MULTISCALED ASYMPTOTIC EXPANSIONS FOR THE ELECTRIC POTENTIAL: SURFACE CHARGE DENSITIES AND ELECTRIC FIELDS AT ROUNDED CORNERS

2007 ◽  
Vol 17 (06) ◽  
pp. 845-876 ◽  
Author(s):  
PATRICK CIARLET ◽  
SAMIR KADDOURI
Keyword(s):  
Electric Field ◽  
Charge Density ◽  
Surface Charge ◽  
Electric Fields ◽  
Asymptotic Expansions ◽  
Electric Potential ◽  
Curvature Radius ◽  
Geometrical Shape ◽  
Empirical Formulas ◽  
Electrostatic Problem

We are interested in computing the charge density and the electric field at the rounded tip of an electrode of small curvature. As a model, we focus on solving the electrostatic problem for the electric potential. For this problem, Peek's empirical formulas describe the relation between the electric field at the surface of the electrode and its curvature radius. However, it can be used only for electrodes with either a purely cylindrical, or a purely spherical, geometrical shape. Our aim is to justify rigorously these formulas, and to extend it to more general, two-dimensional, or three-dimensional axisymmetric, geometries. With the help of multiscaled asymptotic expansions, we establish an explicit formula for the electric potential in geometries that coincide with a cone at infinity. We also prove a formula for the surface charge density, which is very simple to compute with the Finite Element Method. In particular, the meshsize can be chosen independently of the curvature radius. We illustrate our mathematical results by numerical experiments.

scholarly journals Electric potential differences across auroral generator interfaces

2013 ◽  
Vol 31 (2) ◽  
pp. 251-261 ◽  
Author(s):  
J. De Keyser ◽  
M. Echim
Keyword(s):  
Electric Field ◽  
High Altitude ◽  
Electric Fields ◽  
Electric Potential ◽  
Equilibrium Configuration ◽  
Potential Difference ◽  
Field Profile ◽  
Electric Potential Difference ◽  
Electric Field Profile

Abstract. Strong localized high-altitude auroral electric fields, such as those observed by Cluster, are often associated with magnetospheric interfaces. The type of high-altitude electric field profile (monopolar, bipolar, or more complicated) depends on the properties of the plasmas on either side of the interface, as well as on the total electric potential difference across the structure. The present paper explores the role of this cross-field electric potential difference in the situation where the interface is a tangential discontinuity. A self-consistent Vlasov description is used to determine the equilibrium configuration for different values of the transverse potential difference. A major observation is that there exist limits to the potential difference, beyond which no equilibrium configuration of the interface can be sustained. It is further demonstrated how the plasma densities and temperatures affect the type of electric field profile in the transition, with monopolar electric fields appearing primarily when the temperature contrast is large. These findings strongly support the observed association of monopolar fields with the plasma sheet boundary. The role of shear flow tangent to the interface is also examined.

Nanosecond pulsed electric field induced changes in cell surface charge density

Micron ◽  
2017 ◽  
Vol 100 ◽  
pp. 45-49 ◽  
Author(s):  
Diganta Dutta ◽  
Xavier-Lewis Palmer ◽  
Anthony Asmar ◽  
Michael Stacey ◽  
Shizhi Qian
Keyword(s):  
Cell Surface ◽  
Electric Field ◽  
Charge Density ◽  
Surface Charge ◽  
Surface Charge Density ◽  
Pulsed Electric Field ◽  
Cell Surface Charge ◽  
Nanosecond Pulsed Electric Field ◽  
Induced Changes

scholarly journals Supramolecular Stark Effect in Host-Guest Complexes via Charge Density Analysis

2014 ◽  
Vol 70 (a1) ◽  
pp. C674-C674
Author(s):  
Sajesh Thomas ◽  
Rebecca Fuller ◽  
Alexandre Sobolev ◽  
Philip Schauer ◽  
Simon Grabowsky ◽  
...  
Keyword(s):  
Electric Field ◽  
Charge Density ◽  
Electric Fields ◽  
Active Sites ◽  
Stark Effect ◽  
Dipole Moments ◽  
Covalent Bonds ◽  
Guest Molecules ◽  
Density Mapping ◽  
Density Analysis

