Uniform Conductivity Research Articles

An Iterative Method for Problems with Multiscale Conductivity

A model with its conductivity varying highly across a very thin layer will be considered. It is related to a stable phantom model, which is invented to generate a certain apparent conductivity inside a region surrounded by a thin cylinder with holes. The thin cylinder is an insulator and both inside and outside the thin cylinderare filled with the same saline. The injected current can enter only through the holes adopted to the thin cylinder. The model has a high contrast of conductivity discontinuity across the thin cylinder and the thickness of the layer and the size of holes are very small compared to the domain of the model problem. Numerical methods for such a model require a very fine mesh near the thin layer to resolve the conductivity discontinuity. In this work, an efficient numerical method for such a model problem is proposed by employing a uniform mesh, which need not resolve the conductivity discontinuity. The discrete problem is then solved by an iterative method, where the solution is improved by solving a simple discrete problem with a uniform conductivity. At each iteration, the right-hand side is updated by integrating the previous iterate over the thin cylinder. This process results in a certain smoothing effect on microscopic structures and our discrete model can provide a more practical tool for simulating the apparent conductivity. The convergence of the iterative method is analyzed regarding the contrast in the conductivity and the relative thickness of the layer. In numerical experiments, solutions of our method are compared to reference solutions obtained from COMSOL, where very fine meshes are used to resolve the conductivity discontinuity in the model. Errors of the voltage in L2 norm follow O(h) asymptotically and the current density matches quitewell those from the reference solution for a sufficiently small mesh size h. The experimental results present a promising feature of our approach for simulating the apparent conductivity related to changes in microscopic cellular structures.

Homogeneous bilayer graphene film based flexible transparent conductor

Graphene is considered as a promising candidate to replace conventional transparent conductors due to its low opacity, high carrier mobility and flexible structure. Multi-layer graphene or stacked single layer graphenes have been investigated in the past but both have their drawbacks. The uniformity of multi-layer graphene is still questionable, and single layer graphene stacks require many transfer processes to achieve sufficiently low sheet resistance. In this work, bilayer graphene film grown with low pressure chemical vapor deposition was used as a transparent conductor for the first time. The technique was demonstrated to be highly efficient in fabricating a conductive and uniform transparent conductor compared to multi-layer or single layer graphene. Four transfers of bilayer graphene yielded a transparent conducting film with a sheet resistance of 180 Ω(□) at a transmittance of 83%. In addition, bilayer graphene films transferred onto the plastic substrate showed remarkable robustness against bending, with sheet resistance change less than 15% at 2.14% strain, a 20-fold improvement over commercial indium oxide films.

Nanomechanical Properties of Teflon Amorphous Fluoropolymer -MWCNT Bilayer Films

ABSTRACTTeflon amorphous fluoropolymer (TAF) multi-walled carbon nanotube (MWCNT) suspensions have the potential for creating conductive coatings on insulating films for numerous applications. However, there are few studies on polymer MWCNT suspension properties and even fewer that use Teflon. To define mechanical and electrical property relationships, bilayer films of TAF-MWCNT were created with differing concentrations of MWCNTs. Nanoindentation revealed that addition of 8 wt% MWCNTs to TAF increased the elastic modulus by about 25% and hardness by about 15%. Conducting indentation showed 8 wt% MWCNT films exhibit uniform stable conductance once indentation depth exceeds several hundred nanometers. Films with lower concentrations of CNTs were insulating. The two techniques provide a unique description of structure property relationships in this suspension film system.

On the possibility to determine the electrical conductivity of 67P/CG from ROSETTA magnetic field observations

The ROSETTA mission to comet 67P/Churyumov-Gerasimenko presents us for the first time the opportunity to study the interior of a cometary nucleus. Information about the electrical conductivity and its distribution inside the nucleus can be derived by measuring the magnetic fields induced in the nucleus by variations of the interplanetary magnetic field. Due to the relatively small size of the nucleus, this task is not trivial and requires very precise magnetic field measurements.Here we analyze the response of a conductive nucleus to transient step-like magnetic field changes as well as the response in frequency domain to electromagnetic waves. For the nucleus we use a spherical model with either uniform conductivity or consisting of a core and an outer layer with different conductivities. The space outside of the nucleus is modeled either by highly conductive solar wind plasma or by zero conductivity void.Various combinations of conductivities, radii of the nucleus and of the core, and properties of the space outside the nucleus result in different inductive responses. Several such combinations which could be encountered by ROSETTA are studied in detail in order to estimate which conductivity ranges and core radii can be determined using the ROSETTA instruments and which mission operations would facilitate such measurements.

