17 research outputs found
On asymptotically equivalent shallow water wave equations
The integrable 3rd-order Korteweg-de Vries (KdV) equation emerges uniquely at
linear order in the asymptotic expansion for unidirectional shallow water
waves. However, at quadratic order, this asymptotic expansion produces an
entire {\it family} of shallow water wave equations that are asymptotically
equivalent to each other, under a group of nonlinear, nonlocal, normal-form
transformations introduced by Kodama in combination with the application of the
Helmholtz-operator. These Kodama-Helmholtz transformations are used to present
connections between shallow water waves, the integrable 5th-order Korteweg-de
Vries equation, and a generalization of the Camassa-Holm (CH) equation that
contains an additional integrable case. The dispersion relation of the full
water wave problem and any equation in this family agree to 5th order. The
travelling wave solutions of the CH equation are shown to agree to 5th order
with the exact solution
Allan Sandage and the Cosmic Expansion
This is an account of Allan Sandage's work on (1) The character of the
expansion field. For many years he has been the strongest defender of an
expanding Universe. He later explained the CMB dipole by a local velocity of
220 +/- 50 km/s toward the Virgo cluster and by a bulk motion of the Local
supercluster (extending out to ~3500 km/s) of 450-500 km/s toward an apex at
l=275, b=12. Allowing for these streaming velocities he found linear expansion
to hold down to local scales (~300 km/s). (2) The calibration of the Hubble
constant. Probing different methods he finally adopted - from
Cepheid-calibrated SNe Ia and from independent RR Lyr-calibrated TRGBs - H_0 =
62.3 +/- 1.3 +/- 5.0 km/s/Mpc.Comment: 12 pages, 11 figures, 1 table, Submitted to Astrophysics and Space
Science, Special Issue on the Fundamental Cosmic Distance Scale in the Gaia
Er
Ionic and electronic conduction in β-PbF2
β-PbF2 is an extrinsic n-type semiconductor at temperatures below 300 K. The contribution of lattice defects to the electrical conductivity increases rapidly above room temperature. Polarization studies using a Wagner-cell indicate that above 350 K ionic conductivity becomes predominant in undoped β-PbF2 crystals