A perturbation solution to the full Poisson–Nernst–Planck equations yields an asymmetric rectified electric field

Soft Matter ◽  
2020 ◽  
Vol 16 (30) ◽  
pp. 7052-7062
Author(s):  
S. M. H. Hashemi Amrei ◽  
Gregory H. Miller ◽  
Kyle J. M. Bishop ◽  
William D. Ristenpart
Keyword(s):  
Electric Field ◽  
Perturbation Solution ◽  
One Dimensional ◽  
Ionic Mobilities ◽  
The One

We derive a perturbation solution to the one-dimensional Poisson–Nernst–Planck (PNP) equations between parallel electrodes under oscillatory polarization for arbitrary ionic mobilities and valences.

Cadmium Sulfide and Zinc Sulfide Nanostructures Formed by Electrophoretic Deposition

2012 ◽  
Vol 507 ◽  
pp. 101-105 ◽  
Author(s):  
Alejandro Vázquez ◽  
Israel López ◽  
Idalia Gómez
Keyword(s):  
Thin Films ◽  
Electric Field ◽  
Cadmium Sulfide ◽  
Zinc Sulfide ◽  
Electrophoretic Deposition ◽  
Cds Nanoparticles ◽  
One Dimensional ◽  
Cds Thin Films ◽  
The One ◽  
One Dimensional Nanostructures

Cadmium sulfide (CdS) and zinc sulfide (ZnS) nanostructures were formed by means of electrophoretic deposition of nanoparticles with mean diameter of 6 nm and 20 nm, respectively. Nanoparticles were prepared by a microwave assisted synthesis in aqueous dispersion and electrophoretically deposited on aluminum plates. CdS thin films and ZnS one-dimensional nanostructures were grown on the negative electrodes after 24 hours of electrophoretic deposition at direct current voltage. CdS and ZnS nanostructures were characterized by means of scanning electron (SEM) and atomic force (AFM) microscopies analysis. CdS thin films homogeneity can be tunable varying the strength of the applied electric field. Deposition at low electric field produces thin films with particles aggregates, whereas deposition at relative high electric field produces smoothed thin films. The one-dimensional nanostructure size can be also controlled by the electric field strength. Two different mechanisms are considered in order to describe the formation of the nanostructures: lyosphere distortion and thinning and subsequent dipole-dipole interactions phenomena are proposed as a possible mechanism of the one-dimensional nanostructures, and a mechanism considering pre-deposition interactions of the CdS nanoparticles is proposed for the CdS thin films formation.

A modified perturbation solution to the one-dimensional Bratu problem

2019 ◽  
Vol 354 ◽  
pp. 296-304 ◽  
Author(s):  
Mina B. Abd-el-Malek ◽  
Amr Abdelrazek ◽  
Mohammed Ghazy ◽  
Gehad Gamal
Keyword(s):  
Perturbation Solution ◽  
One Dimensional ◽  
The One ◽  
Bratu Problem

Exact damped sinusoidal electric field of nonlinear one-dimensional Vlasov-Maxwell equations

1984 ◽  
Vol 32 (2) ◽  
pp. 197-205 ◽  
Author(s):  
B. Abraham-Shrauner
Keyword(s):  
Distribution Function ◽  
Electric Field ◽  
Maxwell Equations ◽  
Angular Frequency ◽  
Wave Number ◽  
One Dimensional ◽  
Damping Decrement ◽  
Sinusoidal Electric Field ◽  
The One ◽  
Special Case

An exact solution for a temporally damped sinusoidal electric field which obeys the nonlinear, one-dimensional Vlasov-Maxwell equations is given. The electric field is a generalization of the O'Neil model electric field for Landau damping of plasma oscillations. The electric field is a special case of the form found from the invariance of the one-dimensional Vlasov equation under infinitesimal Lie group transformations. The time dependences of the damping decrement, of the wave-number and of the angular frequency are derived. Use of a time-dependent BGK one-particle distribution function is justified for weak damping where, in general, it is necessary to carry out a numerical calculation of the invariant of which the distribution function is a functional.

scholarly journals Selection rule engineering of forbidden transitions of a hydrogen atom near a nanogap

Nanophotonics ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 229-236 ◽  
Author(s):  
Hyunyoung Y. Kim ◽  
Daisik S. Kim
Keyword(s):  
Hydrogen Atom ◽  
Electric Field ◽  
Selection Rule ◽  
Field Vector ◽  
Rapid Variation ◽  
One Dimensional ◽  
Near Zone ◽  
Forbidden Transitions ◽  
The One ◽  
Dipole Sources

