Electric Field Boundary Conditions Research Articles

3D Simulation and Leakage Detection Technique for Deep Foundation Pits Based on Electric Field

To solve the problems of poor accuracy, poor anti-interference ability and unclear distribution of leakage electric field response characteristics of the traditional ground DC method for leakage detection of underground diaphragm walls in foundation pits, this paper proposes a deep foundation pit leakage detection technology based on the electric field. Secondly, it constructed the multi-field coupling equations and boundary conditions of the leakage electric field coupled with the leakage flow field and ion diffusion field, and then realized the three-dimensional forward evolution of the leakage electric field of the pit using the nonstructural mesh dissection method and the finite-element-infinite-element discretization method. Finally, physical model experiments and numerical simulations are used to confirm the reliability and accuracy of the foundation pit leakage detection technology and system. The results shows that monitoring the continuous change of the electric field for a period of time, the electric field detection technology for foundation pit leakage can effectively identify the location of hidden leakage and overcome the site’s strong industrial interference, resulting in a new technical solution for foundation pit leakage detection.

On the semi-classical analysis of Schrödinger operators with linear electric potentials on a bounded domain

The aim of this paper is to establish the asymptotic expansion of the eigenvalues of the Stark Hamiltonian, with a strong uniform electric field and Dirichlet boundary conditions on a smooth bounded domain of R N , N ⩾ 2. This work aims at generalizing the recent results of Cornean, Krejčiřik, Pedersen, Raymond, and Stockmeyer in dimension 2. More precisely, in dimension N, in the strong electric field limit, we derive, under certain local convexity conditions, a full asymptotic expansion of the low-lying eigenvalues. To establish our main result, we perform the construction of quasi-modes. The “optimality” of our constructions is then established thanks to a reduction to model operators and localization estimates.

Tensor-conductance model for reducing the computational artifact in target tissue for low-frequency dosimetry

Objective. In protecting human from low-frequency (<100 kHz) exposure, an induced electric field strength is used as a physical quantity for assessment. However, the computational assessment suffers from a staircasing error because of the approximation of curved boundary discretized with cubic voxels. The international guidelines consider an additional reduction factor of 3 when setting the limit of external field strength computed from the permissible induced electric field. Here, a new method was proposed to reduce the staircasing error considering the tensor conductance in human modeling for low-frequency dosimetry. Approach. We proposed a tensor-based conductance model, which was developed on the basis of the filling ratio and the direction of the tissue interface to satisfy the electric field boundary condition and reduce staircasing errors in the target tissue of a voxel human model. Main results. The proposed model was validated using two-layer nonconcentric cylindrical and spherical models with different conductivity contrasts. A comparison of induced electric field strengths with solutions obtained using an analytical formula and finite element method simulation indicated that for a wide range of conductivity ratios, staircasing errors were reduced compared with a conventional scalar-potential finite-difference method. The induced electric field in a simple anatomical head model using our approach was in good agreement with finite element method for exposure to uniform magnetic field exposure and that from coil, simulating transcranial magnetic stimulation. Significance. The proposed tensor-conductance model demonstrated that the staircasing error in an inner target tissue of a voxel human body can be reduced. This finding can be used for the electromagnetic compliance assessment and dose evaluation in electric or magnetic stimulation at low frequencies.

Phase field model for brittle fracture in multiferroic materials

Multiferroic materials, which simultaneously possess piezomagnetic, piezoelectric, and electromagnetic coupling effects, have a wide range of applications in various fields. Multiferroic materials are generally brittle with low fracture toughness, and accurate prediction of the fracture behaviors of multiferroics is challenging. In this work, a phase field model for brittle fracture in multiferroic materials is developed with the help of the Hamilton principle. In light of the second law of thermodynamics, the constitutive equations are derived in the context of the phase field method. The present theoretical framework unifies two classical phase field models and four combinations of the electric and magnetic boundary conditions. The residual controlled staggered algorithm, which enjoys a higher accuracy and lower computational cost, is extended to the fracture problems in the context of magneto-electro-elasticity. Systematic numerical simulations are performed in both 2D and 3D cases. The influences of the external magnetic field, electric field, and electric and magnetic boundary conditions on fracture behaviors of multiferroic materials are studied in detail. The applied magnetic field may not only accelerate or delay the fracture, but also influence the crack path. The present work is beneficial to assess the safety of multiferroic-based devices in engineering applications.

