Boundary Potential Research Articles

Extension of the Günter Derivatives to the Lipschitz Domains and Application to the Boundary Potentials of Elastic Waves

Regularization techniques for the trace and the traction of elastic waves potentials previously built for domains of the class C^2 are extended to the Lipschitz case. In particular, this yields an elementary way to establish the mapping properties of elastic wave potentials from those of the scalar Helmholtz equation without resorting to the more advanced theory for elliptic systems in the Lipschitz domains. Scalar Gunter derivatives of a function defined on the boundary of a three-dimensional domain are expressed as components (or their opposites) of the tangential vector rotational of this function in the canonical orthonormal basis of the ambient space. This, in particular, implies that these derivatives define bounded operators from H^s to H^{s-1} (0 ≤ s ≤ 1) on the boundary of the Lipschitz domain and can easily be implemented in boundary element codes. Representations of the Gunter operator and potentials of single and double layers of elastic waves in the two-dimensional case are provided.

Extension of the Gnter Derivatives to the Lipschitz Domains and Application to the Boundary Potentials of Elastic Waves

Extension of the Gnter Derivatives to the Lipschitz Domains and Application to the Boundary Potentials of Elastic Waves

A simplified equation of approximate interface profile in stratified coastal aquifers

In this study, we provide a simplified equation with a new concise set of parameters defining the approximate interface profile in stratified coastal aquifers. We derive the solution directly by applying the Dupuit-Forchheimer approximation at the outset, and mathematically prove its sameness for the uniform flow in a vertical plane with the interface profile computed using the comprehensive discharge potential theory by Strack and Ausk (2015). We present a surprising result that interface elevation in the case with a seepage and outflow face at the coastal boundary turns out to be same as in which water table and interface coincides with the coastline. The interface profile is a function of the transmissivity-field centroid elevation and the total transmissivity of the freshwater-flow domain above the interface. We found that the boundary potential at the coast in the discharge-potential theory solution represents the first moment of the transmissivity. We also analyzed the differences in the interface profiles in aquifers with different hydraulic-conductivity contrasts for two sets of boundary conditions—constant head and constant flux. For a given-flux boundary, interface profiles in aquifer configurations with different conductivity contrasts converge in the upper part of the aquifer and diverge at the aquifer bottom, leading to different toe-positions. Conversely, for a given-head boundary, interface profiles in aquifer configurations with different conductivity contrasts significantly differ in the upper part of the aquifer, while converge at the aquifer bottom resulting in the same toe-position. We provide explicit solutions for the toe-position and freshwater discharge in unconfined aquifers, an extension to our previous work for confined aquifers. Insights from the newly identified parameters can also potentially help in reducing the uncertainty in the estimation of the real-world SWI extent and optimize the requirement of the extent of the hydraulic conductivity field characterization.

Solution of Axisymmetric Inhomogeneous Problems with the Markov Chain Monte Carlo

With increasing complexity of EM problems, 1D and 2D axisymmetric approximations in p, z plane are sometimes necessary to quickly solve difficult symmetric problems using limited data storage and within shortest possible time. Inhomogeneous EM problems frequently occur in cases where two or more dielectric media, separated by an interface, exist and could pose challenges in complex EM problems. Simple, fast and efficient numerical techniques are constantly desired. This paper presents the application of simple and efficient Markov Chain Monte Carlo (MCMC) to EM inhomogeneous axisymmetric Laplace’s equations. Two cases are considered based on constant and mixed boundary potentials and MCMC solutions are found to be in close agreement with the finite difference solutions.

Design and Validation of a New Programmable Current Source for Electrical Impedance Tomography Applications

This paper proposed an advanced digital voltage-controlled multi-frequency based constant current source, which is a wide range of loads and high SNR ratio for Electrical Impedance Tomography (EIT) application. In EIT a constant current source is required for injecting a sinusoidal current pulse to the phantom boundary. The boundary potentials are measured by inserting content current from the phantom boundary according to the variation in frequency and current levels. For studying the wide range of tissue conductivity among different type of subjects (the multi-frequency scanning) is desired in medical Electrical impedance tomography. The proposed Current source, which shows that the simulation has good performance at multi-frequency range with accuracy and stability. In proteus simulation software, the results show that the proposed circuit presents a more stable impedance output and the obtained boundary data at multi-frequency for the validation of the obtained data has been shown using suitable image reconstruction algorithm and is found suitable for image reconstruction much easier.

