Relevant bibliographies by topics / Anisotropy

Academic literature on the topic 'Anisotropy'

Author: Grafiati
Published: 4 June 2021
Last updated: 24 August 2024

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Journal articles on the topic "Anisotropy"

1

Hagiwara, Teruhiko. "Apparent dip and apparent anisotropy from multifrequency triaxial induction measurements." GEOPHYSICS 76, no. 1 (January 2011): F1—F13. http://dx.doi.org/10.1190/1.3511349.

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The triaxial (or multicomponent) induction log is used to measure not only the resistivity anisotropy of an anisotropic formation but also the relative dip of the tool with respect to the formation. The anisotropic resistivity and the relative dip of layered formations are also inverted from the triaxial induction-log measurements at a depth by assuming a homogeneous anisotropic formation or at multiple depths by assuming a multilayered formation model. When the triaxial induction log is run at multiple frequencies, multifrequency focusing can be applied to the log measurements. Then, the apparent dip is algebraically defined from the frequency-focused triaxial induction measurements at a depth. The apparent dip yields the true dip in an anisotropic formation. The algebraically calculated apparent dip may be used to determine the effective dip in layered formations. The apparent dip yields the true dip in thinly bedded formations. The apparentdip also yields the true dip in thick anisotropic formations. However, the apparent dip yields a smaller dip than the true dip when the anisotropy is small (the anisotropy effect). It yields a much smaller dip in thick isotropic formations. Like the apparent dip, the apparent anisotropy is algebraically defined from the frequency-focused triaxial induction measurements at a depth. The apparent anisotropy yields the true anisotropy in an anisotropic formation. The algebraically calculated apparent anisotropy may be applied to layered formations. The apparent anisotropic resistivity (horizontal and vertical) can likewise be determined algebraically from the frequency-focused triaxial data. In contrast to the apparent dip, which yields the true dip in thinly bedded formations but not in thicker formations, the apparent anisotropy yields the true anisotropy in thick anisotropic formations but not in thinner anisotropic formations. The apparent anisotropy is affected by the shoulder-bed anisotropy when the formation is not thick (the shoulder-bed effect).
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Thomsen, Leon. "Weak elastic anisotropy." GEOPHYSICS 51, no. 10 (October 1986): 1954–66. http://dx.doi.org/10.1190/1.1442051.

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Most bulk elastic media are weakly anisotropic. The equations governing weak anisotropy are much simpler than those governing strong anisotropy, and they are much easier to grasp intuitively. These equations indicate that a certain anisotropic parameter (denoted δ) controls most anisotropic phenomena of importance in exploration geophysics, some of which are nonnegligible even when the anisotropy is weak. The critical parameter δ is an awkward combination of elastic parameters, a combination which is totally independent of horizontal velocity and which may be either positive or negative in natural contexts.
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Wu, Feng Min, and Yuh Zhang Fang. "Anisotropic Growth of Metal Chains on Anisotropic Substrate." Solid State Phenomena 121-123 (March 2007): 1129–32. http://dx.doi.org/10.4028/www.scientific.net/ssp.121-123.1129.

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Based on the exchange mechanism of metal islands growth on anisotropic metal surfaces, the growth processes of anisotropic Cu islands on the anisotropic Pd (110) surface are investigated by Monte Carlo simulations with realistic growth model and physical parameters. The anisotropic diffusion and anisotropic sticking of Cu adatoms are included in the simulation model after being considered the anisotropy of Pd (110) surface and compared to the experiments. It is found that the larger diffusion rate along the [110] channels of Pd (110) surface gives rise to a slower growth rate of Cu island in this direction, unless special effect of the anisotropic sticking is invoked. The simulation results show that the shape anisotropy of Cu islands is mainly due to the sticking anisotropy rather than the diffusion anisotropy.
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4

Zhu, H., and L. M. Zhang. "Characterizing geotechnical anisotropic spatial variations using random field theory." Canadian Geotechnical Journal 50, no. 7 (July 2013): 723–34. http://dx.doi.org/10.1139/cgj-2012-0345.

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In this study, anisotropic heterogeneous geotechnical fields are characterized using random field theory, in which five basic patterns of material anisotropy are simulated including isotropy, transverse anisotropy, rotated anisotropy, general anisotropy, and general rotated anisotropy. Theoretical formulations of scale of fluctuation as a function of directional angle are developed for the five basic patterns of anisotropy through modifications of the coordinate system. These formulations of scale of fluctuation are identical for different correlation structures. Correlation functions for the exponential and Gaussian correlation structures are also derived. The matrix decomposition method is then applied to generate anisotropic random fields. The generated random field correlated data are verified with two realizations of transverse anisotropy and general rotated anisotropy random fields. Test values of the sample mean, sample deviation, and scales of fluctuation in six directions match well with the prescribed values. This study provides a technique to characterize inherent geotechnical variability and anisotropy, which is required to realistically simulate complex geological properties in engineering reliability analysis and design.
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Luo, Tianya, Xiangyun Hu, Longwei Chen, and Guilin Xu. "Investigating the Magnetotelluric Responses in Electrical Anisotropic Media." Remote Sensing 14, no. 10 (May 11, 2022): 2328. http://dx.doi.org/10.3390/rs14102328.

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When interpreting magnetotelluric (MT) data, because of the inherent anisotropy of the earth, considering electrical anisotropy is crucial. Accordingly, using the edge-based finite element method, we calculated the responses of MT data for electrical isotropic and anisotropic models, and subsequently used the anisotropy index and polar plot to depict MT responses. High values of the anisotropy index were mainly yielded at the boundary domains of anomalous bodies for isotropy cases because the conductive differences among isotropic anomalous bodies or among anomalous bodies and background earth can be regarded as macro-anisotropy. However, they only appeared across anomalous bodies in the anisotropy cases. The anisotropy index can directly differentiate isotropy from anisotropy but exhibits difficulty in reflecting the azimuth of the principal conductivities. For the isotropy cases, polar plots are approximately circular and become curves with a big ratio of the major axis to minor axis, such as an 8-shaped curve for the anisotropic earth. Furthermore, the polar plot can reveal the directions of principal conductivities. However, distorted by anomalous bodies, polar plots with a large ratio of the major axis to minor axis occur in isotropic domains around the anomalous bodies, which may lead to the misinterpretation of these domains as anisotropic earth. Therefore, combining the anisotropy index with a polar plot facilitates the identification of the electrical anisotropy.
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Vladimirov, Ivaylo N., and Stefanie Reese. "Prediction of Springback in Unconstrained Bending by a Model for Evolving Elastic and Plastic Anisotropy." Key Engineering Materials 554-557 (June 2013): 2330–37. http://dx.doi.org/10.4028/www.scientific.net/kem.554-557.2330.

