Theoretical description of electric fields in three-dimensional multipole ion traps

2021 ◽  
pp. 146906672110479
Author(s):  
Maxim Vasilyev ◽  
Semyon Rudyi ◽  
Yuri Rozhdestvensky
Keyword(s):  
Spatial Distribution ◽  
Electric Fields ◽  
Matrix Method ◽  
General Type ◽  
Three Dimensional ◽  
Ion Traps ◽  
Theoretical Description

In this paper, the principle of forming the spatial distribution of the potential in multipole three-dimensional ion traps of a general type is considered. A matrix method for describing the electric fields in ion traps for the [Formula: see text]th order of multipole is proposed. Typical electrode geometries for hexapole and octupole traps are considered.

scholarly journals Three-Dimensional Spatial Distribution of Synapses in the Neocortex: A Dual-Beam Electron Microscopy Study

2013 ◽  
Vol 24 (6) ◽  
pp. 1579-1588 ◽  
Author(s):  
Angel Merchán-Pérez ◽  
José-Rodrigo Rodríguez ◽  
Santiago González ◽  
Víctor Robles ◽  
Javier DeFelipe ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Spatial Distribution ◽  
Three Dimensional ◽  
Microscopy Study ◽  
Electron Microscopy Study ◽  
Beam Electron ◽  
Dual Beam

Paraelektrische Resonanz und dielektrische Dispersion von Wasser in Beryll-Einkristallen / Paraelectric Resonance and Dielectric Dispersion of Water in Beryl Single Crystals

1974 ◽  
Vol 29 (11) ◽  
pp. 1558-1571
Author(s):  
H.-J. Rehm
Keyword(s):  
Electric Fields ◽  
Resonance Effect ◽  
Theoretical Description ◽  
Tunnel Effect ◽  
Zero Field ◽  
Zero Field Splitting ◽  
A Value ◽  
Axis Parallel ◽  
Electric Dipoles ◽  
The One

Paraelectric resonance spectra of beryl crystals are observed in the X-band region between 5 and 20 kV/cm under the condition that the external electric field F[101̅0]. Additional dielectric measurements show, that the paraelectric centres are the monomeric water molecules in the beryl cavities. For water dipoles in beryl only two orientations of the molecular a-axis relative to the crystal C6-axis are possible, and only those with their a-axis parallel to the C6-axis contribute to the paraelectric resonance effect. The electric moment vector µ of these latter molecules may rotate in the (0001)-crystal plane, i. e. around their own a-axis, and has a value of (1.9 ± 0.2) D. A theoretical description of paraelectric resonance is presented for a simplified model: the electric dipoles have 6 equivalent equilibrium positions along the [101̅0]-directions, tunnel effect and external electric fields remove the site degeneracy and we observe a molecular Stark splitting. We calculate a value of (2.0 ± 0.4) GHz for the zero-field splitting in the one-parameter Hamiltonian model.

scholarly journals Where Does the Galaxy End?

1996 ◽  
Vol 169 ◽  
pp. 669-680
Author(s):  
F.D.A. Hartwick
Keyword(s):  
Spatial Distribution ◽  
Globular Clusters ◽  
Semimajor Axis ◽  
Three Dimensional ◽  
Minor Axis ◽  
Spatial Extension ◽  
The Galaxy ◽  
Nested Hierarchy ◽  
Satellite Galaxies ◽  
Dimensional Surface

The spatial distribution of the outlying satellites of the Galaxy has been determined by fitting a three dimensional surface to the positions of 10 companion galaxies and 13 distant globular clusters. Both groups show a highly flattened distribution whose minor axes are aligned to within ∼ 5°. The combined group of 23 objects shows a triaxial distribution with semimajor axis extending ∼ 400 kpc. The minor axis is inclined at ∼ 76° to the Galactic poles. There is a suggestion of a nested hierarchy consisting of satellite galaxies, globular clusters, and distant halo field stars, in order of decreasing spatial extension.

scholarly journals A short geostatistical study of the three-dimensional spatial structure of fumonisins in stored maize

2010 ◽  
Vol 3 (1) ◽  
pp. 95-103 ◽  
Author(s):  
M. Rivas Casado ◽  
D. Parsons ◽  
N. Magan ◽  
R. Weightman ◽  
P. Battilani ◽  
...  
Keyword(s):  
Spatial Distribution ◽  
Spatial Structure ◽  
Spatial Correlation ◽  
Three Dimensional ◽  
Sample Collection ◽  
Data Set ◽  
Research Areas ◽  
Geostatistical Approach ◽  
Sampling Protocols ◽  
Current Sample

The heterogeneous three-dimensional spatial distribution of mycotoxins has proven to be one of the main limitations for the design of effective sampling protocols. Current sample collection protocols for mycotoxins have been designed to estimate the mean concentration and fail to characterise the spatial distribution of the mycotoxin concentration due to the aggregation of the incremental samples. Geostatistical techniques have been successfully applied to overcome similar problems in many research areas. However, little work has been developed on the use of geostatistics for the design of sampling protocols for mycotoxins. This paper focuses on the analysis of the two and three-dimensional spatial structure of fumonisins B1 (FB1) and B2 (FB2) in maize in a bulk store using a geostatistical approach and on how results help determine the number and location of incremental samples to be collected. The spatial correlation between FB1 and FB2, as well as between the number of kernels infected and the level of contamination was investigated. For this purpose, a bed of maize was sampled at different depths to generate a unique three-dimensional data set of FB1 and FB2. The analysis found no clear evidence of spatial structure in either the two-dimensional or three-dimensional analyses. The number of Fusarium infected kernels was not a good indicator for the prediction of fumonisin concentration and there was no spatial correlation between the concentrations of the two fumonisins.