Solid-Contact Ion-Selective Electrodes Comprising Hydrophobic Redox Buffers

A calibration-free measurement with an ionophore-doped polymeric membrane ion-selective electrode requires that the phase boundary potential at the sample/sensing membrane interface is controlled by the activity of the target ion in the sample of interest, while all other phase boundary potentials in the electrochemical cell are constant and long term stable. Historically, the biggest difficulty lies in establishing a reproducible phase boundary potential at the interface of the sensing membrane and the underlying electron conductor. Efforts over several decades to use conducting polymers as an interlayer between the ion-selective membrane and an underlying electron conductor, such as a metal or carbon, have had limited success. While the performance of such devices has been much improved in terms of light sensitivity and hydrophobicity of the conducting polymer layer, devices that can be considered calibration-free are still elusive. To that end, hydrophobic redox buffers have been introduced as an alternative to conducting polymers. While hydrophilic redox buffers play central roles in all living organisms, control many geological and environmental processes, and are often utilized in the laboratory, buffering of redox potentials in hydrophobic media is a topic that has in the past been overlooked. This presentation will address principles for the use of hydrophobic redox buffers, and it will discuss recent examples of hydrophobic redox buffers suitable for the fabrication of ion-selective electrode membranes that are calibration-free. (1) Redox Buffer Capacity of Ion-Selective Electrode Solid Contacts Doped with Organometallic Complexes, Zhen, X. V.; Rousseau, C. R.; Buhlmann, P. Anal. Chem., 2018, 90, 11000-11007. (2) Paper-Based All-Solid-State Ion-Sensing Platform with a Solid Contact Comprising Colloid-Imprinted Mesoporous Carbon and a Redox Buffer, Hu, J.; Zhao, W.; Bühlmann, P.; Stein, A., ACS Appl. Nano Mat. 2018, 1, 293–301.

Optimization of the electric field calculation for a rod-shaped conductor in a uniform electric field

A rod-shaped conductor in a uniform electric field is analyzed based on finite difference method. Most induction charges distribute at the two hemisphere ends, which is similar with two connected conducting spheres in a uniform field. Therefore, the boundary potentials are calculated by multiple image method for the system with two connected conducting spheres. Comparing the results from our method with those from traditional method with constant boundary potentials, our method can improve calculation evidently. Results prove that this method is available and credible, and it can give electric field with high precision.

Changes of the Capacitance and Boundary Potential of a Bilayer Lipid Membrane Associated with a Fast Release of Protons on Its Surface

The kinetics of binding of proton with bilayer lipid membrane (BLM) upon their fast release on the surface of the membrane has been studied by measuring the changes of the capacitance and electrostatic potential of the membrane. The release of proton was a result of excitation of 2-methoxy-5-nitrosulphate (MNPS) molecules, adsorbed on the surface of the membrane, by UV light. The adsorption of anions of MNPS on BLM led to a change of the boundary potential measured either by the inner field compensation method or as a change of ζ-potential of liposomes determined by the dynamic light scattering method. The illumination of BLM with the adsorbed MNPS molecules led to changes of the membrane capacitance and a shift of the boundary potential to positive values. This shift of the boundary potential was due partially to the MNPS decomposition and partially to the binding of protons on the membrane surface. With an increase in the buffer capacity, both the potential jump and the change in capacitance were significantly reduced in magnitude. Restoration of the membrane capacitance and boundary potential after the light flash took about tens of seconds. The changes of the potential and capacitance were observed not only on BLM formed from phospholipids but also on BLM formed from glycerol monooleate. These results are explained assuming that the protons released from MNPS during the flash of light are bound on the surface of the membrane in a layer of oriented water molecules.

A Fast Poisson Solver of Second-order Accuracy for Isolated Systems in Three-dimensional Cartesian and Cylindrical Coordinates

Abstract We present an accurate and efficient method to calculate the gravitational potential of an isolated system in 3D Cartesian and cylindrical coordinates subject to vacuum (open) boundary conditions. Our method consists of two parts: an interior solver and a boundary solver. The interior solver adopts an eigenfunction expansion method together with a tridiagonal matrix solver to solve the Poisson equation subject to the zero boundary condition. The boundary solver employs James’s method to calculate the boundary potential due to the screening charges required to keep the zero boundary condition for the interior solver. A full computation of gravitational potential requires running the interior solver twice and the boundary solver once. We develop a method to compute the discrete Green’s function in cylindrical coordinates, which is an integral part of the James algorithm to maintain second-order accuracy. We implement our method in the Athena++ magnetohydrodynamics code and perform various tests to check that our solver is second-order accurate and exhibits good parallel performance.

