Journal articles: 'Cole-Cole model'

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HANYGA, ANDRZEJ. "AN ANISOTROPIC COLE–COLE MODEL OF SEISMIC ATTENUATION." Journal of Computational Acoustics 11, no. 01 (March 2003): 75–90. http://dx.doi.org/10.1142/s0218396x03001845.

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A simple model of seismic wave attenuation combining anisotropy with anelastic effects is constructed. The anelastic response is based on the Cole–Cole relaxation function. Time-stepping finite-difference and ray-asymptotic methods of numerical solution are discussed.

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Nordsiek, Sven, and Andreas Weller. "A new approach to fitting induced-polarization spectra." GEOPHYSICS 73, no. 6 (November 2008): F235—F245. http://dx.doi.org/10.1190/1.2987412.

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Best fitting of induced-polarization (IP) spectra by different models of Cole-Cole type evidences discrepancies in the resulting model parameters. The time constant determined from the same data could vary in magnitude over several decades. This effect, which makes an evaluation of the results of different models nearly impossible, is demonstrated by induced polarization measurements in the frequency range between [Formula: see text] and [Formula: see text] on thirteen mixtures of quartz sand and slag grains. The samples differ in size and the amount of the slag grains. Parameters describing the IP spectra are derived by fitting models of the Cole-Cole type to the measured data. The fitting quality of the generalized Cole-Cole model, the standard Cole-Cole model, and the Cole-Davidson model is investigated. The parameters derived from these models are compared and correlated with mass percentage and grain size of the slag particles. An alternative fittingapproach is introduced, using the decomposition of observed IP spectra into a variety of Debye spectra. Four integrating parameters are derived and correlated with parameters of the slag-sand mixtures and Cole-Cole parameters, respectively. The alternative approach generally enables a better fitting of measured spectra compared with Cole-Cole type models. It proves to be more flexible and stable, even for complicated phase spectra that cannot be fitted by single Cole-Cole type models. The integrating parameters are well correlated with characterizing parameters of the slag-sand mixtures. The total chargeability well indicates the mass percentage of slag grains, and the mean relaxation time is related to the grain size. The relaxation time distribution can be displayed by cumulative normalized chargeability versus relaxation time, similar to granulation curves. Anologous to the latter, a nonuniformity parameter characterizes the width of the relaxation time distribution.

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Holm, Sverre. "Time domain characterization of the Cole-Cole dielectric model." Journal of Electrical Bioimpedance 11, no. 1 (January 1, 2020): 101–5. http://dx.doi.org/10.2478/joeb-2020-0015.

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Abstract The Cole-Cole model for a dielectric is a generalization of the Debye relaxation model. The most familiar form is in the frequency domain and this manifests itself in a frequency dependent impedance. Dielectrics may also be characterized in the time domain by means of the current and charge responses to a voltage step, called response and relaxation functions respectively. For the Debye model they are both exponentials while in the Cole-Cole model they are expressed by a generalization of the exponential, the Mittag-Leffler function. Its asymptotes are just as interesting and correspond to the Curie-von Schweidler current response which is known from real-life capacitors and the Kohlrausch stretched exponential charge response.

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Holm, Sverre. "Time domain characterization of the Cole-Cole dielectric model." Journal of Electrical Bioimpedance 11, no. 1 (December 31, 2020): 101–5. http://dx.doi.org/10.2478/joeb-2020-0015.

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AbstractThe Cole-Cole model for a dielectric is a generalization of the Debye relaxation model. The most familiar form is in the frequency domain and this manifests itself in a frequency dependent impedance. Dielectrics may also be characterized in the time domain by means of the current and charge responses to a voltage step, called response and relaxation functions respectively. For the Debye model they are both exponentials while in the Cole-Cole model they are expressed by a generalization of the exponential, the Mittag-Leffler function. Its asymptotes are just as interesting and correspond to the Curie-von Schweidler current response which is known from real-life capacitors and the Kohlrausch stretched exponential charge response.

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Deng, Wubing, and Igor B. Morozov. "Mechanical interpretation and generalization of the Cole-Cole model in viscoelasticity." GEOPHYSICS 83, no. 6 (November 1, 2018): MR345—MR352. http://dx.doi.org/10.1190/geo2017-0821.1.

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The mechanical basis of the popular Cole-Cole rheological model in viscoelasticity is investigated by using Lagrangian mechanics with nonlinear energy dissipation. The Cole-Cole model is usually viewed as a convenient way to fit the observed frequency-dependent attenuation and velocity-dispersion spectra, but its time-domain and numerical formulations are complex and contradict standard physical principles. For example, time-domain modeling of Cole-Cole media requires special mathematical tools such as fractional derivatives, convolutional integrals, and/or memory variables. Nevertheless, we find that Cole-Cole spectra naturally arise from conventional mechanics with nonlinear internal friction (non-Newtonian viscosity). The Lagrangian mechanical formulation is applied to a finite body (a rock sample in a laboratory experiment) and a wave-propagating medium, in both cases providing rigorous differential equations of motion and revealing the time- and frequency-independent material properties. The model also leads to a generalized Cole-Cole (GCC) model with multiple internal variables (relaxation mechanisms), similar to the generalized standard linear solid (GSLS). As a practical application, the GSLS and GCC models are compared on interpretations of recent P-wave attenuation and dispersion measurements on bitumen-sand samples in the laboratory. The GSLS and GCC models can be used to predict the observed strain/stress ratios with adequate accuracy. However, each of these models offers certain advantages, which are the linearity (for GSLS) and potentially smaller number of dynamic variables and broader peaks in attenuation spectra (for GCC). Therefore, additional experiments focusing on linearity of internal friction are required to establish which of these models may be preferable for rock. The Lagrangian approach provides a simple and physically meaningful way for comparing all types of observations, formulating numerical modeling schemes, and predicting the propagation of waves and behavior of other deformations of earth media.

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Vastarouchas, Costas, Georgia Tsirimokou, and Costas Psychalinos. "Extraction of Cole-Cole model parameters through low-frequency measurements." AEU - International Journal of Electronics and Communications 84 (February 2018): 355–59. http://dx.doi.org/10.1016/j.aeue.2017.11.020.

