Helmholtz decomposition (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Helmholtz decomposition" in English language version.

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3arxiv.org

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1uni-goettingen.de

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archive.org (Global: 6^th place; English: 6^th place)

J. W. Gibbs, Edwin Bidwell Wilson: Vector Analysis. 1901, p. 237, link from Internet Archive.

arxiv.org (Global: 69^th place; English: 59^th place)

Erhard Glötzl, Oliver Richters: Helmholtz decomposition and potential functions for n-dimensional analytic vector fields. In: Journal of Mathematical Analysis and Applications 525(2), 127138, 2023, doi:10.1016/j.jmaa.2023.127138, arXiv:2102.09556v3. Mathematica worksheet at doi:10.5281/zenodo.7512798.
A. M. Stewart: Longitudinal and transverse components of a vector field. In: Sri Lankan Journal of Physics 12, pp. 33–42, 2011, doi:10.4038/sljp.v12i0.3504 arXiv:0801.0335
Erhard Glötzl, Oliver Richters: Helmholtz Decomposition and Rotation Potentials in n-dimensional Cartesian Coordinates. 2020, arXiv:2012.13157.

berkeley.edu (Global: 580^th place; English: 462^nd place)

bohr.physics.berkeley.edu

Robert Littlejohn: The Classical Electromagnetic Field Hamiltonian. Online lecture notes, berkeley.edu.

bnf.fr (Global: 124^th place; English: 544^th place)

gallica.bnf.fr

Cauchy, Augustin-Louis (1823). "Trente-Cinquième Leçon". Résumé des leçons données à l'École royale polytechnique sur le calcul infinitésimal (in French). Paris: Imprimerie Royale. pp. 133–140.

digizeitschriften.de (Global: 5,626^th place; English: 8,880^th place)

Hermann von Helmholtz: Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen. In: Journal für die reine und angewandte Mathematik 55, 1858, pp. 25–55, doi:10.1515/crll.1858.55.25 (sub.uni-goettingen.de, digizeitschriften.de). On page 38, the components of the fluid's velocity (u, v, w) are expressed in terms of the gradient of a scalar potential P and the curl of a vector potential (L, M, N).

doi.org (Global: 2^nd place; English: 2^nd place)

Erhard Glötzl, Oliver Richters: Helmholtz decomposition and potential functions for n-dimensional analytic vector fields. In: Journal of Mathematical Analysis and Applications 525(2), 127138, 2023, doi:10.1016/j.jmaa.2023.127138, arXiv:2102.09556v3. Mathematica worksheet at doi:10.5281/zenodo.7512798.
George Gabriel Stokes: On the Dynamical Theory of Diffraction. In: Transactions of the Cambridge Philosophical Society 9, 1849, pp. 1–62. doi:10.1017/cbo9780511702259.015, see pp. 9–10.
Hermann von Helmholtz: Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen. In: Journal für die reine und angewandte Mathematik 55, 1858, pp. 25–55, doi:10.1515/crll.1858.55.25 (sub.uni-goettingen.de, digizeitschriften.de). On page 38, the components of the fluid's velocity (u, v, w) are expressed in terms of the gradient of a scalar potential P and the curl of a vector potential (L, M, N).
Alp Kustepeli: On the Helmholtz Theorem and Its Generalization for Multi-Layers. In: Electromagnetics 36.3, 2016, pp. 135–148, doi:10.1080/02726343.2016.1149755.
D. Petrascheck, R. Folk: Helmholtz decomposition theorem and Blumenthal’s extension by regularization. In: Condensed Matter Physics 20(1), 13002, 2017, doi:10.5488/CMP.20.13002.
Wolfgang Sprössig: On Helmholtz decompositions and their generalizations – An overview. In: Mathematical Methods in the Applied Sciences 33.4, 2009, pp. 374–383, doi:10.1002/mma.1212.
Harsh Bhatia, Gregory Norgard, Valerio Pascucci, Peer-Timo Bremer: The Helmholtz-Hodge Decomposition – A Survey. In: IEEE Transactions on Visualization and Computer Graphics 19.8, 2013, pp. 1386–1404, doi:10.1109/tvcg.2012.316.
Dietmar Petrascheck: The Helmholtz decomposition revisited. In: European Journal of Physics 37.1, 2015, Artikel 015201, doi:10.1088/0143-0807/37/1/015201.
Cherif Amrouche, Christine Bernardi, Monique Dauge, Vivette Girault: Vector potentials in three dimensional non-smooth domains. In: Mathematical Methods in the Applied Sciences 21(9), 1998, pp. 823–864, doi:10.1002/(sici)1099-1476(199806)21:9<823::aid-mma976>3.0.co;2-b, Bibcode:1998MMAS...21..823A.
A. M. Stewart: Longitudinal and transverse components of a vector field. In: Sri Lankan Journal of Physics 12, pp. 33–42, 2011, doi:10.4038/sljp.v12i0.3504 arXiv:0801.0335
Frank W. Warner: The Hodge Theorem. In: Foundations of Differentiable Manifolds and Lie Groups. (= Graduate Texts in Mathematics 94). Springer, New York 1983, doi:10.1007/978-1-4757-1799-0_6.
Cantarella, Jason; DeTurck, Dennis; Gluck, Herman (2002). "Vector Calculus and the Topology of Domains in 3-Space". The American Mathematical Monthly. 109 (5): 409–442. doi:10.2307/2695643. JSTOR 2695643.
R. Douglas Gregory: Helmholtz's Theorem when the domain is Infinite and when the field has singular points. In: The Quarterly Journal of Mechanics and Applied Mathematics 49.3, 1996, pp. 439–450, doi:10.1093/qjmam/49.3.439.
Otto Blumenthal: Über die Zerlegung unendlicher Vektorfelder. In: Mathematische Annalen 61.2, 1905, pp. 235–250, doi:10.1007/BF01457564.
Morton E. Gurtin: On Helmholtz’s theorem and the completeness of the Papkovich-Neuber stress functions for infinite domains. In: Archive for Rational Mechanics and Analysis 9.1, 1962, pp. 225–233, doi:10.1007/BF00253346.
Sheldon Axler, Paul Bourdon, Wade Ramey: Bounded Harmonic Functions. In: Harmonic Function Theory (= Graduate Texts in Mathematics 137). Springer, New York 1992, pp. 31–44, doi:10.1007/0-387-21527-1_2.
Alexandre J. Chorin, Jerrold E. Marsden: A Mathematical Introduction to Fluid Mechanics (= Texts in Applied Mathematics 4). Springer US, New York 1990, doi:10.1007/978-1-4684-0364-0.
Tomoharu Suda: Construction of Lyapunov functions using Helmholtz–Hodge decomposition. In: Discrete & Continuous Dynamical Systems – A 39.5, 2019, pp. 2437–2454, doi:10.3934/dcds.2019103.
Tomoharu Suda: Application of Helmholtz–Hodge decomposition to the study of certain vector fields. In: Journal of Physics A: Mathematical and Theoretical 53.37, 2020, pp. 375703. doi:10.1088/1751-8121/aba657.
Joseph Xu Zhou, M. D. S. Aliyu, Erik Aurell, Sui Huang: Quasi-potential landscape in complex multi-stable systems. In: Journal of the Royal Society Interface 9.77, 2012, pp. 3539–3553, doi:10.1098/rsif.2012.0434.
Edward N. Lorenz: Deterministic Nonperiodic Flow. In: Journal of the Atmospheric Sciences 20.2, 1963, pp. 130–141, doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2.
Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe: Strange Attractors: The Locus of Chaos. In: Chaos and Fractals. Springer, New York, pp. 655–768. doi:10.1007/978-1-4757-4740-9_13.
Armando Manduca: MR elastography: Principles, guidelines, and terminology. In: Magnetic Resonance in Medicine, 2021, doi:10.1002/mrm.28627PMID 33296103.
Hersh Bhatia, Valerio Pascucci, Peer-Timo Bremer: The Natural Helmholtz-Hodge Decomposition for Open-Boundary Flow Analysis. In: IEEE Transactions on Visualization and Computer Graphics 20.11, Nov. 2014, pp. 1566–1578, Nov. 2014, doi:10.1109/TVCG.2014.2312012.

