Electrostatic Potential Field Research Articles

Conservative numerical algorithm for simulating thermoelectrical semiconductor device with unconditional optimal convergence analysis

We propose conservative type numerical method to simulate thermoelectrical semiconductor device problem, in which mixed finite element method used for electric potential equation, conservative characteristic finite element method for electron and hole concentration equations, and standard finite element method for heat conduction equation. By temporal-spatial error splitting argument, the optimal error estimates without certain time step restriction are derived, and low order convergence rate of electrostatic potential and electric field intensity will not affect the accuracy of the electron, hole density and temperature. Numerical tests are performed to validate the theoretical results and application performance of the given method.

Statistics of protein electrostatics.

Molecular dynamics simulations of a small redox-active protein plastocyanin address two questions. (i) Do protein electrostatics equilibrate to the Gibbsian ensemble? (ii) Do the electrostatic potential and electric field inside proteins follow the Gaussian distribution? The statistics of electrostatic potential and electric field are probed by applying small charge and dipole perturbations to different sites within the protein. Nonergodic (non-Gibbsian) sampling is detectable through violations of exact statistical rules constraining the first and second statistical moments (fluctuation-dissipation relations) and the linear relation between free-energy surfaces of the collective coordinate representing the Hamiltonian electrostatic perturbation. We find weakly nonergodic statistics of the electrostatic potential (simulation time of 0.4-1.0 μs) and non-Gibbsian and non-Gaussian statistics of the electric field. A small dipolar perturbation of the protein results in structural instabilities of the protein-water interface and multi-modal distributions of the Hamiltonian energy gap. The variance of the electrostatic potential passes through a crossover at the glass transition temperature Ttr ≃ 170 K. The dipolar susceptibility, reflecting the variance of the electric field inside the protein, strongly increases, with lowering temperature, followed by a sharp drop at Ttr. The linear relation between free-energy surfaces can be directly tested by combining absorption and emission spectra of optical dyes. It was found that the statistics of the electrostatic potential perturbation are nearly Gibbsian/Gaussian, with little deviations from the prescribed statistical rules. On the contrary, the (nonergodic) statistics of dipolar perturbations are strongly non-Gibbsian/non-Gaussian due to structural instabilities of the protein hydration shell.

Molecular mechanism of GIRK2 channel gating modulated by cholesteryl hemisuccinate.

Cholesterol, an essential lipid of cell membranes, regulates G protein-gated inwardly rectifying potassium (GIRK) channel activity. Previous studies have shown that cholesterol activates GIRK2 homotetrameric channels, which are expressed in dopaminergic neurons of the brain. Deletion of GIRK2 channels affects both GIRK2 homo- and heterotetrames and can lead to abnormal neuronal excitability, including conditions such as epilepsy and addiction. A 3.5Å cryo-EM structure of GIRK2 in complex with CHS (cholesteryl hemisuccinate) and PIP2 (phosphatidylinositol 4,5-bisphosphate) has been solved. This structure provides the opportunity to study GIRK2 channel gating dynamics regulated by cholesterol using gating molecular dynamics (GMD) simulations. In the present study, we conducted microsecond-long GMD simulations on the GIRK2 channel in its APO, PIP2, and PIP2/CHS bound states, followed by systematic analysis to gain molecular insights into how CHS modulates GIRK2 channel gating. We found that CHS binding facilitates GIRK2 channel opening, with 43 K+ ion permeation events observed, compared to 0 and 2 K+ ion permeation events for GIRK2-APO and GIRK2/PIP2, respectively. Binding of CHS to the GIRK2 channel enhances PIP2 and channel interactions, which is consistent with previous experimental results. The negatively charged PIP2 alters the internal electrostatic potential field in the channel and lowers the negative free energy barrier for K+ ion permeation.

