Modeling the Interaction of Electrodynamic Fields to Circuit Elements

Introduction to Circuit Analysis and Design

Purpose: It has been postulated that electromagnetic fields play a role in transferring biological information during Bi-Digital O-Ring Test (BDORT). At the same time in complementary medicine, such as homeopathy or electro-acupuncture, experimental and theoretical researches in this kind of information have been carried out. Smith reported that the frequency information produced by an oscillator with a solenoid or toroidal coil could be imprinted into water, and that this water had some biological effect. Based on these results he deduced that the magnetic vector potential might have worked in transferring biological information. Supposing the same mechanism is working in the BDORT as in these complementary medicines, it might well be that muscle tone in the BDORT is responding to the magnetic vector potential. In this study we performed some experiments in the transfer of biological information through electromagnetic fields, and checked the effectiveness of the BDORT in detecting it. Then we studied the role of the magnetic vector potential in transferring information using a ferrite toroidal core. In addition, we report two newly invented methods of “phase inversion” of biological information. Methods: (1) Two brass beakers were connected by a single wire. A sample of drug or imprinted water in a glass tube was placed in one beaker, and “clean” water in a tube was placed in another as a target. For imprinting, the latter was “succussed” or a steady magnetic field was applied by a permanent magnet. After that we checked if the information could be detected by the BDORT. (2) Two solenoids having the same turns and same direction of winding were prepared; one end of each was connected by single wire. A sample was placed in one and clean water in another. No current was applied. Transferring and imprinting were performed by the same way as experiment 1, and the confirmation following was carried out by BDORT. (3) Two solenoids having the same turns but opposite directions of winding to each other (clockwise and anti-clockwise) were prepared. One end of each was connected by a single wire. The same experiment of transferring as in experiment 2 was performed. (4) A ferrite toroidal core was placed on a wooden table. A sample was placed on one side of the core, and the target water was placed on the opposite side. Imprinting was performed in the same way as the previous experiment. Results: In experiments 1 and 2, imprinting of information into the target water was detected by the BDORT resonance phenomenon with strong positive resonance response to the sample. In experiment 3, the response detected by BDORT was completely reversed: positive resonance response to the sample could not be obtained, but a strengthening response was obtained to the contrary. If the sample of drug had the strengthening effect in the drug compatibility testing for a patient, the target water became weakening, and vice versa . In experiment 4, transfer with phase inversion was also obtained, only when the sample and target water were placed on the opposite side of the toroidal core in the North-South direction of the geo-magnetic field. This transfer was not recognized when the subjects were placed off this direction. In the experiments with de-magnetized core or wooden one, no transfer could be obtained. Discussion: Based on these results it was suggested that the BDORT is working by the same mechanism of transfer of biological information as in the complementary medicines, such as homeopathy. As for experiment 1 and 2, the carrier of the transferring was not the circulating current. It has been postulated that the information was transferred through the coherent field present in relation to the metal. As for experiment 4, the toroidal core contains the magnetic flux with in the torus but in the surrounding space it provides the magnetic vector potential, which suggests that the magnetic vector potential was involved in the transferring of biological information, as well as in the mechanism of BDORT. The phase inversion effect in experiments 3 and 4 might be obtained through the interaction with vector potential of geo-magnetic field. We also found that the pathological information of the patient which is obtained from the acupuncture point, pathological foci, or organ representation area, could be inverted by these phase inversion methods, at least on the response of BDORT. Omura reported that when the electromagnetic signal coming from the pathological area is applied to the same area after shifting the phase 180° the abnormal response disappeared temporarily. Clinically the effectiveness of the phase inversion to cancel out the pathological oscillation in the patient should be expected, but further clinical experiments with possible theoretical consideration are required.

