Measuring the Redshift of Reionization with a Modest Array of Low-Frequency Dipoles

The designs of the first generation of cosmological 21-cm observatories are split between single dipole experiments which integrate over a large patch of sky in order to find the global (spectral) signature of reionization, and interferometers with arcminute-scale angular resolution whose goal is to measure the 3D power spectrum of ionized regions during reionization. We examine whether intermediate scale instruments with complete Fourier (uv) coverage are capable of placing new constraints on reionization. We find that even without using a full power spectrum analysis, the global redshift of reionization, z_reion, can in principle be measured from the variance in the 21-cm signal among multiple beams as a function of frequency at a roughly 1 degree angular scale. At this scale, the beam-to-beam variance in the differential brightness temperature peaks when the average neutral fraction was around 50%, providing a convenient flag of z_reion. We choose a low angular resolution of order 1 degree to exploit the physical size of the ionized regions and maximize the signal-to-noise ratio. Thermal noise, foregrounds, and instrumental effects should also be manageable at this angular scale, as long as the uv coverage is complete within the compact core required for low-resolution imaging. For example, we find that z_reion can potentially be detected to within a redshift uncertainty of less than around 1 in around 500 hours of integration on the existing MWA prototype (with only 32x16 dipoles), operating at an angular resolution of around 1 degree and a spectral resolution of 2.4 MHz.Comment: 11 pages, 7 figures. Version published in JCAP (appendix removed, some clarifications and changes to definitions

Extremal transmission through a microwave photonic crystal and the observation of edge states in a rectangular Dirac billiard

This article presents experimental results on properties of waves propagating in an unbounded and a bounded photonic crystal consisting of metallic cylinders which are arranged in a triangular lattice. First, we present transmission measurements of plane waves traversing a photonic crystal. The experiments are performed in the vicinity of a Dirac point, i.e., an isolated conical singularity of the photonic band structure. There, the transmission shows a pseudodiffusive 1/L dependence, with $L$ being the thickness of the crystal, a phenomenon also observed in graphene. Second, eigenmode intensity distributions measured in a microwave analog of a relativistic Dirac billiard, a rectangular microwave billiard that contains a photonic crystal, are discussed. Close to the Dirac point states have been detected which are localized at the straight edge of the photonic crystal corresponding to a zigzag edge in graphene

Extent and mechanism of sealing in transected giant axons of squid and earthworms

Transected axons are often assumed to seal at their cut ends by the formation of continuous membrane barriers that allow for the restoration of function in the axonal stumps. We have used several electrophysiological measures (membrane potential, input resistance, injury current density) and several morphological measures (phase-contrast, video-enhanced differential interference contrast, light, and electron microscopies) of living and fixed material to assess the extent and mechanism of sealing within hours after transecting giant axons of squid (Loligo pealeiand Sepioteuthis lessoniana) and earthworms (Lumbricus terrestris). Our electrophysiological data suggest that the proximal and distal ends of transected squid giant axons do not completely seal within 2.5 hr in physiological saline. In contrast, the same set of measures suggest that proximal and distal ends of transected earthworm giant axons seal within 1 hr in physiological saline. Our morphological data show that the cut ends of both squid and earthworm axons constrict, but that a 20- 70-am-diameter opening always remains at the cut end that is filled with vesicles. Axonal transection induces the formation of vesicles that are observed in the axoplasm within minutes in standard salines and that rapidly migrate to the cut ends. These injury-induced vesicles are loosely packed near the cut ends of squid giant axons, which do not functionally seal within 2.5 hr of transection. In contrast, vesicles formed a tightly packed plug at the cut ends of earthworm medial giant axons, which do functionally seal within 1 hr of transection in physiological saline. Since we detect no single continuous membrane that spans the cut end, sealing does not appear to occur by the fusion of constricted axolemmal membrane or the formation of a membranous partition at the cut end. Rather, our data are consistent with the hypothesis that a tightly packed vesicular plug is responsible for sealing of earthworm giant axons.This work was supported in part by NIH Grant NS31256 and ONR Grant N00014-90-J-1137 to H.M.F., an NIAAA fellowship to T.L.K., and an ATP grant to G.D.B.Neuroscienc

Motivic Milnor fibre for nondegenerate function germs on toric singularities

We study function germs on toric varieties which are nondegenerate for their Newton diagram. We express their motivic Milnor fibre in terms of their Newton diagram. We extend a formula for the motivic nearby fibre to the case of a toroidal degeneration. We illustrate this by some examples.Comment: 14 page

Scattering Experiments with Microwave Billiards at an Exceptional Point under Broken Time Reversal Invariance

Scattering experiments with microwave cavities were performed and the effects of broken time-reversal invariance (TRI), induced by means of a magnetized ferrite placed inside the cavity, on an isolated doublet of nearly degenerate resonances were investigated. All elements of the effective Hamiltonian of this two-level system were extracted. As a function of two experimental parameters, the doublet and also the associated eigenvectors could be tuned to coalesce at a so-called exceptional point (EP). The behavior of the eigenvalues and eigenvectors when encircling the EP in parameter space was studied, including the geometric amplitude that builds up in the case of broken TRI. A one-dimensional subspace of parameters was found where the differences of the eigenvalues are either real or purely imaginary. There, the Hamiltonians were found PT-invariant under the combined operation of parity (P) and time reversal (T) in a generalized sense. The EP is the point of transition between both regions. There a spontaneous breaking of PT occurs