A double-sided 3D trench electrode detector using an 8-inch CMOS process: 3D simulation and experimental investigation

A double-sided 3D trench electrode detector (DS-3DTED) structure is proposed in this work to investigate the manufacturing process implementation of 3D detectors for high-energy physics, x-ray spectroscopy and x-ray cosmology applications. The device's electrical characterization, including electrostatic potential and electric field distributions, I–V, C–V, full depletion voltage and transient current with x-ray incidence, was performed with Synopsys® Sentaurus TCAD tools. In addition, a manufacturing method to realize the DS-3DTED device is presented. A 311 μm deep trench has been achieved through the Bosch process on the IMECAS 8-inch CMOS platform to verify the feasibility of the device structure. The maximum depth-to-width ratio is close to 105:1 when the trench width is 2 μm, which is an excellent foundation for manufacturing future 3D detector with a large fill factor and small dead region.

Mixed finite element analysis for a modified Poisson–Fermi interface problem accounting for electrostatic correlations

The Bazant–Storey–Kornyshev (BSK) theory [1–3] recently developed an important continuum framework to expound the nonlocal dielectric permittivity of ionic liquids due to electrostatic correlations, leading to a fourth-order modified Poisson–Fermi equation to model the electrostatic potential field in the solvent (e.g., the electrolyte), while the standard second-order Poisson–Fermi equation is still valid in modeling the electrostatic potential field in the solute. Thus an interface problem is formed between the fourth-order and second-order Poisson–Fermi equations through the interface of solvent and solute with jump coefficients, which has exerted tremendous impacts on applications of electrokinetics, electrochemistry, biophysics, and etc. In this paper, a type of mixed finite element method is developed to solve the proposed interface problem once for all variables: the electrostatic potential, electric field, electric displacement field, electrostatic stress as well as interactional force in the electrolyte in an accurate fashion, and its optimal convergence properties are analyzed for all variables in their respective norms. Numerical experiments are carried out through self-defined mathematical examples to validate all attained theoretical results. Furthermore, as a part of modeling verification for the presented interface problem that models the BSK theory, a practically physical example is investigated to validate the necessity of introducing the fourth-order modified Poisson–Fermi equation to describe the electrostatic correlation effects due to charge reversal phenomenon.

On the magnetostatic scalar potential and magnetic field of a cylindrical magnet

Abstract The magnetostatic potential and magnetic field of a solid and hollow cylindrical magnet is calculated everywhere in space in terms of complete elliptic integrals. These expressions are calculated using an electromagnetic analogy with the electrostatic potential and electric field of two uniformly charged disks with opposite surface density. The analogy is employed to study intuitively the discontinuities and the dipolar approximation of the fields $\vec{H}$ and $\vec{B}$. The range of validity of the dipolar approximation has been studied along the cylinder axis and in the midplane perpendicular to the cylinder axis, comparing them with the obtained general expression.

Engineering Professors' Conceptions on the Conceptual Field of Electrostatics in Mexico

This study explores the conceptual understanding of electromagnetism among physics professors at the Aeronautical University in Querétaro, Mexico. While student misconceptions in electromagnetism have been extensively studied, research on professors' understanding and its potential impact remains limited (Pardhan & Bano, 2001). This research aims to address this gap by focusing on the core concepts of electrostatic force, electric field, and electric potential. Eight professors participated in the study. Their academic background, electromagnetism course history, and teaching experience were documented. A three-tier diagnostic test, based on Vergnaud's theory of conceptual fields, was then used to assess their conceptualisation of these concepts and their interrelationships. The analysis revealed that only one professor consistently demonstrated correct understanding across all three concepts. Interestingly, this professor was also the one with the most extensive teaching experience in the subject. The results suggest a potential connection between teaching experience and a deeper conceptual understanding of electromagnetism. Further research is needed to explore this connection and its implications for mitigating student misconceptions through effective teaching practices.