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Tarasov, Andrey, and Konstantin Titov. "On the use of the Cole–Cole equations in spectral induced polarization." Geophysical Journal International 195, no. 1 (July 22, 2013): 352–56. http://dx.doi.org/10.1093/gji/ggt251.

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Abstract Two different equations, both of which are often called ‘the Cole–Cole equation’, are widely used to fit experimental Spectral Induced Polarization data. The data are compared on the basis of fitting model parameters: the chargeability, the time constant and the exponent. The difference between the above two equations (the Cole–Cole equation proposed by the Cole brothers and Pelton's equation) is manifested in one of the fitting parameters, the time constant. The Cole–Cole time constant is an inverse of the peak angular frequency of the imaginary conductivity, while Pelton's time constant depends on the chargeability and exponent values. The difference between the time constant values corresponding to the above two equations grows with the increase of the chargeability value, and with the decrease of the Cole–Cole exponent value. This issue must be taken into consideration when comparing the experimental data sets for high polarizability media presented in terms of the Cole–Cole parameters.

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Liu, Weiqiang, Rujun Chen, and Liangyong Yang. "Cole-Cole Model Parameter Estimation from Multi-frequency Complex Resistivity Spectrum Based on the Artificial Neural Network." Journal of Environmental and Engineering Geophysics 26, no. 1 (March 2021): 71–77. http://dx.doi.org/10.32389/jeeg20-054.

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In near surface electrical exploration, it is often necessary to estimate the Cole-Cole model parameters according to the measured multi-frequency complex resistivity spectrum of ore and rock samples in advance. Parameter estimation is a nonlinear optimization problem, and the common method is least square fitting. The disadvantage of this method is that it relies on initial value and the result is unstable when data is confronted with noise interference. To further improve the accuracy of parameter estimation, this paper applied artificial neural network (ANN) method to the Cole-Cole model estimation. Firstly, a large number of forward models are generated as samples to train the neural network and when the data fitting error is lower than the error threshold, the training ends. The trained neural network is directly used to efficiently estimate the parameters of vast amounts of new data. The efficiency of the artificial neural network is analyzed by using simulated and measured spectral induced polarization data. The results show that artificial neural network method has a faster computing speed and higher accuracy in Cole-Cole model parameter estimation.

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Xu, Wen Dond, and Jing Zhao Li. "Spectrum Comparative Analysis of the Frequency Domain Complex Cole-Cole Mode." Applied Mechanics and Materials 220-223 (November 2012): 2491–94. http://dx.doi.org/10.4028/www.scientific.net/amm.220-223.2491.

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Using MATLAB the spectrum comparative analysis was gived between complex Cole-Cole model and basic Cole-Cole model when theirs parameters change. The results show that the complex resistivity curve shape of complex model is limitted by total variation of two same kind parameters of complex model. The variation rule of the curve shape is consistent with basic mode when same kind parameters change. The influent of polarization rate and frequency correlation coefficient is bigger than time constant parameter. The resistivity curve of parallel complex model and series complex model is very similar. Then points out the difficulties and problems faced by the extraction of IP parameters.

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Elwakil, A. S., and B. Maundy. "Extracting the Cole-Cole impedance model parameters without direct impedance measurement." Electronics Letters 46, no. 20 (2010): 1367. http://dx.doi.org/10.1049/el.2010.1924.

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Liu, Ruize, and Qingxin Meng. "Time-domain solution of Cole-Cole model with induced polarization method." IOP Conference Series: Earth and Environmental Science 585 (November 4, 2020): 012198. http://dx.doi.org/10.1088/1755-1315/585/1/012198.

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Carcione, José M., Francesco Mainardi, Stefano Picotti, Li-Yun Fu, and Jing Ba. "Thermoelasticity and P-wave simulation based on the Cole-Cole model." Journal of Thermal Stresses 43, no. 4 (February 19, 2020): 512–27. http://dx.doi.org/10.1080/01495739.2020.1722772.

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Hernandez-Jaimes, C., J. Vazquez-Arenas, J. Vernon-Carter, and J. Alvarez-Ramirez. "A nonlinear Cole–Cole model for large-amplitude electrochemical impedance spectroscopy." Chemical Engineering Science 137 (December 2015): 1–8. http://dx.doi.org/10.1016/j.ces.2015.06.015.

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Zhou, Lei, LiangJun Yan, Osborne Kachaje, Xingbing Xie, Yurong Mao, and Haoran Zhang. "The Simulation of Transient Electromagnetic Based on Time-domain IP Model." Journal of Environmental and Engineering Geophysics 24, no. 1 (March 2019): 159–62. http://dx.doi.org/10.2113/jeeg24.1.159.

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When transient electromagnetic investigation methods are carried out in the field, the measured data often contain both the induced polarization (IP) effect and the electromagnetic effect. In order to study the IP effect in the transient electromagnetic response, many researchers first calculate the electromagnetic field which considers the IP effect by replacing traditional resistivity with complex resistivity of the Cole-Cole model in the frequency domain. After the forward modeling calculation of the electromagnetic field in the frequency domain that considers the IP effect, the transient electromagnetic field in time-domain is obtained by a time-frequency transform algorithm. In this paper, the resistivity is directly replaced by the time-variant resistivity expression of the Cole-Cole model by using digital filter algorithms when we simulate the transient electromagnetic fields in time- domain. The calculated result of the Cole-Cole model in time-domain and in frequency-domain are consistent with each other, as observed in the horizontal electric field and the vertical magnetic field comparisons, which indicates the correctness of the numerical computation method adopted in this paper. The research presented herein allows us to observe the influence of the IP effect on transient electromagnetic field as well as study the mechanisms of IP directly.

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Revil, A., A. Ghorbani, C. Mapeli, K. Livo, and M. Prasad. "Differential pressure dependence of the complex conductivity of sandstones." Geophysical Journal International 219, no. 3 (September 20, 2019): 2110–24. http://dx.doi.org/10.1093/gji/ggz420.

