Zobrazeno 1 - 10
of 48
pro vyhledávání: '"Elizabeth L. Mansfield"'
Publikováno v:
Forum of Mathematics, Sigma, Vol 4 (2016)
In recent works [Gonçalves and Mansfield, Stud. Appl. Math., 128 (2012), 1–29; Mansfield, A Practical Guide to the Invariant Calculus (Cambridge University Press, Cambridge, 2010)], the authors considered various Lagrangians, which are invariant u
Externí odkaz:
https://doaj.org/article/48f31c9f15a749b8874f3f701924f21c
Publikováno v:
Studies in Applied Mathematics. 143:244-271
We study variational systems for space curves, for which the Lagrangian or action principle has a Euclidean symmetry, using the Rotation Minimizing frame, also known as the Normal, Parallel or Bishop frame (see [1], [36]). Such systems have previousl
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4efd975f70834ad6032608dd960d4eb8
https://doi.org/10.1111/sapm.12275
https://doi.org/10.1111/sapm.12275
Autor:
Michele Zadra, Elizabeth L. Mansfield
The theory of moving frames has been used successfully to solve one dimensional (1D) variational problems invariant under a Lie group symmetry. In the one dimensional case, Noether's laws give first integrals of the Euler–Lagrange equations. In hig
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::331d6a85d9afc5119f6f6539efe45c6e
https://kar.kent.ac.uk/73255/11/mz-elm-JCD-final-sub.pdf
https://kar.kent.ac.uk/73255/11/mz-elm-JCD-final-sub.pdf
Publikováno v:
Transactions of Mathematics and its Applications
We consider the calculation of Euler--Lagrange systems of ordinary difference equations, including the difference Noether's Theorem, in the light of the recently-developed calculus of difference invariants and discrete moving frames. We introduce the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3c81dfe0f98e95cfab302d920bb800ef
https://kar.kent.ac.uk/74247/11/tnz004.pdf
https://kar.kent.ac.uk/74247/11/tnz004.pdf
Autor:
Tristan Pryer, Elizabeth L. Mansfield
In this work, we prove a weak Noether-type Theorem for a class of variational problems that admit broken extremals. We use this result to prove discrete Noether-type conservation laws for a conforming finite element discretisation of a model elliptic
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::62a078ba3022adad99ed1c5734dc53aa
https://centaur.reading.ac.uk/51886/1/art%3A10.1007%2Fs10208-015-9298-0.pdf
https://centaur.reading.ac.uk/51886/1/art%3A10.1007%2Fs10208-015-9298-0.pdf
Autor:
Elizabeth L. Mansfield, Jun Zhao
Publikováno v:
Mathematics in Computer Science. 7:185-199
In this work, we study discrete variational problems, for B-spline curves, which are invariant under translation and rotation. We show this approach has advantages over studying smooth variational problems whose solutions are approximated by B-spline
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8920c921208e3be694ba36dddb87f207
https://doi.org/10.1007/s11786-013-0155-8
https://doi.org/10.1007/s11786-013-0155-8
In this paper, we develop the theory of the discrete moving frame in two different ways. In the first half of the paper, we consider a discrete moving frame defined on a lattice variety and the equivalence classes of global syzygies that result from
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::508f91284a7572fd38df505a3b9b4067
In recent works [Gonçalves and Mansfield, Stud. Appl. Math., 128 (2012), 1–29; Mansfield, A Practical Guide to the Invariant Calculus (Cambridge University Press, Cambridge, 2010)], the authors considered various Lagrangians, which are invariant u
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2287e8089a8b5f72191be5c0a6be1ca6
https://kar.kent.ac.uk/48996/1/ForumSigmaPaper.pdf
https://kar.kent.ac.uk/48996/1/ForumSigmaPaper.pdf
Publikováno v:
Studies in Applied Mathematics. 130:134-166
In recent work, the authors show the mathematical structure behind both the Euler–Lagrange system and the set of conservation laws, in terms of the differential invariants of the group action and a moving frame. In this paper, the authors demonstra
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::be3ef0e8a3a5d7cbe52c4760722cd9be
https://doi.org/10.1111/j.1467-9590.2012.00566.x
https://doi.org/10.1111/j.1467-9590.2012.00566.x
Publikováno v:
Studies in Applied Mathematics. 128:1-29
Noether’s Theorem yields conservation laws for a Lagrangian with a variational symmetry group. The explicit formulae for the laws are well known and the symmetry group is known to act on the linear space generated by the conservation laws. The aim
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::68ce5d77cb64c57e2bef454191c87f96
https://doi.org/10.1111/j.1467-9590.2011.00522.x
https://doi.org/10.1111/j.1467-9590.2011.00522.x