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Proceedings. Mathematical, Physical, and Engineering Sciences

Ting Tan, Brian Ribbans
Helicoidal fibre structures are widely observed in natural materials. In this paper, an integrated experimental and analytical approach was used to investigate the compressive resistance of helicoidal fibre structures. First, helicoidal fibre-reinforced composites were created using three-dimensionally printed helicoids and polymeric matrices, including plain, ring-reinforced and helix-reinforced helicoids. Then, load-displacement curves under monotonic compression tests were collected to measure the compressive strengths of helicoidal fibre composites...
October 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Michael Atiyah, Maciej Dunajski, Lionel J Mason
We review aspects of twistor theory, its aims and achievements spanning the last five decades. In the twistor approach, space-time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex threefold-the twistor space. After giving an elementary construction of this space, we demonstrate how solutions to linear and nonlinear equations of mathematical physics-anti-self-duality equations on Yang-Mills or conformal curvature-can be encoded into twistor cohomology...
October 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
C Grotta Ragazzo
The purpose of this work is to present an algorithm to determine the motion of a single hydrodynamic vortex on a closed surface of constant curvature and of genus greater than one. The algorithm is based on a relation between the Laplace-Beltrami Green function and the heat kernel. The algorithm is used to compute the motion of a vortex on the Bolza surface. This is the first determination of the orbits of a vortex on a closed surface of genus greater than one. The numerical results show that all the 46 vortex equilibria can be explicitly computed using the symmetries of the Bolza surface...
October 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Kelvin J A Ooi, Dawn T H Tan
The rapid development of graphene has opened up exciting new fields in graphene plasmonics and nonlinear optics. Graphene's unique two-dimensional band structure provides extraordinary linear and nonlinear optical properties, which have led to extreme optical confinement in graphene plasmonics and ultrahigh nonlinear optical coefficients, respectively. The synergy between graphene's linear and nonlinear optical properties gave rise to nonlinear graphene plasmonics, which greatly augments graphene-based nonlinear device performance beyond a billion-fold...
October 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
D J Ivers
The kinematic dynamo problem is solved numerically for a spheroidal conducting fluid of possibly large aspect ratio with an insulating exterior. The solution method uses solenoidal representations of the magnetic field and the velocity by spheroidal toroidal and poloidal fields in a non-orthogonal coordinate system. Scaling of coordinates and fields to a spherical geometry leads to a modified form of the kinematic dynamo problem with a geometric anisotropic diffusion and an anisotropic current-free condition in the exterior, which is solved explicitly...
October 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
K Liu, G H Paulino
Origami-inspired designs possess attractive applications to science and engineering (e.g. deployable, self-assembling, adaptable systems). The special geometric arrangement of panels and creases gives rise to unique mechanical properties of origami, such as reconfigurability, making origami designs well suited for tunable structures. Although often being ignored, origami structures exhibit additional soft modes beyond rigid folding due to the flexibility of thin sheets that further influence their behaviour...
October 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Finn Box, Dominic Vella, Robert W Style, Jerome A Neufeld
The localized loading of an elastic sheet floating on a liquid bath occurs at scales from a frog sitting on a lily pad to a volcano supported by the Earth's tectonic plates. The load is supported by a combination of the stresses within the sheet (which may include applied tensions from, for example, surface tension) and the hydrostatic pressure in the liquid. At the same time, the sheet deforms, and may wrinkle, because of the load. We study this problem in terms of the (relatively weak) applied tension and the indentation depth...
October 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Chaozhen Wei, Brian J Spencer
We construct a Fokker-Planck reaction (FPR) model to investigate the dynamics of the coupled epitaxial growth and shape transition process of an array of quantum dots (QDs). The FPR model is based on a coupled system of Fokker-Planck equations wherein the distribution of each island type is governed by its own Fokker-Planck equation for growth, with reaction terms describing the shape transitions between islands of different types including asymmetric shapes. The reaction terms for the shape transitions depend on the island size and are determined from explicit calculations of the lowest barrier pathway for each shape transition...
October 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Robert Krakow, Robbie J Bennett, Duncan N Johnstone, Zoja Vukmanovic, Wilberth Solano-Alvarez, Steven J Lainé, Joshua F Einsle, Paul A Midgley, Catherine M F Rae, Ralf Hielscher
Determining the local orientation of crystals in engineering and geological materials has become routine with the advent of modern crystallographic mapping techniques. These techniques enable many thousands of orientation measurements to be made, directing attention towards how such orientation data are best studied. Here, we provide a guide to the visualization of misorientation data in three-dimensional vector spaces, reduced by crystal symmetry, to reveal crystallographic orientation relationships. Domains for all point group symmetries are presented and an analysis methodology is developed and applied to identify crystallographic relationships, indicated by clusters in the misorientation space, in examples from materials science and geology...
October 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
F Montiel, V A Squire
A model of ice floe break-up under ocean wave forcing in the marginal ice zone (MIZ) is proposed to investigate how floe size distribution (FSD) evolves under repeated wave break-up events. A three-dimensional linear model of ocean wave scattering by a finite array of compliant circular ice floes is coupled to a flexural failure model, which breaks a floe into two floes provided the two-dimensional stress field satisfies a break-up criterion. A closed-feedback loop algorithm is devised, which (i) solves the wave-scattering problem for a given FSD under time-harmonic plane wave forcing, (ii) computes the stress field in all the floes, (iii) fractures the floes satisfying the break-up criterion, and (iv) generates an updated FSD, initializing the geometry for the next iteration of the loop...
