The effect of grain anisotropy on the electrical properties of sedimentary rocks

Geophysics ◽  
1982 ◽  
Vol 47 (2) ◽  
pp. 257-263 ◽  
Author(s):  
Kenneth S. Mendelson ◽  
Morrel H. Cohen
Keyword(s):  
Dielectric Constant ◽  
Electrical Properties ◽  
Sedimentary Rocks ◽  
Two Dimensions ◽  
Dc Conductivity ◽  
Three Dimensions ◽  
Complex Dielectric Constant ◽  
Archie’S Law ◽  
Principal Axes ◽  
Grain Distribution

We have examined the effect of particulate anisotropy on the electrical properties of sedimentary rocks by generalizing the treatment of Sen et al (1981) to the case of ellipsoidal grains with a distribution of orientations and depolarizing factors. Two distributions in orientation have been treated in detail—randomly oriented grains in three dimensions and grains with aligned principal axes in two dimensions. In the former case the conductivity is a scalar satisfying Archie’s law, [Formula: see text], with [Formula: see text] the conductivity of the pore fluid and ϕ the porosity. The exponent m has a minimum of 1.5 for spherical grains. The presence of highly oblate (disk shaped) grains raises m significantly. As long as grains with extremely large eccentricities (≳15) are not present, the exponent falls in the observed range [Formula: see text]. For aligned grains the conductivity is a tensor with principal values that satisfy a generalized Archie’s law of the form [Formula: see text], where [Formula: see text] is the jth principal value of the conductivity and [Formula: see text] can be expanded as a power series in ϕ with a constant leading term. For grain eccentricities in the range 0–0.95, the coefficients [Formula: see text] fall in the range 0.1–4. The exponent m has a minimum value of 2 for two dimensions, independent of grain shape, if all grains have the same shape, and it is larger for any distribution of grain shapes. If the distribution of grain shapes is chosen so that the rock is isotropic, m and a have the same values as for isotropic rock composed of grains with the same distribution of shapes but with random orientations. Since different distributions of grain orientation can lead to the same effective conductivity, it is clear that measurements of dc conductivity are not sufficient to determine the grain distribution. The model is also used to obtain the complex dielectric constant. If the dielectric constant of solid rock is small compared to the real part of the dielectric constant of water, the complex dielectric constant has the same dependence on porosity as the dc conductivity except at very small porosities.

Structural characterization, electrical properties and gas sensing applications of polypyrrole/Cu-Al2O3 hybrid nanocomposites

2020 ◽  
Vol 32 (6) ◽  
pp. 719-728 ◽  
Author(s):  
S Sankar ◽  
K Parvathi ◽  
MT Ramesan
Keyword(s):  
Dielectric Constant ◽  
Electron Microscope ◽  
Electrical Properties ◽  
Gas Sensing ◽  
Xrd Analysis ◽  
High Energy ◽  
Dc Conductivity ◽  
Hybrid Nanocomposites ◽  
Ammonia Gas ◽  
Sensing Applications

The present work focused on the synthesis of polypyrrole (PPy) wrapped nano copper-alumina (Cu-Al2O3) composite by an in situ polymerization of pyrrole in the presence of Cu-Al2O3 nanoparticles. The polymerized samples were systematically characterized by Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD) analysis, scanning electron microscope (SEM), high-resolution transmission electron microscope (HR-TEM), differential scanning calorimetry (DSC), and thermogravimetric analysis (TGA). The properties such as AC and DC conductivity, dielectric constant, and ammonia gas sensing performance of PPy/Cu-Al2O3 composites were investigated in detail as a function of Cu-Al2O3 content. The FTIR spectra showed the existence of sharp and resolved infrared bands of nanoparticles in the PPy chain. The presence of the crystalline peaks of Cu-Al2O3 in the PPy matrix was confirmed from the XRD analysis. SEM images revealed the homogenous growth of Cu-Al2O3 in the polymer with the formation of spherically shaped particles. The HR-TEM observation showed that Cu-Al2O3 particles were dispersed at a nanometer level in the nanocomposites with a width of 30–60 nm. The glass transition temperature of composites obtained from DSC was found to be increased with increase in the content of nanoparticles. TGA analysis proved that the nano Cu-Al2O3 in the content in the composites acted as a mass transport barrier that retards the degradation of the product. The AC conductivity and dielectric constant of the nanocomposite showed that the maximum electrical properties were observed for the composite with 5 weight percentage loading of Cu-Al2O3. DC conductivity showed that the PPy/Cu-Al2O3 composites have higher electrical conductivity than PPy. The ammonia gas sensing property of the composites was significantly enhanced by the addition of Cu-Al2O3 nanoparticles. Therefore, the improved properties of synthesized PPy/Cu-Al2O3 nanocomposite can be useful for developing functional composite material for the fabrication of sensors, electronic devices, and high energy storage capacitors.

