Second order splitting of a class of fourth order PDEs with point constraints

We formulate a well-posedness and approximation theory for a class of generalised saddle point problems with a specific form of constraints. In this way we develop an approach to a class of fourth order elliptic partial differential equations with point constraints using the idea of splitting into coupled second order equations. An approach is formulated using a penalty method to impose the constraints. Our main motivation is to treat certain fourth order equations involving the biharmonic operator and point Dirichlet constraints for example arising in the modelling of biomembranes on curved and flat surfaces but the approach may be applied more generally. The theory for well-posedness and approximation is presented in an abstract setting. Several examples are described together with some numerical experiments

A mixed-mode shell-model theory for nuclear structure studies

We introduce a shell-model theory that combines traditional spherical states, which yield a diagonal representation of the usual single-particle interaction, with collective configurations that track deformations, and test the validity of this mixed-mode, oblique basis shell-model scheme on $^{24}$Mg. The correct binding energy (within 2% of the full-space result) as well as low-energy configurations that have greater than 90% overlap with full-space results are obtained in a space that spans less than 10% of the full space. The results suggest that a mixed-mode shell-model theory may be useful in situations where competing degrees of freedom dominate the dynamics and full-space calculations are not feasible.Comment: 20 pages, 8 figures, revtex 12p

Exact Solution of the Isovector Proton Neutron Pairing Hamiltonian

The complete exact solution of the T=1 neutron-proton pairing Hamiltonian is presented in the context of the SO(5) Richardson-Gaudin model with non-degenerate single-particle levels and including isospin-symmetry breaking terms. The power of the method is illustrated with a numerical calculation for $^{64}$Ge for a $pf+g_{9/2}$ model space which is out of reach of modern shell-model codes.Comment: To be published by Physical Review Letter

A rapid perturbation procedure for determining nonlinear flow solutions: Application to transonic turbomachinery flows

Perturbation procedures and associated computational codes for determining nonlinear flow solutions were developed to establish a method for minimizing computational requirements associated with parametric studies of transonic flows in turbomachines. The procedure that was developed and evaluated was found to be capable of determining highly accurate approximations to families of strongly nonlinear solutions which are either continuous or discontinuous, and which represent variations in some arbitrary parameter. Coordinate straining is employed to account for the movement of discontinuities and maxima of high gradient regions due to the perturbation. The development and results reported are for the single parameter perturbation problem. Flows past both isolated airfoils and compressor cascades involving a wide variety of flow and geometry parameter changes are reported. Attention is focused in particular on transonic flows which are strongly supercritical and exhibit large surface shock movement over the parametric range studied; and on subsonic flows which display large pressure variations in the stagnation and peak suction pressure regions. Comparisons with the corresponding 'exact' nonlinear solutions indicate a remarkable accuracy and range of validity of such a procedure

U(3) and Pseudo-U(3) Symmetry of the Relativistic Harmonic Oscillator

We show that a Dirac Hamiltonian with equal scalar and vector harmonic oscillator potentials has not only a spin symmetry but an U(3) symmetry and that a Dirac Hamiltonian with scalar and vector harmonic oscillator potentials equal in magnitude but opposite in sign has not only a pseudospin symmetry but a pseudo-U(3) symmetry. We derive the generators of the symmetry for each case.Comment: 8 pages, 0 figures, pusblished in Physical Review Letters 95, 252501 (2005

Development of a multiple-parameter nonlinear perturbation procedure for transonic turbomachinery flows: Preliminary application to design/optimization problems

An investigation was conducted to continue the development of perturbation procedures and associated computational codes for rapidly determining approximations to nonlinear flow solutions, with the purpose of establishing a method for minimizing computational requirements associated with parametric design studies of transonic flows in turbomachines. The results reported here concern the extension of the previously developed successful method for single parameter perturbations to simultaneous multiple-parameter perturbations, and the preliminary application of the multiple-parameter procedure in combination with an optimization method to blade design/optimization problem. In order to provide as severe a test as possible of the method, attention is focused in particular on transonic flows which are highly supercritical. Flows past both isolated blades and compressor cascades, involving simultaneous changes in both flow and geometric parameters, are considered. Comparisons with the corresponding exact nonlinear solutions display remarkable accuracy and range of validity, in direct correspondence with previous results for single-parameter perturbations