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SUMMARY An experimental work is undertaken to understand the effect of the differential pressure (in the range 3–20.7 MPa) upon the complex conductivity of sedimentary rocks. We use five sandstone core samples from outcrops and a sandstone analog built from sintered glass beads. The spectra were fitted with a Cole–Cole complex conductivity model and the four Cole–Cole parameters were plotted as a function of the differential stress (in the range 3–20.7 MPa). The Cole–Cole relaxation times are analysed in terms of the evolution of the pore size with the differential pressure. Neither the relaxation time nor the Cole–Cole exponent show a strong dependence with the differential pressure indicating that the distribution of the relaxation times remains here roughly the same when the differential stress increases. More specifically, the Cole–Cole exponent does not describe the entire distribution of relaxation times, but the broadness of this distribution. Since the relaxation times are related to the pore sizes, this means that the pore sizes do not depend on the differential pressure in this case. The chargeability is essentially independent of the differential pressure and close to the upper value that can be reached in rocks without metallic particles. This also means that the conductivity of these rocks is dominated by their surface conductivity contribution considering the low pore water salinity used in this work. These results are interpreted thanks to the Stern layer polarization model. The Stern layer denotes the inner part of the electrical double layer coating the surface of the grains. The predictions of this model are mostly consistent with the data.

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Freeborn, Todd J., and Shelby Critcher. "Cole-Impedance Model Representations of Right-Side Segmental Arm, Leg, and Full-Body Bioimpedances of Healthy Adults: Comparison of Fractional-Order." Fractal and Fractional 5, no. 1 (January 28, 2021): 13. http://dx.doi.org/10.3390/fractalfract5010013.

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The passive electrical properties of a biological tissue, referred to as the tissue bioimpedance, are related to the underlying tissue physiology. These measurements are often well-represented by a fractional-order equivalent circuit model, referred to as the Cole-impedance model. Objective: Identify if there are differences in the fractional-order (α) of the Cole-impedance parameters that represent the segmental right-body, right-arm, and right-leg of adult participants. Hypothesis: Cole-impedance model parameters often associated with tissue geometry and fluid (R∞, R1, C) will be different between body segments, but parameters often associated with tissue type (α) will not show any statistical differences. Approach: A secondary analysis was applied to a dataset collected for an agreement study between bioimpedance spectroscopy devices and dual-energy X-ray absoptiometry, identifying the Cole-model parameters of the right-side body segments of N=174 participants using a particle swarm optimization approach. Statistical testing was applied to the different groups of Cole-model parameters to evaluate group differences and correlations of parameters with tissue features. Results: All Cole-impedance model parameters showed statistically significant differences between body segments. Significance: The physiological or geometric features of biological tissues that are linked with the fractional-order (α) of data represented by the Cole-impedance model requires further study to elucidate.

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Kanjaa, Mohammed, Khalid Mounirh, Soufiane El Adraoui, Otman El Mrabet, and Mohsine Khalladi. "AN ADE-TLM MODELING OF BIOLOGICAL TISSUES WITH COLE-COLE DISPERSION MODEL." Progress In Electromagnetics Research M 89 (2020): 161–69. http://dx.doi.org/10.2528/pierm19111203.

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Wang, K., X. J. Chen, X. W. Xu, G. Q. Liu, D. X. Zou, and W. D. Liu. "Influence of temperature on Cole-Cole dielectric model of oil-immersed bushing." IOP Conference Series: Materials Science and Engineering 220 (July 2017): 012017. http://dx.doi.org/10.1088/1757-899x/220/1/012017.

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Maundy, B., and A. S. Elwakil. "Extracting single dispersion Cole–Cole impedance model parameters using an integrator setup." Analog Integrated Circuits and Signal Processing 71, no. 1 (August 21, 2011): 107–10. http://dx.doi.org/10.1007/s10470-011-9751-1.

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Kang, Seogi, Dominique Fournier, and Douglas W. Oldenburg. "Inversion of airborne geophysics over the DO-27/DO-18 kimberlites — Part 3: Induced polarization." Interpretation 5, no. 3 (August 31, 2017): T327—T340. http://dx.doi.org/10.1190/int-2016-0141.1.

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The geologically distinct DO-27 and DO-18 kimberlites, often called the Tli Kwi Cho (TKC) kimberlites, have been used as a testbed for airborne geophysical methods applied to kimberlite exploration. This paper focuses on extracting chargeability information from time-domain electromagnetic (TEM) data. Three different TEM surveys, having similar coincident-loop geometry, have been carried out over TKC. Each records negative transients over the main kimberlite units and this is a signature of induced polarization (IP) effects. By applying a TEM-IP inversion workflow to a versatile time domain EM (VTEM) data set we decouple the EM and IP responses in the observations and then recover 3D pseudo-chargeability models at multiple times. A subsequent analysis is used to recover Cole-Cole parameters. Our models demonstrate that both DO-18 and DO-27 pipes are chargeable, but they have different Cole-Cole time constants: 110 and 1160 μs, respectively. At DO-27, we also distinguish between two adjacent kimberlite units based on their respective Cole-Cole time constants. Our chargeability models are combined with the density, magnetic susceptibility and conductivity models to build a 3D petrophysical model of TKC using only information obtained from airborne geophysics. Comparison of this final petrophysical model to a 3D geological model derived from the extensive drilling program demonstrates that we can characterize the three main kimberlite units at TKC: HK, VK, and PK in three dimensions by using airborne geophysics.

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Viezzoli, Andrea, Vladislav Kaminski, and Gianluca Fiandaca. "Modeling induced polarization effects in helicopter time domain electromagnetic data: Synthetic case studies." GEOPHYSICS 82, no. 2 (March 1, 2017): E31—E50. http://dx.doi.org/10.1190/geo2016-0096.1.

