Modeling of electrical field modified by injected space charge

This paper presents the numerical solution of the coupled Poisson equation and charge conservation equation. We present an algorithm to obtain the distributions of electric field and charge density resulting from a corona discharge in the two-dimensional hyperbolic blade-ground plate configuration. We use finite elements method (FEM) to determine the potential distribution, finite volume method (FVM) and method of characteristics (MOC) to determine the distribution of charge density. The structured mesh is redefined at each iteration step to decrease artificial numerical diffusion. For solving the conservation equation, MOC with redefinition of structured mesh appears to be the best technique.     

Sensitivity analysis and optimal design in charge transport problems

The focus of this paper is the accurate and efficient determination of sensitivities of electrostatic potential and charge density in charge transport problems, and the use of these sensitivities to carry out optimal design. Direct differentiations of the boundary integral formulation of Poisson's equation for charge conservation and of the non-linear partial differential equation for current continuity are carried out to obtain equations satisfied by the sensitivities. Methods for solving the sensitivity equations are discussed. A numerical implementation of the methods is validated through several examples. It is demonstrated that the Design Sensitivity Coefficients (DSCs) of the quantities of interest in charge transport are obtained accurately and that optimal design problems can be solved efficiently using these DSCs.     

Exact resonant frequencies for the thickness-twist trapped energy mode in a piezoceramic plate

Summary Thickness-twist modes with energy trapping in a piezoceramic plate covered by infinite strip electrodes of infinitesimal thickness are analysed. By using Fourier transforms, the linear, three-dimensional equations for a piezoceramic plate are reduced to an integral equation for the charge distribution on the electrodes. Expanding the charge density in a finite series, the lowest resonant frequency as a function of the ratio with electrodes over thickness plate is computed. The computed values are compared with the results of an approximate approach given by Holland and Eer Nisse. For small values of the mentioned ratio, considerable deviations occur.     

A numerical algorithm for simulation of the electric corona discharge in the triode system

A numerical algorithm is described to calculate the charge density, electric field and corona current distribution in the corona triode. The algorithm employs a hybrid technique based on the Boundary and Finite Element Methods (FEM). FEM is used to determine the electric field because of free space charge produced by the corona discharge. The Boundary Element Method (BEM) is applied for calculating the other component of electric filed as a result of the voltage applied to the electrodes. The Method of Characteristics (MOC) is used to update the space charge density distribution. The characteristic lines are traced backwards from points of the analysed domain to the corona wire. The current density, electric field and space charge density distributions can be controlled by changing the configuration of the system. Results of calculations in a few different cases show the influence of different parameters on the work of the corona triode.     

Density and capacitance profiles and edge effects in a two-dimensional charge layer on a dielectric surface

The density and capacitance profiles and edge effects in a two-dimensional (2D) layer of electrons held on a liquid helium surface between two horizontal plates of a parallel-plate capacitor are studied by solving Laplace's equation on a computer. An effective length for experimental cells is defined to take into account nonuniform charge density and capacitance near the edges of the cells. The profiles and edge effects are studied as a function of charge density on the helium surface, helium depth inside the cell, repelling voltages on guard electrodes around the capacitor plates, and the frequency of excitation. The results should be useful in designing cells for experiments and better analyzing the results of measurements.     

Thermal diffusion in ionic systems

Starting from the complete set of equations of hydrodynamics and nonequilibrium thermodynamics for a binary uni-univalent salt in an electrolyte solution contained between electrodes, we have solved, in part, both the transient and the steady-state thermal diffusion problems. Full account is taken of nonvanishing space charge near the electrodes. Formulas are obtained for the temperature distribution, the electric field, the salt concentration distribution, the charge distribution, and the voltage. The effect of Joule heating on the temperature distribution is very small. The effect of space charge on the electric field and on the salt concentration distribution is also small. Applications both to solid-state ionic devices such as batteries and to thermal diffusion measurements in aqueous electrolyte solutions are mentioned.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Analytical solution of the Poisson-Boltzmann equation in cases of spherical and axial symmetry

An exact analytical solution of the Poisson-Boltzmann (PB) equation in cases of spherical, axial, and planar geometry has been obtained in the form of the logarithm of a power series. This solution describes an electrostatic potential distribution around a charged macroscopic particle (wire, plane) under conditions of thermal equilibrium at an arbitrary ratio of the density of charge borne by the particles (wires, planes) to the charge density in the surrounding plasma. Previously, an analytical solution of the PB equation was known only in the case of planar geometry.     

