DSpace Collection:
https://dspace.lboro.ac.uk/2134/2484
2014-04-20T11:15:44Z
2014-04-20T11:15:44Z
The mathematical modelling of focussed ion beam systems
Amos, R.J.
Evans, G.A.
Smith, Roger
https://dspace.lboro.ac.uk/2134/14048
2014-01-29T10:20:14Z
1987-01-01T00:00:00Z
Title: The mathematical modelling of focussed ion beam systems
Authors: Amos, R.J.; Evans, G.A.; Smith, Roger
Abstract: Computer simulation of focused ion beam systems plays an important role in the design of many
scientific instruments. This paper describes a computational technique which has been developed for
medium sized computers and which has been applied to a number of instrument design applications . The
applications include individual ion lcn cs, extraction optics for ions in surface analytical instruments and the
design of columns for ion beam lithography.
Description: Closed access. This article was published in the journal, Mathematical Engineering in Industry [© VNU Science Press].
1987-01-01T00:00:00Z
Poisson algebras of block-upper-triangular bilinear forms and braid group action
Chekhov, Leonid
Mazzocco, Marta
https://dspace.lboro.ac.uk/2134/12623
2013-09-04T08:24:45Z
2010-01-01T00:00:00Z
Title: Poisson algebras of block-upper-triangular bilinear forms and braid group action
Authors: Chekhov, Leonid; Mazzocco, Marta
Abstract: In this paper we study a quadratic Poisson algebra structure on
the space of bilinear forms on CN with the property that for any n,m 2 N
such that nm = N, the restriction of the Poisson algebra to the space of
bilinear forms with block-upper-triangular matrix composed from blocks of
size m × m is Poisson. We classify all central elements and characterise the
Lie algebroid structure compatible with the Poisson algebra. We integrate this
algebroid obtaining the corresponding groupoid of morphisms of block-uppertriangular
bilinear forms. The groupoid elements automatically preserve the
Poisson algebra. We then obtain the braid group action on the Poisson algebra
as elementary generators within the groupoid. We discuss the affinisation
and quantisation of this Poisson algebra, showing that in the case m = 1
the quantum affine algebra is the twisted q-Yangian for on and for m = 2
is the twisted q-Yangian for sp2n. We describe the quantum braid group
action in these two examples and conjecture the form of this action for any
m > 2. Finally, we give an R-matrix interpretation of our results and discuss
the relation with Poisson–Lie groups.
Description: Closed access until August 2014. This article was published in the journal, Communications in Mathematical Physics [© Springer Verlag] and the definitive version is available at: http://link.springer.com/article/10.1007%2Fs00220-013-1757-3.
2010-01-01T00:00:00Z
On the non-existence of trapped modes in acoustic wave-guides
McIver, M.
Linton, C.M.
https://dspace.lboro.ac.uk/2134/11800
2013-02-27T12:18:47Z
1995-01-01T00:00:00Z
Title: On the non-existence of trapped modes in acoustic wave-guides
Authors: McIver, M.; Linton, C.M.
Abstract: It is well known that trapped modes exist in certain types of acoustic waveguides. These modes correspond to localized fluid oscillations and occur at frequencies at which propagating modes down the guide are not able to exist, below a so-called ‘cut-off frequency’. For example, antisymmetric trapped-mode motions are known to occur in two-dimensional, parallel-plate waveguides containing bodies, at wavenumbers which are less than π/2d, where 2d is the width of the guide. So far, however, these modes have only been found in waveguides that have acoustically hard walls and either contain acoustically hard bodies or have variable cross-section. The purpose of this work is to investigate the existence or otherwise of trapped modes when one or more of the boundaries is replaced by an acoustically soft boundary.
We prove here that trapped modes do not exist below the cut-off frequency for a large class of sound-soft guides containing both sound-soft and sound-hard bodies. In addition, we show that antisymmetric trapped modes do not exist below the cut-off frequency in many two-dimensional, sound-hard guides containing sound-soft bodies. This second result is also generalized to certain types of trapped-mode motion in axisymmetric waveguides. The method of proof relies on finding a strictly positive function w which satisfies a certain field inequality within the guide and boundary inequalities on the guide walls and body surfaces. A vector identity is established which relates w to the possible trapped-mode potential φ in such a way that it may be deduced that φ must be identically equal to zero throughout the guide.
Description: This article is closed access.
1995-01-01T00:00:00Z
Trapped modes in an axisymmetric water-wave problem
McIver, P.
McIver, M.
https://dspace.lboro.ac.uk/2134/11798
2013-02-27T09:16:06Z
1997-01-01T00:00:00Z
Title: Trapped modes in an axisymmetric water-wave problem
Authors: McIver, P.; McIver, M.
Abstract: Trapped-mode solutions, that is, examples of non-uniqueness, are given for a class of axisymmetric problems in the linearized theory of the interaction of water waves with structures. The solutions are constructed by placing an axisymmetric ring source in the free surface with the radius of the ring chosen to eliminate radial circular waves. The ring-source potential then corresponds to a localized standing wave. Suitable structural surfaces are obtained by looking for stream surfaces of the flow.
Description: This article is closed access.
1997-01-01T00:00:00Z