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Zhu Y.,Hong Kong University of Science and Technology | Chapman S.J.,Mathematical Institute andrew Wiles Building
Materials Science and Engineering A | Year: 2013

The motion of gliding screw dislocation segments in channel-veins and persistent slip band structure is analysed mathematically and the shape of these segments is determined. The model provides a possible explanation of the "length effect" of such dislocation segments observed in magnesium. Finally, the possible implications for the cross-slip of screw segments in fatigue testing are discussed. © 2013 Elsevier B.V.

Lipstein A.E.,Mathematical Institute andrew Wiles Building | Reid-Edwards R.A.,University of Hull
Journal of High Energy Physics | Year: 2014

Abstract: We formulate the theory of a 2-form gauge field on a Euclidean spacetime lattice. In this approach, the fundamental degrees of freedom live on the faces of the lattice, and the action can be constructed from the sum over Wilson surfaces associated with each fundamental cube of the lattice. If we take the gauge group to be U(1), the theory reduces to the well-known abelian gerbe theory in the continuum limit. We also explore a very simple and natural non-abelian generalization with gauge group U(N) × U(N). In the classical continuum limit, it reduces to a free theory, but at non-zero lattice spacing it is an interacting theory which gives rise to U(N) Yang-Mills theory upon dimensional reduction. Formulating the theory on a lattice has several other advantages. In particular, it is possible to compute many observables, such as the expectation value of Wilson surfaces, analytically at strong coupling and numerically for any value of the coupling. © 2014, The Author(s).

Zhu S.-X.,Mathematical Institute andrew Wiles Building | Gu T.-X.,CAS Beijing Institute of Applied Physics And Computational Mathematics | Liu X.-P.,CAS Beijing Institute of Applied Physics And Computational Mathematics
Computers and Mathematics with Applications | Year: 2014

Eliminating synchronizations is one of the important techniques related to minimizing communications for modern high performance computing. This paper discusses principles of reducing communications due to global synchronizations in sparse iterative solvers on distributed supercomputers. We demonstrate how to minimize global synchronizations by rescheduling a typical Krylov subspace method. The benefit of minimizing synchronizations is shown in theoretical analysis and verified by numerical experiments. The experiments also show the local communications for some structured sparse matrix-vector multiplications and global communications in the underlying supercomputers increase in the order P1/2.5 and P4/5 respectively, where P is the number of processors. © 2013 Elsevier Ltd. All rights reserved.

CONLON D.,Mathematical Institute andrew Wiles Building
Combinatorics Probability and Computing | Year: 2016

A construction of Alon yields a sequence of highly pseudorandom triangle-free graphs with edge density significantly higher than one might expect from comparison with random graphs. We give an alternative construction for such graphs. Copyright © Cambridge University Press 2016

GREEN B.,Mathematical Institute andrew Wiles Building
Combinatorics Probability and Computing | Year: 2016

Let G be an abelian group of cardinality n, where hcf(n, 6) = 1, and let A be a random subset of G. Form a graph Γ A on vertex set G by joining x to y if and only if x + y ∈ A. Then, with high probability as n → ∞, the chromatic number χ(ΓA) is at most (Formula presented.). This is asymptotically sharp when G = ℤ/nℤ, n prime. Copyright © Cambridge University Press 2016

Mason L.,Mathematical Institute andrew Wiles Building | Skinner D.,Wilberforce Road
Journal of High Energy Physics | Year: 2014

We show that string theories admit chiral infinite tension analogues in which only the massless parts of the spectrum survive. Geometrically they describe holomorphic maps to spaces of complex null geodesics, known as ambitwistor spaces. They have the standard critical space-time dimensions of string theory (26 in the bosonic case and 10 for the superstring). Quantization leads to the formulae for tree-level scattering amplitudes of massless particles found recently by Cachazo, He and Yuan. These representations localize the vertex operators to solutions of the same equations found by Gross and Mende to govern the behaviour of strings in the limit of high energy, fixed angle scattering. Here, localization to the scattering equations emerges naturally as a consequence of working on ambitwistor space. The worldsheet theory suggests a way to extend these amplitudes to spinor fields and to loop level. We argue that this family of string theories is a natural extension of the existing twistor string theories. © 2014 The Author(s).

