Electrostatic Field Equations Research Articles

Boundary element based multiresolution shape optimisation in electrostatics

We consider the shape optimisation of high-voltage devices subject to electrostatic field equations by combining fast boundary elements with multiresolution subdivision surfaces. The geometry of the domain is described with subdivision surfaces and different resolutions of the same geometry are used for optimisation and analysis. The primal and adjoint problems are discretised with the boundary element method using a sufficiently fine control mesh. For shape optimisation the geometry is updated starting from the coarsest control mesh with increasingly finer control meshes. The multiresolution approach effectively prevents the appearance of non-physical geometry oscillations in the optimised shapes. Moreover, there is no need for mesh regeneration or smoothing during the optimisation due to the absence of a volume mesh. We present several numerical experiments and one industrial application to demonstrate the robustness and versatility of the developed approach.

Modeling and Validating the Optimal Routes of a Sensor Network Using the Electrostatic Field Equations

In this paper, the analogy between the optimal routes within a sensor network and the electrostatic field lines is utilized successfully. In other words, partial differential equations similar to those of the electrostatic field theory are solved using Finite Difference Method (FDM) to find the optimal routes of the network. For the purpose of validation, an Opnet program based on the generated optimal routes is written to find the throughput and delay of the sensor network, a similar program is then applied to some arbitrary routing scenarios. The results show that the throughput and delay performance of the proposed method is better than that of the chosen arbitrary routing scenarios. It is also found from the results that the throughput of some scenarios is 50 % lower than that of the proposed method.

Schottky-Barrier Metal–Oxide–Semiconductor Field-Effect Transistors as Resonant Tunneling Devices

The current–voltage characteristics of double-gated Schottky-barrier metal–oxide–semiconductor field-effect transistor (MOSFET) 10 nm in length and with body thickness of 3 nm is numerically studied, illustrating a similarity between the rectangular quantum well cavity in conventional resonant tunneling diodes and the parabolic-like cavity created by a pair of Schottky junctions in scaled Schottky-barrier MOSFETs. Assuming ballistic transport for electrons within effective mass approximation, the appearance of negative differential resistance due to the resonant tunneling effect between the Schottky junctions of 0.75 eV height is confirmed by non-equilibrium Green's function simulation. In such scaled Schottky-barrier MOSFETs, the tunneling electrons by themselves determine the shape of resonant potential, through the charge terms in electrostatic field equations. Using both the Poisson equation and the Laplace equation, we highlight the importance of the self-consistency for realizing successful resonant tunneling operation in scaled Schottky-barrier MOSFETs.

Structural Optimization for Direct-Decoupling Planar Capacitive Sensor

To optimize the structure of posed direct-decoupling planar capacitive sensor (PCS), methods for capacitance and sensitivity computation are studied, and the structural optimization is established. Firstly, four methods are compared with to find a suitable analytical method for the calculation of posed PCS capacitance and sensitivity. Then, electrostatic field equation method are applied and under the condition of given sensitivity, PCS structural parameters, i.e. the length of side and the number of plates is optimized. Computation results indicate that electrostatic field equation method is available for the calculation of capacitance and sensitivity on one hand, and on the other hand, when the length of side of PCS plate is twice the gap of two parallel part (l≈2d )and the number of plates is seven (N=7), PCS can meet sensitivity requirement and take up the smallest dimension.

Analysis method of negative ion by electrostatic atomization

PurposeThe purpose of this paper is to propose an analysis method of negative ion by electrostatic atomization. Because the electrostatic atomization includes large deformation of a drop of water, it is difficult to analyze with conventional fluid analysis methods such as the finite differences method, the finite element method (FEM) and so on.Design/methodology/approachIn this method, electrostatic field equation is coupled with Navier‐Stokes equation of a drop of water, employing the moving particle semi‐implicit method and FEM. The validity of the method is verified through the measurement.FindingsIt was found that the difference between calculated and measured results becomes large as the voltage increases.Research limitations/implicationsIn order to improve the accuracy, it is necessary to improve the way to calculate surface tension and the analysis condition.Originality/valueThis paper confirms the usefulness of the numerical method to elucidate electrostatic atomization.