harvard.edu (Global: 18^th place; English: 17^th place)

ui.adsabs.harvard.edu

Cherif Amrouche, Christine Bernardi, Monique Dauge, Vivette Girault: Vector potentials in three dimensional non-smooth domains. In: Mathematical Methods in the Applied Sciences 21(9), 1998, pp. 823–864, doi:10.1002/(sici)1099-1476(199806)21:9<823::aid-mma976>3.0.co;2-b, Bibcode:1998MMAS...21..823A.

jstor.org (Global: 26^th place; English: 20^th place)

Ton Tran-Cong: On Helmholtz’s Decomposition Theorem and Poissons’s Equation with an Infinite Domain. In: Quarterly of Applied Mathematics 51.1, 1993, pp. 23–35, JSTOR 43637902.
Cantarella, Jason; DeTurck, Dennis; Gluck, Herman (2002). "Vector Calculus and the Topology of Domains in 3-Space". The American Mathematical Monthly. 109 (5): 409–442. doi:10.2307/2695643. JSTOR 2695643.

nih.gov (Global: 4^th place; English: 4^th place)

pubmed.ncbi.nlm.nih.gov

Armando Manduca: MR elastography: Principles, guidelines, and terminology. In: Magnetic Resonance in Medicine, 2021, doi:10.1002/mrm.28627PMID 33296103.

uni-goettingen.de (Global: 2,594^th place; English: 2,546^th place)

resolver.sub.uni-goettingen.de

Hermann von Helmholtz: Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen. In: Journal für die reine und angewandte Mathematik 55, 1858, pp. 25–55, doi:10.1515/crll.1858.55.25 (sub.uni-goettingen.de, digizeitschriften.de). On page 38, the components of the fluid's velocity (u, v, w) are expressed in terms of the gradient of a scalar potential P and the curl of a vector potential (L, M, N).

uvm.edu (Global: 6,270^th place; English: 4,080^th place)

cems.uvm.edu

"Helmholtz' Theorem" (PDF). University of Vermont. Archived from the original (PDF) on 2012-08-13. Retrieved 2011-03-11.

web.archive.org (Global: 1^st place; English: 1^st place)

"Helmholtz' Theorem" (PDF). University of Vermont. Archived from the original (PDF) on 2012-08-13. Retrieved 2011-03-11.

Helmholtz decomposition (English Wikipedia)

archive.org (Global: 6th place; English: 6th place)

arxiv.org (Global: 69th place; English: 59th place)

berkeley.edu (Global: 580th place; English: 462nd place)

bohr.physics.berkeley.edu

bnf.fr (Global: 124th place; English: 544th place)

gallica.bnf.fr

digizeitschriften.de (Global: 5,626th place; English: 8,880th place)

doi.org (Global: 2nd place; English: 2nd place)

harvard.edu (Global: 18th place; English: 17th place)