Repairing geometrical means of measurement for metrological support to production

Sergeev, A. N.

doi:10.1007/bf00979648

Cited by 2 publications

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“…Indeed, Loeser obtained a fair approximation (Figure 6), in his treatment of many-electron atoms at large-D [68], after reducing the problem to only one radial and one angular variable by assuming that the electrons reside at the corners of a regular simplex, a 'hypertetrahedron' version of Lewis' cubical atom. In the recent analysis by Sergeev of the Bohr model for large atoms [66], minimizing our Equation (2.12), he found that as N increases the electrons within each shell do in fact assume a symmetrical simplex geometry.…”

Section: New Perspectives On Old Modelsmentioning

confidence: 91%

“…For comparison, data are shown also for the Hartree-Fock approximation [58][59][60][61], the ThomasFermi statistical model [67], and Loeser's approximate large-D limit [68]. Dashed curve shows improved results for the Bohr model obtained by Sergeev [66]. Figure 7]. '…”

Section: The Hydrogen Moleculementioning

confidence: 99%

“…For N42, as evident in Figure 5, our version defined by Equation (2.12) differs from Bohr's original model [64]; his continued to employ coplanar, concentric circular orbitals and for Li and Be gave even poorer energy results [65]. Recently, Sergeev has examined the behaviour of our version of E Bohr (N, Z ) as N ¼ Z becomes very large [66]. He found the functional form of the Z-dependence became similar to the Thomas-Fermi statistical model [67].…”

mentioning

confidence: 95%

“…The DR treatment also yielded accurate results for oscillatory structure not present in the TF model and related to angular correlation of the outermost electrons [148][149][150]. The DR method can readily be tried using other inputs, such as the large-D results obtained by Sergeev in his new treatment of the Bohr model [66] or (instead of HF) the Møller-Plesset or other conventional methods.…”

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confidence: 98%

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Bohr model and dimensional scaling analysis of atoms and molecules

Svidzinsky

Chen

Chin

et al. 2008

International Reviews in Physical Chemistry

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It is generally believed that the old quantum theory, as presented by Niels Bohr in 1913, fails when applied to few electron systems, such as the H 2 molecule. Here we review recent developments of the Bohr model that connect it with dimensional scaling procedures adapted from quantum chromodynamics. This approach treats electrons as point particles whose positions are determined by optimizing an algebraic energy function derived from the large-dimension limit of the Schro¨dinger equation. The calculations required are simple yet yield useful accuracy for molecular potential curves and bring out appealing heuristic aspects. We first examine the ground electronic states of H 2 , HeH, He 2 , LiH, BeH and Li 2 . Even a rudimentary Bohr model, employing interpolation between large and small internuclear distances, gives good agreement with potential curves obtained from conventional quantum mechanics. An amended Bohr version, augmented by constraints derived from Heitler-London or Hund-Mulliken results, dispenses with interpolation and gives substantial improvement for H 2 and H 3 . The relation to D-scaling is emphasized. A key factor is the angular dependence of the Jacobian volume element, which competes with interelectron repulsion. Another version, incorporating principal quantum numbers in the D-scaling transformation, extends the Bohr model to excited S states of multielectron atoms. We also discuss kindred Bohr-style applications of D-scaling to the H atom subjected to superstrong magnetic fields or to atomic anions subjected to high frequency, superintense laser fields. In conclusion, we note correspondences to the prequantum bonding models of Lewis and Langmuir and to the later resonance theory of Pauling, and discuss prospects for joining D-scaling with other methods to extend its utility and scope.

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Section: New Perspectives On Old Modelsmentioning

confidence: 91%

Section: The Hydrogen Moleculementioning

confidence: 99%

mentioning

confidence: 95%

mentioning

confidence: 98%

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Bohr model and dimensional scaling analysis of atoms and molecules

Svidzinsky

Chen

Chin

et al. 2008

International Reviews in Physical Chemistry

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“…Selection of Measurement Instruments Depending on the Production Accuracy of Details. In this method for selection of measurement instruments depending on the manufacturing tolerance the acceptable measurement error D A is determined, using specially designed tables and the total error of measurement method for specific measurement instruments D ∑ [2,3].…”

Section: Methods For Selecting Measurement Instrumentsmentioning

confidence: 99%

Methods for Selection of Measuring Instruments

Toteva

Vasileva

Mihaylova

2014

AMM

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One of the tasks at planning of quality inspection is selection of measuring instruments. The measuring instruments are the most important part of the measuring process so their selection have to be done carefully. The selection of measuring instruments is a complex task, which depend on the size, the character and the value of measured magnitude. The purpose of this paper is to analyze the existing methods for selection of measuring equipment. In the paper are presented the advantages and disadvantages of existing methods and recommendation for their implementation, according to the metrological tasks given. There are results obtained, using the Measurement System Analysis (MSA), for: selection of the correct measuring instrument and method; assessment the capabilities of measuring instruments; assessment of the procedures and operators; assessment of any measuring interactions, calculating the uncertainty of measuring of individual measuring instrument and/or measuring systems.

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Repairing geometrical means of measurement for metrological support to production

Cited by 2 publications

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Bohr model and dimensional scaling analysis of atoms and molecules

Bohr model and dimensional scaling analysis of atoms and molecules

Methods for Selection of Measuring Instruments

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