Convergence of the mass-transport steepest descent scheme for the sub-critical Patlak-Keller-Segel model

Variational steepest descent approximation schemes for the modified Patlak-Keller-Segel equation with a logarithmic interaction kernel in any dimension are considered. We prove the convergence of the suitably interpolated in time implicit Euler scheme, defined in terms of the Euclidean Wasserstein distance, associated to this equation for sub-critical masses. As a consequence, we recover the recent result about the global in time existence of weak-solutions to the modified Patlak-Keller-Segel equation for the logarithmic interaction kernel in any dimension in the sub-critical case. Moreover, we show how this method performs numerically in one dimension. In this particular case, this numerical scheme corresponds to a standard implicit Euler method for the pseudo-inverse of the cumulative distribution function. We demonstrate its capabilities to reproduce easily without the need of mesh-refinement the blow-up of solutions for super-critical masses.

Evaluation of the reconstruction limits of a frequency-independent crosshole georadar waveform inversion scheme in the presence of dispersion

Waveform tomographic imaging of crosshole georadar data is a powerful method to investigate the shallow subsurface because of its ability to provide images of pertinent petrophysical parameters with extremely high spatial resolution. All current crosshole georadar waveform inversion strategies are based on the assumption of frequency-independent electromagnetic constitutive parameters. However, in reality, these parameters are known to be frequency-dependent and complex and thus recorded georadar data may show significant dispersive behavior. In this paper, we evaluate synthetically the reconstruction limits of a recently published crosshole georadar waveform inversion scheme in the presence of varying degrees of dielectric dispersion. Our results indicate that, when combined with a source wavelet estimation procedure that provides a means of partially accounting for the frequency-dependent effects through an "effective" wavelet, the inversion algorithm performs remarkably well in weakly to moderately dispersive environments and has the ability to provide adequate tomographic reconstructions.

Taxation and Total Government Take from the UK Continental Shelf (UKCS) Following Phase 3 of the European Emissions Trading Scheme (EU ETS)

NORTH SEA STUDY OCCASIONAL PAPER No. 117

The Effects of the European Emissions Trading Scheme (EU ETS) on Activity in the UK Continental Shelf (UKCS) and CO2 Leakage

NORTH SEA STUDY OCCASIONAL PAPER No. 115

Home Childcarer Approval Scheme Application Form HCC1 (PDF 62.3KB)

Home Childcarer Approval Scheme Application Form HCC1

Early Years Home Childcare Approval Scheme FAQ (PDF 40.2KB)

Early Years Home Childcare Approval Scheme - frequently asked questions

Craigavon & Banbridge Community HSS Trust - Primary Care Mental Health Services Triage Pilot Scheme (PDF 266 KB)

Craigavon & Banbridge Community HSS Trust's final report on Primary Care Mental Health Services Triage Pilot Scheme. Part of the Department's redesign of community nursing project.

HPSS Consultant and Distinction Awards Scheme (DMSAC)

HPSS Consultant and Distinction Awards Scheme (DMSAC)

New HPSS Clinical Excellence Awards Scheme (PDF 42 KB)

New HPSS Clinical Excellence Awards Scheme

Literature Review: Equality of Opportunity in Relation to the DHSSPS Draft Equality Scheme

This review of the literature on equality of opportunity issues was commissioned by the Department of Public Health, Social Sevices and Public Safety.