Journal articles: 'Tensor Field Visualization'

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Guoning Chen, Darrel Palke, Zhongzang Lin, Harry Yeh, Paul Vincent, Robert S. Laramee, and Eugene Zhang. "Asymmetric Tensor Field Visualization for Surfaces." IEEE Transactions on Visualization and Computer Graphics 17, no. 12 (December 2011): 1979–88. http://dx.doi.org/10.1109/tvcg.2011.170.

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Bi, Chongke, Lu Yang, Yulin Duan, and Yun Shi. "A survey on visualization of tensor field." Journal of Visualization 22, no. 3 (March 22, 2019): 641–60. http://dx.doi.org/10.1007/s12650-019-00555-8.

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Zhang, Eugene, James Hays, and Greg Turk. "Interactive Tensor Field Design and Visualization on Surfaces." IEEE Transactions on Visualization and Computer Graphics 13, no. 1 (January 2007): 94–107. http://dx.doi.org/10.1109/tvcg.2007.16.

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Hesselink, L., F. H. Post, and J. J. van Wijk. "Research issues in vector and tensor field visualization." IEEE Computer Graphics and Applications 14, no. 2 (March 1994): 76–79. http://dx.doi.org/10.1109/38.267477.

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Dick, C., J. Georgii, R. Burgkart, and R. Westermann. "Stress Tensor Field Visualization for Implant Planning in Orthopedics." IEEE Transactions on Visualization and Computer Graphics 15, no. 6 (November 2009): 1399–406. http://dx.doi.org/10.1109/tvcg.2009.184.

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Raith, Felix, Christian Blecha, Thomas Nagel, Francesco Parisio, Olaf Kolditz, Fabian Gunther, Markus Stommel, and Gerik Scheuermann. "Tensor Field Visualization using Fiber Surfaces of Invariant Space." IEEE Transactions on Visualization and Computer Graphics 25, no. 1 (January 2019): 1122–31. http://dx.doi.org/10.1109/tvcg.2018.2864846.

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Liang, Xundong, Bin Li, and Shenquan Liu. "Three-dimensional vector field visualization based on tensor decomposition." Journal of Computer Science and Technology 11, no. 5 (September 1996): 452–60. http://dx.doi.org/10.1007/bf02947212.

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McGraw, Tim, Takamitsu Kawai, Inas Yassine, and Lierong Zhu. "Visualizing High-Order Symmetric Tensor Field Structure with Differential Operators." Journal of Applied Mathematics 2011 (2011): 1–27. http://dx.doi.org/10.1155/2011/142923.

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The challenge of tensor field visualization is to provide simple and comprehensible representations of data which vary both directionallyandspatially. We explore the use of differential operators to extract features from tensor fields. These features can be used to generate skeleton representations of the data that accurately characterize the global field structure. Previously, vector field operators such as gradient, divergence, and curl have previously been used to visualize of flow fields. In this paper, we use generalizations of these operators to locate and classify tensor field degenerate points and to partition the field into regions of homogeneous behavior. We describe the implementation of our feature extraction and demonstrate our new techniques on synthetic data sets of order 2, 3 and 4.

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Zhu, Yang-Ming, and Paul A. Farrell. "A vector grouping algorithm for liquid crystal tensor field visualization." Liquid Crystals 29, no. 10 (October 2002): 1259–64. http://dx.doi.org/10.1080/713935624.

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Caldwell, T. Grant, and Hugh M. Bibby. "The instantaneous apparent resistivity tensor: a visualization scheme for LOTEM electric field measurements." Geophysical Journal International 135, no. 3 (December 1998): 817–34. http://dx.doi.org/10.1046/j.1365-246x.1998.00668.x.

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Rasolofosaon, Patrick N. J., and Bernard E. Zinszner. "Comparison between permeability anisotropy and elasticity anisotropy of reservoir rocks." GEOPHYSICS 67, no. 1 (January 2002): 230–40. http://dx.doi.org/10.1190/1.1451647.

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We developed new experimental and theoretical tools for the measurement and the characterization of arbitrary elasticity tensors and permeability tensors in rocks. They include an experimental technique for the 3‐D visualization of hydraulic invasion fronts in rock samples by monitoring the injection of salt solutions by X‐ray tomography, and a technique for inverting the complete set of the six coefficients of the permeability tensor from invasion front images. In addition, a technique for measuring the complete set of the 21 elastic coefficients, a technique allowing the identification and the orientation in the 3‐D space of the symmetry elements (planes, axes), and a technique for approximating the considered elastic tensor by a tensor of simpler symmetry with the quantification of the error induced by such an approximation have been developed. We apply these tools to various types of reservoir rocks and observed quite contrasted behaviors. In some rocks, the elastic anisotropy and the hydraulic anisotropy are closely correlated, for instance in terms of the symmetry directions. This is the case when elastic anisotropy and hydraulic anisotropy share the same cause (e.g., layering, fractures). In contrast, in some other rocks, hydraulic properties and elastic properties are clearly uncorrelated. These results highlight the challenge we have to face in order to estimate the rock permeability and to monitor the fluid flow from seismic measurements in the field.

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Michelson, Georg, Tobias Engelhorn, Simone Waerntges, and Arnd Doerfler. "Diffusion Tensor Imaging for In Vivo Detection of Degenerated Optic Radiation." ISRN Ophthalmology 2011 (December 27, 2011): 1–6. http://dx.doi.org/10.5402/2011/648450.

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Glaucomatous optic nerve atrophy may continue to the linked optic radiation by transneuronal degeneration, as described in animal models of glaucoma. In vivo visualization of the visual pathway represents a new challenge in the field of ophthalmology. We present a new approach for illustration of the optic radiation by diffusion tensor imaging (DTI) based on magnetic resonance imaging (MRI). The DTI was established by use of a 3T high-field scanner. The case of a patient with primary open-angle glaucoma is opposed to this one of a healthy subject to demonstrate the visible rarefication of the optic radiation. The goal was to introduce the technique of the DTI also in ophthalmology and to demonstrate that it may be useful to judge glaucoma-related differences.

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Thudium, Marcus O., Alexandre R. Campos, Horst Urbach, and Hans Clusmann. "The Basal Temporal Approach for Mesial Temporal Surgery: Sparing the Meyer Loop With Navigated Diffusion Tensor Tractography." Operative Neurosurgery 67, suppl_2 (December 1, 2010): ons385—ons390. http://dx.doi.org/10.1227/neu.0b013e3181f7424b.

