Field Calculations Research Articles

Highly accurate calculation of electric field for transcranial magnetic stimulation using hybridizable discontinuous galerkin method

The computation of electric field in transcranial magnetic stimulation (TMS) is essentially a problem of gradient calculation for thin layers. This paper introduces a hybrid-order hybridizable discontinuous Galerkin finite element method (HDG-FEM) and systematically demonstrates its superiority in TMS computations. The discrete format of HDG-FEM employing hybrid orders for TMS is derived and, from a fundamental numerical principle perspective, this study provides the elucidation of why HDG-FEM exhibits superior gradient computation capabilities compared to the widely used CG-FEM. Furthermore, the exceptional performance of HDG-FEM in thin layer calculation is demonstrated on both modified head models and realistic head models, focusing on three aspects: calculation errors, utilization of hybrid order, and computational cost. For the calculation of E-field in thin-layer regions with parameter mutation, the L∞ norm error of the first-order HDG-FEM with the same tetrahedral mesh is comparable to the L∞ norm error of the second-order CG-FEM. The L2 norm error of the same-order HDG-FEM is smaller than that of the same-order CG-FEM. By utilizing the hybrid order, HDG-FEM achieves a rapid reduction in errors of thin layers without a significant increase in the computational cost. This study transforms the three-dimensional TMS problem into a special two-dimensional problem for computation, reducing computational complexity from p3 in three dimensions to p2 in two dimensions, while achieving significantly higher accuracy compared to the commonly used CG-FEM. The utilization of hybrid orders in thin layers of the head demonstrates significant flexibility, making HDG-FEM a new alternative choice for TMS computations.

A concurrent multiscale model of stress-induced delamination behaviours of epoxy-impregnated rare-earth barium copper oxide superconducting pancake winding

Abstract Rare-earth barium copper oxide (REBCO) coated conductor (CC) tapes are promising for high-energy and high-electromagnetic field applications. In epoxy-impregnated REBCO superconducting coils, due to the weak c-axial strength of REBCO CC tapes, delamination induced by thermal-mismatch stress and Lorentz force significantly threatens stable operation. The commonly used numerical modelling methods mainly include homogenized model and refined model. The former can realize the efficient calculation of the overall physical field but lose the local details including interfacial delamination behaviour, while the latter can realize the refined calculation but cost massive calculation. In this study, combining with bilinear cohesive zone model (CZM), a two-dimensional axisymmetric concurrent multiscale model was developed to balance the efficiency-accuracy trade-off for numerically investigating the mechanical properties and interface failure behaviours of REBCO superconducting coils under cryogenics and high-electromagnetic field. In the presented model, the homogenized superconducting coil was firstly constructed based on composites homogenized approach to estimate the electromagnetic-thermal-mechanical properties at macro scale. Then, the ‘dangerous regions’ in the macro scale was recognized based on quadratic failure criterion and replaced with a refined model considering delamination failure defined by CZM. Finally, the two scales are linked through the coupling interface. The accuracy and efficiency of the concurrent multiscale model were validated by refined model for the cases of delamination behaviour during cooling and excitation.

Magnetic Hopfions: A Review

Recent advances in the research area of 3D magnetic topological solitons (hopfions) in restricted geometries are reviewed. The description of the magnetic solitons is based on a macroscopic micromagnetic approach and the Landau–Lifshitz equation of the magnetization motion. The concepts of the gauge emergent vector potential and emergent magnetic field are widely used to calculate the 3D topological charge (the Hopf index) of magnetic textures. The relation of the magnetic hopfions with classical field theory is demonstrated, and a special role of the curvilinear toroidal coordinates in the description of the hopfions is underlined. The hopfion stability and dynamics in ferromagnetic films and dots are considered. A critical discussion of calculations of the magnetization emergent magnetic field and the Hopf index of the toroidal magnetic hopfions in restricted geometries is presented.

Analysis of the influence of thermal insulation parameters on the effectiveness of enclosing structures and building heating systems

The results of thermal engineering calculations of external multilayer enclosing structures of buildings and the thermal power of the heating system of residential buildings are presented, including calculations of temperature fields and partial pressures of water vapor at various parameters of structural layers and thermal insulation layers. Variants are considered and an assessment is given of the variation of parameters and the different location of thermal insulation in external multilayer fences for changes in temperature fields and partial pressures of water vapor in the fence, as well as for changes in the thermal power of the heating system of the building premises for two climatological design areas. The calculations were performed according to the methodology presented below using a specially developed computer program.