Analytic Wigner distribution function for tunneling and trajectory models

The Wigner function is assembled from analytic wave functions for a one-dimensional closed system (well with infinite barriers). A sudden change in the boundary potentials allows for the investigation of time-dependent effects in an analytically solvable model. A trajectory model is developed to account for tunneling when the barrier is finite. The behavior of the density (the zeroth moment of the Wigner function) after an abrupt change in potential shows net accumulation and depletion over time for a weighting of energy levels characteristic of the supply function in field emission. However, for a closed system, the methods have application to investigations of tunneling and transmission associated with field and photoemission at short time scales.

Short-range combined water model

The short-range combined water model (SRCW model) for the calculation of the hydration free energy of the non-polar solutes is presented. A mixed explicit/implicit representation of the solvent is used in the model. A thermodynamic basis for the boundary potential between explicit and implicit parts of the simulation area is derived. A simple functional form for the boundary potential minimizing the water density fluctuations in the explicit part is found. Hydration free energies of the model solutes are calculated in the frame of the developed model. Obtained values are in the good agreement with results of the Monte Carlo simulation using the periodic boundary conditions.

Specific ion effects on electrocapillarity in aqueous electrolytes confined within nanochannels

A nanoslit is a long, extremely narrow (nanometers apart) opening between two parallel plates. An overlapped electric double layer is formed when an electrolyte is present inside the slit and there exist distributions of the osmotic pressure and the Maxwell stress across the nanoslit, which lead to the electrocapillarity effect. This feature can be incorporated with the specific ion effects by considering the nonelectrostatic interactions between ions and confining walls, as they significantly influence the potential, electric field, and ion distributions across the nanoslit. In the present work, the electromechanical approach is integrated with the concept of specific ion effects to analyze the behavior of an electrolyte confined in a one-dimensional nanochannel. For a nanochannel, the average outward normal stress exerted on the cross section of a channel (P_{zz}[over ¯]) can be regarded as a measure of electrocapillarity and it is the driving force of the flow. This electrocapillarity measure is analyzed by using the solution of the modified Poisson-Boltzmann equation as a function of the bulk concentration of the electrolyte, the boundary potential, and most importantly, the ion-specific interfacial interactions. The significance of the present work can be manifested by the increasing usage of extremely narrow channels in nanoscaled systems, which will require proper consideration of specific ion effects in determining the behavior of the confined electrolyte.

Damage Mechanisms of Polymer Impregnated Carbon Textiles Used as Anode Material for Cathodic Protection

Carbon textiles as anode material for cathodic corrosion protection (CP) have been used in several reinforced steel structures. However, experience with durability is limited. To date, various influencing factors have been discovered and systematic tests on different carbon textiles with different impregnation materials in various environmental media have been carried out and considered the degradation of the impregnation materials. In this work the boundary potentials are determined at which the impregnation and sizing is destroyed under anodic polarization and the damage mechanisms are described.

Nanoscale charge transport and local surface potential distribution to probe defect passivation in Ag doped Cu2ZnSnS4 absorbing layer

The performance of earth abundant Cu2ZnSnS4 (CZTS) material is limited by high deficit of open circuit voltage (VOC) which is mainly due to the easy formation of CuZn antisite defects. Suppression of CuZn defects is thus inevitably required for further developments in CZTS based solar cells. We studied systematic increase of Ag doping in CZTS thin film and investigated the nanoscale electrical properties using Kelvin probe force microscopy and current sensing atomic force microscopy (CAFM) to probe CuZn defects. Crystallographic analysis indicated the successful partial substitution of Cu+ ions by large size Ag+ ions. The considerable decrease in grain boundary potential from 66.50 ± 5.44 mV to 13.50 ± 2.61 mV with Ag doping, suggesting the substantial decrease in CuZn defects. Consequently, CAFM measurement confirms the remarkable increment in minority carrier current with Ag doping and their local mobility in CZTS layer. Finally, the lower persistent photoconductivity and fast decay response of photogenerated carriers for Ag doped CZTS photodetector further validate our results. This study provides a fresh approach of controlling deleterious CuZn defects in CZTS by tuning Ag content that may guide researchers to develop next generation high-performance CZTS based solar cells.

