Ergodic properties of a model for turbulent dispersion of inertial particles

We study a simple stochastic differential equation that models the dispersion of close heavy particles moving in a turbulent flow. In one and two dimensions, the model is closely related to the one-dimensional stationary Schroedinger equation in a random delta-correlated potential. The ergodic properties of the dispersion process are investigated by proving that its generator is hypoelliptic and using control theory

Gaussian process manifold interpolation for probabilistic atrial activation maps and uncertain conduction velocity

In patients with atrial fibrillation, local activation time (LAT) maps are routinely used for characterizing patient pathophysiology. The gradient of LAT maps can be used to calculate conduction velocity (CV), which directly relates to material conductivity and may provide an important measure of atrial substrate properties. Including uncertainty in CV calculations would help with interpreting the reliability of these measurements. Here, we build upon a recent insight into reduced-rank Gaussian processes (GPs) to perform probabilistic interpolation of uncertain LAT directly on human atrial manifolds. Our Gaussian process manifold interpolation (GPMI) method accounts for the topology of the atrium, and allows for calculation of statistics for predicted CV. We demonstrate our method on two clinical cases, and perform validation against a simulated ground truth. CV uncertainty depends on data density, wave propagation direction and CV magnitude. GPMI is suitable for probabilistic interpolation of other uncertain quantities on non-Euclidean manifolds. This article is part of the theme issue ‘Uncertainty quantification in cardiac and cardiovascular modelling and simulation’

Researching trust in the police and trust in justice: a UK perspective

This paper describes the immediate and more distant origins of a programme of comparative research that is examining cross-national variations in public trust in justice and in the police. The programme is built around a module of the fifth European Social Survey, and evolved from a study funded by the European Commission. The paper describes the conceptual framework within which we are operating – developed in large measure from theories of procedural justice. It reviews some of the methodological issues raised by the use of sample surveys to research issues of public trust in the police, public perceptions of institutional legitimacy and compliance with the law. Finally it gives a flavour of some of the early findings emerging from the programme

Raising the participation age in historical perspective : Policy learning from the past?

The raising of the participation age (RPA) to 17 in 2013 and 18 in 2015 marks a historic expansion of compulsory education. Despite the tendency of New Labour governments to eschew historical understanding and explanation, RPA was conceived with the benefit of an analysis of previous attempts to extend compulsion in schooling. This paper assesses the value of a historical understanding of education policy. The period from inception to the projected implementation of RPA is an extended one which has crossed over the change of government, from Labour to Coalition, in 2010. The shifting emphases and meanings of RPA are not simply technical issues but connect to profound historical and social changes. An analysis of the history of the raising of the school leaving age reveals many points of comparison with the contemporary situation. In a number of key areas it is possible to gain insights into the ways in which the study of the past can help to comprehend the present: the role of human capital, the structures of education, in curriculum development and in terms of preparations for change

Fluctuation Relations for Diffusion Processes

The paper presents a unified approach to different fluctuation relations for classical nonequilibrium dynamics described by diffusion processes. Such relations compare the statistics of fluctuations of the entropy production or work in the original process to the similar statistics in the time-reversed process. The origin of a variety of fluctuation relations is traced to the use of different time reversals. It is also shown how the application of the presented approach to the tangent process describing the joint evolution of infinitesimally close trajectories of the original process leads to a multiplicative extension of the fluctuation relations.Comment: 38 page

Perturbation theory for large Stokes number particles in random velocity fields

We derive a perturbative approach to study, in the large inertia limit, the dynamics of solid particles in a smooth, incompressible and finite-time correlated random velocity field. We carry on an expansion in powers of the inverse square root of the Stokes number, defined as the ratio of the relaxation time for the particle velocities and the correlation time of the velocity field. We describe in this limit the residual concentration fluctuations of the particle suspension, and determine the contribution to the collision statistics produced by clustering. For both concentration fluctuations and collision velocities, we analyze the differences with the compressible one-dimensional case.Comment: Latex, 12 pages, 2 eps figures include

Two-sided Grassmann-Rayleigh quotient iteration

The two-sided Rayleigh quotient iteration proposed by Ostrowski computes a pair of corresponding left-right eigenvectors of a matrix $C$. We propose a Grassmannian version of this iteration, i.e., its iterates are pairs of $p$-dimensional subspaces instead of one-dimensional subspaces in the classical case. The new iteration generically converges locally cubically to the pairs of left-right $p$-dimensional invariant subspaces of $C$. Moreover, Grassmannian versions of the Rayleigh quotient iteration are given for the generalized Hermitian eigenproblem, the Hamiltonian eigenproblem and the skew-Hamiltonian eigenproblem.Comment: The text is identical to a manuscript that was submitted for publication on 19 April 200

Turnover of passerine birds on islands in the Aegean Sea (Greece)

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73442/1/j.1365-2699.2007.01695.x.pd