Geyer Y.,Mathematical Institute andrew Wiles Building | Lipstein A.E.,Mathematical Institute andrew Wiles Building | Mason L.,Mathematical Institute andrew Wiles Building
Physical Review Letters | Year: 2014

We develop ambitwistor string theories for four dimensions to obtain new formulas for tree-level gauge and gravity amplitudes with arbitrary amounts of supersymmetry. Ambitwistor space is the space of complex null geodesics in complexified Minkowski space, and in contrast to earlier ambitwistor strings, we use twistors rather than vectors to represent this space. Although superficially similar to the original twistor string theories of Witten, Berkovits, and Skinner, these theories differ in the assignment of world sheet spins of the fields, rely on both twistor and dual twistor representatives for the vertex operators, and use the ambitwistor procedure for calculating correlation functions. Our models are much more flexible, no longer requiring maximal supersymmetry, and the resulting formulas for amplitudes are simpler, having substantially reduced moduli. These are supported on the solutions to the scattering equations refined according to helicity and can be checked by comparison with corresponding formulas of Witten and of Cachazo and Skinner. © 2014 American Physical Society.

Geyer Y.,Mathematical Institute andrew Wiles Building | Lipstein A.E.,Mathematical Institute andrew Wiles Building | Mason L.,Mathematical Institute andrew Wiles Building
Classical and Quantum Gravity | Year: 2015

The relationship between BMS symmetries at null infinity and Weinberg's soft theorems for gravitons and photons together with their subleading extensions are developed using ambitwistor string theory. Ambitwistor space is the phase space of complex null geodesics in complexified space-time. We show how it can be canonically identified with the cotangent bundle of complexified null infinity. BMS symmetries of null infinity lift to give a Hamiltonian action on ambitwistor space, both in general dimension and in its twistorial four-dimensional representation. General vertex operators arise from Hamiltonians generating diffeomorphisms of ambitwistor space that determine the scattering from past to future null infinity. When a momentum eigenstate goes soft, the diffeomorphism defined by its leading and its subleading part are extended BMS generators realized in the world sheet conformal field theory of the ambitwistor string. More generally, this gives an explicit perturbative correspondence between the scattering of null geodesics and that of the gravitational field via ambitwistor string theory. © 2015 IOP Publishing Ltd.

Penrose R.,Mathematical Institute andrew Wiles Building
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences | Year: 2015

A key obstruction to the twistor programme has been its so-called 'googly problem', unresolved for nearly 40 years, which asks for a twistor description of right-handed interacting massless fields (positive helicity), using the same twistor conventions that give rise to left-handed fields (negative helicity) in the standard 'nonlinear graviton' and Ward constructions. An explicit proposal for resolving this obstruction - palatial twistor theory - is put forward (illustrated in the case of gravitation). This incorporates the concept of a non-commutative holomorphic quantized twistor 'Heisenberg algebra', extending the sheaves of holomorphic functions of conventional twistor theory to include the operators of twistor differentiation. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

Gorce J.-B.,Mathematical Institute andrew Wiles Building | Hewitt I.J.,Mathematical Institute andrew Wiles Building | Vella D.,Mathematical Institute andrew Wiles Building
Langmuir | Year: 2016

We consider the problem of capillary imbibition into an axisymmetric tube for which the tube radius decreases in the direction of increasing imbibition. For tubes with constant radius, imbibition is described by Washburn's law (referred to here as the BCLW law to recognize the contributions of Bell, Cameron, and Lucas that predate Washburn). We show that imbibition into tubes with a power-law relationship between the radius and axial position generally occurs more quickly than imbibition into a constant-radius tube. By a suitable choice of the shape exponent, it is possible to decrease the time taken for the liquid to imbibe from one position to another by a factor of 2 compared to the BCLW law. We then show that a further small decrease in the imbibition time may be obtained by using a tube consisting of a cylinder joined to a cone of 3 times the cylinder length. For a given inlet radius, this composite shape attains the minimum imbibition time possible. We confirm our theoretical results with experiments on the tips of micropipettes and discuss the possible significance of these results for the control of liquid motion in microfluidic devices. © 2016 American Chemical Society.

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