Summary form only given. In many high current pulsed power systems much, if not all, of the energy is inductive or magnetic rather than electric and the electric fields are dominantly inductive rather than electrostatic. That is, in the usual expression for generalized electric field, E=-grad(V)-dA /dt, V is the scalar potential that gives rise to the electrostatic field, and A is the magnetic vector potential, from which the inductive field is derived. In problems where there are regions without voltage sources or charge separation, the electrostatic component does not exist, and the usual technique of solving the scalar Laplace's equation for the potential is inappropriate for determining the electric fields. Calculation of the magnetic vector potential is plagued by choice of gauge condition and specification of correct boundary conditions. Especially for coaxial (axisymmetric) systems typical of many pulsed power components and systems, where the current flow is in the (r,z) plane, there are two components of the vector potential that must be solved-each with its own boundary conditions. Specification of all the correct boundary conditions is non-trivial. In this paper, we present a convenient technique for the calculation of inductive electric fields in coaxial systems. The technique is based on the introduction of a vector electric potential that is derived from Poisson's equation, in combination with Faraday's Law and the E-D constitutive relation. In coaxial geometry, the electric vector potential is only azimuthal and, therefore, quasi-scalar. It is conveniently calculated with any two-dimensional Poisson equation solver, and the resultant inductive field distribution easily derived. We have used the technique in several pulsed power system designs with success. Specific examples of the application of the technique are given.

The theory of nonlinear electrodynamics has got a lot of attentions in recent years. It was shown that Born-Infeld nonlinear electrodynamics is not the only modification of the linear Maxwell's field which keeps the electric field of a charged point particle finite at the origin, and other type of nonlinear Lagrangian such as exponential and logarithmic nonlinear electrodynamics can play the same role. In this paper, we generalize the study on the exponential nonlinear electrodynamics by adding a scalar dilaton field to the action. By suitably choosing the coupling of the matter field to the dilaton field, we vary the action and obtain the corresponding field equations. Then, by making a proper ansatz, we construct a new class of charged dilaton black hole solutions coupled to the exponential nonlinear electrodynamics field in the presence of two Liouville-type potentials for the dilaton field. Due to the presence of the dilaton field, the asymptotic behavior of these solutions are neither flat nor (A)dS. In the limiting case where the nonlinear parameter $\beta^2$ goes to infinity, our solution reduces to the Einstein-Maxwell dilaton black holes. We obtain the mass, temperature, entropy and electric potential of these solutions. We also study the behaviour of the electric field as well as the electric potential of these black holes near the origin. We find that the electric field has a finite value \textit{near} the origin, which is the same as the electric field of Born-Infeld nonlinear electrodynamics, but it can diverge exactly at $r=0$ depending on the model parameters. We also investigate the effects of the dilaton field on the behaviour of the electric field and electric potential. Finally, we check the validity of the first law of black hole thermodynamics on the black hole horizon.

Error analysis of the linearized Crank-Nicolson FEM for the incompressible vector potential magnetohydrodynamic system

Numerical simulation and experimental investigation of structural optimization of capacitance sensors for measuring steam wetness with different coaxial cylinders

We investigate the electron transport and conductance properties in Fibonacci quasi-periodic graphene superlattices with electrostatic barriers and magnetic vector potentials. It is found that a new Dirac point appears in the band structure of graphene superlattice and the position of the Dirac point is exactly located at the energy corresponding to the zero-averaged wave number. The magnetic and electric potentials modify the energy band structure and transmission spectrum in entirely diverse ways. In addition, the angular-dependent transmission is blocked by the potential barriers at certain incident angles due to the appearance of the evanescent states. The effects of lattice constants and different potentials on angular-averaged conductance are also discussed.

