Non-equilibrium phenomena and molecular reaction dynamics: mode space, energy space and conformer space

status: publishe

Umbral Moonshine and the Niemeier Lattices

In this paper we relate umbral moonshine to the Niemeier lattices: the 23 even unimodular positive-definite lattices of rank 24 with non-trivial root systems. To each Niemeier lattice we attach a finite group by considering a naturally defined quotient of the lattice automorphism group, and for each conjugacy class of each of these groups we identify a vector-valued mock modular form whose components coincide with mock theta functions of Ramanujan in many cases. This leads to the umbral moonshine conjecture, stating that an infinite-dimensional module is assigned to each of the Niemeier lattices in such a way that the associated graded trace functions are mock modular forms of a distinguished nature. These constructions and conjectures extend those of our earlier paper, and in particular include the Mathieu moonshine observed by Eguchi-Ooguri-Tachikawa as a special case. Our analysis also highlights a correspondence between genus zero groups and Niemeier lattices. As a part of this relation we recognise the Coxeter numbers of Niemeier root systems with a type A component as exactly those levels for which the corresponding classical modular curve has genus zero.Comment: 181 pages including 95 pages of Appendices; journal version, minor typos corrected, Research in the Mathematical Sciences, 2014, vol.

The Adjudication and Enforcement of Rights After Brexit

This report records the inaugural meeting and roundtable of the Brexit and Rights Engagement Network (BREN) on Tuesday 3rd July 2018 at Edinburgh Law School. Attendees at the roundtable included network members, fellow academics, representatives of the Scottish Parliament, the Scottish Government, the Scottish Human Rights Commission, the Equality and Human Rights Commission, the legal professions, and NGOs. Two years after the EU Referendum and only a few days after the European Union (Withdrawal) Act 2018 (the 2018 Act) receiving Royal Assent, the Brexit and Rights Engagement Network met for the first time. The purpose of the roundtable was to ignite debate amongst legal scholars and policy makers, and others working in a rights environment relating to interpretation, adjudication and enforcement of rights in the lead up to, and following “Brexit Day,” (March 29, 2019). This report is split into two sections, Part A will consider the adjudication of EU rights, but also their enforcement under the 2018 Act and the Withdrawal Agreement, whilst ‘options for the future’ will be broached in Part B

Final evaluation of the saving gateway 2 pilot: main report

The Saving Gateway is a government initiative aimed at encouraging savings behaviour among people who do not usually save. Each pound placed into a Saving Gateway account is matched by the government at a certain rate and up to a monthly contribution limit. Matching provides a transparent and understandable incentive for eligible individuals to place funds in an account

A review of fatal outburst incidents in the Bulli Seam

The Bulli Coal Seam, located in the Illawarra Coalfield of New South Wales, has a long and varied history of sudden outbursts. From available information this problem has resulted in twelve fatalities over the last one hundred and one years, with over five hundred separate outburst incidents being identified. These incidents have varied in severity and intensity from the discharge of 1 to 2 tonne of coal, with a slight increase in gas emission, to the discharge of 200 to 400 tonne of coal with some 6,000 m3 of gas being liberated and large items of mining equipment being pushed 1 to 2 metres down the roadway. Geological features associated with these outbursts can be mapped on a regional and mine by mine basis, to provide some indication or warning. Similarly changes in gas content and gas composition can also be determined on a regional and mine by mine basis. However sudden geological changes (such as a 6.5 metre seam displacement within 15 metres) variations in gas content (such as 6 m3/tonne to 15 m3/tonne) and changes in gas composition (from 95% CH4 to 90% CO2) all within one mine does make the prediction or forecasting of outburst incidents exceedingly difficult. A review of the fatal outburst incidents in the Bulli seam can give valuable insight into how efficient coal mining, within the Bulli coal seam is now linked with the effective use of gas drainage techniques and the management of the outburst risk. The number of variables and unknowns associated with outbursts have required the development of fully documented procedures and systems, so that at all stages during the mining operation the risk of injury to mine workers is minimised. The main emphasis for these management systems is the prevention of outbursts by relieving gas pressures using drainage techniques to achieve specified threshold gas level to permit safe mining conditions

Noncommutative Solitons and Intersecting D-Branes

We construct intersecting D-branes as noncommutative solitons in bosonic and type II string theory. ``Defect'' branes which are D-branes containing bubbles of the closed string vacuum play an important role in the construction.Comment: 17 pages, harvmac; published version with added clarification