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Статті в журналах з теми "Phase tensor"

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Автор: Grafiati

Опубліковано: 10 грудня 2022

Оновлено: 28 січня 2023

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1

Milton, Graeme W., and Andrej V. Cherkaev. "Which Elasticity Tensors are Realizable?" Journal of Engineering Materials and Technology 117, no. 4 (October 1, 1995): 483–93. http://dx.doi.org/10.1115/1.2804743.

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It is shown that any given positive definite fourth order tensor satisfying the usual symmetries of elasticity tensors can be realized as the effective elasticity tensor of a two-phase composite comprised of a sufficiently compliant isotropic phase and a sufficiently rigid isotropic phase configured in an suitable microstructure. The building blocks for constructing this composite are what we call extremal materials. These are composites of the two phases which are extremely stiff to a set of arbitrary given stresses and, at the same time, are extremely compliant to any orthogonal stress. An appropriately chosen subset of the extremal materials are layered together to form the composite with elasticity tensor matching the given tensor.

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2

Neukirch, Maik, Daniel Rudolf, Xavier Garcia, and Savitri Galiana. "Amplitude-phase decomposition of the magnetotelluric impedance tensor." GEOPHYSICS 84, no. 5 (September 1, 2019): E301—E310. http://dx.doi.org/10.1190/geo2018-0352.1.

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The introduction of the phase tensor marked a breakthrough in the understanding and analysis of electric galvanic distortion effects. It has been used for (distortion-free) dimensionality analysis, distortion analysis, mapping, and subsurface model inversion. However, the phase tensor can only represent half of the information contained in a complete impedance data set. Nevertheless, to avoid uncertainty due to galvanic distortion effects, practitioners often choose to discard half of the measured data and concentrate interpretation efforts on the phase tensor part. Our work assesses the information loss due to pure phase tensor interpretation of a complete impedance data set. To achieve this, a new MT impedance tensor decomposition into the known phase tensor and a newly defined amplitude tensor is motivated and established. In addition, the existence and uniqueness of the amplitude tensor is proven. Synthetic data are used to illustrate the amplitude tensor information content compared with the phase tensor. Although the phase tensor only describes the inductive effects within the subsurface, the amplitude tensor holds information about inductive and galvanic effects that can help to identify conductivity or thickness of (conductive) anomalies more accurately than the phase tensor. Furthermore, the amplitude and phase tensors sense anomalies at different periods, and thus the combination of both provides a means to evaluate and differentiate anomaly top depths in the event of data unavailability at extended period ranges, e.g., due to severe noise.

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3

Basak, Anup, and Valery I. Levitas. "An exact formulation for exponential-logarithmic transformation stretches in a multiphase phase field approach to martensitic transformations." Mathematics and Mechanics of Solids 25, no. 6 (February 14, 2020): 1219–46. http://dx.doi.org/10.1177/1081286520905352.

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A general theoretical and computational procedure for dealing with an exponential-logarithmic kinematic model for transformation stretch tensor in a multiphase phase field approach to stress- and temperature-induced martensitic transformations with N martensitic variants is developed for transformations between all possible crystal lattices. This kinematic model, where the natural logarithm of transformation stretch tensor is a linear combination of natural logarithm of the Bain tensors, yields isochoric variant–variant transformations for the entire transformation path. Such a condition is plausible and cannot be satisfied by the widely used kinematic model where the transformation stretch tensor is linear in Bain tensors. Earlier general multiphase phase field studies can handle commutative Bain tensors only. In the present treatment, the exact expressions for the first and second derivatives of the transformation stretch tensor with respect to the order parameters are obtained. Using these relations, the transformation work for austenite ↔ martensite and variant ↔ variant transformations is analyzed and the thermodynamic instability criteria for all homogeneous phases are expressed explicitly. The finite element procedure with an emphasis on the derivation of the tangent matrix for the phase field equations, which involves second derivatives of the transformation deformation gradients with respect to the order parameters, is developed. Change in anisotropic elastic properties during austenite–martensitic variants and variant–variant transformations is taken into account. The numerical results exhibiting twinned microstructures for cubic to orthorhombic and cubic to monoclinic-I transformations are presented.

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4

Neukirch, Maik, Savitri Galiana, and Xavier Garcia. "Appraisal of magnetotelluric galvanic electric distortion by optimizing amplitude and phase tensor relations." GEOPHYSICS 85, no. 3 (April 29, 2020): E79—E98. http://dx.doi.org/10.1190/geo2019-0359.1.

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Анотація:

The introduction of the phase tensor marked a major breakthrough in the analysis and treatment of electric field galvanic distortion in the magnetotellurics method. Recently, the phase tensor formulation has been extended to a complete impedance tensor decomposition by introducing the complementary amplitude tensor, and both tensors can be further parameterized to represent geometric properties such as dimensionality, strike angle, and macroscopic anisotropy. Both tensors are characteristic for the electromagnetic induction phenomenon in the conductive subsurface with its specific geometric structure. The central hypothesis is that this coupling should result in similarities in both tensor’s geometric parameters, skew, strike, and anisotropy. A synthetic example illustrates that the undistorted amplitude tensor parameters are more similar to the phase tensor than increasingly distorted ones and provides empiric evidence for the predictability of the proposed hypothesis. Conclusions drawn are reverse engineered to produce an objective function that minimizes when amplitude and phase tensor parameter dissimilarity is, along with any present distortion, minimal. A genetic algorithm with such an objective function is used to systematically seek the distortion parameters necessary to correct any affected amplitude tensor and, thus, impedance data. The successful correction of a large synthetic impedance data set with random distortion further supports the central hypothesis and serves as comparison to the state-of-the-art. The classic BC87 data set sites lit007/ lit008 and lit901/ lit902 have been noted by various authors to contain significant distortion and a 3D regional response, thus invalidating current distortion analysis methods and eluding geologic interpretation. Correction of the BC87 responses based on the present hypothesis conforms to the regional geology.

