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Relevant bibliographies by topics / Geometric analysis

Academic literature on the topic 'Geometric analysis'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 August 2024

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Journal articles on the topic "Geometric analysis"

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Pinus, A. G. "Geometric and conditional geometric equivalences of algebras." Algebra and Logic 51, no. 6 (January 2013): 507–10. http://dx.doi.org/10.1007/s10469-013-9210-4.

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Gong, Wenjuan, Bin Zhang, Chaoqi Wang, Hanbing Yue, Chuantao Li, Linjie Xing, Yu Qiao, Weishan Zhang, and Faming Gong. "A Literature Review: Geometric Methods and Their Applications in Human-Related Analysis." Sensors 19, no. 12 (June 23, 2019): 2809. http://dx.doi.org/10.3390/s19122809.

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Geometric features, such as the topological and manifold properties, are utilized to extract geometric properties. Geometric methods that exploit the applications of geometrics, e.g., geometric features, are widely used in computer graphics and computer vision problems. This review presents a literature review on geometric concepts, geometric methods, and their applications in human-related analysis, e.g., human shape analysis, human pose analysis, and human action analysis. This review proposes to categorize geometric methods based on the scope of the geometric properties that are extracted: object-oriented geometric methods, feature-oriented geometric methods, and routine-based geometric methods. Considering the broad applications of deep learning methods, this review also studies geometric deep learning, which has recently become a popular topic of research. Validation datasets are collected, and method performances are collected and compared. Finally, research trends and possible research topics are discussed.

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Ali, Akbar, M. Matejić, Igor Ž. Milovanović, Emina I. Milovanović, Stefan D. Stankov, and Zahid Raza. "On arithmetic-geometric and geometric-arithmetic indices of graphs." Journal of Mathematical Inequalities, no. 4 (2023): 1565–79. http://dx.doi.org/10.7153/jmi-2023-17-103.

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Mostajeran, Cyrus, Christian Grussler, and Rodolphe Sepulchre. "Geometric Matrix Midranges." SIAM Journal on Matrix Analysis and Applications 41, no. 3 (January 2020): 1347–68. http://dx.doi.org/10.1137/19m1273475.

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J. Washington, Andres. "Fingerprint Geometric Analysis." International Journal of Criminal and Forensic Science 1, no. 1 (2017): 08–10. http://dx.doi.org/10.25141/2576-3563-2017-1.0008.

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Artstein-Avidan, Shiri, Hermann König, and Alexander Koldobsky. "Asymptotic Geometric Analysis." Oberwolfach Reports 13, no. 1 (2016): 507–65. http://dx.doi.org/10.4171/owr/2016/11.

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Blasius, Joerg. "Geometric Data Analysis." Bulletin of Sociological Methodology/Bulletin de Méthodologie Sociologique 68, no. 1 (October 2000): 54–55. http://dx.doi.org/10.1177/075910630006800123.

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Hong, Seok-In. "Geometric circuit analysis." Physics Education 58, no. 6 (October 6, 2023): 065021. http://dx.doi.org/10.1088/1361-6552/acf108.

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Abstract The Smith rectangle symbolises the resistor and its width, height, aspect ratio, and area represent the current through, the voltage across, the resistance of, and the power dissipated in the resistor, respectively. In this article, the mosaic of rectangles (MOR) is introduced as a geometric approach to connected planar resistive network circuits with an ideal voltage source. In the MOR, the geometric Kirchhoff’s current and voltage laws are expressed as width and height conservations, respectively and are automatically satisfied. Four basic circuits are considered as applications of geometric circuit analysis. Resistors in series and in parallel are analysed using the MOR, and the effect of changing one resistor is visualised by superposing the initial and new MORs. The effect of loading an unloaded voltage divider with a parallel resistor is also visualised. The Wheatstone bridge is explored as an example of rather complicated resistive networks and the consistency of the assumed current directions, the shape of the MOR, and the geometric Kirchhoff’s laws is discussed. The geometric and game-like circuit analysis would be beneficial to high school and university students as well as their teachers.

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Yau, Shing-Tung. "A survey of geometric structure in geometric analysis." Surveys in Differential Geometry 16, no. 1 (2011): 325–48. http://dx.doi.org/10.4310/sdg.2011.v16.n1.a7.

