Electric Field Model Research Articles

An enhanced distance-dependent electric field model for contact-separation triboelectric nanogenerator: Air-breakdown limit as a case study

Theoretical models have been proposed to bring an in-depth understanding of the working mechanisms of triboelectric nanogenerators (TENGs), aiming to enhance their output performance. This work proposes an enhanced distance-dependent electric field (EDDEF) model to predict triboelectric characteristics of TENGs more accurately. The model bridges the gap between the distance-dependent and distance-independent electric field models in terms of open-circuit (OC) voltage (VOC), short-circuit (SC) voltage (Vgap,SC), and SC surface charge density (σSC) at small separation distances by developing more accurate mathematical formulations of the electric potential. The EDDEF model was validated by finite element modeling (FEM) simulation. It introduced an accurate theoretical analysis of the air-breakdown boundary under the OC condition for the first time. The maximum surface charge density that can be obtained without air breakdown was predicted to be lateral size-dependent. It shows a monotonical decrease from 51.94 to 33.59 µC/m2 with a lateral size increase from 0.5 to 10 cm. Meanwhile, the corresponding separation distance increased from 0.915 to 12.48 mm, suggesting that improving CS-TENG’s performance by boosting the surface charge density is more effective at smaller lateral sizes and shorter separation distances. These findings serve as a guide towards the miniaturization of highly efficient CS-TENG technology. In addition, under SC condition, the EDDEF model showed great consistency with the distance-independent model in predicting the air-breakdown limit, supporting the distance-independent model applicability for predicting the air-breakdown under the CS condition.

Optimizing TMS Coil Placement Approaches for Targeting the Dorsolateral Prefrontal Cortex in Depressed Adolescents: An Electric Field Modeling Study.

High-frequency repetitive transcranial magnetic stimulation (rTMS) to the left dorsolateral prefrontal cortex (L-DLPFC) shows promise as a treatment for treatment-resistant depression in adolescents. Conventional rTMS coil placement strategies include the 5 cm, the Beam F3, and the magnetic resonance imaging (MRI) neuronavigation methods. The purpose of this study was to use electric field (E-field) models to compare the three targeting approaches to a computational E-field optimization coil placement method in depressed adolescents. Ten depressed adolescents (4 females, age: 15.9±1.1) participated in an open-label rTMS treatment study and were offered MRI-guided rTMS five times per week over 6-8 weeks. Head models were generated based on individual MRI images, and E-fields were simulated for the four targeting approaches. Results showed a significant difference in the induced E-fields at the L-DLPFC between the four targeting methods (χ2=24.7, p<0.001). Post hoc pairwise comparisons showed that there was a significant difference between any two of the targeting methods (Holm adjusted p<0.05), with the 5 cm rule producing the weakest E-field (46.0±17.4V/m), followed by the F3 method (87.4±35.4V/m), followed by MRI-guided (112.1±14.6V/m), and followed by the computational approach (130.1±18.1V/m). Variance analysis showed that there was a significant difference in sample variance between the groups (K2=8.0, p<0.05), with F3 having the largest variance. Participants who completed the full course of treatment had median E-fields correlated with depression symptom improvement (r=-0.77, p<0.05). E-field models revealed limitations of scalp-based methods compared to MRI guidance, suggesting computational optimization could enhance dose delivery to the target.

Dorsal subthalamic deep brain stimulation improves pain in Parkinson's disease.

