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Full-Text Articles in Arts and Humanities

Dislocations Of Arbitrary Topology In Coulomb Eigenfunctions, Alberto Enciso, David James Hartley, Daniel Peralta-Salas Jan 2018

Dislocations Of Arbitrary Topology In Coulomb Eigenfunctions, Alberto Enciso, David James Hartley, Daniel Peralta-Salas

Senior Deputy Vice-Chancellor and Deputy Vice-Chancellor (Education) - Papers

For any finite link L in R3 we prove the existence of a complex-valued eigenfunction of the Coulomb Hamiltonian such that its nodal set contains a union of connected components diffeomorphic to L. This problem goes back to Berry, who constructed such eigenfunctions in the case where L is the trefoil knot or the Hopf link and asked the question about the general result.


A Problem Of Berry And Knotted Zeros In The Eigenfunctions Of The Harmonic Oscillator, Alberto Enciso, David James Hartley, Daniel Peralta-Salas Jan 2018

A Problem Of Berry And Knotted Zeros In The Eigenfunctions Of The Harmonic Oscillator, Alberto Enciso, David James Hartley, Daniel Peralta-Salas

Senior Deputy Vice-Chancellor and Deputy Vice-Chancellor (Education) - Papers

European Mathematical Society 2018 We prove that, given any finite link L in R 3 , there is a high-energy complex-valued eigenfunction of the harmonic oscillator such that its nodal set contains a union of connected components diffeomorphic to L. This solves a problem of Berry on the existence of knotted zeros in bound states of a quantum system.


Motion By Mixed Volume Preserving Curvature Functions Near Spheres, David James Hartley Jan 2015

Motion By Mixed Volume Preserving Curvature Functions Near Spheres, David James Hartley

Senior Deputy Vice-Chancellor and Deputy Vice-Chancellor (Education) - Papers

In this paper we investigate the flow of hypersurfaces by a class of symmetric functions of the principal curvatures with a mixed volume constraint. We consider compact hypersurfaces without boundary that can be written as a graph over a sphere. The linearisation of the resulting fully nonlinear PDE is used to prove a short-time existence theorem for hypersurfaces that are sufficiently close to a sphere and, using centre manifold analysis, the stability of the sphere as a stationary solution to the flow is determined. We will find that for initial hypersurfaces sufficiently close to a sphere, the flow will exist ...


The Effect Of Detraining On Muscle Strength And Cross-Sectional Area Following Unilateral Resistance Training, Herbert Groeller, John A. Sampson Jan 2009

The Effect Of Detraining On Muscle Strength And Cross-Sectional Area Following Unilateral Resistance Training, Herbert Groeller, John A. Sampson

Faculty of Health and Behavioural Sciences - Papers (Archive)

Muscle strength appears well preserved following short periods of detraining, despite a decline in muscle cross-sectional area and muscle activation. PURPOSE: This study determined the effect a 12-week unilateral elbow flexor resistance training regimen followed by 8 weeks of detraining on muscle cross-sectional area, muscle activation, and dynamic and static strength in trained and non-exercising contralateral limbs. METHODS: Ten males volunteered for the investigation and completed a 4-week pre-treatment training period (50-80%1RM) prior to commencing the experimental resistance training regimen. Subjects attended 3 sessions per week over 12 weeks of experimental training wherein they exercised at 85%1RM. Each ...