Dirac Equations, Light Cone Supersymmetry, and Superconformal Algebras

After a brief historical survey that emphasizes the role of the algebra obeyed by the Dirac operator, we examine an algebraic Dirac operator associated with Lie algebras and Lie algebra cosets. For symmetric cosets, its ``massless'' solutions display non-relativistic supersymmetry, and can be identified with the massless degrees of freedom of some supersymmetric theories: N=1 supergravity in eleven dimensions (M-theory), type IIB string theory in ten and four dimensions, and in four dimensions, N=8 supergravity, N=4 super-Yang-Mills, and the N=1 Wess-Zumino multiplet. By generalizing this Dirac operator to the affine case, we generate superconformal algebras associated with cosets ${\bf g}/\bf h$, where $\bf h$ contains the {\it space} little group. Only for eleven dimensional supergravity is $\bf h$ simple. This suggests, albeit in a non-relativistic setting, that these may be the limit of theories with underlying two-dimensional superconformal structure.Comment: 19 pages, latex, [sprocl]. Contributed article to Golfand's Memorial Volume, M. Shifman ed., World Scientifi

Direct Detection of Non-Chiral Dark Matter

Direct detection experiments rule out fermion dark matter that is a chiral representation of the electroweak gauge group. Non-chiral real, complex and singlet representations, however, provide viable fermion dark matter candidates. Although any one of these candidates will be virtually impossible to detect at the LHC, it is shown that they may be detected at future planned direct detection experiments. For the real case, an irreducible radiative coupling to quarks may allow a detection. The complex case in general has an experimentally ruled out tree-level coupling to quarks via Z-boson exchange. However, in the case of two SU(2)_L doublets, a higher dimensional coupling to the Higgs can suppress this coupling, and a remaining irreducible radiative coupling may allow a detection. Singlet dark matter could be detected through a coupling to quarks via Higgs exchange. Since all non-chiral dark matter can have a coupling to the Higgs, at least some of its mass can be obtained from electroweak symmetry breaking, and this mass is a useful characterization of its direct detection cross-section.Comment: 22 pages, 3 figures. References added. Minor corrections to match published versio

Determining the Electron-Phonon Coupling Strength in Correlated Electron Systems from Resonant Inelastic X-ray Scattering

We show that high resolution Resonant Inelastic X-ray Scattering (RIXS) provides direct, element-specific and momentum-resolved information on the electron-phonon (e-p) coupling strength. Our theoretical analysis demonstrates that the e-p coupling can be extracted from RIXS spectra by determining the differential phonon scattering cross section. An alternative, very direct manner to extract the coupling is to use the one and two-phonon loss ratio, which is governed by the e-p coupling strength and the core-hole life-time. This allows measurement of the e-p coupling on an absolute energy scale.Comment: 4 pages, 3 figure

Towards adaptive operational requirements for optimal application of evaporation-suppressing monolayer to reservoirs via a 'universal design framework'

Much of the chemical monolayer-based evaporation mitigation research was generated in the 1950s, 60s and 70s centred on the use of spreading long-chain fatty alcohols, such as hexadecanol (C16) and octadecanol (C18), on the water surface. Many researchers from this era have reported highly variable performance results (anywhere from 0-30% efficiency) attributing the highly variable evaporation reduction achieved to film volatilisation, drift, beaching on the lee shore and waves which can break-up or submerge the film.Failure to address this requirement has undoubtedly contributed to the lack of development in the use of monolayers despite some demonstration of useful evaporation suppression performance. In addition recent studies have also indicated that all water bodies have a naturally-occurring surface film, referred to as a microlayer, which can interact with artificial (chemical) monolayers. Natural microlayers are produced by hydrophobic plant waxes, phenolic compounds and other humified material, which concentrates populations of micro-organisms capable of utilizing these materials as organic substrates. This explains why common artificial monolayers (with carbon chain lengths of up to 16) are highly susceptible to biodegradation. Studies on Australian brown water storages reveal highly concentrated microbial microlayer communities, due to the coincidence of leaf and bark fall with low rainfall (Pittaway and van den Ancker 2009). This variation in the concentration of humified organic compounds in the storages is associated with both the volume of the storage, and the riparian vegetation within the water catchment. This paper sets out a strategic approach to the use of monolayer on a reservoir for evaporation mitigation. The approach recognises that every reservoir will have a specific set of user and environmental considerations which leads to a unique set of operational requirements. In order to capture and utilise this information a Universal Design Framework (UDF) has been developed. The UDF serves two purposes, firstly to inform the selection of monolayer material and system design for any given site (‘Planning Mode’), and secondly to inform (and potentially autonomously manage) day-to-day operations, i.e. the timing and amounts of monolayer application (‘Operational Mode’). The UDF takes into account the following parameters: • Critical water requirement periods: These will vary from location to location and at different times of the year. Hence, this is a user determined input. • Economics: The dollars-per-megalitre value of water will also vary from location to location and at different time of the year with respect to critical water requirement periods (e.g. irrigated cropping close to harvest). Included in this input is a user defined annual maximum cost outlay for the monolayer-based system. • Water storage factors: Inputs differ slightly depending on storage type (i.e. ring tank versus gully dam), but generally require information of length, width, shape, bank height, freeboard, full supply volume and geographical co-ordinate points for storage orientation. This would be determined by a basic on-site analysis • Climate and weather factors: Monthly average evaporation demand, rainfall and ambient air temperature information is required, including particularly wind speed frequency and prevailing wind direction, (e.g. from a local Automatic Weather Station (AWS) or via the Bureau of Meteorology SILO database, http://www.longpaddock.qld.gov.au/silo/). In the Planning Mode mean and extreme historical climate data are used; and in the Operational Mode prevailing conditions are required. • Water quality and biological factors: Assessments are made of water source/s (e.g. runoff versus bore), water colour, turbidity, water chemistry (pH, electrical conductivity and UV absorbency), plus density of local catchment vegetation and catchment area. Once the above parameters are known, the UDF is used to determine (in Planning Mode) the most suitable monolayer material/s and optimal arrangement of application equipment, including number of applicators, their arrangement and application strategies for the particular reservoir and monolayer product. In Operational Mode the UDF will guide (or if required, fully control) operational procedures, i.e. the implementation of a unique application strategy for a specific product according to the hour-by-hour prevailing conditions. This paper also outlines decision-making processes within the UDF. Firstly, to determine suitable monolayer materials the UDF compares water quality and biological characteristics of the particular site to those of six benchmark reservoirs in SE Queensland which have been studied in detail (Pittaway and van den Ancker 2009). The biologically-closest informs the choice of appropriate monolayer material/s. Once the selection of a monolayer is made there are a number of unique characteristics that material possesses that will substantially influence the application strategies. Secondly, a simulation platform has been developed to determine the application strategies and operational requirements for the reservoir. The simulation enables rapid evaluation of a range of different sample water bodies to populate a decision chart similar to that for monolayer material selection. A central component of the simulation platform is a fluid-mechanical model of the dispersal of monolayer across a water surface area under the influence of environmental variables, principally wind speed and wind direction, which (in Planning Mode) determines: • optimal spacing between application points, • amount of monolayer applied from each applicator as well as the total amount applied, • placement of applicators to achieve optimal surface coverage, • number of applicator types required, and • percentage of surface coverage under a range of wind speeds and directions. The above simulated output information is unique to the particular reservoir and is essentially a specification for the design and operation of a monolayer application system for that specific site, and is used firstly (Planning Mode) to select appropriate application equipment capable of satisfying the monolayer application requirements; and secondly, if installed as planned, as the basis for day-to-day monolayer application (Operational Mode). Simulation results to date indicate that from large reservoirs, optimal surface coverage is best achieved by a number of fixed application points surrounding and within the reservoir spaced no further than 12 metres apart; and that a greater concentration of applicators is required upwind from the prevailing wind direction in addition to higher rates of monolayer application