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ABSTRACT BACKGROUND: Visual field defects are a common side effect after mesial temporal resections such as selective amygdalohippocampectomy (SelAH). OBJECTIVE: To present a method of diffusion tensor tractography (DTT) of the Meyer loop for preoperative planning of the surgical approach for SelAH and for intraoperative visualization on a navigation-guided operating microscope. METHODS: Twelve patients were selected for SelAH to treat mesial temporal lobe epilepsy. All received preoperative MRI with diffusion tensor imaging sequences. The Meyer loop was determined and reconstructed as an object with DTT. Images were utilized for preoperative planning in which a safe approach not affecting the Meyer loop was specified. A navigation-guided operating microscope was used for image-guided surgery. RESULTS: DTT was a reliable method for visualization of the Meyer loop. Reconstruction of the Meyer loop had a direct impact on the approach planning. In all 12 cases, the optic tract could only be spared using a basal approach. Ten patients underwent SelAH by the subtemporal approach, and 2 underwent SelAH by the transcortical approach through the inferior temporal gyrus. During the critical early phase of the operation image guidance remained accurate until entry into the ventricle. Nine of 12 patients had no postoperative field deficits (75%). Three patients (25%) experienced peripheral incomplete quadrantanopia. CONCLUSION: DTT and intraoperative visualization of the Meyer loop is a helpful tool for preoperative planning and during surgery to find a safe trajectory to mesial temporal structures while avoiding the optic radiation. This technique in combination with a basal approach seems to be a promising strategy to prevent postoperative visual field deficits in most patients.

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Kuhnt, Daniela, Miriam H. A. Bauer, Andreas Becker, Dorit Merhof, Amir Zolal, Mirco Richter, Peter Grummich, Oliver Ganslandt, Michael Buchfelder, and Christopher Nimsky. "Intraoperative Visualization of Fiber Tracking Based Reconstruction of Language Pathways in Glioma Surgery." Neurosurgery 70, no. 4 (September 23, 2011): 911–20. http://dx.doi.org/10.1227/neu.0b013e318237a807.

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Abstract BACKGROUND: For neuroepithelial tumors, the surgical goal is maximum resection with preservation of neurological function. This is contributed to by intraoperative magnetic resonance imaging (iMRI) combined with multimodal navigation. OBJECTIVE: We evaluated the contribution of diffusion tensor imaging (DTI)-based fiber tracking of language pathways with 2 different algorithms (tensor deflection, connectivity analysis [CA]) integrated in the navigation on the surgical outcome. METHODS: We evaluated 32 patients with neuroepithelial tumors who underwent surgery with DTI-based fiber tracking of language pathways integrated in neuronavigation. The tensor deflection algorithm was routinely used and its results intraoperatively displayed in all cases. The CA algorithm was furthermore evaluated in 23 cases. Volumetric assessment was performed in pre- and intraoperative MR images. To evaluate the benefit of fiber tractography, language deficits were evaluated pre- and postoperatively and compared with the volumetric analysis. RESULTS: Final gross-total resection was performed in 40.6% of patients. Absolute tumor volume was reduced from 55.33 ± 63.77 cm3 to 20.61 ± 21.67 cm3 in first iMRI resection control, to finally 11.56 ± 21.92 cm3 (P < .01). Fiber tracking of the 2 algorithms showed a deviation of the displayed 3D objects by <5 mm. In long-term follow-up only 1 patient (3.1%) had a persistent language deficit. CONCLUSION: Intraoperative visualization of language-related cortical areas and the connecting pathways with DTI-based fiber tracking can be successfully performed and integrated in the navigation system. In a setting of intraoperative high-field MRI this contributes to maximum tumor resection with low postoperative morbidity.

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Guo, Zhe, Yi Wang, Tao Lei, Yangyu Fan, and Xiuwei Zhang. "DTI Image Registration under Probabilistic Fiber Bundles Tractography Learning." BioMed Research International 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/4674658.

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Diffusion Tensor Imaging (DTI) image registration is an essential step for diffusion tensor image analysis. Most of the fiber bundle based registration algorithms use deterministic fiber tracking technique to get the white matter fiber bundles, which will be affected by the noise and volume. In order to overcome the above problem, we proposed a Diffusion Tensor Imaging image registration method under probabilistic fiber bundles tractography learning. Probabilistic tractography technique can more reasonably trace to the structure of the nerve fibers. The residual error estimation step in active sample selection learning is improved by modifying the residual error model using finite sample set. The calculated deformation field is then registered on the DTI images. The results of our proposed registration method are compared with 6 state-of-the-art DTI image registration methods under visualization and 3 quantitative evaluation standards. The experimental results show that our proposed method has a good comprehensive performance.

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Yuan, Yongfeng, and Kuanquan Wang. "A Mixed Gauss and Directional Distance Filter for Fiber Direction Tracking." International Journal of Image and Graphics 14, no. 01n02 (January 2014): 1450001. http://dx.doi.org/10.1142/s0219467814500016.

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Fiber directional tracking through diffusion tensor magnetic resonance imaging (DT-MRI) is a promising research field in visualization and computer graphics and is widely applied in the reconstruction of fiber orientation and the structure of biological tissues. The filter technique used to blur noise in data is of critical importance for fiber directional tracking, particularly because existing tracking methods are very sensitive to impulsive noise. In this paper, a mixed filter of the 3D Gauss and directional distance filter (GDDF) is proposed to suppress noises in corrupted vector fields. Simulation results and objective evaluation of vector datasets demonstrate that GDDF not only possesses the capability of noise attenuation but also preserves vector directions. By validating the simulated vector data against experimental heart data, it is also shown that the GDDF is an effective and stable preprocessing method that accurately reconstructs fiber orientation.

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Höller, Mark, Kay-M. Otto, Uwe Klose, Samuel Groeschel, and Hans-H. Ehricke. "Fiber Visualization with LIC Maps Using Multidirectional Anisotropic Glyph Samples." International Journal of Biomedical Imaging 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/401819.

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Line integral convolution (LIC) is used as a texture-based technique in computer graphics for flow field visualization. In diffusion tensor imaging (DTI), LIC bridges the gap between local approaches, for example directionally encoded fractional anisotropy mapping and techniques analyzing global relationships between brain regions, such as streamline tracking. In this paper an advancement of a previously published multikernel LIC approach for high angular resolution diffusion imaging visualization is proposed: a novel sampling scheme is developed to generate anisotropic glyph samples that can be used as an input pattern to the LIC algorithm. Multicylindrical glyph samples, derived from fiber orientation distribution (FOD) functions, are used, which provide a method for anisotropic packing along integrated fiber lines controlled by a uniform random algorithm. This allows two- and three-dimensional LIC maps to be generated, depicting fiber structures with excellent contrast, even in regions of crossing and branching fibers. Furthermore, a color-coding model for the fused visualization of slices from T1 datasets together with directionally encoded LIC maps is proposed. The methodology is evaluated by a simulation study with a synthetic dataset, representing crossing and bending fibers. In addition, results fromin vivostudies with a healthy volunteer and a brain tumor patient are presented to demonstrate the method's practicality.