An improved finite element analysis of eddy current problemsconnected to voltage source

In conventional methods, a 3-D scalar potential problem must be solved in order to obtain a current source producing magnetic fields. In the proposed method, electric power is supplied to a region under consideration by the Poynting vector of a transverse electromagnetic (TEM) wave through a semi-infinite twin-lead-type feeder. Therefore, it is sufficient to solve the 2-D Laplace equation of the TEM wave before the calculation of the 3-D eddy current problem. Numerical analyses of conducting electrodes are shown. Reasonable results with phase lag and skin effect are obtained     

Adsorption and thermo desorption characteristics of hydrocarbons on single walled carbon nanotubes

We investigated the heterogeneous adsorption and thermal desorption behaviors of acetone, n-hexane and trichloroethylene (TCE) on single walled carbon nanotubes (SWCNTs). Adsorption isotherms for selected molecules on SWCNTs were measured using a quartz spring balance at temperatures ranging from 303.15 to 323.15 K. Thermal gravimetric desorption experiments were also conducted at different heating rates (2-10 K/min) to obtain information about the interaction strength of hydrocarbons with SWCNTs surfaces. The adsorption isotherm data were analyzed successfully with the temperature dependent Toth equation. To obtain the adsorption and desorption energy distribution functions (AED/DED) for hydrocarbons and nitrogen, the integral equation with Fowler-Guggenheim isotherm (for AED) and first order desorption rate equation (for DED) were solved using the generalized nonlinear regularization method. It was found that Henry's constants, the isosteric heats of adsorption, and the pattern of energy distribution function were highly dependent on the polarizability.     

Space charge distributions of an electric double layer capacitor with carbon nanotubes electrode

Space charge distributions of an electric double layer capacitors (EDLCs) based on polarizable nanoporous electrodes, containing carbon nanotubes (CNTs) as electrode material, were investigated by a pulsed electro acoustic (PEA) method. The EDLCs samples were prepared using CNTs and carbon black (i.e. acetylene and ketjen black) as electrode materials with different types pore structures. The charge distributions of positive/negative ions were spatially uneven and charge accumulation region concentrated on central part of electrode. The polarizable electrodes with ketjen black and CNTs-5 wt.% had higher space charge density. From the results of discharge characteristics, it is clear that EDLCs based on the ketjen black/CNTs-3 wt.% have better capacitive behavior. The specific capacitance of about 14 F/g of EDLCs using the polarizable electrodes with ketjen black and CNTs-3 wt.% were obtained. It can be found that CNTs plays an essential role in the improvement of the charge density and the electrostatic capacity in EDLCs. The use of PEA method allowed us to perform the direct observations of spatio-temporal charge distributions in EDLCs based on CNTs.     

An accurate and fast regularization approach to thermodynamic topology optimization

In a series of previous works, we established a novel approach to topology optimization for compliance minimization based on thermodynamic principles known from the field of material modeling. Hamilton's principle for dissipative processes directly yields a partial differential equation (referred to as the evolution equation) as an update scheme for the spatial distribution of density mass describing the topology. Consequently, no additional mathematical minimization algorithms are needed. In this article, we introduce a regularization scheme by penalization of the gradient of the spatial distribution of mass density. The parabolic evolution equation (owing to a similar structure to the transient heat-conduction equation) is solved most efficiently by an explicit time discretization. The Laplace operator is discretized via a Taylor series expansion yielding an operator matrix that is constant for the entire optimization process. This method shares some similarities to meshless methods and allows for an accurate application also on unstructured finite element meshes. The minimal size of the structure member can directly be controlled, a priori, by a numerical parameter introduced along with the regularization, similar to classical filter radii.     

