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.

Conducting Medium Electrical Conductivity at High Current Density

The experimental research example of electrical characteristics of structurally heterogeneous thinlayer conductors (nickel, copper) at high current density (108--109 А/m2) is shown. This current density in conditions of the samples intensive cooling is sufficient for the process of irreversible, nonthermally activated deformation. The experiment results show that the conducting medium at high current density has essential nonlinearities expressed in nonlinear dependence of the samples electrical resistance from current density. With repeated current treatments of the samples the conductors' electrical resistivity decreases. The number of defects removed from the volume of material as a result of nickel foil treatment by electric current is estimated. It is shown that under conditions of highdensity direct electric current flow in microvolumes of homogeneous and inhomogeneous conducting media a volume charge can appear. The appearance of the volume charge in a conducting medium can be caused by interaction forces during the motion of electrons and ions. Due to the interaction forces between ions and electrons of basic material and impurities, additional local ionization occurs which is realized in nano-volumes of a conductor. In the case of heterogeneous medium, the volume charge depends on the nature of the specific conductivity distribution. In a homogeneous conductor the volume charge is proportional to the square of the current density in the sample

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.

The Influence of Smoke From Forest Fires on the Meteorological and Electrical Characteristics of the Atmosphere

The impact of smoke from forest fires in western Siberia on meteorological, atmospheric electric, and aerological variables has been analyzed. The anomalous distribution of water vapor in the atmosphere associated with the peculiarities of the evaporation regime and the absence of advective moisture transfer over the southern regions of Western Siberia during the fires. With an increase in the height of the homogeneous surface smoke layer with an unchanged aerosol optical thickness, the cooling of the earth's surface and heating of the atmosphere was weakened. The smoke plume spreads predominantly in the middle of the troposphere, creating aerosol layers elevated above the ground, the lower part of which had a negative volume charge. The effect of diurnal variations in the electrical field in the near-surface layer, differs from the known similar effects.