On the automorphisms of a graph product of abelian groups

We study the automorphisms of a graph product of finitely-generated abelian groups W. More precisely, we study a natural subgroup Aut* W of Aut W, with Aut* W = Aut W whenever vertex groups are finite and in a number of other cases. We prove a number of structure results, including a semi-direct product decomposition of Aut* W in which one of the factors is Inn W. We also give a number of applications, some of which are geometric in nature.Comment: 38 pages, 4 figure

Quark mass effects in the soft-collinear effective theory and B -> X_s + photon in the endpoint region

We consider the effects of a light quark mass in the soft-collinear effective theory (SCET) and we apply them to B -> X_s gamma in the endpoint region. We find that the reparameterization invariance can be extended by including the collinear quark mass in the SCET Lagrangian. This symmetry constrains the theory with the quark mass terms, and we present explicit results at one loop. It also relates the Wilson coefficients of some mass operators to those of the leading operators, which are useful in organizing the subleading effects due to the quark mass in B -> X_s gamma. We present strange quark mass corrections to B -> X_s gamma in the endpoint region as an application. The forward scattering amplitude from the mass corrections is factorized, and it can be expressed as a convolution of the m_s^2/p_X^2-suppressed jet function and the leading-order shape function of the B meson. This contribution should be added to the existing subleading contributions from the B meson shape functions to obtain complete subleading corrections.Comment: 30 pages, 6 figures; some errors are corrected and numerical estimates are adde

The automorphism group of the free group of rank two is a CAT(0) group

We prove that the automorphism group of the braid group on four strands acts faithfully and geometrically on a CAT(0) 2-complex. This implies that the automorphism group of the free group of rank two acts faithfully and geometrically on a CAT(0) 2-complex, in contrast to the situation for rank three and above.Comment: 7 pages, 2 figures. The manuscript has been modified in minor ways in accordance with a referee's recommendations, and a misattribution of the result "Aut F_2 is biautomatic" has been correcte

Probing electroweak physics using B -> XM decays in the endpoint region

Using soft-collinear effective theory we describe at leading order in 1/m_b all the semi-inclusive hadronic B -> XM decays near the endpoint, where an energetic light meson M recoils against an inclusive jet X. We also include the decays involving eta, eta' mesons that receive additional contributions from gluonic operators. The predicted branching ratios and CP asymmetries depend on fewer hadronic parameters than the corresponding two-body B decays. This makes semi-inclusive hadronic B -> XM decays a powerful probe of the potential nonperturbative nature of charming penguins as well as a useful probe of new physics effects in electroweak flavor changing transitions. A comparison with B -> KX data from BaBar points to an enhanced charming penguin, albeit with large experimental errors.Comment: 27 pages, 6 figure

Interactional aerodynamics and acoustics of a propeller-augmented compound coaxial helicopter

The aerodynamic and acoustic characteristics of a generic hingeless coaxial helicopter with a tail-mounted propulsor and stabiliser have been simulated using Brown's Vorticity Transport Model. This has been done to investigate the ability of models of this type to capture the aerodynamic interactions that are generated between the various components of realistic, complex helicopter configurations. Simulations reveal the aerodynamic environment of the coaxial main rotor of the configuration to be dominated by internal interactions that lead to high vibration and noise. The wake of the main rotor is predicted to interact strongly with the tailplane, particularly at low forward speed, to produce a strong nose-up pitching moment that must be countered by significant longitudinal cyclic input to the main rotor. The wake from the main rotor is ingested directly into the tail propulsor over a broad range of forward speeds, where it produces significant vibratory excitation of the system as well as broadband noise. The numerical calculations also suggest the possibility that poor scheduling of the partition of the propulsive force between the main rotor and propulsor as a function of forward speed may yield a situation where the propulsor produces little thrust but high vibration as a result of this interaction. Although many of the predicted effects might be ameliorated or eliminated entirely by more careful or considered design, the model captures many of the aerodynamic interactions, and the resultant effects on the loading on the system, that might be expected to characterise the dynamics of such a vehicle. It is suggested that the use of such numerical techniques might eventually allow the various aeromechanical problems that often beset new designs to be circumvented - hopefully well before they manifest on the prototype or production aircraft