Planar Disk Research Articles

Planar Disk μ-Aptasensors by Monolayer Assembly in a Dissolving Microdroplet.

Electrochemical aptamer-based sensors provide a highly modular platform for real-time monitoring of small molecules. Their ability to selectively recognize target molecules in complex environments like biological fluids makes them an attractive technology for the analysis of micro- and nanoscale systems. The signal-to-noise of the measurement depends on the electroactive surface (i.e., how many aptamers one can place), which has previously precluded miniaturization of aptamer-based sensors to planar disk ultramicroelectrodes (r ∼ 5-10 μm). Here, we employ a concentration enrichment strategy based on the active dissolution of an aqueous, aptamer-containing microdroplet on an ultramicroelectrode submerged in an organic continuous phase (1,2-dichloroethane). We show consistent voltammetric signal increase as a function of droplet lifetime, indicating the successful immobalization of the thiol-terminated aminoglycoside aptamers to the electrode surface. We observe a diagnostic methylene blue peak and 10-fold increase in current magnitude as compared to bare microelectrodes. We report robust sensor behavior with a linear dynamic range extending from milli- to micromolar concentrations of kanamycin in buffer. This research offers a successful method for optimized electrochemical aptamer-based sensor fabrication and miniaturization on ultramicroelectrodes without the need for electrode surface area enhancement.

Measurement of Zinc Ions in Seawater Samples Using a Microfluidic System Based on the GR/CeO2/Nafion Material.

Considering that heavy-metal contamination of seawater is getting worse, building a quick, accurate and portable device for detecting trace zinc in seawater in real time would be very beneficial. In this work, a microfluidic system was developed that includes a planar disc electrode, a micro-cavity for detection, an electrochemical workstation, a computer, a container for waste liquid reprocessing, an external pipeline and other components as well as a graphene/cerium oxide/nano-cerium oxide/Nafion composite membrane was used to modify the planar disc electrode (GR/CeO2/Nafion/Au) to investigate the electrochemical behaviour of Zn(II) using cyclic voltammetry, square-wave voltammetry and orthogonal test methods. Under optimal experimental conditions, the peak reaction current of Zn(II) showed a good linear relationship with the concentration of Zn(II) in the range of 1-900 μg/L with a correlation coefficient of 0.998, and the detection limit of the method was 0.87 μg/L. In addition, the microfluidic system had good stability, reproducibility and anti-interference. The system was used for determining zinc ions in real seawater samples, and the results were very similar to those of inductively coupled plasma-emission spectrometry, demonstrating the practicality of the system for the detection of trace zinc.

How does the blade element momentum method see swept or prebent blades?

The blade element momentum (BEM) method is among the mostly used engineering aerodynamic models for wind turbine rotors. Even though the BEM method is strictly only applicable to straight blades forming a planar rotor, it is in practice used for load calculation and design optimization of blades with relatively large sweep, prebend or coning. The present work aims to answer the question: How does the BEM method see swept or prebent blades? The blade element part of the method can be adapted for swept or prebent blades by projecting the velocity and loads between the 2-D airfoil section and the 3-D blade geometry under the cross-flow principle. However, momentum theory considers the 3-D wake and the induction of a planar actuator disc with straight blades. There could be significant differences between the results calculated from different implementations of the BEM method, while the details of the implementations are often omitted in the literature. In the present work, a consistent implementation including the definition of airfoil section alignments and the coordinate systems is provided. It is shown that for a given circulation distribution, the BEM method will predict approximately the same local aerodynamic loads for non-straight blades as if the blades were straight and the rotor was planar. This means using the BEM method to perform aerodynamic optimization of modern rotors with curved blades and/or rotors that are not planar can only have little meaningful result. In order to model the impact of the wake geometry on the induction, more advanced models that take into account the wake geometry on the induction are necessary.

Electronic Control of the Position of the Pb Atom on the Surface of B8 Borozene in the PbB8 Cluster.