Three-dimensional multi-species mathematical model of the aerobic granulation process based on cellular automata theory

2018 ◽  
Vol 77 (12) ◽  
pp. 2761-2771
Author(s):  
Guoqiang Zheng ◽  
Kuizu Su ◽  
Shuai Zhang ◽  
Yulan Wang ◽  
Weihong Wang
Keyword(s):  
Mathematical Model ◽  
Spatial Distribution ◽  
Cellular Automata ◽  
Three Dimensional ◽  
Granular Sludge ◽  
Automata Theory ◽  
Aerobic Granular Sludge ◽  
Granulation Process ◽  
Autotrophic Bacteria ◽  
Degrading Bacteria

Abstract Aerobic granular sludge is a kind of microbial polymer formed by self-immobilization under aerobic conditions. It has been widely studied because of its promising application in wastewater treatment. However, the granulation process of aerobic sludge is still a key factor affecting its practical application. In this paper, a three-dimensional (3D) multi-species mathematical model of aerobic granular sludge was constructed using the cellular automata (CA) theory. The growth process of aerobic granular sludge and its spatial distribution of microorganisms were studied under different conditions. The simulation results show that the aerobic granules were smaller under high shear stress and that the autotrophic bacterial content of the granular sludge interior was higher. However, the higher the dissolved oxygen concentration, the larger the size of granular sludge and the higher the content of autotrophic bacteria in the interior of the granular sludge. In addition, inhibition of toxic substances made the aerobic granule size increase more slowly, and the spatial distribution of the autotrophic bacteria and the toxic-substance-degrading bacteria were mainly located in the outer layer, with the heterotrophic bacteria mainly existing in the interior of the granular sludge.

Numerical modelling of twisted nematic devices

1983 ◽  
Vol 309 (1507) ◽  
pp. 203-216 ◽  
Keyword(s):  
Liquid Crystal ◽  
Electric Fields ◽  
Low Cost ◽  
Three Dimensional ◽  
Physical Parameters ◽  
Crystal Layer ◽  
Liquid Crystal Layer ◽  
Chiral Nematic ◽  
Twisted Nematic ◽  
Three Dimensional Simulations

Over most of each active region in nematic and chiral nematic twist cells the motion and configuration of the liquid crystal layer does not vary appreciably with position parallel to the surfaces. In such laminar regions the statics, dynamics and optics ot the cell can be accurately simulated at low cost on a computer of moderate size, given the appropriate physical parameters. Methods and recent advances in simulation of laminar regions are reviewed. Bistable twist cells are simulated for illustration. Important problems of stability and edge effects in the presence of electric fields await solution with two- or three-dimensional simulations.

scholarly journals POSSIBLE DEFECTS IN WOOD, WOOD PARAMETERS VARIABILITY AND SOME OF ITS INFLUENCE ON QUALITY OF BUILDING STRUCTURE

2015 ◽  
Vol 7 (2) ◽  
pp. 67-80
Author(s):  
Jaroslaw Malesza
Keyword(s):  
Three Dimensional ◽  
Residential Building ◽  
Theoretical Description ◽  
Construction Technology ◽  
Structural Elements ◽  
Require Time ◽  
Factory Production ◽  
3D Elements ◽  
Load Increase

Paper specifies the wood-framed with sheathing construction including phases of realization and exploitation. Methods of investigation based on practice and theory has been employed where practical identification of processes and their phases were presented with theoretical description of structure deformation within the exploitation period. Obtained results of investigations are presented in the form of technologic and mechanic of structure diagrams for buildings with adequate algorithms of analysis. Paper presents practical systematic of construction stages, technological problems and hazards in respect of loading and construction technology with method of computation of vertical deformations of building. Paper presents evaluation of contribution of wood defects in response to loading in the wood-framed residential building in exploitation process. Location of knots, allocation of pith in the elements cross section, defects of slope of grain and influence of moisture decreasing is examined in the paper. The wood-framed with sheathing in the form of large panel or modular three dimensional 3D elements are the most often used technology. This kind of buildings are actually constructed up to four story as a multifamily or varying universal buildings like school, kid-garden or offices. Low dead load from 0.30 to 1.00 kN/m2 and its favorable proportion to the live load increase energy saving factor in realization and within the exploitation time. Low own weight of structure enables complete prefabrication of wall, floor and roof panels, improving quality of construction and shortening time of construction. Process of prefabrication, wide assortment and variety of factory production does not require time consuming processes and complicated moulds or shuttering indispensable in precast RC structural elements.

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