scholarly journals Anomalous localized resonance using a folded geometry in three dimensions

2013 ◽  
Vol 469 (2154) ◽  
pp. 20130048 ◽  
Author(s):  
Habib Ammari ◽  
Giulio Ciraolo ◽  
Hyeonbae Kang ◽  
Hyundae Lee ◽  
Graeme W. Milton
Keyword(s):  
Dielectric Constant ◽  
Dielectric Material ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Dielectric Tensor ◽  
Anisotropic Dielectric ◽  
Plasmonic Structure ◽  
Negative Constant ◽  
Loss Parameter

If a body of dielectric material is coated by a plasmonic structure of negative dielectric material with non-zero loss parameter, then cloaking by anomalous localized resonance (CALR) may occur as the loss parameter tends to zero. If the coated structure is circular (two dimensions) and the dielectric constant of the shell is a negative constant (with loss parameter), then CALR occurs, and if the coated structure is spherical (three dimensions), then CALR does not occur. The aim of this paper is to show that CALR takes place if the spherical coated structure has a specially designed anisotropic dielectric tensor. The anisotropic dielectric tensor is designed by unfolding a folded geometry.

A self‐similar model for sedimentary rocks with application to the dielectric constant of fused glass beads

Geophysics ◽  
1981 ◽  
Vol 46 (5) ◽  
pp. 781-795 ◽  
Author(s):  
P. N. Sen ◽  
C. Scala ◽  
M. H. Cohen
Keyword(s):  
Dielectric Constant ◽  
External Field ◽  
Sedimentary Rocks ◽  
Glass Beads ◽  
The Self ◽  
Similar Model ◽  
Archie’S Law ◽  
Self Consistent ◽  
Self Similar ◽  
Coated Spheres

We develop a theory for dielectric response of water‐saturated rocks based on a realistic model of the pore space. The absence of a percolation threshold manifest in Archie’s law, porecasts, electron‐micrographs, and general theories of formation of detrital sedimentary rocks indicates that the pore spaces within such rocks remain interconnected to very low values of the porosity ϕ. In the simplest geometric model for which the conducting paths remain interconnected, each grain is envisioned to be coated with water. The dielectric constant of the assembly of water‐coated grains is obtained by a self‐consistent effective medium theory. In the dc limit, this gives Maxwell’s relation for conductivity σ of the rock [Formula: see text], where [Formula: see text] is the conductivity of water. In order to include the local environmental effects around a grain, a self‐similar model is generated by envisioning that each rock grain itself is coated with a skin made of other coated spheres; the coating at each level consists of other coated spheres. The self‐consistent complex dielectric constant [Formula: see text] is given in this model in terms of that of water [Formula: see text] and of rock [Formula: see text], by [Formula: see text] for spherical particles. This gives, in the dc limit, [Formula: see text]. For nonspherical particles, the exponent m in Archie’s law [Formula: see text] is greater than 3/2 for the plate‐like grains or cylinders with axis perpendicular to the external field and smaller than 3/2 for plates or cylindrical particles with axis parallel to the external field. Artificial rocks with a wide range of porosities were made from glass beads. We present data on the glass bead rocks for dc conductivity and the dielectric constant at 1.1 GHz. The data follow the conductivity and the dielectric responses given by the self‐similar model. The present theory fails to explain the salinity dependence of [Formula: see text] at lower frequencies.

Influence of Structural Parameters of Conducting Polymers on their Microwave Properties

1993 ◽  
Vol 328 ◽  
Author(s):  
P. Hourquebie
Keyword(s):  
Dielectric Constant ◽  
Electrical Properties ◽  
Conducting Polymers ◽  
Molar Mass ◽  
Alkyl Chain ◽  
Structural Parameters ◽  
Microwave Properties ◽  
Complex Dielectric Constant ◽  
Frequency Range ◽  
Counter Anion

ABSTRACTThe complex dielectric constant ε* (ε* = ε′-iε″) of conducting polymers (polyaniline and poly (3-alkyl thiophene)) is studied over a frequency range spanning from 130 MHz to 20 GHz. The effects of structural parameters (counter-anion size, Molar Mass, length of the alkyl chain on the substituted Monomer) on electrical properties (σdc and ε* values) have been investigated.