Uniform peak optical conductivity in single-walled carbon nanotubes

Recent Rayleigh scattering measurements show that all single-walled carbon nanotubes have a peak optical conductivity of approximately 8 ${e}^{2}/h$, independent of radius, chiral angle, or whether the nanotube is semiconducting or metallic [D. Y. Joh et al., Nat. Nanotechnol. 6, 51 (2011)]. We show that this uniform peak conductivity is a consequence of the relativistic band structure and strength of the Coulomb interaction in carbon nanotubes. We also show that a simple exciton model accurately describes the general phenomenology and the numerical value of the peak optical conductivity. Our work illustrates the need for careful treatment of relaxation mechanisms in modeling the optoelectronic properties of carbon nanotubes.

Structure-Dependent Electrical and Concentration Processes in the Dendrites of Pyramidal Neurons of Superficial Neocortical Layers: Model Study

On mathematical models of pyramidal neurons localized in the neocortical layers 2/3, whose reconstructed dendritic arborization possessed passive linear or active nonlinear membrane properties, we studied the effect of morphology of the dendrites on their passive electrical transfer characteristics and also on the formation of patterns of spike discharges at the output of the cell under conditions of tonic activation via uniformly distributed excitatory synapses along the dendrites. For this purpose, we calculated morphometric characteristics of the size, complexity, metric asymmetry, and function of effectiveness of somatopetal transmission of the current (with estimation of the sensitivity of this efficacy to changes in the uniform membrane conductance) for the reconstructed dendritic arborization in general and also for its apical and basal subtrees. Spatial maps of the membrane potential and intracellular calcium concentration, which corresponded to certain temporal patterns of spike discharges generated by the neuron upon different intensities of synaptic activation, were superimposed on the 3D image and dendrograms of the neuron. These maps were considered “spatial autographs” of the above patterns. The main discharge pattern included periodic two-spike bursts (dublets) generated with relatively stable intraburst interspike intervals and interburst intervals decreasing with a rise in the intensity of activation. Under conditions of intense activation, the interburst intervals became close to the intraburst intervals, so the cell began to generate continuous trains of action potentials. Such a repertoire (consisting of two patterns of the activity, periodical dublets and continuous discharges) is considerably scantier than that described earlier in pyramidal neurons of the neocortical layer 5. Under analogous conditions of activation, we observed in the latter cells a variety of patterns of output discharges of different complexities, including stochastic ones. A relatively short length of the apical dendrite subtree of layer 2/3 neurons and, correspondingly, a smaller metric asymmetry (differences between the lengths of the apical and basal dendritic branches and paths), as compared with those in layer 5 pyramidal neurons, are morphological factors responsible for the predominance of periodic spike dublets. As a result, there were two combinations of different electrical states of the sites of dendritic arborization (“spatial autographs”). In the case of dublets, these were high depolarization of the apical dendrites vs. low depolarization of the basal dendrites and a reverse combination; only the latter (reverse) combination corresponded to the case of continuous discharges. The relative simplicity and uniformity of spike patterns in the cells, apparently, promotes the predominance of network interaction in the processes of formation of the activity of pyramidal neurons of layers 2/3 and, thereby, a higher efficiency of the processes of intracortical association.

Four-terminal measurement of the distribution of electrical resistance across stress corrosion cracking

This study measures electrical resistance of a stress corrosion crack directly by the four-terminal method to discuss appropriate modeling from the viewpoint of electromagnetic nondestructive evaluation. Two type-316 stainless steel plate specimens containing artificial stress corrosion cracks were prepared, and columnar samples containing penetrating cracks were cut from the plates for the measurements. The results obtained agree with recent reports discussing appropriate numerical modeling of stress corrosion cracking on the basis of finite element simulations. In contrast, this study also reveals that it is not always valid to assume that a stress corrosion crack has uniform conductivity internally.