Evolution laws of charge mobility of transformer oil and pressboard material with temperature and electric field strength

Abstract Charge mobility, a pivotal parameter in the space charge analysis model for oil-pressboard insulation of converter transformer under DC electric fields, predominantly relies on theoretical or empirical data. The prevalent omission of empirical, measurement-based evaluations, combined with the neglect of temperature and electric field intensity effects, introduces uncertainties in the calculation of electric field and charge dynamics. Grounded on the principles of the electroacoustic pulse technique for space charge measurements, our investigation established a temperature-controlled platform to determine the charge-charge mobility in oil and pressboard insulation mediums. Utilizing diverse oil-pressboard insulation systems, this study identified the temporal patterns of both positive and negative charge mobilities and unravelled the mechanisms modulated by temperature and electric field intensity: (1) with increasing temperatures (from 20 °C to 80 °C) and intensifying electric field strengths (from 5kV mm−1 to 25kV mm−1), the charge mobility within transformer oil and pressboard exhibits a rising trend. Notably, temperature variations exert the most significant influence, yielding amplifications up to 24.8 times. (2) The intrinsic properties of different transformer oils and oil-impregnated pressboards result in pronounced differences in their charge transport behaviors. Specifically, naphthenic-based oil demonstrates enhanced charge mobility relative to its paraffin-based counterpart. In contrast, transformer oils with higher kinematic viscosities exhibit diminished charge mobility compared to those with lower viscosities. (3) A linear relationship is observed between the oil absorption rate and electrical conductivity, aligning closely with the insulating pressboard’s charge mobility. The evaluation of electric field and interface charge dynamics in oil-pressboard insulation under both DC and polarity-reversed conditions revealed that the electric field decay in naphthenic-based oil is more rapid than in paraffin-based oils. Moreover, both the magnitude and rate of interface charge accumulation in naphthenic-based oils exceed those in paraffin-based variants, further validating the accuracy of our charge mobility measurements and ensuing analysis.

Uniform electric-field optimal design method using machine learning

The demand for uniform electric fields (UEFs) in engineering is very high, particularly in high-voltage devices. The existing methods encounter limitations in terms of optimization region and universality. Herein, we propose a method for designing UEFs based on finite element calculations of electromagnetic fields and machine learning. First, the electric-field distribution of the plate-to-plate electrode structure determined using three electrode-shape parameters (ESPs) is calculated using finite element software and is drawn. Thereafter, a dataset of 2000 images is created with different electric-field strength distributions using various ESPs. Net, we employ image-processing techniques to extract nine statistical features from the gray-level information in the images. Models are trained through machine learning to predict ESPs based on the gray-level features (GLFs). Finally, the electric-field strength distribution image of the expected ideal uniform field is artificially selected. In addition, the ESPs from which the uniform electric-field is produced are predicted by the models. The proposed method provides an accurate solution for optimizing the design of a uniform electric-field and a new approach for solving inverse problems of electric-field. This involves drawing the required electric-field strength distribution image for high-voltage engineering and obtaining the required ESPs.

Buckling by disordered growth

Buckling instabilities driven by tissue growth underpin key developmental events such as the folding of the brain. Tissue growth is disordered due to cell-to-cell variability, but the effects of this variability on buckling are unknown. Here, we analyze what is perhaps the simplest setup of this problem: the buckling of an elastic rod with fixed ends driven by spatially varying, yet highly symmetric growth. Combining analytical calculations for simple growth fields and numerical sampling of random growth fields, we show that variability can increase as well as decrease the growth threshold for buckling, even when growth variability does not cause any residual stresses. For random growth, we find numerically that the shift of the buckling threshold correlates with spatial moments of the growth field. Our results imply that biological systems can either trigger or avoid buckling by exploiting the spatial arrangement of growth variability. Published by the American Physical Society 2024

Efficient Calculation of the Self-Magnetic Field, Self-Force, and Self-Inductance for Electromagnetic Coils

Efficient Calculation of the Self-Magnetic Field, Self-Force, and Self-Inductance for Electromagnetic Coils

Краткосрочный прогноз смерчеопасных ситуаций для прибрежной акватории Черного моря с использованием усовершенствованного индекса WRI

