Showing papers on "Electric potential published in 2022"

Uncertainty quantification and sensitivity analysis of transcranial electric stimulation for 9-subdomain human head model

Abstract: This paper deals with uncertainty quantification of transcranial electric stimulation (TES) of realistic human head model. The head model taken from Visible Human Project consists of 9 subdomains: scalp, skull, CSF, grey matter, white matter, cerebellum, ventricles, jaw and tongue. The deterministic computation of quasi-static induced electric scalar potential features boundary element method (BEM). Conductivities of each subdomain are modelled as uniformly distributed random variables and stochastic analysis features a non-intrusive stochastic collocation method (SCM). The input uncertainties impact only the magnitude of the electric scalar potential and not the position of the potential extrema. Skin and brain conductivities play the most important role, while CSF conductivity has negligible impact on the output potential variance. The significance of the skull conductivity is not high for the chosen input parameter setup. In the previous work authors considered 3-compartment head model which consisted of scalp, skull and brain compartments. The presented model is a step forward in SCM+BEM TES analysis, primarily in terms of model complexity. Comparing the results of the two analyses it can be concluded that the uncertainty in the added tissues’ conductivities do not impact the variation of the output electric potential.

Time periodic electroosmotic flow in a pH-regulated parallel-plate nanochannel

Abstract: In this paper, the separation of variables method is applied to investigate the effects of solution pH, background salt concentration and AC electric field frequency on time periodic electroosmotic flow in a pH-regulated parallel-plate nanochannel. The surface charge is generated by the protonation and deprotonation of the functional group SiOH. The background salt is KCl. The pH value of the solution is adjusted by HCl and KOH. Analytical and semi-analytical solutions for electric potential and velocity distributions are obtained. The results show that the electric potential caused by the electric double layer depends greatly on the solution pH and background salt concentration. The amplitudes of the velocity and flow rate of the time periodic electroosmotic flow decrease with the background salt concentration and increase with the deviation of the solution pH from the isoelectric point. In a nanochannel having a height less than 100 nm, the electroosmotic velocity amplitude is not affected by the AC electric field frequency because the oscillating Reynolds number is much less than unity.

Finite Element Modeling of the Combined Faradaic and Electrostatic Contributions to the Voltammetric Response of Monolayer Redox Films

Abstract: The voltammetric response of electrodes coated with a redox-active monolayer is computed by finite element simulations based on a generalized model that couples the Butler–Volmer, Nernst–Planck, and Poisson equations. This model represents the most complete treatment of the voltammetric response of a redox film to date and is made accessible to the experimentalist via the use of finite element modeling and a COMSOL-generated report. The model yields a full description of the electric potential and charge distributions across the monolayer and bulk solution, including the potential distribution associated with ohmic resistance. In this way, it is possible to properly account for electrostatic effects at the molecular film/electrolyte interface, which are present due to the changing charge states of the redox head groups as they undergo electron transfer, under both equilibrium and nonequilibrium conditions. Specifically, our numerical simulations significantly extend previous theoretical predictions by including the effects of finite electron-transfer rates (k0) and electrolyte conductivity. Distortion of the voltammetric wave due to ohmic potential drop is shown to be a function of electrolyte concentration and scan rate, in agreement with experimental observations. The commonly used Laviron analysis for the determination of k0 fails to account for ohmic drop effects, which may be non-negligible at high scan rates. This model provides a more accurate alternative for k0 determination at all scan rates. The electric potential and charge distributions across an electrochemically inactive monolayer and electrolyte solution are also simulated as a function of applied potential and are found to agree with the Gouy-Chapman-Stern theory.