Entropy production minimization in steady state heat conduction

The rate of entropy generation during the steady conduction through a solid slab is investigated analytically. The effects of thermal conductivity and internal heat generation/sink on the total rate of entropy generation are discussed. Cases of uniform, spatial variable and temperature dependent thermal conductivity are considered. In addition, the case of introducing internal heat source/sink is discussed. It is concluded that the total rate of entropy generation per heat transfer rate in steady heat conduction through solid material is a function of only the rate of heat transfer, regardless of the distribution and or dependence of the thermal conductivity. The total rate of entropy generation during conduction in solid material can be eliminated by introducing internal heat generation/sink. The total rate of entropy generation during the transient heat conduction decreases with time and approaches its minimum value as the steady conduction is reached.

A least squares method for a longitudinal fin with temperature dependent internal heat generation and thermal conductivity

Approximate but highly accurate solutions for the temperature distribution, fin efficiency, and optimum fin parameter for a constant area longitudinal fin with temperature dependent internal heat generation and thermal conductivity are derived analytically. The method of least squares recently used by the authors is applied to treat the two nonlinearities, one associated with the temperature dependent internal heat generation and the other due to temperature dependent thermal conductivity. The solution is built from the classical solution for a fin with uniform internal heat generation and constant thermal conductivity. The results are presented graphically and compared with the direct numerical solutions. The analytical solutions retain their accuracy (within 1% of the numerical solution) even when there is a 60% increase in thermal conductivity and internal heat generation at the base temperature from their corresponding values at the sink temperature. The present solution is simple (involves hyperbolic functions only) compared with the fairly complex approximate solutions based on the homotopy perturbation method, variational iteration method, and the double series regular perturbation method and offers high accuracy. The simple analytical expressions for the temperature distribution, the fin efficiency and the optimum fin parameter are convenient for use by engineers dealing with the design and analysis of heat generating fins operating with a large temperature difference between the base and the environment.

Modelling of block-scale macrodispersion as a random function

Numerical modelling of solute dispersion in natural heterogeneous porous media is facing several challenges. Amongst these we highlight the challenge of accounting for high-frequency variability that is filtered out by homogenization at the subgrid scale and the uncertainty in the dispersive flux for transport under non-ergodic conditions. These two effects when combined lead to inaccurate representation of the dispersive fluxes. We propose to compensate for this deficiency by defining a block-scale dispersion tensor and modelling it as a random space function ℳij. The derived dispersion tensor is a function of several length scales and time. Grid blocks will be assigned dispersion coefficients generated from the ℳijdistribution. We will show the dependence of ℳijon the spatial variability of the conductivity field, on the contaminant source size, on the travel time and on the grid-block scale. For an ergodic source, a statistically uniform conductivity field and very large grid blocks, ℳijis equal to the macrodispersion coefficients proposed by Dagan (J. Fluid Mech., vol. 145, 1984, p. 151) with zero variance. For an ergodic source and non-uniform conductivity field with a finite-size grid block, ℳijapproaches the model proposed by Rubinet al. (J. Fluid Mech., vol. 395, 1999, p. 161). In both cases, ℳijis defined by its mean value with zero variance. ℳijis subject to uncertainty when the source is non-ergodic and when the grid block is defined by a finite scale. When the grid-block scale approaches zero, which means that the spatial variability is captured completely on the numerical grid, ℳijapproaches zero with zero variance. In addition, we provide a complete statistical characterization of ℳijby invoking the concept of minimum relative entropy, thus providing upper bounds on the uncertainty associated with ℳij.

