Bulk modulus for fluid-saturated rocks at high frequency: Modification of squirt flow model proposed by Mavko & Jizba

2021 ◽  
Author(s):  
Liming Zhao ◽  
Tongjun Chen ◽  
Tapan Mukerji ◽  
Genyang Tang
Keyword(s):  
Bulk Modulus ◽  
High Frequency ◽  
Flow Model ◽  
Crack Density ◽  
Total Porosity ◽  
Original Matrix ◽  
The Matrix ◽  
Potential Applications ◽  
Applicable Range ◽  
Pore Fraction

Summary The squirt flow model, proposed by Mavko & Jizba, has been widely used in explaining the frequency-related modulus and velocity dispersion between ultrasonic and seismic measurements. In this model, the saturated bulk modulus at high frequency is obtained by taking the so-called unrelaxed frame bulk modulus into Biot's or Gassmann's formula. When using Gassmann's formula, the mineral bulk modulus is taken as matrix bulk modulus. However, the soft pores (cracks) in rocks have a weakening effect on the matrix bulk modulus. The saturated bulk modulus at high frequency calculated with mineral bulk modulus as matrix bulk modulus is higher than the real values. To overcome this shortcoming we propose a modified matrix bulk modulus based on the Betti-Rayleigh reciprocity theorem and non-interaction approximation. This modification takes the weakening effect of soft pores (cracks) into consideration and allows calculating the correct saturated bulk modulus at high frequency under different soft-pore fractions (the ratio of soft porosity to total porosity) or crack densities. We also propose an alternative expression of the modified matrix bulk modulus, which can be directly obtained from laboratory measurements. The numerical results show that the saturated bulk modulus at high frequency using the original matrix bulk modulus (i.e. mineral bulk modulus) is approximated to that using the modified one only for rocks containing a small amount of soft-pore fraction. However, as the soft-pore fraction becomes substantial, using the original bulk matrix modulus is not applicable, but the modified one is still applicable. Furthermore, the results of the modified squirt flow model show good consistency with published numerical and experimental data. The proposed modification extends the applicable range of soft-pore fraction (crack density) of the previous model, and has potential applications in media having a relatively substantial fraction of soft pores or almost only soft pores, such as granite, basalt, and thermally-cracked glasses.

Bulk modulus for fluid-saturated rocks at intermediate frequencies: Modification of squirt flow model proposed by Gurevich et al.

2021 ◽  
Author(s):  
Liming Zhao ◽  
Tongjun Chen ◽  
Genyang Tang
Keyword(s):  
Bulk Modulus ◽  
Flow Model ◽  
Full Range ◽  
Total Porosity ◽  
Wave Dispersion ◽  
Intermediate Frequency ◽  
Original Model ◽  
Frequency Range ◽  
The Matrix ◽  
Pore Fraction

Summary Squirt flow is an essential cause of wave dispersion and attenuation in saturated rocks. The squirt flow model, proposed by Gurevich et al. (2010), has been widely applied to explain the wave dispersion and associated attenuation for saturated rocks at sonic and seismic frequency bands. In this model, the saturated bulk modulus is obtained by taking the partially relaxed frame bulk modulus as the dry frame modulus into Gassmann's formula with the mineral bulk modulus as the matrix bulk modulus. However, because of the weakening effect of soft pores on rock matrix bulk modulus, the model cannot accurately predict the saturated bulk modulus when the soft-pore fraction (the ratio of the soft porosity to total porosity) becomes large. We modified this model following Gurevich et al. (2010) by setting a different boundary condition. The modified squirt flow model can obtain correct saturated bulk modulus for large soft-pore fractions in the full range of frequencies, showing excellent consistency with the predictions of Gassmann and Mavko & Jizba (modified) at both low- and high-frequency limits, respectively. Modeling results show that the saturated bulk moduli and their dispersions calculated by the original and modified models exhibit little difference when the soft-pore fraction is small. Under this condition, the original model is as effective and accurate as the modified one. When the soft-pore fraction becomes larger, the differences in the bulk moduli and their dispersions become substantial, suggesting the original model is not applicable any longer. Furthermore, the differences calculated for the intermediate frequency range is even more obvious than other ranges, suggesting that the modified model should be used to calculate the bulk modulus and the dispersion in this frequency range. In summary, the modified squirt flow model can extend the original model's applicable range in terms of soft-pore fraction and has a potential application in rocks having a relatively large amount of soft-pore fraction such as basalts.