Spontaneous symmetry-breaking is common in chemical and physical systems. Here, we show that by adding an electron to the C7v PbB8 cluster, which consists of a planar B8 disk with the Pb atom situated along the C7 axis, the Pb atom spontaneously moves to the off-axis position in the PbB8- anion. Photoelectron spectroscopy of PbB8- reveals a broad ground-state transition and a large energy gap, suggesting a highly stable closed-shell PbB8 borozene complex and a significant geometry change upon electron detachment. Quantum chemistry calculations indicate that the lowest unoccupied molecular orbital of the C7v PbB8 cluster is a degenerate π orbital mainly consisting of the Pb 6px and 6py atomic orbitals. Occupation of one of the 6p orbitals spontaneously break the C7v symmetry in the anion due to the Jahn-Teller effect. The large amplitude of the position change of Pb in PbB8- relative to PbB8 is surprising owing to bonding interactions between the Pb 6p orbital with the π orbital of the B8 borozene.

A Planar Disk Electrode Chip Based on MWCNT/CS/Pb2+ Ionophore IV Nanomaterial Membrane for Trace Level Pb2+ Detection.

Unlike conventional lead ion (Pb2+) detecting methods, electrochemical methods have the attractive advantages of rapid response, good portability and high sensitivity. In this paper, a planar disk electrode modified by multiwalled carbon nanotube (MWCNTs)/chitosan (CS)/lead (Pb2+) ionophore IV nanomaterial and its matched system are proposed. This system presented a good linear relationship between the concentration of Pb2+ ions and the peak current in differential pulse stripping voltammetry (DPSV), under optimized conditions of -0.8 V deposition potential, 5.5 pH value, 240 s deposition time, performed sensitive detection of Pb2+ within sensitivity of 1.811 μA · μg-1 and detection limit of 0.08 μg · L-1. Meanwhile, the results of the system in detecting lead ions in real seawater samples are highly similar to that of inductively coupled plasma emission spectrometer (ICP-MS), which proved a practicability for the system in detection of trace-level Pb2+.

Collective bending motion of a two-dimensionally correlated bowl-stacked columnar liquid crystalline assembly under a shear force.

Stacked teacups inspired the idea that columnar assemblies of stacked bowl-shaped molecules may exhibit a unique dynamic behavior, unlike usual assemblies of planar disc- and rod-shaped molecules. On the basis of the molecular design concept for creating higher-order discotic liquid crystals, found in our group, we synthesized a sumanene derivative with octyloxycarbonyl side chains. This molecule forms an ordered hexagonal columnar mesophase, but unexpectedly, the columnar assembly is very soft, similar to sugar syrup. It displays, upon application of a shear force on solid substrates, a flexible bending motion with continuous angle variations of bowl-stacked columns while preserving the two-dimensional hexagonal order. In general, alignment control of higher-order liquid crystals is difficult to achieve due to their high viscosity. The present system that brings together higher structural order and mechanical softness will spark interest in bowl-shaped molecules as a component for developing higher-order liquid crystals with unique mechanical and stimuli-responsive properties.