Electromechanical analysis of electrostatic nano‐actuators using the differential quadrature method

AbstractThe nonlinear analysis of nanoelectromechanical systems using the differential quadrature model is investigated. The differential quadrature method is applied to overcome the difficulty of determining the nonlinear equation of motion. The characteristics of various combinations of curved electrodes and cantilever beams are considered to optimize the design. Various nano‐actuators, such as the cantilever beam actuator, are derived and simulated to examine the feasibility of applying the differential quadrature method to the nonlinear deflection in solving the nano‐actuator problem. The effects of the electrode shapes, the lengths of the actuators, and the moments of inertia of the actuators on the pull‐in behavior of the cantilever actuators in electrostatic nanoelectromechanical systems are investigated. The differential quadrature approach is used to generate the electrostatic field equations in matrix form. Copyright © 2007 John Wiley & Sons, Ltd.

Lattice Boltzmann simulation on the liquid junction potential in a microchannel

The lattice Boltzmann method (LBM) is applied to investigate the liquid junction potential (LJP) at an interface between two electrolyte layers. The Poisson equation for electrostatic field is solved to extend the applicable range to micro- and nanoscales in which electroneutrality does not hold. The LBM solutions are validated against analytical and finite difference method (FDM) results for evolution of concentration, net charge density and electrostatic potential. Noticeable separation of the concentration profiles of positive and negative ions occurs for κd less than 67 in simulation, where κ is the inverse of the thickness of electrical double layer and d is the system length. Parametric study is performed for the peak potential and the time to reach the peak with respect to κd and ξ which is the initial thickness ratio of the lower concentration to entire stream. Simple coding and easy parallelization will allow the LBM to make an efficient analysis tool for complex electrochemical systems.

Numerical simulation of electrohydrodynamic (EHD) atomization

The objective of the present work was to use a commercial Computational Fluid Dynamics (CFD) code to simulate the electrohydrodynamic (EHD) atomization process. Although the physics of the atomization and cone formation has been discussed in numerous publications, a comprehensive theory has not been presented. Some of the previous approaches are discussed below. A CFD model can give a unique capability to describe and simulate the liquid cone formation and atomization. The approach in this work was to simultaneously solve the coupled (EHD) and electrostatic equations. The heat conduction equation, solved by the CFD solver, has been modified to solve the electrostatic field equations. From the electrostatic field, the electric body forces have been determined and included in the Navier–Stokes equations. The model does not include any current. The key liquid property for the coupling is the permittivity. The predicted velocity fields for heptane and ethanol and the operating window of heptane were found to be consistent with published results. The model does not include a droplet break-up model. If the jet is cylindrical, the droplet size can be calculated from the jet diameter. The droplet size of ethanol was predicted and compared well with experiments.

Electrostatic analysis of a comb-finger actuator with Schwarz–Christoffel conformal mapping

The design and the analysis of a comb-finger actuator require the evaluation of the coupling capacitances as well as the estimation of the electrostatic forces. Several approaches are possible: very rough approximations based on combinations of parallel plate capacitor elements, analytical or numerical Schwarz–Christoffel (SC) conformal mapping-based techniques, numerical solutions of the electrostatic field equations. Powerful numerical approaches can be very accurate, but heavy and time-consuming, while simple approaches are very inaccurate. A partially analytical approximate method based on SC conformal mapping is discussed. The comparison with results from standard simulators and experimental measurements demonstrates that the studied procedure is fast and satisfactorily accurate.

Modeling of electromechanical charge sensing in ionic polymer transducers

A model for charge sensing due to imposed deformation in ionic polymer materials is presented. The basic concept of this model is that mechanical deformation induces charge at the surface of the polymer and produces a measureable discharge of current as the material is deformed. This discharge of current occurs when a short-circuit electrical boundary condition is applied across the material electrodes. An expression for charge density, electric field and electric potential under short-circuit conditions is developed from the electrostatic field equations. The solution for charge density is coupled with the mechanical deformation through a proportionality constant. Expressions for induced charge and current flow are then derived from the equations for electric displacement at the surface of the material. Experimental results support the basic form of the model and also demonstrate that the geometric scaling predicted in the model agrees with measured data. Analysis of the length scale predicted by the model produces qualitative agreement with previously published results but also points to the need for a greater understanding of the interfacial mechanics in the ionic polymer transducers.

