Aharonov-Bohm scattering on a cone

The Aharonov-Bohm scattering amplitude is calculated in the context of planar gravity with localized sources which also carry a magnetic flux. These sources cause space-time to develop conical singularities at their location, thus introducing novel effects in the scattering of electrically charged particles. The behaviour of the wave function in the proximity of the classical scattering directions is analyzed by means of an asymptotic expansion previously introduced by the author. It is found that, in contrast with the Aharonov-Bohm effect in flat space, integer values of the numerical flux can produce observable effects.Comment: 6 pages, 1 figur

Spin and abelian electromagnetic duality on four-manifolds

We investigate the electromagnetic duality properties of an abelian gauge theory on a compact oriented four-manifold by analysing the behaviour of a generalised partition function under modular transformations of the dimensionless coupling constants. The true partition function is invariant under the full modular group but the generalised partition function exhibits more complicated behaviour depending on topological properties of the four-manifold concerned. It is already known that there may be "modular weights" which are linear combinations of the Euler number and Hirzebruch signature of the four-manifold. But sometimes the partition function transforms only under a subgroup of the modular group (the Hecke subgroup). In this case it is impossible to define real spinor wave functions on the four-manifold. But complex spinors are possible provided the background magnetic fluxes are appropriately fractional rather that integral. This gives rise to a second partition function which enables the full modular group to be realised by permuting the two partition functions, together with a third. Thus the full modular group is realised in all cases. The demonstration makes use of various constructions concerning integral lattices and theta functions that seem to be of intrinsic interest.Comment: 29 pages, Plain Te

Towards comprehensive characterisation and modelling of the forming and wrinkling mechanics of engineering fabrics

Through a combination of direct measurement and inverse modelling, a route to characterising the main mechanical forming properties of engineering fabric is demonstrated. The process involves just two experimental tests, a cantilever bending test and a modified version of the uniaxial bias extension test. The mechanical forming properties of a twill weave carbon fabric have been determined, including estimates of the in-plane bending stiffness and the torsional stiffness of a sheared fabric. As a result of measuring and incorporating all the main mechanical properties of the fabric in forming simulations (tensile, shear, out-of-plane bending, in-plane bending & torsion), the specimen size-dependent shear kinematics and wrinkling response measured in experiments, is faithfully reproduced in simulations of the uniaxial bias extension (UBE) test

Numerical evaluation of three non-coaxial kinematic models using the distinct element method for elliptical granular materials

This is the accepted version of the following article: [Jiang, M. J., Liu, J. D., and Arroyo, M. (2016) Numerical evaluation of three non-coaxial kinematic models using the distinct element method for elliptical granular materials. Int. J. Numer. Anal. Meth. Geomech., 40: 2468–2488. doi: 10.1002/nag.2540.], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nag.2540/fullThis paper presents a numerical evaluation of three non-coaxial kinematic models by performing Distinct Element Method (DEM) simple shear tests on specimens composed of elliptical particles with different aspect ratios of 1.4 and 1.7. The models evaluated are the double-shearing model, the double-sliding free-rotating model and the double slip and rotation rate model (DSR2 model). Two modes of monotonic and cyclic simple shear tests were simulated to evaluate the role played by the inherent anisotropy of the specimens. The main findings are supported by all the DEM simple shear tests, irrespective of particle shape, specimen density or shear mode. The evaluation demonstrates that the assumption in the double-shearing model is inconsistent with the DEM results and that the energy dissipation requirements in the double-sliding free-rotating model appear to be too restrictive to describe the kinematic flow of elliptical particle systems. In contrast, the predictions made by the DSR2 model agree reasonably well with the DEM data, which demonstrates that the DSR2 model can effectively predict the non-coaxial kinematic behavior of elliptical particle systems.Peer ReviewedPostprint (author's final draft

Large Softly broken N=2 QCD

We analyze the possible soft breaking of $N=2$ supersymmetric Yang-Mills theory with and without matter flavour preserving the analyticity properties of the Seiberg-Witten solution. For small supersymmetry breaking parameter with respect to the dynamical scale of the theory we obtain an exact expression for the effective potential. We describe in detail the onset of the confinement transition and some of the patterns of chiral symmetry breaking. If we extrapolate the results to the limit where supersymmetry decouples, we obtain hints indicating that perhaps a description of the QCD vacuum will require the use of Lagrangians containing simultaneously mutually non-local degrees of freedom (monopoles and dyons).Comment: 40 pages, LaTeX, 13 figures, uses epsf.st

Blackhole/String Transition for the Small Schwarzschild Blackhole of AdS5×S5AdS_5 \times S^5 and Critical Unitary Matrix Models

In this paper we discuss the blackhole-string transition of the small Schwarzschild blackhole of $AdS_5 \times S^5$ using the AdS/CFT correspondence at finite temperature. The finite temperature gauge theory effective action, at weak {\it and} strong coupling, can be expressed entirely in terms of constant Polyakov lines which are $SU (N)$ matrices. In showing this we have taken into account that there are no Nambu-Goldstone modes associated with the fact that the 10 dimensional blackhole solution sits at a point in $S^5$. We show that the phase of the gauge theory in which the eigenvalue spectrum has a gap corresponds to supergravity saddle points in the bulk theory. We identify the third order $N = \infty$ phase transition with the blackhole-string transition. This singularity can be resolved using a double scaling limit in the transition region where the large N expansion is organized in terms of powers of $N^{-2/3}$. The $N = \infty$ transition now becomes a smooth crossover in terms of a renormalized string coupling constant, reflecting the physics of large but finite N. Multiply wound Polyakov lines condense in the crossover region. We also discuss the implications of our results for the resolution of the singularity of the Lorenztian section of the small Schwarzschild blackhole.Comment: 44 pages, Minor changes,the submitted version in the journa

Use of tire derived aggregate in tunnel cut-and-cover

A case-history is reported in which tire derived aggregate (TDA) was successfully applied to reduce the weight of fill upon a cut-and-cover railway tunnel. Subsequent 3D numerical analyses are used to explore the effect of different assumptions about the constitutive model of the TDA material. Alternative dispositions of TDA around the tunnel section are also examined. Reductions of up to 60% in lining bending moment may be achieved. For the case analyzed the elastic description of the TDA has little influence on tunnel lining loads, although is important for fill settlement estimates.Peer ReviewedPostprint (author's final draft