Gravitational waves from neutron stars: promises and challenges

We discuss different ways that neutron stars can generate gravitational waves, describe recent improvements in modelling the relevant scenarios in the context of improving detector sensitivity, and show how observations are beginning to test our understanding of fundamental physics. The main purpose of the discussion is to establish promising science goals for third-generation ground-based detectors, like the Einstein Telescope, and identify the various challenges that need to be met if we want to use gravitational-wave data to probe neutron star physics.     

High-modulus polydiacetylene single-crystal fibers

The relationship between structure and mechanical properties of polydiactetylene single-crystal fibers has been studied in detail. It is shown by transmission electron microscopy that the fibers have a high degree of internal perfection, with the polymer molecules aligned parallel to the fiber axes. The fibers of the dicarbazolyl derivative investigated were found to have a Young's modulus of 45 GPa and fracture strengths of up to 1.5 GPa, the strengths being controlled by defects such as surface steps. It is shown that the stiffness of the polymer backbone is similar to that of polyethylene, and the theoretical strength of the polydiacetylene singlecrystal fibers is determined to be about 3 GPa, corresponding to a fracture strain of between 6 and 8% and a force required to break molecules to the order of 3 nN. The derivative studied is also found to have good thermal stability, not degrading below 300°C, and excellent creep resistance up to at least 100°C. The possibility of using the single-crystal fibers in composites is also discussed.     

The invariant subspace problem for a class of Banach spaces, 2: Hypercyclic operators

We continue here the line of investigation begun in [7], where we showed that on every Banach spaceX=l ₁⊗W (whereW is separable) there is an operatorT with no nontrivial invariant subspaces. Here, we work on the same class of Banach spaces, and produce operators which not only have no invariant subspaces, but are also hypercyclic. This means that for every nonzero vectorx inX, the translatesT ^r x (r=1, 2, 3,...) are dense inX. This is an interesting result even if stated in a form which disregards the linearity ofT: it tells us that there is a continuous map ofX{0\{ into itself such that the orbit {T ^rx :r≧0{ of anyx teX \{0\{ is dense inX \{0\{. The methods used to construct the new operatorT are similar to those in [7], but we need to have somewhat greater complexity in order to obtain a hypercyclic operator.     

Design of a 3-MW 140-GHz gyrotron with a coaxial cavity

A design for a 3-MW 140-GHz gyrotron based on the use of a coaxial cavity is given. The cavity mode is TE_21,13, chosen so that the ohmic heating on both the inner and outer conductors would be low enough for CW operation. The mode selection process, nonlinear, multimode and time-dependent modeling of the beam wave interaction, and gun design are discussed in detail. An inverted magnetron injection gun (MIG) is used to accommodate the inner conductor. The radiation is coupled out via a quasi-optical mode converter, consisting of an irregular cylindrical waveguide section followed by a step-cut launching aperture and a single near-parabolic mirror. The design of these components is also described     

In Memoriam

In memoriam Michael John Richardson.     

Power limits in cylindrical gyromonotrons using TEon1 modes

Upper and lower limits to the output power of highly efficient gyrotron oscillators operating with TE_on1 modes, due to lower and upper limits on the cavity Q, are given.     

Enantioselective total syntheses of nankakurines A and B: confirmation of structure and establishment of absolute configuration

Total syntheses of (+)-nankakurine A (2) and (+)-nankakurine B (3) were accomplished by a sequence that employs an intramolecular dipolar cycloaddition of an azomethine imine intermediate to form the azatricyclic moiety and establish the relative configuration of the spiropiperidine ring. These syntheses, together with the synthesis of the originally purported structure 1 of nankakurine A, rigorously establish the relative and absolute configuration of these structurally unusual Lycopodium alkaloids. The syntheses are sufficiently concise that gram quantities of (+)-nankakurine A (2) and (+)-nankakurine B (3) will be available for further biological studies.     

Demixing instability in coil-rod blends undergoing polycondensation reactions

The authors extend their earlier work on the stability of a reacting binary polymer blend with respect to demixing [D. J. Read, Macromolecules 31, 899 (1998); P. I. C. Teixeira et al., Macromolecules 33, 387 (2000)] to the case where one of the polymers is rod-like and may order nematically. As before, the authors combine the random phase approximation for the free energy with a Markov chain model for the chemistry to obtain the spinodal as a function of the relevant degrees of reaction. These are then calculated by assuming a simple second-order chemical kinetics. Results are presented, for linear systems, which illustrate the effects of varying the proportion of coils and rods, their relative sizes, and the strength of the nematic interaction between the rods.     

Associative-algebraic approach to logarithmic conformal field theories

We set up a strategy for studying large families of logarithmic conformal field theories by using the enlarged symmetries and non-semisimple associative algebras appearing in their lattice regularizations (as discussed in a companion paper [N. Read, H. Saleur, Enlarged symmetry algebras of spin chains, loop models, and S-matrices, cond-mat/0701259]). Here we work out in detail two examples of theories derived as the continuum limit of XXZ spin-1/2 chains, which are related to spin chains with supersymmetry algebras gl(n|n)$\mathrm{gl}(n|n)$ and gl(n+1|n)$\mathrm{gl}(n+1|n)$, respectively, with open (or free) boundary conditions in all cases. These theories can also be viewed as vertex models, or as loop models. Their continuum limits are boundary conformal field theories (CFTs) with central charge c=−2$c=-2$ and c=0$c=0$ respectively, and in the loop interpretation they describe dense polymers and the boundaries of critical percolation clusters, respectively. We also discuss the case of dilute (critical) polymers as another boundary CFT with c=0$c=0$. Within the supersymmetric formulations, these boundary CFTs describe the fixed points of certain nonlinear sigma models that have a supercoset space as the target manifold, and of Landau–Ginzburg field theories. The submodule structures of indecomposable representations of the Virasoro algebra appearing in the boundary CFT, representing local fields, are derived from the lattice. A central result is the derivation of the fusion rules for these fields.