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We have developed a synthetic multiparametric modeling and inversion exercise undertaken to study the robustness of inverting airborne time-domain electromagnetic (TDEM) data to extract Cole-Cole parameters. The following issues were addressed: nonuniqueness, ill posedness, dependency on manual processing and the effect of constraints, and a priori information. We have used a 1D layered earth model approximation and lateral constraints. Synthetic simulations were performed for several models and the corresponding Cole-Cole parameters. The possibility to recover these models by means of laterally constrained multiparametric inversion was evaluated, including recovery of chargeability distributions from shallow and deep targets based on analysis of induced polarization (IP) effects, simulated in airborne TDEM data. Different scenarios were studied, including chargeable targets associated with the conductive and resistive environments. In particular, four generic models were considered for the exercise: a sulfide model, a kimberlite model, and two generic models focusing on the depth of investigation. Our study indicated that, in cases when relaxation time ([Formula: see text]) values are in the range to which the airborne electromagnetic is most sensitive (e.g., approximately 1 ms), it is possible to recover deep chargeable targets (to depths more than 130 m) in association with high electrical conductivity and in resistive environments. Furthermore, it was found that the recovery of a deep conductor, masked by a shallower chargeable target, became possible only when full Cole-Cole modeling was used in the inversion. Lateral constraints improved the recoverability of model parameters. Finally, modeling IP effects increased the accuracy of recovered electrical resistivity models.

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Wang, Hong, Liang Yang, Xining Zhang, and Marcelo H. Ang. "Permittivity, loss factor and Cole-Cole model of acrylic materials for dielectric elastomers." Results in Physics 29 (October 2021): 104781. http://dx.doi.org/10.1016/j.rinp.2021.104781.

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González-Correa, C. A., E. Colina-Gallo, and D. A. Miranda-Mercado. "The alpha parameter of the Cole-Cole model as an indicator of fibromyalgia." Journal of Physics: Conference Series 1272 (July 2019): 012003. http://dx.doi.org/10.1088/1742-6596/1272/1/012003.

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Slater, Lee, Dimitrios Ntarlagiannis, and DeBonne Wishart. "On the relationship between induced polarization and surface area in metal-sand and clay-sand mixtures." GEOPHYSICS 71, no. 2 (March 2006): A1—A5. http://dx.doi.org/10.1190/1.2187707.

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Induced polarization (IP) measurements were conducted on saturated kaolinite-, iron-, and magnetite-sand mixtures as a function of varying percentage weight of a mineral constituent: 0%–100% for iron and magnetite and 0%–32% for kaolinite. We determined the specific surface area for each mineral using nitrogen gas adsorption, where the porosity of each mixture was calculated from weight loss after drying. We fit a Cole-Cole model (Cole and Cole, 1941) to the electrical data obtained for the magnetite and iron mixtures. In contrast, the kaolinite mixtures showed a power-law dependence of phase-on frequency. The global polarization magnitude we obtained from the Cole-Cole modeling of the iron and magnetite mixtures displays a single, near-linear dependence on the ratio of surface area to pore volume ([Formula: see text]) calculated for the mixtures. A similar relationship is found using a local measure of polarization (imaginary conductivity at 1 Hz) for the clay-sand mixtures. The [Formula: see text] appears to be a critical parameter for determining IP in both metallic- and clay-containing soils. This result is not easily reconciled with traditional models of induced polarization.

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Ke, Ganpan, Merrick Johnston, and Hefeng Dong. "Rock-physics models for bitumen-saturated sands: Fractional gradient model and Hashin-Shtrikman iterative model." GEOPHYSICS 77, no. 2 (March 2012): D7—D15. http://dx.doi.org/10.1190/geo2011-0338.1.

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Rock-physics modeling of heavy-oil-saturated sands requires adjustments and new approaches to the available fluid-substitution schemes used on conventional reservoirs. This paper introduces two models: the fractional-gradient model (FGM) for simulating the frequency dispersion of the shear modulus of pure bitumen and the Hashin-Shtrikman iterative model (HSIM) for modeling the moduli of bitumen-saturated sands as a function of frequency and temperature. Taylor expansion shows that the first-order FGM has higher resolution than the Maxwell model and lower complexity than the Cole-Cole model. In addition, FGM is superior to Maxwell and Cole-Cole models in that viscosity modeling does not need to be done prior to shear-modulus modeling. The building of HSIM is based on observations of the microstructure of the bitumen-saturated sands. Three main characteristics in the sands are observed in the simplified model, producing a range of stiff, medium, and soft effective matrices. Bitumen can dominate the matrix as if the quartz grains were suspended in it (soft); quartz grains can surround the bitumen (stiff); and a bitumen layer can form around the quartz grain (medium). The quartz grains are assumed to be statistically spherical. HSIM is obtained by iteratively calculating the HS bounds of the stiff and soft parts of the sands. The measured shear modulus of pure bitumen and bitumen-saturated sands at different frequencies and temperatures verify the validity of these two models. The combination of these two models gives a novel fluid-substitution routine for modeling the time-lapse response during steam-assist gravity draining thermal production of bitumen. The limitations of the two models also are discussed.

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Ley, Sebastian, Susanne Schilling, Ondrej Fiser, Jan Vrba, Jürgen Sachs, and Marko Helbig. "Ultra-Wideband Temperature Dependent Dielectric Spectroscopy of Porcine Tissue and Blood in the Microwave Frequency Range." Sensors 19, no. 7 (April 10, 2019): 1707. http://dx.doi.org/10.3390/s19071707.

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The knowledge of frequency and temperature dependent dielectric properties of tissue is essential to develop ultra-wideband diagnostic technologies, such as a non-invasive temperature monitoring system during hyperthermia treatment. To this end, we characterized the dielectric properties of animal liver, muscle, fat and blood in the microwave frequency range from 0.5 GHz to 7 GHz and in the temperature range between 30 °C and 50 °C. The measured data were modeled to a two-pole Cole-Cole model and a second-order polynomial was introduced to fit the Cole-Cole parameters as a function of temperature. The parametric model provides access to the dielectric properties of tissue at any frequency and temperature in the specified range.

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Liu, Ming, Jin Yang, Ju Feng, Tianyi Wang, and Hao Zhang. "A discussion on the performance of seven existing models proposed to describe induced polarization." GEOPHYSICS 81, no. 6 (November 2016): E459—E469. http://dx.doi.org/10.1190/geo2015-0672.1.