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Blackburn, Hugh M., Nagi N. Mansour, and Brian J. Cantwell. "Topology of fine-scale motions in turbulent channel flow." Journal of Fluid Mechanics 310 (March 10, 1996): 269–92. http://dx.doi.org/10.1017/s0022112096001802.

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An investigation of topological features of the velocity gradient field of turbulent channel flow has been carried out using results from a direct numerical simulation for which the Reynolds number based on the channel half-width and the centreline velocity was 7860. Plots of the joint probability density functions of the invariants of the rate of strain and velocity gradient tensors indicated that away from the wall region, the fine-scale motions in the flow have many characteristics in common with a variety of other turbulent and transitional flows: the intermediate principal strain rate tended to be positive at sites of high viscous dissipation of kinetic energy, while the invariants of the velocity gradient tensor showed that a preference existed for stable focus/stretching and unstable node/saddle/saddle topologies. Visualization of regions in the flow with stable focus/stretching topologies revealed arrays of discrete downstream-leaning flow structures which originated near the wall and penetrated into the outer region of the flow. In all regions of the flow, there was a strong preference for the vorticity to be aligned with the intermediate principal strain rate direction, with the effect increasing near the walls in response to boundary conditions.

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Faust, Katharina, and Peter Vajkoczy. "Distinct displacements of the optic radiation based on tumor location revealed using preoperative diffusion tensor imaging." Journal of Neurosurgery 124, no. 5 (May 2016): 1343–52. http://dx.doi.org/10.3171/2015.3.jns141584.

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OBJECT Visual field defects (VFDs) due to optic radiation (OR) injury are a common complication of temporal lobe surgery. The authors analyzed whether preoperative visualization of the optic tract would reduce this complication by influencing the surgeon’s decisions about surgical approaches. The authors also determined whether white matter shifts caused by temporal lobe tumors would follow predetermined patterns based on the tumor’s topography. METHODS One hundred thirteen patients with intraaxial tumors of the temporal lobe underwent preoperative diffusion tensor imaging (DTI) fiber tracking. In 54 of those patients, both pre- and postoperative VFDs were documented using computerized perimetry. Brainlab’s iPlan 2.5 navigation software was used for tumor reconstruction and fiber visualization after the fusion of DTI studies with their respective magnetization-prepared rapid gradient-echo (MP-RAGE) images. The tracking algorithm was as follows: minimum fiber length 100 mm, fractional anisotropy threshold 0.1. The lateral geniculate body and the calcarine cortex were employed as tract seeding points. Shifts of the OR caused by tumor were visualized in comparison with the fiber tracking of the patient’s healthy hemisphere. RESULTS Temporal tumors produced a dislocation of the OR but no apparent fiber destruction. The shift of white matter tracts followed fixed patterns dependent on tumor location: Temporolateral tumors resulted in a medial fiber shift, and thus a lateral transcortical approach is recommended. Temporopolar tumors led to a posterior shift, always including Meyer’s loop; therefore, a pterional transcortical approach is recommended. Temporomesial tumors produced a lateral and superior shift; thus, a transsylvian-transcisternal approach will result in maximum sparing of the fibers. Temporocentric tumors also induced a lateral fiber shift. For those tumors, a transsylvian-transopercular approach is recommended. Tumors of the fusiform gyrus generated a superior (and lateral) shift; consequently, a subtemporal approach is recommended to avoid white matter injury. In applying the approaches recommended above, new or worsened VFDs occurred in 4% of the patient cohort. Total neurological and surgical morbidity were less than 10%. In 90% of patients, gross-total resection was accomplished. CONCLUSIONS Preoperative visualization of the OR may help in avoiding postoperative VFDs.

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Kanamoto, Hirohito, Yawara Eguchi, Yasuhiro Oikawa, Sumihisa Orita, Kazuhide Inage, Kazuki Fujimoto, Yasuhiro Shiga, et al. "Visualization of lumbar nerves using reduced field of view diffusion tensor imaging in healthy volunteers and patients with degenerative lumbar disorders." British Journal of Radiology 90, no. 1080 (December 2017): 20160929. http://dx.doi.org/10.1259/bjr.20160929.

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Combrisson, Etienne, Timothy Nest, Andrea Brovelli, Robin A. A. Ince, Juan L. P. Soto, Aymeric Guillot, and Karim Jerbi. "Tensorpac: An open-source Python toolbox for tensor-based phase-amplitude coupling measurement in electrophysiological brain signals." PLOS Computational Biology 16, no. 10 (October 29, 2020): e1008302. http://dx.doi.org/10.1371/journal.pcbi.1008302.

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Despite being the focus of a thriving field of research, the biological mechanisms that underlie information integration in the brain are not yet fully understood. A theory that has gained a lot of traction in recent years suggests that multi-scale integration is regulated by a hierarchy of mutually interacting neural oscillations. In particular, there is accumulating evidence that phase-amplitude coupling (PAC), a specific form of cross-frequency interaction, plays a key role in numerous cognitive processes. Current research in the field is not only hampered by the absence of a gold standard for PAC analysis, but also by the computational costs of running exhaustive computations on large and high-dimensional electrophysiological brain signals. In addition, various signal properties and analyses parameters can lead to spurious PAC. Here, we present Tensorpac, an open-source Python toolbox dedicated to PAC analysis of neurophysiological data. The advantages of Tensorpac include (1) higher computational efficiency thanks to software design that combines tensor computations and parallel computing, (2) the implementation of all most widely used PAC methods in one package, (3) the statistical analysis of PAC measures, and (4) extended PAC visualization capabilities. Tensorpac is distributed under a BSD-3-Clause license and can be launched on any operating system (Linux, OSX and Windows). It can be installed directly via pip or downloaded from Github (https://github.com/EtienneCmb/tensorpac). By making Tensorpac available, we aim to enhance the reproducibility and quality of PAC research, and provide open tools that will accelerate future method development in neuroscience.

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Dimitrienko, Yu I., E. A. Gubareva, and S. V. Sborshikov. "Visualization of tensor fields based on geometric representation of tensors." Scientific Visualization 10, no. 2 (July 2, 2018): 95–111. http://dx.doi.org/10.26583/sv.10.2.08.

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Abtahi, Sayyed Mohammad, Laust Börsting Pedersen, Jochen Kamm, and Thomas Kalscheuer. "Extracting geoelectrical maps from vintage very-low-frequency airborne data, tipper inversion, and interpretation: A case study from northern Sweden." GEOPHYSICS 81, no. 5 (September 2016): B135—B147. http://dx.doi.org/10.1190/geo2015-0296.1.