Relation of certain geometrical features to the dielectric anomaly of rocks

Geophysics ◽  
1981 ◽  
Vol 46 (12) ◽  
pp. 1714-1720 ◽  
Author(s):  
P. N. Sen
Keyword(s):  
Dielectric Constant ◽  
Aspect Ratio ◽  
Sedimentary Rocks ◽  
Dielectric Anomaly ◽  
Small Concentration ◽  
Dc Conductivity ◽  
Low Frequencies ◽  
Depolarization Factor ◽  
Oblate Spheroidal ◽  
Geometrical Features

We show that the real part of the dielectric constant ε′ of rocks at low frequencies can be anomalously high due to the presence of a small concentration η of high aspect ratio particles. For oblate spheroidal grains [Formula: see text] with depolarization factor along symmetry [Formula: see text] axis, [Formula: see text] [Formula: see text] the static value of the dielectric constant of rock [Formula: see text] and dc conductivity [Formula: see text] are given for [Formula: see text] by [Formula: see text] [Formula: see text] and for (2) [Formula: see text] [Formula: see text] Here [Formula: see text] is the dielectric constant of the grain; [Formula: see text] is the dc conductivity of the host rock. Case (1) corresponds to the well known Maxwell‐Wagner effect with [Formula: see text] diverging as η → 0, and [Formula: see text] Case (2) gives a novel result that [Formula: see text] may diverge for [Formula: see text], with a nonvanishing σ(0). Case (2) is applied to explain frequency and salinity dependences and the giant values [Formula: see text] of the dielectric constant of conducting sedimentary rocks. For [Formula: see text], [Formula: see text], [Formula: see text], we find [Formula: see text], which is large compared to [Formula: see text] or the dielectric constant of water [Formula: see text].

Development of a Capacitor Probe to Detect Subsurface Deterioration in Concrete

1997 ◽  
Vol 503 ◽  
Author(s):  
B. K. Diefenderfer ◽  
I. L. Al-Qadi ◽  
J. J. Yoho ◽  
S. M. Riad ◽  
A. Loulizi
Keyword(s):  
Dielectric Constant ◽  
Portland Cement ◽  
Electromagnetic Waves ◽  
Low Cost ◽  
Complex Dielectric Constant ◽  
Life Cycle Costs ◽  
Parallel Plates ◽  
Portland Cement Concrete ◽  
Cement Concrete ◽  
Set Up

ABSTRACTPortland cement concrete (PCC) structures deteriorate with age and need to be maintained or replaced. Early detection of deterioration in PCC (e.g., alkali-silica reaction, freeze/thaw damage, or chloride presence) can lead to significant reductions in maintenance costs. However, it is often too late to perform low-cost preventative maintenance by the time deterioration becomes evident. By developing techniques that would enable civil engineers to evaluate PCC structures and detect deterioration at early stages (without causing further damage), optimization of life-cycle costs of the constructed facility and minimization of disturbance to the facility users can be achieved.Nondestructive evaluation (NDE) methods are potentially one of the most useful techniques ever developed for assessing constructed facilities. They are noninvasive and can be performed rapidly. Portland cement concrete can be nondestructively evaluated by electrically characterizing its complex dielectric constant. The real part of the dielectric constant depicts the velocity of electromagnetic waves in PCC. The imaginary part, termed the “loss factor,” describes the conductivity of PCC and the attenuation of electromagnetic waves.Dielectric properties of PCC have been investigated in a laboratory setting using a parallel plate capacitor operating in the frequency range of 0.1 to 40.1MIHz. This capacitor set-up consists of two horizontal-parallel plates with an adjustable separation for insertion of a dielectric specimen (PCC). While useful in research, this approach is not practical for field implementation. A new capacitor probe has been developed which consists of two plates, located within the same horizontal plane, for placement upon the specimen to be tested. Preliminary results show that this technique is feasible and results are promising; further testing and evaluation is currently underway.

scholarly journals Data on Orientation to Happiness in Higher Education Institutions from Mexico and El Salvador

Data ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 27
Author(s):  
Domingo Villavicencio-Aguilar ◽  
Edgardo René Chacón-Andrade ◽  
Maria Fernanda Durón-Ramos
Keyword(s):  
Higher Education ◽  
El Salvador ◽  
Latin American ◽  
Higher Education Institutions ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Stepwise Multiple Regression ◽  
Teacher Student ◽  
And Gender ◽  
Student’S T