Da eine oder mehrere betroffen …

2020 ◽  
Vol 48 (1) ◽  
pp. 47-100
Author(s):  
Melitta Gillmann
Keyword(s):  
High Frequency ◽  
Formal Language ◽  
Subordinate Clause ◽  
Matrix Clause ◽  
Very High Frequency ◽  
Corpus Study ◽  
Causal Relations ◽  
Legal Texts ◽  
The Matrix ◽  
Very High

AbstractBased on a corpus study conducted using the GerManC corpus (1650–1800), the paper sketches the functional and sociosymbolic development of subordinate clause constructions introduced by the subjunctor da ‘since’ in different text genres. In the second half of the 17th and the first half of the 18th century, the da clauses were characterized by semantic vagueness: Besides temporal, spatial and causal relations, the subjunctor established conditional, concessive, and adversative links between clauses. The corpus study reveals that different genres are crucial to the readings of da clauses. Spatial and temporal usages, for example, occur more often in sermons than in other genres. The conditional reading, in contrast, strongly tends to occur in legal texts, where it displays very high frequency. This could be the reason why da clauses carry indexical meaning in contemporary German and are associated with formal language. Over the course of the 18th century, the causal usages increase in all genres. Surprisingly, these causal da clauses tend to be placed in front of the matrix clause despite the overall tendency of causal clauses to follow the matrix clause.

scholarly journals Development of a Decellularized Porcine Esophageal Matrix for Potential Applications in Cancer Modeling

Cells ◽  
2021 ◽  
Vol 10 (5) ◽  
pp. 1055
Author(s):  
Hersh Chaitin ◽  
Michael L. Lu ◽  
Michael B. Wallace ◽  
Yunqing Kang
Keyword(s):  
Cell Growth ◽  
Lymphatic Vessels ◽  
Significant Loss ◽  
Cancer Cell Growth ◽  
Cell Growth And Migration ◽  
Decellularized Extracellular Matrix ◽  
Cancer Models ◽  
The Matrix ◽  
Potential Applications ◽  
And Migration

Many decellularized extracellular matrix-derived whole organs have been widely used in studies of tissue engineering and cancer models. However, decellularizing porcine esophagus to obtain decellularized esophageal matrix (DEM) for potential biomedical applications has not been widely investigated. In this study a modified decellularization protocol was employed to prepare a porcine esophageal DEM for the study of cancer cell growth. The cellular removal and retention of matrix components in the porcine DEM were fully characterized. The microstructure of the DEM was observed using scanning electronic microscopy. Human esophageal squamous cell carcinoma (ESCC) and human primary esophageal fibroblast cells (FBCs) were seeded in the DEM to observe their growth. Results show that the decellularization process did not cause significant loss of mechanical properties and that blood ducts and lymphatic vessels in the submucosa layer were also preserved. ESCC and FBCs grew on the DEM well and the matrix did not show any toxicity to cells. When FBS and ESCC were cocultured on the matrix, they secreted more periostin, a protein that supports cell adhesion on matrix. This study shows that the modified decellularization protocol can effectively remove the cell materials and maintain the microstructure of the porcine esophageal matrix, which has the potential application of studying cell growth and migration for esophageal cancer models.