A close examination of the Maxwell-Lorentz theory of electrodynamics reveals that polarization and magnetization of material media need not be treated as local averages over small volumes – volumes that nevertheless contain a large number of electric and/or magnetic dipoles. Indeed, Maxwell’s macroscopic equations are exact and self-consistent mathematical relations between electromagnetic fields and their sources, which consist of free charge, free current, polarization, and magnetization. When necessary, the discrete nature of the constituents of matter and the granularity of material media can be handled with the aid of special functions, such as Dirac’s delta-function. The energy of the electromagnetic field and the exchange of this energy with material media are treated with a single postulate that establishes the Poynting vector S = E × H as the rate of flow of electromagnetic energy under all circumstances. Similarly, the linear and angular momentum densities of the fields are simple functions of the Poynting vector that can be unambiguously evaluated at all points in space and time, irrespective of the type of material media, if any, that might reside at various locations. Finally, we examine the Einstein-Laub force- and torque-density equations, and point out the consistency of these equations with the preceding postulates, with the conservation laws, and with the special theory of relativity. The set of postulates thus obtained constitutes a foundation for the classical theory of electrodynamics.

A method for the calculation of fully three-dimensional electromagnetic fields is presented. The continuous field problem is modelled by a network representation. Solution of the field is performed in terms of a scalar magnetic potential in nonconducting regions. In conductors the curl v curl A equation is solved by a loop variable method for the magnetic vector potential alone. No scalar is required in conducting regions. As in previous network methods, the new method is derived in terms of a minimum independent set of discrete variables, so that the field solution is unique. The uniqueness of the curl v curl A equation has always provoked discussion, and so this is examined in detail. It is shown how nonuniqueness is manifested in the discrete linear simultaneous equations. The methods commonly used for ensuring uniqueness are also examined, and it is shown that, with a clear understanding of the conditions required for uniqueness, it is always possible to guarantee a unique solution, as in the network methods. The new method has the advantage over the existing network methods in that it only requires a single field subdivision. It is also very simple to use and it should give accurate results, because, in the absence of a scalar in the conducting region, there is no cancellation problem.

We consider a theory of electrodynamics in three-dimensional space-time in the presence of the topological (Chern-Simons) interaction term $(\frac{\ensuremath{\kappa}}{2}){\ensuremath{\epsilon}}^{\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\rho}}{A}_{\ensuremath{\mu}}{\ensuremath{\partial}}_{\ensuremath{\nu}}{A}_{\ensuremath{\rho}}$. It is appropriate to quantize electrodynamics in the radiation gauge because in that gauge the states in the Hilbert space have positive-definite norms. However, in that gauge the vector potential ${A}^{\ensuremath{\mu}}$ cannot transform as a vector under the Lorentz group. We show that the vector potential does transform covariantly as a representation of the Lorentz group, but the representation is infinite dimensional and, surprisingly, the specific representation depends on the value of the parameter $\ensuremath{\kappa}$.

The aim of this paper is to introduce and to study the performance of some multiscale finite-element formulations for the eddy current problem in laminated iron in two dimensions. The case of the main magnetic flux that is parallel to the laminates and assumed to be perpendicular to the plane of projection is considered. Exact solutions of relevant boundary value problems for eddy currents are presented. Multiscale formulations based on the magnetic vector potential (MVP) and the single component current vector potential and on a mixed formulation of the MVP and the current density are discussed. An approach for a multiscale formulation with the MVP is constructed at the best based on an exact solution. The associated weak form of the multiscale finite-element method (MSFEM) is presented. Similar to the MVP, multiscale formulations for the single component current vector potential and for a mixed formulation with the MVP and the current density are studied. This paper does not present a mathematical analysis of the MSFEM for eddy currents in laminates. The performance of the MSFEM is studied by numerous numerical experiments of different examples. This paper covers the topics exact integration versus averaging of coefficients, stability of the MSFEM in a particular case, p-refinement of micro-shape functions and standard finite-element polynomials and edge effect. Simulations show the capability of MSFEM to approximate eddy currents in iron laminates efficiently and accurately. The simulations shall also provide a collection of numerical examples to evaluate other multiscale or homogenization methods.