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Moakher, Maher. "A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices." SIAM Journal on Matrix Analysis and Applications 26, no. 3 (January 2005): 735–47. http://dx.doi.org/10.1137/s0895479803436937.

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Dissertations / Theses on the topic "Geometric analysis"

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Roysdon, Michael A. "ON SOME GEOMETRIC AND FUNCTIONAL INEQUALITIES INASYMPTOTIC GEOMETRIC ANALYSIS." Kent State University / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=kent1599821442510494.

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Wink, Matthias. "Ricci solitons and geometric analysis." Thesis, University of Oxford, 2018. http://ora.ox.ac.uk/objects/uuid:3aae2c5e-58aa-42da-9a1b-ec15cacafdad.

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This thesis studies Ricci solitons of cohomogeneity one and uniform Poincaré inequalities for differentials on Riemann surfaces. In the two summands case, which assumes that the isotropy representation of the principal orbit consists of two inequivalent Ad-invariant irreducible summands, complete steady and expanding Ricci solitons have been detected numerically by Buzano-Dancer-Gallaugher-Wang. This work provides a rigorous construction thereof. A Lyapunov function is introduced to prove that the Ricci soliton metrics lie in a bounded region of an associated phase space. This also gives an alternative construction of non-compact Einstein metrics of non-positive scalar curvature due to Böhm. It is explained how the asymptotics of the Ricci flat trajectories induce Böhm's Einstein metrics on spheres and other low dimensional spaces. A numerical study suggests that all other Einstein metrics of positive scalar curvature which are induced by the generalised Hopf fibrations occur in an entirely non-linear regime of the Einstein equations. Extending the theory of cohomogeneity one steady and expanding Ricci solitons, an estimate which allows to prescribe the growth rate of the soliton potential at any given time is shown. As an application, continuous families of Ricci solitons on complex line bundles over products of Fano Kähler Einstein manifolds are constructed. This generalises work of Appleton and Stolarski. The method also applies to the Lü-Page-Pope set-up and allows to cover an optimal parameter range in the two summands case. The Ricci soliton equation on manifolds foliated by torus bundles over products of Fano Kähler Einstein manifolds is discussed. A rigidity theorem is obtained and a preserved curvature condition is discovered. The cohomogeneity one initial value problem is solved for m-quasi-Einstein metrics and complete metrics are described. L^p-Poincaré inequalities for k-differentials on closed Riemann surfaces are shown. The estimates are uniform in the sense that the Poincaré constant only depends on p &GE;1, k ≥ 2 and the genus γ ≥ 2 of the surface but not on its complex structure. Examples show that the analogous estimate for 1-differentials cannot be uniform. This part is based on joint work with Melanie Rupflin.

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Gasparini, Riccardo. "Engineering Analysis in Imprecise Geometric Models." FIU Digital Commons, 2014. http://digitalcommons.fiu.edu/etd/1793.

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Engineering analysis in geometric models has been the main if not the only credible/reasonable tool used by engineers and scientists to resolve physical boundaries problems. New high speed computers have facilitated the accuracy and validation of the expected results. In practice, an engineering analysis is composed of two parts; the design of the model and the analysis of the geometry with the boundary conditions and constraints imposed on it. Numerical methods are used to resolve a large number of physical boundary problems independent of the model geometry. The time expended due to the computational process are related to the imposed boundary conditions and the well conformed geometry. Any geometric model that contains gaps or open lines is considered an imperfect geometry model and major commercial solver packages are incapable of handling such inputs. Others packages apply different kinds of methods to resolve this problems like patching or zippering; but the final resolved geometry may be different from the original geometry, and the changes may be unacceptable. The study proposed in this dissertation is based on a new technique to process models with geometrical imperfection without the necessity to repair or change the original geometry. An algorithm is presented that is able to analyze the imperfect geometric model with the imposed boundary conditions using a meshfree method and a distance field approximation to the boundaries. Experiments are proposed to analyze the convergence of the algorithm in imperfect models geometries and will be compared with the same models but with perfect geometries. Plotting results will be presented for further analysis and conclusions of the algorithm convergence

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Raub, Corey Bevan. "Geometric analysis of axisymmetric disk forging." Ohio : Ohio University, 2000. http://www.ohiolink.edu/etd/view.cgi?ohiou1172778393.

