Measure Problem for Eternal and Non-Eternal Inflation

We study various probability measures for eternal inflation by applying their regularization prescriptions to models where inflation is not eternal. For simplicity we work with a toy model describing inflation that can interpolate between eternal and non-eternal inflation by continuous variation of a parameter. We investigate whether the predictions of four different measures (proper time, scale factor cutoff, stationary and causal {diamond}) change continuously with the change of this parameter. We will show that {only} for the stationary measure the predictions change continuously. For the proper-time and the scale factor cutoff, the predictions are strongly discontinuous. For the causal diamond measure, the predictions are continuous only if the stage of the slow-roll inflation is sufficiently long.Comment: 9 pages, 4 figure

House of Commons Select Committee on Transport: Inquiry into Urban Congestion Charging

INTRODUCTION This evidence, submitted to the Select Committee for its inquiry into Urban Congestion Charging, is based on my research into the subject, and professional involvement in studies of methods for managing the demand for urban travel, over the last twenty years. In the 1970s I was responsible, within the Greater London Council, for their studies of the use of comprehensive parking control, physical restriction of road space, and supplementary licensing (a low technology method of congestion charging) as methods of traffic restraint. At the same time, I was an adviser to the World Bank in its study of Singapore's area licensing scheme which is still the only congestion charging system in operation. In the 1980s I was an adviser to the US Transport Research Board in its investigation of appropriate methods for managing urban traffic, and to The MVA Consultancy in its study of electronic road pricing for Hong Kong. Since 1987 I have been involved, as a director of The MVA Consultancy, in a series of integrated transport studies in London (for the London Planning Advisory Committee), Birmingham, Edinburgh, Bristol and Merseyside, each of which has investigated the role of congestion charging as part of a wider transport strategy. I am currently directing a programme of research, funded by the Engineering and Physical Sciences Research Council, which is assessing the relative impact on urban road networks of different methods of imposing congestion charging, on their own and in combination with traffic signal control and bus priorities. This research has used Cambridge and York as case studies. In addition, I am currently acting as one of the technical advisers to the Department of Transport's study of congestion charging in London. (Continues..

Implications of fisheries during the spawning season for the sustainable management and recovery of depleted fish stocks: a conceptual framework

Fishing during the spawning season may negatively affects the reproductive potential and reproductive dynamics of exploited fish stocks due to a variety of mechanisms such as the disturbance of the natural spawning behaviour, effects on the age, size and sex composition of the spawning population and effects on the population genetics. The effect may differ between species in relation to the spawning strategy and population dynamic characteristics. Based on first principles of reproductive biology, population biology and fishing methods, a theoretical framework is developed on the effects of fishing during the spawning period. This framework is used to structure a review of the available scientific evidence. Implications of the findings on the recovery of depleted fish stocks and the sustainability of exploitation will be discussed and illustrated for a selection of North Sea fish stocks (flatfish, roundfish and pelagic)

Integrated Transport Strategies: A New Initiaitve, or a Return to the 1960’s?

A recurring theme in the debate on urban transport policy in the last few years has been the appropriateness of developing Integrated Transport Strategies as a basis for identifying solutions to current and future urban transport problems. Their proponents, including a growing number of local authorities, see them as a means of ensuring that each element of transport policy complements the others. Those who argue against them, and particularly the Department of Transport, have likened them to the gramd and unattainable, blueprints produced by 1960s land use - transport studies. This paper draws on experience with such studies in London, Birmingham and Edinburgh to assess the strengths and weaknesses of the approach now being adopted, to suggest ways in which it might be further developed, and to identify, in the light of experience to date, those elements of policy which might most effectively contribute to the solution of transport problems

Origin of strange metallic phase in cuprate superconductors

The origin of strange metallic phase is shown to exist due to these two conditions---(i) the electrons are strongly interacting such that there are no band and Mott-Hubbard gaps, and (ii) the electronic energy levels are crossed in such a way that there is an electronic energy gap between two energy levels associated to two different wave functions. The theory is also exploited to explain (i) the upward- and downward-shifts in the $T$-linear resistivity curves, and (ii) the spectral weight transfer observed in the soft X-ray absorption spectroscopic measurements of the La-Sr-Cu-O Mott insulator.Comment: To be published in J. Supercond. Nov. Mag