The jumping dielectric breakdown behavior induced by crack propagation in ferroelectric materials: A phase field study

Ferroelectric materials often experience fracture and dielectric breakdown under large mechanical and/or electrical loads. These two failure behaviors can affect each other and may lead to new phenomena. This study predicts a new type of jumping dielectric breakdown during crack propagation in ferroelectric materials using a phase field model involving multiple order parameters. The driving forces for the evolution of polarization, fracture, and dielectric breakdown were analysed based on the concept of configurational forces. The jumping dielectric breakdown was attributed to the competition between crack propagation and breakdown initiation at the moving crack tip. The breakdown pattern is related to the polarization domain structure and is significantly influenced by the applied electric field and crack boundary conditions. Furthermore, the jumping breakdown associated with possible mechanical degradation of the material can change the driving and resistance forces for crack propagation. This study introduces a novel dielectric breakdown behavior during crack propagation and provides new insights into the coupling failure of ferroelectric materials.

On the Enforcement of Electric Field Boundary Condition in the Moment Method Solution of Volume-Surface Integral Equation

When the volume-surface integral equation (VSIE) is used to model the composite objects, the electric field boundary condition (BC) can be explicitly enforced on the dielectric-perfect electric conductor (PEC) interfaces to reduce the volumetric unknowns. In the proposed BC-based VSIE, using the least-square method, one of the four coefficients of SWG basis functions belonging to a same tetrahedron terminated by a PEC triangle is directly calculated by the other three, which is no longer a volumetric unknown. The matrix equation generated by the method of moments is iteratively solved in a straightforward manner, which can be accelerated by the multilevel fast multipole algorithm. Through reliable numerical results, it is illustrated that the enforcement of the BC can reduce the memory usage and the number of iterations without compromising accuracy, in addition to good versatility.

Tuning the resonance frequency of piezoelectric energy harvesters by applying direct current electric field on piezoelectric elements

Different from previous strategies utilized to improve the energy conservation efficiency of piezoelectric energy harvesters (PEHs) from the environment, by broadening the frequency-bandwidth of energy harvesters using a specifically designed structure or tuning their resonance frequency (RF) through changing the geometrical/dynamical constraints, we report a method—by applying a direct current (DC) electric field on piezoelectric elements—to tune the RF of PEH based on the phenomenon that the elastic parameters of piezoelectric material are related to its electric field boundary condition. The results of a confirmatory experiment revealed that with a pre-loading DC electric field of −0.5 to 0.75 kV/mm, the RF of a piezoelectric cantilever energy harvester can be tuned from 144 to 156 Hz. The effectiveness of this strategy was further verified by comparing the energy conservation output of the PEH at a frequency that deviates from its RF, and at the same frequency, with pre-loading DC electric field adjustment.

Effects of Convective Boundary Condition and Activation Energy on Chemically Reacting Nanofluid Flow with Radiation

The combined impact of activation energy and radiation on the magnetohydrodynamic flow of nanofluid near a stagnation point with the electric field and convective boundary conditions are exposed in this study. By using similarity transformations, the non-linear partial differential equations renewed into non-linear ODEs. The resultant non-linear ODEs were solved numerically by using a shooting scheme. The impact of non-dimensional parameters on temperature, velocity, solute concentration, and nanoparticle volume fraction profiles are discussed graphically. The velocity and solute concentration increased by increasing the activation energy.

Data-driven, time-dependent modeling of pre-eruptive coronal magnetic field configuration at the periphery of NOAA AR 11726

Context. Data-driven, time-dependent magnetofrictional modeling has proved to be an efficient tool for studying the pre-eruptive build-up of energy for solar eruptions, and sometimes even the ejection of coronal flux ropes during eruptions. However, previous modeling works have illustrated the sensitivity of the results on the data-driven boundary condition, as well as the difficulty in modeling the ejections with proper time scales. Aims. We aim to study the pre- and post-eruptive evolution of a weak coronal mass ejection producing eruption at the periphery of isolated NOAA active region (AR) 11726 using a data-driven, time-dependent magnetofrictional simulation, and aim to illustrate the strengths and weaknesses of our simulation approach. Methods. We used state-of-the-art data processing and electric field inversion methods to provide the data-driven boundary condition for the simulation. We analyzed the field-line evolution, magnetic connectivity, twist, as well as the energy and helicity budgets in the simulation to study the pre- and post-eruptive magnetic field evolution of the observed eruption from AR11726. Results. We find the simulation to produce a pre-eruptive flux rope system consistent with several features in the extreme ultraviolet and X-ray observations of the eruption, but the simulation largely fails to reproduce the ejection of the flux rope. We find the flux rope formation to be likely driven by the photospheric vorticity at one of the footpoints, although reconnection at a coronal null-point may also feed poloidal flux to the flux rope. The accurate determination of the non-inductive (curl-free) component of the photospheric electric field boundary condition is found to be essential for producing the flux rope in the simulation. Conclusions. Our results illustrate the applicability of the data-driven, time-dependent magnetofrictional simulations in modeling the pre-eruptive evolution and formation process of a flux rope system, but they indicate that the modeling output becomes problematic for the post-eruptive times. For the studied event, the flux rope also constituted only a small part of the related active region.

