A semi-analytical numerical method for time-dependent radiative transfer problems in slab geometry with coherent isotropic scattering

We describe a semi-analytical numerical method for coherent isotropic scattering time-dependent radiative transfer problems in slab geometry. This numerical method is based on a combination of two classes of numerical methods: the spectral methods and the Laplace transform (LTS_N) methods applied to the radiative transfer equation in the discrete ordinates (S_N) formulation. The basic idea is to use the essence of the spectral methods and expand the intensity of radiation in a truncated series of Laguerre polynomials in the time variable and then solve recursively the resulting set of “time-independent” S_N problems by using the LTS_N method. We show some numerical experiments for a typical model problem.     

Study of the charge-exchange reactions\pi ^ - p \to (\pi ^0 ,\eta ,\eta \prime )n at 63 GeV

Muon electron pairs were detected in an Al multiplate spark chamber, exposed to a neutrino beam from the CERN PS. The leptons were not accompanied by other particles, except occasionally by protons. The background came mainly from muon associated π⁰ production, with one decay gamma lost. It was determined empirically, together with the small contribution from υ _e reactions. For electron energies above 2 GeV the background is 5.7±1.5 events, whereas 18 (μe)-candidates have been observed. Hence the effect is established, with a rate of about 10^?4 as compared to the muonic reactions above 3 GeV. Charm creation as the origin of this (μe)-production process is excluded; heavy neutral lepton production does not fit the kinematics observed. Instead the events are compatible with the two-body decay of an object with variable invariant mass of order 1 GeV, possibly resulting from axion interactions.     

Grating coatings with gain

Using an integral theory of grating diffraction we calculate efficiencies greater than 100% if a coating with gain is taken into account. A connection with guided modes is conjectured. The application in optical computing seems to be possible.     

A New Distribution Function for Risk Analysis

This paper presents an alternative to the beta continuous probability distribution for risk analysis. Particular attention has been given to two major applications of distributions, namely project management risk and critical path analysis (PERT). In conjunction with the beta, the triangular and normal distributions are frequently employed in order to give sufficient robustness to risk analysis. The beta distribution, as used in PERT, has a major theoretical implementation flaw. The new distribution was developed to give a possible alternative method of assessing risk. It is shown that the requirement to estimate the most pessimistic variate may be replaced by the probability to exceed the mode. Proposals for other simplifications in risk analysis are discussed. Practical means to validate the most appropriate distributions for risk analysis are outlined, and a cost-data case study is included.     

Existence and Stability for Spherical Crystals Growing in a Supersaturated Solution

We consider the growth of a spherical crystal in a supersaturatedsolution. In the first part, existence and uniqueness resultsfor radially symmetric growth are obtained, provided that thesupersaturation is not too large; conversely, when the far-fieldsupersaturation exceeds a critical value, it is shown that theradially symmetric solution ceases to exist in finite time.In the second part, we examine the linear stability of a radiallysymmetric similarity solution (in which the radius grows ast?) to shape perturbations. The results are compared with previousquasi-static analyses, and, in particular, the critical radiusat which the crystal becomes unstable is found to be largerfor small supersaturations, but smaller for large supersaturations,than those predicted by the quasi-static analysis     

Transport as a consequence of state-dependent diffusion

Overdamped particles subject to a drift in a force field with sinusoidal space dependence and also a sinusoidally modulated space-dependent diffusion, with the same period as the drift, experience a net driving force. The resulting current depends on the amplitude of the modulation of the diffusion and is a periodic function of the phase difference between the sinusoidal drift and the sinusoidal modulation of the diffusion. For small modulation amplitudes a particle subject to state-dependent noise behaves the same way as a particle subject to thermal noise but with a drift which, in addition to the sinusoidal term, contains a net force term.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday