Academic literature on the topic 'Uniform-electric-field-approximation'

This paper presents the derivation of Schwinger's gauge-invariant result of Im ℒ eff up to one loop approximation, for particle production in an uniform electric field through the method of complex trajectory WKB approximation (CWKB). The CWKB proposed by one of the authors1 looks upon particle production as being due to the motion of a particle in complex space–time plane, thereby requiring tunneling paths both in space and time. Recently2,3 there have been some efforts to calculate the reflection and the transmission coefficients for particle production in an uniform electric field that differ from our expressions for the same. In this paper we clarify the confusion in this regard and establish the correctness of CWKB.

We consider an elastic medium with a disclination and investigate the topological effects on the interaction of a spinless electron with radial electric fields through the WKB (Wentzel, Kramers, Brillouin) approximation. We show how the centrifugal term of the radial equation must be modified due to the influence of the topological defect in order that the WKB approximation can be valid. Then, we search for bound states solutions from the interaction of a spinless electron with the electric field produced by this linear distribution of electric charges. In addition, we search for bound states solutions from the interaction of a spinless electron with radial electric field produced by uniform electric charge distribution inside a long non-conductor cylinder.

The paper addresses the problem of acceleration of particles in a constant, uniform magnetic field of magnitude B and a uniform electric field perpendicular to it, which slowly increases with time. Assuming that the electric field grows linearly up to the maximum value Em=B, approximate analytical relations have been found which determine the particle velocity dependence on the acceleration time. The particles are shown to accelerate for the entire time of the increase in the electric field to a certain final energy, whose value depends on the acceleration rate. It has been established that the lower the acceleration rate, the greater the limiting energy. In the case when the ratio Em/B <0.9, using the solution method proposed by Alfvén in the drift approximation, an analytical solution of the relativistic equation of particle motion has been obtained. The results can be used to find the energy of particles in various pulsed processes in space plasma.

The paper addresses the problem of acceleration of particles in a constant, uniform magnetic field of magnitude B and a uniform electric field perpendicular to it, which slowly increases with time. Assuming that the electric field grows linearly up to the maximum value Em=B, approximate analytical relations have been found which determine the particle velocity dependence on the acceleration time. The particles are shown to accelerate for the entire time of the increase in the electric field to a certain final energy, whose value depends on the acceleration rate. It has been established that the lower the acceleration rate, the greater the limiting energy. In the case when the ratio Em/B <0.9, using the solution method proposed by Alfvén in the drift approximation, an analytical solution of the relativistic equation of particle motion has been obtained. The results can be used to find the energy of particles in various pulsed processes in space plasma.

Electrorheological (ER) materials are suspensions of specialized, micron-sized particles in nonconducting oils. When electric fields are applied to ER materials, they exhibit dramatic changes (within milli-seconds) in material properties. Pre-yield, yielding, and post-yield mechanisms are all influenced by the electric field. Namely, an applied electric field dramatically increases the stiffness and energy dissipation properties of these materials. A previously known cubic equation which describes the flow of fluids with a yield stress through a rectangular duct can be applied to annular flow, provided that certain conditions on the material properties are satisfied. An analytic solution and a uniform approximation to the solution, for the rectangular duct Poiseuille flow case is presented. A numerical method is required to solve the flow in annular geometries. The approximation for rectangular ducts is extended to deal with the annular duct case.

Nonperturbative dynamical effects in fermion-antifermion pair production by classical electric fields are investigated. Following a summary of the results previously given in the literature, a formal connection between fermion pair production in an external field and supersymmetric quantum mechanics is pointed out. Pair production probabilities are calculated in a uniform semiclassical approximation, which yields the Schwinger result in the constant field limit. The multiplicity distributions of the created pairs are shown to be related to the elementary symmetric functions.

The analytical solution for the displacements of an anisotropic piezoelectric material in the uniform electric field is presented for practical use in the “global excitation mode” of piezoresponse force microscopy. The solution is given in the Wolfram Mathematica interactive program code, allowing the derivation of the expression of the piezoresponse both in cases of the anisotropic and isotropic elastic properties. The piezoresponse’s angular dependencies are analyzed using model lithium niobate and barium titanate single crystals as examples. The validity of the isotropic approximation is verified in comparison to the fully anisotropic solution. The approach developed in the paper is important for the quantitative measurements of the piezoelectric response in nanomaterials as well as for the development of novel piezoelectric materials for the sensors/actuators applications.

Abstract Distortions of the structure of a uniform electric field when a dielectric body with a toroidal shape is placed in it are considered in the quasi-static approximation. The rate of distortion is proposed to estimate through the effective permittivity of toroid determined by solving the corresponding boundary value problem. Some numerical estimates obtained using specially developed software in the language of Matlab are given.

A zero net charge ideally polarizable particle is suspended within an electrolyte solution, nearly in contact with an uncharged non-polarizable wall. This system is exposed to a uniform electric field that is applied parallel to the wall. Assuming a thin Debye thickness, the induced-charge electro-osmotic flow is investigated with the goal of obtaining an approximation for the force experienced by the particle. Singular perturbations in terms of the dimensionless gap width δ are used to represent the small-gap singular limit δ ≪1. The fluid is decomposed into two asymptotic regions: an inner gap region, where the electric field and strain rate are large, and an outer region, where they are moderate. The leading contribution to the force arises from hydrodynamic stresses in the inner region, while contributions from both hydrodynamic stresses at the outer region and Maxwell stresses in both regions appear in higher order correction terms.

An initially uncharged ideally polarizable particle is freely suspended in an electrolyte solution in the vicinity of an uncharged dielectric wall. A uniform electric field is externally applied parallel to the wall, inflicting particle drift perpendicular to it. Assuming a thin Debye thickness, the electrokinetic flow is analysed for large particle–wall separations using reflection methods, thereby yielding an asymptotic approximation for the particle velocity. The leading-order correction term in that approximations stems from wall polarization.

Longitudinal piezoelectric transducers (LPT), which collectively refer to piezoelectric actuators, vibrators, sensors and actuators designed for longitudinal deformations or vibrations, are the most widely used piezoelectric devices. LPT model, which can be used to predict the behavior or performance in time/frequency domain, plays a vital role in the design and optimization of these LPT-based applications. Existing models which can be used for dynamic behavior prediction, are based on the complex electromechanical coupled fundamentals of piezoelectricity, which involves a complex position-varying electric field. Therefore, solving these models for the design and optimization of LPT-based applications is very computationally inefficient. After initial extensive investigations of possible effective simplifications in the complex fundamentals for modeling LPT, it is found that the electric field in LPT could be effectively approximated to be uniform (i.e. electric field is independent of its position) and this approximation could greatly simplify and facilitate the modeling of LPT-based applications. Therefore, the aim of this research is to study the uniformelectric-field approximation in simplifying the analysis, modelling and calculations of LPT for facilitating design and optimization of the LPT-based applications. LPT can, in principle, be divided into d31-mode LPT and d33-mode LPT. Both types are investigated in this thesis work. The main contributions of this thesis work are presented in 6 chapters, with each based on an individual scientific paper. Paper 1 presents the rationale behind the uniform-electric-field-approximation for d33- mode LPT together with its scope and limitation. Then, based on the approximation, novel simplified fundamentals of both simple-layer-type and stack-type d33-mode LPT are formulated, which could provide a very simple analytical solution, especially for the stack-type. To facilitate the modeling of free and loaded vibration of d33-mode LPT in a more straightforward way, a simple equivalent circuit is presented in Paper 2. The presented circuit is inspired by the network theory and formulated exactly based on the simplified fundamentals of d33-mode LPT presented in Paper 1. In many LPT-based applications, LPT are joined with other layers, such as backing layers and propagating layers. For the calculations and analysis of a multilayer structure, a transfer matrix method is always used. Therefore, to further facilitate the calculation when LPT are joined with other layers, the simplified fundamentals of LPT in Paper 1 is wrapped into a transfer matrix form as detailed in Paper 3. When LPT are used in a complex structure, a finite element model is widely applied for computation and analysis. Based on the uniform-electric-field-approximation, two simple equivalent finite element models of LPT are presented in Paper 4, which can largely simplify the modeling process and reduce the computational efforts of direct finite element modeling of LPT. Then, Paper 5 presents the rationale behind the uniform-electric-field-approximation for d31-mode LPT, which is different in nature to those of d33-mode. Also, an equivalent mixing method is proposed to consider electrode and adhesive layers within d31-mode LPT. The related equivalent circuit and transfer matrix of d31-mode LPT are formulated. Inspired by d33-mode, Paper 6 presents simple equivalent finite element models of d31-mode LPT.
Thesis (Ph.D.) (Research by Publication) -- University of Adelaide, School of Mechanical Engineering, 2016.