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Many types of classical models of the induced polarization (IP) effects of rock ore have been introduced in previous studies. Our focus is on determining the most effective model for describing the rock ore IP effects based on a numerical simulation calculation and a rock mineral spectrum experiment. We have constructed a Delphi 7 program for seven models to calculate the complex resistivity spectrum of phase. We have also evaluated the influences of the parameters on the spectrum and the spectral scope. More than 50 pieces of various natural rock ore samples from 16 regions were selected, and the frequency sweep measurements were completed using an SI-1260 Solartron spectrometer. Another program of seven models was developed using a differential evolution algorithm and least-squares for fitting the experimental spectral data. The purpose was to evaluate the ability of these models for fitting the IP effects. The results found that the influence laws on the spectrum of the different parameters, as well as the spectral scope of the models, were different. The natural samples measured revealed unimodal and bimodal phase spectra. Dias and multi-Cole-Cole models were optimal for characterizing the unimodal and bimodal phase spectra of the selected metal minerals, with the highest fitting precision root-mean-square (rms) error of 2.5% and 1.16%, respectively. Warburg, Cole-Cole, and generalized Cole-Cole models were suitable for the unimodal phase spectra, with the highest fitting precision of 3.67%, 3.01%, and 3.27%, respectively. Madden and Cantwell model was suitable for characterizing the silver-ore- and gold-bearing pyrite, but the rms was [Formula: see text] for other samples. The Debye model had an rms [Formula: see text] for characterizing all our experimental samples.

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Li, Jian, Dongji Lei, Chenguang Zhao, and Hui Meng. "Complex Resistivity Dispersion Characteristics of Water-Bearing Coal Based on Double Cole-Cole Model." Advances in Civil Engineering 2019 (December 11, 2019): 1–9. http://dx.doi.org/10.1155/2019/4913767.

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Reservoir fracture evaluation is an important research topic in the coalfield. In recent years, complex resistivity (CR) has been widely used in oil logging and achieved good results, such as permeability evaluation, water saturation (Sw) prediction, and aquifer identification. Therefore, the method has the potential to evaluate coal seam fracture. In the experiment, the real part R and imaginary part X of bituminous and anthracite coal with different Sw were measured by the impedance measuring instrument, then the Double Cole-Cole model was used to fit experimental data and analyze conductive mechanism. The main results are as follows: (1) the dispersion of CR parameters Reρ and Imρ is closely related to the metamorphism degree, frequency, and Sw; (2) induced polarization is the fundamental reason for the variation of coal samples’ complex resistivity parameters with frequency change; and (3) the Double Cole-Cole model agrees well with the experimental data, and the model parameters m1 and τ2 are strongly correlated with Sw. The parameters m1 and τ2 can be used to evaluate the Sw of fractures in coal seams and thus to evaluate the effect of hydraulic fracturing.

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Hannachi, Chaouki, Frédérique Deshours, George Alquie, and Hamid Kokabi. "Assessment of Finger Fat Pad Effect on CSRR-Based Sensor Scattering Parameters for Non-Invasive Blood Glucose Level Detection." Sensors 23, no. 1 (January 2, 2023): 473. http://dx.doi.org/10.3390/s23010473.

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This paper examines the effect of finger fat pad thickness on the accuracy performance of complementary split-ring resonator (CSRR)-based microwave sensors for non-invasive blood glucose level detection. For this purpose, a simplified four-layer Cole–Cole model along with a CSRR-based microwave sensor have been comprehensively analyzed and validated through experimentation. Computed scattering parameter (S-parameter) responses to different fat layer thicknesses are employed to verify the concordance of the studied model with the measurement results. In this respect, a figure of merit (FM) based on the normalized squared difference is introduced to assess the accuracy of the considered Cole–Cole model. We have demonstrated that the analyzed model agrees closely with the experimental validation. In fact, the maximum error difference for all five fingertips does not exceed 1.73 dB over the entire frequency range of interest, from 1 GHz to 4 GHz.

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Gudivaka, R., D. A. Schoeller, R. F. Kushner, and M. J. G. Bolt. "Single- and multifrequency models for bioelectrical impedance analysis of body water compartments." Journal of Applied Physiology 87, no. 3 (September 1, 1999): 1087–96. http://dx.doi.org/10.1152/jappl.1999.87.3.1087.

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The 1994 National Institutes of Health Technology Conference on bioelectrical impedance analysis (BIA) did not support the use of BIA under conditions that alter the normal relationship between the extracellular (ECW) and intracellular water (ICW) compartments. To extend applications of BIA to these populations, we investigated the accuracy and precision of seven previously published BIA models for the measurement of change in body water compartmentalization among individuals infused with lactated Ringer solution or administered a diuretic agent. Results were compared with dilution by using deuterium oxide and bromide combined with short-term changes of body weight. BIA, with use of proximal, tetrapolar electrodes, was measured from 5 to 500 kHz, including 50 kHz. Single-frequency, 50-kHz models did not accurately predict change in total body water, but the 50-kHz parallel model did accurately measure changes in ICW. The only model that accurately predicted change in ECW, ICW, and total body water was the 0/∞-kHz parallel (Cole-Cole) multifrequency model. Use of the Hanai correction for mixing was less accurate. We conclude that the multifrequency Cole-Cole model is superior under conditions in which body water compartmentalization is altered from the normal state.

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Revil, André, Antoine Coperey, Deqiang Mao, Feras Abdulsamad, Ahmad Ghorbani, Magali Rossi, and Dominique Gasquet. "Induced polarization response of porous media with metallic particles — Part 8: Influence of temperature and salinity." GEOPHYSICS 83, no. 6 (November 1, 2018): E435—E456. http://dx.doi.org/10.1190/geo2018-0089.1.

