The 2D Euler-Poisson System with Spherical Symmetry

This article concerns the global-in-time existence of smooth solutions with small amplitude to two space dimensional Euler-Poisson system. The main difficulty lies in the slow time decay $(1+t)^{-1}$ of the linear system. Inspired by Ozawa, Tsutaya, and Tsutsumi's work, we show that such smooth solutions exist for radially symmetric flows

Two-slit diffraction with highly charged particles: Niels Bohr's consistency argument that the electromagnetic field must be quantized

We analyze Niels Bohr's proposed two-slit interference experiment with highly charged particles that argues that the consistency of elementary quantum mechanics requires that the electromagnetic field must be quantized. In the experiment a particle's path through the slits is determined by measuring the Coulomb field that it produces at large distances; under these conditions the interference pattern must be suppressed. The key is that as the particle's trajectory is bent in diffraction by the slits it must radiate and the radiation must carry away phase information. Thus the radiation field must be a quantized dynamical degree of freedom. On the other hand, if one similarly tries to determine the path of a massive particle through an inferometer by measuring the Newtonian gravitational potential the particle produces, the interference pattern would have to be finer than the Planck length and thus undiscernable. Unlike for the electromagnetic field, Bohr's argument does not imply that the gravitational field must be quantized.Comment: 8 pages, 4 figures. To appear in Proc. Natl. Acad. Sc

Portable reflectance spectrometer

A portable reflectance spectrometer is disclosed. The spectrometer essentially includes an optical unit and an electronic recording unit. The optical unit includes a pair of thermoelectrically-cooled detectors, for detecting total radiance and selected radiance projected through a circular variable filter wheel, and is capable of operating to provide spectral data in the range 0.4 to 2.5 micrometers without requiring coventional substitution of filter elements. The electronic recording unit includes power supplies, amplifiers, and digital recording electronics designed to permit recordation of data on tape casettes. Both the optical unit and electronic recording unit are packaged to be manually portable

Conservation laws, uncertainty relations, and quantum limits of measurements

The uncertainty relation between the noise operator and the conserved quantity leads to a bound for the accuracy of general measurements. The bound extends the assertion by Wigner, Araki, and Yanase that conservation laws limit the accuracy of ``repeatable'', or ``nondisturbing'', measurements to general measurements, and improves the one previously obtained by Yanase for spin measurements. The bound also sets an obstacle to making a small quantum computer.Comment: 4 pages, RevTex, to appear in PR

Larval ontogeny of a percichthyid fish, Synagrops philippinensis (Günther) in Kagoshima Bay, southern Japan

The larval ontogeny of a developmental series (1.2-8.3mm body length, BL) of Synagrops philippinensis from Kagoshima Bay, southern Japan is described and illustrated. The yolk was completely absorbed in larva of ≥1.5 mm BL. Notochord flexion commenced at about 3.5mm BL and was completed by about 4.0-4.5mm BL. S. philippinensis larvae were distinguished from their congeners based on melanophore patterns, head spination and fin spines and rays. Larvae of 7.5-8.3 mm BL were characterized by anteriorly serrated pelvic spine, two anal spines, nine inner preopercular spines and no melanophore on lateral side of the caudal peduncle; 7.0 to 7.5mm BL larvae by the above characters except serration on pelvic spine; and yolk-sac, pre-flexion, flexing and post-flexion larvae up to 7.0mm BL by unique melanophores on lower lobe of pectoral finfold/fin

LECTURES ON NONLINEAR DISPERSIVE EQUATIONS II

Program N. Tzvetkov Ill-posedness issues for nonlinear dispersive equations H. Koch Dispersive estimates and application

Schrdinger Equations with nonlinearity of integral type

We consider the Cauchy problem for the nonlinear Schrodinger equation with interaction described by the integral of the intensity with respect to one direction in two space dimensions. Concerning the problem with finite initial time, we prove the global well-posedness in the largest space L2(!R2 ). Concerning the problem with infinite initial time, we prove the existence of modified wave operators on a dense set of small and sufficiently regular asymptotic states