Protein labeling reactions in electrochemical microchannel flow: Numerical simulation and uncertainty propagation

This paper presents a model for two-dimensional electrochemical microchannel flow including the propagation of uncertainty from model parameters to the simulation results. For a detailed representation of electroosmotic and pressure-driven microchannel flow, the model considers the coupled momentum, species transport, and electrostatic field equations, including variable zeta potential. The chemistry model accounts for pH-dependent protein labeling reactions as well as detailed buffer electrochemistry in a mixed finite-rate/equilibrium formulation. Uncertainty from the model parameters and boundary conditions is propagated to the model predictions using a pseudo-spectral stochastic formulation with polynomial chaos (PC) representations for parameters and field quantities. Using a Galerkin approach, the governing equations are reformulated into equations for the coefficients in the PC expansion. The implementation of the physical model with the stochastic uncertainty propagation is applied to protein-labeling in a homogeneous buffer, as well as in two-dimensional electrochemical microchannel flow. The results for the two-dimensional channel show strong distortion of sample profiles due to ion movement and consequent buffer disturbances. The uncertainty in these results is dominated by the uncertainty in the applied voltage across the channel.

A Numerical Study of High Resolution Latent Image Formation by Laser Beam Exposure

In order to study the latent image formation process including the characteristics of laser beam and photoreceptor, a numerical method which solves the three dimensional time dependent coupled system of the transport equations for charges, and the Poisson equation for electrostatic field, is proposed. Combining the simulation with electrostatic field computation in the development zone, the strength and the extent of spreading of the electrostatic field due to the latent image is analyzed. The image of isolated one dot exposure shows larger spreading, while that of a dot alongside another dot shows weaker electrostatic-field strength. The dependence of the spreading on the beam radius indicates that the repulsion of charge due to space-charge effect becomes significant as the beam diameter decreases. The numerical results are compared with experimental ones obtained on a test bed with high resolution development, and show excellent correlation with the experimentally developed images.

On the Static Limit of Strong Fluctuation Theory

An integral equation for electrostatic field in inhomogeneous medium is deduced by employing dyadic Green function. On this basis the strong fluctuation theory is build for electrostatic field. It is shown that the theory gives the Bruggeman formula for effective permittivity in zero order of perturbation theory. The accuracy of the strong fluctuation theory is analyzed.

Extensional stress waves in one-dimensional elastic waveguides

Computations of linear, one-dimensional wave propagation problems are often accomplished with integral transform methods. Time-domain approaches that usually involve a infinite-difference or method-of-characteristics approach have usually been reserved for nonlinear problems. However, time-domain algorithms have unique advantages for many problems with complex combinations of geometry, internal energy sources, and boundary conditions. One such algorithm will be examined in this work. It was originally developed for an unusual waveguide problem—acoustical wave transmission through drill strings that are used to drill geothermal and petrochemical wells. The development of this algorithm takes advantage of a unique property of the linear problem. The result is a computational method that is a combination of the finite-difference and characteristics methods. A variety of example problems are treated in this work. They involve linear elastic, ferroelectric, and fading-memory materials. Examples are given of solutions to the coupled mechanical and electrostatic field equations, and to problems with nonhomogeneous material properties.

The fluid theory of steady-state magnetically confined electron clouds sustained by ionization and emission

The fluid theory is applied to study the axisymmetrical steady-state magnetically confined electron clouds sustained by ionization or emission. These electron clouds can be obtained by means of low-pressure Penning discharge, thermoelectronic emission, ion beam ionization, etc. In the electron clouds the property of motion of electrons can be described by the fluid equations: the continuity equation, the momentum equation, the energy equation, the heat transfer equation and the electrostatic field equation. These equations are used to discuss the equilibrium between supplement and escape of electrons in the clouds and the distributions of the physical quantities of some long electron clouds.