Electrostatic potential of a uniformly charged annulus

The calculation of the electrostatic potential and/or electrostatic field due to a continuous distribution of charge is a well-covered topic in all calculus-based undergraduate physics courses. The most common approach is to consider bodies with uniform charge distribution and obtain the quantity of interest by integrating over the contributions from all the differential charges. The examples of a uniformly charged disk and ring are prominent in many physics textbooks since they illustrate well this technique at least for special points or directions of symmetry where the calculations are relatively simple. Surprisingly, the case of a uniformly charged annulus, namely, an annular disk, is largely absent from the literature. One might speculate that a uniformly charged annulus is not extremely interesting since after all, it is a uniformly charged disk with a central circular hole. However, we show in this work that the electrostatic potential created by a uniformly charged annulus has features that are much more interesting than one might have expected. A uniformly charged annulus interpolates between a uniformly charged disk and ring. However, the results of this work suggest that a uniformly charged annulus has such electrostatic features that may be essentially viewed as ring-like. The ring-like characteristics of the electrostatic potential of a uniformly charged annulus are evident as soon as a hole is present no matter how small the hole might be. The solution of this problem allows us to draw attention to the pedagogical aspects of this overlooked, but very interesting case study in electrostatics. In our opinion, the problem of a uniformly charged annulus and its electrostatic properties deserves to be treated at more depth in all calculus-based undergraduate physics courses covering electricity and magnetism.

First measurements of an imaging heavy ion beam probe at the ASDEX Upgrade tokamak.

The imaging heavy ion beam probe (i-HIBP) diagnostic has been successfully commissioned at ASDEX Upgrade. The i-HIBP injects a primary neutral beam into the plasma, where it is ionized, leading to a fan of secondary (charged) beams. These are deflected by the magnetic field of the tokamak and collected by a scintillator detector, generating a strike-line light pattern that encodes information on the density, electrostatic potential, and magnetic field of the plasma edge. The first measurements have been made, demonstrating the proof-of-principle of this diagnostic technique. A primary beam of 85/87Rb has been used with energies ranging between 60 and 72keV and extracted currents up to 1.5 mA. The first signals have been obtained in experiments covering a wide range of parameter spaces, with plasma currents (Ip) between 0.2 and 0.8 MA and on-axis toroidal magnetic field (Bt) between 1.9 and 2.7T. Low densities appear to be critical for the performance of the diagnostic, as signals are typically observed only when the line integrated density is below 2.0-3.0 × 1019m-2 in the central interferometer chord, depending on the plasma shape. The strike line moves as expected when Ip is ramped, indicating that current measurements are possible. Additionally, clear dynamics in the intensity of the strike line are often observed, which might be linked to changes in the edge profile structure. However, the signal-to-background ratio of the signals is hampered by stray light, and the image guide degradation is due to neutron irradiation. Finally, simulations have been carried out to investigate the sensitivity of the expected signals to plasma density and temperature. The results are in qualitative agreement with the experimental observations, suggesting that the diagnostic is almost insensitive to fluctuations in the temperature profile, while the signal level is highly determined by the density profile due to the beam attenuation.

Modeling the electrostatic field of a charged ring located inside an infinite cylinder in the presence of a torus

Objectives. Analytical solution of the boundary value problem of electrostatics for modeling the electrostatic field of a charged ring located inside a grounded infinite circular cylinder in the presence of a perfectly conducting torus is considered. The field source is a thin charged ring located on a plane perpendicular to the axis of the cylindrical screen.Methods. To solve the problem, the method of addition theorems is used. The potential of the initial electrostatic field is presented in the form of spherical harmonic functions and in the form of a superposition of cylindrical and toroidal harmonic functions, using addition theorems relating spherical, cylindrical and toroidal harmonic functions. The secondary potential of the electrostatic field is also represented as a superposition of cylindrical and toroidal harmonic functions.Results. The solution of the formulated boundary problem is reduced to the solution of an infinite system of linear algebraic equations of the second kind with respect to the coefficients included in the representation of the secondary field. The influence of some parameters of the problem on the value of the electrostatic potential inside a grounded cylindrical shield in the presence of a toroidal inclusion is numerically studied. The calculation results are presented in the form of graphs.Conclusion. The proposed technique and the developed software can find practical application in the development and design of screens in various fields of technology.