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Benkert, Marc. "Construction and Analysis of Geometric Networks." [S.l. : s.n.], 2007. http://digbib.ubka.uni-karlsruhe.de/volltexte/1000007167.

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Litsgård, Malte. "The Orbit Method and Geometric Quantisation." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-351508.

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Arroyave-Tobón, Santiago. "Polyhedral models reduction in geometric tolerance analysis." Thesis, Bordeaux, 2017. http://www.theses.fr/2017BORD0720/document.

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L’analyse de tolérances par des ensembles de contraintes repose sur la détermination de l’accumulation de variations géométriques par des sommes et intersections d’ensembles opérandes 6d. Les degrés de liberté des liaisons et les degrés d’invariance des surfaces génèrent des opérandes non-bornés (polyèdres), posant des problèmes de simulation. En 2014, L. Homria proposé une méthode pour résoudre ce problème, consistant à ajouter des limites artificielles(contraintes bouchon) sur les déplacements non-bornés. Même si cette méthode permet la manipulation d’objets bornés (polytopes), les contraintes bouchon augmentent la complexité des simulations. En réponse à cette difficulté, une méthode dérivée est proposée dans cette thèse.Cette méthode consiste à tracer et simplifier les contraintes bouchon au travers des opérations.Puis une seconde stratégie basée sur la décomposition d’un polyèdre en une somme d’un polytope et de lignes droites (associées aux déplacements non-bornés). Cette stratégie consiste à simuler d’une part les sommes de droites, et d’autre part, à déterminer la somme de polytopes dans un sous-espace de dimension inférieur à 6. Ces trois stratégies sont comparées au travers d’une application industrielle. Cela montre que la traçabilité des contraintes bouchons est un aspect fondamental pour contrôler leur propagation et pour réduire le temps de calcul des simulations. Toutefois, cette méthode exige encore de déterminer les limites des déplacements non-bornés. La deuxième méthode, adaptant systématiquement la dimension de l’espace de calcul, elle permet de diminuer davantage le temps de calcul. Ce travail permet d’envisager la mise en oeuvre de cette méthode selon des formulations statistiques avec la prise en compte des défauts de forme des surfaces
The cumulative stack-up of geometric variations in mechanical systems can be modelled summing and intersecting sets of constraints. These constraints derive from tolerance zones or from contact restrictions between parts. The degrees of freedom (DOF) of jointsgenerate unbounded sets (i.e. polyhedra) which are difficult to deal with. L. Homri presented in 2014 a solution based on the setting of fictitious limits (called cap constraints) to each DOFto obtain bounded 6D sets (i.e. polytopes). These additional constraints, however, increase the complexity of the models, and therefore, of the computations. In response to this situation,we defined a derived strategy to control the effects of the propagation of the fictitious limits by tracing and simplifying the generated, new cap constraints. We proposed a second strategy based on the decomposition of polyhedra into the sum of a polytope and a set of straight lines.The strategy consists in isolating the straight lines (associated to the DOF) and summing the polytopes in the smallest sub-space. After solving an industrial case, we concluded that tracing caps constraints during the operations allows reducing the models complexity and,consequently, the computational time; however, it still involves working in 6d even in caseswhere this is not necessary. In contrast, the strategy based on the operands decompositionis more efficient due to the dimension reduction. This study allowed us to conclude that the management of mechanisms’ mobility is a crucial aspect in tolerance simulations. The gain on efficiency resulting from the developed strategies opens up the possibility for doing statistical treatment of tolerances and tolerance synthesis

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Lindgren, Natalia. "Geometric and Mechanical Analysis of Aortic Aneurysm." Thesis, KTH, Hållfasthetslära, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-284352.

