scholarly journals NMR diffusion-encoding with axial symmetry and variable anisotropy: Distinguishing between prolate and oblate microscopic diffusion tensors with unknown orientation distribution

2015 ◽  
Vol 142 (10) ◽  
pp. 104201 ◽  
Author(s):  
Stefanie Eriksson ◽  
Samo Lasič ◽  
Markus Nilsson ◽  
Carl-Fredrik Westin ◽  
Daniel Topgaard
Keyword(s):  
Axial Symmetry ◽  
Orientation Distribution ◽  
Nmr Diffusion ◽  
Diffusion Tensors ◽  
Variable Anisotropy

scholarly journals Fast and Analytical EAP Approximation from a 4th-Order Tensor

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Aurobrata Ghosh ◽  
Rachid Deriche
Keyword(s):  
Diffusion Tensor ◽  
Hermite Polynomials ◽  
Synthetic Data ◽  
Orientation Distribution ◽  
Underlying Structure ◽  
Diffusivity Coefficient ◽  
Model Complex ◽  
Higher Order Tensors ◽  
Diffusion Tensors

Generalized diffusion tensor imaging (GDTI) was developed to model complex apparent diffusivity coefficient (ADC) using higher-order tensors (HOTs) and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be inferred from the shape of the ensemble average propagator (EAP). Though interesting methods for estimating a positive ADC using 4th-order diffusion tensors were developed, GDTI in general was overtaken by other approaches, for example, the orientation distribution function (ODF), since it is considerably difficult to recuperate the EAP from a HOT model of the ADC in GDTI. In this paper, we present a novel closed-form approximation of the EAP using Hermite polynomials from a modified HOT model of the original GDTI-ADC. Since the solution is analytical, it is fast, differentiable, and the approximation converges well to the true EAP. This method also makes the effort of computing a positive ADC worthwhile, since now both the ADC and the EAP can be used and have closed forms. We demonstrate our approach with 4th-order tensors on synthetic data and in vivo human data.

Influence of extinction phenomenon on determination of the orientation distribution function

2006 ◽  
Vol 2006 (suppl_23_2006) ◽  
pp. 175-180
Author(s):  
G. Gómez-Gasga ◽  
T. Kryshtab ◽  
J. Palacios-Gómez ◽  
A. de Ita de la Torre
Keyword(s):  
Distribution Function ◽  
Orientation Distribution Function ◽  
Orientation Distribution

On the method of ultrasonic control of mechanical stresses

2018 ◽  
Vol 84 (7) ◽  
pp. 62-66
Author(s):  
K. V. Kurashkin
Keyword(s):  
Elastic Wave ◽  
Orientation Distribution ◽  
Elastic Wave Velocity ◽  
Mechanical Stresses ◽  
Material Structure ◽  
Stress Determination ◽  
Welded Steel ◽  
Ultrasonic Control ◽  
Cubic Crystallites ◽  
Proportional Relationship

A method of ultrasonic control of the mechanical stresses which takes into account the heterogeneity of the material structure and does not require unloading of the structure or using reference samples is considered. The procedure is based on echo-method of measuring time of the bulk elastic wave propagation and determination of the relative values ν31 and ν32 related to the material structure and mechanical stresses. It is shown that stresses violate the linearity of the relationship observed between the parameters in the absence of the mechanical stresses in the rolled material. This effect formed a basis for developing a method of the deviator stress determination. The purpose of the study is to demonstrate the main advantages of the developed method against the known ultrasonic techniques used for evaluation of the mechanical stresses, give theoretical grounds to the effect which allows taking into account the heterogeneity of the material structure, and also to exemplify the procedure. An analytical expression is derived using bulk elastic wave velocity in an orthotropic material composed of cubic crystallites and an assumption on the existence of simple proportional relationship between the coefficients of the orientation distribution function in rolled metal. Presented results of the mathematical modeling confirm the experimentally observed linear dependence between the parameters ν31 and ν32 in the absence of mechanical stresses. The results of evaluating residual stresses in a welded steel plate are presented as an example of the applicability of the developed procedure. Data of ultrasonic technique and data of strain gage measurements are compared. The features of the described method of stress determination are marked and the applicability limits are specified.