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We have investigated the influence of temperature and salinity upon the spectral induced polarization of 10 samples including rocks with their mineralization (galena, chalcopyrite) plus sand mixed with semiconductors such as magnetite grains, graphite, and pyrite cubes of two different sizes. Measurements are made in a temperature-controlled bath with a high-precision impedance meter and using NaCl solutions. We cover the temperature range 5°C−50°C and the frequency range [Formula: see text] to 45 kHz. For one large pyrite cube, we also investigated six salinities from 0.1 to [Formula: see text] (at 25°C, NaCl) and three salinities for graphite. The spectra are fitted with a Cole-Cole complex parametric conductivity model for which we provide a physical meaning to the four Cole-Cole parameters. As expected, the Cole-Cole exponent and the chargeability are independent of the temperature and salinity. The instantaneous and steady state (direct current [DC]) conductivities depend on the salinity and temperature. This temperature dependence can be fitted with an Arrhenius law (combining the Stokes-Einstein and Vogel-Fulcher-Tammann equations) with an activation energy in the range of [Formula: see text]. This activation energy is the same as for the bulk pore-water conductivity demonstrating the control by the background electrolyte of these quantities, as expected. The instantaneous and DC conductivities depend on the salinity in a predictable way. The Cole-Cole relaxation time decreases with the temperature and decreases with the salinity. This behavior can be modeled with an Arrhenius law with an apparent activation energy of [Formula: see text]. A finite-element model is used further to analyze the mechanisms of polarization, and it can reproduce the temperature and salinity dependencies observed in the laboratory.

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Butryło, Bogusław. "Modeling of linear dispersive materials using scalable time domain finite element scheme." Archives of Electrical Engineering 65, no. 4 (December 1, 2016): 719–32. http://dx.doi.org/10.1515/aee-2016-0050.

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Abstract This paper deals with some aspects of formulation and implementation of a broadband algorithm with build-in analysis of some dispersive media. The construction of the finite element method (FEM) based on direct integration of Maxwell’s equations and solution of some additional convolution integrals is presented. The broadband, fractional model of permittivity is approximated by a set of some relaxation sub-models. The properties of the 3D time-dependent formulation of the FEM algorithm are determined using a benchmark problem with the Cole-Cole and the Davidson-Cole models. Several issues associated with the implementation and some constraints of the broadband finite element algorithm are presented.

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33

Lytvynova, S. H. "All-Ukrainian project “Cloud services in education” as a factor of development of cloud-oriented educational environments in general educational institutions." CTE Workshop Proceedings 3 (March 20, 2015): 16–23. http://dx.doi.org/10.55056/cte.223.

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Purpose is to develop, study and experimental verification of the model cloud oriented learning environment of an educational institution (COLE CEI). Based on the specific purpose to develop and justify the following objectives: to identify the main characteristics of COLE CEI; develop and implement a model of COLE CEI; design activities of students and teachers and organize their interaction in a time limit of COLE and outside school hours; analyze the use of electronic educational resources in COLE; develop guidelines for use of the COLE CEI; develop organizational and methodological support, including the development of the necessary documentation, planning, monitoring and control. The object of the research is: the process of designing and using cloud-based learning environment of an educational institution. The subjects of the study is: the model of cloud oriented learning environment of educational institution. The hypothesis of the study is that the use of cloud oriented learning environment of an educational institution positively affect the training, create conditions for the development of new methods and technology education students, increase student motivation to learn, ensure the development of ICT competence of teachers, which in turn lead to positive qualitative changes in the organization of the members of the educational process. The experiment is based on a general, theoretical (analysis, synthesis, abstraction, idealization, formalization and generalization data), empirical (diagnostic, observational and mathematical statistical data processing) and experimental (stating formative experiments) research methods. The main research method – comprehensive experiment (period: 2014-2017 academic years).

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Lee, Junghaeng, Sangmo Kim, and Kwang Soo Cho. "Calculation of molecular weight distribution using extended Cole-Cole model and quadratic mixing rule." Korea-Australia Rheology Journal 33, no. 1 (February 2021): 65–78. http://dx.doi.org/10.1007/s13367-021-0006-0.

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35

Ji, Yanju, Xiangdong Meng, Jingya Shao, Yanqi Wu, and Qiong Wu. "The Generalized Skin Depth for Polarized Porous Media Based on the Cole–Cole Model." Applied Sciences 10, no. 4 (February 21, 2020): 1456. http://dx.doi.org/10.3390/app10041456.

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In the field of frequency-domain electromagnetic detection, skin depth is an important parameter for electromagnetic data interpretation and imaging. The classic skin depth formula is calculated based only on conductivity; the induced-polarization effect in real earth is not considered, so the imaging results have obvious errors. To solve these problems, based on plane wave theory and the Cole–Cole conductivity model, a generalized skin depth formula of polarized media is derived in the frequency domain. The accuracy of the generalized skin depth is verified through comparison with the classical skin depth. To show the practicability of this study, the theoretical data with induced polarization (IP) effects are used to explain the generalized skin depth for polarized porous media. The generalized skin depth calculation for a typical porous polarization model is related not only to conductivity, but also to polarization parameters, such as chargeability, characteristic time constant, and frequency dependence. At low-frequency excitation, the generalized skin depth formula can be used to calculate the propagation depth of electromagnetic waves relatively accurately for porous polarized media. This method can be applied to the calculation of electromagnetic wave propagation depths in complex dispersive media. Compared with non-polarized media, in porous polarized media, under low-frequency excitation, the electromagnetic wave propagates deeper, allowing the detection of deeper objects. The data interpretation and imaging of polarized porous media by the generalized skin depth formula have higher accuracy.

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Weigand, M., and A. Kemna. "Relationship between Cole–Cole model parameters and spectral decomposition parameters derived from SIP data." Geophysical Journal International 205, no. 3 (March 14, 2016): 1414–19. http://dx.doi.org/10.1093/gji/ggw099.

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BROWN, R. J. "EM COUPLING IN MULTIFREQUENCY IP AND A GENERALIZATION OF THE COLE-COLE IMPEDANCE MODEL*." Geophysical Prospecting 33, no. 2 (April 1985): 282–302. http://dx.doi.org/10.1111/j.1365-2478.1985.tb00435.x.

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Guo, Bin, Jian Li, and Henry Zmuda. "A New FDTD Formulation for Wave Propagation in Biological Media With Cole–Cole Model." IEEE Microwave and Wireless Components Letters 16, no. 12 (December 2006): 633–35. http://dx.doi.org/10.1109/lmwc.2006.885583.