The Sobolev Jordan-Schönflies problem

We consider the planar unit disk D as the reference configuration and a Jordan domain Y as the deformed configuration, and study the problem of extending a given boundary homeomorphism φ:∂D→onto∂Y as a Sobolev homeomorphism of the complex plane. Investigating such a Sobolev variant of the classical Jordan-Schönflies theorem is motivated by the well-posedness of the related pure displacement variational questions in the theory of Nonlinear Elasticity (NE) and Geometric Function Theory (GFT). Clearly, the necessary condition for the boundary mapping φ to admit a W1,p-Sobolev homeomorphic extension is that it first admits a continuous W1,p-Sobolev extension. For an arbitrary target domain Y this, however, is not sufficient. Indeed, first for each p<∞ we construct a Jordan domain Y and a homeomorphism φ:∂D→onto∂Y which admits a continuous W1,p-extension but does not even admit a W1,1-homeomorphic extension. Second, for a quasidisk target Y and the whole range of p, we prove that a boundary homeomorphism φ:∂D→onto∂Y admits a Wloc1,p-homeomorphic extension to C if and only if it admits a W1,p-extension to the unit disk. Quasidisks have been a subject of intensive study in GFT. They do not allow for singularities on the boundary such as cusps. Third, for any power-type cusp target there is a boundary homeomorphism from the unit circle whose harmonic extension has finite Dirichlet energy but does not have a homeomorphic extension in W1,2(D,C). Surprisingly, the Dirichlet integral (p=2) plays a unique role for the Sobolev Jordan-Schönflies Problem in the case of cusp targets. Even more, fourth we prove that if the target Y has piecewise smooth boundary, p≠2 and φ:∂D→onto∂Y has a W1,p-Sobolev extension to D, then it admits a homeomorphic extension to C in Wloc1,p(C,C). Fifth, if in addition Y is quasiconvex, then the one-sided Sobolev Jordan-Schönflies problem has a solution when p=2. Indeed, we show that the harmonic extension of φ:∂D→onto∂Y has a finite Dirichlet integral if and only if φ admits a homeomorphic extension h:D‾→ontoY‾ with finite Dirichlet energy.

An inequality of Bessel functions and applications to transcritical bifurcation problems of nonlinear elliptic equations

We prove a weighted integral inequality of the Bessel function of zero order, which implies the positivity of the integral of the cube of nodal radial eigenfunctions of the Laplacian operator in the planar disk. This solves an open problem in Bonheure et al. (2016) and Corsato et al. (2020). The positivity plays a crucial role in transcritical bifurcation problems of nodal radial solutions of nonlinear elliptic equations.

A review of different mascon approaches for regional gravity field modelling since 1968

Abstract. The geodetic and geophysical literature shows an abundance of mascon approaches for modelling the gravity field of the Moon or Earth on global or regional scales. This article illustrates the differences and similarities between the methods, which are labelled as mascon approaches by their authors. Point mass mascons and planar disc mascons were developed for modelling the lunar gravity field from Doppler tracking data. These early models had to consider restrictions in observation geometry, computational resources or geographical pre-knowledge, which influenced the implementation. Mascon approaches were later adapted and applied for the analysis of GRACE observations of the Earth's gravity field, with the most recent methods based on the simple layer potential. Differences among the methods relate to the geometry of the mascon patches and to the implementation of the gradient and potential for field analysis and synthesis. Most mascon approaches provide a direct link between observation and mascon parameters – usually the surface density or the mass of an element – while some methods serve as a post-processing tool of spherical harmonic solutions. This article provides a historical overview of the different mascon approaches and sketches their properties from a theoretical perspective.

A Tutorial on Calculating Space-Charge-Limited Current Density for General Geometries and Multiple Dimensions

Space-charge-limited current (SCLC) remains a critical issue across material phases (vacuum, gas, liquids, and solids) and timescales. The solution for one-dimensional (1D), planar SCLC density (SCLCD), referred to as the Child–Langmuir (CL) law, remains the common benchmark for these calculations; however, practical devices are neither 1D nor planar. This article reviews recent progress on developing approaches to derive SCLCD for nonplanar and multidimensional diodes. First, we summarize the application of variational calculus (VC) to derive 1D SCLCD based on minimizing the current in the gap. We also describe the nuances of applying Poisson’s equation to 1D nonplanar diodes compared to three-dimensional (3D) geometries. We next discuss the application of conformal mapping (CM) to extend 1D, planar SCLCD to more complicated 1D geometries, including a detailed justification of the application of CM for solving Poisson’s equation. We then discuss the application of vacuum capacitance and a generalized relationship between the electric potential in vacuum and space-charge-limited (SCL) diodes to derive exact analytic solutions for SCLCD in two-dimensional (2D) and 3D diodes with emission from the full cathode. We further relate the SCLCD for 3D planar square and disk electrodes across a wide range of electrode sizes. We conclude by discussing future theoretical and practical extensions of these approaches.