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Sheet metals exhibit anisotropic plastic behavior due to the large plastic deformations that occur during the rolling of the sheet and which induce texture and are responsible for the initial anisotropy. There exist various possibilities to introduce plastic anisotropy into the finite element modelling of sheet metal forming. The initial yield anisotropy can be incorporated either through an anisotropic yield surface or directly by means of a crystallographic texture model. Here, one basically differentiates between empirical and phenomenological anisotropic yield function equations, where the anisotropy coefficients can be obtained from mechanical tests, and texture-based models the coefficients of which are directly determined based on experimentally obtained orientation distributions. Another type of anisotropy that can be usually found in anisotropic materials is the elastic anisotropy. In metal plasticity one often considers the effect of elastic anisotropy significantly smaller than the effect of plastic anisotropy. Consequently, elastic isotropic expressions are often used for elastic stored energy functions with anisotropic yield criteria. However, the influence of elastic anisotropy in the elastoplastic behavior can be very important especially during elastic recovery processes during unloading after forming and springback. This research focuses, therefore, on the study of the influence of elastic anisotropy on the amount of springback in bending processes such as e.g. unconstrained bending. We discuss a finite strain material model for evolving elastic and plastic anisotropy combining nonlinear isotropic and kinematic hardening. The evolution of elastic anisotropy is described by representing the Helmholtz free energy as a function of a family of evolving structure tensors. In addition, plastic anisotropy is modelled via the dependence of the yield surface on the same family of structure tensors. Exploiting the dissipation inequality leads to the interesting result that all tensor-valued internal variables are symmetric. Thus, the integration of the evolution equations can be efficiently performed by means of an algorithm that automatically retains the symmetry of the internal variables in every time step. The material model has been implemented as a user material subroutine UMAT into the commercial finite element software ABAQUS/Standard and has been applied to the simulation of springback of unconstrained bending.
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Secco, R. A., and P. S. Balog. "On the possibility of anisotropic heat flow in the inner core." Canadian Journal of Earth Sciences 38, no. 6 (June 1, 2001): 975–82. http://dx.doi.org/10.1139/e00-116.

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We consider the possibility of anisotropic heat flow in the inner core by examining the potential for anisotropic thermal conductivity of hexagonal close-packed (hcp-)Fe. Because hcp-Fe exists only at pressures above 13 GPa at room temperature, we investigate thermal conductivity anisotropy in analog material Gd by measuring the electrical conductivity and applying the Wiedemann–Franz Law to determine thermal conductivity (k). The electrical conductivity anisotropy of Gd was measured at pressures up to 1.4 GPa and temperatures up to 873 K in the hcp phase range. At elevated pressure, the variation with temperature of anisotropic thermal conductivity of Gd single crystal resembles the anisotropic behavior at high temperature and 1 atm observed in earlier work. The temperature range of anisotropy of thermal conductivity of Gd, where kc > ka, is extended by pressure, but the anisotropy disappears before the high temperature hcp[Formula: see text]bcc (body-centered cubic) transformation. Our results on hcp-Gd lead us to raise the question of the possibility of hcp-Fe exhibiting anisotropy of thermal conductivity. Together with the known seismic anisotropy of the inner core, and the inferred textural alignment of hcp crystals causing it, we suggest some implications that an anisotropy of thermal conductivity of hcp-Fe, and a concomitant anisotropy of inner core heat flow, could have on thermally driven core processes.
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Zhang, Chao, Xiangzhuang Kong, Xian Wang, Yanxia Du, and Guangming Xiao. "A Predicting Model for the Effective Thermal Conductivity of Anisotropic Open-Cell Foam." Energies 15, no. 16 (August 22, 2022): 6091. http://dx.doi.org/10.3390/en15166091.

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The structural anisotropy of open-cell foam leads to the anisotropy of effective thermal conductivity (ETC). To quantitatively analyze the effect of structural anisotropy on the anisotropy of ETC, a new predicting model for the ETC of anisotropic open-cell foam was proposed based on an anisotropy tetrakaidecahedron cell (ATC). Feret diameters in three orthogonal directions obtained by morphological analysis of real foam structures were used to characterize the anisotropy of ATC. To validate our proposed anisotropic model, the ETCs of real foam structures in three orthogonal directions predicted by it were compared with the numerical results, for which the structures of numerical models are reconstructed by X-ray computed tomography (X-CT). Using the present anisotropic model, the influences of the thermal conductivity ratio (TCR) and porosity of the foams on the anisotropic ratios of ETCs are also investigated. Results show that there is good consistency between the ETCs obtained by the anisotropic model and the numerical method. The maximum relative errors between them are 2.84% and 13.57% when TCRs are 10 and 100, respectively. The present anisotropic model can not only predict the ETCs in different orthogonal directions but also quantitatively predict the anisotropy of ETC. The anisotropies of the ETCs decrease with porosity because the proportion of the foam skeleton decreases. However, the anisotropies of ETCs increase with TCR, and there exist asymptotic values in anisotropic ratios of ETCs as TCR approaches infinity and they are equal to the relative Feret diameters in different orthogonal directions.
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Edwin, Privita Edwina Rayappan George, Sumeet Kumar, Srestha Roy, Basudev Roy, and Saumendra Kumar Bajpai. "Anisotropic 3D confinement of MCF-7 cells induces directed cell-migration and viscoelastic anisotropy of cell-membrane." Physical Biology 20, no. 1 (November 9, 2022): 016003. http://dx.doi.org/10.1088/1478-3975/ac9bc1.