October 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Behrouz Tavakol, Guillaume Froehlicher, Douglas P Holmes, Howard A Stone
Lubrication theory is broadly applicable to the flow characterization of thin fluid films and the motion of particles near surfaces. We offer an extension to lubrication theory by starting with Stokes equations and considering higher-order terms in a systematic perturbation expansion to describe the fluid flow in a channel with features of a modest aspect ratio. Experimental results qualitatively confirm the higher-order analytical solutions, while numerical results are in very good agreement with the higher-order analytical results...
October 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Valeriy Yu Filimonov
In this paper, the comparative analysis of the thermal explosion (TE) critical conditions on the planes temperature-conversion degree and temperature-time was conducted. It was established that the ignition criteria are almost identical only at relatively small values of Todes parameter. Otherwise, the results of critical conditions analysis on the plane temperature-conversion degree may be wrong. The asymptotic method of critical conditions calculation for the first-order reactions was proposed (taking into account the reactant consumption)...
October 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Beñat Gurrutxaga-Lerma
The elastodynamic image forces acting on straight screw dislocations in the presence of planar phase boundaries are derived. Two separate dislocations are studied: (i) the injected, non-moving screw dislocation and (ii) the injected (or pre-existing), generally non-uniformly moving screw dislocation. The image forces are derived for both the case of a rigid surface and of a planar interface between two homogeneous, isotropic phases. The case of a rigid interface is shown to be solvable employing Head's image dislocation construction...
September 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Shuyi Zhang, Bin Guo, Anlan Dong, Jing He, Ziping Xu, Song Xi Chen
The official air-quality statistic reported that Beijing had a 9.9% decline in the annual concentration of PM2.5 in 2016. While this statistic offered some relief for the inhabitants of the capital, we present several analyses based on Beijing's PM2.5 data of the past 4 years at 36 monitoring sites along with meteorological data of the past 7 years. The analyses reveal the air pollution situation in 2016 was not as rosy as the 9.9% decline would convey, and improvement if any was rather uncertain. The paper also provides an assessment on the city's PM2...
September 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Dominic Horsman, Chris Heunen, Matthew F Pusey, Jonathan Barrett, Robert W Spekkens
The standard formalism of quantum theory treats space and time in fundamentally different ways. In particular, a composite system at a given time is represented by a joint state, but the formalism does not prescribe a joint state for a composite of systems at different times. If there were a way of defining such a joint state, this would potentially permit a more even-handed treatment of space and time, and would strengthen the existing analogy between quantum states and classical probability distributions...
September 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
C J Cotter, G A Gottwald, D D Holm
In Holm (Holm 2015 Proc. R. Soc. A471, 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation...
September 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Silvana S S Cardoso, Julyan H E Cartwright
Black smokers and Lost City-type springs are varieties of hydrothermal vents on the ocean floors that emit hot, acidic water and cool, alkaline water, respectively. While both produce precipitation structures as the issuing fluid encounters oceanic water, Lost City-type hydrothermal vents in particular have been implicated in the origin of life on the Earth. We present a parallel-velocity flow model for the radius and flow rate of a cylindrical jet of fluid that forms the template for the growth of a tube precipitated about itself and we compare the solution with previous laboratory experimental results from growth of silicate chemical gardens...
September 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Ayoub Gouasmi, Eric J Parish, Karthik Duraisamy
Reduced models of nonlinear dynamical systems require closure, or the modelling of the unresolved modes. The Mori-Zwanzig procedure can be used to derive formally closed evolution equations for the resolved physics. In these equations, the unclosed terms are recast as a memory integral involving the time history of the resolved variables. While this procedure does not reduce the complexity of the original system, these equations can serve as a mathematically consistent basis to develop closures based on memory approximations...
September 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Tali Pinsky
We present a new paradigm for three-dimensional chaos, and specifically for the Lorenz equations. The main difficulty in these equations and for a generic flow in dimension 3 is the existence of singularities. We show how to use knot theory as a way to remove the singularities. Specifically, we claim: (i) for certain parameters, the Lorenz system has an invariant one-dimensional curve, which is a trefoil knot. The knot is a union of invariant manifolds of the singular points. (ii) The flow is topologically equivalent to an Anosov flow on the complement of this curve, and moreover to a geodesic flow...
September 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Dénes Száz, Alexandra Farkas, András Barta, Balázs Kretzer, Miklós Blahó, Ádám Egri, Gyula Szabó, Gábor Horváth
According to Thorkild Ramskou's theory proposed in 1967, under overcast and foggy skies, Viking seafarers might have used skylight polarization analysed with special crystals called sunstones to determine the position of the invisible Sun. After finding the occluded Sun with sunstones, its elevation angle had to be measured and its shadow had to be projected onto the horizontal surface of a sun compass. According to Ramskou's theory, these sunstones might have been birefringent calcite or dichroic cordierite or tourmaline crystals working as polarizers...
September 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
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