Purpose The purpose of this paper is to evaluate analytically the magnetic flux density and the magnetic vector potential produced by a linear current density or a linear magnetization inside an arbitrary polyhedron. Design/methodology/approach In order to obtain expressions of the field and potential integrals in an intrinsic vector form, independently of any reference frame, the approach is to avoid the use of a local coordinate system to perform the integrations. Findings The expressions obtained contain only the same functions just needed for the uniform sources case, do not introduce any new singularity or discontinuity, and computed results illustrate their effectiveness. Research limitations/implications Being in intrinsic vector form the expressions obtained are well suited to cope with the data structures, i.e. faces-edges and edges-vertices incidence matrices, provided by unstructured polygonal meshes generators. Their use, especially when dealing with a generic mixed unstructured polygonal mesh, avoids the need of different routines, thus decreasing the complexity of the numerical code. Practical implications Besides, avoiding numerical integration, the results do not require usage of any function other than those already defined for the uniform sources case, and do not introduce any new singularity or discontinuity. Thus, the calculation of the magnetic flux density and the magnetic vector potential produced by linear sources needs nearly the same effort as the uniform sources one. Originality/value The closed-form expressions obtained are in intrinsic vector form and can be implemented in a unique routine suitable for the calculation of the magnetic flux density and vector potential produced by any linear or uniform polyhedral source.

We present a finite-difference time-domain (FDTD) technique suitable for coupling with quantum-transport solvers. We derive first-order equations for the electric and magnetic vector potentials and the electric scalar potential which, upon the adoption of the Coulomb gauge, decouple into solenoidal and irrotational equation sets and are sourced by the solenoidal and irrotational parts of the current density, respectively. The solenoidal electric and magnetic vector potentials obey equations analogous to the normal curl equations for the electric and magnetic fields, a fact we exploit to develop an effective absorbing boundary layer used to simulate unbounded regions in a way identical to standard FDTD. We demonstrate coupling to a simple quantum transport technique known as the Usuki transfer matrix technique.

Although the Spice program is very useful in many applications for standard circuit analysis, it has limited capability for R?? and microwave circuits analysis. This is because those circuits are usually described in terms of power-wave variables and defined by S-parameters, while the Spice program copes with standard circuit variables: node voltages and branch currents. However, if we introduce a simple mapping between incident power-wave and node voltage from one side and between reflected power-wave and branch current o i.e. bp!) = (I (n , and bp@) = ap(m). For legal connection of S-blocks into the network N it is required to blfil this interconnecting condition. According to the adopted mapping this condition can be easily iklfilled by a pair of VCVS with unit coupling coefficient at every internal port. Other types of connection between S-blocks can be transformed into cascaded connection using an additional S-block that is described by S-parameters with real coefficients. Therefore we get the equivalent S-parameters of the entire network using the same set-up circuit that is suitable for the y-parameter determination by Spice. The results obtained with our method are compared with results obtained by Touchstone program and no considerable discrepancies are observed.

Extensive research papers of three-dimensional computational techniques are widely used for the investigation of human brain pathophysiology. Eddy current analyzing could provide an indication of conductivity change within a biological body. A significant obstacle to current trend analyses is the development of a numerically stable and efficiency-finite element scheme that performs well at low frequency and does not require a large number of degrees of freedom. Here, a custom finite element method (FEM) solver based on edge elements is proposed using the weakly coupled theory, which separates the solution into two steps. First, the background field (the magnetic vector potential on each edge) is calculated and stored. Then, the electric scalar potential on each node is obtained by FEM based on Galerkin formulations. Consequently, the electric field and eddy current distribution in the object can be obtained. This solver is more efficient than typical commercial solvers since it reduces the vector eddy current equation to a scalar one, and reduces the meshing domain to just the eddy current region. It can therefore tackle complex eddy current calculations for models with much larger numbers of elements, such as those encountered in eddy current computation in biological tissues. An example is presented with a realistic human brain mesh of 2 million elements. In addition, with this solver, the equivalent magnetic field induced from the excitation coil is applied, and therefore there is no need to mesh the excitation coil. In combination, these significantly increase the efficiency of the solver. Bioelectromagnetics. 39:604-616, 2018. © 2018 Wiley Periodicals, Inc.