for describing them has grown enormously in the last few decades. The number of articles scattered in the literature of various disciplines must run to thousands, and special journals are devoted to the subject. Yet the physicist or chemist who wants to become acquainted with the field cannot easily find a suitable introduction. He reads the seminal articles of Wang and Uhlenbeck and of Chandrasekhar, which are almost forty years old, and he culls some useful information from the books of Feller, Bharucha-Reid, Stratonovich, and a few others. Apart from that he is confronted with a forbidding mass of mathematical literature, much of which is of little relevance to his needs. This book is an attempt to fill this gap in the literature. 

Induction times are very scattered and, particularly at low driving forces (under isothermal conditions), nucleation is stochastic and therefore unpredictable. 

Hydrate nucleation (the initiation of growth, occuring during the induction period) is a stochastic process (with significant scatter in the data at low driving force under isothermal conditions). 

Studying the electron tracks with the Monte Carlo method, the authors of Refs. 302 and 303 have used the so-called stochastic approach, within which one fixes a simultaneous picture of the spatial distribution of excitation and ionization events. The tracks found this way are sets of spatial points where the inelastic scattering events took place. With this at hand it proves to be possible to calculate the energy absorption spectrum in sensitive volumes of the irradiated medium303 and to calculate the shape of the line and the slope of electronic spin echo signals.302 Such a... 

N. When this is combined with the light scattering equation of Rayleigh, and allowance made for a distribution in the particle size because of the stochastic nature of the process, one obtains (37)... 

In this paper, we will consider only the dynamic aspects of this percolation problem, i.e., the stochastic distribution of velocities between the flow structures. To analyze a percolation process, it is useful to represent the scattering medium (i.e. the packed bed) by a lattice as depicted in Figure 2. The sites of the lattice correspond to the contact points between the particles whereas the bonds correspond to the pores connecting two neighbour contact points. The walls of these pores are delimited by the external surface of the particles. The percolation process is... 

Gutzwiller, M.C. (1983). Stochastic behavior in quantum scattering, Physica D7, 341-355. 

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