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In 1985, the mining company Luossavaara-Kiirunavaara Aktiebolag collected airborne very-low-frequency (VLF) data in northern Sweden. The operators stored only the vertical component and the total magnetic field, which at that time were believed to be sufficient for qualitative interpretation. Therefore, the data could not be directly used for quantitative tensor VLF processing and inversion. To avoid the costs of resurveying, we have developed a novel technique to estimate the tippers from the measured VLF data by computing anomalous and normal parts of the horizontal components of the magnetic field from two transmitters separately. Retrieval of the normal horizontal components was possible because one component of the horizontal magnetic field was used as the phase reference during the measurements. Additionally, we have determined how the approximate apparent resistivity suitable for data visualization can be computed from the components of the magnetic field assuming an average normal resistivity of the subsurface. Maps of apparent resistivity combined with topography show a clear correlation between high topography and high resistivity, whereas conductive zones are found in valleys in between. More importantly, the 3D model inverted from the calculated tippers shows excellent agreement with a map of the surface geology. Based on this comparison, some less resistive zones can be related to fluids in fractures and others can be related to mineralized contact zones. We suggest to focus further exploration on conductive zones surrounding areas with basaltic composition.

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Archip, Neculai, Olivier Clatz, Stephen Whalen, Simon P. DiMaio, Peter M. Black, Ferenc A. Jolesz, Alexandra Golby, and Simon K. Warfield. "Compensation of Geometric Distortion Effects on Intraoperative Magnetic Resonance Imaging for Enhanced Visualization in Image-guided Neurosurgery." Operative Neurosurgery 62, suppl_1 (March 1, 2008): ONS209—ONS216. http://dx.doi.org/10.1227/01.neu.0000317395.08466.e6.

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Abstract Objective: Preoperative magnetic resonance imaging (MRI), functional MRI, diffusion tensor MRI, magnetic resonance spectroscopy, and positron-emission tomographic scans may be aligned to intraoperative MRI to enhance visualization and navigation during image-guided neurosurgery. However, several effects (both machine- and patient-induced distortions) lead to significant geometric distortion of intraoperative MRI. Therefore, a precise alignment of these image modalities requires correction of the geometric distortion. We propose and evaluate a novel method to compensate for the geometric distortion of intraoperative 0.5-T MRI in image-guided neurosurgery. Methods: In this initial pilot study, 11 neurosurgical procedures were prospectively enrolled. The scheme used to correct the geometric distortion is based on a nonrigid registration algorithm introduced by our group. This registration scheme uses image features to establish correspondence between images. It estimates a smooth geometric distortion compensation field by regularizing the displacements estimated at the correspondences. A patient-specific linear elastic material model is used to achieve the regularization. The geometry of intraoperative images (0.5 T) is changed so that the images match the preoperative MRI scans (3 T). Results: We compared the alignment between preoperative and intraoperative imaging using 1) only rigid registration without correction of the geometric distortion, and 2) rigid registration and compensation for the geometric distortion. We evaluated the success of the geometric distortion correction algorithm by measuring the Hausdorff distance between boundaries in the 3-T and 0.5-T MRIs after rigid registration alone and with the addition of geometric distortion correction of the 0.5-T MRI. Overall, the mean magnitude of the geometric distortion measured on the intraoperative images is 10.3 mm with a minimum of 2.91 mm and a maximum of 21.5 mm. The measured accuracy of the geometric distortion compensation algorithm is 1.93 mm. There is a statistically significant difference between the accuracy of the alignment of preoperative and intraoperative images, both with and without the correction of geometric distortion (P < 0.001). Conclusion: The major contributions of this study are 1) identification of geometric distortion of intraoperative images relative to preoperative images, 2) measurement of the geometric distortion, 3) application of nonrigid registration to compensate for geometric distortion during neurosurgery, 4) measurement of residual distortion after geometric distortion correction, and 5) phantom study to quantify geometric distortion.

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Ennis, Daniel B., Gordon Kindlman, Ignacio Rodriguez, Patrick A. Helm, and Elliot R. McVeigh. "Visualization of tensor fields using superquadric glyphs." Magnetic Resonance in Medicine 53, no. 1 (2004): 169–76. http://dx.doi.org/10.1002/mrm.20318.

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Kareem, Waleed Abdel. "A vortex identification method based on strain and enstrophy production invariants." International Journal of Modern Physics C 31, no. 01 (November 12, 2019): 2050003. http://dx.doi.org/10.1142/s0129183120500035.

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A new vortex identification method is proposed for extracting vortical structures from homogeneous isotropic turbulence. The method is compared with other identification schemes such as the high rotational method ([Formula: see text]), the vorticity magnitude method ([Formula: see text]), the negative eigenvalue method ([Formula: see text]) and the normalized vorticity method ([Formula: see text]). A new normalization method based on the probability distribution function (PDF) of the identification invariants is also introduced. In addition, a modification for the discriminant criterion known as the [Formula: see text] method is carried out and it is denoted as the modified delta method ([Formula: see text]). The velocity of the isotropic turbulent field is simulated using the lattice Boltzmann method with resolution [Formula: see text]. The new identification method depends on the higher-orders of the invariants of the velocity gradient tensor as well as the strain rate and the enstrophy production terms. The elongated tube-like vortices are extracted successfully using the new method and several features of the vortices are demonstrated and compared with the vortical structures that are extracted using the [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] identification methods. The recommended normalization method enabled the justification of the visualization threshold value to be within the order of unity and the threshold value [Formula: see text] is used in all identification methods. A remarkably similar geometrical worm-like vortices are extracted and a high similarity between the identification methods is observed and statistically studied.

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Akula, Bhanesh, and Devesh Ranjan. "Dynamics of buoyancy-driven flows at moderately high Atwood numbers." Journal of Fluid Mechanics 795 (April 14, 2016): 313–55. http://dx.doi.org/10.1017/jfm.2016.199.

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Simultaneous density and velocity turbulence statistics for Rayleigh–Taylor-driven flows at a moderately high Atwood number ($A_{t}$) of $0.73\pm 0.02$ are obtained using a new convective type or statistically steady gas tunnel facility. Air and air–helium mixture are used as working fluids to create a density difference in this facility, with a thin splitter plate separating the two streams flowing parallel to each other at the same velocity ($U=3~\text{m}~\text{s}^{-1}$). At the end of the splitter plate, the two miscible fluids are allowed to mix and the instability develops. Visualization and Mie-scattering techniques are used to obtain structure shape, volume fraction profile and mixing height growth information. Particle image velocimetry (PIV) and hot-wire techniques are used to measure planar and point-wise velocity statistics in the developing mixing layer. Asymmetry is evident in the flow field from the Mie-scattering images, with the spike side showing a more gradual decline in volume fraction than the bubble side. The spike side of the mixing layer grows 50 % faster than the bubble side. PIV is implemented for the first time in these moderately high-Atwood-number experiments ($A_{t}>0.1$) to obtain root-mean-square velocities, anisotropy tensor components and Reynolds stresses across the mixing layer. Overall, the turbulence statistics measured have shown different scaling compared to small-Atwood-number experiments. However, the total probability density functions for the velocities and turbulent mass fluxes exhibit behaviour similar to small-Atwood-number experiments. Conditional statistics reveal different values for turbulence statistics for spikes and bubbles, unlike small-Atwood-number experiments.