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5

Abdelwahed, Mohamed, Luigi C. Berselli, and Nejmeddine Chorfi. "On the uniqueness for weak solutions of steady double-phase fluids." Advances in Nonlinear Analysis 11, no. 1 (September 8, 2021): 454–68. http://dx.doi.org/10.1515/anona-2020-0196.

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Abstract We consider a double-phase non-Newtonian fluid, described by a stress tensor which is the sum of a p-Stokes and a q-Stokes stress tensor, with 1 < p<2 < q<∞. For a wide range of parameters (p, q), we prove the uniqueness of small solutions. We use the p < 2 features to obtain quadratic-type estimates for the stress-tensor, while we use the improved regularity coming from the term with q > 2 to justify calculations for weak solutions. Results are obtained through a careful use of the symmetries of the convective term and are also valid for rather general (even anisotropic) stress-tensors.

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6

Caldwell, T. Grant, Hugh M. Bibby, and Colin Brown. "The magnetotelluric phase tensor." Geophysical Journal International 158, no. 2 (August 2004): 457–69. http://dx.doi.org/10.1111/j.1365-246x.2004.02281.x.

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7

Farutin, A. M. "On tensor phase transitions." Journal of Experimental and Theoretical Physics 108, no. 3 (March 2009): 469–76. http://dx.doi.org/10.1134/s1063776109030108.

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8

Dolinšek, J., and R. Blinc. "A Note on the 14N Electric Field Gradient Notizen: Tensors in Incommensurate [N(CH3)4]2ZnCl4." Zeitschrift für Naturforschung A 42, no. 3 (March 1, 1987): 305–6. http://dx.doi.org/10.1515/zna-1987-0318.

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Анотація:

The 14N electric field gradient tensors of [N(CH3)4]2ZnCl4 have been re-determined in the paraelectric phase at 26 °C and in the incommensurate phase at 16 °C. The results in the incommensurate phase show the “non-local” nature of the 14N EFG tensor interaction.

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9

Macholl, Sven, Frank Börner, and Gerd Buntkowsky. "Revealing CSA Tensors and Hydrogen Bonding in Methoxycarbonyl Urea: A combined 13C, 15N and 13C14N2 Dipolar Chemical Shift NMR and DFT Study." Zeitschrift für Physikalische Chemie 217, no. 12 (December 1, 2003): 1473–506. http://dx.doi.org/10.1524/zpch.217.12.1473.20470.

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AbstractMethoxycarbonyl urea (MCU), a potential long-term nitrogen fertilizer, is studied by 13C and 15N dipolar chemical shift NMR spectroscopy and ab initio calculations. Employing a combination of dipolar chemical shift NMR, selective isotope labeling and ab initio gas phase calculations, possible molecular structures and chemical shielding tensors of all 15N nuclei and of two out of the three 13C nuclei were revealed. Four possible stable configurations of the molecule with different energies were found in the calculations. The CSA tensors were calculated for these configurations. While the calculated 13C(urea) CSA tensor orientation of the configuration with the lowest energy is in good agreement with the experimental tensor orientation, there are pronounced differences between calculated and experimental tensor eigenvalues. These differences are a clear indication of the presence of intermolecular hydrogen bonds in the experimental sample, which are neglected in the gas phase calculations. Four different possible orientations of the experimental 13C(urea) CSA tensor exist, due to symmetry. This ambiguity is solved by comparison with results from GIAO calculations of the 13C CSA tensor, employing the minimum energy configuration (EEZ). It is found that the orientation, where δ11 points approximately in direction of N(imide), δ22 approximately in direction of the C=O bond, and δ33 is oriented perpendicular to the molecular frame, is adopted in the molecule.

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10

Kopský, Vojtěch. "Tensor parameters of ferroic phase transitions." Phase Transitions 73, no. 1-2 (January 2001): 1–422. http://dx.doi.org/10.1080/01411590108226583.

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11

Muñíz, Yunuhen, Enrique Gómez-Treviño, Francisco J. Esparza, and Mayra Cuellar. "Stable 2D magnetotelluric strikes and impedances via the phase tensor and the quadratic equation." GEOPHYSICS 82, no. 4 (July 1, 2017): E169—E186. http://dx.doi.org/10.1190/geo2015-0700.1.

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Анотація:

A combination of the magnetotelluric phase tensor and the quadratic algorithm provides a fast and simple solution to the problem of a 2D impedance tensor distorted by 3D electrogalvanic effects. The strike direction is provided by the phase tensor, which is known to provide unstable estimates for noisy data. We obtain stable directions in three steps. First, we use bootstrapping to find the most stable estimate among the different periods. Second, this value is used as the seed to select the neighbor strikes assuming continuity over periods. This second step is repeated several times to compute variances. The third step, which we call prerotating, consists of rotating the original impedance tensor to a most favorable angle for optimal stability and then rotating it back for compensation. The procedure is developed as a progressing algorithm through its application to the gradually more difficult data sets COPROD2S1, COPROD2, far-hi, and BC87, all available for testing new ideas. Alternately, using the Groom-Bailey terminology, the quadratic algorithm provides the amplitudes and phases independently of the strike direction and twist. The amplitudes and phases still need to be tuned up by the correct shear. The correct shear is obtained by contrasting the phases from the phase tensor and from the quadratic equation until they match for all available periods. The results are the undistorted impedances. Uncertainties are computed using formulas derived for the quadratic equation. We use the same data sets as for the strike to illustrate the recovery of impedances and their uncertainties.