An Overall Approach for Microcrack and Inhomogeneity Toughening in Brittle Solids

1999 ◽  
Vol 15 (2) ◽  
pp. 57-68
Author(s):  
Huang Hsing Pan
Keyword(s):  
Poisson Ratio ◽  
Crack Density ◽  
Mean Field ◽  
Analytic Form ◽  
Density Parameter ◽  
Brittle Solids ◽  
The Matrix ◽  
Microcrack Toughening ◽  
Average Quantity ◽  
The Mean

ABSTRACTBased on the weight function theory and Hutchinson's technique, the analytic form of the toughness change near a crack-tip is derived. The inhomogeneity toughening is treated as an average quantity calculated from the mean-field approach. The solutions are suitable for the composite materials with moderate concentration as compared with Hutchinson's lowest order formula. The composite has the more toughened property if the matrix owns the higher value of the Poisson ratio. The composite with thin-disc inclusions obtains the highest toughening and that with spheres always provides the least effective one. For the microcrack toughening, the variations of the crack shape do not significantly affect the toughness change if the Budiansky and O'Connell crack density parameter is used. The explicit forms for three types of the void toughening and two types of the microcrack toughening are also shown.

scholarly journals Bibliometric Analysis of Studies on Tumor Organoids

2021 ◽  
Author(s):  
Qiwei Chen ◽  
Yu Zhang ◽  
Kun Li ◽  
Zhikai Zhang ◽  
Ya Wang ◽  
...  
Keyword(s):  
Future Development ◽  
Hot Spots ◽  
High Frequency ◽  
Visual Analysis ◽  
Drug Effects ◽  
Research Field ◽  
The Matrix ◽  
Genetic Mechanisms ◽  
Double Clustering ◽  
High Frequency Words

Abstract Background: Organoid is an artificially grown mass of cells or tissues, which is similar to an organ. It can replicate the complexity of an organ and can be used for gaining a better understanding of diseases. In this study, the hot spots of “organoids” were classified into 6 categories and 10 aspects, and organoids used for studying genetic mechanisms, drug effect, and metabolism of tumors showed the greatest potential for future development.Methods: A total of 1550 articles relevant to organoid in tumor research field were recruited as research samples. High-frequency words and text/co-word matrix were constructed by BICOMB software. gCLUTO software was applied to analyze the matrix by double-clustering and visual analysis subsequently to identify the hotspot in this area.Results: We constructed a text and co-word matrix composed of 21 high-frequency words and 1550 articles and generated a hotspot “peak map” based on double-clustering analysis. The strategic coordinates approach was used to assess the research prospects of each hotspot and the connections between these hotspots.Conclusions: In this study, we classified the hot-spots of “organoid” into 6 categories and 10 aspects. Calculation and analysis revealed that the field of tumor organoid shows a slight trend of polarization, and organoid for studying the genetic mechanisms, drug effects and metabolism of tumor shows the greatest potential for future development.

scholarly journals Lossless Linear Integer signal Resampling

2012 ◽  
pp. 225-233
Author(s):  
S.Raghavendra Prasad ◽  
Dr.P.Ramana Reddy
Keyword(s):  
Matrix Factorization ◽  
High Frequency ◽  
Irreversible Process ◽  
Polynomial Interpolation ◽  
Factorization Method ◽  
Special Cases ◽  
The Matrix ◽  
Frequency Components ◽  
Linear Transform ◽  
Signal Resampling

This paper describes about signal resampling based on polynomial interpolation is reversible for all types of signals, i.e., the original signal can be reconstructed losslessly from the resampled data. This paper also discusses Matrix factorization method for reversible uniform shifted resampling and uniform scaled and shifted resampling. Generally, signal resampling is considered to be irreversible process except in some special cases because of strong attenuation of high frequency components. The matrix factorization method is actually a new way to compute linear transform. The factorization yields three elementary integer-reversible matrices. This method is actually a lossless integer-reversible implementation of linear transform. Some examples of lower order resampling solutions are also presented in this paper.

scholarly journals Institutional Traps of Digitalization of Russian Higher Education

2021 ◽  
Vol 30 (3) ◽  
pp. 59-75
Author(s):  
M. A. Golovchin
Keyword(s):  
Higher Education ◽  
Large Scale ◽  
New Technologies ◽  
Teaching Staff ◽  
Original Matrix ◽  
Russian Higher Education ◽  
The Matrix ◽  
Institutional Traps ◽  
The Impact ◽  
Russian Universities