Study on Abundant Dust-Ion-Acoustic Solitary Wave Solutions of a (3+1)-Dimensional Extended Zakharov–Kuznetsov Dynamical Model in a Magnetized Plasma and Its Linear Stability

This article examines how shocks and three-dimensional nonlinear dust-ion-acoustic waves propagate across uniform magnetized electron–positron–ion plasmas. The two-variable (G′/G,1/G)-expansion and generalized exp(−ϕ(ξ))-expansion techniques are presented to construct the ion-acoustic wave results of a (3+1)-dimensional extended Zakharov–Kuznetsov (eZK) model. As a result, the novel soliton and other wave solutions in a variety of forms, including kink- and anti-kink-type breather waves, dark and bright solitons, kink solitons, and multi-peak solitons, etc., are attained. With the help of software, the solitary wave results (that signify the electrostatic potential field), electric and magnetic fields, and quantum statistical pressures are also constructed. These solutions have numerous applications in various areas of physics and other areas of applied sciences. Graphical representations of some of the obtained results, and the electric and magnetic fields as well as the electrostatic field potential are also presented. These results demonstrate the effectiveness of the presented techniques, which will also be useful in solving many other nonlinear models that arise in mathematical physics and several other applied sciences fields.

Quantitative electric field mapping between electrically biased needles by scanning transmission electron microscopy and electron holography

Stray electric fields in free space generated by two biased gold needles have been quantified in comprehensive finite-element (FE) simulations, accompanied by first moment (FM) scanning TEM (STEM) and electron holography (EH) experiments. The projected electrostatic potential and electric field have been derived numerically under geometrical variations of the needle setup. In contrast to the FE simulation, application of an analytical model based on line charges yields a qualitative understanding. By experimentally probing the electric field employing FM STEM and EH under alike conditions, a discrepancy of about 60% became apparent initially. However, the EH setup suggests the reconstructed phase to be significantly affected by the perturbed reference wave effect, opposite to STEM where the field-free reference was recorded subsequently with unbiased needles in which possibly remaining electrostatic influences are regarded as being minor. In that respect, the observed discrepancy between FM imaging and EH is resolved after including the long-range potential landscape from FE simulations into the phase of the reference wave in EH.

Modeling of micellar‐catalyzed bimolecular ionic reactions by a nonlinear Poisson−Boltzmann equation and an electrostatic free energy model

AbstractThe hydrolysis reactions of crystal violet (CV) and p‐nitrophenyl acetate (PNPA) by sodium hydroxide in cetyltrimethylammonium bromide (CTAB) micellar solution were studied in this work. Combined with the Boltzmann probability of ionic species in an electrostatic potential field, a model with a numerical scheme was developed based on the nonlinear Poisson−Boltzmann equation in the micelle‐cell consisting of the reactants and the surfactant. The numerical solution gives the ionic species distribution in the micelle phase and the radius of the micelle‐phase. The dielectric constant of the micelle‐phase varies in the range of 39.8−54.4. The second‐order reaction rate constants in the micelle‐phase were determined using the electrostatic and dipolar free energy models. For the basic hydrolysis of CV and PNPA, the overall second‐order rate constants are three to five times and 1.4 times greater than the corresponding values in water, respectively. The rate enhancement occurs due to the distribution of the reactive ionic species in the cell region and the enhancement of the Coulombic and dipolar interactions among the ionic and polar reactants.

Electrical Manipulation of Spin-Dependent Anisotropy of a Dirac Cone in a Graphene Superlattice with Alternating Periodic Electrostatic and Exchange Fields

We studied the spin-dependent behavior of the electronic properties of alternating periodic potentials applied to finite and infinite graphene superlattices coupled with tunable electrostatic and exchange fields. The band structures were evaluated using the transfer matrix approach. The results of tuning the coupled electrostatic potential and exchange field showed that the spin-dependent anisotropy of a Dirac cone depends on the difference between the amplitude of periodically modulated coupling. Spin-dependent collimation occurs when the modulations become zero-average potentials with the ratio of both periodically modulated strengths equals one, in which one spin can be moved freely, but the other one is highly collimated. In addition, we find that the number of extra Dirac points in the infinite superlattice is spin-dependent. In terms of spin-ups, their number increases with an increase in the strength of both modulated fields. To ensure this calculation, we also compute the conductance of finite periodic modulation at zero energy. It is shown that the peaks of the conductance occur when the extra Dirac point emerges. This result may be utilized to design graphene-based devices with highly spin-polarized collimators.