Durability of plasma sprayed Thermal Barrier Coatings with controlled properties part II: Effects of geometrical curvature

The present investigation elucidates the effects of substrate curvature on the durability of Air Plasma Sprayed (APS) Thermal Barrier Coatings (TBCs). Traditionally, planar disk specimens are utilized in Furnace Cycle Testing (FCT). In most cases, delamination is initiated at the disk's free edge and then propagates along the TBC-bond coat interface. However, in turbine components (e.g., blades/vanes), they lack significant free edges and the coatings are deposited on non-flat surfaces of varying radii of curvature. These geometrical discrepancies imply significant differences in the stress states as compared to planar disk specimens. Therefore, the part geometry inevitably affects the TBC failure mechanisms in the turbine system, and consequently influences TBC durability. Nevertheless, these effects have not been fully explored in the past, despite the anecdotal knowledge which suggests the leading edge of turbine blades to be one of the most common failure/spallation locations. In this study, representative TBC systems were deposited onto superalloy disks with flat substrate and rods with curved substrate. The experimental results from FCT suggest TBC durability on rods is significantly lower than when sprayed on disks. Furthermore, the durability of TBCs on rods appears to increase with higher porosity, which is contradictory to reported trends for TBCs on disks. In addition, the effects of various bond coats are not consistent with those observed in disks. To clarify the underlying effects of curved geometries, detailed stress analyses were performed. They revealed a state of thermal stresses which is unique to curved geometries. It was found that TBC on rods experience tensile radial stresses as well as tensile hoop stresses during the cooling. These stresses result in a complex interplay in failure processes in rods, which explains the different observed trends in the durability from those obtained with disks.

Durability of plasma sprayed thermal barrier coatings with controlled properties part I: For planar disk substrates

Thermal Barrier Coatings (TBCs) have been qualified for their thermo-mechanical performance and durability using Furnace Cycle Testing (FCT) for decades. FCT provides guidance toward materials and process improvements. Although FCT is a relatively straightforward test, the interpretation can often be subject to uncertainty, making it difficult to link test results directly to engine performance. This is because in FCT, the coating and substrate are isothermally treated, while real turbine components experience strong thermal gradients and time transients. Gradient testing can be time-consuming and expensive, thus FCT tests provide a cost-effective first-order confidence screening for development.

Development of an L-band resonator optimized for fast scan EPR imaging of the mouse head.

To develop a novel resonator for high-quality fast scan electron paramagnetic resonance (EPR) and EPR/NMR co-imaging of the head and brain of mice at 1.25 GHz. Resonator dimensions were scaled to fit the mouse head with maximum filling factor. A single-loop 6-gap resonator of 20 mm diameter and 20 mm length was constructed. High resonator stability was achieved utilizing a fixed position double coupling loop. Symmetrical mutually inverted connections rendered it insensitive to field modulation and fast scan. Coupling adjustment was provided by a parallel-connected variable capacitor located at the feeding line at λ/4 distance. To minimize radiation loss, the shield around the resonator was supplemented with a planar conductive disc that focuses return magnetic flux. Coupling of the resonator loaded with the mouse head was efficient and easy. This resonator enabled high-quality in vivo 3D EPR imaging of the mouse head following intravenous infusion of nitroxide probes. With this resonator and rapid scan EPR system, 4 ms scans were acquired in forward and reverse directions so that images with 2-scan 3,136 projections were acquired in 25 s. Head images were achieved with resolutions of 0.4 mm, enabling visualization of probe localization and uptake across the blood-brain barrier. This resonator design provides good sensitivity, high stability, and B1 field homogeneity for in vivo fast scan EPR of the mouse head and brain, enabling faster measurements and higher resolution imaging of probe uptake, localization, and metabolism than previously possible.

