Topic
Vector calculus identities
About: Vector calculus identities is a research topic. Over the lifetime, 390 publications have been published within this topic receiving 7804 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: In this paper, the authors consider the model of a spinor field with arbitrary internal degrees of freedom having arbitrary nonderivative coupling to external scalar, pseudoscalar, vector, and axial-vector fields.
Abstract: We consider the model of a spinor field with arbitrary internal degrees of freedom having arbitrary nonderivative coupling to external scalar, pseudoscalar, vector, and axial-vector fields. By carefully defining the $S$ matrix in the interaction picture, the vector and axial-vector currents associated with the external vector and axial-vector fields are found to satisfy anomalous Ward identities. If we require that the vector currents satisfy the usual Ward identities, the divergence of the axial-vector current contains well-defined anomalous terms. These terms are explicitly calculated.
1,180 citations
1 Apr 2006
TL;DR: The Vlasov, two-fluid, and MHD models of plasma dynamics are discussed in this article, where a vector calculus in orthogonal curvilinear coordinates is defined.
Abstract: Preface 1. Basic concepts 2. The Vlasov, two-fluid, and MHD models of plasma dynamics 3. Motion of a single plasma particle 4. Elementary plasma waves 5. Streaming instabilities and the Landau problem 6. Cold plasma waves in a magnetized plasma 7. Waves in inhomogeneous plasmas and wave energy relations 8. Vlasov theory of warm electrostatic waves in a magnetized plasma 9. MHD equilibria 10. Stability of static MHD equilibria 11. Magnetic helicity interpreted and Woltjer-Taylor relaxation 12. Magnetic reconnection 13. Fokker-Planck theory of collisions 14. Wave-particle nonlinearities 15. Wave-wave nonlinearities 16. Non-neutral plasmas 17. Dusty plasmas Appendix A. Intuitive method for vector calculus identities Appendix B. Vector calculus in orthogonal curvilinear coordinates Appendix C. Frequently used physical constants and formulae Bibliography References Index.
817 citations
TL;DR: In this paper, the authors present a set of conditions générales d'utilisation of systématiques, i.e., the copie ou impression of a fichier do not contenir the présente mention de copyright.
Abstract: © Publications mathématiques de l’I.H.É.S., 1974, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http:// www.ihes.fr/IHES/Publications/Publications.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
703 citations
TL;DR: In this paper, it was shown that all singularities with characteristic orbits are topologically determined by a finite jet, and for each n, there are only a finite number of topological equivalence classes of codimension n singularities having characteristic orbits.
256 citations
172 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 2 |
| 2020 | 2 |
| 2019 | 1 |
| 2018 | 3 |
| 2017 | 4 |
| 2016 | 2 |