Analysis of an FRW cosmological model

The Einstein field equations for the Friedmann universe reduce to a system of three first-order equations for the space-like components and a constraint from the temporal component. We analyse the system from the viewpoints of symmetry and singularity analyses. The solutions of particular relevance to Cosmology are highlighted.      

First integrals versus configurational invariants and a weak form of complete integrability

A confusion over the concept of first integrals, which has been created in a recent paper by Hall [13] is clarified. The clear distinction between first integrals and functions which are first integrals only on a specific, fixed hypersurface is discussed. Hall's terminology of configurational invariants is adopted for the latter case. The possible relevance of knowing configurational invariants for a Hamiltonian system is illustrated by results concerning a weak form of the theory on complete integrability.     

Creating permanent 3D arrangements of isolated cells using holographic optical tweezers

We report the creation of permanent 3D configurations of cells, at predefined positions, within a gelatin matrix. The technique used holographic optical tweezers to manipulate individual E. coli within a solution comprising monomer precursors. The matrix was then set and after the laser beam was removed, we were able to demonstrate that the structures remained intact for many days. We were also able to demonstrate that, in the presence of appropriate nutrients, the E. coli survived within the gelatin matrix for several days. The technique could have a number of potential future applications, including the arrangement of a variety of different cell types in complex architectures, as motifs for promoting tissue differentiation and growth within the field of cell engineering.     

Cavity QED with quantized center of mass motion

We investigate the quantum fluctuations of a single atom in a weakly driven cavity, where the center of mass motion of the atom is quantized in one dimension. We present analytic results for the second order intensity correlation function g((2))(tau) and the intensity-field correlation function h(theta)(tau), for transmitted light in the weak driving field limit. We find that the coupling of the center of mass motion to the intracavity field mode can be deleterious to nonclassical effects in photon statistics and field-intensity correlations, and compare the use of trapped atoms in a cavity to atomic beams.     

Initial attempts at directly detecting alpha wave activity in the brain using MRI

The “direct detection” of neuronal activity by MRI could offer improved spatial and temporal resolution compared to the blood oxygenation level-dependent (BOLD) effect. Here we describe initial attempts to use MRI to detect directly the neuronal currents resulting from spontaneous alpha wave activity, which have previously been shown to generate the largest extracranial magnetic fields. Experiments were successfully carried out on four subjects at 3 T. A single slice was imaged at a rate of 25 images per second under two conditions. The first (in darkness with eyes-closed) was chosen to promote alpha wave activity, while the second (eyes-open viewing a visual stimulus) was chosen to suppress it. The fluctuations of the phase and magnitude of the resulting MR image data were frequency analysed, and tested for the signature of both alpha wave activity and neuronal activity evoked by the visual stimulus.

Regions were found that consistently showed elevated power in fluctuations of the phase of the MR signal, in the frequency range of alpha waves, during the eyes-closed condition. It was conservatively assumed that if oscillations occurred at the same frequency in the magnitude signal from the same region or at the same frequency in the phase or magnitude signal from other regions overlying large vessels or cerebrospinal fluid (CSF), then the phase changes were not due to neuronal activity related to alpha waves. Using these criteria the data obtained were consistent with direct detection of alpha wave activity in three of the four volunteers. No significant MR signal fluctuations due to evoked activity were identified.     

The quantitative 19F-imaging of albumin at 1.5 T: a potential in-vivo tool

19F-MR-imaging has been used to quantitate albumin concentration in a phantom at 1.5 T. The experimentally derived relationship between albumin concentration and the T1 relaxation time of a fluorinated marker, tetrafluorosuccinic acid (TFSA) was used to calculate the albumin concentration from a quantitative 19F T1 map acquired using a gradient echo sequence. There was close correlation between calculated and actual BSA concentrations (r = 0.99, SE = 0.15). The potentially interfering effect of paramagnetic species on T1 relaxation times was also investigated. Relaxivity data show that albumin concentration measurements should be performed prior to any contrast agent administration.     

Pattern formation in a simple chemical system with general orders of autocatalysis and decay. I. Stability analysis

In this preliminary paper we introduce a mathematical model based on an autocatalytic reaction scheme with termination, and general reaction orders. Rigorous stability analysis and numerical solutions are presented which illustrate that the problem can for certain parameter values admit a stable stationary pattern in the concentration of the autocatalyst and reactant. This pattern forms at the rear of a permanent form travelling wave or pulse solution.     

Symmetry and singularity properties of second-order ordinary differential equations of Lie's type III

We extend the work of Abraham-Shrauner [B. Abraham-Shrauner, Hidden symmetries and linearization of the modified Painlevé-Ince equation, J. Math. Phys. 34 (1993) 4809-4816] on the linearization of the modified Painlevé-Ince equation to a wider class of nonlinear second-order ordinary differential equations invariant under the symmetries of time translation and self-similarity. In the process we demonstrate a remarkable connection with the parameters obtained in the singularity analysis of this class of equations.