Inconsistent effects of subthalamic deep brain stimulation (STN DBS) on pain, a common non-motor symptom of Parkinson's disease (PD), may be due to variations in active contact location relative to some pain-reducing locus of stimulation. This study models and compares the loci of maximal effect for pain reduction and motor improvement in STN DBS. We measured Movement Disorder Society Unified PD Rating Scale (MDS-UPDRS) Part I pain score (item-9), and MDS-UPDRS Part III motor score, preoperatively and 6-12 months after STN DBS. An ordinary least-squares regression model was used to examine active contact location as a predictor of follow-up pain score while controlling for baseline pain, age, dopaminergic medication, and motor improvement. An atlas-independent isotropic electric field model was applied to distinguish sites of maximally effective stimulation for pain and motor improvement. In 74 PD patients, mean pain score significantly improved after STN DBS (p = 0.01). In a regression model, more dorsal active contact location was the only significant predictor of pain improvement (R2 = 0.17, p = 0.03). The stimulation locus for maximal pain improvement was lateral, anterior, and dorsal to that for maximal motor improvement. STN stimulation, dorsal to the site of optimal motor improvement, improves pain. This region contains the zona incerta, which is known to modulate pain in humans, and may explain this observation.

Research on depth control of machining trace in electrochemical trepanning

Electrochemical trepanning (ECTr) is a highly effective and economic manufacturing technology for machining difficult-to-cut metal materials that are often used in aeroengine components. Integral structural components such as blisks, diffusers, etc. are composed of hubs and blades. In continuous ECTr, machining trace stems from on the hub between adjacent blades. The depth of machining trace significantly influences the surface integrity of the integrated components, even causes the scrapping of the workpiece. In order to solve the problem of machining trace in ECTr, a cathode design method based on the relation between cathode profile and electric field distribution is proposed in this study, the edge of the cathode that affects the machining trace is chamfered. A electric field model of ECTr is established and dynamic electric field simulation of ECTr for cathodes with different chamfered edges is performed. The electric field intensity distribution at the cathode edge and the forming profile of the hub are compared. The simulation results show that optimal chamfering parameters can improve the machining trace. Subsequently, a group of cathodes with different chamfered edge is designed, and corresponding ECTr experiments are conducted. The optimal chamfering parameters are determined (α = 5°, b = 2 mm), the depth of the machining trace is reduced from 0.370 mm to 0.122 mm, the surface flatness is significantly improved. Overall, this depth control method of machining trace is verified effectively.

Drift phase resolved diffusive radiation belt model: 2. implementation in a case of random electric potential fluctuations

In the first part of this work, we highlighted a drift-diffusion equation capable of resolving the magnetic local time dimension when describing the effects of trapped particle transport on radiation belt intensity. Here, we implement these general considerations in a special case. Specifically, we determine the various transport and diffusion coefficients required to solve the drift-diffusion equation for equatorial electrons drifting in a dipole magnetic field in the presence of a specific model of time-varying electric fields. Random electric potential fluctuations, described as white noise, drive fluctuations of trapped particle drift motion. We also run a numerical experiment that consists of tracking trapped particles’ drift motion. We use the results to illustrate the validity of the drift-diffusion equation by showing agreement in the solutions. Our findings depict how a structure initially localized in magnetic local time generates drift-periodic signatures that progressively dampen with time due to the combined effects of radial and azimuthal diffusions. In other words, we model the transition from a drift-dominated regime, to a diffusion-dominated regime. We also demonstrate that the drift-diffusion equation is equivalent to a standard radial diffusion equation once the distribution function is phase-mixed. The drift-diffusion equation will allow for radiation belt modeling with a better spatiotemporal resolution than radial diffusion models once realistic inputs, including localized transport and diffusion coefficients, are determined.

Electric field distribution predicts efficacy of accelerated intermittent theta burst stimulation for late-life depression.