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Abstract Tumor-associated collagen signature-3 (TACS-3) is a prognostic indicator for breast cancer survival. It is characterized by highly organized, parallel bundles of collagen fibers oriented perpendicular to the tumor boundary, serving as directional, confining channels for cancer cell invasion. Here we design a TACS-3-mimetic anisotropic, confined collagen I matrix and examine the relation between anisotropy of matrix, directed cellular migration, and anisotropy of cell membrane-the first direct contact between TACS-3 and cell-using Michigan Cancer Foundation-7 (MCF-7) cells as cancer-model. Using unidirectional freezing, we generated ∼50 μm-wide channels filled with collagen I. Optical tweezer (OT) microrheology shows that anisotropic confinement increases collagen viscoelasticity by two orders of magnitude, and the elastic modulus is significantly greater along the direction of anisotropic confinement compared to that along the orthogonal direction, thus establishing matrix anisotropy. Furthermore, MCF-7 cells embedded in anisotropic collagen I, exhibit directionality in cellular morphology and migration. Finally, using customized OT to trap polystyrene probes bound to cell-membrane (and not to ECM) of either free cells or cells under anisotropic confinement, we quantified the effect of matrix anisotropy on membrane viscoelasticity, both in-plane and out-of-plane, vis-à-vis the membrane. Both bulk and viscous modulus of cell-membrane of MCF-7 cells exhibit significant anisotropy under anisotropic confinement. Moreover, the cell membrane of MCF-7 cells under anisotropic confinement is significantly softer (both in-plane and out-of-plane moduli) despite their local environment being five times stiffer than free cells. In order to test if the coupling between anisotropy of extracellular matrix and anisotropy of cell-membrane is regulated by cell-cytoskeleton, actin cytoskeleton was depolymerized for both free and confined cells. Results show that cell membrane viscoelasticity of confined MCF-7 cells is unaffected by actin de-polymerization, in contrast to free cells. Together, these findings suggest that anisotropy of ECM induces directed migration and correlates with anisotropy of cell-membrane viscoelasticity of the MCF-7 cells in an actin-independent manner.
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ACHARYYA, MUKTISH. "AXIAL AND OFF-AXIAL DYNAMIC TRANSITIONS IN UNIAXIALLY ANISOTROPIC HEISENBERG FERROMAGNET: A COMPARISON." International Journal of Modern Physics C 14, no. 01 (January 2003): 49–59. http://dx.doi.org/10.1142/s0129183103004206.

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Uniaxially anisotropic Heisenberg ferromagnet, in the presence of a magnetic field varying sinusoidally in time, is studied by Monte Carlo simulation. The axial (field applied only along the direction of anisotropy) and off-axial (field applied only along the direction which is perpendicular to the direction of anisotropy) dynamic transitions are studied. By studying the distribution of the dynamic order parameter component, it is observed that the axial transition is discontinuous for low anisotropy and becomes continuous in high anisotropy. The off-axial transition is found to be continuous for all values of anisotropy. In the infinite anisotropy limit, both types of transitions are compared with that observed in an Ising ferromagnet for the same value of the field and frequency. The infinitely anisotropic axial transition and dynamic transition in the Ising ferromagnet occur at different temperatures, whereas the infinitely anisotropic off-axial transition and the equilibrium ferro-para transition in the Ising model occur at the same temperature.
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Dissertations / Theses on the topic "Anisotropy"

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Chen, Xiaoming. "Two-dimensional constrained anisotropic inversion of magnetotelluric data." Phd thesis, Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/6316/.