Understanding charge transfer on the clinically used conical Utah electrode array: charge storage capacity, electrochemical impedance spectroscopy and effective electrode area

Objective. The Utah electrode is used for pre/clinical studies on neural recording and stimulation. Anecdotal and empirical reports on their performance have been made, resulting in variable testing methods. An in depth investigation was performed to understand the electrochemical behaviour and charge transfer mechanisms occurring on these clinically important electrodes. The impact of electrode geometry and material on performance was determined. Approach. Platinum and iridium electrodes were assessed by cyclic voltammetry and electrochemical impedance spectroscopy. The effective electrode area was measured by reduction of Ru(NH3)6 3+. Main results. Pristine Utah electrodes have little to no oxide present and the surface roughness is less than the diffusion length of Ru(NH3)6 3+ during voltammetry, which was ∼30 µm. Pristine iridium electrodes pass charge through capacitance and oxide formation. Hydride and anion adsorption occurs on the platinum electrode. Anodic current oxidises both metal surfaces, altering the charge transfer mechanisms at the electrode-solution interface. Charge storage capacity depends on measurement technique and electrode structure, this simplified number ignores more detailed information on charge transfer mechanisms that can be obtained from cyclic voltammetry. Electrode oxidation increases pseudocapacitance, reducing impedance. Charge transfer was non-homogeneous, most likely due to the electrode geometry enhancing charge density at the electrode tip and base. Oxidation of the electrode surface enhanced charge transfer inhomogeneity. The effective electrode area could be measured by reduction of Ru(NH3)6 3+ and calculated with a finite cone geometry. Significance. Increasing electrode pseudocapacitance, demonstrated by metal oxidation, reduces impedance. Increasing electrode capacitance offers a potential route to reducing thermal noise and increasing signal-to-noise ratio of neural recording. The effective electrode area of conical electrodes can be measured. The charge density of the conical electrode was greater than expected compared to a planar disc electrode, indicating modification of electrode geometry can increase an electrodes safe charge injection capacity. in vivo electrochemical measurements often do not include sufficient details to understand the electrode behaviour. Electrode oxidation most likely accounts for a significant amount of variation in previously published Utah electrode impedance data.

Increasing the rate of the hydrogen evolution reaction in neutral water with protic buffer electrolytes

Electrocatalytic generation of H2 is challenging in neutral pH water, where high catalytic currents for the hydrogen evolution reaction (HER) are particularly sensitive to the proton source and solution characteristics. A tris(hydroxymethyl)aminomethane (TRIS) solution at pH 7 with a [2Fe-2S]-metallopolymer electrocatalyst gave catalytic current densities around two orders of magnitude greater than either a more conventional sodium phosphate solution or a potassium chloride (KCl) electrolyte solution. For a planar polycrystalline Pt disk electrode, a TRIS solution at pH 7 increased the catalytic current densities for H2 generation by 50 mA/cm2 at current densities over 100 mA/cm2 compared to a sodium phosphate solution. As a special feature of this study, TRIS is acting not only as the primary source of protons and the buffer of the pH, but the protonated TRIS ([TRIS-H]+) is also the sole cation of the electrolyte. A species that is simultaneously the proton source, buffer, and sole electrolyte is termed a protic buffer electrolyte (PBE). The structure-activity relationships of the TRIS PBE that increase the HER rate of the metallopolymer and platinum catalysts are discussed. These results suggest that appropriately designed PBEs can improve HER rates of any homogeneous or heterogeneous electrocatalyst system. General guidelines for selecting a PBE to improve the catalytic current density of HER systems are offered.

Rigidity results of free boundary maximal hypersurfaces in the region bounded by a de Sitter space

This paper provides the rigidity results of free boundary maximal hypersurfaces in a region bounded by a de Sitter space in the Lorentz–Minkowski space. First, it is proved that any smooth, compact free boundary maximal hypersurface in a de Sitter ball is the spacelike coordinate planar disk passing through the center of the de Sitter space. Second, a smooth, noncompact, complete free boundary maximal hypersurface in the exterior of a de Sitter ball is considered. For maximal hypersurfaces with one planar end in the exterior of a de Sitter ball, every complete noncompact free boundary maximal hypersurface is shown to be a part of the spacelike coordinate hyperplane.