Repetitive transcranial magnetic stimulation (rTMS) is a promising intervention for late-life depression (LLD) but may have lower rates of response and remission owing to age-related brain changes. In particular, rTMS induced electric field strength may be attenuated by cortical atrophy in the prefrontal cortex. To identify clinical characteristics and treatment parameters associated with response, we undertook a pilot study of accelerated fMRI-guided intermittent theta burst stimulation (iTBS) to the right dorsolateral prefrontal cortex in 25 adults aged 50 or greater diagnosed with LLD and qualifying to receive clinical rTMS. Participants underwent baseline behavioral assessment, cognitive testing, and structural and functional MRI to generate individualized targets and perform electric field modeling. Forty-five sessions of iTBS were delivered over 9 days (1800 pulses per session, 50-min inter-session interval). Assessments and testing were repeated after 15 sessions (Visit 2) and 45 sessions (Visit 3). Primary outcome measure was the change in depressive symptoms on the Inventory of Depressive Symptomatology-30-Clinician (IDS-C-30) from Visit 1 to Visit 3. Overall there was a significant improvement in IDS score with the treatment (Visit 1: 38.6; Visit 2: 31.0; Visit 3: 21.3; mean improvement 45.5%) with 13/25 (52%) achieving response and 5/25 (20%) achieving remission (IDS-C-30 < 12). Electric field strength and antidepressant effect were positively correlated in a subregion of the ventrolateral prefrontal cortex (VLPFC) (Brodmann area 47) and negatively correlated in the posterior dorsolateral prefrontal cortex (DLPFC). Response and remission rates were lower than in recently published trials of accelerated fMRI-guided iTBS to the left DLPFC. These results suggest that sufficient electric field strength in VLPFC may be a contributor to effective rTMS, and that modeling to optimize electric field strength in this area may improve response and remission rates. Further studies are needed to clarify the relationship of induced electric field strength with antidepressant effects of rTMS for LLD.

Research of the effect of different corrugated dust collection plates on particle removal in electrostatic precipitators

In this paper, a multi-physics field coupled model of electric, flow and particle fields was constructed by COMSOL to compare the effects of three different corrugated dust collector plates on electric field distribution, airflow field, particle trajectories and dust removal efficiency in an electrostatic precipitator, and to compare them with a conventional electrostatic precipitator with a parallel plate structure. The results indicated that the corrugated dust collection plate influenced the electric field within the ESP channel, while the wire plate spacing directly affected the size and distribution of space charge density. Furthermore, the corrugated dust collection plate also affected the EHD flow within the channel, with the D2-ESP and D3-ESP being the most strongly influenced by the ionic wind. By comparing the dust removal efficiency of the four ESPs, we found that D2-ESP has the highest dust removal efficiency, followed by D3-ESP, then Flat-ESP, and finally D1-ESP. The ranking order of the four ESPs' dust removal efficiency is consistent with the ranking order of the space charge density within the four ESP channels, which shows that the size of the space charge density directly affects the dust removal efficiency of ESPs. Numerical simulation results show that the change of wire plate spacing is the main reason why corrugated ESP affects the dust removal efficiency of electrostatic precipitators.

Spatial distribution of electric field measurement system: straight characterization of one or more original electric field sources in association with a new triaxial sensor

Several original point charge like electric field sources and a new tri-axial capacitive based electric field sensor have been designed to be associated together to build a new instrument able to characterize the electrical properties of the environment. The paper presents two fundamental features of the target electric imaging instrument: the characterization of the constituent parts of the system and the validation of the low-level data processing functions. The original electric field sources are composed of several conductive spheres with conical support so that they can be assimilated to point charges. The various arrangements of the sources can generate monopolar or multipolar electric fields. The tri-axial sensor is is integrated in a 2D scanning setup and used to map simultaneously the three components of the electric field generated by original electric field sources composed of several conductive spheres. The measured electric field images are compared to images calculated with an analytical model using the method of image charges. The agreement between measured electric field images and model validates both the original design of the sources and the geometrical features of the sensor which opens the door to application such as the detection of non-conductive buried object and smart detection with autoconfiguration.