An electron temperature model of the nMOSFETs

With the development of IC manufacturing process, the device dimensions have been on the nanoscale, while the device performance, such as the electron velocity, mobility and thermal noise, is significantly affected by the hot carrier effect. This paper proposes an electron temperature model to accurately predict the hot carrier effect. The channel transverse electric field is firstly derived by using the channel electric potential equation, taking into account the boundary conditions of the electric field. Based on the electric field equation, the energy balance equation is solved involving the impact of the temperature gradient and then the electron temperature model is established. The impact of the electron temperature on the channel mobility and of temperature gradient on the electron velocity has also been investigated. The results show that when the device enters the nanoscale, the electron mobility is more susceptible to the influence of the electric field and the electron temperature, and the impact of the temperature gradient on the velocity becomes obviously greater. The electron temperature model proposed in this paper can be applied to the performance analysis and modeling of nanosized MOSFETs.

Enhancement of modal birefringence in solid core Bragg fibers with high-index-contrast claddings

Abstract We present two types of highly birefringent solid core Bragg fibers (SCBFs) with high-index-contrast claddings by asymmetrically introducing low index parts (LIPs) into the solid core. The characteristics of their modal birefringence and confinement loss are numerically investigated by using a full-vector finite element method. The simulation results reveal that the modal birefringences in such highly birefringent SCBFs essentially depend not only on the difference in electric field boundary condition between the orthogonal-polarized modes, but also on the photonic bandgap effect. Both types of highly birefringent SCBFs have higher modal birefringence than those with low-index-contrast claddings, owing to the large refractive index (RI) modulation ranges of the LIPs. The modal birefringence of the fundamental mode at the targeted 1550 nm is strongly dependent on the size, RI and location of LIPs. Notably, the linear relationship between the modal birefringence and the RI of LIPs in the y-direction in a highly birefringent SCBF with four LIPs included can serve as a new sensing mechanism for the RI measurement of liquid analytes. We believe that the results would be beneficial to the design and application of highly birefringent SCBFs with high-index-contrast claddings.

Locating events in a segment of a segmented HPGe detector at KRISS

Abstract A specific segment of the 24 fold segmented HPGe detector was studied for improving the interaction position resolution from several cm to mm. The segmented HPGe detector was modeled by CAD program with their electrodes which was isolated by the Boolean function. The Shockley-Ramo theorem changed the Gauss law to Laplace equation problem for calculating the induced charge on each electrode. Finite Element Method solved the Poisson and Laplace equation with their boundary conditions for Electric field and potential. The drift velocities of charge carriers were compared between both along the 100 > and one between 100 > and 110 > Ge crystal axis at a specific segment and used to simulate the pulse shapes with 1 mm position resolution. Coincidence system between a specific segment and 3 × 3 HPGe detector verified the simulated pulse shapes by comparing these with the experimental ones which are generated at the specific target region with a fixed scattering angle. The experimental and simulated ones were χ 2 fitted to find the least χ 2 value and locate the interaction positions. The interaction positions of experimental pulse shapes were analyzed statistically after the rise time correction along 100 > and 110 > Ge crystal axis. The position resolution as FWHM on x, y, and z axis is the 3.12, 4.38 and 8.69 mm with the collimator size 3, 6, and 6 mm, respectively.

Adaptive Sampling of Physical Optics Currents Based on EFIE Error Prediction

Simple and efficient method for a numerical analysis of an electromagnetic scattering problem is developed by converting the electric field integral equation (EFIE) into a simple integral equation with known variables. Regarding electrically large conducting objects, the surface current density can be easily approximated by the physical equivalent principle. The combination of the equivalent surface current and the EFIE generates unexpected tangential field component right on the perfectly conducting surface, which is against the boundary condition for electric field. The unexpected tangential field component which is against the physical behavior of electric field can be used to define numerical error that represents abnormality of the object. Instead of taking more samples over the entire surface, focusing on the abnormal surfaces by subdividing adaptively according to predefined error can improve the computation efficiency. In this paper, an adaptive sampling of physical optics (PO) currents is performed based on the error prediction by EFIE. Furthermore, the proposed method is applied to the conventional iterative PO algorithm in order to increase the calculation efficiency by adaptively meshing the target domain. The resulting radar cross section is compared to the results from the method of moments as well as the general PO method.