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Zhang, Changgong, Thomas Schultz, Kai Lawonn, Elmar Eisemann, and Anna Vilanova. "Glyph-Based Comparative Visualization for Diffusion Tensor Fields." IEEE Transactions on Visualization and Computer Graphics 22, no. 1 (January 31, 2016): 797–806. http://dx.doi.org/10.1109/tvcg.2015.2467435.

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Tricoche, X., G. Scheuermann, and H. Hagen. "Tensor Topology Tracking: A Visualization Method for Time-Dependent 2D Symmetric Tensor Fields." Computer Graphics Forum 20, no. 3 (September 2001): 461–70. http://dx.doi.org/10.1111/1467-8659.00539.

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Dodd, R. K. "A New Approach to the Visualization of Tensor Fields." Graphical Models and Image Processing 60, no. 4 (July 1998): 286–303. http://dx.doi.org/10.1006/gmip.1998.0473.

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Bezborodov, Mikhail A., Mikhail A. Eremin, Vitaly V. Korolev, Ilya G. Kovalenko, and Elena V. Zhukova. "Visualization of the Anisotropy of the Velocity Dispersion and Characteristics of the Multi-Velocity Continuum in the Regions of Multi-Stream Flows of Gas-Dust Media with Polydisperse Dust." Journal of Imaging 6, no. 9 (September 17, 2020): 98. http://dx.doi.org/10.3390/jimaging6090098.

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Collisionless media devoid of intrinsic stresses, for example, a dispersed phase in a multiphase medium, have a much wider variety of space-time structures and features formed in them than collisional media, for example, a carrier, gas, or liquid phase. This is a consequence of the fact that evolution in such media occurs in phase space, i.e., in a space of greater dimensions than the usual coordinate space. As a consequence, the process of the formation of features in collisionless media (clustering or vice versa, a loss of continuity) can occur primarily in the velocity space, which, in contrast to the features in the coordinate space (folds, caustics, or voids), is poorly observed directly. To identify such features, it is necessary to use visualization methods that allow us to consider, in detail, the evolution of the medium in the velocity space. This article is devoted to the development of techniques that allow visualizing the degree of anisotropy of the velocity fields of collisionless interpenetrating media. Simultaneously tracking the behavior of different fractions in such media is important, as their behavior can be significantly different. We propose three different techniques for visualizing the anisotropy of velocity fields using the example of two- and three-continuum dispersed media models. We proposed the construction of spatial distributions of eccentricity fields (scalar fields), or fields of principal directions of the velocity dispersion tensor (tensor fields). In the first case, we used some simple eccentricity functions for dispersion tensors for two fractions simultaneously, which we call surrogate entropy. In the second case, to visualize the anisotropy of the velocity fields of three fractions simultaneously, we used an ordered array (3-vector) of eccentricities for the color representation through decomposition in three basic colors. In the case of a multi-stream flow, we used cluster analysis methods to identify sections of a multi-stream flow (beams) and used glyphs to visualize the entire set of beams (vector-tensor fields).

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NILSSON, OLA, MARTIN REIMERS, KEN MUSETH, and ANDERS BRUN. "A NEW ALGORITHM FOR COMPUTING RIEMANNIAN GEODESIC DISTANCE IN RECTANGULAR 2-D AND 3-D GRIDS." International Journal on Artificial Intelligence Tools 22, no. 06 (December 2013): 1360020. http://dx.doi.org/10.1142/s0218213013600208.

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We present a novel way to efficiently compute Riemannian geodesic distance over a two- or three-dimensional domain. It is based on a previously presented method for computation of geodesic distances on surface meshes. Our method is adapted for rectangular grids, equipped with a variable anisotropic metric tensor. Processing and visualization of such tensor fields is common in certain applications, for instance structure tensor fields in image analysis and diffusion tensor fields in medical imaging. The included benchmark study shows that our method provides significantly better results in anisotropic regions in 2-D and 3-D and is faster than current stat-of-the-art solvers in 2-D grids. Additionally, our method is straightforward to code; the test implementation is less than 150 lines of C++ code. The paper is an extension of a previously presented conference paper and includes new sections on 3-D grids in particular.

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ORLANDI, P. "Energy spectra power laws and structures." Journal of Fluid Mechanics 623 (March 6, 2009): 353–74. http://dx.doi.org/10.1017/s0022112008005016.

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Direct numerical simulations (DNS) of two inviscid flows, the Taylor–Green flow and two orthogonal interacting Lamb dipoles, together with the DNS of forced isotropic turbulence, were performed to generate data for a comparative study. The isotropic turbulent field was considered after the transient and, in particular, when the velocity derivative skewness oscillates around −0.5. At this time, Rλ ≈ 257 and a one decade wide k−5/3 range was present in the energy spectrum. For the inviscid flows the fields were considered when a wide k−3 range was achieved. This power law spectral decay corresponds to infinite enstrophy and is considered one of the requirements to demonstrate that the Euler equations lead to a finite time singularity (FTS). Flow visualizations and statistics of the strain rate tensor and vorticity components in the principal axes of the strain rate tensor (λ, λ) were used to classify structures. The key role of the intermediate component 2 is demonstrated by its good correlation with enstrophy production. Filtering of the fields shows that the slope of the power law is directly connected to self-similar structures, whose radius of curvature is smaller the steeper the spectrum.

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Song, Weijie. "Fast Visualization of Stress and Strain Tensor Fields on Streamsurfaces with LIC Texture." Journal of Information and Computational Science 12, no. 8 (May 20, 2015): 3207–19. http://dx.doi.org/10.12733/jics20105835.

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Roessler, Karl, Andrea Hofmann, Bjoern Sommer, Peter Grummich, Roland Coras, Burkard Sebastian Kasper, Hajo M. Hamer, et al. "Resective surgery for medically refractory epilepsy using intraoperative MRI and functional neuronavigation: the Erlangen experience of 415 patients." Neurosurgical Focus 40, no. 3 (March 2016): E15. http://dx.doi.org/10.3171/2015.12.focus15554.