Transport and magnetic properties in the Nd diluted system Y$_{1-x}$Nd$_{x}$Co$_{2}$Zn$_{20}$

We report the electrical resistivity, specific heat, and magnetization measurements of Y_{1-x}1−xNd_{x}xCo_{2}2Zn_{20}20 for 0.017 \leq x \leq 0.950.017≤x≤0.95. The Schottky-type specific heat peak at around 13 K for all the samples is reproduced by the crystalline electric field model with the \Gamma_{6}Γ6 doublet ground state of a Nd^{3+}3+ ion. The magnetization and magnetic susceptibility data of the samples for x \leq 0.06x≤0.06 are well reproduced by the calculation without intersite magnetic interactions among Nd moments. Therefore, the dilute Nd system Y_{1-x}1−xNd_{x}xCo_{2}2Zn_{20}20 for x \leq 0.06x≤0.06 is a good candidate to study on-site interaction of the \Gamma_{6}Γ6 doublet ground state of 4ff electrons with conduction electrons.

An Analytical Approach to Study the Impact of Traps on Ge-Source Double Gate PNPN TFET

The analytical models for surface potential, electric field, and drain current of a Ge-source double gate hetero-structure PNPN Tunnel FET are developed taking into account the oxide-semiconductor interfacial trap charges. Although other researchers have used similar modeling techniques on various structures, the proposed structure has not yet utilized them when considering the source/drain depletion region and interfacial trap charges that reflect changes in the flat band voltage. The proposed device consists of Ge-source, Si1−xGex pocket (mole fraction 0.3), and Si channel and drain. Moreover, the non-uniform concentration of trap charges is considered at the oxide/semiconductor interfaces: 1013 cm−2 at HfO2/ Si1−xGex interface and 1012 cm−2 at HfO2/Si interface. 2D Poisson’s equation is solved with the help of parabolic potential approximation and different boundary conditions to develop the surface potential model. The developed potential model is subsequently used to construct the electric field model. The drain current model of the proposed TFET is finally developed with the help of the generated electric field and some other parameters. All the developed models are validated using TCAD-simulated data. The studies show that there is good agreement between the simulated and modeled results, ensuring the applicability of the device in charge-trapped memory systems based on tunneling.

Biophysical modeling of the electric field magnitude and distribution induced by electrical stimulation with intracerebral electrodes

Intracranial electrodes are used clinically for diagnostic or therapeutic purposes, notably in drug-refractory epilepsy (DRE) among others. Visualization and quantification of the energy delivered through such electrodes is key to understanding how the resulting electric fields modulate neuronal excitability, i.e. the ratio between excitation and inhibition. Quantifying the electric field induced by electrical stimulation in a patient-specific manner is challenging, because these electric fields depend on a number of factors: electrode trajectory with respect to folded brain anatomy, biophysical (electrical conductivity / permittivity) properties of brain tissue and stimulation parameters such as electrode contacts position and intensity. Here, we aimed to evaluate various biophysical models for characterizing the electric fields induced by electrical stimulation in DRE patients undergoing stereoelectroencephalography (SEEG) recordings in the context of pre-surgical evaluation. This stimulation was performed with multiple-contact intracranial electrodes used in routine clinical practice. We introduced realistic 3D models of electrode geometry and trajectory in the neocortex. For the electrodes, we compared point (0D) and line (1D) sources approximations. For brain tissue, we considered three configurations of increasing complexity: a 6-layer spherical model, a toy model with a sulcus representation, replicating results from previous approaches; and went beyond the state-of-the-art by using a realistic head model geometry. Electrode geometry influenced the electric field distribution at close distances (∼3 mm) from the electrode axis. For larger distances, the volume conductor geometry and electrical conductivity dominated electric field distribution. These results are the first step towards accurate and computationally tractable patient-specific models of electric fields induced by neuromodulation and neurostimulation procedures.

Cardioneuroablation Using Epicardial Pulsed Field Ablation for the Treatment of Atrial Fibrillation.

Atrial fibrillation (AF) is the most common cardiac arrhythmia affecting millions of people worldwide. The cardiac autonomic nervous system (ANS) is widely recognized as playing a key role in both the initiation and propagation of AF. This paper reviews the background and development of a unique cardioneuroablation technique for the modulation of the cardiac ANS as a potential treatment for AF. The treatment uses pulsed electric field energy to selectively electroporate ANS structures on the epicardial surface of the heart. Insights from in vitro studies and electric field models are presented as well as data from both pre-clinical and early clinical studies.