Wave function collapses and 1/n energy spectrum induced by a Coulomb potential in a one-dimensional flat band system

Abstract: We investigate the bound state problem in a one-dimensional flat band system with a Coulomb potential. It is found that, in the presence of a Coulomb potential of type I (with three equal diagonal elements), similarly to that in the two-dimensional case, the flat band could not survive. At the same time, the flat band states are transformed into localized states with a logarithmic singularity near the center position. In addition, the wave function near the origin would collapse for an arbitrarily weak Coulomb potential. Due to the wave function collapses, the eigen-energies for a shifted Coulomb potential depend sensitively on the cut-off parameter. For a Coulomb potential of type II, there exist infinite bound states that are generated from the flat band. Furthermore, when the bound state energy is very near the flat band, the energy is inversely proportional to the natural number, e.g., E n ∝ 1/ n , n = 1,2,3,… It is expected that the 1/ n energy spectrum could be observed experimentally in the near future.

Coulomb effects on time-trajectory-resolved high-order harmonic generation

Abstract: We study the effect of Coulomb potential on high-order harmonic generation (HHG) numerically and analytically. We focus on the influence of Coulomb potential on emission times of HHG associated with specific electron trajectories. By using a numerical procedure based on numerical solution of time-dependent Schr\"{o}dinger equation (TDSE) in three dimensions, we extract the HHG emission times both for long and short electron trajectories. We compare TDSE predictions with those of a Coulomb-modified model arising from strong-field approximation (SFA). We show that the Coulomb effect induces earlier HHG emission times than those predicted by the general SFA model without considering the Coulomb potential. In particular, this effect influences differently on long and short electron trajectories and is more remarkable for low-energy harmonics than high ones. It also changes the HHG amplitudes for long and short electron trajectories. We validate our discussions with diverse laser parameters and forms of Coulomb potential. Our results strongly support a four-step model of HHG.

Active Electric Dipole Energy Sources: Transduction via Electric Scalar and Vector Potentials

Abstract: An active electrical network contains a voltage or current source that creates electromagnetic energy through a method of transduction that enables the separation of opposite polarity charges from an external source. The end result is the creation of an active dipole with a permanent polarisation and a non-zero electric vector curl. The external energy input impresses a force per unit charge within the voltage source, to form an active physical dipole in the static case, or an active Hertzian dipole in the time dependent case. This system is the dual of an electromagnet or permanent magnet excited by a circulating electrical current or fictitious bound current respectively, which supplies a magnetomotive force described by a magnetic vector potential with a magnetic geometric phase proportional to the enclosed magnetic flux. In contrast, the active electric dipole may be described macroscopically by a circulating fictitious magnetic current boundary source described by an electric vector potential with an electric geometric phase proportional to the enclosed electric flux density. This macroscopic description of an active dipole is an average description of some underlying microscopic description exhibiting emergent nonconservative behaviour not found in classical conservative laws of electrodynamics. We show that the electromotive force produced by an active dipole must have both electric scalar and vector potential components to account for the magnitude of the voltage it produces. Following this we analyse an active cylindrical dipole in terms of scalar and vector potential and confirm that the electromotive force produced, and hence potential difference across the terminals is a combination of vector and scalar potential difference depending on aspect ratio of the dipole.

Mixed potential

Abstract: The open circuit potential (zero current potential) includes not only “equilibrium potential” determined by a single charge-transfer reaction but also “mixed potential” determined by two or more charge-transfer reactions. The mixed potential is often measured as corrosion potential or the ion-selective electrode potential responsive to interference ions. This paper describes a method for calculating the mixed potential, limited to reversible electrochemical reactions.

Effect of pollution layer discontinuity due to the dry bands presence on potential and electric field along insulator

Abstract: This paper aims to study the effect of the presence of dry bands on the distribution of the electric field and potential on high voltage polluted insulator model subjected to impulse voltage. To take account of the influence of pollution thickness 3D computations were achieved with COMSOL Multiphysics Software. This Software uses Finite Element Method. The results of the simulation demonstrated that in presence of dry band, the electric field distribution is affected and becomes distorted along the surface of the polluted insulator. Numerical simulation showed also that the dry bands near the electrodes are responsible for more critical voltage and field stresses than in the case of a continuous pollution layer. It was observed extremely high stresses at the dry bands. The intensity of the electric field depends on the location and the width of dry bands.It was also observed that the potential grading can be improved by increasing the number of dry bands.