Modelling of block-scale macrodispersion as a random function

Numerical modelling of solute dispersion in natural heterogeneous porous media is facing several challenges. Amongst these we highlight the challenge of accounting for high-frequency variability that is filtered out by homogenization at the subgrid scale and the uncertainty in the dispersive flux for transport under non-ergodic conditions. These two effects when combined lead to inaccurate representation of the dispersive fluxes. We propose to compensate for this deficiency by defining a block-scale dispersion tensor and modelling it as a random space function ℳij. The derived dispersion tensor is a function of several length scales and time. Grid blocks will be assigned dispersion coefficients generated from the ℳij distribution. We will show the dependence of ℳij on the spatial variability of the conductivity field, on the contaminant source size, on the travel time and on the grid-block scale. For an ergodic source, a statistically uniform conductivity field and very large grid blocks, ℳij is equal to the macrodispersion coefficients proposed by Dagan (J. Fluid Mech., vol. 145, 1984, p. 151) with zero variance. For an ergodic source and non-uniform conductivity field with a finite-size grid block, ℳij approaches the model proposed by Rubin et al. (J. Fluid Mech., vol. 395, 1999, p. 161). In both cases, ℳij is defined by its mean value with zero variance. ℳij is subject to uncertainty when the source is non-ergodic and when the grid block is defined by a finite scale. When the grid-block scale approaches zero, which means that the spatial variability is captured completely on the numerical grid, ℳij approaches zero with zero variance. In addition, we provide a complete statistical characterization of ℳij by invoking the concept of minimum relative entropy, thus providing upper bounds on the uncertainty associated with ℳij.

Heparin-doped affinity electromembranes for thrombin purification

Heparin-doped affinity electromembrane was fabricated by synthesizing conducting polymers polypyrrole onto porous polyethersulfone membrane using heparin as both ligand and dopant. The obtained affinity electromembrane exhibited a uniform conductivity value of 1.73 × 10 −4 S/cm. The content of heparin of affinity electromembrane was ∼0.894 mg/g membrane. Such heparin-doped affinity electromembranes were used to purify thrombin. The adsorption mechanism of thrombin and the effects of temperature, initial concentration of thrombin and potential on adsorption were investigated by batch experiments. The results showed that the adsorption capacity increased with increasing the temperature, initial concentration of thrombin and potential, and the adsorption isotherm fitted the Freundlich model well. Elution of protein showed desorption ratio was up to 93.1% using 2.0 M NaSCN solution as the desorption agent. The adsorption capacities of all the tested affinity electromembranes did not significantly change during the repeated adsorption–desorption operations.

Synaptic Integration Gradients in Single Cortical Pyramidal Cell Dendrites

Cortical pyramidal neurons receive thousands of synaptic inputs arriving at different dendritic locations with varying degrees of temporal synchrony. It is not known if different locations along single cortical dendrites integrate excitatory inputs in different ways. Here we have used two-photon glutamate uncaging and compartmental modeling to reveal a gradient of nonlinear synaptic integration in basal and apical oblique dendrites of cortical pyramidal neurons. Excitatory inputs to the proximal dendrite sum linearly and require precise temporal coincidence for effective summation, whereas distal inputs are amplified with high gain and integrated over broader time windows. This allows distal inputs to overcome their electrotonic disadvantage, and become surprisingly more effective than proximal inputs at influencing action potential output. Thus, single dendritic branches can already exhibit nonuniform synaptic integration, with the computational strategy shifting from temporal coding to rate coding along the dendrite.

The Role of Prior Model Calibration on Predictions with Ensemble Kalman Filter

This paper, based on a real world case study (Limmat aquifer, Switzerland), compares inverse groundwater flow models calibrated with specified numbers of monitoring head locations. These models are updated in real time with the ensemble Kalman filter (EnKF) and the prediction improvement is assessed in relation to the amount of monitoring locations used for calibration and updating. The prediction errors of the models calibrated in transient state are smaller if the amount of monitoring locations used for the calibration is larger. For highly dynamic groundwater flow systems a transient calibration is recommended as a model calibrated in steady state can lead to worse results than a noncalibrated model with a well-chosen uniform conductivity. The model predictions can be improved further with the assimilation of new measurement data from on-line sensors with the EnKF. Within all the studied models the reduction of 1-day hydraulic head prediction error (in terms of mean absolute error [MAE]) with EnKF lies between 31% (assimilation of head data from 5 locations) and 72% (assimilation of head data from 85 locations). The largest prediction improvements are expected for models that were calibrated with only a limited amount of historical information. It is worthwhile to update the model even with few monitoring locations as it seems that the error reduction with EnKF decreases exponentially with the amount of monitoring locations used. These results prove the feasibility of data assimilation with EnKF also for a real world case and show that improved predictions of groundwater levels can be obtained.