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OBJECTIVE Intraoperative overestimation of resection volume in epilepsy surgery is a well-known problem that can lead to an unfavorable seizure outcome. Intraoperative MRI (iMRI) combined with neuronavigation may help surgeons avoid this pitfall and facilitate visualization and targeting of sometimes ill-defined heterogeneous lesions or epileptogenic zones and may increase the number of complete resections and improve seizure outcome. METHODS To investigate this hypothesis, the authors conducted a retrospective clinical study of consecutive surgical procedures performed during a 10-year period for epilepsy in which they used neuronavigation combined with iMRI and functional imaging (functional MRI for speech and motor areas; diffusion tensor imaging for pyramidal, speech, and visual tracts; and magnetoencephalography and electrocorticography for spike detection). Altogether, there were 415 patients (192 female and 223 male, mean age 37.2 years; 41% left-sided lesions and 84.9% temporal epileptogenic zones). The mean preoperative duration of epilepsy was 17.5 years. The most common epilepsy-associated pathologies included hippocampal sclerosis (n = 146 [35.2%]), long-term epilepsy-associated tumor (LEAT) (n = 67 [16.1%]), cavernoma (n = 45 [10.8%]), focal cortical dysplasia (n = 31 [7.5%]), and epilepsy caused by scar tissue (n = 23 [5.5%]). RESULTS In 11.8% (n = 49) of the surgeries, an intraoperative second-look surgery (SLS) after incomplete resection verified by iMRI had to be performed. Of those incomplete resections, LEATs were involved most often (40.8% of intraoperative SLSs, 29.9% of patients with LEAT). In addition, 37.5% (6 of 16) of patients in the diffuse glioma group and 12.9% of the patients with focal cortical dysplasia underwent an SLS. Moreover, iMRI provided additional advantages during implantation of grid, strip, and depth electrodes and enabled intraoperative correction of electrode position in 13.0% (3 of 23) of the cases. Altogether, an excellent seizure outcome (Engel Class I) was found in 72.7% of the patients during a mean follow-up of 36 months (range 3 months to 10.8 years). The greatest likelihood of an Engel Class I outcome was found in patients with cavernoma (83.7%), hippocampal sclerosis (78.8%), and LEAT (75.8%). Operative revisions that resulted from infection occurred in 0.3% of the patients, from hematomas in 1.6%, and from hydrocephalus in 0.8%. Severe visual field defects were found in 5.2% of the patients, aphasia in 5.7%, and hemiparesis in 2.7%, and the total mortality rate was 0%. CONCLUSIONS Neuronavigation combined with iMRI was beneficial during surgical procedures for epilepsy and led to favorable seizure outcome with few specific complications. A significantly higher resection volume associated with a higher chance of favorable seizure outcome was found, especially in lesional epilepsy involving LEAT or diffuse glioma.

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Krawczuk, Anna, Daniel Pérez, and Piero Macchi. "PolaBer: a program to calculate and visualize distributed atomic polarizabilities based on electron density partitioning." Journal of Applied Crystallography 47, no. 4 (June 14, 2014): 1452–58. http://dx.doi.org/10.1107/s1600576714010838.

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This paper describes the program PolaBer, which calculates atomic polarizability tensors from electric field perturbations of a partitioned electron density distribution. Among many possible partitioning schemes, PolaBer is currently using the quantum theory of atoms in molecules and it is interfaced to programs that apply such a partitioning. The calculation of the atomic tensors follows the idea suggested by Keith [The Quantum Theory of Atoms in Molecules: From Solid State to DNA and Drug Design, (2007), edited by C. F. Matta & R. J. Boyd. Weinheim: Wiley-VCH], which enables the removal of the intrinsic origin dependence of the atomic charge contributions to the molecular dipole moment. This scheme allows the export, within chemically equivalent functional groups, of properties calculated from atomic dipoles, such as for example the atomic polarizabilities. The software permits visualization of the tensors and calculation of straightforward optical properties of a molecule (like the molar refractive index) or a crystal (assuming the molecule in a given crystal lattice).

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BUXTON, O. R. H., and B. GANAPATHISUBRAMANI. "Amplification of enstrophy in the far field of an axisymmetric turbulent jet." Journal of Fluid Mechanics 651 (March 19, 2010): 483–502. http://dx.doi.org/10.1017/s0022112009993892.

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The amplification of enstrophy is explored using cinematographic stereoscopic particle image velocimetry data. The enstrophy production rate is investigated by observation of the statistical tendency of the vorticity vector (ω) to align with the eigenvectors of the rate of strain tensor (ei). Previous studies have shown thatωpreferentially aligns with the intermediate strain-rate eigenvector (e2) and is arbitrarily aligned with the extensive strain-rate eigenvector (e1). This study shows, however, that the nature of enstrophy amplification, whether it is positive (enstrophy production) or negative (enstrophy destruction), is dictated by the alignment betweenωande1. Parallel alignment leads to enstrophy production (ωiSijωj>0), whereas perpendicular alignment leads to enstrophy destruction (ωiSijωj<0). In this way, the arbitrary alignment betweenωande1is the summation of the effects of enstrophy producing and enstrophy destroying regions. The structure of enstrophy production is also examined with regards to the intermediate strain-rate eigenvalue,s2. Enstrophy producing regions are found to be topologically ‘sheet-forming’, due to an extensive (positive) value ofs2in these regions, whereas enstrophy destroying regions are found to be ‘spotty’. Strong enstrophy producing regions are observed to occur in areas of strong local swirling as well as in highly dissipative regions. Instantaneous visualizations, produced from the volume of data created by Taylor's hypothesis, reveal that these ‘sheet-like’ strong enstrophy producing regions encompass the high enstrophy, strongly swirling ‘worms’. These ‘worms’ induce high local strain fields leading to the formation of dissipation ‘sheets’, thereby revealing enstrophy production to be a complex interaction between rotation and strain – the skew-symmetric and symmetric components of the velocity gradient tensor, respectively.

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Drakopoulos, Georgios, Andreas Kanavos, Phivos Mylonas, and Panagiotis Pintelas. "Extending Fuzzy Cognitive Maps with Tensor-Based Distance Metrics." Mathematics 8, no. 11 (October 31, 2020): 1898. http://dx.doi.org/10.3390/math8111898.