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Ojha, Sandip Kumar, Prithwiraj Purkait, Biswendu Chatterjee, and Sivaji Chakravorti. "Application of Cole–Cole model to transformer oil‐paper insulation considering distributed dielectric relaxation." High Voltage 4, no. 1 (February 4, 2019): 72–79. http://dx.doi.org/10.1049/hve.2018.5079.

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Buendia, R., R. Gil-Pita, and F. Seoane. "Cole Parameter Estimation from the Modulus of the Electrical Bioimpeadance for Assessment of Body Composition. A Full Spectroscopy Approach." Journal of Electrical Bioimpedance 2, no. 1 (July 23, 2019): 72–78. http://dx.doi.org/10.5617/jeb.197.

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Abstract Activities around applications of Electrical Bioimpedance Spectroscopy (EBIS) have proliferated in the past decade significantly. Most of these activities have been focused in the analysis of the EBIS measurements, which eventually might enable novel applications. In Body Composition Assessment (BCA), the most common analysis approach currently used in EBIS is based on the Cole function, which most often requires curve fitting. One of the most implemented approaches for obtaining the Cole parameters is performed in the impedance plane through the geometrical properties that the Cole function exhibit in such domain as depressed semi-circle. To fit the measured impedance data to a semi-circle in the impedance plane, obtaining the Cole parameters in an indirect and sequential manner has several drawbacks. Applying a Non-Linear Least Square (NLLS) iterative fitting on the spectroscopy measurement, obtains the Cole parameters considering the frequency information contained in the measurement. In this work, from experimental total right side EBIS measurements, the BCA parameters have been obtained to assess the amount and distribution of whole body fluids. The values for the BCA parameters have been obtained using values for the Cole parameters estimated with both approaches: circular fitting on the impedance plane and NLLS impedance-only fitting. The comparison of the values obtained for the BCA parameters with both methods confirms that the NLLS impedance-only is an effective alternative as Cole parameter estimation method in BCA from EBIS measurements. Using the modulus of the Cole function as the model for the fitting would eliminate the need for performing phase detection in the acquisition process, simplifying the hardware specifications of the measurement instrumentation when implementing a bioimpedance spectrometer.

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Macnae, James. "Quantitative estimation of intrinsic induced polarization and superparamagnetic parameters from airborne electromagnetic data." GEOPHYSICS 81, no. 6 (November 2016): E433—E446. http://dx.doi.org/10.1190/geo2016-0110.1.

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The primary aim of my research is to improve the characterization of induced polarization (IP) responses in airborne electromagnetic (AEM) survey data. The principal objectives are to test alternative methodologies for quantitative modeling and inversion to extract the spatial variation of IP parameters using the inductively thin-sheet model. The methods tested first fit, by nonnegative least squares, an AEM decay to the early delay time data, using thin-sheet basis functions. This modeled AEM decay is assumed to represent the IP source. It is then convolved with a few Cole-Cole models spanning the range of parameter sensitivity to get IP basis functions appropriate for the AEM excitation. Method 1 fits a linear sum of several AEM basis functions plus one IP basis function at a time and chooses the model with least-fitting error at late delay times. Method 2 fits a linear sum of several IP and several AEM basis functions. Both methods fit IP affected airborne data well, with normalized fitting errors being reduced by a significant factor when IP affects the data and is taken into account. Using penalty weights, superparamagnetic (SPM) effects can be simultaneously estimated in the fitting process. Without such weighting, SPM and IP parameter estimations are unstable. Cole-Cole models predict that the sensitivity of inductive airborne IP collected at 25 or 30 Hz base frequency indicates little overlap with galvanic ground IP collected with a 0.125 Hz waveform. Many easy IP sulfide targets with IP physical properties determined by ground surveys are predicted not to have a detectable airborne IP response. Clays, however, are predicted to have a small detectable background response that for airborne data would not be well-fitted by a single Cole-Cole response.

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42

Compañ, Vicente, Ricardo Diaz-Calleja, Joaquín Diaz-Boils, and Jorge Escorihuela. "Distribution of Relaxation Times: Debye Length Distribution vs Electrode Polarization by a Cole−Cole Relaxation Model." Journal of The Electrochemical Society 169, no. 1 (January 1, 2022): 013506. http://dx.doi.org/10.1149/1945-7111/ac4bf9.

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Mobility, diffusivity and charge density in polyelectrolytes, are generally determined from electrochemical impedance spectroscopy following the electrode polarization analysis, in which at a given temperature the peaks in tan δ are fitted based on a model. These results can be different depending on the model used in the fitting of the curves. Generally, the models are based on a single Debye model or on the existence of an overlap in relaxation times (Cole–Cole model). In this work, we propose the alternative use of the distribution of the relaxation times by a distribution of the Debye length (LD), which allows the calculation of parameters such as mobility, diffusivity, and charge density as a function of LD in a more concise approach.

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Tartrat, Timothé, André Revil, Feras Abdulsamad, Ahmad Ghorbani, Damien Jougnot, Antoine Coperey, Béatrice Yven, and Rémi de la Vaissière. "Induced polarization response of porous media with metallic particles — Part 10: Influence of desiccation." GEOPHYSICS 84, no. 5 (September 1, 2019): E357—E375. http://dx.doi.org/10.1190/geo2019-0048.1.