Active contour method for ILM segmentation in ONH volume scans in retinal OCT.

The optic nerve head (ONH) is affected by many neurodegenerative and autoimmune inflammatory conditions. Optical coherence tomography can acquire high-resolution 3D ONH scans. However, the ONH's complex anatomy and pathology make image segmentation challenging. This paper proposes a robust approach to segment the inner limiting membrane (ILM) in ONH volume scans based on an active contour method of Chan-Vese type, which can work in challenging topological structures. A local intensity fitting energy is added in order to handle very inhomogeneous image intensities. A suitable boundary potential is introduced to avoid structures belonging to outer retinal layers being detected as part of the segmentation. The average intensities in the inner and outer region are then rescaled locally to account for different brightness values occurring among the ONH center. The appropriate values for the parameters used in the complex computational model are found using an optimization based on the differential evolution algorithm. The evaluation of results showed that the proposed framework significantly improved segmentation results compared to the commercial solution.

Radiation and Exciting Forces of Axisymmetric Structures with a Moonpool in Waves

A highly efficient “hybrid integral-equation method” for computing hydrodynamic added-mass, wave-damping, and wave-exciting force of general body geometries with a vertical axis of symmetry is presented. The hybrid method utilizes a numerical inner domain and a semi-infinite analytical outer domain separated by a vertical cylindrical matching boundary. Eigenfunction representation of velocity potential is used in the outer domain; the three-dimensional potential in the inner domain is solved using a “two-dimensional” boundary element method with ring sources and ring dipoles to exploit the body symmetry for efficiency. With proper solution matching at the common boundary, both radiation and diffraction potentials can be solved efficiently while satisfying the far-field radiation condition exactly. This method is applied to compute the hydrodynamic properties of two different body geometries: a vertical-walled moonpool with a bottom plate that restricts the opening and a spar-like structure with a diverging bottom opening inspired by designs of floating Oscillating Water Columns. The effects of the size of the bottom opening on the hydrodynamic properties of the body are investigated for both geometries. The heave motion of the floater as well as the motion of the internal free surface under incident wave excitation are computed and studied for the spar-like structure.

CX-5461-loaded nucleolus-targeting nanoplatform for cancer therapy through induction of pro-death autophagy

Various drugs have been designed in the past to act on intracellular targets. For the desired effects to be exerted, these drugs should reach and accumulate in specific subcellular organelles. CX-5461 represents a potent small-molecule inhibitor of rRNA synthesis that specifically inhibits the transcription driven by RNA polymerase (Pol) I and induces tumor cell death through triggering a pro-death autophagy. In the current study an innovative kind of CX-5461-loaded mesoporous silica nano-particles enveloped by polyethylene glycol (PEG), polydopamine (PDA) and AS-1411 aptamer (MSNs-CX-5461@PDA-PEG-APt) with the aim of treating cancer cells was constructed, in which the high-surface-area MSNs allowed for high drug loading, PDA acted as gatekeeper to prevent the leakage of CX-5461 from MSNs, PEG grafts on PDA surfaces increased the stable and biocompatible property in physiological condition, and AS-1411 aptamer promoted the nucleolar accumulation of CX-5461. MSNs-CX-5461@PDA-PEG-APt was characterized regarding releasing characteristics, steadiness, encapsulation of drugs, phase boundary potential as well as sizes of particles. Expectedly, In vitro assays showed that aptamer AS-1411 significantly increased the nucleolar accumulation of CX-5461. The aptamer-tagged CX-5461-loaded MSNs demonstrated to be more cytotoxic to cervical cancer cells compared to the control MSNs, due to relatively strong inhibition of rRNA transcription and induction of pro-death autophagy. The in vivo treatment with AS-1411-tagged CX-5461-loaded MSNs showed a stronger distribution in tumor tissues by animal imaging assay and a significantly higher inhibition effect on the growth of HeLa xenografts compared to AS-1411-untagged CX-5461-loaded MSNs. In addition, histology analysis indicated that MSNs-CX-5461@PDA-PEG-APt did not exhibit any significant toxicity on main organs. These results collectively suggested that MSNs-CX-5461@PDA-PEG-APt represents both a safe and potentially nucleolus-targeting anti-cancer drug. Statement of SignificanceMany drugs function in specific subcellular organelles. CX-5461 is a specific inhibitor of nucleolar rRNA synthesis. Here, we reported a novel aptamer-tagged nucleolus-targeting CX-5461-loaded nanoparticle, which specifically accumulated in nucleoli and significantly inhibited the tumor growth in vitro and in vivo through inhibiting rRNA transcription and triggering a pro-death autophagy.

