Random distortion

Gerber, Gubernator, and Muller have described a method for generating large flexible ring structures which are then subjected to random distortion and... 

The various methods of error removal should be carried out in some routine way so that data is treated systematically, avoiding random distortions that might be introduced by the clean-up procedures themselves. The order of operations might be as follows ... 

For example, a capillary sampling tube can be inserted into the effluent at the end of the reactor and led directly to the vacuum chamber of the ionizer of a mass spectrometer. Issues concerning capillary size to avoid overloading the vacuum pumps of the mass spectrometer, of variation in sample flow rate with temperature and composition changes during reaction, of condensation during transit to the mass spectrometer, and other such factors may be important and have to be examined and dealt with to avoid distortion in the results. Random distortion from various sources can be adequately dealt with as noise, in ways described in Chapter 7. Systematic distortion, which can be caused by neglecting any of the above issues, is more treacherous and must be carefully avoided. 

It was pointed out independently by Williams (1967) and Culvahouse et al. (1967) that for a non-Kramers ion at a site lacking in full inversion symmetry, terms linear in an electric held may exist for a doublet state. Thus for Cj, symmetry (but not for C y) the system may have a permanent electric dipole moment, and its interaction with an electric held may be represented by additional terms of the form -I- SyEy). Transitions then occur with an RF electric held normal to the z-axis, even in the absence of a distortion from axial symmetry. As before, random distortions again produce an asymmetrical line shape, but with a maximum corresponding to the point for zero distortion, unlike the magnetic transitions referred to above. The asymmetry is present because in each case the distortions move the transitions to higher frequency at constant applied held, or to lower held at constant frequency. Such electric dipole moments also give rise to electric interactions between the ions (see section 5.6). 

The second mechanism of broadening is also due to the random displacements of atoms in the lattice, but it is manifested by means of variations of lanthanide magnetic moments from one lattice site to another, because of the random distortion of the crystalline... 

Technically, the Boltzmann distribution applies to particles in an ideal gas, not to molecules in crystal structures. However, we have considered the group of related molecules in crystals to be subject to random distortions from crystal packing effects in each separate crystal structure. The energies of the particles in the ideal gas depend on the temperature through Boltzmann s constant or the ideal gas constant. If a Boltzmann-type distribution holds for distortions in crystal structures, the actual value of the constant, or the effective temperature, is unknown. This subject is discussed further in French et. al. (2000). 

Our simulations were initialized from randomly distorted geometries of different isomers of Li, and zero initial velocities (cf. Ref. The... 

We have recently shown that the presence of phase-separated structures in polymer-blend microparticles can be indicated qualitatively by a distortion in the two-dimensional diffraction pattern. The origin of fringe distortion from a multi-phase composite particle can be understood as a result of refraction at the boundary between domains of different polymers, which typically exhibit large differences in refractive index. Thus, the presence of separate sub-domains introduces optical phase shifts and refraction resulting in a randomization (distortion) in the internal electric field intensity distribution that is manifested as a distortion in the far-field diffraction pattern. 

Assuming that ensembles of randomly oriented identieal sites and randomly distorted sites are mutually independent, the EPR speetra in a glassy material ean be expressed taking into aecount all fine-structure transitions and all orientations of Mn(II) ions, following Taylor and Bray (1972), as... 

In order to study the influence of internal energy (temperature) on the dynamic properties of the Lig cluster, simulations were initiated by randomly distorting equilibrium geometries of different isomers, since zero initial velocities were chosen (cf. Section 2.4 and Refs. 16-19). In previous work on stmctural properties, the tetrahedral (Tj) structure has been identified as the most stable isomer at the HF level and remained the lowest-energy stmcture after electron correlation... 

Freeze-etching studies on frozen aqueous suspensions of polyes-tyrene microspheres (Park and Branton, 1968) exemplify random distorting effects of the microtome knife impact on the shape and position of ice-embedded particles. 

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