A simple geometrical model of the electrostatic environment around the catalytic center of the ribosome and its significance for the elongation cycle kinetics

The central function of the large subunit of the ribosome is to catalyze peptide bond formation. This biochemical reaction is conducted at the peptidyl transferase center (PTC). Experimental evidence shows that the catalytic activity is affected by the electrostatic environment around the peptidyl transferase center. Here, we set up a minimal geometrical model fitting the available x-ray solved structures of the ribonucleic cavity around the catalytic center of the large subunit of the ribosome. The purpose of this phenomenological model is to estimate quantitatively the electrostatic potential and electric field that are experienced during the peptidyl transfer reaction. At least two reasons motivate the need for developing this quantification. First, we inquire whether the electric field in this particular catalytic environment, made only of nucleic acids, is of the same order of magnitude as the one prevailing in catalytic centers of the proteic enzymes counterparts. Second, the protein synthesis rate is dependent on the nature of the amino acid sequentially incorporated in the nascent chain. The activation energy of the catalytic reaction and its detailed kinetics are shown to be dependent on the mechanical work exerted on the amino acids by the electric field, especially when one of the four charged amino acid residues (R, K, E, D) has previously been incorporated at the carboxy-terminal end of the peptidyl-tRNA. Physical values of the electric field provide quantitative knowledge of mechanical work, activation energy and rate of the peptide bond formation catalyzed by the ribosome. We show that our theoretical calculations are consistent with two independent sets of previously published experimental results. Experimental results for E.coli in the minimal case of the dipeptide bond formation when puromycin is used as the final amino acid acceptor strongly support our theoretically derived reaction time courses. Experimental Ribo-Seq results on E. coli and S. cerevisiae comparing the residence time distribution of ribosomes upon specific codons are also well accounted for by our theoretical calculations. The statistical queueing time theory was used to model the ribosome residence time per codon during nascent protein elongation and applied for the interpretation of the Ribo-Seq data. The hypo-exponential distribution fits the residence time observed distribution of the ribosome on a codon. An educated deconvolution of this distribution is used to estimate the rates of each elongation step in a codon specific manner. Our interpretation of all these results sheds light on the functional role of the electrostatic profile around the PTC and its impact on the ribosome elongation cycle.

Calculation of Electrostatic Potential Field of Coronavirus S Proteins for Brownian Dynamics Simulations

Calculation of Electrostatic Potential Field of Coronavirus S Proteins for Brownian Dynamics Simulations

Electrostatic Map of the SARS-CoV-2 Virion Specifies Binding Sites of the Antiviral Cationic Photosensitizer.

Electrostatics is an important part of virus life. Understanding the detailed distribution of charges over the surface of a virus is important to predict its interactions with host cells, antibodies, drugs, and different materials. Using a coarse-grained model of the entire viral envelope developed by D. Korkin and S.-J. Marrink’s scientific groups, we created an electrostatic map of the external surface of SARS-CoV-2 and found a highly heterogeneous distribution of the electrostatic potential field of the viral envelope. Numerous negative patches originate mainly from negatively charged lipid domains in the viral membrane and negatively charged areas on the “stalks” of the spike (S) proteins. Membrane (M) and envelope (E) proteins with the total positive charge tend to colocalize with the negatively charged lipids. In the E protein pentamer exposed to the outer surface, negatively charged glutamate residues and surrounding lipids form a negative electrostatic potential ring around the channel entrance. We simulated the interaction of the antiviral octacationic photosensitizer octakis(cholinyl)zinc phthalocyanine with the surface structures of the entire model virion using the Brownian dynamics computational method implemented in ProKSim software (version r661). All mentioned negatively charged envelope components attracted the photosensitizer molecules and are thus potential targets for reactive oxygen generated in photosensitized reactions.

Integration of Ligand-Based and Structure-Based Methods for the Design of Small-Molecule TLR7 Antagonists.