Microarray Chip and Method for Simultaneous and Highly Consistent Electroporation of Multiple Cells of Different Sizes.

Cell electroporation is an important cell manipulation technology to artificially transfer specific extracellular components into cells. However, the consistency of substance transport during the electroporation process is still an issue due to the wide size distribution of the natural cells. In this study, a cell electroporation microfluidic chip based on a microtrap array is proposed. The microtrap structure was optimized for single-cell capture and electric field focusing. The effects of the cell size on the cell electroporation in the microchip were investigated through simulation and experiment methods using the giant unilamellar vesicle as the simplified cell model, and a numerical model of a uniform electric field was used as a comparison. Compared with the uniform electric field, a lower threshold electric field is required to induce electroporation and produces a higher transmembrane voltage on the cell under a specific electric field in the microchip, showing an improvement in cell viability and electroporation efficiency. The larger perforated area produced on the cells in the microchip under a specific electric field allows a higher substance transfer efficiency, and the electroporation results are less affected by the cell size, which is beneficial for improving substance transfer consistency. Furthermore, the relative perforation area increases with the decrease of the cell diameter in the microchip, which is exactly opposite to that in a uniform electric field. By manipulating the electric field applied to the microtrap individually, a consistent proportion of substance transfer during electroporation of cells with different sizes can be achieved.

Rapid estimation of cortical neuron activation thresholds by transcranial magnetic stimulation using convolutional neural networks

BackgroundTranscranial magnetic stimulation (TMS) can modulate neural activity by evoking action potentials in cortical neurons. TMS neural activation can be predicted by coupling subject-specific head models of the TMS-induced electric field (E-field) to populations of biophysically realistic neuron models; however, the significant computational cost associated with these models limits their utility and eventual translation to clinically relevant applications. ObjectiveTo develop computationally efficient estimators of the activation thresholds of multi-compartmental cortical neuron models in response to TMS-induced E-field distributions. MethodsMulti-scale models combining anatomically accurate finite element method (FEM) simulations of the TMS E-field with layer-specific representations of cortical neurons were used to generate a large dataset of activation thresholds. 3D convolutional neural networks (CNNs) were trained on these data to predict thresholds of model neurons given their local E-field distribution. The CNN estimator was compared to an approach using the uniform E-field approximation to estimate thresholds in the non-uniform TMS-induced E-field. ResultsThe 3D CNNs estimated thresholds with mean absolute percent error (MAPE) on the test dataset below 2.5% and strong correlation between the CNN predicted and actual thresholds for all cell types (R2 > 0.96). The CNNs estimated thresholds with a 2–4 orders of magnitude reduction in the computational cost of the multi-compartmental neuron models. The CNNs were also trained to predict the median threshold of populations of neurons, speeding up computation further. Conclusion3D CNNs can estimate rapidly and accurately the TMS activation thresholds of biophysically realistic neuron models using sparse samples of the local E-field, enabling simulating responses of large neuron populations or parameter space exploration on a personal computer.

Space-Charging Interfacial Layer by Illumination for Efficient Sb2S3 Bulk-Heterojunction Solar Cells with High Open-Circuit Voltage

Solution-processed material systems for effective photovoltaic conversion are the key to low-cost and efficient solar cells. While antimony trisulfide (Sb2S3) is a promising photovoltaic absorber, solution-processed quality Sb2S3-based heterojunction systems for solar cells, particularly with an open-circuit voltage (Voc) higher than 0.70 V, are challenging issues. Here, a cadmium sulfide (CdS) interfacial engineering method is developed for the Sb2S3-based bulk-heterojunction (BHJ) solar cells with an efficiency of 6.14% and a Voc up to 0.76 V that is the highest one among solution-processed Sb2S3 solar cells. The prepared Sb2S3-based BHJ solar cells feature a Sb2S3 nanoparticle film interdigitated by a titania (TiO2) nanorod array with a nanostructured CdS shell as an interfacial layer on each TiO2 nanorod core. Upon understanding the interfacial interactions and band alignments in the TiO2-CdS-Sb2S3 system, the function of the CdS interfacial layer as a band-bended spatial spacer interacting strongly with both the TiO2 electron transporter and Sb2S3 absorber for increasing charge collecting efficiency is revealed; moreover, space-charging the band-bended CdS layer by illumination is found and a photogenerated interfacial dipole electric field model is proposed for understanding the high Voc subjected to the presence of the CdS interfacial layer. This work provides a conceptual guide for designing efficient inorganic heterojunction solar cells.

