Introduction

This is the post print version of the chapter - Copyright @ 2003 The editorsThis book is about surrogacy and, more specifically, surrogate motherhood. It is a collection of essays that aims to provide a contemporary and international picture of a practice, traceable to ancient times, devised to solve the problem of childlessness. The collection, which explores surrogacy from a variety of perspectives including law, policy, medicine and psychology, is timely. For although there is nothing new in the notion that a woman might bear a child for someone else, there is some evidence that the incidence of surrogacy is increasing and technology has developed to make ever more complex arrangements possible

Multiple scattering in random mechanical systems and diffusion approximation

This paper is concerned with stochastic processes that model multiple (or iterated) scattering in classical mechanical systems of billiard type, defined below. From a given (deterministic) system of billiard type, a random process with transition probabilities operator P is introduced by assuming that some of the dynamical variables are random with prescribed probability distributions. Of particular interest are systems with weak scattering, which are associated to parametric families of operators P_h, depending on a geometric or mechanical parameter h, that approaches the identity as h goes to 0. It is shown that (P_h -I)/h converges for small h to a second order elliptic differential operator L on compactly supported functions and that the Markov chain process associated to P_h converges to a diffusion with infinitesimal generator L. Both P_h and L are selfadjoint (densely) defined on the space L2(H,{\eta}) of square-integrable functions over the (lower) half-space H in R^m, where {\eta} is a stationary measure. This measure's density is either (post-collision) Maxwell-Boltzmann distribution or Knudsen cosine law, and the random processes with infinitesimal generator L respectively correspond to what we call MB diffusion and (generalized) Legendre diffusion. Concrete examples of simple mechanical systems are given and illustrated by numerically simulating the random processes.Comment: 34 pages, 13 figure

Detection Techniques of Microsecond Gamma-Ray Bursts using Ground-Based Telescopes

Gamma-ray observations above 200 MeV are conventionally made by satellite-based detectors. The EGRET detector on the Compton Gamma Ray Observatory (CGRO) has provided good sensitivity for the detection of bursts lasting for more than 200 ms. Theoretical predictions of high-energy gamma-ray bursts produced by quantum-mechanical decay of primordial black holes (Hawking 1971) suggest the emission of bursts on shorter time scales. The final stage of a primordial black hole results in a burst of gamma-rays, peaking around 250 MeV and lasting for a tenth of a microsecond or longer depending on particle physics. In this work we show that there is an observational window using ground-based imaging Cherenkov detectors to measure gamma-ray burst emission at energies E greater than 200 MeV. This technique, with a sensitivity for bursts lasting nanoseconds to several microseconds, is based on the detection of multi-photon-initiated air showers.Comment: accepted for publication in the Astrophysical Journa