Explicit determination of a 727-dimensional root space of the hyperbolic Lie algebra E10E_{10}

The 727-dimensional root space associated with the level-2 root \bLambda_1 of the hyperbolic Kac--Moody algebra $E_{10}$ is determined using a recently developed string theoretic approach to hyperbolic algebras. The explicit form of the basis reveals a complicated structure with transversal as well as longitudinal string states present.Comment: 12 pages, LaTeX 2

Protection of the LHC against Unsynchronised Beam Aborts

An unsynchronised beam abort in the LHC could damage downstream accelerator components, in particular the extraction septum magnets, the experimental low-beta triplet magnet apertures and the tertiary collimators. Although the LHC beam dumping system includes design features to minimise their frequency, such unsynchronised aborts cannot be excluded. A system of protection devices comprising fixed and moveable diluters and collimators will protect the downstream LHC aperture from the misdirected bunches in case of such a failure. The sources of unsynchronised aborts are described, together with the requirements and design of the protection devices and their expected performance. The accompanying operational requirements and envisaged solutions are discussed, in particular the problem of ensuring the local orbit at the protection devices

On the fundamental representation of Borcherds algebras with one imaginary simple root

Borcherds algebras represent a new class of Lie algebras which have almost all the properties that ordinary Kac-Moody algebras have, and the only major difference is that these generalized Kac-Moody algebras are allowed to have imaginary simple roots. The simplest nontrivial examples one can think of are those where one adds ``by hand'' one imaginary simple root to an ordinary Kac-Moody algebra. We study the fundamental representation of this class of examples and prove that an irreducible module is given by the full tensor algebra over some integrable highest weight module of the underlying Kac-Moody algebra. We also comment on possible realizations of these Lie algebras in physics as symmetry algebras in quantum field theory.Comment: 8 page

Strongly correlated wave functions for artificial atoms and molecules

A method for constructing semianalytical strongly correlated wave functions for single and molecular quantum dots is presented. It employs a two-step approach of symmetry breaking at the Hartree-Fock level and of subsequent restoration of total spin and angular momentum symmetries via Projection Techniques. Illustrative applications are presented for the case of a two-electron helium-like single quantum dot and a hydrogen-like quantum dot molecule.Comment: 9 pages. Revtex with 2 GIF and 1 EPS figures. Published version with extensive clarifications. A version of the manuscript with high quality figures incorporated in the text is available at http://calcite.physics.gatech.edu/~costas/qdhelproj.html For related papers, see http://www.prism.gatech.edu/~ph274c

Charges, Monopoles and Duality Relations

A charge-monopole theory is derived from simple and self-evident postulates. Charges and monopoles take an analogous theoretical structure. It is proved that charges interact with free waves emitted from monopoles but not with the corresponding velocity fields. Analogous relations hold for monopole equations of motion. The system's equations of motion can be derived from a regular Lagrangian function.Comment: 17 pages + 3 figures

The 1998 Center for Simulation of Dynamic Response in Materials Annual Technical Report

Introduction: This annual report describes research accomplishments for FY 98 of the Center for Simulation of Dynamic Response of Materials. The Center is constructing a virtual shock physics facility in which the full three dimensional response of a variety of target materials can be computed for a wide range of compressive, tensional, and shear loadings, including those produced by detonation of energetic materials. The goals are to facilitate computation of a variety of experiments in which strong shock and detonation waves are made to impinge on targets consisting of various combinations of materials, compute the subsequent dynamic response of the target materials, and validate these computations against experimental data

Improved Combination of Multiple Atmospheric GCM Ensembles for Seasonal Prediction

An improved Bayesian optimal weighting scheme is developed and used to combine six atmospheric general circulation model (GCM) seasonal hindcast ensembles. The approach is based on the prior belief that the forecast probabilities of tercile-category precipitation and near-surface temperature are equal to the climatological ones. The six GCMs are integrated over the 1950–97 period with observed monthly SST prescribed at the lower boundary, with 9–24 ensemble members. The weights of the individual models are determined by maximizing the log likelihood of the combination by season over the integration period. A key ingredient of the scheme is the climatological equal-odds forecast, which is included as one of the "models" in the multimodel combination. Simulation skill is quantified in terms of the cross-validated ranked probability skill score (RPSS) for the three-category probabilistic hindcasts. The individual GCM ensembles, simple poolings of three and six models, and the optimally combined multimodel ensemble are compared. The Bayesian optimal weighting scheme outperforms the pooled ensemble, which in turn outperforms the individual models. In the extratropics, its main benefit is to bring much of the large area of negative-precipitation RPSS values up to near-zero values. The skill of the optimal combination is almost always increased (in the large spatial averages considered) when the number of models in the combination is increased from three to six, regardless of which models are included in the three-model combination. Improvements are made to the original Bayesian scheme of Rajagopalan et al. by reducing the dimensionality of the numerical optimization, averaging across data subsamples, and including spatial smoothing of the likelihood function. These modifications are shown to yield increases in cross-validated RPSS skills. The revised scheme appears to be better suited to combining larger sets of models, and, in the future, it should be possible to include statistical models into the weighted ensemble without fundamental difficulty

Note and Comment

The Permanent International Court of Justice - For the first time in history leading powers both great and small have been able to agree upon a plan for an international court of justice. The plan was formulated last summer by an advisory committee of jurists sitting at The Hague. Since then it has been submitted to the Council and the Assembly of the League of Nations and has been approved. It will come into operation as soon as the project has been ratified by a majority of the nations belonging to the Leagu

An Exact String Theory Model of Closed Time-Like Curves and Cosmological Singularities

We study an exact model of string theory propagating in a space-time containing regions with closed time-like curves (CTCs) separated from a finite cosmological region bounded by a Big Bang and a Big Crunch. The model is an non-trivial embedding of the Taub-NUT geometry into heterotic string theory with a full conformal field theory (CFT) definition, discovered over a decade ago as a heterotic coset model. Having a CFT definition makes this an excellent laboratory for the study of the stringy fate of CTCs, the Taub cosmology, and the Milne/Misner-type chronology horizon which separates them. In an effort to uncover the role of stringy corrections to such geometries, we calculate the complete set of alpha' corrections to the geometry. We observe that the key features of Taub-NUT persist in the exact theory, together with the emergence of a region of space with Euclidean signature bounded by time-like curvature singularities. Although such remarks are premature, their persistence in the exact geometry is suggestive that string theory theory is able to make physical sense of the Milne/Misner singularities and the CTCs, despite their pathological character in General Relativity. This may also support the possibility that CTCs may be viable in some physical situations, and may be a natural ingredient in pre-Big-Bang cosmological scenarios.Comment: 37 pages, 4 figures. V2: discussion of computation of metric refined, references adde