Queue Management Project Model: Strategies for the Management of Queues at Upstream Junctions

This Working Paper is one of a series representing work under a SERC grant on queue management strategies for urban traffic control systems, whose objectives are:- (i)to generalise the strategies developed in an earlier study of queue management; (ii)to develop a computer graphics based representation of queue propagation and management; (iii)to test the strategies' applicability and performance in UK networks; (iv)to investigate their incorporation into standard signal optimisation programs. The study is based on earlier work in Bangkok (May et al, 1988) also funded by SERC, in which queue management measures were developed by trial and error to allow for the fact that queues from downstream junctions frequently blocked upstream junctions and could, as a result, unnecessarily obstruct crossing movements thereby reducing junction capacity and spreading congestion to other areas. The methods developed in that study involved:- (i)predicting the growth and decline of queues from downstream junctions; (ii)estimating the speeds of the starting and stopping waves which determine (i); (iii)identifying the most appropriate stage at the upstream junction in which queues should arrive; (iv)identifying the most appropriate time in that stage during which queues should be present; (v)adjusting the split between stages to allow for loss of throughput in blocked stages; (vi)adjusting the cycle time as necessary in the light of (v). It was steps (iii) and (iv) which involved the greatest element of trial and error, and it was accepted that further work was needed to identify alternative strategies for determining:- (i)during which stage to allow queues to block an upstream junction; (ii)how to adjust the stage timings at that junction to allow for the loss of capacity. This paper reviews these approaches and makes recommendations. It considers first of all, in Section 2, the options at an individual junction. It then considers in Section 3, the application of these options in a range of increasingly complex networks

Almost sure subexponential decay rates of scalar Ito-Volterra equations.

The paper studies the subexponential convergence of solutions of scalar Itˆo-Volterra equations. First, we consider linear equations with an instantaneous multiplicative noise term with intensity . If the kernel obeys lim t!1 k0(t)/k(t) = 0, and another nonexponential decay criterion, and the solution X tends to zero as t ! 1, then limsup t!1 log |X(t)| log(tk(t)) = 1 − (||), a.s. where the random variable (||) ! 0 as ! 1 a.s. We also prove a decay result for equations with a superlinear diffusion coefficient at zero. If the deterministic equation has solution which is uniformly asymptotically stable, and the kernel is subexponential, the decay rate of the stochastic problem is exactly the same as that of the underlying deterministic problem

Ferromagnetic properties of charged vector boson condensate

Bose-Einstein condensation of W bosons in the early universe is studied. It is shown that, in the broken phase of the standard electroweak theory, condensed W bosons form a ferromagnetic state with aligned spins. In this case the primeval plasma may be spontaneously magnetized inside macroscopically large domains and form magnetic fields which may be seeds for the observed today galactic and intergalactic fields. However, in a modified theory, e.g. in a theory without quartic self interactions of gauge bosons or for a smaller value of the weak mixing angle, antiferromagnetic condensation is possible. In the latter case W bosons form scalar condensate with macroscopically large electric charge density i.e. with a large average value of the bilinear product of W-vector fields but with microscopically small average value of the field itself.Comment: Some numerical estimates and discussions are added according to the referee's suggestions. This version is accepted for publication in JCA

Inflation with Ω≠1\Omega \not = 1

We discuss various models of inflationary universe with $\Omega \not = 1$. A homogeneous universe with $\Omega > 1$ may appear due to creation of the universe "from nothing" in the theories where the effective potential becomes very steep at large $\phi$, or in the theories where the inflaton field $\phi$ nonminimally couples to gravity. Inflation with $\Omega < 1$ generally requires intermediate first order phase transition with the bubble formation, and with a second stage of inflation inside the bubble. It is possible to realize this scenario in the context of a theory of one scalar field, but typically it requires artificially bent effective potentials and/or nonminimal kinetic terms. It is much easier to obtain an open universe in the models involving two scalar fields. However, these models have their own specific problems. We propose three different models of this type which can describe an open homogeneous inflationary universe.Comment: 29 pages, LaTeX, parameters of one of the models are slightly modifie