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Desiccation influences the complex conductivity of porous media with disseminated metallic particles. We expand the mechanistic model developed in the previous papers of this series to include the effect of saturation upon the complex conductivity of mixtures of mineral grains, pyrite, and pore water. During desiccation, the salt is assumed to be segregated in the liquid pore water; therefore, the conductivity of the pore water increases when saturation decreases. We have performed 14 experiments corresponding to 91 complex conductivity spectra. In these experiments, the saturation of the water phase is changed over time by desiccation. The resulting spectra are fitted by a double Cole-Cole model used as the fitting model. We also developed a mechanistic model in which the chargeability and the relaxation time of the low-frequency polarization are expected to change with saturation in a predictable way. We first characterized the properties of the background material made by an illitic clay material. We determine how the Cole-Cole parameters depend on saturation. The Cole-Cole exponent is essentially independent on saturation. When the chargeability of the mixture is dominated by the presence of pyrite, it becomes independent of the saturation but a small effect on the chargeability is observed at low pyrite contents. The instantaneous conductivity of the background decreases with the saturation in a predictable way. The relaxation time depends on the inverse of the instantaneous conductivity and therefore on saturation. This dependence is well-explained through numerical simulations made with the finite-element method. Finally, we analyze the complex conductivity spectra of two clay-rock core samples from the Callovo-Oxfordian formation in the Paris Basin (France). The spectra are shown as a function of their desiccation and explained thanks to the newly developed model.

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Maenhout, Gertjan, Tomislav Markovic, and Bart Nauwelaers. "Controlled Measurement Setup for Ultra-Wideband Dielectric Modeling of Muscle Tissue in 20–45 °C Temperature Range." Sensors 21, no. 22 (November 17, 2021): 7644. http://dx.doi.org/10.3390/s21227644.

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In order to design electromagnetic applicators for diagnostic and therapeutic applications, an adequate dielectric tissue model is required. In addition, tissue temperature will heavily influence the dielectric properties and the dielectric model should, thus, be extended to incorporate this temperature dependence. Thus, this work has a dual purpose. Given the influence of temperature, dehydration, and probe-to-tissue contact pressure on dielectric measurements, this work will initially present the first setup to actively control and monitor the temperature of the sample, the dehydration rate of the investigated sample, and the applied probe-to-tissue contact pressure. Secondly, this work measured the dielectric properties of porcine muscle in the 0.5–40 GHz frequency range for temperatures from 20 °C to 45 °C. Following measurements, a single-pole Cole–Cole model is presented, in which the five Cole–Cole parameters (ϵ∞, σs, Δϵ, τ, and α) are given by a first order polynomial as function of tissue temperature. The dielectric model closely agrees with the limited dielectric models known in literature for muscle tissue at 37 °C, which makes it suited for the design of in vivo applicators. Furthermore, the dielectric data at 41–45 °C is of great importance for the design of hyperthermia applicators.

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Freeborn, Todd, and Bo Fu. "Fatigue-Induced Cole Electrical Impedance Model Changes of Biceps Tissue Bioimpedance." Fractal and Fractional 2, no. 4 (October 24, 2018): 27. http://dx.doi.org/10.3390/fractalfract2040027.

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Bioimpedance, or the electrical impedance of biological tissues, describes the passive electrical properties of these materials. To simplify bioimpedance datasets, fractional-order equivalent circuit presentations are often used, with the Cole-impedance model being one of the most widely used fractional-order circuits for this purpose. In this work, bioimpedance measurements from 10 kHz to 100 kHz were collected from participants biceps tissues immediately prior and immediately post completion of a fatiguing exercise protocol. The Cole-impedance parameters that best fit these datasets were determined using numerical optimization procedures, with relative errors of within approximately ± 0.5 % and ± 2 % for the simulated resistance and reactance compared to the experimental data. Comparison between the pre and post fatigue Cole-impedance parameters shows that the R ∞ , R 1 , and f p components exhibited statistically significant mean differences as a result of the fatigue induced changes in the study participants.

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46

Dias, Carlos A. "Developments in a model to describe low‐frequency electrical polarization of rocks." GEOPHYSICS 65, no. 2 (March 2000): 437–51. http://dx.doi.org/10.1190/1.1444738.

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The author reworks his total current conductivity function introduced in a previous paper, related to electrical polarization of rocks in the frequency range of 1 MHz to 10−3 Hz. The original five parameters in this function are replaced by new ones, which from the beginning have clear petrophysical and electrochemical meanings and well‐defined ranges of variation. Some classical models are derived as particular cases of it. The main existing models proposed to describe induced polarization (IP) are analyzed, and most of them are grouped together under a common circuit analog representation and a respective generating function. A circuit analog is assigned to each model. The multi‐Cole‐Cole model circuit analog reveals intrinsic constraints involving the values of its circuit elements. Because of these constraint relations and the relaxation times ratio (τ1/τ2)—usually many orders of magnitude from unity—the model has no physical validation to represent single‐phase material systems (in the sense of the polarization). The performance and analysis of the various models to describe a few well‐selected experimental data show that only two of the models, the multi‐Cole‐Cole and Dias models, can provide a function structure capable of fitting these data. This fact, the associated petrophysical interpretation consistency, and the basic characteristics of these two models, such as the way they were derived (empirically, the former; phenomenologically, the latter) and the number of coefficients in the function (directly related to the degree of ambiguity of their determination), make the author’s model attractive and promising.

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Fiandaca, Gianluca, Line Meldgaard Madsen, and Pradip Kumar Maurya. "Re‐parameterisations of the Cole–Cole model for improved spectral inversion of induced polarization data." Near Surface Geophysics 16, no. 4 (July 27, 2018): 385–99. http://dx.doi.org/10.3997/1873-0604.2017065.

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Ming-fu, Fu, Ju Hai-yan, Xu Bin, and Xu Man-qing. "Dynamic Responses of Ground Vibration due to a Moving Load by using Cole–Cole Model." Procedia Engineering 28 (2012): 220–23. http://dx.doi.org/10.1016/j.proeng.2012.01.709.

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Khamzin, A. A., R. R. Nigmatullin, and I. I. Popov. "Microscopic model of a non-Debye dielectric relaxation: The Cole-Cole law and its generalization." Theoretical and Mathematical Physics 173, no. 2 (November 2012): 1604–19. http://dx.doi.org/10.1007/s11232-012-0135-1.

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Picotti, Stefano, and José M. Carcione. "Numerical simulation of wave-induced fluid flow seismic attenuation based on the Cole-Cole model." Journal of the Acoustical Society of America 142, no. 1 (July 2017): 134–45. http://dx.doi.org/10.1121/1.4990965.

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Journal articles on the topic 'Cole-Cole model'

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