The effect of an electric field on the vibrational spectra, the Vibrational Stark Effect (VSE), has been utilized extensively to probe the local electric field in the active sites of enzymes [1, 2]. For this reason, the electric field and consequent polarization effects induced by a supramolecular host system upon its guest molecules attain special interest due to the implications for various biological processes. Although the host-guest chemistry of crown ether complexes and clathrates is of fundamental importance in supramolecular chemistry, many of these multicomponent systems have yet to be explored in detail using modern techniques [3]. In this direction, the electrostatic features associated with the host-guest interactions in the inclusion complexes of halogenated acetonitriles and formamide with 18-crown-6 host molecules have been analyzed in terms of their experimental charge density distribution. The charge density models provide estimates of the molecular dipole moment enhancements which correlate with the simulated values of dipole moments under electric field. The accurate electron density mapping using the multipole formalism also enable the estimation of the electric field experienced by the guest molecules. The electric field vectors thus obtained were utilized to estimate the vibrational stark effect in the nitrile (-C≡N) and carbonyl (C=O) stretching frequencies of the guest molecules via quantum chemical calculations in gas phase. The results of these calculations indicate remarkable elongation of C≡N and C=O bonds due to the electric fields. The electronic polarization in these covalent bonds induced by the field manifests as notable red shifts in their characteristic vibrational frequencies. These results derived from the charge densities are further supported by FT-IR experiments and thus establish the significance of a phenomenon that could be termed as the "supramolecular Stark effect" in crystal environment.

scholarly journals Numerical simulation of electrostatic field and flow field in an electro- static precipitator

2019 ◽  
Author(s):  
Yuying Xu ◽  
Baoqing Deng ◽  
Haiyan Zhang ◽  
Xianpeng Chen
Keyword(s):  
Field Strength ◽  
Electric Field ◽  
Charge Density ◽  
Electric Field Strength ◽  
Electric Potential ◽  
Electrostatic Precipitator ◽  
Ionic Charge ◽  
The Wire ◽  
Corona Electrode ◽  
Plate Distance

Introduction: The computational fluid dynamics (CFD) simulation of three- dimensional wire-plate electrostatic precipitator is performed in the present study. Materials and methods: The momentum equation, the electric potential equation and current continuity equation are solved by using ANSYS Fluent. The ion charge density at the corona is calculated iteratively using the Peek formula. The SIMPLE algorithm is used to treat the pressure-velocity cou- pling. The RNG k-ε model is used to describe turbulence. Results: The airflow keeps stable away from the first corona electrode. The distribution of the electric potential is dependent on the wire-plate distance and the wire-wire distance. The potential and ion charge density increase with the increase of the wire-plate distance. With the increase of wire-wire dis- tance, the maximum electric field strength decreases whereas the maximum ionic charge density increases. The ion charge density near the second corona electrode is relatively small. A small wire-wire distance will make the electric field concentrated around the wires. Conclusion: According to this study, the wire-wire distance and the wire- plate distance have great effect on the distribution of ion charge density and electric field strength.

scholarly journals Control of microtubule trajectory within an electric field by altering surface charge density

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
Naoto Isozaki ◽  
Suguru Ando ◽  
Tasuku Nakahara ◽  
Hirofumi Shintaku ◽  
Hidetoshi Kotera ◽  
...  
Keyword(s):  
Electric Field ◽  
Charge Density ◽  
Surface Charge ◽  
Surface Charge Density

scholarly journals On triple trigonometrical equations

1973 ◽  
Vol 14 (2) ◽  
pp. 174-178 ◽  
Author(s):  
B. M. Singh
Keyword(s):  
Exact Solution ◽  
Charge Density ◽  
Surface Charge ◽  
Electrostatic Potential ◽  
Surface Charge Density ◽  
Equal Length ◽  
Two Dimensional ◽  
Electrostatic Problem ◽  
Unit Depth

An exact solution of triple trigonometrical equations is obtained by using the finiteHilbert transform. The solution of these equations is used to solve a two-dimensional electrostatic problem. The problem of determining the electrostatic potential due to two parallel coplanar strips of equal length, charged to equal and opposite potentials, each parallel to and equidistant from an earthed strip, is considered. Both the charged strips lie along the x-axis and they are equally spaced with respect to the y-axis. Finally the expression for the surface charge density (per unit depth) of the strip is derived

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