Toll-like receptor 7 (TLR7) is activated in response to the binding of single-stranded RNA. Its over-activation has been implicated in several autoimmune disorders, and thus, it is an established therapeutic target in such circumstances. TLR7 small-molecule antagonists are not yet available for therapeutic use. We conducted a ligand-based drug design of new TLR7 antagonists through a concerted effort encompassing 2D-QSAR, 3D-QSAR, and pharmacophore modelling of 54 reported TLR7 antagonists. The developed 2D-QSAR model depicted an excellent correlation coefficient (R2training: 0.86 and R2test: 0.78) between the experimental and estimated activities. The ligand-based drug design approach utilizing the 3D-QSAR model (R2training: 0.95 and R2test: 0.84) demonstrated a significant contribution of electrostatic potential and steric fields towards the TLR7 antagonism. This consolidated approach, along with a pharmacophore model with high correlation (Rtraining: 0.94 and Rtest: 0.92), was used to design quinazoline-core-based hTLR7 antagonists. Subsequently, the newly designed molecules were subjected to molecular docking onto the previously proposed binding model and a molecular dynamics study for a better understanding of their binding pattern. The toxicity profiles and drug-likeness characteristics of the designed compounds were evaluated with in silico ADMET predictions. This ligand-based study contributes towards a better understanding of lead optimization and the future development of potent TLR7 antagonists.

Epitaxial Electrocrystallization of Magnesium via Synergy of Magnesiophilic Interface, Lattice Matching, and Electrostatic Confinement.

Rechargeable magnesium batteries are particularly advantageous for renewable energy storage systems. However, the inhomogeneous Mg electrodeposits greatly shorten their cycle life under practical conditions. Herein, the epitaxial electrocrystallization of Mg on a three-dimensional magnesiophilic host is implemented via the synergy of a magnesiophilic interface, lattice matching, and electrostatic confinement effects. The vertically aligned nickel hydroxide nanosheet arrays grown on carbon cloth (abbreviated as "Ni(OH)2@CC") have been delicately designed, which satisfy the essential prerequisite of a low lattice geometrical misfit with Mg (about 2.8%) to realize epitaxial electrocrystallization. Simultaneously, the ionic crystal nature of Ni(OH)2 displays a periodic and hillock-like electrostatic potential field over its exposed facets, which can precisely capture and confine the reduced Mg0 species onto the local electron-enriched sites at the atomic level. The Ni(OH)2@CC substrate undergoes sequential Mg-ion intercalation, underpotential deposition, and electrocrystallization processes, during which the uniform, lamellar Mg electrodeposits with a locked crystallographic orientation are formed. Under practical conditions (10 mA cm-2 and 10 mAh cm-2), the Ni(OH)2@CC substrate exhibits stable Mg stripping/plating cycle performances over 600 h, 2 orders of magnitude longer than those of the pristine copper foil and carbon cloth substrates.

Finite element approximations to a fourth-order modified Poisson-Fermi equation for electrostatic correlations in concentrated electrolytes

In this paper, both the standard finite element method (FEM) and the mixed FEM are developed for the fourth-order modified Poisson-Fermi equation resulted from the Bazant-Storey-Kornyshev (BSK) theory to account for electrostatic correlations in concentrated electrolytes. Optimal convergence properties are obtained for both FEMs in their respective norms, additionally, the mixed FEM can produce one-order higher approximation accuracy for the electric field in L2 norm than that of the standard FEM, resulting in more accurate approximations to the electrostatic stress and the force of interaction in concentrated electrolytes. All attained theoretical results are validated by numerical experiments. Furthermore, a practical example is studied to validate the necessity of introducing the fourth-order modified Poisson-Fermi equation to describe the electrostatic potential field due to correlation effects by comparing with the classical Poisson equation that accounts for the classical mean-field Poisson-Boltzmann (PB) theory, illustrating that numerical trends obtained from the modified model are all consistent with experimental results under the circumstance of electrostatic correlations in concentrated electrolytes, which however cannot be predicted by the classical model.