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The aorta, the main and largest artery in the human body, is susceptible for many types of problems. One of the most common aortic disease is the formation of an aneurysm. Endovascular aortic aneurysm repair (EVAR) is a minimally invasive treatment option for aortic aneurysms, involving the deployment of an expandable stent graft within the aorta without operating the aneurysm directly. With 1.5 to 43 % of EVAR patients having postoperative complications, research to help predict these complications of EVAR is of essence. In this study, the deformations of the aorta induced by a deployed stent graft have been investigated and visualized in order to aid understanding of the geometrical behaviour of the aorta post EVAR. This has been carried out by the development and analysis of patient-specific aortic 3D reconstruction models, 3D printed physical models and FE simulation models. A qualitative assessment of the deformations was achieved by superimposing reconstructed geometries, revealing a light straightening of the aorta and iliac vessels, as well as anterior movement of the iliac branches. Based on the good agreement between the simulated and reconstructed geometries, the findings suggest that such deformations could be derived from the pressure being removed from the aneurysm due to the deployed stent graft, in combination with stent radial forces from the proximal and distal landing zones. Despite that the simulation seemed to underestimate distal movement of the iliac vessel, this study emphasizes the potential of 3D printing and FE analysis as promising tools for planning and research of EVAR.
Den stora kroppspulsådern, aortan, kan drabbas av flera olika sjukdomstillstånd. En av de vanligaste är bildandet av en aortaaneurysm. Endovaskulär Aneruysm Reparation (EVAR) är en operationsteknik för att behandla aortaaneurysmer och involverar positionering av ett rörformat, självexpanderande stentgraft innanför aortaaneurysmen via ljumskartärerna. Eftersom 1,5 till 43 % av EVAR-patienter råkar ut för postoperativa komplikationer är det väsentligt att bedriva vidare studier för att förutse dessa. I denna studie har deformationerna av en aorta på grund av positionerade stentar undersökts och visualiserade för att underlätta förståelsen av aortans geometriska beteende efter EVAR. Detta har gjorts genom att utveckla och analysera patientspecifika 3D-rekonstruktioner, 3D-printade fysiska modeller och simulerade modeller av en aorta. En kvalitativ bedömning av deformationerna uppnåddes genom att superpositionering av rekonstruerade geometrier, vilket avslöjade en lätt uträtning av aortan och tarmbensartärerna, samt en framförflyttning av de senare. Baserat på den goda överensstämmelsen mellan de simulerade och rekonstruerade modellerna, antyder resultaten att sådana deformationer kan härledas av att trycket avlägsnats från aneurysmen på grund av stentgraften, i kombination med radiellt tryck från stentar över och under aneurysmen. Trots att simuleringen underskattade framförflyttningen av tarmbensartärerna, belyser denna studie potentialen hos 3D-printing och FE-analyser som ett värdefullt verktyg för att planera och studera EVAR.

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Tiwari, Abhishek Murray Richard M. Murray Richard M. "Geometric analysis of spatio-temporal planning problems /." Diss., Pasadena, Calif. : Caltech, 2007. http://resolver.caltech.edu/CaltechETD:etd-05202007-135411.

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Gautam, Sushrut Zubin Sulaksh. "Two geometric obstruction results in harmonic analysis." Diss., Restricted to subscribing institutions, 2009. http://proquest.umi.com/pqdweb?did=1872162601&sid=1&Fmt=2&clientId=1564&RQT=309&VName=PQD.

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Books on the topic "Geometric analysis"

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Grinberg, Eric L., ed. Geometric Analysis. Providence, Rhode Island: American Mathematical Society, 1992. http://dx.doi.org/10.1090/conm/140.

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Pérez, Joaquín, and José Gálvez, eds. Geometric Analysis. Providence, Rhode Island: American Mathematical Society, 2012. http://dx.doi.org/10.1090/conm/570.

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Chen, Jingyi, Peng Lu, Zhiqin Lu, and Zhou Zhang, eds. Geometric Analysis. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-34953-0.

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Fraser, Ailana, André Neves, Peter M. Topping, and Paul C. Yang. Geometric Analysis. Edited by Matthew J. Gursky and Andrea Malchiodi. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-53725-8.

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Bray, Hubert L. Geometric analysis. Providence: American Mathematical Society, Institute for Advanced Study, 2015.

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Jordán, Tibor, and Andrzej Zuk. Discrete geometric analysis. [Tokyo]: Mathematical Society of Japan, 2016.

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Kotani, Motoko, Tomoyuki Shirai, and Toshikazu Sunada, eds. Discrete Geometric Analysis. Providence, Rhode Island: American Mathematical Society, 2004. http://dx.doi.org/10.1090/conm/347.

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Byun, Jisoo, Hong Rae Cho, Sung Yeon Kim, Kang-Hyurk Lee, and Jong-Do Park, eds. Geometric Complex Analysis. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-1672-2.