MRS Response of Water-bearing Geological Body of Coal in Uniform Conductivity

The MRS forward calculation of 3D water-contained medium involves two difficulties. First of them is to calculate the expression of the exciting field, which is an integration including 2 Bessel functions’ product. In this paper, the integration was divided into 2 integral intervals. In the first interval, using the Hankel expression of Bessel functions and the latter asymptotic properties of large volume, the double bessel integration was converted into Fourier sine(cosine) transformations and fast calculation to the transformations was adopted to finish the integration in this interval. Traditional calculation method can achieve high accuracy in the second interval. The second difficulty is the space dicretization of the 3D water-contained medium. Dicretization methods in both cylindrical and rectangular coordinates system were introduced in this paper. The cubic grids in rectangular coordinates system can construct 3D water-contained bodies of any shape. At last, MRS forward calculation of 3D water-contained bodies in uniform media achieved. Based on what mentioned above, water-filled tunnel and water-filled gob models are build, and both models MRS forward curves are calculated.

Surface Properties of Laser-etched LTCC Ceramic

In the LTCC process, metal layers are usually deposited by screen printing conductor material on unfired tape substrate. Despite being widely used, this method has certain disadvantages, such as limited resolution of the printing process. An alternative method of producing conductor patterns is to deposit a uniform conductor paste layer on the substrate and the use a Nd:YAG laser to selectively ablate the conductor material, producing a desired pattern. This method allows achieving a higher patterning precision and also eliminates photochemical process of screen preparation, which makes it an attractive choice for rapid prototyping applications. Laser ablation step can be performed either post-firing (for a top conductor layer) or pre-firing (which allows for patterning buried layers). The aim of this paper is to investigate surface properties of LTCC ceramics processed by laser etching. Precision optical imaging and SEM are used to determine etched surface properties, and EDS analysis is used to determine its chemical composition. Effectiveness of conductor removal is investigated by comparing surface resistivity and metal content in raw and etched samples.

Electric field-induced nanopatterning of reduced graphene oxide on Si and a p–n diode junction

Electric field-induced (EFI) reduction of graphene oxide (GO) was performed by conductive atomic force microscopy (C-AFM) in order to create a reduced GO (rGO) p–n nanopattern diode in a dry and non-destructive single-pot process. Single GO sheets were deposited by the Langmuir–Blodgett (LB) method onto semiconducting (n- and p-doping Si) substrates that control charge transfer at the rGO interface. EFI nanolithography resulted in locally reduced GO nanopatterns on GO sheets corresponding to the application of a negative bias voltage on an n-doping Si substrate. EFI nanolithography was performed as a function of applied voltage, and the rGO nanopatterned at −10.0 Vsub showed high conductivity, comparable with that of the chemically reduced GO. In addition, transport of rGO sheets, which were efficiently reduced under a local electric field, showed a uniform conductivity at sheet edges and the basal plane. Current–voltage (I–V) characteristics of rGO on n- and p-doping Si substrates indicated that EFI reduction nanolithography produced p-type rGO nanopatterns on the Si substrates. In conclusion, we successfully fabricated a p–n diode junction of p-type rGO/n-doping Si into nanopatterns. This junction is an indispensable electronic component that rectifies charge transport and prevents interference between neighboring electronic components in high density integrated crossbar devices.

Single-walled carbon nanotubes as excitonic optical wires

Although metallic nanostructures are useful for nanoscale optics, all of their key optical properties are determined by their geometry. This makes it difficult to adjust these properties independently, and can restrict applications. Here we use the absolute intensity of Rayleigh scattering to show that single-walled carbon nanotubes can form ideal optical wires. The spatial distribution of the radiation scattered by the nanotubes is determined by their shape, but the intensity and spectrum of the scattered radiation are determined by exciton dynamics, quantum-dot-like optical resonances and other intrinsic properties. Moreover, the nanotubes display a uniform peak optical conductivity of approximately 8 e(2)/h, which we derive using an exciton model, suggesting universal behaviour similar to that observed in nanotube conductance. We further demonstrate a radiative coupling between two distant nanotubes, with potential applications in metamaterials and optical antennas.

