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Publikováno v:
Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences. 452:859-880
Taking advantage of the considerable amount of work done in the search for first integrals (invariants) for the two-dimensional Lotka-Volterra system and the quadratic system (lvs and qs), we compare the relations needed to exhibit invariants (one fo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b5fa2dfecf38d8d35cb6e3347f08b49e
https://doi.org/10.1098/rspa.1996.0043
https://doi.org/10.1098/rspa.1996.0043
Autor:
D. D. Hua, T.K. Fowler
Publikováno v:
Journal of Fusion Energy. 14:181-185
The reactor study of Hagenson and Krakowski demonstrated the attractiveness of the spheromak as a compact fusion reactor, based on physics principles confirmed in CTX experiments in many respects. Most uncertain was the energy confinement time and th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7232fed818758060e1d7a87ece084323
https://doi.org/10.1007/bf02209055
https://doi.org/10.1007/bf02209055
Publikováno v:
Journal of Physics A: Mathematical and General. 27:6495-6507
The generalized Hamiltonian structures of several three-dimensional dynamical systems of interest in physical applications are considered. In general, Hamiltonians exist only for systems that possess at least one time-independent constant of motion.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a9c6660e0ecbe24f9ed2f1d8d6614e0f
https://doi.org/10.1088/0305-4470/27/19/020
https://doi.org/10.1088/0305-4470/27/19/020
Publikováno v:
Journal of Physics A: Mathematical and General. 27:L547-L551
Invariants of the motion (in general time-dependent first integrals) for a cubic three-wave system are obtained using the generalized Carleman method. It is shown that a subset of these invariants are of Lotka-Volterra type.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6aba72c25590c421e65c79791e31124a
https://doi.org/10.1088/0305-4470/27/15/003
https://doi.org/10.1088/0305-4470/27/15/003
Publikováno v:
Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences. 444:643-650
We derive a general time-dependent invariant (first integral) for the quadratic system (QS) that requires only one condition on the coefficients of the QS. The general invariant could yield asymptotic behaviour of phase-space trajectories. With more
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::10247013522da76ebb6a7a2312fa4117
https://doi.org/10.1098/rspa.1994.0044
https://doi.org/10.1098/rspa.1994.0044
Autor:
D. D. Hua, T. K. Fowler
Publikováno v:
Plasma Physics Reports. 28:773-775
Calculations are presented showing the temperatures expected in a spheromak sustained by continuous injection of helicity, based on a model previously shown to agree with temperatures achieved in spheromak experiments carried out in the 1980's. New e
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::edf63d1d0716a4ba0173e1f167f863b3
https://doi.org/10.1134/1.1508028
https://doi.org/10.1134/1.1508028
Publikováno v:
Journal of Physics A: Mathematical and General. 26:7097-7114
A Hamiltonian method is developed to obtain first integrals of the form P Qmu and P Qmu Rnu for a general system of two-dimensional autonomous ordinary differential equations with quadratic terms, where P, Q and R are linear or quadratic polynomials,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b62f72a69595eca74604aa7895218596
https://doi.org/10.1088/0305-4470/26/23/045
https://doi.org/10.1088/0305-4470/26/23/045
Publikováno v:
Journal of Physics A: Mathematical and General. 26:4371-4386
The Hamiltonian formalism for a two-dimensional system of ODE possessing an invariant of the motion not containing the time explicitly has suggested a method for the search of first integrals. Applied to the quadratic system it leads to the finding o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f4218f498b98de9b9acef07b6538c801
https://doi.org/10.1088/0305-4470/26/17/042
https://doi.org/10.1088/0305-4470/26/17/042
Publikováno v:
Physics of Fluids B: Plasma Physics. 4:3216-3225
The work of Xu and Rosenbluth [Phys. Fluids B 3, 627 (1991)] on ion‐temperature‐gradient modes in toroidal geometry is extended to noncircular cross sections to examine the scaling with the elongation κ. The growth rate, wave numbers, and stabil
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3b7d11446519cdac6140529e34f158b2
https://doi.org/10.1063/1.860377
https://doi.org/10.1063/1.860377