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Cognitive maps are high level representations of the key topological attributes of real or abstract spatial environments progressively built by a sequence of noisy observations. Currently such maps play a crucial role in cognitive sciences as it is believed this is how clusters of dedicated neurons at hippocampus construct internal representations. The latter include physical space and, perhaps more interestingly, abstract fields comprising of interconnected notions such as natural languages. In deep learning cognitive graphs are effective tools for simultaneous dimensionality reduction and visualization with applications among others to edge prediction, ontology alignment, and transfer learning. Fuzzy cognitive graphs have been proposed for representing maps with incomplete knowledge or errors caused by noisy or insufficient observations. The primary contribution of this article is the construction of cognitive map for the sixteen Myers-Briggs personality types with a tensor distance metric. The latter combines two categories of natural language attributes extracted from the namesake Kaggle dataset. To the best of our knowledge linguistic attributes are separated in categories. Moreover, a fuzzy variant of this map is also proposed where a certain personality may be assigned to up to two types with equal probability. The two maps were evaluated based on their topological properties, on their clustering quality, and on how well they fared against the dataset ground truth. The results indicate a superior performance of both maps with the fuzzy variant being better. Based on the findings recommendations are given for engineers and practitioners.

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Hennemuth, A., B. Fischer, O. Friman, and M. Schwenke. "A Novel Anisotropic Fast Marching Method and its Application to Blood Flow Computation in Phase-contrast MRI." Methods of Information in Medicine 51, no. 05 (2012): 423–28. http://dx.doi.org/10.3414/me11.02.0032.

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SummaryBackground: Phase-contrast MRI (PC MRI) can be used to assess blood flow dynamics noninvasively inside the human body. The acquired images can be reconstructed into flow vector fields. Traditionally, streamlines can be computed based on the vector fields to visualize flow patterns and particle trajectories.Objectives: The traditional methods may give a false impression of precision, as they do not consider the measurement uncertainty in the PC MRI images. In our prior work, we incorporated the uncertainty of the measurement into the computation of particle trajectories.Methods: As a major part of the contribution, a novel numerical scheme for solving the anisotropic Fast Marching problem is presented. A computing time comparison to state-of-theart methods is conducted on artificial tensor fields. A visual comparison of healthy to pathological blood flow patterns is given.Results: The comparison shows that the novel anisotropic Fast Marching solver outperforms previous schemes in terms of computing time. The visual comparison of flow patterns directly visualizes large deviations of pathological flow from healthy flow.Conclusions: The novel anisotropic Fast Marching solver efficiently resolves even strongly anisotropic path costs. The visualization method enables the user to assess the uncertainty of particle trajectories derived from PC MRI images.

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López Isaza, Julián Andrés, Mario Andrés Cuéllar Cárdenas, Lina María Cetina Tarazona, Anny Julieth Forero Ortega, Ana Milena Suárez Arias, Oscar Freddy Muñoz Rodríguez, Luis Miguel Aguirre Hoyos, and María Juliana Gutiérrez López. "Graphical representation of structural data in the field: A methodological proposal for application in deformed areas." Boletín Geológico 48, no. 1 (July 12, 2021): 123–39. http://dx.doi.org/10.32685/0120-1425/bol.geol.48.1.2021.504.

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The description of the fabric elements represented by the linear and planar structures present at different scales is a key component of fieldwork. A scheme is proposed for the systematic registration of planes and lineations, coded as S (planar surfaces), F (folds), and L (lineations), among others, that allows for the orderly storage of the measurements taken. This scheme includes information related to the kinematics, the kinematic indicators, and the certainty or reliability ascribed to the assigned movement. In the fieldwork, the graphic representation of the structural measures in modified projection nets includes concentric circles for each dip. Direct drawing of the outcrop data is undertaken, dispensing with the use of tracing or transparent paper. The stereograms resulting from the graphic representation in the modified Wulff stereographic projection net, and the modified Schmidt equal-area net, can be complemented by rose diagrams for visualization of the spatial ordering. During field campaigns in the outcrops, it is essential to visualize the spatial orientation of the data in the diagrams to determine the main structural trends, the vergence, the kinematic nature of faults and shear zones, paleo-stress tensors, and to differentiate structural domains, among others. This information supports the reconstruction of geological and tectonic history and the establishment of relationships between the different geological processes.

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Roche, D., C. Michel, P. Daudé, A. Le Troter, C. Chagnaud, J. P. Mattei, L. Pini, M. Guye, D. Bendahan, and S. Guis. "AB1098 STRUCTURAL ELEMENTS OF THE KNEE ENTHESES ASSESSED IN HEALTHY SUBJECTS WITH ULTRA HIGH FIELD MRI (150 MICRONS)." Annals of the Rheumatic Diseases 79, Suppl 1 (June 2020): 1838. http://dx.doi.org/10.1136/annrheumdis-2020-eular.1191.

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Background:Fibrocartilaginous enthesis is composed of different histological zones which are commonly referred to the tendon distal extremity (a lamellar tissue with a low cell density, collagen and connective tissue), the fibrocartilaginous zone (with chondrocytes), a progressively mineralized zone and the bone. The MRI visualization of the water content of entheses is challenging given the very short relation time so that entheses has been very poorly assessed using MRI (1).Objectives:The main objective of the study was to assess the structural elements of the knee enthesis based on the quantitative T2* measurements using Ultra High Field (UHF) MRI.Methods:Twelve healthy subjects without any osteoarticular pathology were included in the study after they provided their informed consent. 3D gradient echo sequence with a 4.3 ms echo time and T2* mapping were performed. The lateral internal, external and crossed ligaments, patellar and quadricipital tendons were assessed. T2* measurements were performed specifically on the quadricipital tendon.Results:The quadricipital tendon and the bone trabeculation could be visualized on the UHF MR image. The T2* mapping analysis illustrated a large value (16.4 ± 4 ms) for the subchondral bone and much lower values for the trabecular bone (11 ± 4.5 ms) and the different zones of the keen entheses (7.7 ± 1.9 ms).Conclusion:Based on T2* measurements performed using UHF MRI, the different structural elements of the knee entheses were distinguished. This quantitative stratification could be used to assess changes in pathological conditions such as SpA and trauma.References:[1]Benjamin M, Bydder GM. Magnetic resonance imaging of entheses using ultrashort TE (UTE) pulse sequences. Journal of magnetic resonance imaging: JMRI. 2007;25(2):381-9.Disclosure of Interests:None declared

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TEJADA-MARTÍNEZ, A. E., and C. E. GROSCH. "Langmuir turbulence in shallow water. Part 2. Large-eddy simulation." Journal of Fluid Mechanics 576 (March 28, 2007): 63–108. http://dx.doi.org/10.1017/s0022112006004587.