In 2016-2018 the state in Russia adopted a package of program documents, which implies the transfer of education to the large-scale introduction of digital technologies. This phenomenon has been called “digitalization of education”. In scientific literature, electronization and digitalization are increasingly called one of the institutional traps for the development of Russian universities, since the corresponding institutional environment has not yet been formed due to the forced nature of innovations. As a result, the processes of introducing new technologies into education are still not regulated. Within the framework of the purpose of the study, the manifestations of the trap of electronization and digitalization of Russian higher education were analyzed on the basis of sociological data, and the theoretical modeling of the process of adaptation of educational agents to the institution of digitalization was carried out.In the course of the study, the approaches were summarized that have been developed in discussions on educational digitalization. The article presents the author’s vision of the studied phenomenon as an institutional trap; as well as understanding of the institutional features and characteristics of electronization and digitalization in education.The research method is the analysis of estimates obtained in the course of an expert survey which was conducted by the Vologda Scientific Center of the Russian Academy of Sciences among the representatives of the teaching staff of state universities in the Vologda region. In the course of this analysis, the indicators of educational digitalization as an effective innovation were clarified such as an increased accessibility of educational resources; simplification of communication and the process of transferring knowledge from teacher to student; increased opportunities for training specialists for the new (digital) economy; improving the quality of education in universities, etc. Based on the results of the empirical study, it has been determined that the conditions for the development of digitalization in Russian universities are currently ambiguous, which is closely related to the level of competitiveness of the educational organization.The scientific novelty of the research consists in the presentation of an original matrix describing the process of university employees adaptation to the conditions of digital transformation of education. The matrix is proposed on the basis of a sociological analysis of the impact of the trap of electronization and digitalization on the activities of educational agents. The matrix can be taken into account in the practice of higher education management.

scholarly journals Lateral boundary conditions for a local anisotropic ice-flow model

2002 ◽  
Vol 35 ◽  
pp. 503-509 ◽  
Author(s):  
Olivier Gagliardini ◽  
Jacques Meyssonnier
Keyword(s):  
Boundary Conditions ◽  
Flow Model ◽  
Ice Sheet ◽  
Lateral Boundary ◽  
Local Flow ◽  
Ice Flow ◽  
Lateral Boundary Conditions ◽  
Potential Applications ◽  
Two Dimensional Flow ◽  
Spatial Domains

AbstractA local two-dimensional flow model which accounts for the anisotropic behaviour of polar ice and the evolution of its strain-induced anisotropy is briefly reviewed. Due to its complexity, it is not yet possible to use this model to simulate the flow of a whole ice sheet, and its potential applications are presently restricted to limited spatial domains around existing drilling sites. In order to calculate the local flow of ice, boundary conditions must be applied on the lateral edges of the studied domain. Since these limits correspond to fictitious sections of the ice sheet, the type of boundary condition to adopt is not obvious. In the present paper, different kinds of boundary conditions of the Dirichlet type, applied at the lateral boundary of an idealized ice sheet of simplified geometry, are discussed. This will serve as a first step towards the coupling of the local flow model with a global ice-sheet flow model.

Thermoelastic Constitutive Equations for Chemically Hardening Materials

1974 ◽  
Vol 41 (3) ◽  
pp. 652-657 ◽  
Author(s):  
Bernard W. Shaffer ◽  
Myron Levitsky
Keyword(s):  
Bulk Modulus ◽  
Strain Rate ◽  
Chemical Reaction ◽  
Constitutive Equations ◽  
Strain Energy ◽  
Elastic Solid ◽  
Time Dependent ◽  
Component Model ◽  
Two Component ◽  
Potential Applications

Thermoelastic constitutive equations are derived for a material undergoing solidification or hardening as the result of a chemical reaction. The derivation is based upon a two component model whose composition is determined by the degree of hardening, and makes use of strain-energy considerations. Constitutive equations take the form of stress rate-strain rate relations, in which the coefficients are time-dependent functions of the composition. Specific results are developed for the case of a material of constant bulk modulus which undergoes a transition from an initial liquidlike state into an isotropic elastic solid. Potential applications are discussed.

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