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Tectonic and geological processes on Earth often result in structural anisotropy of the subsurface, which can be imaged by various geophysical methods. In order to achieve appropriate and realistic Earth models for interpretation, inversion algorithms have to allow for an anisotropic subsurface. Within the framework of this thesis, I analyzed a magnetotelluric (MT) data set taken from the Cape Fold Belt in South Africa. This data set exhibited strong indications for crustal anisotropy, e.g. MT phases out of the expected quadrant, which are beyond of fitting and interpreting with standard isotropic inversion algorithms. To overcome this obstacle, I have developed a two-dimensional inversion method for reconstructing anisotropic electrical conductivity distributions. The MT inverse problem represents in general a non-linear and ill-posed minimization problem with many degrees of freedom: In isotropic case, we have to assign an electrical conductivity value to each cell of a large grid to assimilate the Earth's subsurface, e.g. a grid with 100 x 50 cells results in 5000 unknown model parameters in an isotropic case; in contrast, we have the sixfold in an anisotropic scenario where the single value of electrical conductivity becomes a symmetric, real-valued tensor while the number of the data remains unchanged. In order to successfully invert for anisotropic conductivities and to overcome the non-uniqueness of the solution of the inverse problem it is necessary to use appropriate constraints on the class of allowed models. This becomes even more important as MT data is not equally sensitive to all anisotropic parameters. In this thesis, I have developed an algorithm through which the solution of the anisotropic inversion problem is calculated by minimization of a global penalty functional consisting of three entries: the data misfit, the model roughness constraint and the anisotropy constraint. For comparison, in an isotropic approach only the first two entries are minimized. The newly defined anisotropy term is measured by the sum of the square difference of the principal conductivity values of the model. The basic idea of this constraint is straightforward. If an isotropic model is already adequate to explain the data, there is no need to introduce electrical anisotropy at all. In order to ensure successful inversion, appropriate trade-off parameters, also known as regularization parameters, have to be chosen for the different model constraints. Synthetic tests show that using fixed trade-off parameters usually causes the inversion to end up by either a smooth model with large RMS error or a rough model with small RMS error. Using of a relaxation approach on the regularization parameters after each successful inversion iteration will result in smoother inversion model and a better convergence. This approach seems to be a sophisticated way for the selection of trade-off parameters. In general, the proposed inversion method is adequate for resolving the principal conductivities defined in horizontal plane. Once none of the principal directions of the anisotropic structure is coincided with the predefined strike direction, only the corresponding effective conductivities, which is the projection of the principal conductivities onto the model coordinate axes direction, can be resolved and the information about the rotation angles is lost. In the end the MT data from the Cape Fold Belt in South Africa has been analyzed. The MT data exhibits an area (> 10 km) where MT phases over 90 degrees occur. This part of data cannot be modeled by standard isotropic modeling procedures and hence can not be properly interpreted. The proposed inversion method, however, could not reproduce the anomalous large phases as desired because of losing the information about rotation angles. MT phases outside the first quadrant are usually obtained by different anisotropic anomalies with oblique anisotropy strike. In order to achieve this challenge, the algorithm needs further developments. However, forward modeling studies with the MT data have shown that surface highly conductive heterogeneity in combination with a mid-crustal electrically anisotropic zone are required to fit the data. According to known geological and tectonic information the mid-crustal zone is interpreted as a deep aquifer related to the fractured Table Mountain Group rocks in the Cape Fold Belt.
Tektonische und geologische Prozesse verursachen häufig eine strukturelle Anisotropie des Untergrundes, welche von verschiedenen geophysikalischen Methoden beobachtet werden kann. Zur Erstellung und Interpretation geeigneter, realistischer Modelle der Erde sind Inversionsalgorithmen notwendig, die einen anisotropen Untergrund einbeziehen können. Für die vorliegende Arbeit habe ich einen magnetotellurischen (MT) Datensatz vom Cape Fold Gürtel in Südafrika untersucht. Diese Daten weisen auf eine ausgeprägte Anisotropie der Kruste hin, da z.B. die MT Phasen außerhalb des erwarteten Quadranten liegen und nicht durch standardisierte isotrope Inversionsalgorithmen angepasst und ausgewertet werden können. Um dieses Problem zu beheben, habe ich eine zweidimensionale Inversionsmethode entwickelt, welche eine anisotrope elektrische Leitfähigkeitsverteilungen in den Modellen zulässt. Die MT Inversion ist im allgemeinen ein nichtlineares, schlecht gestelltes Minimierungsproblem mit einer hohen Anzahl an Freiheitsgraden. Im isotropen Fall wird jeder Gitterzelle eines Modells ein elektrischer Leitfähigkeitswert zugewiesen um den Erduntergrund nachzubilden. Ein Modell mit beispielsweise 100 x 50 Zellen besitzt 5000 unbekannte Modellparameter. Im Gegensatz dazu haben wir im anisotropen Fall die sechsfache Anzahl, da hier aus dem einfachen Zahlenwert der elektrischen Leitfähigkeit ein symmetrischer, reellwertiger Tensor wird, wobei die Anzahl der Daten gleich bleibt. Für die erfolgreiche Inversion von anisotropen Leitfähigkeiten und um die Nicht-Eindeutigkeit der Lösung des inversen Problems zu überwinden, ist eine geeignete Einschränkung der möglichen Modelle absolut notwendig. Dies wird umso wichtiger, da die Sensitivität von MT Daten nicht für alle Anisotropieparameter gleich ist. In der vorliegenden Arbeit habe ich einen Algorithmus entwickelt, welcher die Lösung des anisotropen Inversionsproblems unter Minimierung einer globalen Straffunktion berechnet. Diese besteht aus drei Teilen: der Datenanpassung, den Zusatzbedingungen an die Glätte des Modells und die Anisotropie. Im Gegensatz dazu werden beim isotropen Fall nur die ersten zwei Parameter minimiert. Der neu definierte Anisotropieterm wird mit Hilfe der Summe der quadratischen Abweichung der Hauptleitfähigkeitswerte des Modells gemessen. Die grundlegende Idee dieser Zusatzbedingung ist einfach. Falls ein isotropes Modell die Daten ausreichend gut anpassen kann, wird keine elektrische Anisotropie zusätzlich in das Modell eingefügt. Um eine erfolgreiche Inversion zu garantieren müssen geeignete Regularisierungsparameter für die verschiedenen Nebenbedingungen an das Modell gewählt werden. Tests mit synthetischen Modellen zeigen, dass bei festgesetzten Regularisierungsparametern die Inversion meistens entweder in einem glatten Modell mit hohem RMS Fehler oder einem groben Modell mit kleinem RMS Fehler endet. Die Anwendung einer Relaxationsbedingung auf die Regularisierung nach jedem Iterationsschritt resultiert in glatteren Inversionsmodellen und einer höheren Konvergenz und scheint ein ausgereifter Weg zur Wahl der Parameter zu sein. Die vorgestellte Inversionsmethode ist im allgemeinen in der Lage die Hauptleitfähigkeiten in der horizontalen Ebene zu finden. Wenn keine der Hauptrichtungen der Anisotropiestruktur mit der vorgegebenen Streichrichtung übereinstimmt, können nur die dazugehörigen effektiven Leitfähigkeiten, welche die Projektion der Hauptleitfähigkeiten auf die Koordinatenachsen des Modells darstellen, aufgelöst werden. Allerdings gehen die Informationen über die Rotationswinkel verloren. Am Ende meiner Arbeit werden die MT Daten des Cape Fold Gürtels in Südafrika analysiert. Die MT Daten zeigen in einem Abschnitt des Messprofils (> 10 km) Phasen über 90 Grad. Dieser Teil der Daten kann nicht mit herkömmlichen isotropen Modellierungsverfahren angepasst und daher mit diesen auch nicht vollständig ausgewertet werden. Die vorgestellte Inversionsmethode konnte die außergewöhnlich hohen Phasenwerte nicht wie gewünscht im Inversionsergebnis erreichen, was mit dem erwähnten Informationsverlust der Rotationswinkel begründet werden kann. MT Phasen außerhalb des ersten Quadranten können für gewöhnlich bei Anomalien mit geneigter Streichrichtung der Anisotropie gemessen werden. Um diese auch in den Inversionsergebnissen zu erreichen ist eine Weiterentwicklung des Algorithmus notwendig. Vorwärtsmodellierungen des MT Datensatzes haben allerdings gezeigt, dass eine hohe Leitfähigkeitsheterogenität an der Oberfläche in Kombination mit einer Zone elektrischer Anisotropie in der mittleren Kruste notwendig sind um die Daten anzupassen. Aufgrund geologischer und tektonischer Informationen kann diese Zone in der mittleren Kruste als tiefer Aquifer interpretiert werden, der im Zusammenhang mit den zerrütteten Gesteinen der Table Mountain Group des Cape Fold Gürtels steht.
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Adams, Amy Lynn. "Permeability anisotropy and resistivity anisotropy of mechanically compressed mudrocks." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/90036.

