Superconducting Correlations in Metallic Nanoparticles: Exact Solution of the BCS Model by the Algebraic Bethe Ansatz

Superconducting pairing of electrons in nanoscale metallic particles with discrete energy levels and a fixed number of electrons is described by the reduced Bardeen, Cooper, and Schrieffer model Hamiltonian. We show that this model is integrable by the algebraic Bethe ansatz. The eigenstates, spectrum, conserved operators, integrals of motion, and norms of wave functions are obtained. Furthermore, the quantum inverse problem is solved, meaning that form factors and correlation functions can be explicitly evaluated. Closed form expressions are given for the form factors and correlation functions that describe superconducting pairing.

Activation of the human diaphragm during a repetitive postural task

1. The co-ordination between respiratory and postural functions of the diaphragm was investigated during repetitive upper Limb movement. It was hypothesised that diaphragm activity would occur either tonically or phasically in association with the forces from each movement and that this activity would combine with phasic respiratory activity. 2. Movements of the upper limb and ribcage were measured while standing subjects performed repetitive upper limb movements 'as fast as possible'. Electromyographic (EMG) recordings of the costal diaphragm were made using intramuscular electrodes in four subjects. Surface electrodes were placed over the deltoid and erector spinae muscles. 3. In contrast to standing at rest, diaphragm activity was present throughout expiration at 78 +/- 17% (mean +/- S.D.) of its peak inspiratory magnitude during repeated upper limb movement. 4. Bursts of deltoid and erector spinae EMG activity occurred at the Limb movement frequency (similar to 2.9 Hz). Although the majority of diaphragm EMG power was at the respiratory frequency (similar to 0.4 Hz), a peak was also present at the movement frequency. This finding was corroborated by averaged EMG activity triggered from upper limb movement. In addition, diaphragm EMG activity was coherent with ribcage motion at the respiratory frequency and with upper limb movement at the movement frequency. 5. The diaphragm response was similar when movement was performed while sitting. In addition, when subjects moved with increasing frequency the peak upper limb acceleration correlated with diaphragm EMG amplitude. These findings support the argument that diaphragm contraction is related to trunk control. 6. The results indicate that activity of human phrenic motoneurones is organised such that it contributes to both posture and respiration during a task which repetitively challenges trunk posture.

Functional MR Imaging of visuo-spatial network in Autism Spectrum Disorder

Individuals with Autism Spectrum Disorder (ASD) are generally thought to have impaired attentional and executive function upon which all their cognitive and behaviour functions are based. Mental Rotation is a recognized visuo-spatial task, involving spatial working memory, known to involve activation in the fronto-parietal networks. To elucidate the functioning of fronto-parietal networks in ASD, the aim of this study was to use fMRI techniques with a mental rotation task, to characterize the underlying functional neural system. Sixteen male participants (seven highfunctioning autism or Asperger's syndrome; nine ageand performance IQ-matched controls) underwent fMRI. Participants were presented with 18 baseline and 18 rotation trials, with stimuli rotated 3- dimensionaUy (45°-180°). Data were acquired on a 3- Tesla scanner. The most widely accepted area reported to be involved in processing of visuo-spatial information. Posterior Parietal Cortex, was found to be activated in both groups, however, the ASD group showed decreased activation in cortical and subcortical frontal structures that are highly interconnected, including lateral and medial Brodmann area 6, frontal eye fields, caudate, dorsolateral prefrontal cortex and anterior cingulate. The suggested connectivity between these regions indicates that one or more circuits are impaired as a result of the disorder. In future it is hoped that we are able to identify the possible point of origin of this dysfunction, or indeed if the entire network is dysfunctional.

Three-dimensional orthotropic viscoelastic finite element model of a human ligament

Ligaments undergo finite strain displaying hyperelastic behaviour as the initially tangled fibrils present straighten out, combined with viscoelastic behaviour (strain rate sensitivity). In the present study the anterior cruciate ligament of the human knee joint is modelled in three dimensions to gain an understanding of the stress distribution over the ligament due to motion imposed on the ends, determined from experimental studies. A three dimensional, finite strain material model of ligaments has recently been proposed by Pioletti in Ref. [2]. It is attractive as it separates out elastic stress from that due to the present strain rate and that due to the past history of deformation. However, it treats the ligament as isotropic and incompressible. While the second assumption is reasonable, the first is clearly untrue. In the present study an alternative model of the elastic behaviour due to Bonet and Burton (Ref. [4]) is generalized. Bonet and Burton consider finite strain with constant modulii for the fibres and for the matrix of a transversely isotropic composite. In the present work, the fibre modulus is first made to increase exponentially from zero with an invariant that provides a measure of the stretch in the fibre direction. At 12% strain in the fibre direction, a new reference state is then adopted, after which the material modulus is made constant, as in Bonet and Burton's model. The strain rate dependence can be added, either using Pioletti's isotropic approximation, or by making the effect depend on the strain rate in the fibre direction only. A solid model of a ligament is constructed, based on experimentally measured sections, and the deformation predicted using explicit integration in time. This approach simplifies the coding of the material model, but has a limitation due to the detrimental effect on stability of integration of the substantial damping implied by the nonlinear dependence of stress on strain rate. At present, an artificially high density is being used to provide stability, while the dynamics are being removed from the solution using artificial viscosity. The result is a quasi-static solution incorporating the effect of strain rate. Alternate approaches to material modelling and integration are discussed, that may result in a better model.

Winding patterns for actively shielded shim coils with asymmetric target-fields

A method is presented for calculating the currents and winding patterns required to design independent zonal and tesseral shim coils for magnetic resonance imaging. Both actively shielded and unshielded configurations are considered, and the region of interest can be located asymmetrically with respect to the coil's length. Streamline, target-field and Fourier-series methods are utilized. The desired target-field is specified at two cylindrical radii, on and inside a circular conducting cylinder of length 2L and radius a. The specification is over some asymmetric portion pL < z < qL of the coil's length (-1 < p < q < 1). Arbitrary functions are used in the outer sections, -L < z < pL and qL < z < L, to ensure continuity of the magnetic field across the entire length of the coil. The entire field is then periodically extended as a half-range cosine Fourier series about either end of the coil. The resultant Fourier coefficients are then substituted into the Fourier-series expressions for the internal and external magnetic fields, and current densities and stream functions on both the primary coil and shield. A contour plot of the stream function directly gives the required coil winding patterns. Spherical harmonic analysis and shielding analysis on field calculations from a ZX shim coil indicate that example designs and theory are well matched.