Effects of nightside O+ outflow on magnetospheric dynamics: Results of multifluid MHD modeling

Through spacecraft observations and numerical modeling, it is becoming increasingly well established that ionospheric oxygen is present in the magnetosphere in amounts that can have an effect on magnetospheric dynamics, affecting pressure balance, currents, convection flows, and cross polar cap potential (CPCP). However, an understanding of the various processes through which oxygen may bring about changes in magnetospheric structure and dynamics is still lacking. In this paper, we focus on the role that ionospheric oxygen outflow from the nightside auroral zone plays in determining plasma sheet density, size, and pressure and relate the changes in plasma sheet parameters to changes in CPCP, tail geometry, and magnetospheric convection. We use the Multifluid Lyon‐Fedder‐Mobarry model as a virtual laboratory to analyze the effects of ionospheric oxygen on magnetospheric parameters. Our simulations use idealized solar wind conditions, constant and uniform ionospheric conductance, and constant nightside oxygen outflow in order to isolate the effects of a change in outflow flux. We concentrate the ionospheric outflow in the nightside auroral region, so as to avoid the possibility of directly loading the distant tail X line with oxygen and hence to avoid a direct modification of the reconnection rate in order to focus on effects within the magnetosphere. We show that the presence of O+ outflowing from an isolated patch in the nightside auroral zone increases plasma sheet density and thermal pressure, slows convection, decreases the polar cap potential, and increases the length and width of the nightside magnetosphere. We determine that ionospheric O+ mass loading can play a significant role but that strong effects on magnetospheric dynamics require a nightside flux that significantly exceeds statistical observed levels. A more realistic outflow would include both dayside and nightside sources whose total combined flux would be similar to the total fluxes used here.

Anthropogenic Venice uplift by seawater pumping into a heterogeneous aquifer system

In recent years, a project of anthropogenic Venice uplift caused by seawater injection into a 600–850 m deep brackish aquifer underlying the lagoon has been advanced. While an extensive data set based on marker measurements from a number of gas‐producing wells of the northern Adriatic is available for a realistic evaluation of the geomechanical properties of the injected geologic formation, permeability data are very scarce and sparse throughout the area. Previous finite element (FE) predictions relying on a uniform hydraulic conductivity K as derived from pumping tests suggest that a flat uplift of the city is produced over 10 years from the inception of injection. However, it is well‐known and widely recognized that in natural porous media very seldom K exhibits an even spatial distribution. In this study, a random distribution is then assumed to address the influence of a variable K on the uniformity of the city uplift. To limit the otherwise prohibitive computational burden, the study is performed relative to the pilot project designed to raise a reduced area at the margin of the lagoon. Monte Carlo groundwater flow simulations are performed using a FE discretization of the injected aquifer system based upon a hydraulic conductivity distribution characterized by a lognormal, stationary random process. The resulting pore overpressure is then implemented into a deterministic FE geomechanical model. A sensitivity analysis is performed to account for the uncertainty on the stochastic process, reflected by both the log K variance σ2 and the correlation length λ over the ranges 0.2–1.0 and 20–1000 m, respectively, which are quite plausible for normally consolidated sedimentary formations such as the Northern Adriatic basin. The cumulative distribution function (CDF) of the ground surface uplift, uz, and its horizontal gradient, ρz, are computed and used to evaluate the probability for ρz to be larger than a few significant threshold values as discussed later. It is shown that, even within the most pessimistic scenario (i.e., σ2 = 1.0 and λ = 1000 m), the maximum ρz is comparable, namely of the same order, with the one obtained from the deterministic case and (1) 2–3 times smaller than the ρz caused in the city by groundwater withdrawal in the nearby industrial area over the 1960s (10 × 10−5), (2) 1 order of magnitude less than the maximum bound as indicated in the literature for the safety of multifloor masonry buildings (50 × 10−5), and (3) about 20 times smaller than the maximum ρz values that the city is currently experiencing (100 × 10−5). The results highlight the strong effect exerted by the overburden in smoothing the uneven expansion of the injected heterogeneous formation.