随机结构动力反应的极值分布

提出了求解随机结构动力反应极值分布的概率密度演化方法。基于随机结构动力反应概率密度演化分析的基本思想，可构造一个与随机结构动力反应极值有关的具有“虚拟时间参数”的随机过程及其导数过程，导出了一维概率密度演化方程。结合结构动力反应的时程分析方法与有限差分方法，可求解该随机过程的一维概率密度函数。当虚拟时间参数为1时，即得到随机结构动力反应的极值分布。这一方法可用来求解一般的随机抽样和随机过程的极值分布。与随机抽样极大值分布的理论结果比较表明，本文建议方法具有良好的精度。在此基础上，分析了八层框架结构随机动力反应极值分布的若干特征。     

Computing the survival probability density function in jump-diffusion models: A new approach based on radial basis functions

We propose a numerical method to compute the survival (first-passage) probability density function in jump-diffusion models. This function is obtained by numerical approximation of the associated Fokker–Planck partial integro-differential equation, with suitable boundary conditions and delta initial condition. In order to obtain an accurate numerical solution, the singularity of the Dirac delta function is removed using a change of variables based on the fundamental solution of the pure diffusion model. This approach allows to transform the original problem to a regular problem, which is solved using a radial basis functions (RBFs) meshless collocation method. In particular the RBFs approximation is carried out in conjunction with a suitable change of variables, which allows to use radial basis functions with equally spaced centers and at the same time to obtain a sharp resolution of the gradients of the survival probability density function near the barrier. Numerical experiments are presented in which several different kinds of radial basis functions are employed. The results obtained reveal that the numerical method proposed is extremely accurate and fast, and performs significantly better than a conventional finite difference approach.     

Transient Fokker–Planck–Kolmogorov equation solved with smoothed particle hydrodynamics method

Probabilistic theories aim at describing the properties of systems subjected to random excitations by means of statistical characteristics such as the probability density function ψ (pdf). The time evolution of the pdf of the response of a randomly excited deterministic system is commonly described with the transient Fokker–Planck–Kolmogorov (FPK) equation. The FPK equation is a conservation equation of a hypothetical or abstract fluid, which models the transport of probability. This paper presents a generalized formalism for the resolution of the transient FPK equation by using the well‐known mesh‐free Lagrangian method, smoothed particle hydrodynamics). Numerical implementation shows notable advantages of this method in an unbounded state space: (1) the conservation of total probability in the state space is explicitly written; (2) no artifact is required to manage far‐field boundary conditions; (3) the positivity of the pdf is ensured; and (4) the extension to higher dimensions is straightforward. Furthermore, thanks to the moving particles, this method is adapted for a large kind of initial conditions, even slightly dispersed distributions. The FPK equation is solved without any a priori knowledge of the stationary distribution, just a precise representation of the initial distribution is required.Copyright © 2013 John Wiley & Sons, Ltd.     

Quantitative photoacoustic tomography from boundary pressure measurements: noniterative recovery of optical absorption coefficient from the reconstructed absorbed energy map

We describe a noniterative method for recovering optical absorption coefficient distribution from the absorbed energy map reconstructed using simulated and noisy boundary pressure measurements. The source reconstruction problem is first solved for the absorbed energy map corresponding to single- and multiple-source illuminations from the side of the imaging plane. It is shown that the absorbed energy map and the absorption coefficient distribution, recovered from the single-source illumination with a large variation in photon flux distribution, have signal-to-noise ratios comparable to those of the reconstructed parameters from a more uniform photon density distribution corresponding to multiple-source illuminations. The absorbed energy map is input as absorption coefficient times photon flux in the time-independent diffusion equation (DE) governing photon transport to recover the photon flux in a single step. The recovered photon flux is used to compute the optical absorption coefficient distribution from the absorbed energy map. In the absence of experimental data, we obtain the boundary measurements through Monte Carlo simulations, and we attempt to address the possible limitations of the DE model in the overall reconstruction procedure.     