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Thesis: Ph. D. in Geotechnical and Geoenvironmental Engineering, Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, 2014.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 313-322).
Permeability anisotropy (the ratio of the horizontal to vertical permeability) is an important parameter used in sedimentary basin models and geotechnical design to model fluid flow, locate hydrocarbon reserves and estimate stress and pressure evolution. The magnitude of the permeability anisotropy for a given mudrock is difficult to measure; further, whether the permeability anisotropy is a constant value or evolves with the basin state is of active debate. This thesis experimentally investigates the development of permeability anisotropy in mechanically compressed mudrocks. A novel measurement method is developed using resedimented cubic specimens. The permeability anisotropy of Resedimented Boston Blue Clay (RBBC) is systematically measured to determine both the magnitude and evolution of the permeability anisotropy. The permeability anisotropy predicted using measurements of the mudrock fabric is compared with the measured permeability anisotropy to understand the relationship between fabric evolution and permeability anisotropy. Finally, resistivity anisotropy is compared with permeability anisotropy to reveal useful field correlations. The results of the RBBC study are contrasted with additional measurements made using mudrocks covering a range of plasticity, clay fraction and mineralogical composition. The permeability anisotropy and the conductivity anisotropy (inverse of the resistivity anisotropy) of uniform RBBC increase from 1.2 to 1.9 as the porosity decreases from 0.49 to 0.36. The permeability decreases by over one order of magnitude and the formation factor triples over this porosity range. Platy particles rotate from ~ 42 to 28 degrees to the horizontal, driving permeability anisotropy development. Further decreasing the porosity of RBBC below porosity 0.36 decreases both the permeability anisotropy and the conductivity anisotropy. Finally, the conductivity anisotropy is shown to equal to the permeability anisotropy within +/-20%. This general behaviour is characteristic of all mudrocks studied. Though small (<2), the permeability anisotropy of uniform mudrocks can significantly increase the permeability anisotropy of larger systems, as shown through layered system models. These models also reveal that the large scale conductivity anisotropy is not equal to the permeability anisotropy, though the relationship identified for uniform mudrocks may still be useful for sites with high measurement resolution.
by Amy Lynn Adams.
Ph. D. in Geotechnical and Geoenvironmental Engineering
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Rostamabad, Houshang Mansouri. "Distinguishing stress-induced anisotropy from fracture-induced anisotropy, and the implications of stress-induced anisotropy for time-lapse seismic." Thesis, Heriot-Watt University, 2006. http://hdl.handle.net/10399/108.

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Ouahioune, Nedjma. "MOKE set-upto measure magnetic anisotropy : MOKE set-upto measure magnetic anisotropy." Thesis, Uppsala universitet, Materialfysik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-414388.

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Wack, Michael Richard. "Anisotropy of magnetic remanence." Diss., lmu, 2012. http://nbn-resolving.de/urn:nbn:de:bvb:19-145717.

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Robson, Martin. "The Cosmic Anisotropy Telescope." Thesis, University of Cambridge, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.319559.

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Wheatley, Richard James. "The anisotropy of repulsion." Thesis, University of Cambridge, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.359829.

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Eisenbach, Markus. "Magnetic anisotropy in nanostructures." Thesis, University of Bristol, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.364862.

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Walsh, James Paul Slater. "Anisotropy in molecular magnetism." Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/anisotropy-in-molecular-magnetism(11474b91-0d3d-4b0a-97cd-214d1713674e).html.

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A collection of studies are reported that focus on the examination of exchange interactions in complexes containing paramagnetic ions with a large magnetic anisotropy. A number of complementary techniques are used to analyse the complicated systems that arise, including high-field high-frequency electron paramagnetic resonance, inelastic neutron scattering, SQUID magnetometry, and ab initio calculations. The nuclearity of the complexes ranges from dimetallic, to trimetallic, to octametallic. A family of five water- and carboxylate-bridged nickel(II) dimetallics are the focus of a magneto-structural correlation study that succeeds in measuring the magnitude of the exchange interaction despite dominating effects from large zero-field splitting effects. Similar work is reported for four cobalt(II) analogues of these compounds, with the relationship between exchange interactions and geometry also being probed by pressure INS. Charge density studies that combine high resolution X-ray and neutron diffraction studies are reported on cobalt and nickel analogues from the same family of dimetallics, revealing strong evidence for non-direct exchange. A family of four trimetallic triangle complexes containing two nickel(II) ions and one chromium(III) ion bridged by a central fluoride and a total of six carboxylates are reported, and the exchange interactions are elucidated from a global model that accounts for the low-field magnetic, heat capacity, and EPR data. Two new octametallic vanadium(III) wheels—where each pair of adjacent metals are bridged by a fluoride and two carboxylates—are reported along with preliminary results from magnetic measurements and solid state proton NMR spectra, which reveal significant field-dependent effects arising from level crossings at high fields.
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Thorsteinsson, Throstur. "Anisotropy of ice Ih : development of fabric and effects of anisotropy on deformation /." Thesis, Connect to this title online; UW restricted, 2000. http://hdl.handle.net/1773/6844.

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Books on the topic "Anisotropy"

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International Workshop on Seismic Anisotropy (6th 1994 Trondheim, Norway). Seismic anisotropy. Tulsa, Okla: Society of Exploration Geophysicists, 1996.

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Negi, J. G. Anisotropy in geoelectromagnetism. Amsterdam: Elsevier, 1989.

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Groupe français de rhéologie. Colloque national. Rhéologie des matériaux anisotropes =: Rheology of anisotropic materials. Toulouse: Cepadues-Éditions, 1986.

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M, Hood G., AECL Research, and Atomic Energy of Canada Limited., eds. -Zr self-diffusion anisotropy. Chalk River, Ont: Reactor Materials Research Branch, Chalk River Laboratories, 1994.

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United States. National Aeronautics and Space Administration. Map Project Office., ed. MAP, microwave anisotropy probe. Greenbelt, MD: MAP Project Office, 1997.

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Lemu, Hirpa. Anisotropy research: New developments. Hauppauge, N.Y: Nova Science Publishers, 2011.

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Tarling, D. H. The magnetic anisotropy of rocks. London: Chapman & Hall, 1993.

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Babuska, V., and M. Cara. Seismic Anisotropy in the Earth. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3600-6.

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Özarslan, Evren, Thomas Schultz, Eugene Zhang, and Andrea Fuster, eds. Anisotropy Across Fields and Scales. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-56215-1.

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Babuška, Vladislav. Seismic anisotropy in the earth. Dordrecht, The Netherlands: Kluwer Academic Publishers, 1991.

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Book chapters on the topic "Anisotropy"

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Pacault, A., J. Hoarau, and J. Favède. "Anisotropie Diamagnétique — Diamagnetic Anisotropy." In Eigenschaften der Materie in Ihren Aggregatzuständen, 141–67. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-662-43334-8_2.

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Jiang, Hao, Wu Liu, Jin Cheng, Huayan Yao, Renjie Li, and Jinhang Shang. "Numerical Analysis of Large-Diameter Shield Tunneling Disturbance Considering Stratum Strength Anisotropy." In Lecture Notes in Civil Engineering, 500–513. Singapore: Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-97-5814-2_45.