Sobolev homeomorphic extensions onto John domains

Given the planar unit disk as the source and a Jordan domain as the target, we study the problem of extending a given boundary homeomorphism as a Sobolev homeomorphism. For general targets, this Sobolev variant of the classical Jordan-Schöenflies theorem may admit no solution - it is possible to have a boundary homeomorphism which admits a continuous W1,2-extension but not even a homeomorphic W1,1-extension. We prove that if the target is assumed to be a John disk, then any boundary homeomorphism from the unit circle admits a Sobolev homeomorphic extension for all exponents p<2. John disks, being one sided quasidisks, are of fundamental importance in Geometric Function Theory.

Instability of non-Keplerian warped discs

ABSTRACT Many accretion discs are thought to be warped. Recent hydrodynamical simulations show that (i) discs can break into distinct planes when the amplitude of an imposed warp is sufficiently high and the viscosity sufficiently low, and that (ii) discs can tear up into discrete rings when an initially planar disc is subject to a forced precession. Previously, we investigated the local stability of isolated, Keplerian, warped discs in order to understand the physics causing an accretion disc to break into distinct planes, finding that antidiffusion of the warp amplitude is the underlying cause. Here, we explore the behaviour of this instability in disc regions where the rotation profile deviates from Keplerian. We find that at small warp amplitudes non-Keplerian rotation can stabilize the disc by increasing the critical warp amplitude for instability, while at large warp amplitudes non-Keplerian rotation can lead to an increased growth rate for discs that are unstable. Tidal effects on discs in binary systems are typically weak enough such that the disc remains close to Keplerian rotation. However, the inner regions of discs around black holes are strongly affected, with the smallest radius at which the disc can break into discrete planes being a function of the black hole spin. We suggest that interpreting observed frequencies in the power spectra of light curves from accreting compact objects as nodal and apsidal precession of discrete orbits requires an instability that can break the disc into discrete rings such as the one explored here.

Combinatorial Construction of Seamless Parameter Domains

AbstractThe problem of seamless parametrization of surfaces is of interest in the context of structured quadrilateral mesh generation and spline‐based surface approximation. It has been tackled by a variety of approaches, commonly relying on continuous numerical optimization to ultimately obtain suitable parameter domains. We present a general combinatorial seamless parameter domain construction, free from the potential numerical issues inherent to continuous optimization techniques in practice. The domains are constructed as abstract polygonal complexes which can be embedded in a discrete planar grid space, as unions of unit squares. We ensure that the domain structure matches any prescribed parametrization singularities (cones) and satisfies seamlessness conditions. Surfaces of arbitrary genus are supported. Once a domain suitable for a given surface is constructed, a seamless and locally injective parametrization over this domain can be obtained using existing planar disk mapping techniques, making recourse to Tutte's classical embedding theorem.

Developing a Parametric 3D Face Model Editing Algorithm

In the fields of computer graphics and computer vision, a great amount of research and analysis has been conducted on expression-carrying face models. How to construct more realistic and effective 3D face models has become an immense challenge to researchers. This paper proposes a parametric 3D face model editing algorithm based on existing 3D face models. The algorithm takes a number of existing 3D face models with different expressions as input, edits the models through mostly through model deformation and interpolation, and generates a new 3D face model. In particular, the face model editing process begins with selecting multiple face models with different expressions as input. Second, with one of the selected models as the source model and others as the target models, the source model and all target models are registered one by one; meanwhile, the vertex correspondence between the registered models is established. Third, the selected 3D models are parameterized to a planar disc through quasi-conformal mapping. Fourth, relying on the vertex correspondence, a set of corresponding control points between different models are established. The model is then deformed and interpolated under the guidance of the control points and by using the quasi-conformal iteration method, which produces the 2D face models with transitional expressions between the source model and the target models. Finally, the 2D models are restored to the corresponding 3D face models using the model restoration algorithm. Additionally, this paper proposes to use the Beltrami coefficient to guide the quasi-conformal iteration in performing the mapping between two planes. This coefficient then serves as a measure to evaluate the similarity between the edited model and the original one. The proposed algorithm has been evaluated through extensive experiments. The results suggest that compared with existing editing methods, the proposed method is more effective and efficient in constructing various 3D face models.