Label-free detection of heparin, streptavidin, and other probes by pulsed streaming potentials in plastic microfluidic channels

In this paper, pulsed streaming potentials generated in plastic microfluidic channels are used for the label-free detection of some model analytes. The microchannels are fabricated with the commodity plastic cyclic olefin copolymer (COC), and the detection signal arises from a change in the surface charge upon analyte adsorption on the modified microchannel surface. The role of the surface modification is to confer the microchannel with a predetermined charge and a particular specificity toward the adsorption of the target analyte. In this work, several target probes displaying different levels of specificity were investigated. Heparin and streptavidin were detected by adsorption on microchannel surfaces modified with protamine and biotin, respectively, whereas bovine serum albumin (BSA) and methylene blue (MB) showed nonspecific adsorption on almost any modified or unmodified COC microchannel surface. The magnitude of the streaming potential was found to be proportional to the liquid pressure and the surface charge of the microchannel in accord with the Smoluchowski equation. Because the relative polarity of the streaming potential is determined by the surface charge, the most straightforward detection with this method occurs when the charge is reversed upon analyte adsorption. This strategy was used for the species described in this work, and the lowest concentrations detected were approximately 0.01 units/mL for heparin (below clinical relevance), approximately 10 (-9) M for BSA, and approximately 10 (-6) M for MB. Unlike the conventional method of steady flow, in this work, the streaming potentials were measured under pulsed conditions of flow and using nonreference electrodes. This approach removes the need of special electrolytes as it is usually required when using reference electrodes, and at the same time, it mitigates the interference of electrochemical drift from the electrodes. Relative standard deviations of approximately 1-2% and measuring times of approximately 10 s are readily attained with this experimental setup. The on-channel modification of the surface was carried out by UV-photografting methods given the significant UV transparency of COC.     

Current states and domains in systems with electron-hole pairing

Nonlinear collective excitations and inhomogeneous states of the excitonic phase are examined with the interband transitions of pairing particles taken into account. We obtain a Ginzburg-Landau-like equation and find the necessary conditions for a second-order phase transition to take place. The nonlinear equation describing the excited (inhomogeneous) state of the system in a simple case appears to be the Sine-Gordon equation. It is shown that domains of magnetization or polarization appear in the excited state of the excitonic antiferromagnetic or antiferroelectric. There are also other excited states, where the charge density coexists with the magnetization density. The collective excitations are manifested as nonlinear magnetization or polarization waves, moving domains of magnetization, etc.     

Permeance computation using indirect boundary integral equation method

An approach using indirect boundary integral equation method is proposed to determine the permeance between ferromagnetic poles in axisymmetric and three-dimensional magnetic systems. A generalised mathematical model is given for both types of magnetic systems. It consists of Fredholm integral equations of the first kind with respect to fictitious magnetic charge density sought in the form of simple layer potential. The system of boundary integral equations is solved using the method of mechanical quadratures. The approach is implemented in its own computer code. Results are presented for axisymmetric poles of electromagnets (cylinders, cones and frustum cones) and for a three-dimensional clapper-type system. Comparisons with known formulas are made and their accuracies are estimated. The approach presented is useful at the stage of preliminary design of magnetic systems. It is also applicable to computation of capacitances and electrical conductances     

Simulation and analysis of the capacitance–voltage characteristics of the δ-doped semiconductors

In this paper, a self-consistent model to simulate the general characteristics of one-dimensional semiconductor structures is demonstrated. During calculation, possible quantum effects and the distributions of both electrons and holes are all considered. In this model, a continuity equation is solved to calculate the distribution of free electrons and holes. The possible quantum wells are sought using the Schrödinger equation. The overall charge density and potential are obtained self-consistently by an iteration scheme. The C–V characteristics of the δ-doped structures are simulated and then compared with those of practical samples. By comparing with these δ-doped samples, the effective numbers of dopant atoms can be precisely determined. For these highly doped samples, it is found that the activation rates are only about half. This finding can be verified by Hall measurements which confirms the accuracy in this study.