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AbstractThe anisotropic characteristics of natural strata could have a significant effect on the tunneling disturbance of shield tunnels. A shield tunneling disturbance simulation method considering the effect of stratum strength anisotropy is proposed in this study. The proposed method adopts the microstructure tensor theory to characterize the anisotropy effects of the stratum material cohesion c and the internal friction angle φ, and finely simulates the shield tunneling processes, including the shield shell advancement, the lining installation, and the shield tail grouting. The shield tunneling refined simulation method is validated by simulating the tunneling process in a certain section of a super-large-diameter shield tunnel in Wuhu City, Anhui Province, China, with good agreement between the simulated surface settlements on the axial and transverse profiles of the excavated tunnel after tunneling to different lining-ring numbers and the monitoring data. On this basis, according to the anisotropic compression strength property of the layered stratum in other sections, the effect of the stratum shear strength anisotropy on the shield tunneling disturbance is analyzed. The shield tunneling-induced surface settlement under the case considering stratum shear strength parameters anisotropy is obviously greater than that without accounting for the anisotropy, demonstrating the importance of considering strata anisotropy caused by geological structures during shield tunneling disturbance modeling.
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Brosius, Alexander, and Dorel Banabic. "Anisotropy." In CIRP Encyclopedia of Production Engineering, 1–8. Berlin, Heidelberg: Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-642-35950-7_6679-3.

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Cheng, Alexander H. D. "Anisotropy." In Poroelasticity, 171–87. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-25202-5_5.

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Brosius, Alexander, and Dorel Banabic. "Anisotropy." In CIRP Encyclopedia of Production Engineering, 66–72. Berlin, Heidelberg: Springer Berlin Heidelberg, 2019. http://dx.doi.org/10.1007/978-3-662-53120-4_6679.

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Brosius, Alexander, and Dorel Banabic. "Anisotropy." In CIRP Encyclopedia of Production Engineering, 40–47. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-20617-7_6679.

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Lekner, John. "Anisotropy." In Theory of Reflection of Electromagnetic and Particle Waves, 141–53. Dordrecht: Springer Netherlands, 1987. http://dx.doi.org/10.1007/978-94-015-7748-9_7.

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Maceri, Aldo. "Anisotropy." In Theory of Elasticity, 635–61. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11392-5_7.

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Chen, Zengtao, and Cliff Butcher. "Anisotropy." In Micromechanics Modelling of Ductile Fracture, 75–100. Dordrecht: Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-94-007-6098-1_3.

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Gooch, Jan W. "Anisotropy." In Encyclopedic Dictionary of Polymers, 41. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-6247-8_669.

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Conference papers on the topic "Anisotropy"

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Holt, R. M., A. Bakk, and S. Lozovyi. "Shale Anisotropy Made Simple." In 58th U.S. Rock Mechanics/Geomechanics Symposium. ARMA, 2024. http://dx.doi.org/10.56952/arma-2024-1061.

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ABSTRACT: Shales are anisotropic, but their anisotropy is often neglected in geomechanical field applications. A major reason for this omission is the need for input data, which includes at least five different elastic parameters that are not commonly available. Recent developments have pointed to internal correlations between elastic anisotropy parameters that can be linked to textural and compositional similarities between different shales. Oriented clay minerals constitute the main source of lithological anisotropy. Utilizing the internal correlations in a pragmatic and simple manner, we demonstrate that a reasonably good anisotropic characterization can be given, even if only one or two input parameters are available. Such a default anisotropic formulation is likely to yield more accurate results for several engineering applications rather than simply assuming isotropy. Several improvements are available, and some already exist, but at the cost of requiring more input from logs or core measurements. Further refinement of our current approach is a low-hanging fruit. 1. INTRODUCTION Shales serve as caprocks above hydrocarbon and CO2 storage as well as unconventional reservoir rocks. Shales are anisotropic, which has impact on reservoir compaction or extension, surface displacements, borehole stability during drilling, as well as depletion or injection induced stress and pore pressure changes. Still, most rock mechanical analyses assume isotropy, simplifying the computational process. Anisotropic analysis requires at least five elastic moduli, depending on symmetry, and if poroelasticity is incorporated, this number increases further. Subsurface formations are normally not sufficiently characterized to enable determination of all the required elastic parameters. To determine all five static moduli for a transversely isotropic (TI) rock, at least three differently oriented cores would be needed. With a cylindrical core drilled with its axis aligned with the symmetry axis, an undrained triaxial test gives the undrained Young's modulus and Poisson's ratio for that specific orientation. In the field, gamma ray (to identify shale formations), density and sonic log data would be available, which may provide P-wave modulus and in most cases also shear modulus. However, three additional elastic moduli are required to fully characterize the anisotropy. Further, the discrepancy between static and dynamic moduli needs to be corrected for.
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Raghupathy, Ramesh, Spencer P. Lake, Edward A. Sander, and Victor H. Barocas. "Generalized Anisotropic Inverse Mechanics: Mechanical Anisotropy Correlates With Structural Anisotropy in Collagen Based Tissue Equivalents." In ASME 2010 Summer Bioengineering Conference. American Society of Mechanical Engineers, 2010. http://dx.doi.org/10.1115/sbc2010-19215.

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Few elastographic methods handle both anisotropy and inhomogeneity. Much of the focus has been on inhomogeneous materials that are locally isotropic. However, most load-bearing tissues (heart, ligament, blood vessels) are highly anisotropic, and the underlying structure is distinct and essential for function. With disease or damage, this structure is altered, and hence the potential for an elastographic tool that identifies regional changes in anisotropy is high. In this study we present a generalized anisotropic inverse mechanics (GAIM) method that is applicable to soft tissues and demonstrate its performance on tissue equivalents which serve as a convenient test case due to their inhomogeneity and the ease of pre-specifying the fiber alignment pattern.
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Hagiwara, Teruhiko. "Predicting Permeability Anisotropy from Resistivity Anisotropy." In Unconventional Resources Technology Conference. Tulsa, OK, USA: American Association of Petroleum Geologists, 2016. http://dx.doi.org/10.15530/urtec-2016-2459699.

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Mitra, A., A. Merzoug, S. Cobb, and M. Mokhtari. "Elastic Anisotropy in Bakken Formation." In 58th U.S. Rock Mechanics/Geomechanics Symposium. ARMA, 2024. http://dx.doi.org/10.56952/arma-2024-0114.

