Maximum entropy reconstruction of spin densities involving non-uniform prior [Pg.48]

Figure 3. Contour plots of the bias corrected MEM densities in the (110) plane of metallic beryllium (a) uniform prior, (b) non-uniform prior. The plots are on a linear scale with 0.05 el A1 intervals. Truncation at 1.0e/A3. Maximum values in e/A3 are given at the Be position and in the bipyramidal space of the hep structure. |

In a qualitative way, the non uniformity of the beam was demonstrated in the experiment with a glass slide (1.25) the darkening of which varied considerably across the beam. Such an experiment is a quick way to check intensity distribution in an x-ray beam or to locate a region of uniform density for the positioning of a small sample. [Pg.235]

Appropriate cell design, including the application of current shields where required, may compensate for current density non-uniformities even the absence of a high Wa number. To increase the electrode polarization, leveling additives are often incorporated in the bath. Since the additives are present in minute amounts, their distribution across the wafer is typically influenced by the flow. The macroscopic current distribution may also be affected by the seed resistance due to the so called terminal effect as discussed below. [Pg.28]

Weights will be unconsciously applied if operating conditions are non-uniformly distributed in the experimental space. Estimated model parameters will then better reproduce the experimental data from that part of the space where the density of experimentation is greater. Therefore, statistical methods of planning of kinetic experiments, possibly modified by appropriate transformation of variables, are strongly recommended. [Pg.541]

There are many varieties of density functional theories depending on the choice of ideal systems and approximations for the excess free energy functional. In the study of non-uniform polymers, density functional theories have been more popular than integral equations for a variety of reasons. A survey of various theories can be found in the proceedings of a symposium on chemical applications of density functional methods [102]. This section reviews the basic concepts and tools in these theoretical methods including techniques for numerical implementation. [Pg.116]

Secondly, the influence of the cations on their surrounding space is not negligible. The cations produce strong non-uniform electrostatic fields and the electron density in such a model is far from constant, or even slowly varying. The free electrons experience a very strong attraction when they approach the cations. [Pg.211]

Dependence of results from the prior-prejudice distribution. Non-uniform prior-prejudice distributions (NUP for short in what follows) were initially introduced by Jauch and Palmer by centering 3D Gaussian functions at the nuclear positions [29]. They found that the low-density regions of the crystal changed significantly upon introduction of the NUP, but the uneven distribution of errors persisted. [Pg.15]

Figure 2. L-alanine. Dynamic deformation density in the COO plane, (a) Model dynamic deformation density A Modei. (b) MaxEnt dynamic deformation density (Agj, (x)) map obtained with a non-uniform prior of spherical-valence shells. Map size 6.0A x 6.0A Contour levels from -1.0 to 1.0 eA 3, step 0.075 e A-f |

Now Al is the volume, between the plates, that is occupied by the uniform field X. Hence, if the energy of the charged condenser is to be regarded as associated with the field, the energy density lias to be N2/8ir per unit volume. The same result may be reached for a condenser or conductor of any shape. Consider any element of volume dv in a non-uniform field. Since (2) applies to unit volume, if (2) is multiplied by dv, we may take [Pg.7]

Figures, l-Alanine.Fits to noisy data Calculations A (experimental noise) and B (10% experimental noise). MaxEnt, deformation and error density profiles along the Cl-01 bond. Solid line Model valence density. Dashed line MaxEnt density A. Dot-dashed line MaxEnt density B. Dotted line valence-shells non-uniform prior. |

Elutriation differs from sedimentation in that fluid moves vertically upwards and thereby carries with it all particles whose settling velocity by gravity is less than the fluid velocity. In practice, complications are introduced by such factors as the non-uniformity of the fluid velocity across a section of an elutriating tube, the influence of the walls of the tube, and the effect of eddies in the flow. In consequence, any assumption that the separated particle size corresponds to the mean velocity of fluid flow is only approximately true it also requires an infinite time to effect complete separation. This method is predicated on the assumption that Stokes law relating the free-falling velocity of a spherical particle to its density and diameter, and to the density and viscosity of the medium is valid [Pg.510]

Copper can be electro-deposited on to a silvered article the plating bath consists of 10 gm of copper sulphate in 100 gm water. The article is taken from the silvering bath, washed, and put wet in the plating bath—on to a copper cathode so that electrical contact is made to the silver. A copper anode is placed 1-2 cm above the article. The electrodes should be about the same size as the article. The current density should be about 0-05 amp/cm, and in 2-4 minutes a thin copper film should be made. If the current density is too high a granular deposit will be formed which will rub off, and if it is too low a non-uniform deposit will be formed. [Pg.143]

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