Monstrous Branes

 We study D-branes in the bosonic closed string theory whose automorphism group is the Bimonster group (the wreath product of the Monster simple group with ℤ₂). We give a complete classification of D-branes preserving the chiral subalgebra of Monster invariants and show that they transform in a representation of the Bimonster. Our results apply more generally to self-dual conformal field theories which admit the action of a compact Lie group on both the left- and right-moving sectors. Received: 20 February 2002 / Accepted: 17 August 2002 Published online: 19 December 2002 Communicated by R.H. Dijkgraaf     

Calculus of functors and model categories

The category of small covariant functors from simplicial sets to simplicial sets supports the projective model structure [B. Chorny, W.G. Dwyer, Homotopy theory of small diagrams over large categories, preprint, 2005]. In this paper we construct various localizations of the projective model structure and also give a variant for functors from simplicial sets to spectra. We apply these model categories in the study of calculus of functors, namely for a classification of polynomial and homogeneous functors. In the n-homogeneous model structure, the nth derivative is a Quillen functor to the category of spectra with Σn-action. After taking into account only finitary functors—which may be done in two different ways—the above Quillen map becomes a Quillen equivalence. This improves the classification of finitary homogeneous functors by T.G. Goodwillie [T.G. Goodwillie, Calculus. III. Taylor series, Geom. Topol. 7 (2003) 645-711 (electronic)].     

Growth of Lévy trees

We construct random locally compact real trees called Lévy trees that are the genealogical trees associated with continuous-state branching processes. More precisely, we define a growing family of discrete Galton–Watson trees with i.i.d. exponential branch lengths that is consistent under Bernoulli percolation on leaves; we define the Lévy tree as the limit of this growing family with respect to the Gromov–Hausdorff topology on metric spaces. This elementary approach notably includes supercritical trees and does not make use of the height process introduced by Le Gall and Le Jan to code the genealogy of (sub)critical continuous-state branching processes. We construct the mass measure of Lévy trees and we give a decomposition along the ancestral subtree of a Poisson sampling directed by the mass measure. T. Duquesne is supported by NSF Grants DMS-0203066 and DMS-0405779. M. Winkel is supported by Aon and the Institute of Actuaries, EPSRC Grant GR/T26368/01, le département de mathématique de l’Université d’Orsay and NSF Grant DMS-0405779.     

Converged properties of clean metal surfaces by all-electron first-principles calculations

All-electron full-potential linearized augmented plane-wave calculations of the surface energy, work function, and interlayer spacings of close-packed metal surfaces are presented, in particular, for the free-electron-like metal surfaces, Mg(0 0 0 1) and Al(1 1 1), and for the transition metal surfaces, Ti(0 0 0 1), Cu(1 1 1), Pd(1 1 1), and Pt(1 1 1). We investigate the convergence of the surface energy as a function of the number of layers in the slab, using the Cu(1 1 1) surface as an example. The results show that the surface energy, as obtained using total energies of the slab and bulk from separate calculations, converges well with respect to the number of layers in the slab. Obviously, it is necessary that bulk and surface calculations are performed with the same high accuracy. Furthermore, we discuss the performance of the local-density and generalized gradient approximations for the exchange-correlation functional in describing the various surface properties.     

Atomistic packing models for experimentally investigated swelling states induced by CO2 in glassy polysulfone and poly(ether sulfone)

Atomistic packing models have been created, which help to better understand the experimentally observed swelling behavior of glassy polysulfone and poly (ether sulfone), under CO₂ gas pressures up to 50 bar at 308 K. The experimental characterization includes the measurement of the time‐dependent volume dilation of the polymer samples after a pressure step and the determination of the corresponding gas concentrations by gravimetric gas‐sorption measurements. The models obtained by force‐field‐based molecular mechanics and molecular dynamics methods allow a detailed atomistic analysis of representative swelling states of polymer/gas systems, with respect to the dilation of the matrix. Also, changes of free volume distribution and backbone mobility are accessible. The behavior of gas molecules in unswollen and swollen polymer matrices is characterized in terms of sorption, diffusion, and plasticization. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1874–1897, 2006     

Dynamic NMR study of the flexibility of 2-amino-3-aroyl-4,6-diaryl-pyrylium salts

Dynamic NMR investigations of a number of 2-amino-3-aroyl-4,6-diaryl-pyrylium salts were carried out. The barrier to rotation of the partial C, N double bond was determined and proved to be in the range of 62 to 63 kJ/mol. Quantum chemical calculations of bond orders and electron densities of the different atoms in the molecules show the distinct double bond character of the exocyclic C, N bond. This is in agreement with the relatively high barrier to rotation. By quantum chemical ab initio 3-21G calculations, the dynamic behaviour of this kind of compounds was simulated; two pairs (image and mirror image) of ground state conformations, in coincidence with the experiment, were obtained. Received: 10 May 1996 / Revised: 1 July 1996 / Accepted: 4 July 1996     

Theory of Non-Equilibrium Stationary States as a Theory of Resonances

We study a small quantum system (e.g., a simplified model for an atom or molecule) interacting with two bosonic or fermionic reservoirs (say, photon or phonon fields). We show that the combined system has a family of stationary states parametrized by two numbers, T ₁ and T ₂ (‘reservoir temperatures’). If T ₁ ≠ T ₂, then these states are non-equilibrium stationary states (NESS). In the latter case we show that they have nonvanishing heat fluxes and positive entropy production and are dynamically asymptotically stable. The latter means that the evolution with an initial condition, normal with respect to any state where the reservoirs are in equilibria at temperatures T ₁ and T ₂, converges to the corresponding NESS. Our results are valid for the temperatures satisfying the bound min (T ₁,T ₂) > g ^{2 + α}, where g is the coupling constant and 0 < α < 1 is a power related to the infra-red behaviour of the coupling functions. Submitted: March 20, 2006. Revised: March 19, 2007. Accepted: May 11, 2007. Marco Merkli: Partly supported by an NSERC PDF, the Institute of Theoretical Physics of ETH Zürich, Switzerland, the Departments of Mathematics of McGill University and the University of Toronto, Canada. Matthias Mück: Supported by DAAD under grant HSP III. Israel Michael Sigal: Supported by NSERC under grant NA7901.