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12

Kühn, Daniela, Sebastian Heimann, Marius P. Isken, Elmer Ruigrok, and Bernard Dost. "Probabilistic Moment Tensor Inversion for Hydrocarbon-Induced Seismicity in the Groningen Gas Field, The Netherlands, Part 1: Testing." Bulletin of the Seismological Society of America 110, no. 5 (August 11, 2020): 2095–111. http://dx.doi.org/10.1785/0120200099.

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ABSTRACT Since 1991, induced earthquakes have been observed and linked to gas production in the Groningen field. Recorded waveforms are complex, resulting partly from a Zechstein salt layer overlying the reservoir and partly from free-surface reverberations, internal multiples, interface conversions, guided waves, and waves diving below the reservoir. Therefore, picking of polarities or amplitudes for use in moment tensor inversion is problematic, whereas phase identification may be circumvented employing full waveform techniques. Although moment tensors have become a basic tool to analyze earthquake sources, their uncertainties are rarely reported. We introduce a method for probabilistic moment tensor estimation and demonstrate its use on the basis of a single event within the Groningen field, concentrating on detailed tests of input data and inversion parameters to derive rules of good practice for moment tensor estimation of events recorded in the Groningen field. In addition to the moment tensor, event locations are provided. Hypocenters estimated simultaneously with moment tensors are often less sensitive to uncertainties in crustal structure, which is pertinent for the application to the Groningen field, because the task of relating earthquakes to specific faults hitherto suffers from a limited resolution of earthquake locations. Because of the probabilistic approach, parameter trade-offs, uncertainties, and ambiguities are mapped. In addition, the implemented bootstrap method implicitly accounts for modeling errors affecting every station and phase differently. A local 1D velocity model extracted from a full 3D velocity model yields more consistent results than other models applied previously. For all velocity models and combinations of input data tested, a shift in location of 1 km to the south is observed for the test event compared to the public catalog. A full moment tensor computed employing the local 1D velocity model features negative isotropic components and may be interpreted as normal fault and collapse at reservoir level.

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13

Litvin, Daniel B. "Tensor distinction of domain pairs in ferroic crystals." Acta Crystallographica Section A Foundations of Crystallography 55, no. 5 (September 1, 1999): 884–90. http://dx.doi.org/10.1107/s0108767399003499.

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Анотація:

A classification of domain pairs in ferroic crystals is given in which all domain pairs in each class can be distinguished by the same set of physical property tensors. Tabulations are presented giving in which ferroic phase transitions such domain pairs arise. Whether a physical property tensor can or cannot distinguish between the domains of domain pairs of each class is given for a wide variety of physical properties.

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14

Cunningham, William J., Bianca Dittrich, and Sebastian Steinhaus. "Tensor Network Renormalization with Fusion Charges—Applications to 3D Lattice Gauge Theory." Universe 6, no. 7 (July 12, 2020): 97. http://dx.doi.org/10.3390/universe6070097.

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Tensor network methods are powerful and efficient tools for studying the properties and dynamics of statistical and quantum systems, in particular in one and two dimensions. In recent years, these methods have been applied to lattice gauge theories, yet these theories remain a challenge in ( 2 + 1 ) dimensions. In this article, we present a new (decorated) tensor network algorithm, in which the tensors encode the lattice gauge amplitude expressed in the fusion basis. This has several advantages—firstly, the fusion basis does diagonalize operators measuring the magnetic fluxes and electric charges associated to a hierarchical set of regions. The algorithm allows therefore a direct access to these observables. Secondly the fusion basis is, as opposed to the previously employed spin network basis, stable under coarse-graining. Thirdly, due to the hierarchical structure of the fusion basis, the algorithm does implement predefined disentanglers. We apply this new algorithm to lattice gauge theories defined for the quantum group SU ( 2 ) k and identify a weak and a strong coupling phase for various levels k . As we increase the level k , the critical coupling g c decreases linearly, suggesting the absence of a deconfining phase for the continuous group SU ( 2 ) . Moreover, we illustrate the scaling behaviour of the Wilson loops in the two phases.

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15

Booker, John R. "The Magnetotelluric Phase Tensor: A Critical Review." Surveys in Geophysics 35, no. 1 (May 23, 2013): 7–40. http://dx.doi.org/10.1007/s10712-013-9234-2.

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16

Shapovalov, I. "Phase transitions in magnetodielectrics with tensor interactions." Journal of Physical Studies 3, no. 2 (1999): 192–98. http://dx.doi.org/10.30970/jps.03.192.

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17

Faraoni, Valerio. "Phase space geometry in scalar-tensor cosmology." Annals of Physics 317, no. 2 (June 2005): 366–82. http://dx.doi.org/10.1016/j.aop.2004.11.009.

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18

Bakke, K., and H. Belich. "Relativistic geometric quantum phases from the Lorentz symmetry violation effects in the CPT-even gauge sector of Standard Model Extension." International Journal of Modern Physics A 30, no. 33 (November 26, 2015): 1550197. http://dx.doi.org/10.1142/s0217751x15501973.