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Rosén, Andreas. Geometric Multivector Analysis. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-31411-8.

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Ludwig, Monika, Vitali D. Milman, Vladimir Pestov, and Nicole Tomczak-Jaegermann, eds. Asymptotic Geometric Analysis. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-6406-8.

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Book chapters on the topic "Geometric analysis"

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D’Angelo, John P. "Geometric Considerations." In Hermitian Analysis, 121–78. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-8526-1_4.

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D’Angelo, John P. "Geometric considerations." In Hermitian Analysis, 119–76. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-16514-7_4.

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Fraser, Ailana. "Extremal Eigenvalue Problems and Free Boundary Minimal Surfaces in the Ball." In Geometric Analysis, 1–40. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-53725-8_1.

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Marques, Fernando C., and André Neves. "Applications of Min–Max Methods to Geometry." In Geometric Analysis, 41–77. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-53725-8_2.

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Topping, Peter M. "Ricci Flow and Ricci Limit Spaces." In Geometric Analysis, 79–112. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-53725-8_3.

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Yang, Paul C. "Pseudo-Hermitian Geometry in 3D." In Geometric Analysis, 113–44. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-53725-8_4.

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Huisken, Gerhard. "Heat diffusion in geometry." In Geometric Analysis, 1–14. Providence, Rhode Island: American Mathematical Society, 2016. http://dx.doi.org/10.1090/pcms/022/01.

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Topping, Peter. "Applications of Hamilton’s compactness theorem for Ricci flow." In Geometric Analysis, 15–50. Providence, Rhode Island: American Mathematical Society, 2016. http://dx.doi.org/10.1090/pcms/022/02.

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Weinkove, Ben. "The Kähler-Ricci flow on compact Kähler manifolds." In Geometric Analysis, 51–108. Providence, Rhode Island: American Mathematical Society, 2016. http://dx.doi.org/10.1090/pcms/022/03.

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Zelditch, Steve. "Park City lectures on eigenfunctions." In Geometric Analysis, 109–93. Providence, Rhode Island: American Mathematical Society, 2016. http://dx.doi.org/10.1090/pcms/022/04.

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Conference papers on the topic "Geometric analysis"

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Noguchi, J., H. Fujimoto, J. Kajiwara, and T. Ohsawa. "Geometric Complex Analysis." In Third International Research Institute of Mathematical Society of Japan. WORLD SCIENTIFIC, 1996. http://dx.doi.org/10.1142/9789814532143.

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Lane, R. G., R. M. Clare, and T. Y. Chew. "Analysis of Geometric Wavefront Sensing." In Adaptive Optics: Methods, Analysis and Applications. Washington, D.C.: OSA, 2005. http://dx.doi.org/10.1364/aopt.2005.athc1.

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Hildenbrand, Dietmar. "Foundations of Geometric Algebra computing." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756054.

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Armstrong, C. G., R. M. McKeag, H. Ou, and M. A. Price. "Geometric processing for analysis." In Proceedings Geometric Modeling and Processing 2000. Theory and Applications. IEEE, 2000. http://dx.doi.org/10.1109/gmap.2000.838237.

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Brugnano, Luigi, and Felice Iavernaro. "Geometric integration by playing with matrices." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756051.

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Castelli, Mauro, Luca Manzoni, Ivo Gonçalves, Leonardo Vanneschi, Leonardo Trujillo, and Sara Silva. "An Analysis of Geometric Semantic Crossover: A Computational Geometry Approach." In 8th International Conference on Evolutionary Computation Theory and Applications. SCITEPRESS - Science and Technology Publications, 2016. http://dx.doi.org/10.5220/0006056402010208.

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Cortés, Jorge. "Motion coordination algorithms resulting from classical geometric optimization problems." In GLOBAL ANALYSIS AND APPLIED MATHEMATICS: International Workshop on Global Analysis. AIP, 2004. http://dx.doi.org/10.1063/1.1814715.

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Skeel, Robert D., Ruijun Zhao, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Solving Geometric Two-Point Boundary Value Problems." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636663.

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Erdogan, Fatma Ozen, Basri Celik, Suleyman Ciftci, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "On Some Geometric Structures and Local Rings." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636730.

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Modin, K., C. Führer, G. Soöderlind, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Geometric Integration of Weakly Dissipative Systems." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241619.