Potential Simplification of Charge and the Coulomb Force without Affecting Predictions

Abstract: We are taking a deeper look at charge and the Coulomb force and other electric properties. There is an embedded 10 −7 in the Coulomb constant that we will claim is “only” needed to cancel out an embedded 10 7 in the charge squared. We suggest three alternatives to redefine the charge and the Coulomb constant that give considerable simplification. The Coulomb constant is not needed as a separate constant as, in the new suggested framework, it can be replaced with simply the speed of light without affecting predicted output values. We also point out potential issues with the 2019 redefinition of the Coulomb constant and elementary charge. This is not meant conclusive but to open up for further discussion on how one potential can simplify parts of physics.

Finite Element Modelling of the Combined Faradaic and Electrostatic Contributions to the Voltammetric Response of Monolayer Redox Films

Abstract: The voltammetric response of electrodes coated with a redox-active monolayer is computed by finite element simulations based on a generalized model that couples the Butler-Volmer, Nernst-Planck and Poisson equations. The model yields a full description of the electric potential and charge distributions across the monolayer and into the bulk solution, including the potential distribution associated with ohmic resistance in the bulk solution. In this way, it is possible to properly account for electrostatic effects at the molecular film/electrolyte interface, which are present due to the changing charge states of the redox head groups as they undergo electron transfer, under both equilibrium and non-equilibrium conditions. Our numerical simulations also significantly extend previous theoretical predictions by simultaneously including both the effects of finite electron-transfer rates and electrolyte conductivity. Distortion of the voltammetric wave due to ohmic potential drop in the solution is shown to be a function of the supporting electrolyte concentration and scan rate, in agreement with experimental observations. The electric potential and charge distributions across an electrochemically inactive monolayer and into the solution are also simulated as a function of applied potential and are found to agree with the Gouy-Chapman-Stern theory, allowing numerical predictions of the capacitive background currents in voltammetric experiments.

Measurements of the Net Charge Density of Space Plasmas

Abstract: Space plasmas are composed of charged particles that play a key role in electromagnetic dynamics. However, to date, there has been no direct measurement of the distribution of such charges in space. In this study, three schemes for measuring charge densities in space are proposed. The first scheme is based on electric field measurements by multiple spacecraft. This method is applied to deduce the charge density distribution within Earth’s magnetopause boundary layer using Magnetospheric MultiScale constellation (MMS) 4-point measurements, and indicates the existence of a charge separation there. The second and third schemes proposed are both based on electric potential measurements from multiple electric probes. The second scheme, which requires 10 or more electric potential probes, can yield the net charge density to first-order accuracy, while the third scheme, which makes use of seven to eight specifically distributed probes, can give the net charge density with second-order accuracy. The feasibility, reliability, and accuracy of these three schemes are successfully verified for a charged-ball model. These charge density measurement schemes could potentially be applied in both space exploration and ground-based laboratory experiments.

Vibration analysis of a composite magnetoelectroelastic bimorph depending on the volume fractions of its components based on applied theory

Abstract: Introduction. Transverse vibrations of a bimorph consisting of two piezomagnetoelectric layers and located in the alternating magnetic field are investigated. Piezomagnetoelectric layers are multilayer composites with alternating piezoelectric and piezomagnetic layers. The mechanical and physical properties of such a composite are given by known effective constants.Materials and Methods. The applied theory of multilayer plate vibrations takes into account the nonlinear distribution of electric and magnetic potential in piezoactive layers in the longitudinal and transverse directions. On the basis of this theory, the stress-strain state, the dependences of deflection, electric and magnetic potentials on the volume ratio of the composition of the hinged bimorph, are investigated. The electric potential is assumed to be zero at all electrodes, while the magnetic potential is zero at the inner boundary and unknown at the outer boundaries. Therefore, the distribution of electric and magnetic potentials in the middle of the layer are unknown functions. In the case of the magnetic potential, the distribution at the outer boundary is also unknown. In the problem, the Kirchhoff hypotheses for mechanical characteristics were accepted. The use of the variational principle and the quadratic dependence of the electric and magnetic potentials on the thickness of piezoactive layers made it possible to obtain a system of differential equations and boundary conditions.Results. When the volume ratio of the composition of piezoactive bimorph materials changes, the electric potential in the middle of the layer changes nonlinearly. The magnetic potential in the middle of the layer and at the outer boundary increases almost linearly with an increase in the volume percentage of BaTiO3. The dependence of the deflection in the middle of the layer is determined.Discussion and Conclusions. An applied theory for calculating transverse vibrations of a bimorph with two piezomagnetoelectric layers is constructed. The dependence of the characteristics of the stress-strain state, electric and magnetic fields on the volume fractions of piezomagnetic and piezoelectric materials, is investigated.