The paper considers the issues of improving the quality of short-term forecasts of waterspout-risk conditions for the Black Sea coastal water. The results related to the development of new versions for calculating the regional waterspout risk index (WRI) for both the warm (WRI21) and cold (WRIW) seasons are presented. The WRI is used to identify zones of high-risk waterspout formation and subsequent localization of waterspout-risk areas of the coast. Calculations of the WRI fields are based on the output of the COSMO-Ru2 mesoscale model with a grid spacing of 2.2 km. Calculations are carried out in real time within the technology for assessing the risk of waterspouts. The skill of forecasting new WRI versions for different periods is analyzed. It is shown that the probability of waterspout detection in the warm season can reach 82% on average. At the same time, there is also a high false alarm rate (about 70%), mainly due to the excessively predicted waterspout risk in certain areas of the coast (Sochi and Tuapse). In the cold season, as expected, a significantly smaller number of waterspout-risk days is predicted as compared to the warm period. Examples of forecasts for different seasons are presented. Recommendations on the use of forecasts for preparing storm warnings are given.

Analysis of Flow Loss Characteristics of a Multistage Pump Based on Entropy Production

To reveal the internal flow loss characteristics of a multi-stage pump, the unsteady calculation of the internal flow field of a seven-stage centrifugal pump was carried out, and the entropy production theory and Q criterion were utilized to analyze the unsteady flow characteristics of each flow component under different flow rates. The research results show that as the flow rate increases, the entropy production value and the energy loss inside the flow components also increase accordingly. The viscous dissipation entropy production caused by fluid viscosity is very small, and the turbulent dissipation entropy production caused by turbulent fluctuations and wall dissipation entropy production are the main sources of energy loss. The impellers, diffusers, and outlet chamber are the main regions of energy loss in the multistage pump. The entropy production value of the first-stage impeller is significantly higher than that of other impellers, while the entropy production value of the first-stage diffuser is significantly lower than that of other diffusers. Through vortex structure analysis, it is found that the high entropy production regions in the impeller are concentrated in the impeller inlet area, the blade suction surface, and the impeller outlet area.

Effects of wall heating on wall pressure fluctuations and flow noise in a low-Reynolds-number turbulent channel flow with temperature-dependent viscosity

Wall pressure fluctuations and flow noise substantially degrade sonar detection performance and the acoustic stealth performance of underwater vehicles. This paper numerically investigates the effects of wall heating on wall pressure fluctuations in turbulent channel flow of water with temperature-dependent viscosity, exploring a novel method for controlling wall pressure fluctuations and flow noise in underwater vehicles. Large-eddy simulation (LES) is employed for the numerical calculation of the flow field, while a hybrid method combining LES with Lighthills acoustic analogy is employed to predict flow noise. The numerical results show that when the temperature difference between the wall and the incoming flow is 30 K and 50 K, the peak root-mean-square pressure fluctuations decrease by 6.76% and 8.91%, respectively. Wall heating stabilizes the pressure field near the wall, with the spectral levels of wall pressure fluctuations showing average decreases of approximately 1 dB and 2 dB. Wall heating weakens the energy-containing structures of wall pressure fluctuations and increases the overall convection velocity by 1.22% and 3.81%, respectively. Flow structure analysis reveals that the weakening of energy-containing structures results from the suppression of the vortex structures in the near-wall region. In the wall heating cases, peak turbulent kinetic energy decreases by 12.6% and 15.8%, respectively. Moreover, the sound pressure level of flow noise decreases with increasing wall temperature, with the maximum noise reduction exceeding 3 dB. Previous studies have not yet explored the effects of viscosity reduction caused by wall heating on wall pressure fluctuations and flow noise. This study demonstrates that wall heating is a promising method for reducing wall pressure fluctuations and flow noise.

Scattering of Acoustic Waves by an Inhomogeneous Elastic Cylindrical Shell of Finite Length in a Half-Space

An analytical solution to the problem of diffraction of a plane acoustic wave on a radially inhomogeneous thick-walled elastic cylindrical shell of finite length is obtained. The cylindrical shell is located in an acoustic half-space filled with an ideal liquid. The boundary of the half-space is an acoustically rigid or acoustically soft surface. The results of calculations of the acoustic field in the far zone are presented.

Precise determination of electric field applied to charged materials in liquid via van der Pauw technique

The electric field is a fundamental physical quantity that determines the characteristics or behavior of charged materials in liquids. The precise characterization of charged materials involving nanoparticles or biomaterials such as cells and extracellular vesicles (EVs) requires a rigorous calculation of the electric field applied to these materials. However, unlike solid-state materials, the precise measurement of the electric field applied in liquids is challenging because of liquid-electrode interface resistance and non-uniform electric-field regions near electrodes. This study proposes a method for determining the precise electric field in liquids using the van der Pauw measurement technique. The conductivity of the liquid was measured using a microfluidic channel with a van der Pauw configuration. The electric field in the liquid was then calculated based on the relationship between the conductivity and current density. The accuracy of the proposed method was verified by measuring the conductivity of standard solutions and phosphate-buffered saline (PBS), followed by determining the electric field applied to the nanoparticles in these solutions. In addition, the proposed method was used to determine the zeta potential of charged nanoparticles. This simple method for determining liquid conductivity and calculating electric fields in liquids could be effectively used for various electrochemical studies.

