scholarly journals Correction to: Coulomb force on a line charge in an anisotropic piezoelectric biomaterial

2021 ◽  
Author(s):  
Xu Wang ◽  
Peter Schiavone
Keyword(s):  
Coulomb Force ◽  
Line Charge

Fault Tolerant Guidance of Under-Actuated Satellite Formation Flying Using Inter-Vehicle Coulomb Force

2019 ◽  
Vol 2 (1) ◽  
pp. 43-52
Author(s):  
Alireza Alikhani ◽  
Safa Dehghan M ◽  
Iman Shafieenejad
Keyword(s):  
Fault Tolerance ◽  
Formation Flying ◽  
Fault Tolerant ◽  
Coulomb Force ◽  
Control Law ◽  
Triangular Form ◽  
Satellite Formation Flying ◽  
Satellite Formation ◽  
Guidance Law ◽  
Tolerance Approach

In this study, satellite formation flying guidance in the presence of under actuation using inter-vehicle Coulomb force is investigated. The Coulomb forces are used to stabilize the formation flying mission. For this purpose, the charge of satellites is determined to create appropriate attraction and repulsion and also, to maintain the distance between satellites. Static Coulomb formation of satellites equations including three satellites in triangular form was developed. Furthermore, the charge value of the Coulomb propulsion system required for such formation was obtained. Considering Under actuation of one of the formation satellites, the fault-tolerance approach is proposed for achieving mission goals. Following this approach, in the first step fault-tolerant guidance law is designed. Accordingly, the obtained results show stationary formation. In the next step, tomaintain the formation shape and dimension, a fault-tolerant control law is designed.

Angular terms in the electron density for the phosphine molecule

1956 ◽  
Vol 52 (4) ◽  
pp. 703-711 ◽  
Author(s):  
R. A. Ballinger ◽  
N. H. March
Keyword(s):  
Variational Method ◽  
Charge Density ◽  
Electron Density ◽  
Legendre Polynomials ◽  
Molecular Axis ◽  
Thomas Fermi ◽  
Line Charge ◽  
Density Map ◽  
Circular Line

ABSTRACTAn attempt is made to calculate the first few angular terms in an expansion of the electron density for the phosphine molecule in Legendre polynomials. Such an expansion is appropriate for a model in which the three hydrogen nuclei are smeared to form a circular line charge. The Thomas–Fermi approximation has been used in conjunction with the variational method. The variational density employed includes p and f angular terms. An approximate charge density map is constructed for a plane containing the molecular axis in order to demonstrate the effect of the angular terms.

Evolution of line charge density of steadily-developing upward positive leaders in triggered lightning

2013 ◽  
Vol 118 (10) ◽  
pp. 4670-4678 ◽  
Author(s):  
Mingli Chen ◽  
Dong Zheng ◽  
Yaping Du ◽  
Yijun Zhang
Keyword(s):  
Charge Density ◽  
Line Charge ◽  
Triggered Lightning

Influence of the Coulomb Force on Spray Cooling

2007 ◽  
Author(s):  
John M. Kuhlman ◽  
Paul J. Kreitzer ◽  
Deepak Mehra ◽  
Donald D. Gray ◽  
Kirk L. Yerkes
Keyword(s):  
Coulomb Force ◽  
Spray Cooling

scholarly journals The proton-proton scattering without Coulomb force renormalization

2010 ◽  
Vol 3 ◽  
pp. 05014
Author(s):  
R. Skibiński ◽  
J. Golak ◽  
H. Witała ◽  
W. Glöckle
Keyword(s):  
Coulomb Force ◽  
Proton Scattering ◽  
Proton Proton

scholarly journals Control of the Longitudinal Compression and Transverse Focus of Ultrafast Electron Beam for Detecting the Transient Evolution of Materials

Materials ◽  
2022 ◽  
Vol 15 (2) ◽  
pp. 571
Author(s):  
Xintian Cai ◽  
Zhen Wang ◽  
Chaoyue Ji ◽  
Xuan Wang ◽  
Zhiyin Gan ◽  
...  
Keyword(s):  
Electron Beam ◽  
Temporal Resolution ◽  
Fast Electron ◽  
Single Pulse ◽  
Coulomb Force ◽  
Single Shot ◽  
Longitudinal Compression ◽  
Rf Cavity ◽  
Tracking Model ◽  
The Impact

Ultrafast detection is an effective method to reveal the transient evolution mechanism of materials. Compared with ultra-fast X-ray diffraction (XRD), the ultra-fast electron beam is increasingly adopted because the larger scattering cross-section is less harmful to the sample. The keV single-shot ultra-fast electron imaging system has been widely used with its compact structure and easy integration. To achieve both the single pulse imaging and the ultra-high temporal resolution, magnetic lenses are typically used for transverse focus to increase signal strength, while radio frequency (RF) cavities are generally utilized for longitudinal compression to improve temporal resolution. However, the detection signal is relatively weak due to the Coulomb force between electrons. Moreover, the effect of RF compression on the transverse focus is usually ignored. We established a particle tracking model to simulate the electron pulse propagation based on the 1-D fluid equation and the 2-D mean-field equation. Under considering the relativity effect and Coulomb force, the impact of RF compression on the transverse focus was studied by solving the fifth-order Rung–Kutta equation. The results show that the RF cavity is not only a key component of longitudinal compression but also affects the transverse focusing. While the effect of transverse focus on longitudinal duration is negligible. By adjusting the position and compression strength of the RF cavity, the beam spot radius can be reduced from 100 μm to 30 μm under the simulation conditions in this paper. When the number of single pulse electrons remains constant, the electrons density incident on the sample could be increased from 3.18×1012 m−2 to 3.54×1013 m−2, which is 11 times the original. The larger the electron density incident on the sample, the greater the signal intensity, which is more conducive to detecting the transient evolution of the material.

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