Electrically Conducting Fluid Flow and Electric Potential in a Square Cavity Subjected to a Point Magnetic Source

Abstract: ABSTRACT Magnetohydrodynamics (MHD) flow in cavities subjected to both the magnetisation and the Lorentz forces due to a point magnetic source is studied. The governing PDEs are derived and iteratively solved by the dual reciprocity boundary elements method (DRBEM) with linear elements. It is shown that the magnetic field decelerates the axial flow around the point magnetic source, and a further increase in Ha causes a reverse flow in the pipe axis direction. An increase in Re, Ha, or Mn reduces the electric potential in magnitude. The planar velocity values decrease at the same rate as the Re increment. The influence of the magnetisation force lessens in high Re cases without alternating the axial velocity and the electric potential within the pipe. This study is the first to give the effects of both the magnetisation and the Lorentz forces on the fluid behaviour in terms of velocity, pressure, and electric potential.

Physical Application of Taylor Formula

Abstract: Taylor's formula is an important content in advanced mathematics, and it is also an indispensable mathematical tool in the study of function limits and error estimation. In this paper, Taylor's formula is used to deduce the electric potential energy of the charge system in the applied electric field and to prove the Noether's theorem of the point particle system under the action of conservative force. Finally, the expression of potential energy of multi electrode in external electric field and the reason why Noether's theorem is established in conservative system are given, and the superposition principle of potential energy of point particle system is indirectly explained.

FiPo FDTD: Computational Electrodynamics Technique Producing Both Fields and Potentials

Abstract: We present the field-potential finite-difference time-domain (FiPo FDTD) algorithm, which solves a set of first-order equations for the electric and magnetic fields (E and H), as well as the magnetic vector potential A and the scalar electric potential $\phi$ in the Lorenz gauge. We also present the derivation and implementation of a convolutional perfectly matched layer absorbing boundary condition for this new set of equations. Potentials A and $\phi$ can be used as input for the single-particle electron Hamiltonian in quantum transport solvers.

Bound states in the continuum (BIC) protected by self-sustained potential barriers in a flat band system

Abstract: In this work, we investigate the bound states in the continuum (BIC) of a one-dimensional spin-1 flat band system. It is found that, when the potential is sufficiently strong, there exists an effective attractive potential well surrounded by infinitely high self-sustained barriers. Consequently, there exist some BIC in the effective potential well. These bound states are protected by the infinitely high potential barriers, which could not decay into the continuum. Taking a long-ranged Coulomb potential and a short-ranged exponential potential as two examples, the bound state energies are obtained. For a Coulomb potential, there exists a series of critical potential strengths, near which the bound state energy can go to infinity. For a sufficiently strong exponential potential, there exist two different bound states with a same number of wave function nodes. The existence of BIC protected by the self-sustained potential barriers is quite a universal phenomenon in the flat band system under a strong potential. A necessary condition for the existence of BIC is that the maximum of potential is larger than two times band gap.

