All Outputs (5)

Theory and numerical modelling of parity-time symmetric structures in photonics: Introduction and grating structures in one dimension (2016)
Book Chapter
Phang, S., Benson, T. M., Susanto, H., Creagh, S. C., Gradoni, G., Sewell, P. D., & Vukovic, A. (2016). Theory and numerical modelling of parity-time symmetric structures in photonics: Introduction and grating structures in one dimension. In A. Agrawal, T. M. Benson, R. De La Rue, & G. Wurtz (Eds.), Recent trends in computational photonics (161-205). Springer. https://doi.org/10.1007/978-3-319-55438-9_6

A class of structures based on PT PT-symmetric Bragg gratings in the presence of both gain and loss is studied. The basic concepts and properties of parity and time reversal in one-dimensional structures that possess idealised material properties are... Read More about Theory and numerical modelling of parity-time symmetric structures in photonics: Introduction and grating structures in one dimension.

Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains (2016)
Book Chapter
Antonietti, P. F., Cangiani, A., Collis, J., Dong, Z., Georgoulis, E. H., Giani, S., & Houston, P. (2016). Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains. In G. R. Barrenechea, F. Brezzi, A. Cangiani, & E. H. Georgoulis (Eds.), Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations (281-310). Cham: Springer Publishing Company. https://doi.org/10.1007/978-3-319-41640-3_9

The numerical approximation of partial differential equations (PDEs) posed on complicated geometries, which include a large number of small geometrical features or microstructures, represents a challenging computational problem. Indeed, the use of st... Read More about Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains.

Nonparametric Statistical Methods on Manifolds (2016)
Book Chapter
Dryden, I. L., Le, H., Preston, S. P., & Wood, A. T. A. (2016). Nonparametric Statistical Methods on Manifolds. In M. Denker, & E. C. Waymire (Eds.), Rabi N. Bhattacharya: Selected Papers (587-597). Springer. https://doi.org/10.1007/978-3-319-30190-7_17

One of the many fundamental contributions that Rabi Bhattacharya, together with his coauthors, has made is the development of a general nonparametric theory of statistical inference on manifolds, in particular related to both intrinsic and extrinsic... Read More about Nonparametric Statistical Methods on Manifolds.

Variational water wave modelling: from continuum to experiment (2016)
Book Chapter
Bokhove, O., & Kalogirou, A. (2016). Variational water wave modelling: from continuum to experiment. In Lectures on the Theory of Water Waves (226-260). Cambridge University Press. https://doi.org/10.1017/CBO9781316411155.012

© Cambridge University Press 2016. Variational methods are investigated asymptotically and numerically to model water waves in tanks with wave generators. As a validation, our modelling results using (dis)continuous Galerkin finite element methods wi... Read More about Variational water wave modelling: from continuum to experiment.

Vanishing of some Galois cohomology groups for elliptic curves (2016)
Book Chapter
Lawson, T., & Wuthrich, C. (2016). Vanishing of some Galois cohomology groups for elliptic curves. In D. Loeffler, & S. L. Zerbes (Eds.), Elliptic curves, modular forms and Iwasawa theory: in honour of John H. Coates' 70th birthday, Cambridge, UK, March 2015. Springer

Let E/Q be an elliptic curve and p be a prime number, and let G be the Galois group of the extension of Q obtained by adjoining the coordinates of the p-torsion points on E. We determine all cases when the Galois cohomology group H1(G;E[p] does not v... Read More about Vanishing of some Galois cohomology groups for elliptic curves.