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We discuss the appearance of geometric quantum phases for a Dirac neutral particle in the context of relativistic quantum mechanics based on possible scenarios of the Lorentz symmetry violation tensor background in the CPT-even gauge sector of Standard Model Extension. We assume that the Lorentz symmetry breaking is determined by a tensor background given by [Formula: see text], then, relativistic analogues of the Anandan quantum phase [J. Anandan, Phys. Lett. A 138, 347 (1989)] are obtained based on the parity-even and parity-odd sectors of the tensor [Formula: see text].

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19

SEGAL, ARKADY Y. "POINT PARTICLE–SYMMETRIC TENSORS INTERACTION AND GENERALIZED GAUGE PRINCIPLE." International Journal of Modern Physics A 18, no. 27 (October 30, 2003): 5021–38. http://dx.doi.org/10.1142/s0217751x03015842.

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The model of a point particle in the background of external symmetric tensor fields is analyzed from the higher spin theory perspective. It is proposed that the gauge transformations of the infinite collection of symmetric tensor fields may be read off from the covariance properties of the point particle action w.r.t. general canonical transformations. The gauge group turns out to be a semidirect product of all phase space canonical transformations to an Abelian ideal of "hyperWeyl" transformations and includes U(1) and general coordinate symmetries as a subgroup. A general configuration of external fields includes rank-0,1,2 symmetric tensors, so the whole system may be truncated to ordinary particle in Einstein–Maxwell backgrounds by switching off the higher-rank symmetric tensors. When otherwise all the higher rank tensors are switched on, the full gauge group provides a huge gauge symmetry acting on the whole infinite collection of symmetric tensors. We analyze this gauge symmetry and show that the symmetric tensors which couple to the point particle should not be interpreted as Fronsdal gauge fields, but rather as gauge fields of some conformal higher spin theories. It is shown that the Fronsdal fields system possesses twice as many symmetric tensor fields as is contained in the general background of the point particle. Besides, the particle action in general backgrounds is shown to reproduce De Wit–Freedman point particle–symmetric tensors first order interaction suggested many years ago, and extends their result to all orders in interaction, while the generalized equivalence principle completes the first order covariance transformations found in their paper, in all orders.

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20

Mikata, Y., and S. Nemat-Nasser. "Elastic Field Due to a Dynamically Transforming Spherical Inclusion." Journal of Applied Mechanics 57, no. 4 (December 1, 1990): 845–49. http://dx.doi.org/10.1115/1.2897650.

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As a first step towards a systematic study of the interaction between a stress-pulse traveling in transformation toughened ceramics and possible phase transformation of zirconia particles, a dynamic inclusion problem is investigated. An exact closed-form solution is obtained for the case of a spherical inclusion. With this result, the dynamic Eshelby tensors for the inside and outside fields of the spherical inclusion are defined and determined. It is confirmed that the static Eshelby tensor is obtained as a static limit of the dynamic Eshelby tensor. It is found in the numerical results that the frequency of the dynamic inclusion has a relatively large influence on the amplitudes of the stress components inside and outside the inclusion.

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21

Shapovalov, I. P. "Quadrupole phases and phase transitions in uniaxial magnets with tensor interactions." Low Temperature Physics 39, no. 6 (June 2013): 515–21. http://dx.doi.org/10.1063/1.4811336.

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22

Gusev, Alexander. "Phase Transition at the Metric Elastic Universe." Symposium - International Astronomical Union 168 (1996): 569–70. http://dx.doi.org/10.1017/s007418090011071x.

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At the last time the concept of the curved space-time as the some medium with stress tensor σαβon the right part of Einstein equation is extensively studied in the frame of the Sakharov - Wheeler metric elasticity(Sakharov (1967), Wheeler (1970)). The physical cosmology pre- dicts a different phase transitions (Linde (1990), Guth (1991)). In the frame of Relativistic Theory of Finite Deformations (RTFD) (Gusev (1986)) the transition from the initial stateof the Universe (Minkowskian's vacuum, quasi-vacuum(Gliner (1965), Zel'dovich (1968)) to the final stateof the Universe(Friedmann space, de Sitter space) has the form of phase transition(Gusev (1989) which is connected with different space-time symmetry of the initial and final states of Universe(from the point of view of isometric groupGnof space). In the RTFD (Gusev (1983), Gusev (1989)) the space-time is described by deformation tensorof the three-dimensional surfaces, and the Einstein's equations are viewed as the constitutive relations between the deformations ∊αβand stresses σαβ. The vacuum state of Universe have the visible zero physical characteristics and one is unsteady relatively quantum and topological deformations (Gunzig & Nardone (1989), Guth (1991)). Deformations of vacuum state, identifying with empty Mikowskian's space are described the deformations tensor ∊αβ, wherethe metrical tensor of deformation state of 3-geometry on the hypersurface, which is ortogonaled to the four-velocityis the 3 -geometry of initial state,is a projection tensor.

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23

Lilley, Frederick E. M., and Christopher J. E. Phillips. "A property of the determinant of a 2 × 2 tensor relevant to magnetotellurics." GEOPHYSICS 83, no. 4 (July 1, 2018): A59—A64. http://dx.doi.org/10.1190/geo2017-0315.1.

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Where a [Formula: see text] tensor relates two geophysical quantities that are measured in the field as time-varying vectors, its determinant is shown to be positive when, for two different events occurring at different times, a step clockwise in the direction of one vector from the first event to the second is accompanied by a step clockwise in the direction of the other vector from the first event to the second. The determinant would be negative were the azimuths of the two field vectors to “counter step,” i.e., change in opposite directions. In magnetotellurics (MT), the technique known as phase-tensor analysis brings a focus on the determinant signs of MT impedance tensors and telluric distortion tensors, and the azimuth-stepping rules should apply to both categories. Any determinants which may be negative are then seen in the light that they imply a counter stepping of the azimuths of the two relevant field vectors.