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ABSTRACT: The first laboratory study describing elastic anisotropy of Bakken shale reservoir was reported almost three decades ago. Since then, several efforts have been made in this direction, with the most recent being in 2022 to characterize hydraulic fracture-driven interaction. Separately, a study reported the relationship between various anisotropic stiffness tensor components using published data. However, none of these studies address the variability observed between different formations, nor did they highlight static-dynamic inversion, crucial to 1D geomechanics modeling. This paper utilizes the data presented in the 2022 publication to advance current understanding of anisotropy for Bakken reservoir. First, we try to understand static mechanical property anisotropy observed in various formations. We also study stress-dependency of the observed anisotropy. We examine relationships between various anisotropic stiffness tensor components and reconcile with published data. Finally, we estimate Thomsen parameter for the formations studies and subsequently utilize that to build 1D geomechanics model for Bakken. Separately, we built another iteration of 1D geomechanics model using a different workflow. The results presented here improve our understanding of anisotropy in Bakken, as well as demonstrating two different ways to build 1D geomechanics model. 1. INTRODUCTION The Bakken and Three Forks formations cover a significant portion of North Dakota, South Dakota, and Montana in the United States; and Saskatchewan and Manitoba in Canada. Drilling activity since 2000 has been primarily focused on these two formations because of new advances in horizontal drilling technology. With these advances, the need for additional cores and data has enabled investigations into previous undrilled portions of the basin. Organic shales present in the Bakken and Three Forks formation, and other formations all over the world, are characterized by velocity anisotropy with lower velocity in the direction perpendicular to the lamination. Characterizing anisotropy is critical not only from the seismic attribute standpoint, but also for geomechanics modeling with application to frac design. While the seminal paper by Thomsen (1986) first mathematically described the observed anisotropy almost 40 years back, past decades have seen a number of publications aimed at characterizing anisotropy in Bakken formations via core-based measurement (Vernik and Nur, 1992; Guedez et al., 2018, and very recently, Merzoug et al., 2022). Guedez et al. (2018), for example, reviewed extensive literature data to establish relationship between different components of the anisotropic stiffness tensor. They were then applied to sonic data from a vertical well in the Bakken formation, in an effort to circumvent the uncertainty involved in using Stonely wave data (for C66 estimation). They then compared the predicted insitu horizontal stress using the relationship developed by them with that obtained using ANNIE and MANNIE models. Merzoug et al., 2022 (and Chellal et al., 2022), on the other hand, used core-based measurements targeted on Bakken and Three Forks formation to model insitu horizontal stress aimed at understanding fracture driven interaction.
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Zharnikov, Timur, Roman Ponomarenko, Anatoly Nikitin, and Chris Ayadiuno. "Analysis of the Effect of Geomechanical Stress on the Acoustic Response of Anisotropic Rocks." In International Petroleum Technology Conference. IPTC, 2022. http://dx.doi.org/10.2523/iptc-22321-ea.

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Abstract This paper presents the analysis of borehole acoustic logging response in anisotropic rocks under geomechanical stress. Several effects, which are relevant to the interpretation of sonic logs, are observed and discussed. First, it is shown that the crossover of flexural modes dispersion curves in stress-induced anisotropic formation do not necessarily occur. Second, it is demonstrated that the effects of the difference in orientation of principal stress and anisotropy axes directions, stress magnitudes, and degree of anisotropy on the flexural dispersions can compensate each other at least partially. Finally, the examples of measurable stress effects on the dispersion curves in anisotropic formations are presented. The implication of these observations for the formation stress evaluation from sonic logs in the case of anisotropic formation is that the stress estimation from sonic logs should focus not only on stress magnitudes, but also take into account formation anisotropy and stress orientation with respect to the borehole and anisotropy axes.
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Weldeselassie, Yonas T., Saba El-Hilo, and M. S. Atkins. "Shape anisotropy: tensor distance to anisotropy measure." In SPIE Medical Imaging, edited by Benoit M. Dawant and David R. Haynor. SPIE, 2011. http://dx.doi.org/10.1117/12.878423.

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Hagiwara, Teruhiko. "To estimate permeability anisotropy from resistivity anisotropy." In SEG Technical Program Expanded Abstracts 2016. Society of Exploration Geophysicists, 2016. http://dx.doi.org/10.1190/segam2016-13174233.1.

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Hilgert, Oliver, Steffen Zimmermann, and Christoph Kalwa. "Anisotropy: Benefits for UOE Line Pipe." In 2012 9th International Pipeline Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/ipc2012-90063.

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Plastic anisotropic material behavior of UOE line pipe is investigated in view of its structural response. Common load cases are considered and their resultant strain capacity concerning Strain Based Design demands are discussed. Hill’s yield function is used to analyze steel line pipe under internal pressure and bending moment. Here, a three-dimensional anisotropic plastic strain evolution is considered. It was shown, that underlying anisotropic material behavior can be beneficial for the structural response of line pipe, although it depends on the load case and the directional anisotropy. That is in some way contrary to the demands in specifications, where isotropic material behavior is desired.
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Sasaki, T., and J. Rutqvist. "The Impact of the Anisotropy of Shale Creep on the Long-Term Stress Evolution of a Geological Nuclear Waste Repository." In 57th U.S. Rock Mechanics/Geomechanics Symposium. ARMA, 2023. http://dx.doi.org/10.56952/arma-2023-0945.