Electrostatic fields in inhomogeneous dielectrics

Conditions under which simple, closed-form solutions to the electrostatic field equations in linear inhomogeneous dielectrics can be obtained are investigated. It is shown that such solutions can be found in general orthogonal coordinates (q1,q2,q3), in which equipotential surfaces are given by constant values of the axial q1 coordinate, whenever the permittivity can be expressed as ε(q1,q2,q3)=ε0(h1/h2h3)f(q1) g(q2,q3). In this formula, h1,h2, and h3 are arc length factors, while f(q1) and g(q2,q3) are essentially arbitrary functions of the coordinates. These solutions have the property that the E and D fields have components only in the axial q1 direction. Explicit formulas for field, displacement, polarization, potential, capacitance, etc. are obtained in terms of the generalized coordinates and the functions f and g. These expressions encompass virtually all the ‘‘workable’’ capacitor problems posed in standard texts. In the case of Cartesian coordinates where x is the axial coordinate, the conditions for closed-form solutions of this type reduce to ε=ε0 f(x)g(y,z), where f(x) and g(y,z) are arbitrary functions, and it is found that Ex depends only on x, while Dx depends only upon y and z. Effects arising from the presence of volume distributions of free charge are investigated, and it is found that their presence severely restricts the conditions under which simple solutions may exist. The methods used, and the results obtained, are applicable to structures such as capacitors, superlattices, optical fibers, inhomogeneous thin films, semiconductor heterojunctions, etc.

A numerical model of the ionospheric dynamo—I. Formulation and numerical technique

A new method of numerically solving a suitably formulated ionospheric wind dynamo equation for electrostatic potential and field is developed. Unlike in many other dynamo models, the upper boundary does not exist and the formulation asymptotically approaches the equatorial boundary condition. Therefore, it naturally incorporates the symmetric, asymmetric E- and F-region dynamo actions in any given ionosphere and any given global or local wind field. It also enables the equation to be posed as an initial value problem and solved numerically using an efficient, accurate, stable and fast integration method of ordinary differential equations. The numerical technique can be extended to compute three dimensional dynamo-generated electric currents in the ionosphere.

Adapting available finite element heat transfer programs to solve 2-D and 3-D electrostatic field problems

heat transfer problems of the Poisson and Laplace type have for years been solved by the finite element (FE) method. There exist many codes on the market today for solving such problems. A brief review of the analogy of heat transfer and electrostatic field equations is presented, followed by a more detailed discussion of the adaptation of current finite element heat transfer capabilities to the solution of two- and three- dimensional electrostatic field problems. An optimization module in the ANSYS® finite element program is also used to design a microstrip transmission line and optimize the design of a coaxial cable. All results show excellent agreement with analytical solutions.

Coordinate modelling for static axially symmetric electrovac metrics

A new technique of coordinate modelling is introduced. It is shown that the static axially symmetric electrovac field equations are easier to solve in terms of coordinates which are specially adapted to the electrostatic equipotential contours of the system. Several new exact solutions are readily found by separating variables and by employing complex analytic functions. A framework for the construction of general solutions of the axially symmetric electrostatic vacuum field equations is presented and the Weyl solutions are shown to be trivially extractable.

The linear, hydrodynamic stability of an interfacially perturbed, transversely isotropic, thin, planar viscoelastic film: I. General formulation and a derivation of the dispersion equation

A dispersion equation which describes the linear, hydrodynamic stability of an interfacially perturbed, thin ( O(10–100 nm)), planar, uncharged, transversely isotropic, viscoelastic film bounded by electrolytic Newtonian fluids is developed for the case in which the film interfaces are tangentially immobile. The linear viscoelastic rheology of the film is described by a Boltzmann superposition in which the stress relaxation tensor is formulated by utilizing Kelvin models. The influence of the electrical interactions of the film system on the linear dynamics is derived explicitly by integrating the normal mode electrostatic field equations. An investigation of the adjoint properties of the normal mode mechanical field relations indicates that for a certain class of films, (i) the principle of exchange of stabilities is valid, (ii) instability is nonoscillatory, and (iii) oscillatory states decay. A simplified dispersion equation for a symmetric film system is deduced, and it is shown that this equation describes squeezing and stretching eigenmodes.