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24

Quevedo, Fernando, and Carlo A. Trugenberger. "Condensation of p-Branes and Generalized Higgs/Confinement Duality." International Journal of Modern Physics A 12, no. 06 (March 10, 1997): 1227–35. http://dx.doi.org/10.1142/s0217751x97000955.

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We review our recent work on the low-energy actions and the realizations of strong-weak coupling dualities in non-perturbative phases of compact antisymmetric tensor field theories due to p-brane condensation. As examples we derive and discuss the confining string and confining membrane actions obtained from compact vector and tensor theories in 4D. We also mention the relevance of our results for the description of the Hagedorn phase transition of finite temperature strings.

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25

Erofeev, V. I., A. V. Shekoyan, and M. V. Belubekyan. "SPATIALLY-LOCALIZED NONLINEAR MAGNETOELASTIC WAVES IN A MICROPOLAR ELECTRICAL CONDUCTING MEDIUM." Problems of strenght and plasticity 81, no. 4 (2019): 402–15. http://dx.doi.org/10.32326/1814-9146-2019-81-4-402-415.

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Анотація:

A nonlinear model of an electrically conducting micropolar medium interacting with an external magnetic field is proposed. The deformable state of such a medium is described by two asymmetric tensors: tensor of deformations and bending-torsion tensor. In both tensors, linear and nonlinear terms are taken into account in rotation gradients and displacement gradients (geometric nonlinearity). The components of the bending-torsion tensor, which have identical indices, describe torsional deformations, and the rest - bending deformations. The stress state of the medium is described by two asymmetric tensors: stress tensor and moment stress tensor. It is assumed, as it is usual in magnetoelasticity, that the action of the electromagnetic field on the deformation field occurs through the Lorentz forces. From the system of Maxwell equations follow the equations for electrical and magnetic inductions, which, together with the electromagnetic equations of state, must be added to the equations of the dynamics of a micropolar medium. Within the framework of the proposed model, a one-dimensional nonlinear shear-rotation magnetoelastic wave is considered. The nonlinear term is selected and taken into account in the equations of dynamics, making the most significant contribution to wave processes. It is shown that two factors will influence the wave propagation: dispersion and nonlinearity. Nonlinearity leads to the emergence of new harmonics in the wave, which contributes to the appearance of a sharp drop in the moving profile. The dispersion, on the contrary, smoothes the differences due to the difference in the phase velocities of the harmonic components of the waves. The combined effect of these factors can lead to the formation of stationary waves that propagate at a constant speed without changing the shape. Only those cases are physically feasible when there is no constant component in the deformation wave. Stationary waves can be both periodic and aperiodic. The latter are spatially localized waves - solitons. It is shown that the behavior of "subsonic" and “supersonic” solitons will be qualitatively different.

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26

Dalaq, Ahmed S., and Shivakumar I. Ranganathan. "Invariants of mesoscale thermal conductivity and resistivity tensors in random checkerboards." Engineering Computations 32, no. 6 (August 3, 2015): 1601–18. http://dx.doi.org/10.1108/ec-08-2014-0162.

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Purpose – The purpose of this paper is to study the statistics of thermal conductivity and resistivity tensors in two-phase random checkerboard microstructures at finite mesoscales. Design/methodology/approach – Microstructures at finite scales are generated by randomly sampling an infinite checkerboard at 50 percent nominal fraction. Boundary conditions that stem from the Hill-Mandel homogenization condition are then applied as thermal loadings on these microstructures. Findings – It is observed that the thermal response of the sampled microstructures is in general anisotropic at finite mesoscales. Based on 1,728 boundary value problems, the statistics of the tensor invariants (trace and determinant) are obtained as a function of material contrast, mesoscale and applied boundary conditions. The histograms as well as the moments (mean, variance, skewness and kurtosis) of the invariants are computed and discussed. A simple analytical form for the variance of the trace of mesoscale conductivity tensor is proposed as a function of individual phase conductivities and the mesoscale. Originality/value – A rigorous methodology to determine the evolution of the invariants of thermal conductivity (and resistivity) tensors across a variety of length scales (microscale to macroscale) is presented. The objective is to enable setting up of constitutive equations applicable to heat conduction that are valid across all length scales.

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27

Hassan, Mosaad W., Arabi Keshk, Amira Abd El-atey, and Elham Alfeky. "BRAIN STROKE DETECTION USING TENSOR FACTORIZATION AND MACHINE LEARNING MODELS." International Journal of Engineering Technologies and Management Research 8, no. 8 (August 16, 2021): 1–12. http://dx.doi.org/10.29121/ijetmr.v8.i8.2021.1006.

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Stroke is one of the foremost common disorders among the elderly. Early detection of stroke from Magnetic Resonance Imaging (MRI) is typically based on the representation method of these images. Representing MRI slices in two dimensional structures (matrices) implies ignoring the dependencies between these slices. Additionally, to combine all features exist in these slices requires more computations and time. However, this results in inexact diagnosis. In this paper, we propose a new tensor-based approach for stroke detection from MRI. The proposed methodology has two phases. In first phase, each patient’s MRI are represented as a tensor. Tensor representations are powerful because they capture the dependencies in high-dimensional data, MRI of patient, which gives more reliable and accurate results. Also, tensor factorization is used as a method for feature extraction and reduction, which improves the performance and accuracy of classifiers. In second phase, these extracted features are used to train support vector machine (SVM) and XGBoost classifiers to classify MRI images into normal and abnormal. The proposed method is assessed with MRI dataset, and the conducted experiments illustrate the efficiency of this approach. It achieves classification accuracy of 98%.