Influence of Voltage on Pore Water Pressure for Soft Soil Treated with Electro-Osmosis Technique

Geotechnical engineers have a difficult time working with soft soils because they take so long to reach their final settlement and drain water under pressure. Granular columns and other modern technology are just two of the many methods utilized to hasten this leveling. In this study, the alteration of clay soils with a granular column and the evacuation of water by an electric field were replicated using 2D engineering and a finite component. solid mechanics and electrical interfaces are built using the drag interface. Mohr-Coulomb relied on a granular column and fine clay soil at the mechanical contact and employed electro-osmosis to describe the model's electric field's impact. For a period of six months, the pore water pressure for the fine clay soil was calculated. The result showed that when the electric current is applied with a voltage (5 v) the pwp in soil increases in first two months and then begins to gradually decrease, reaching in sixth month (120 kPa) and when applied voltage increases (15 v) the pwp decrease in the first two months from the previous ratio of voltage then it begins to gradually decrease and reaches in sixth month (70 kPa), When applied voltage increases more (30 v) the pwp in the soil decreases in first two months from the previous ratios of voltages, then it begins to gradually decrease and reaches (40 kPa), The percentage of water leaving the soil when an electric current is applied from (5-15 v) was (64%) and when voltage increased to (15-30 v) became (75%) which means the applied voltage increases, cause more water is discharged from the soil. The soil settlement also increases with an increase in the voltage, as the improvement percentage and the water exit from the soil (50%) at (5-15 v) and (71%) at (15-30 v).

Properties of percolation channels in planar memristive structures base on epitaxial films of oxide perovskite compounds YBa&lt;sub&gt;2&lt;/sub&gt;Cu&lt;sub&gt;3&lt;/sub&gt;O&lt;sub&gt;7 – δ&lt;/sub&gt; and La&lt;sub&gt;1 – &lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;Sr&lt;sub&gt;&lt;i&gt;x&lt;/i&gt;&lt;/sub&gt;MnO&lt;sub&gt;3 – δ&lt;/sub&gt;

The choice of base materials and the use of their functional properties in the development of the structure and elucidation of the mechanism of resistive switching has been analyzed. Mesoscopic heterostructures based on epitaxial oriented 〈001〉 films of high-temperature superconductor YBa2Cu3O7 – δ and doped manganite La1 – xSrxMnO3 – δ, were obtained, and the properties of percolation channels of structures based on these compounds were studied. The effects of “self-adapting electroforming” in microcontact heterostructures based on epitaxial films of manganite are observed. Numerical calculations using the critical electric field model have shown that “self-electroforming” occurs in strong electric fields and a gap structure is formed in the contact zone. This structure provides reproducibility of resistive switching.

Transcranial Direct Current Stimulation for Chronic Stroke: Is Neuroimaging the Answer to the Next Leap Forward?

