Plasma Magnetosphere Formation Around Oscillating Magnetized Neutron Stars

The notion of death line of rotating pulsars is applied to model of oscillating neutron stars. It is shown that the magnetosphere of typical non-rotating oscillating stars may not contain secondary plasma to support the generation of radio emission in the region of open field lines of plasma magnetosphere.Comment: Accepted for publication in Astrophysics & Space Scienc

Fluctuating Nematic Elastomer Membranes: a New Universality Class

We study the flat phase of nematic elastomer membranes with rotational symmetry spontaneously broken by in-plane nematic order. Such state is characterized by a vanishing elastic modulus for simple shear and soft transverse phonons. At harmonic level, in-plane orientational (nematic) order is stable to thermal fluctuations, that lead to short-range in-plane translational (phonon) correlations. To treat thermal fluctuations and relevant elastic nonlinearities, we introduce two generalizations of two-dimensional membranes in a three dimensional space to arbitrary D-dimensional membranes embedded in a d-dimensional space, and analyze their anomalous elasticities in an expansion about D=4. We find a new stable fixed point, that controls long-scale properties of nematic elastomer membranes. It is characterized by singular in-plane elastic moduli that vanish as a power-law eta_lambda=4-D of a relevant inverse length scale (e.g., wavevector) and a finite bending rigidity. Our predictions are asymptotically exact near 4 dimensions.Comment: 18 pages, 4 eps figures. submitted to PR

Short Presentations for Finite Groups

AbstractWe conjecture that every finite groupGhas a short presentation (in terms of generators and relations) in the sense that the totallengthof the relations is (log|G|)O(1).We show that it suffices to prove this conjecture for simple groups.Motivated by applications in computational complexity theory, we conjecture that for finite simple groups, such a short presentation is computable in polynomial time from the standard name ofG, assuming in the case of Lie type simple groups overGF(pm) that an irreducible polynomialfof degreemoverGF(p) and a primitive root ofGF(pm) are given.We verify this (stronger) conjecture for all finite simple groups except for the three families of rank 1 twisted groups: we do not handle the unitary groupsPSU(3,q)=2A2(q), the Suzuki groupsSz(q)=2B2(q), and the Ree groupsR(q)=2G2(q). In particular,all finite groups G without composition factors of these types have presentations of length O((log|G|)3).For groups of Lie type (normal or twisted) of rank≥2, we use a reduced version of the Curtis–Steinberg–Tits presentation