Material Selection Analysis for Certain Absorption and Diffraction Camouflage Screen Based on the Lossy Medium Plate Model

Absorption and diffraction camouflage screen performance to some extent depends on the screen material for electromagnetic diffraction of radar wave behavior, by establishing a lossy medium plate model, on the basis of electric and magnetic field distribution and boundary conditions, calculating the relationship between the material of radar reflectivity, transmittance, absorption rate and its electric conductivity, theoretically analysis the optimal range of the electric conductivity of screen materials, to provide theoretical support for follow-up experiments and research.

Effects of Uncertainties in Electric Field Boundary Conditions for Ring Current Simulations

AbstractPhysics‐based simulation results can vary widely depending on the applied boundary conditions. As a first step toward assessing the effect of boundary conditions on ring current simulations, we analyze the uncertainty of cross‐polar cap potentials (CPCP) on electric field boundary conditions applied to the Rice Convection Model‐Equilibrium (RCM‐E). The empirical Weimer model of CPCP is chosen as the reference model and Defense Meteorological Satellite Program CPCP measurements as the reference data. Using temporal correlations from a statistical analysis of the “errors” between the reference model and data, we construct a Monte Carlo CPCP discrete time series model that can be generalized to other model boundary conditions. RCM‐E simulations using electric field boundary conditions from the reference model and from 20 randomly generated Monte Carlo discrete time series of CPCP are performed for two large storms. During the 10 August 2000 storm main phase, the proton density at 10 RE at midnight was observed to be low (&lt; 1.4 cm−3) and the observed disturbance Dst index is bounded by the simulated Dst values. In contrast, the simulated Dst values during the recovery phases of the 10 August 2000 and 31 August 2005 storms tend to underestimate systematically the observed late Dst recovery. This suggests a need to improve the accuracy of particle loss calculations in the RCM‐E model. Application of this technique can aid modelers to make efficient choices on either investing more effort on improving specification of boundary conditions or on improving descriptions of physical processes.

Two-dimensional scattering of a Gaussian beam by a homogeneous gyrotropic circular cylinder

Two-dimensional scattering of a Gaussian beam by a homogeneous gyrotropic circular cylinder is presented. The incident Gaussian beam source is expanded as an approximate expression with Taylor's series. The transmitted field in the homogeneous gyrotropic cylinder is expressed in terms of the series of wave functions based on the integral equation. The unknown coefficients of the scattered fields are obtained with the aid of the boundary conditions of continuous tangential electric and magnetic fields. Some numerical results are presented and discussed. The result is in agreement with that available as expected when the Gaussian beam degenerates to a plane wave incidence case.

Sensitivity analysis for radiofrequency induced thermal therapies using the complex finite element method

In radiofrequency induced thermal procedures for cancer treatment, the temperature of the cancerous tissue is raised over therapeutic values while maintaining the temperature of the surrounding tissue at normal levels. In order to control these temperature levels during a thermal therapy, it is important to predict the temperature distribution over the region of interest and analyze how the variations of the different parameters can affect the temperature in the healthy and damaged tissue. This paper proposes a sensitivity analysis of the radiofrequency induced thermal procedures using the complex Taylor series expansion (CTSE) finite element method (ZFEM), which is more accurate and robust compared to the finite difference method. The radiofrequency induced thermal procedure is modeled by the bioheat and the Joule heating equations. Both equations are coupled and solved using complex-variable finite element analysis. As a result, the temperature sensitivity with respect to any material property or boundary condition involved in the process can be calculated using CTSE.Two thermal therapeutical examples, hyperthermia and ablation induced by radio frequency, are presented to illustrate the capabilities and accuracy of the method. Relative sensitivities of the temperature were computed for a broad range of parameters involved in the radiofrequency induced thermal process using ZFEM. The major feature of the method is that it enables a comprehensive evaluation of the problem sensitivities, including both model parameters and boundary conditions. The accuracy and efficiency of the method was shown to be superior to the finite difference method. The computing time of a complex finite element analysis is about 1.6 times the computing time of real finite element analysis; significantly lower than the 2 times of forward/backward finite differencing or 3 times of central differencing. It was found that the radiofrequency hyperthermia procedure is very sensitive to the electric field and temperature boundary conditions. In the case of the radiofrequency ablation procedure, the cooling temperature of the electrodes has the highest liver/tumor temperature sensitivity. Also, thermal and electrical conductivities of the healthy tissue were the properties with the highest temperature sensitivities. The result of the sensitive analysis can be used to design very robust and safe medical procedures as well as to plan specific patient procedures.