Happiness-oriented people are vital in every society; this is a construct formed by three different types of happiness: pleasure, meaning, and engagement, and it is considered as an indicator of mental health. This study aims to provide data on the levels of orientation to happiness in higher-education teachers and students. The present paper contains data about the perception of this positive aspect in two Latin American countries, Mexico and El Salvador. Structure instruments to measure the orientation to happiness were administrated to 397 teachers and 260 students. This data descriptor presents descriptive statistics (mean, standard deviation), internal consistency (Cronbach’s alpha), and differences (Student’s t-test) presented by country, population (teacher/student), and gender of their orientation to happiness and its three dimensions: meaning, pleasure, and engagement. Stepwise-multiple-regression-analysis results are also presented. Results indicated that participants from both countries reported medium–high levels of meaning and engagement happiness; teachers reported higher levels than those of students in these two dimensions. Happiness resulting from pleasure activities was the least reported in general. Males and females presented very similar levels of orientation to happiness. Only the population (teacher/student) showed a predictive relationship with orientation to happiness; however, the model explained a small portion of variance in this variable, which indicated that other factors are more critical when promoting orientation to happiness in higher-education institutions.

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

Turbulent three-dimensional dielectric electrohydrodynamic convection between two plates

2012 ◽  
Vol 696 ◽  
pp. 228-262 ◽  
Author(s):  
A. Kourmatzis ◽  
J. S. Shrimpton
Keyword(s):  
Spatial Data ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Energy Budgets ◽  
Turbulent Regime ◽  
Scalar Flux ◽  
Wide Range ◽  
Scalar Variance

AbstractThe fundamental mechanisms responsible for the creation of electrohydrodynamically driven roll structures in free electroconvection between two plates are analysed with reference to traditional Rayleigh–Bénard convection (RBC). Previously available knowledge limited to two dimensions is extended to three-dimensions, and a wide range of electric Reynolds numbers is analysed, extending into a fully inherently three-dimensional turbulent regime. Results reveal that structures appearing in three-dimensional electrohydrodynamics (EHD) are similar to those observed for RBC, and while two-dimensional EHD results bear some similarities with the three-dimensional results there are distinct differences. Analysis of two-point correlations and integral length scales show that full three-dimensional electroconvection is more chaotic than in two dimensions and this is also noted by qualitatively observing the roll structures that arise for both low (${\mathit{Re}}_{E} = 1$) and high electric Reynolds numbers (up to ${\mathit{Re}}_{E} = 120$). Furthermore, calculations of mean profiles and second-order moments along with energy budgets and spectra have examined the validity of neglecting the fluctuating electric field ${ E}_{i}^{\ensuremath{\prime} } $ in the Reynolds-averaged EHD equations and provide insight into the generation and transport mechanisms of turbulent EHD. Spectral and spatial data clearly indicate how fluctuating energy is transferred from electrical to hydrodynamic forms, on moving through the domain away from the charging electrode. It is shown that ${ E}_{i}^{\ensuremath{\prime} } $ is not negligible close to the walls and terms acting as sources and sinks in the turbulent kinetic energy, turbulent scalar flux and turbulent scalar variance equations are examined. Profiles of hydrodynamic terms in the budgets resemble those in the literature for RBC; however there are terms specific to EHD that are significant, indicating that the transfer of energy in EHD is also attributed to further electrodynamic terms and a strong coupling exists between the charge flux and variance, due to the ionic drift term.

scholarly journals On the forces that cable webs under tension can support and how to design cable webs to channel stresses

2019 ◽  
Vol 475 (2223) ◽  
pp. 20180781 ◽  
Author(s):  
Guy Bouchitté ◽  
Ornella Mattei ◽  
Graeme W. Milton ◽  
Pierre Seppecher
Keyword(s):  
Linear Programming ◽  
Convex Hull ◽  
Structural Engineering ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Finite Dimensional ◽  
Necessary And Sufficient

In many applications of structural engineering, the following question arises: given a set of forces f 1 ,  f 2 , …,  f N applied at prescribed points x 1 ,  x 2 , …,  x N , under what constraints on the forces does there exist a truss structure (or wire web) with all elements under tension that supports these forces? Here we provide answer to such a question for any configuration of the terminal points x 1 ,  x 2 , …,  x N in the two- and three-dimensional cases. Specifically, the existence of a web is guaranteed by a necessary and sufficient condition on the loading which corresponds to a finite dimensional linear programming problem. In two dimensions, we show that any such web can be replaced by one in which there are at most P elementary loops, where elementary means that the loop cannot be subdivided into subloops, and where P is the number of forces f 1 ,  f 2 , …,  f N applied at points strictly within the convex hull of x 1 ,  x 2 , …,  x N . In three dimensions, we show that, by slightly perturbing f 1 ,  f 2 , …,  f N , there exists a uniloadable web supporting this loading. Uniloadable means it supports this loading and all positive multiples of it, but not any other loading. Uniloadable webs provide a mechanism for channelling stress in desired ways.

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