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28

Zhu, Mian, Amara Ilyas, Yunlong Zheng, Yi-Fu Cai, and Emmanuel N. Saridakis. "Scalar and tensor perturbations in DHOST bounce cosmology." Journal of Cosmology and Astroparticle Physics 2021, no. 11 (November 1, 2021): 045. http://dx.doi.org/10.1088/1475-7516/2021/11/045.

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Abstract We investigate the bounce realization in the framework of DHOST cosmology, focusing on the relation with observables. We perform a detailed analysis of the scalar and tensor perturbations during the Ekpyrotic contraction phase, the bounce phase, and the fast-roll expansion phase, calculating the power spectra, the spectral indices and the tensor-to-scalar ratio. Furthermore, we study the initial conditions, incorporating perturbations generated by Ekpyrotic vacuum fluctuations, by matter vacuum fluctuations, and by thermal fluctuations. The scale invariance of the scalar power spectrum can be acquired introducing a matter contraction phase before the Ekpyrotic phase, or invoking a thermal gas as the source. The DHOST bounce scenario with cosmological perturbations generated by thermal fluctuations proves to be the most efficient one, and the corresponding predictions are in perfect agreement with observational bounds. Especially the tensor-to-scalar ratio is many orders of magnitude within the allowed region, since it is suppressed by the Hubble parameter at the beginning of the bounce phase.

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29

FitzGerald, D. J., H. Holstein, and D. Argast. "The amplitude / phase treatment of full tensor gradiometry." ASEG Extended Abstracts 2007, no. 1 (December 1, 2007): 1–4. http://dx.doi.org/10.1071/aseg2007ab040.

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30

Patro, P. K., M. Uyeshima, and W. Siripunvaraporn. "Three-dimensional inversion of magnetotelluric phase tensor data." Geophysical Journal International 192, no. 1 (November 9, 2012): 58–66. http://dx.doi.org/10.1093/gji/ggs014.

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31

Lu, Xiao-Ming, and Xiaoguang Wang. "Operator quantum geometric tensor and quantum phase transitions." EPL (Europhysics Letters) 91, no. 3 (August 1, 2010): 30003. http://dx.doi.org/10.1209/0295-5075/91/30003.

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32

Benedetti, Dario, and Razvan Gurau. "Phase transition in dually weighted colored tensor models." Nuclear Physics B 855, no. 2 (February 2012): 420–37. http://dx.doi.org/10.1016/j.nuclphysb.2011.10.015.

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33

Zheng, Wei, Jingshen Yan, Fadi Li, and Feng Huang. "Elucidation of “phase difference” in Raman tensor formalism." Photonics Research 6, no. 7 (June 20, 2018): 709. http://dx.doi.org/10.1364/prj.6.000709.

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34

Momeni, Kasra, and Valery I. Levitas. "A phase-field approach to solid–solid phase transformations via intermediate interfacial phases under stress tensor." International Journal of Solids and Structures 71 (October 2015): 39–56. http://dx.doi.org/10.1016/j.ijsolstr.2015.05.027.

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35

Balashov, Vladislav. "A regularized isothermal phase-field model of two-phase solid–fluid mixture and its spatial dissipative discretization equations." Russian Journal of Numerical Analysis and Mathematical Modelling 36, no. 4 (August 1, 2021): 197–217. http://dx.doi.org/10.1515/rnam-2021-0017.

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Abstract The present paper is devoted to a model describing a two-phase isothermal mixture, in which one of the phases obeys solid-like (namely, elastic) rheology. A fully Eulerian description is considered. To describe the stress–strain behaviour of the solid phase the elastic energy term is added to the Helmholtz free energy. The term depends on Almansi strain tensor. In its turn, the strain tensor is defined as the solution of the corresponding evolutionary equation. Considered model belongs to the phase field family. Formally it describes two-component mixture and uses mass densities of the components as order parameters. A distinctive feature of the considered model is its preliminary regularization according to the quasi-hydrodynamic framework. The dissipativity in total energy is proved when periodic boundary conditions are imposed. A spatial dissipative semi-discrete (continuous in time and discrete in space) scheme based on staggered grids is suggested. The theoretical results remain valid in the absence of the regularization. The results of a numerical study in a 2D setting are presented.

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36

Balashov, Vladislav. "A regularized isothermal phase-field model of two-phase solid–fluid mixture and its spatial dissipative discretization equations." Russian Journal of Numerical Analysis and Mathematical Modelling 36, no. 4 (August 1, 2021): 197–217. http://dx.doi.org/10.1515/rnam-2021-0017.

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Анотація:

Abstract The present paper is devoted to a model describing a two-phase isothermal mixture, in which one of the phases obeys solid-like (namely, elastic) rheology. A fully Eulerian description is considered. To describe the stress–strain behaviour of the solid phase the elastic energy term is added to the Helmholtz free energy. The term depends on Almansi strain tensor. In its turn, the strain tensor is defined as the solution of the corresponding evolutionary equation. Considered model belongs to the phase field family. Formally it describes two-component mixture and uses mass densities of the components as order parameters. A distinctive feature of the considered model is its preliminary regularization according to the quasi-hydrodynamic framework. The dissipativity in total energy is proved when periodic boundary conditions are imposed. A spatial dissipative semi-discrete (continuous in time and discrete in space) scheme based on staggered grids is suggested. The theoretical results remain valid in the absence of the regularization. The results of a numerical study in a 2D setting are presented.