The long gamma-ray burst rate and the correlation with host galaxy properties

To answer questions on the start and duration of the epoch of reionisation, periods of galaxy mergers and properties of other cosmological encounters, the cosmic star formation history (CSFH), is of fundamental importance. Using the association of long gamma-ray bursts (LGRBs) with the death of massive stars and their ultra-luminous nature, the CSFH can be probed to higher redshifts than current conventional methods. Unfortunately, no consensus has been reached on the manner in which the LGRB rate (LGRBR) traces the CSFH, leaving many of the questions mentioned mostly unexplored by this method. Observations by the GRB NIR detector (GROND) over the past 4 years have, for the first time, acquired highly complete LGRB samples. Driven by these completeness levels and new evidence of LGRBs also occurring in more massive and metal rich galaxies than previously thought, the possible biases of the LGRBR-CSFH connection are investigated over a large range of galaxy properties. The CSFH is modelled using empirical fits to the galaxy mass function and galaxy star formation rates. Biasing the CSFH by metallicity cuts, mass range boundaries, and other unknown redshift dependencies, a LGRBR is generated and compared to the highly complete GROND sample. It is found that there is no strong preference for a metallicity cut or fixed galaxy mass boundaries and that there are no unknown redshift effects, in contrast to previous work which suggest values of Z/Z_sun~0.1-0.3. From the best-fit models, we predict that ~1.2% of the LGRB burst sample exists above z=6. The linear relationship between the LGRBR and the CSFH suggested by our results implies that redshift biases present in previous LGRB samples significantly affect the inferred dependencies of LGRBs on their host galaxy properties. Such biases can lead to, e.g., an interpretation of metallicity limitations and evolving LGRB luminosity functions.Comment: 15 pages, 14 figures, 7 tables, accepted for publication in Astronomy & Astrophysic

A problem structuring method for ecosystem-based management : the DPSIR modelling process

The purpose of this paper is to learn from Complex Adaptive Systems (CAS) theory to inform the development of Problem Structuring Methods (PSMs) both in general and in the specific context of marine management. The focus on marine management is important because it is concerned with a CAS (formed through the interconnection between natural systems, designed systems and social systems) which exemplifies their particularly ‘wicked' nature. Recognition of this compels us to take seriously the need to develop tools for knowledge elicitation and structuring which meet the demands of CAS. In marine management, chief among those tools is the DPSIR (Drivers - Pressures - State Changes - Impacts - Responses) model and, although widely applied, the extent to which it is appropriate for dealing with the demands of a CAS is questionable. Such questioning is particularly pertinent in the context of the marine environment where there is a need to not only recognise a broad range of stakeholders (a question of boundary critique) but also to manage competing knowledge (economic, local and scientific) and value claims. Hence this paper emphasises how a CAS perspective might add impetus to the development of a critical perspective on DPSIR and PSM theory and practice to promote a more systemic view of decision-making and policy development

Diversity, Dilemmas and Transformation in Post-Compulsory Education: an Introduction to the Special Issue on Work Based Research

As governments recognize the central place of post-compulsory education in regenerating and modernizing the economic and social fabric of society (BIS 2008), it is appropriate for us as educational researchers to question whether this recognition beckons a different role for research in post-compulsory education. Much of this research is work based, using a broad interpretation of this term, and the majority of articles received by this journal (though the proportion published is a lower one) reflect this balance. Work based research in education poses particular challenges for the researcher and the practitioner, whether the focus is practitioner research, in which case the dilemmas can centre on potential role conflict between practitioner and researcher roles, or whether the work based research is observational – analyzing others’ professional practice, in which case the dilemmas can centre on power relations between researcher and researched, the politics of research, and ethical questions around care for participants and the degree of their involvement or non-involvement in the total research enterprise. This article reviews the prospects for work based research in post-compulsory education and introduces the articles in this special issue