Decorating Random Quadrangulations

On various regular lattices (simple cubic, body centred cubic..) decorating an edge with an Ising spin coupled by bonds of strength L to the original vertex spins and competing with a direct anti-ferromagnetic bond of strength alpha L can give rise to three transition temperatures for suitable alpha. The system passes through ferromagnetic, paramagnetic, anti-ferromagnetic and paramagnetic phases respectively as the temperature is increased. For the square lattice on the other hand multiple decoration is required to see this effect. We note here that a single decoration suffices for the Ising model on planar random quadrangulations (coupled to 2D quantum gravity). Other random bipartite lattices such as the Penrose tiling are more akin to the regular square lattice and require multiple decoration to have any affect.Comment: 6 pages + 5 figure

Does perceived organisational support influence career intentions?:The qualitative stories shared by UK early career doctors

Our thanks to all those FP2 doctors who participated in the interviews. Our thanks also to the Foundation Programme Directorate staff in the Scotland Deanery, NHS Education for Scotland, for sending out the email correspondence to the two regions involved in the interviews. No patients or any members of the public were involved in this study. Funding: Our thanks go to NHS Education for Scotland for funding Gillian Scanlan’s programme of work through the Scottish Medical Education Research Consortium (SMERC) and for funding the open-access fee for this paper.Peer reviewedPublisher PD

Potts Models with (17) Invisible States on Thin Graphs

The order of a phase transition is usually determined by the nature of the symmetry breaking at the phase transition point and the dimension of the model under consideration. For instance, q-state Potts models in two dimensions display a second order, continuous transition for q = 2,3,4 and first order for higher q. Tamura et al recently introduced Potts models with "invisible" states which contribute to the entropy but not the internal energy and noted that adding such invisible states could transmute continuous transitions into first order transitions. This was observed both in a Bragg-Williams type mean-field calculation and 2D Monte-Carlo simulations. It was suggested that the invisible state mechanism for transmuting the order of a transition might play a role where transition orders inconsistent with the usual scheme had been observed. In this paper we note that an alternative mean-field approach employing 3-regular random ("thin") graphs also displays this change in the order of the transition as the number of invisible states is varied, although the number of states required to effect the transmutation, 17 invisible states when there are 2 visible states, is much higher than in the Bragg-Williams case. The calculation proceeds by using the equivalence of the Potts model with 2 visible and r invisible states to the Blume-Emery-Griffiths (BEG) model, so a by-product is the solution of the BEG model on thin random graphs.Comment: (2) Minor typos corrected, references update

Does initial postgraduate career intention and social demographics predict perceived career behaviour?:A national cross-sectional survey of UK postgraduate doctors

Acknowledgements: Our thanks to all those FP2 doctors who participated in the survey. Our thanks also to the Foundation Programme Directors across the UK for allowing permission to conduct research on this data set. No patients or any members of the public were involved in this study. Funding: Our thanks go to NHS Education for Scotland for funding Gillian Scanlan’s programme of work through the Scottish Medical Education Research Consortium (SMERC). Data sharing statement: The data reported is from the UKFPO dataset, and any data shared would need the permission of the UK Foundation Programme directorsPeer reviewedPublisher PD

The Gonihedric Ising Model and Glassiness

The Gonihedric 3D Ising model is a lattice spin model in which planar Peierls boundaries between + and - spins can be created at zero energy cost. Instead of weighting the area of Peierls boundaries as the case for the usual 3D Ising model with nearest neighbour interactions, the edges, or "bends" in an interface are weighted, a concept which is related to the intrinsic curvature of the boundaries in the continuum. In these notes we follow a roughly chronological order by first reviewing the background to the formulation of the model, before moving on to the elucidation of the equilibrium phase diagram by various means and then to investigation of the non-equilibrium, glassy behaviour of the model.Comment: To appear as Chapter 7 in Rugged Free-Energy Landscapes - An Introduction, Springer Lecture Notes in Physics, 736, ed. W. Janke, (2008

Modelling the Self-Assembly of Virus Capsids

We use computer simulations to study a model, first proposed by Wales [1], for the reversible and monodisperse self-assembly of simple icosahedral virus capsid structures. The success and efficiency of assembly as a function of thermodynamic and geometric factors can be qualitatively related to the potential energy landscape structure of the assembling system. Even though the model is strongly coarse-grained, it exhibits a number of features also observed in experiments, such as sigmoidal assembly dynamics, hysteresis in capsid formation and numerous kinetic traps. We also investigate the effect of macromolecular crowding on the assembly dynamics. Crowding agents generally reduce capsid yields at optimal conditions for non-crowded assembly, but may increase yields for parameter regimes away from the optimum. Finally, we generalize the model to a larger triangulation number T = 3, and observe more complex assembly dynamics than that seen for the original T = 1 model.Comment: 16 pages, 11 figure

Subsonic longitudinal aerodynamic characteristics and engine pressure distributions for an aircraft with an integrated scramjet designed for Mach 6 cruise

A 1/10-scale model of a proposed hypersonic aircraft with an integrated scramjet was tested. The investigation took place over a Mach number range from 0.2 to 0.7 and an angle of attack range from 2 deg to approximately 17 deg at a sideslip angle of 0 deg. The primary configuration variables studied were engine location, internal engine geometry, and external engine geometry. The results are presented without analysis

Variable renewal rate and growth properties of cell populations in colon crypts

A nonlinear mathematical model is used to investigate the time evolution of the cell populations in colon crypts (stem, semidifferentiated and fully differentiated cells). To mimic pathological alteration of the biochemical pathways leading to abnormal proliferative activity of the population of semidifferentiated cells their renewal rate is assumed to be dependent on the population size. Then, the effects of such perturbation on the population dynamics are investigated theoretically. Using both theoretical methods and numerical simulations it is shown that the increase in the renewal rate of semidifferentiated cells strongly impacts the dynamical behavior of the cell populations