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37

Diamantini, M. C. "Compact Gauge Theories of Open p-Branes." International Journal of Modern Physics A 12, no. 06 (March 10, 1997): 1237–41. http://dx.doi.org/10.1142/s0217751x97000967.

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We study phase transitions induced by topological defects in compact Abelian gauge theories of openp-branes in (d+1) space-time dimensions. Starting from a massive antisymmetric tensor theory for the open p-branes we show how the condensation of topological defects can lead to a decoupled phase with a massless tensor coupled to closed (p - 1)-branes and a massive tensor coupled to open (p + 1)-branes. We also consider the case, relevant in string theory, in which the boundaries of the p-branes are constrained to live on a Dirichlet n-brane.

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38

Sangani, A. S., and A. K. Didwania. "Dispersed-phase stress tensor in flows of bubbly liquids at large Reynolds numbers." Journal of Fluid Mechanics 248 (March 1993): 27–54. http://dx.doi.org/10.1017/s0022112093000679.

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We derive averaged equations for large Reynolds number laminar flows of gas–liquid dispersions accounting for slowly varying spatial and temporal fields. In particular, we obtain an exact expression for the dispersed-phase stress tensor to be used in the force balance equation for gas bubbles and illustrate its application by evaluating the stress tensor for a few special cases. It is shown that the dispersed-phase stress tensor gradient with respect to the mean relative motion or the void fraction for the uniformly random bubbly liquids under conditions of large Reynolds number laminar flows is negative and thus has a destabilizing influence on the dynamics of void fraction waves in bubbly liquids.

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39

Knight, K. S. "A high temperature structural phase transition in crocoite (PbCrO4) at 1068 K: crystal structure refinement at 1073 K and thermal expansion tensor determination at 1000 K." Mineralogical Magazine 64, no. 2 (April 2000): 291–300. http://dx.doi.org/10.1180/002646100549193.

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AbstractHigh-resolution, neutron time-of-flight, powder diffraction data have been collected on natural crocoite between 873 and 1073 K. Thermal analysis carried out in the 1920s had suggested that chemically pure PbCrO4 exhibited two structural phase transitions, at 964 K, to the β phase, and at 1056 K, to the γ phase. In this study, no evidence was found for the α-β structural phase transition, however a high-temperature phase transition was found at ∼1068 K from the ambient-temperature monazite structure type to the baryte structure type. The phase transition, close to the temperatures reported for the β to γ phase modifications, is first order and is accompanied by a change in volume of −1.6%. The crystal structure of this phase has been refined using the Rietveld method to agreement factors of Rp = 0.018, Rwp = 0.019, Rp = 0.011. No evidence for premonitory behaviour was found in the temperature dependence of the monoclinic lattice constants rom 873 K to 1063 K and these have been used to determine the thermal expansion tensor of crocoite just below the phase transition. At 1000 K the magnitudes of the tensor coefficients are α11, 2.66(1) × 10−5 K−1; α22, 2.04(1) × 10−5 K−1; α33, 4.67(4) × 10−5 K−1; and α13, −1.80(2) × 10−5 K−1 using the IRE convention for the orientation of the tensor basis. The orientation of the principal axes of the thermal expansion tensor are very close to those reported previously for the temperature range 50–300 K.

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40

Moulin, Kévin, Ilya A. Verzhbinsky, Nyasha G. Maforo, Luigi E. Perotti, and Daniel B. Ennis. "Probing cardiomyocyte mobility with multi-phase cardiac diffusion tensor MRI." PLOS ONE 15, no. 11 (November 12, 2020): e0241996. http://dx.doi.org/10.1371/journal.pone.0241996.

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Purpose Cardiomyocyte organization and performance underlie cardiac function, but the in vivo mobility of these cells during contraction and filling remains difficult to probe. Herein, a novel trigger delay (TD) scout sequence was used to acquire high in-plane resolution (1.6 mm) Spin-Echo (SE) cardiac diffusion tensor imaging (cDTI) at three distinct cardiac phases. The objective was to characterize cardiomyocyte organization and mobility throughout the cardiac cycle in healthy volunteers. Materials and methods Nine healthy volunteers were imaged with cDTI at three distinct cardiac phases (early systole, late systole, and diastasis). The sequence used a free-breathing Spin-Echo (SE) cDTI protocol (b-values = 350s/mm2, twelve diffusion encoding directions, eight repetitions) to acquire high-resolution images (1.6x1.6x8mm3) at 3T in ~7 minutes/cardiac phase. Helix Angle (HA), Helix Angle Range (HAR), E2 angle (E2A), Transverse Angle (TA), Mean Diffusivity (MD), diffusion tensor eigenvalues (λ1-2-3), and Fractional Anisotropy (FA) in the left ventricle (LV) were characterized. Results Images from the patient-specific TD scout sequence demonstrated that SE cDTI acquisition was possible at early systole, late systole, and diastasis in 78%, 100% and 67% of the cases, respectively. At the mid-ventricular level, mobility (reported as median [IQR]) was observed in HAR between early systole and late systole (76.9 [72.6, 80.5]° vs 96.6 [85.9, 100.3]°, p<0.001). E2A also changed significantly between early systole, late systole, and diastasis (27.7 [20.8, 35.1]° vs 45.2 [42.1, 49]° vs 20.7 [16.6, 26.4]°, p<0.001). Conclusion We demonstrate that it is possible to probe cardiomyocyte mobility using multi-phase and high resolution cDTI. In healthy volunteers, aggregate cardiomyocytes re-orient themselves more longitudinally during contraction, while cardiomyocyte sheetlets tilt radially during wall thickening. These observations provide new insights into the three-dimensional mobility of myocardial microstructure during systolic contraction.

