Volume Charge Density in Geometric Product Lorentz Transformation

Lorentz Transformation is the relationship between two different coordinate frames time and space when one inertial reference frame is relative to another inertial reference frame with traveling at relative speed. In this paper, we have derived the transformation formula for the volume charge density in Geometric Product Lorentz Transformation. The changes of volume charge density of moving frame in terms of that rest frame in Geometric Product Lorentz Transformation at various velocities and angles were studied as well.

On the methodology of calculating volume charge density in a MIFGMOS substrate using Poisson’s equation

Purpose This study aims to present a mathematical method based on Poisson’s equation to calculate the voltage and volume charge density formed in the substrate under the floating gate area of a multiple-input floating-gate metal-oxide semiconductor metal-oxide semiconductor (MOS) transistor. Design/methodology/approach Based on this method, the authors calculate electric fields and electric potentials from the charges generated when voltages are applied to the control gates (CG). This technique allows us to consider cases when the floating gate has any trapped charge generated during the manufacturing process. Moreover, the authors introduce a mathematical function to describe the potential behavior through the substrate. From the resultant electric field, the authors compute the volume charge density at different depths. Findings The authors generate some three-dimensional graphics to show the volume charge density behavior, which allows us to predict regions in which the volume charge density tends to increase. This will be determined by the voltages on terminals, which reveal the relationship between CG and volume charge density and will allow us to analyze some superior-order phenomena. Originality/value The procedure presented here and based on coordinates has not been reported before, and it is an aid to generate a model of the device and to build simulation tools in an analog design environment.

Electric Double Layer and Orientational Ordering of Water Dipoles in Narrow Channels within a Modified Langevin Poisson-Boltzmann Model

The electric double layer (EDL) is an important phenomenon that arises in systems where a charged surface comes into contact with an electrolyte solution. In this work we describe the generalization of classic Poisson-Boltzmann (PB) theory for point-like ions by taking into account orientational ordering of water molecules. The modified Langevin Poisson-Boltzmann (LPB) model of EDL is derived by minimizing the corresponding Helmholtz free energy functional, which includes also orientational entropy contribution of water dipoles. The formation of EDL is important in many artificial and biological systems bound by a cylindrical geometry. We therefore numerically solve the modified LPB equation in cylindrical coordinates, determining the spatial dependencies of electric potential, relative permittivity and average orientations of water dipoles within charged tubes of different radii. Results show that for tubes of a large radius, macroscopic (net) volume charge density of coions and counterions is zero at the geometrical axis. This is attributed to effective electrolyte charge screening in the vicinity of the inner charged surface of the tube. For tubes of small radii, the screening region extends into the whole inner space of the tube, leading to non-zero net volume charge density and non-zero orientational ordering of water dipoles near the axis.

Streaming Electrification Phenomenon of Electrical Insulating Oils for Power Transformers

The subject matter of this study was the problem of the ECT (electrostatic charging tendency) of mineral insulation oils during their flow. The electrostatic charges generated may lead to partial discharges, and as a consequence, to the breakdown of a power transformer insulation system. In this study, the results of the ECT of mineral oils used in transformers were compared. The method of streaming electrification of insulation liquids using a flow-through system was used. The influence of flow speed, temperature, and the pipe material on the values of the electrification current and volume charge density qw were analyzed. The results obtained in this study should be taken into account regarding the operation of power transformers.

Comparative Study of the Volume Charge Density in Most General Lorentz Transformation and Quaternion Lorentz Transformation

Lorentz transformation is the relation of space and time coordinates of one inertial frame relative to another inertial frame in special relativity. In this paper we have studied the volume charge density in most general and quaternion Lorentz transformations for different angles with different velocities of the moving frame. We have also used numerical data to see the comparative situation.

Volome Charge Density in Mixed Number Lorentz Transformation

We know charge density is changed when it observes from a moving frame of reference due to the length contraction. In this paper we have studied the volume charge density in special and mixed number Lorentz transformation. We also investigate the changes of the volume charge density of moving system in terms of rest system in mixed number Lorentz Transformations at different angles and velocities.

Об инкрементах неустойчивости волн различной симметрии на движущейся относительно материальной среды объемно заряженной струе

The increments of instability of capillary waves with arbitrary symmetry (with arbitrary azimuthal numbers ) on the surface of a volume charged cylindrical jet of an ideal incompressible dielectric fluid moving relative to an ideal incompressible material dielectric medium are investigated. It is shown that at not too high velocities of the jet motion, with an increase in the volume charge density, the axisymmetric mode ( m=0) becomes unstable first, then the bending mode ( m=1), and then the bending-deformation mode (m=2 ).This sequence of realization of the instability of azimuthal modes and determines the patterns of fragmentation of charged jets in the experiments. At jet speeds comparable to the critical for the realization of aerodynamic instability, the first loses stability mode whis . For all azimuthal modes, the dependences of the maximum increments on the wave numbers are determined.

Travelling Surface Plasmons with Interference Envelope and A Vision for Time Crystals

The influence of the film thickness and the substrate’s refractive index on the surface mode at the superstrate is an important study step that may help clearing some of the misunderstandings surrounding their propagation mechanism. A single sub-wavelength slit perforating a thin metallic film is among the simplest nanostructure capable of launching Surface Plasmon Polaritons on its surrounding surface when excited by an incident field. Here, the impact of the substrate and the film thickness on surface waves is investigated. When the thickness of the film is comparable to its skin depth, SPP waves from the substrate penetrate the film and emerge from the superstrate, creating a superposition of two SPP waves, that leads to a beat interference envelope with well-defined loci which are the function of both the drive frequency and the dielectric constant of the substrate/superstrate. As the film thickness is reduced to the SPP’s penetration depth, surface waves from optically denser dielectric/metal interface would dominate, leading to volume plasmons that propagate inside the film at optical frequencies. Interference of periodic volume charge density with the incident field over the film creates charge bundles that are periodic in space and time.