Ultrashort Lifetime Expansion for Indirect Resonant Inelastic X-ray Scattering

In indirect resonant inelastic X-ray scattering (RIXS) an intermediate state is created with a core-hole that has a ultrashort lifetime. The core-hole potential therefore acts as a femtosecond pulse on the valence electrons. We show that this fact can be exploited to integrate out the intermediate states from the expressions for the scattering cross section. By this we obtain an effective scattering cross section that only contains the initial and final scattering states. We derive in detail the effective cross section which turns out to be a resonant scattering factor times a linear combination of the charge response function $S({\bf q},\omega)$ and the dynamic longitudinal spin density correlation function. This result is asymptotically exact for both strong and weak local core-hole potentials and ultrashort lifetimes. The resonant scattering pre-factor is shown to be weakly temperature dependent. We also derive a sum-rule for the total scattering intensity and generalize the results to multi-band systems. One of the remarkable outcomes is that one can change the relative charge and spin contribution to the inelastic spectral weight by varying the incident photon energy.Comment: 9 pages, 3 figures embedde

Computing the Greedy Spanner in Linear Space

The greedy spanner is a high-quality spanner: its total weight, edge count and maximal degree are asymptotically optimal and in practice significantly better than for any other spanner with reasonable construction time. Unfortunately, all known algorithms that compute the greedy spanner of n points use Omega(n^2) space, which is impractical on large instances. To the best of our knowledge, the largest instance for which the greedy spanner was computed so far has about 13,000 vertices. We present a O(n)-space algorithm that computes the same spanner for points in R^d running in O(n^2 log^2 n) time for any fixed stretch factor and dimension. We discuss and evaluate a number of optimizations to its running time, which allowed us to compute the greedy spanner on a graph with a million vertices. To our knowledge, this is also the first algorithm for the greedy spanner with a near-quadratic running time guarantee that has actually been implemented

Kernel solutions of the Kostant operator on eight-dimensional quotient spaces

After introducing the generators and irreducible representations of the ${\rm su}(5)$ and ${\rm so}(6)$ Lie algebras in terms of the Schwinger's scillators, the general kernel solutions of the Kostant operators on eight-dimensional quotient spaces ${\rm su}(5)/{\rm su}(4)\times {\rm u}(1)$ and ${\rm so}(6)/{\rm so}(4)\times {\rm so}(2)$ are derived in terms of the diagonal subalgebras ${\rm su}(4)\times {\rm u}(1)$ and ${\rm so}(4)\times {\rm so}(2)$, respectively.Comment: 13 pages. Typos correcte

Results from the CDMS II Experiment

I report recent results and the status of the Cryogenic Dark Matter Search (CDMS II) experiment at the Soudan Underground Laboratory in Minnesota, USA. A blind analysis of data taken by 30 detectors between October 2006 and July 2007 found zero events consistent with WIMPs elastically scattering in our Ge detectors. This resulted in an upper limit on the spin-independent, WIMP-nucleon cross section of 6.6 x 10^-44 cm^2 (4.6 x 10^-44 cm^2 when combined with our previous results) at the 90% C.L. for a WIMP of mass 60 GeV/c^2. In March 2009 data taking with CDMS II stopped in order to install the first of 5 SuperTowers of detectors for the SuperCDMS Soudan project. Analysis of data taken between August 2007 and March 2009 is ongoing.Comment: 5 pages, 4 figures, to appear in the proceedings of the TAUP09 conference (Rome, July 1st-5th 2009