Application of the interface equilibria-triggered dynamic diffusion model of the boundary potential for the numerical simulation of neutral carrier-based ion-selective electrodes response

It is shown that a simple dynamic diffusion model of the boundary potential based on a separate, step-by-step, account of ion transfer across the membrane/aqueous solution interface and the diffusion processes within both phases which was proposed earlier for describing the response of ionophore-free membranes, can be successfully used for ionophore-based membranes as well. The model makes it possible to carry out both separate and joint account of the effects of co-extraction, transmembrane transport and ion exchange on the boundary potential and retains robustness in all the variants studied. The model adequately describes the ionophore-based electrode response over the entire range of concentrations and allows one to clearly demonstrate the dependence of lower detection limit on such parameters as the diffusion coefficients and the concentration of electroactive substances in the membrane phase, the thickness of the diffusion layer in the sample solution, the duration of the measurement, and the composition of the internal reference solution. The results of numerical simulation are in good agreement with the experimental data presented in the literature. As all the factors of influence considered above can easily be regulated in more or less wide limits, but at the same time, an estimation of their cumulative effect is not always possible on an intuitive level, the present model can be of practical interest for justifying the ways of optimizing the design of the ISE and the algorithm for performing measurements in solving specific analytical problems.

Redox Buffer Capacity of Ion-Selective Electrode Solid Contacts Doped with Organometallic Complexes.

While ion-selective electrodes (ISEs) with inner filling solutions are used widely, solid-contact ISEs are better suited for miniaturization and mass manufacturing. Calibration-free measurements with such electrodes require the reproducible control of the phase boundary potential between the ion-selective membrane and the underlying electron conductor. The most promising approach to achieve this goal is based on redox buffers incorporated into the ion-selective membrane. Here we introduce the theory and present experimental data for Co(III), Co(II), Ru(II), Fe(II), and Os(II) compounds that show quantitatively how the phase boundary potential at a solid contact doped with redox-active compounds is affected by weighing errors, reagent impurities, and redox-active interferents. Perhaps surprisingly, theory predicts that there is only a minimal dependence of the phase boundary potential on the ratio of the concentrations of a pure oxidized and a pure reduced compounds if those two compounds are not a redox couple. However, theory predicts that even small redox-active impurities of those compounds shift the phase boundary potential drastically. Experimentally, a surprisingly good in-batch reproducibility was observed by us and others for solid contacts prepared to contain either only the reduced or only the oxidized species of a redox couple. This can be explained by redox-active impurities and is unlikely to be repeatable when different suppliers of reagents are used or long-term experiments are performed. This work confirms that the preferred approach to calibration-free sensing is based on redox buffers that comprise the reduced and oxidized species of a redox couple in well-controlled concentrations.

Many-body wave functions for correlated systems in magnetic fields: Monte Carlo simulations in the lowest Landau level

We put forward possible wave functions for quantum Hall states in the lowest Landau level. These were deduced from the topological approach based on the relation between braid groups and the quantum statistics, as well as the commensurability condition unavoidable for collective states in magnetic fields. In this paper we demonstrate that the -field imposes restrictions on braid trajectories (i.e. elements of the full braid group). This results in the appearance of cyclotron subgroups, instead of the full braid group, for certain filling factors. The fermion representation of cyclotron subgroups defines transformations of wave functions in the quantum Hall regime. Hence, it sets quantum statistics (transformations of under exchanges of arguments), which is unavoidable for collective states (in compliance with the framework of Feynman’s path integrals). Finally, the topological approach allows to define the hierarchy of fillings in the lowest Landau level, which agree with the hierarchy observed in quantum Hall devices (i.e. in transport measurements).The symmetry of a many-body wave function (i.e. quantum statistics) is always determined by a 1D unitary representation of the system’s braid group. Using this topologically-originated property, we demonstrate that many-body wave functions for selected fillings of the lowest Landau level may not be purely antisymmetric. Only systems composed of fermions are investigated.Additionally, we present Monte Carlo calculations in a disc geometry, which remain in a nice agreement with predictions of exact diagonalizations (expected values of potential energy and pair distribution functions are presented). No boundary potential is assumed.