Displacements of the surface of a piezoelectric half-space with functionally-graded coating and circle electrode on the surface

Abstract: A mathematical model describing the deformation of a material caused by the reverse piezoelectric effect is proposed. The model is based on an axisymmetric problem of electroelasticity for a half-space with a functionally-graded coating. An electric potential difference is applied across a circle area on the surface (an electrode whose thickness and elastic properties are neglected) and an infinity boundary of the half-space. Arbitrary independent variation of all electroelastic properties in depth of the coating is considered. The coating is assumed to be perfectly bonded to the substrate. The problem is solved using the bilateral asymptotic method in an approximated analytical form effective for any value of the relative thickness of the coating. Approximated analytical expressions containing finite quadratures are obtained for the distribution of radial and normal displacements and electric potential on the surface under the electrode and outside of it. Numerical calculations are provided for the distribution of radial and normal displacements and electric potential for two typical examples of functionally-graded coatings in a wide range of relative thickness values of the coating. Convergence of the results to those for a homogeneous non-coated half-space is obtained for small and large values of the relative coating thickness. Special attention is paid to the comparison of the results with those for a non-coated half-space. The redistribution of the electromechanical characteristics caused by the presence of the coating is most noticeably observed near the boundary of the electrode especially for thin and intermediate thickness coatings (in comparison with the size of the electrode).

On the l = 0 binding eigenstates of a cut-off Coulomb potential

Abstract: The cut-off Coulomb potential (CCP) [Formula: see text], with [Formula: see text] a constant, is a radial interaction which is free from singularities in the whole radial range [Formula: see text]. The CCP is useful for modeling interacting systems when a Coulomb-like behavior is called for far from the source but with no singularity near it. The binding energies of the [Formula: see text] states of the CCP may be approximated. We further exhibit that the radiative corrections of phenomena such as the double Sudakov logarithm should be treated in the standard way.

Finite element analysis of the voltage induced by a pair of electrodes in a cell membrane

Abstract: This document analyses the distribution of the electric potential due to two electrodes that excite a membrane. The solution obtained numerically was approximated by means of the finite element method. The qualitative analysis of the results allows to know the intensity of the electric potential along the membrane in such a way that said electrodes that excite the membrane can be strategically located for academic and clinical purposes. Additionally, in a two- dimensional domain that represents the geometry of a membrane, the finite element method was executed, which allowed the behavior of the potential to be analyzed for an electric pulse at any point in the membrane. The above was generated by two electrodes.

Concentrations for nonlinear Schrodinger equation with magnetic potentials and constant electric potentials

Abstract: This paper studies the concentration phenomena to nonlinear Schrodinger equations with magnetic potentials and constant electric potentials. We find that the magnetic field plays an important role in the location of concentrations if the electric potential is constant. This is a completely new result compared with the case of non-constant electric potentials.

The evaluation of the interaction potential of two non-polar molecules in Green function approach

Abstract: In this research, by assuming that the vacuum electric field fluctuations can convert a molecule (or an atom) into an oscillating electric dipole, the interaction potential of the two atoms or two non-polar molecules is calculated in terms of the molecular polarizabilities and the distance between them. Considering the net electric field at the position of a molecule as a sum of the vacuum electric field and the electric field due to the induced electric dipole of the other molecule, and substituting in the quadratic stark shift formula, the interaction potential of the two molecules is related to the vacuum electric field correlation function. By writing the interaction potential in terms of the imaginary parts of vector potential Green function tensor components (via the fluctuation- dissipation theorem and Kubo’s formula in statistical mechanics) and computing the required Green function components, the interaction potential between the two molecules is evaluated. The small and large distances limits of the general formula investigated and the consistencies with the previous works are shown.‎

Electric vector potential and the Biot-Savart like law in electrostatics

Abstract: A vector potential formulation is shown in this article to compute the electric field of planar surface electrodes. The electric field is derived from from the solution of the Laplace’s equation in the free-charge space. Neumann-boundary conditions must be set on the region between planar metallic sheets as the separation goes to zero. It is shown that the electric field can be written via a Biot Savart- like integral. The strategy enables to generalize the analytical result for its application in the gaped surface electrodes description.