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ABSTRACT Shale is considered a suitable host rock for geological nuclear waste repositories due to its low permeability and tendency to reduce stress concentrations via creep. However, such a claim has not been carefully examined from the perspective of shale anisotropy caused by its bedding. It is thus crucial to examine the effect of shale anisotropy on the long-term performance of geological nuclear waste repositories. In this study, we assessed the effect of mechanical (i.e., elastic and creep) anisotropy of shale on the long-term stress evolution of a hypothetical geological repository. A new constitutive model for anisotropic shale creep was developed based on the power-law creep model and the anisotropic plasticity theory. The developed anisotropic creep model was implemented in the TOUGH-FLAC simulator and a thermo-hydromechanically (THM) coupled simulation was carried out for the long-term (&gt;10,000 years) performance assessment of the geological repository. We examined three different shale formation scenarios: (i) isotropic elasticity & creep, (ii) anisotropic elasticity & isotropic creep, and (iii) anisotropic elasticity & creep. Results show that the stresses in the repository were not significantly affected by the simulated anisotropic shale elasticity and/or creep, suggesting that isotropic elasticity & creep would sufficiently capture the long-term mechanical behavior of geological nuclear waste repositories. INTRODUCTION It is known that the behavior of geological nuclear waste repositories is highly thermo-hydromechanically (THM) coupled and it is thus crucial to incorporate each of the THM processes in the performance assessment of the repository. Although the mechanical process is sometimes considered time-independent as rock deformation would not evolve under constant stress conditions, they can creep (i.e., deform viscoelastically or viscoplastically) over the timescale considered for the geological disposal (&gt; 10,000 years) and hence creep can affect its long-term performance. Meanwhile, shale is considered a suitable host rock for the geological disposal due to its low permeability, and it is characteristic of shale to possess inherent anisotropy due to the presence of bedding planes. However, it remains uncertain if/how such inherent anisotropy affects the creep behavior of shale and the performance of a shale repository. Without understanding the anisotropy effect, it would not be possible to carry out robust performance assessment of shale repositories, hence it is critical to examine such an anisotropy effect. In this study, a THM coupled numerical modelling of a hypothetical geological repository was carried out to assess the effect of elastic and creep anisotropy of shale on the stress evolution of the repository for over 10,000 years. A new constitutive model for anisotropic creep was developed based on the power-law creep model and the anisotropic plasticity theory. The model parameters were calibrated against laboratory creep test results on shale with varied loading angle to the bedding plane. In order to assess the effect of elastic and creep anisotropy, three different shale cases were simulated: (i) isotropic elasticity and creep, (ii) anisotropic elasticity and isotropic creep, and (iii) anisotropic elasticity and creep. The results of these simulation cases along with the detail of the numerical model and anisotropic creep model are provided in the following sections.
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Volkov, Valentyn S. "Anisotropic Photonics with Single-Crystal Halide Perovskites." In Novel Optical Materials and Applications. Washington, D.C.: Optica Publishing Group, 2023. http://dx.doi.org/10.1364/noma.2023.noth3c.7.

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In spite of recent advances in the field, the achievement of continuous tunability of optical anisotropy remains an outstanding challenge. Here, we present a solution to the problem through the chemical alteration of halogen atoms in single-crystal halide perovskites. Our results reveal that this anisotropy could be in-plane and out-of-plane depending on perovskite shape - rectangular and square. As a practical demonstration, we have created perovskite anisotropic nanowaveguides and shown a significant impact of anisotropy on high-order guiding modes. These findings pave the way for halide perovskites as a next-generation platform for tunable anisotropic photonics.
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Reports on the topic "Anisotropy"

1

Pechan, M. J. Magnetic multilayer interface anisotropy. Office of Scientific and Technical Information (OSTI), January 1991. http://dx.doi.org/10.2172/5158883.

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Pechan, M. J. Magnetic multilayer interface anisotropy. Office of Scientific and Technical Information (OSTI), January 1992. http://dx.doi.org/10.2172/6958467.

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Pechan, M. J. Magnetic multilayer interface anisotropy. Office of Scientific and Technical Information (OSTI), January 1990. http://dx.doi.org/10.2172/6554380.

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Hart, M. LLNL Explosives Anisotropy Research. Office of Scientific and Technical Information (OSTI), December 2022. http://dx.doi.org/10.2172/1959450.

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Li, Liang-shi. Anisotropy in CdSe quantum rods. Office of Scientific and Technical Information (OSTI), January 2003. http://dx.doi.org/10.2172/827094.

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Evans, Jordan Andrew. Nuclear Reactor Materials and Anisotropy. Office of Scientific and Technical Information (OSTI), December 2019. http://dx.doi.org/10.2172/1578013.

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Hart and Zulfiqar. L52324 Characterization of Anisotropic Pipe Steel Stress-Strain Relationships Influence On Strain Demand. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), November 2011. http://dx.doi.org/10.55274/r0010014.

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This report summarizes a PRCI research project aimed at evaluation of the effects of anisotropy and the shape of pipe steel stress-strain relationships on pipeline strain demand for X80 and X100 UOE pipe. The research included: a review of pipeline industry literature on the subject matter; a discussion of pipe steel plasticity concepts for UOE pipe; characterization of the anisotropy and stress-strain curve shapes for both conventional and high strain pipe steels; development of representative analytical X80 and X100 stress-strain relationships; and evaluation of a large matrix of ground-movement induced pipeline deformation scenarios to evaluate key pipe stress-strain relationship shape and anisotropy parameters. One goal of this research was to apply the findings toward guidance for supplemental pipe material specifications aimed at minimizing undesirable effects of anisotropy and stress-strain curve shape on pipe deformations under displacement-controlled loads.
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Hart, Carl, and Gregory Lyons. A tutorial on the rapid distortion theory model for unidirectional, plane shearing of homogeneous turbulence. Engineer Research and Development Center (U.S.), July 2022. http://dx.doi.org/10.21079/11681/44766.

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The theory of near-surface atmospheric wind noise is largely predicated on assuming turbulence is homogeneous and isotropic. For high turbulent wavenumbers, this is a fairly reasonable approximation, though it can introduce non-negligible errors in shear flows. Recent near-surface measurements of atmospheric turbulence suggest that anisotropic turbulence can be adequately modeled by rapid-distortion theory (RDT), which can serve as a natural extension of wind noise theory. Here, a solution for the RDT equations of unidirectional plane shearing of homogeneous turbulence is reproduced. It is assumed that the time-varying velocity spectral tensor can be made stationary by substituting an eddy-lifetime parameter in place of time. General and particular RDT evolution equations for stochastic increments are derived in detail. Analytical solutions for the RDT evolution equation, with and without an effective eddy viscosity, are given. An alternative expression for the eddy-lifetime parameter is shown. The turbulence kinetic energy budget is examined for RDT. Predictions by RDT are shown for velocity (co)variances, one-dimensional streamwise spectra, length scales, and the second invariant of the anisotropy tensor of the moments of velocity. The RDT prediction of the second invariant for the velocity anisotropy tensor is shown to agree better with direct numerical simulations than previously reported.
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Toney, Michael F. High Anisotropy CoPtCrB Magnetic Recording Media. Office of Scientific and Technical Information (OSTI), June 2003. http://dx.doi.org/10.2172/813356.

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Barros, Kipton, and Hao Zhang. Generalized spin dynamics and anisotropy renormalization. Office of Scientific and Technical Information (OSTI), October 2023. http://dx.doi.org/10.2172/2008255.

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