Vibrothermography for NDT : dynamic control of thermal sources by acoustic fields

Among the plethora of Non-Destructive Evaluation (NDE) techniques, the coupling of acoustic/vibration and thermography has emerged as a powerful method, more particularly denoted as sonothermography, utilizing the principle of energy conversion from acoustic waves to thermal heat sources to reveal structural abnormalities or create tunable volumic sources in materials. The calculation of the displacement field induced by acousto-vibrational excitations, using the analytical expression of energy conversion, has led to the generation and modeling of localized thermal sources in space over time within a material. By manipulating the input parameters of acoustic signals (frequency, phase, amplitude), we have demonstrated that it is possible to strategically position these sources in space and optimize the dissipation of thermal energy. The variation of parameters (creating a phase shift, a beat, a reversal law, etc.) makes it possible to control and move these internal heat sources to scan the material (in numerical approach and in the near future experimentally). The analysis of the resulting fields (acoustic-vibration and thermal), using inverse methods, opens up new possibilities for measuring the physical properties (mechanical, thermal) or characterizing defects in a material.

Magnetic Field Calculation of the U-Shaped Interior Permanent-Magnet Synchronous Machine Considering the Parallel Magnetization and Bridge Saturation

Magnetic Field Calculation of the U-Shaped Interior Permanent-Magnet Synchronous Machine Considering the Parallel Magnetization and Bridge Saturation

Modeling of Filtration and Heat and Mass Transfer Processes in Groundwater

Purpose. The method of mathematical modeling is an important tool for solving complex problems involving the analysis of groundwater dynamics and heat and mass transfer processes in them when studying their contamination from various anthropogenic sources in the event of accidental spills of chemically hazardous substances, etc. The main purpose of the article is to develop a set of mathematical models for calculating the process of filtration of non-pressure groundwater, mass transfer of impurities and the process of heat transfer in groundwater. Methodology. The two-dimensional Boussinesq equation of filtration was used to predict the dynamics of groundwater. The two-dimensional equation of convective-diffusive transport of impurities was used to model the processes of mass transfer in groundwater. The process of freezing of individual sections of the groundwater flow is modeled using the Laplace equation for the velocity potential (calculation of the flow velocity field in a time-varying geometry) and the two-dimensional equation of heat transfer in groundwater. Finite difference schemes were used to solve the modeling equations of groundwater dynamics and heat and mass transfer. Findings. A set of mathematical models has been developed to calculate the process of filtration of non-pressure groundwater and its chemical contamination. The experiment has confirmed the adequacy of the constructed numerical model of filtration of a non-pressure groundwater flow. An effective mathematical model was developed that allows determining the temperature fields in groundwater during the operation of a well used to freeze certain sections of the flow. The results of computer modeling indicate the effectiveness of the developed mathematical models. Originality. Effective mathematical models for predicting the level of chemical contamination of groundwater, its dynamics and thermal regime are proposed. The constructed mathematical models make it possible to determine the dynamics of changes in the temperature regime of groundwater during the operation of wells through which refrigerant is supplied to freeze individual areas. A computer program has been developed that allows for a comprehensive assessment of groundwater conditions. Practical value. A set of computer programs has been developed to conduct a computational experiment to study the processes of filtration, chemical contamination of groundwater and heat transfer processes in them. This set of programs can be used for the scientific substantiation of engineering solutions aimed at protecting groundwater.

Strong cosmic censorship in de Sitter spacetimes with dark matter

After imposing the weak energy condition on dark matter, we find that even in the absence of charge, a spherically symmetric de Sitter black hole with perfect fluid dark matter may still possess a Cauchy horizon. This paper investigates the stability of the Cauchy horizon in such a black hole under perturbations from a massless scalar field. Through numerical calculations of the massless scalar field's quasinormal modes, we discover that in this spacetime, when the black hole approaches extremality, i.e., when the dark-matter parameter b approaches its maximum value bmax, the Strong Cosmic Censorship (SCC) conjecture may be violated. This is the first instance of classical SCC violation observed in a spherically symmetric, uncharged black hole. Additionally, we explore the region of SCC violation within the parameter space ΛM2−b/bmax. Our findings indicate that as the cosmological constant increases, the violation region initially expands and then contracts.