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41

Dufumier, Hugues, and Jeannot Trampert. "Contribution of seismic tomography in moment-tensor inversions using teleseismic surface-wave spectra." Bulletin of the Seismological Society of America 87, no. 1 (February 1, 1997): 114–22. http://dx.doi.org/10.1785/bssa0870010114.

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Abstract The knowledge of lateral heterogeneities is crucial for path corrections in moment tensor inversions using surface waves. After some attempts to use regionalized Earth models for very long-period surface-wave moment-tensor inversions, recent tomographic Earth models offer the possibility to make short-period path corrections and therefore retrieve more reliable moment tensors for teleseismic earthquakes. First we try to evaluate the precision required for path corrections in comparison with source effects. Some selected Earth models are tested to evaluate how their results compare to those using multiple-frequency filtering techniques. Some real cases illustrate the sensitivity of moment-tensor solutions to the different path corrections, and it appears clearly that regionalized Earth models and tomographic models deduced from long-period data alone (greater than 150 sec) cannot lead to trustworthy broadband moment-tensor inversions. Recent tomographic models using phase velocities at much shorter periods (40 to 200 sec) offer a precision comparable to that of the multiple-frequency filtering technique. Both methods lead to acceptable source mechanisms, using a small number of stations, in more than two cases out of three. The use of recent global tomographic models based upon shorter-period surface waves might thus be a useful alternative to heavy multiple-frequency filtering techniques to automate source studies, especially for rapid determinations using a small number of stations.

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42

Becken, Michael, and Laust B. Pedersen. "Transformation of VLF anomaly maps into apparent resistivity and phase." GEOPHYSICS 68, no. 2 (March 2003): 497–505. http://dx.doi.org/10.1190/1.1567217.

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We investigate a transformation of magnetic transfer functions into the tangential‐electric mode part of the impedance tensor in the scope of the plane‐wave electromagnetic tensor–VLF method. The transformation, which is applicable to any 2D data representing the response of arbitrary 3D geoelectric structures, overcomes the difficulties of quantitative interpretation of magnetic transfer functions, which predominantly provide a measure of the lateral changes of the electrical conductivity in the earth. We require densely sampled magnetic transfer functions of one frequency as input data. These may be decomposed into their normal and anomalous parts (deviation from the response of a layered earth) for a unit external plane‐wave source field using the Hilbert transform relationship between the magnetic field components. Faraday's law then directly provides the anomalous toroidal electric field. Unfortunately, there is no chance to estimate the normal electric field from magnetic data, since the magnetic field is not sensitive to a layered earth. This constant must be provided as a boundary condition, e.g., from one ground measurement, to derive an impedance tensor and related apparent resistivities and phases.

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43

Harder, Steven. "Inversion of phase velocities for the anisotropic elastic tensor." Journal of Geophysical Research 90, B12 (1985): 10275. http://dx.doi.org/10.1029/jb090ib12p10275.

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44

Kopský, Vojtěch. "The change of tensor properties at ferroic phase transitions." Ferroelectrics 237, no. 1 (January 2000): 127–34. http://dx.doi.org/10.1080/00150190008216241.

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45

Kopský, V. "Tensor distinction of domain states in ferroic phase transitions." Acta Crystallographica Section A Foundations of Crystallography 61, a1 (August 23, 2005): c320. http://dx.doi.org/10.1107/s0108767305086393.

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46

Stoeck, Christian T., Aleksandra Kalinowska, Constantin von Deuster, Jack Harmer, Rachel W. Chan, Markus Niemann, Robert Manka, et al. "Dual-Phase Cardiac Diffusion Tensor Imaging with Strain Correction." PLoS ONE 9, no. 9 (September 5, 2014): e107159. http://dx.doi.org/10.1371/journal.pone.0107159.

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47

Basini, G., and S. Capozziello. "Neutrino oscillation phase dynamically induced by scalar-tensor gravity." General Relativity and Gravitation 38, no. 3 (February 25, 2006): 507–15. http://dx.doi.org/10.1007/s10714-006-0237-x.

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48

Chang, Wontae, Jeffrey A. Bellotti, Steven W. Kirchoefer, and Jeffrey M. Pond. "Strain tensor effects on SrTiO3 incipient ferroelectric phase transition." Journal of Electroceramics 17, no. 2-4 (December 2006): 487–94. http://dx.doi.org/10.1007/s10832-006-9337-y.

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49

Zheng, Wei, Jingshen Yan, Fadi Li, and Feng Huang. "Elucidation of “phase difference” in Raman tensor formalism: erratum." Photonics Research 8, no. 3 (February 12, 2020): 286. http://dx.doi.org/10.1364/prj.387673.

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50

Weaver, J. T., A. K. Agarwal, and F. E. M. Lilley. "The relationship between the magnetotelluric tensor invariants and the phase tensor of Caldwell, Bibby and Brown." ASEG Extended Abstracts 2003, no. 1 (April 2003): 1–8. http://dx.doi.org/10.1071/aseg2003_3demab024.

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