AbstractWe perform an analytical study on the allowance of forbidden transitions for a hydrogen atom placed near line dipole sources, mimicking light emanating from a one-dimensional metallic nanogap. It is shown that the rapid variation of the electric field vector, inevitable in the near zone, completely breaks the selection rule of Δl=±1. While the forbidden transitions between spherically symmetric S states, such as 2S to 1S or 3S to 1S (Δl=0), are rather robust against selection rule breakage, Δl=±2 transitions such as between 3D and 1S or 3D and 2S states are very vulnerable to the spatial variation of the perturbing electric field. Transitions between 2S and 3D states are enhanced by many orders of magnitude, aided by the quadratic nature of both the perturbing Hamiltonian and D wavefunctions. The forbidden dipole moment, which approaches one Bohr radius times the electric charge in the vicinity of the gap, can be written in a simple closed form owing to the one-dimensional nature of our gap. With large enough effective volume together with the symmetric nature of the excited state wavefunctions, our work paves way towards atomic physics application of infinitely long nanogaps.

scholarly journals A solvable model of Vlasov-kinetic plasma turbulence in Fourier–Hermite phase space

2018 ◽  
Vol 84 (1) ◽  
Author(s):  
T. Adkins ◽  
A. A. Schekochihin
Keyword(s):  
Phase Space ◽  
Electric Field ◽  
Landau Equation ◽  
Electric Energy ◽  
Solvable Model ◽  
Chaotic Advection ◽  
Phase Mixing ◽  
One Dimensional ◽  
Kolmogorov Scale ◽  
The One

A class of simple kinetic systems is considered, described by the one-dimensional Vlasov–Landau equation with Poisson or Boltzmann electrostatic response and an energy source. Assuming a stochastic electric field, a solvable model is constructed for the phase-space turbulence of the particle distribution. The model is a kinetic analogue of the Kraichnan–Batchelor model of chaotic advection. The solution of the model is found in Fourier–Hermite space and shows that the free-energy flux from low to high Hermite moments is suppressed, with phase mixing cancelled on average by anti-phase-mixing (stochastic plasma echo). This implies that Landau damping is an ineffective route to dissipation (i.e. to thermalisation of electric energy via velocity space). The full Fourier–Hermite spectrum is derived. Its asymptotics are $m^{-3/2}$ at low wavenumbers and high Hermite moments ($m$) and $m^{-1/2}k^{-2}$ at low Hermite moments and high wavenumbers ($k$). These conclusions hold at wavenumbers below a certain cutoff (analogue of Kolmogorov scale), which increases with the amplitude of the stochastic electric field and scales as inverse square of the collision rate. The energy distribution and flows in phase space are a simple and, therefore, useful example of competition between phase mixing and nonlinear dynamics in kinetic turbulence, reminiscent of more realistic but more complicated multi-dimensional systems that have not so far been amenable to complete analytical solution.

scholarly journals Compound viscous thread with electrostatic and electrokinetic effects

2012 ◽  
Vol 701 ◽  
pp. 171-200 ◽  
Author(s):  
D. T. Conroy ◽  
O. K. Matar ◽  
R. V. Craster ◽  
D. T. Papageorgiou
Keyword(s):  
Electric Field ◽  
Fluid Viscosity ◽  
One Dimensional ◽  
The Core ◽  
Jet Breakup ◽  
Voltage Potential ◽  
Leaky Dielectric Model ◽  
Model Equations ◽  
The One ◽  
Wave Limit

AbstractBreakup of an electrified viscous compound jet, surrounded by a dielectric gas, is investigated theoretically. The fluids are considered to be electrolytes and the core fluid viscosity is assumed to be much larger than that of the annular fluid. Axisymmetric configurations are considered with the three fluids bound by a cylindrical electrode that is held at a constant voltage potential. The model equations are investigated asymptotically in the long-wave limit, yielding two cases corresponding to a negligible surface charge with electrokinetic effects and a leaky dielectric model. A linear stability analysis for both cases is performed and the electrical effects are found to have a stabilizing effect, which is consistent with previous investigations of single electrified jet breakup at small wavenumbers. The one-dimensional equations are also solved numerically. The electric field is found to cause satellite formation in the core fluid, which does not occur in the purely hydrodynamic case, with the satellite size increasing with the strength of the electric field.

scholarly journals Addendum: Considerations about the incompleteness of the Ehrenfest's theorem in quantum mechanics (2021 Eur. J. Phys. 42 065405)

2021 ◽  
Author(s):  
Domenico Giordano ◽  
Pierluigi Amodio
Keyword(s):  
Quantum Mechanics ◽  
Analytical Solution ◽  
Eigenvalue Problem ◽  
Electric Field ◽  
Electric Charge ◽  
One Dimensional ◽  
The One ◽  
External Forces ◽  
Analytical Expressions

Abstract We describe the analytical solution of the eigenvalue problem introduced in our article mentioned in the title and relative to a punctiform electric charge confined in an one-dimensional box in the presence of an electric field. We also derive and discuss the analytical expressions of the external forces acting on the punctiform charge and associated with the boundaries of the one-dimensional box in the presence of the electric field.

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