MISORIENTATION DISTRIBUTION FUNCTION FOR CUBIC CRYSTALS

2019 ◽  
Vol 85 (5) ◽  
pp. 28-32
Author(s):  
A. S. Kolyanova ◽  
Y. N. Yaltsev
Keyword(s):  
Distribution Function ◽  
Grain Boundaries ◽  
Orientation Distribution ◽  
Recrystallization Annealing ◽  
Misorientation Distribution ◽  
Cubic Crystals ◽  
Special Boundaries ◽  
Pole Figures ◽  
Two Samples ◽  
Euler Space

A calculation method for obtaining the misorientation distribution function (MDF) for cubic crystals which can be used to estimate the presence or absence of special boundaries in the materials is presented. The calculation was carried out for two samples of Al-Mg-Si alloy subjected to various mechanical and thermal treatments: the first sample is subjected to rolling; the second sample is subjected to recrystallization annealing. MDF is calculated for each sample; the results are presented in the Euler space and in the angle-axis space. The novelty of the method consists in the possibility of gaining data on the grain boundaries from X-ray texture analysis without using electron microscopy. A calculation involving only mathematical operations on matrices was performed on the basis of the orientation distribution function restored from incomplete pole figures. It is shown that no special boundaries are observed in the deformed sample, whereas in the recrystallized alloy, special boundaries are detected at Ʃ = 23, 13, and 17. The shortcoming of the proposed method can be attributed to the lack of accurate data on grain boundaries, since all possible orientation in the polycrystal should be taken into account in MDF calculation.

scholarly journals Symmetry Breakdown Related Fracture in 42CrMo4 Steel

Metals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 344
Author(s):  
Jian Feng ◽  
Stefan Barth ◽  
Marc Wettlaufer
Keyword(s):  
Orientation Distribution ◽  
High Symmetry ◽  
Symmetry Breakdown ◽  
Pole Figures ◽  
Crystallographic Symmetry ◽  
42Crmo4 Steel ◽  
Austenite Grains ◽  
Ebsd Technique ◽  
Complete Transformation ◽  
Start Temperature

Austenite grains that underwent the f.c.c. to b.c.c. (or b.c.t.) transformation are typically composed of 24 Kurdjumov–Sachs variants that can be categorized by three axes of Bain transformations; thus, a complete transformation generally displays 3-fold symmetry in (001) pole figures. In the present work, crystallographic symmetry in 42CrMo4 steel austempered below martensite start temperature was investigated with the help of the orientation distribution function (ODF) analysis based on the FEG-SEM/EBSD technique. It is shown that, upon phase transformations, the specimens contained 6-fold symmetry in all (001), (011), and (111) pole figures of an ODF. The ODF analysis, verified by theoretical modeling, showed that under plane-strain conditions cracks prefer to propagate through areas strongly offset by the high symmetry. The origin of high symmetry was investigated, and the mechanism of the symmetry breakdown was explained.

Analysis of Spatial Orientation Distribution of Highly Oriented Polyimide Film Using Micro ATR-FTIR Spectroscopic Imaging Method

Polymer ◽  
2021 ◽  
pp. 123616
Author(s):  
Ryohei Ishige ◽  
Cai Li Song ◽  
Shohei Hara ◽  
Shinji Ando ◽  
Sergei G. Kazarian
Keyword(s):  
Spatial Orientation ◽  
Spectroscopic Imaging ◽  
Orientation Distribution ◽  
Polyimide Film ◽  
Imaging Method

scholarly journals Variable Anisotropic Hardy Spaces with Variable Exponents

2021 ◽  
Vol 9 (1) ◽  
pp. 65-89
Author(s):  
Zhenzhen Yang ◽  
Yajuan Yang ◽  
Jiawei Sun ◽  
Baode Li
Keyword(s):  
Hardy Spaces ◽  
Variable Exponent ◽  
Atomic Decomposition ◽  
Integral Operators ◽  
Moment Condition ◽  
Variable Exponents ◽  
Hölder Continuous ◽  
Multi Level ◽  
The Moment ◽  
Variable Anisotropy

Abstract Let p(·) : ℝ n → (0, ∞] be a variable exponent function satisfying the globally log-Hölder continuous and let Θ be a continuous multi-level ellipsoid cover of ℝ n introduced by Dekel et al. [12]. In this article, we introduce highly geometric Hardy spaces Hp (·)(Θ) via the radial grand maximal function and then obtain its atomic decomposition, which generalizes that of Hardy spaces Hp (Θ) on ℝ n with pointwise variable anisotropy of Dekel et al. [16] and variable anisotropic Hardy spaces of Liu et al. [24]. As an application, we establish the boundedness of variable anisotropic singular integral operators from Hp (·)(Θ) to Lp (·)(ℝ n ) in general and from Hp (·)(Θ) to itself under the moment condition, which generalizes the previous work of Bownik et al. [6] on Hp (Θ).

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