During rehabilitation, a large proportion of stroke patients either plateau or begin to lose motor skills. By priming the motor system, transcranial direct current stimulation (tDCS) is a promising clinical adjunct that could augment the gains acquired during therapy sessions. However, the extent to which patients show improvements following tDCS is highly variable. This variability may be due to heterogeneity in regions of cortical infarct, descending motor tract injury, and/or connectivity changes, all factors that require neuroimaging for precise quantification and that affect the actual amount and location of current delivery. If the relationship between these factors and tDCS efficacy were clarified, recovery from stroke using tDCS might be become more predictable. This review provides a comprehensive summary and timeline of the development of tDCS for stroke from the viewpoint of neuroimaging. Both animal and human studies that have explored detailed aspects of anatomy, connectivity, and brain activation dynamics relevant to tDCS are discussed. Selected computational works are also included to demonstrate how sophisticated strategies for reducing variable effects of tDCS, including electric field modeling, are moving the field ever closer towards the goal of personalizing tDCS for each individual. Finally, larger and more comprehensive randomized controlled trials involving tDCS for chronic stroke recovery are underway that likely will shed light on how specific tDCS parameters, such as dose, affect stroke outcomes. The success of these collective efforts will determine whether tDCS for chronic stroke gains regulatory approval and becomes clinical practice in the future.

Charge density wave and crystalline electric field effects inTmNiC2

Single crystals of ${\mathrm{TmNiC}}_{2}$ were grown by the optical floating-zone technique and were investigated by x-ray diffraction (XRD), thermal expansion, electrical resistivity, specific heat, and magnetic susceptibility measurements. Single-crystal XRD reveals the formation of a commensurate charge density wave (CDW) characterized by a CDW modulation vector ${\mathbf{q}}_{\mathbf{2}\mathbf{c}}=(0.5,0.5,0.5)$, which is accompanied by a symmetry change from the orthorhombic space group $Amm2$ to the monoclinic space group $Cm$, i.e., to a CDW superstructure which is isostructural with that of ${\mathrm{LuNiC}}_{2}$. For all transport and thermodynamic properties, anomalies related to a second order-type thermodynamic CDW phase transition are observed at around ${T}_{\mathrm{CDW}}\ensuremath{\simeq}375\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The large specific heat anomaly at ${T}_{\mathrm{CDW}}, \mathrm{\ensuremath{\Delta}}C\ensuremath{\simeq}6.2\phantom{\rule{4pt}{0ex}}\mathrm{J}\phantom{\rule{0.16em}{0ex}}{\mathrm{mol}}^{\ensuremath{-}1}{\mathrm{K}}^{\ensuremath{-}1}$, together with noticeable changes in entropy and enthalpy related to the CDW transition, suggests that this point group symmetry breaking CDW phase transition affects more significant parts of the Fermi surface as compared to the incommensurate CDW transition of, e.g., ${\mathrm{SmNiC}}_{2}$ with no change in point group symmetry. The results on the antiferromagnetic and paramagnetic state of ${\mathrm{TmNiC}}_{2}$ obtained by the above macroscopic techniques were complemented by microscopic studies via inelastic neutron scattering. A crystalline electric field modeling of macroscopic susceptibility and magnetic specific heat and entropy contributions as well as microscopic neutron scattering data, reveal crystal field eigenstates and eigenvalues with a ground-state doublet of the Tm-$4f$ electrons, which is well separated by about 25 meV from exited states of the $J=6$ ground-state multiplet.

Physics informed neural networks for electric field distribution characteristics analysis

Electric field calculations based on the Poisson equation have been widely used in high voltage and plasma technology. However, in practical applications, the electric field distribution in space is relatively complex, and the simulation technology based on the traditional method is often a simplification of reality, which leads to a large error between the simulation and the actual measured value. In the actual application process, due to the limitation of measurement methods, it is necessary to infer the electric field data at other locations in space according to the measurement results. Physics informed neural networks (PINNs) are introduced into the electric field calculation. PINNs are considered partial differential equation solvers based on deep neural networks. In this paper, 2D and 3D electric field distributions are discussed and compared with the finite element method. A method of dividing the dielectric distribution based on the sigmoid function is proposed, which can be effectively used to construct the spatial electric field model of the homogeneous dielectric. The combination of the data and physical model based on PINNs establishes a method to solve the inverse problem of the relative permittivity in the electric field. The results show that PINNs can calculate the distribution of the electric field according to the physical equations and different types of constraints and parameters.