A polynomial approach to determine the time-dependent electric and magnetic fields in anisotropic materials by symbolic computations

2016 ◽  
Vol 35 (3) ◽  
Author(s):  
Valery George Yakhno ◽  
Meltem Altunkaynak
Keyword(s):  
Magnetic Fields ◽  
Design Methodology ◽  
Dimensional Space ◽  
General Structure ◽  
Three Dimensional ◽  
Approximate Solutions ◽  
Time Dependent ◽  
Bounded Region ◽  
Symbolic Computations ◽  
Electric And Magnetic Fields

Purpose The purpose of this paper is to calculate the time-dependent electric and magnetic fields in anisotropic media with a general structure of anisotropy by symbolic computations. Design/methodology/approach An analytical approach for the computation of the time-dependent electric and magnetic fields is suggested. This approach consists of the following. Input data, electric and magnetic fields are presented in polynomial form.The exact formulae for electric and magnetic fields are computed by symbolic transformations in Maple. Findings The time-dependent second order partial differential equations for the electric and magnetic fields with polynomial data were obtained from Maxwell's equations when the current density is presented in a polynomial form with respect to space variables in a bounded region of three dimensional space. The exact solutions of obtained equations were computed symbolically using Maple. Originality/value The obtained polynomial solutions do not contain errors if data are polynomials. We have shown that these solutions are approximate solutions with good accuracy for data which are approximated by polynomials in a bounded region of 3D space.

On the Fermi–Walker Derivative for Inextensible Flows

2015 ◽  
Vol 70 (7) ◽  
pp. 477-482 ◽  
Author(s):  
Talat Körpinar
Keyword(s):  
Charged Particle ◽  
Partial Differential Equations ◽  
Magnetic Fields ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Frenet Frame ◽  
Electric And Magnetic Fields ◽  
Inextensible Flows ◽  
The Given ◽  
Three Dimensional Space

AbstractIn this paper, we explicitly determine some curves corresponding to the their flows on the three-dimensional space. We construct a new characterisation for inextensible flows of curves by using the Fermi–Walker derivative and the Fermi–Walker parallelism in space. Using the Frenet frame of the given curve, we present partial differential equations. Finally, we construct the Fermi–Walker derivative in the motion of a charged particle under the action of electric and magnetic fields.

Energy and Momentum Eigenspectrum of the Hulthén-screened Cosine Kratzer Potential Using Proper Quantization Rule and SUSYQM Method

2021 ◽  
Author(s):  
Kaushal R Purohit ◽  
Rajendrasinh H PARMAR ◽  
Ajay Kumar Rai
Keyword(s):  
Quantum Mechanics ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Numerical Data ◽  
Time Dependent ◽  
Quantization Rule ◽  
Approximation Approach ◽  
Momentum Spectra ◽  
Energy And Momentum ◽  
Three Dimensional Space

Abstract Using the Qiang-Dong proper quantization rule (PQR) and the supersymmetric quantum mechanics approach, we obtained the eigenspectrum of the energy and momentum for time independent and time dependent Hulthen-screened cosine Kratzer potentials. For the suggested time independent Hulthen-screened cosine Kratzer potential, we solved the Schrodinger equation in D dimensions (HSCKP). The Feinberg-Horodecki equation for time-dependent Hulthen-screened cosine Kratzer potential was also solved (tHSCKP). To address the inverse square term in the time independent and time dependent equations, we employed the Greene-Aldrich approximation approach. We were able to extract time independent and time dependent potentials, as well as their accompanying energy and momentum spectra. In three-dimensional space, we estimated the rotational vibrational (RV) energy spectrum for many homodimers ($H_2, I_2, O_2$) and heterodimers ($MnH, ScN, LiH, HCl$). We also used the recently introduced formula approach to obtain the relevant eigen function. We also calculated momentum spectra for the dimers $MnH$ and $ScN$. The method is compared to prior methodologies for accuracy and validity using numerical data for heterodimer $LiH, HCl$ and homodimer $I_2, O_2,H_2$. The calculated energy and momentum spectra are tabulated and analysed.

Photodetachment microscopy of H– ion in time-dependent electric and magnetic fields

2018 ◽  
Vol 96 (9) ◽  
pp. 961-968
Author(s):  
De-hua Wang
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Electric Field ◽  
Interference Pattern ◽  
Current Distribution ◽  
Time Dependent ◽  
Electron Current ◽  
Detector Plane ◽  
Electron Trajectories ◽  
Electric And Magnetic Fields

We examine the dynamics of electrons photodetached from the H– ion in time-dependent electric and magnetic fields for the first time. The photodetachment microscopy patterns caused by a time-dependent gradient electric field and magnetic field have been analyzed in great detail based on the semiclassical theory. The interplay of the gradient electric field and magnetic field forces causes an intricate shape of the electron wave and multiple electron trajectories generated by a fixed energy point source can arrive at a given point on the microchannel-plate detector. The interference effects between these electron trajectories cause the oscillatory structures of the electron probability density and electron current distribution, and a set of concentric interference fringes are found at the detector. Our calculation results suggest that the photodetachment microscopy interference pattern on the detector can be adjusted by the electron energy, magnetic field strength, and position of the detector plane. Under certain conditions, the interference pattern in the electron current distribution might be seen on the detector plane localized at a macroscopic distance from the photodetachment source, which can be observed in an actual photodetachment microscopy experiment. Therefore, we make predictions that our work should serve as a guide for future photodetachment microscopy experiments in time-dependent electric and magnetic fields.

scholarly journals Inductive quantum space-time

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Vector Fields ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Space Time ◽  
Quantum Structures ◽  
Quantum Field ◽  
Quantum Space ◽  
Electric And Magnetic Fields ◽  
Quantum Vector ◽  
Three Dimensional Space

The main problem of the theory of the emergence of space-time is that how to restore the Minkowsky geometry from the original quantum structures. In this paper, we consider the reverse reaction, obtaining space-time from quantum vector fields, similarly to the electric and magnetic fields in the Maxwell equation. In addition, time itself is split into components in three-dimensional space in the form of an inductive quantum field.

Movement of charge carriers in electric and magnetic fields

2020 ◽  
pp. 89-126
Author(s):  
Hermann Kolanoski ◽  
Norbert Wermes
Keyword(s):  
Magnetic Fields ◽  
Transport Equation ◽  
Approximate Solutions ◽  
Critical Energy ◽  
Charge Carriers ◽  
Einstein Relation ◽  
Boltzmann Transport ◽  
Electric And Magnetic Fields ◽  
Electrons And Ions ◽  
And Diffusion

For the detection of charged particles many detector principles exploit the ionisation in sensing layers and the collection of the generated charges by electrical fields on electrodes, from where the signals can be deduced. In gases and liquids the charge carriers are electrons and ions, in semiconductors they are electrons and holes. To describe the ordered and unordered movement of the charge carriers in electric and magnetic fields the Boltzmann transport equation is introduced and approximate solutions are derived. On the basis of the transport equation drift and diffusion are discussed, first in general and then for applications to gases and semiconductors. It turns out that, at least for the simple approximations, the treatment for both media is very similar, for example also for the description of the movement in magnetic fields (Lorentz angle and Hall effect) or of the critical energy (Nernst-Townsend-Einstein relation).

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