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Results of large-eddy simulation (LES) of Langmuir circulations (LC) in a wind-driven shear current in shallow water are reported. The LC are generated via the well-known Craik–Leibovich vortex force modelling the interaction between the Stokes drift, induced by surface gravity waves, and the shear current. LC in shallow water is defined as a flow in sufficiently shallow water that the interaction between the LC and the bottom boundary layer cannot be ignored, thus requiring resolution of the bottom boundary layer. After the introduction and a description of the governing equations, major differences in the statistical equilibrium dynamics of wind-driven shear flow and the same flow with LC (both with a bottom boundary layer) are highlighted. Three flows with LC will be discussed. In the first flow, the LC were generated by intermediate-depth waves (relative to the wavelength of the waves and the water depth). The amplitude and wavelength of these waves are representative of the conditions reported in the observations of A. E. Gargett & J. R. Wells in Part 1 (J. Fluid Mech. vol .000, 2007, p. 00). In the second flow, the LC were generated by shorter waves. In the third flow, the LC were generated by intermediate waves of greater amplitude than those in the first flow. The comparison between the different flows relies on visualizations and diagnostics including (i) profiles of mean velocity, (ii) profiles of resolved Reynolds stress components, (iii) autocorrelations, (iv) invariants of the resolved Reynolds stress anisotropy tensor and (v) balances of the transport equations for mean resolved turbulent kinetic energy and resolved Reynolds stresses. Additionally, dependencies of LES results on Reynolds number, subgrid-scale closure, size of the domain and grid resolution are addressed.In the shear flow without LC, downwind (streamwise) velocity fluctuations are characterized by streaks highly elongated in the downwind direction and alternating in sign in the crosswind (spanwise) direction. Forcing this flow with the Craik–Leibovich force generating LC leads to streaks with larger characteristic crosswind length scales consistent with those recorded by observations. In the flows with LC, in the mean, positive streaks exhibit strong intensification near the bottom and near the surface leading to intensified downwind velocity ‘jets’ in these regions. In the flow without LC, such intensification is noticeably absent. A revealing diagnostic of the structure of the turbulence is the depth trajectory of the invariants of the resolved Reynolds stress anisotropy tensor, which for a realizable flow must lie within the Lumley triangle. The trajectory for the flow without LC reveals the typical structure of shear-dominated turbulence in which the downwind component of the resolved normal Reynolds stresses is greater than the crosswind and vertical components. In the near bottom and surface regions, the trajectory for the flow with LC driven by wave and wind forcing conditions representative of the field observations reveals a two-component structure in which the downwind and crosswind components are of the same order and both are much greater than the vertical component. The two-component structure of the Langmuir turbulence predicted by LES is consistent with the observations in the bottom third of the water column above the bottom boundary layer.

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Yin, Mengchen, Chongqing Xu, Junming Ma, Jie Ye, and Wen Mo. "A Bibliometric Analysis and Visualization of Current Research Trends in the Treatment of Cervical Spondylotic Myelopathy." Global Spine Journal, September 1, 2020, 219256822094883. http://dx.doi.org/10.1177/2192568220948832.

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Study Design: Bibliometric analysis. Objective: Cervical spondylotic myelopathy (CSM) has become the most common cause of spinal cord dysfunction. Many topics of CSM still remain controversial. This study aimed to illustrate the overall knowledge structure and development trends of CSM. Methods: Research data sets were acquired from the Web of Science database and the time span was defined as “2000 to 2019.” VOS viewer and Citespace software was used to analyze the data and generate visualization knowledge maps. Annual trends of publications, distribution, H-index status, co-authorship status, and research hotspots were analyzed. Results: A total of 2367 publications met the requirement. The largest number of articles was from the United States, followed by Japan, China, Canada, and India. The highest H-index was found for articles from the United States. The highest number of articles was published in Spine. The cooperation between the countries, institutes, and authors were relatively weak. Cervical sagittal alignment, predictive factor, diffusion tensor imaging, and the natural history of CSM may become a frontier in this research field. Conclusion: The number of publications showed an upward trend with a stable rise. Most of the publications are limited to a few countries and institutions with relatively weak interaction. The United States, Canada, Japan, China, and India have made significant contributions to the field of CSM. The United States is the country with the highest productivity, not only in quality but also in quantity. Cervical sagittal alignment, predictive factor, diffusion tensor imaging, and the natural history of CSM are the research hotspots in the recent years.

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Panigrahi, P. K. "PIV Investigation of Flow Behind Surface Mounted Detached Square Cylinder." Journal of Fluids Engineering 131, no. 1 (November 26, 2008). http://dx.doi.org/10.1115/1.3026721.

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The flow field behind surface mounted detached square ribs under the approaching flat plate turbulent boundary layer has been experimentally studied using the particle image velocimetry (PIV) (two-component and stereo) technique in both streamwise and cross stream measurement planes. An oil film visualization study has been carried out for correlating the surface flow patterns to the flow structures. The Reynolds number based on the rib height is equal to 11,075. The ratio of the gap height to the square rib size is set equal to 0.2, 0.37, 0.57, and 1.0. The ratio of approaching boundary layer thickness to rib height is equal to 0.2. The mean and rms velocity fields, streamwise and spanwise vorticity fields, velocity gradient and velocity vector fields, turbulent kinetic energy budgets, and stream trace results are reported. The second invariant of the velocity gradient tensor results are presented to distinguish between the rotational and shear contribution of the vorticity field. The recirculation bubbles with a focilike structure are observed behind the detached ribs. These structures are displaced upward, i.e., away from the wall surface with an increase in gap size of the detached cylinder. The size of the recirculation bubble also drops with an increase in the gap size. The stream traces in the cross stream plane show node-saddle patterns, whose near wall concentration is high for a lower gap size detached cylinder. The oil film visualization images show saddle patterns at the meeting point between the flow through the gap and the reattaching shear layer for the lower gap size detached cylinder. The v-velocity magnitude distribution shows greater wall-normal motion across the wake for the detached cylinder of lower gap size. There is a significant near wall velocity fluctuation for the lower gap size detached cylinder. The higher velocity fluctuation due to the near wall flow structures contributes toward an increase in the near wall mixing of a detached cylinder geometry. Overall, the present study clearly demonstrates the flow structures behind detached ribs, which are responsible for effective near wall mixing. The results from this study provide useful understanding for the design of turbulators in various practical applications.

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Hergl, Chiara, Christian Blecha, Vanessa Kretzschmar, Felix Raith, Fabian Günther, Markus Stommel, Jochen Jankowai, Ingrid Hotz, Thomas Nagel, and Gerik Scheuermann. "Visualization of Tensor Fields in Mechanics." Computer Graphics Forum, March 30, 2021. http://dx.doi.org/10.1111/cgf.14209.

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Patel, Mohak, and David H. Laidlaw. "Visualization of 3D stress tensor fields using superquadric glyphs on displacement streamlines." IEEE Transactions on Visualization and Computer Graphics, 2020, 1. http://dx.doi.org/10.1109/tvcg.2020.2968911.

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Journal articles on the topic 'Tensor Field Visualization'

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