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Reports on the topic "Geometric analysis"

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Carlsson, Gunnar, and Mike Mahoney. Geometric Networks Analysis. Fort Belvoir, VA: Defense Technical Information Center, August 2012. http://dx.doi.org/10.21236/ada567132.

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Watterberg, P. A. Geometric simplification of analysis models. Office of Scientific and Technical Information (OSTI), December 1999. http://dx.doi.org/10.2172/750027.

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Little, Charles, and David Biedenharn. Technical assessment of the Old, Mississippi, Atchafalaya, and Red (OMAR) Rivers : channel geometry analysis. Engineer Research and Development Center (U.S.), August 2022. http://dx.doi.org/10.21079/11681/45147.

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The Old River Control Complex (ORCC) consists of the Low Sill, Auxiliary, and Overbank structures as features of the Old River Control Structure (ORCS) and the privately owned hydro-electric power plant. Operations of the ORCC manage the hydrologic connectivity between the Mississippi River and the Atchafalaya River/Red River systems. The morphology of the Old, the Mississippi, the Atchafalaya, and the Red Rivers (OMAR) has been influenced by the flow distribution at the ORCC, as well as the accompanying bed sediments. A geomorphic assessment of the OMAR is underway to understand the morphological changes associated with operation of the ORCC. Supporting the geomorphic assessment, a channel geometry analysis herein documents observed adjustments of the affected river channels. Historical hydrographic survey data were used in the Geographic Information System to create river channel geometric models, which inform the analysis. Geometric parameters for cross sections and volume polygons were computed for each survey and evaluated for morphological trends which may be ascribed to the influence of the ORCC. Additionally, the geometric parameters for the Atchafalaya River were used to extend the geometry analyses from the 1951 Mississippi River Commission report on the Atchafalaya River, which was the primary catalyst for the initial development of the ORCS.

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Przebienda, Louis M., and Shawna Youst. Geometric Processor and Multivariate Categorical Processor Market Analysis. Fort Belvoir, VA: Defense Technical Information Center, July 1988. http://dx.doi.org/10.21236/ada207281.

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Baraniuk, Richard G., and Hyeokho Choi. Higher-Dimensional Signal Processing via Multiscale Geometric Analysis. Fort Belvoir, VA: Defense Technical Information Center, February 2010. http://dx.doi.org/10.21236/ada514181.

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Barlow, Richard E., and Max B. Mendel. Failure Data Analysis Based on Engineering and Geometric Principles. Fort Belvoir, VA: Defense Technical Information Center, April 1995. http://dx.doi.org/10.21236/ada296135.

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Fabbri, A. G., C. A. Kushigbor, C. R. Valenzuela, and F. D. van der Meer. Automated strategies for geometric characterization in geological remote sensing analysis. Natural Resources Canada/ESS/Scientific and Technical Publishing Services, 1994. http://dx.doi.org/10.4095/193962.

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Jadbabaie, Ali, Shing-Tung Yau, Fan Chung-Graham, Gabor Lippner, Victor Preciado, and Paul Horn. Topological and Geometric Tools for the Analysis fo Complex Networks. Fort Belvoir, VA: Defense Technical Information Center, October 2013. http://dx.doi.org/10.21236/ad1013162.

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W. Brent Lindquist. Final Report, DE-FG02-92ER14261, Pore Scale Geometric and Fluid Distribution Analysis. Office of Scientific and Technical Information (OSTI), January 2005. http://dx.doi.org/10.2172/836090.

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Muhlestein, Michael, and Carl Hart. Geometric-acoustics analysis of singly scattered, nonlinearly evolving waves by circular cylinders. Engineer Research and Development Center (U.S.), October 2020. http://dx.doi.org/10.21079/11681/38521.

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Abstract:

Geometric acoustics, or acoustic ray theory, is used to analyze the scattering of high-amplitude acoustic waves incident upon rigid circular cylinders. Theoretical predictions of the nonlinear evolution of the scattered wave field are provided, as well as measures of the importance of accounting for nonlinearity. An analysis of scattering by many cylinders is also provided, though the effects of multiple scattering are not considered. Provided the characteristic nonlinear distortion length is much larger than a cylinder radius, the nonlinear evolution of the incident wave is shown to be of much greater importance to the overall evolution than the nonlinear evolution of the individual scattered waves.

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