In the central field, the energy and angular momentum are conserved. It allows for the reduction of this problem to the problem of the motion of the particle in the effective one-dimensional field. Here the motion of a particle in Coulomb field or in the field of the isotropic harmonic oscillation with small perturbations are the most important ones. The authors discuss how the motion of a particle in the given central field can be described qualitatively for different values of the angular momentum and of the energy. Several problems deal with the motion of a particle in the Coulomb field under influence of weak constant uniform electric or magnetic fields (the classical analog of the Stark or Zeeman effect). In addition, the authors consider the motion of a charged particle in the field of the magnetic monopole and magnetic dipole. The motion of the Earth–Moon system in the field of the Sun is considered in some approximation. The displacement of the Coulomb orbit under the influence of a small force of radiation damping.

In the central field, the energy and angular momentum are conserved. It allows for the reduction of this problem to the problem of the motion of the particle in the effective one-dimensional field. Here the motion of a particle in Coulomb field or in the field of the isotropic harmonic oscillation with small perturbations are the most important ones. The authors discuss how the motion of a particle in the given central field can be described qualitatively for different values of the angular momentum and of the energy. Several problems deal with the motion of a particle in the Coulomb field under influence of weak constant uniform electric or magnetic fields (the classical analog of the Stark or Zeeman effect). In addition, the authors consider the motion of a charged particle in the field of the magnetic monopole and magnetic dipole. The motion of the Earth–Moon system in the field of the Sun is considered in some approximation. The displacement of the Coulomb orbit under the influence of a small force of radiation damping.

A numerical scheme based on the distributed Lagrange multiplier method (DLM) is used to study the motion of particles of a dielectric suspensions subjected to uniform and nonuniform electric fields. The Maxwell stress tensor method is used for computing electrostatic forces. In the point dipole approximation the total electrostatic force acting on a particle can be divided into two distinct contributions, one due to dielectrophoresis and the second due to particle-particle interactions. The former is zero when the applied electric field is uniform and the latter depends on the distance between the particles. In the Maxwell stress tensor approach these two contribution appear together. Simulations show that as expected the error in the point dipole approximation decreases, as the distance between the particles increases.

Abstract A new distributed multiplier/fictitious (DLM) domain method is developed for direct simulation of electrorheological (ER) suspensions subjected to spatially uniform electrical fields. The method is implemented both in two and three dimensions. The fluid-particle system is treated implicitly using the combined weak formulation described in [1,2]. The governing Navier-Stokes equations for the fluid are solved everywhere, including the interior of the particles. The flow inside the particles is forced to be a rigid body motion by a distribution of Lagrange multipliers. The electrostatic force acting on the polarized spherical particles is modeled based on the point-dipole approximation. Using our code we have studied the time evolution of particle-scale structures of ER suspensions in channels subjected to the pressure driven flow. In our study, the flow direction is perpendicular to that of the electric field. Simulations show that when the hydrodynamic force is zero, or very small compared to the electrostatic force, the particles form chains that are aligned approximately parallel to the direction of electric field. But, when the magnitude of hydrodynamic force is comparable to that of the electrostatic force the particle chains orient at an angle with the direction of the electric field. The angle between the particle chain and the direction of the electric field depends on the relative strengths of the hydrodynamic and electrostatic forces.