Comparative assessment and QA measurement array validation of Monte Carlo and Collapsed Cone dose algorithms for small fields and clinical treatment plans.

Many studies have demonstrated superior performance of Monte Carlo (MC) over type B algorithms in heterogeneous structures. However, even in homogeneous media, MC dose simulations should outperform type B algorithms in situations of electronic disequilibrium, such as small and highly modulated fields. Our study compares MC and Collapsed Cone (CC) dose algorithms in RayStation 12A. Under consideration are 6 MV and 6 MV flattening filter-free (FFF) photon beams, relevant for VMAT plans such as head-and-neck and stereotactic lung treatments with heterogeneities, as well as plans for multiple brain metastases in one isocenter, involving highly modulated small fields. We aim to investigate collimator angle dependence of small fields and performance differences between different combinations of ArcCHECK configuration and dose algorithm. Several verification tests were performed, ranging from simple rectangular fields to highly modulated clinical plans. To evaluate and compare the performance of the models, the agreements between calculation and measurement are compared between MC and CC. Measurements include water tank measurements for test fields, ArcCHECK measurements for test fields and VMAT plans, and film dosimetry for small fields. In very small or narrow fields, our measurements reveal a strong dependency of dose output to collimator angle for VersaHD with Agility MLC, reproduced by both dose algorithms. ArcCHECK results highlight a suboptimal agreement between measurements and MC calculations for simple rectangular fields when using inhomogeneous ArcCHECK images. Therefore, we advocate for the use of homogeneous phantom images, particularly for static fields, in ArcCHECK verification with MC. MC might offer performance benefits for more modulated treatment fields. In ArcCHECK results for clinical plans, MC performed comparable to CC for 6 MV. For 6 MV FFF and the preferred homogeneous phantom image, MC resulted in consistently better results (13%-64% lower mean gamma index) compared to CC.

Semi-analytic three-shell forward calculation for magnetoencephalography

In previous studies, the magnetic lead field theorem in the quasi-static approximation was derived and used for the development of a method for the forward problem of MEG. It was applied and tested on a single-shell model of the human head and the question whether one shell is adequate enough for the calculation of the magnetic field is the main reason for this study. This forward method is based on the fundamental concept that one can calculate the lead field for MEG by decomposing it into two parts: the lead field of an arbitrary volume conductor that is already known and the gradient of basis functions that have to be harmonic, here derived from spherical harmonics. The problem then is reduced to evaluating the coefficients found in the basis functions. In this research we aim to improve the accuracy of the forward model, hence improving the localization accuracy in inverse methods by introducing a more detailed realistic head model. We here generalize the algorithm developed for a single-shell volume conductor to a three-shell volume conductor representing the brain, the skull and the skin with homogenous and isotropic conductivities in realistic ratios. The expansion to three shells could be tested as the three-shell algorithm is approaching the single-shell with high accuracy in special cases where three-shell solutions can also be calculated using a single-shell solution, especially for higher levels of expansion. The deviation in the calculation of the lead field is also evaluated when using three shells with realistic conductivities. The magnetic field turned out to differ to an important measurable extend in particular for deeper sources, making the three-shell algorithm substantially more accurate for these dipole locations.

A Coupled Magnetohydrodynamics (MHD) and Thermal Stress-Strain Model to Explore the Impact of Gas Cooling on Ingot Solidification Shrinkage in Vacuum Arc Remelting (VAR) Process

An advanced 2D axisymmetric magnetohydrodynamics model, including calculations for electromagnetic, thermal, and flow fields, fully coupled with a thermal stress-strain model, allowing the computation of solid mechanical parameters like stress, strain, and deformation within the ingot of the vacuum arc remelting process is presented. This process encounters challenges due to solidification shrinkage, which causes losing contact between the ingot and the mold, reducing the cooling efficiency of the system, resulting in a deeper melt pool and decreasing ingot quality. Herein, the width of the air gap along the ingot, the precise position of contact between the ingot and mold, and the profile of the melt pool, affected by gas cooling, are calculated. The global pattern of transport phenomena, such as (electro-vortex) flow and electromagnetic fields in the bulk of the ingot, is insensitive to helium gas cooling through the shrinkage gap. However, including gas cooling significantly improves heat removal through the mold, which consequently reduces the pool depth of the Alloy 718 ingot, leading to an improvement in the quality of the ingot.