Buckling and post-buckling analyses of piezoelectric hybrid microplates subject to thermo–electro-mechanical loads based on the modified couple stress theory

In the present paper, the post-buckling behavior of a simply supported piezoelectric hybrid microplate subject to thermal, electrical and mechanical loads is studied. The size effect in the mechanical behavior of the microplate is captured by using the modified couple stress theory. The Mindlin plate theory is adopted to describe its deflection behavior with the von Karman’s geometric nonlinearity taken into account. Based on these assumptions and the principle of minimum potential energy, the equilibrium equations of the microplate and associated boundary conditions are derived. By applying the Galerkin method to the equilibrium equations, closed-form solutions for the critical thermal/mechanical buckling load and the load–displacement relation in the post-buckling stage are obtained. Furthermore, the effects of the material length scale parameter to thickness ratio, the applied electric field and in-plane boundary conditions on the buckling and post-buckling behavior of the piezoelectric hybrid microplate are discussed in detail.

44. Considerations for electromagnetic warming of vitrified biomaterials

During vitrification, nucleation of ice crystals occurs most rapidly at low temperatures during later stages of cooling, while actual growth of ice crystals is most rapid at warmer temperatures near the solution melting point. Warming rates required to avoid significant ice growth during recovery from vitrification are therefore larger than the cooling rates required during vitrification, when the sample is relatively un-nucleated. Large samples vitrified by external conduction cooling therefore require more rapid warming by internal means if damaging ice growth and cryoprotectant toxicity are to be avoided. Oscillating electric fields coupling to polar molecules (dielectric heating) and mobile ions (ohmic heating) can achieve this. For uniform warming, the oscillation frequency must be low enough to deposit energy inefficiently into the sample (skin depth > > sample size). However the inefficiency cannot be so low that the electric field strength necessary for a desired warming rate causes dielectric breakdown of the sample or surrounding air (arcing). The wavelength inside and outside the sample must also be much larger than the sample to avoid field nodes and antinodes. For vitrified samples of tens or hundreds of grams (human organs), the skin depth and wavelength constraints are met by frequencies of tens of megahertz. Dielectric absorption as a function of frequency is maximal at the Debye relaxation frequency of dipoles. This frequency increases as viscosity decreases, and is therefore temperature-dependent. It’s desirable to choose a frequency with maximal absorption at the temperature at which the ice growth rate is maximal so that the warming rate is fastest when ice growth is fastest. This also promotes temperature uniformity by slowing warming in sample regions that warm past the temperature of maximal energy absorption. In the vitrification solution M22, the target temperature for maximum warming is approximately −60°. The corresponding frequency appears to be on the order of 30 MHz, which fortuitously also meets the aforementioned skin depth and wavelength constraints. Unlike dielectric heating that has a characteristic temperature of maximum absorption for a given frequency, ohmic heating only increases as temperatures increases, leading to “thermal runaway.” It’s therefore desirable to use a cryoprotectant carrier solution of low ionic strength, such as lactose/mannitol-based LM5. Boundary conditions of electric fields at dielectric interfaces also make sample geometry important for achieving a uniform internal field. Previous work in our laboratory with a 27 MHz 200-watt RF source demonstrated peak warming rates of 160 °C during warming a vitrified 20-mL cylindrical volume of M22 in LM5, and half that rate in a vitrified rabbit kidney in the same volume, with 3 °C and 15 °C maximum internal temperature differences respectively. Greater temperature non-uniformity within the organ vs. plain solution reflects decreased dielectric absorption within the non-polar lipid-rich renal pelvis. The maximum warming rate achievable within organs will likely be determined by such differential energy absorption, and the maximum tolerable temperature non-uniformities that result. Future study requires higher power, larger samples, variable frequency, and detailed measurements of cryoprotected tissue electrical properties as a function of frequency to permit accurate modeling.

Electro-osmotic slip flow of Eyring fluid in a slit microchannel

The electro-osmotic flow of a non-Newtonian fluid in a slit micro-channel under the Navier's slip boundary condition is investigated. The Eyring constitutive relationship model is adopted to describe the non-Newtonian characteristics of the flow driven by the applied electric field force and pressure. In consideration of the micro-scale effects, electric field, non-Newtonian behavior and slip boundary condition, a mechanical model is built and the effects of these factors on the flow are studied. Analytical expressions are derived for the electric potential and velocity profile by solving the linearized Poisson-Boltzmann equation and the modified Cauchy equation. Approximate expressions of the velocity distribution are also given and discussed. Furthermore, by comparing the effects of electric force with that of pressure on the velocity distribution, some meaningful conclusions are drawn from the obtained graphics.