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Proceedings. Mathematical, Physical, and Engineering Sciences

C Armanini, F Dal Corso, D Misseroni, D Bigoni
An elastic rod is clamped at one end and has a dead load attached to the other (free) end. The rod is then slowly rotated using the clamp. When the load is smaller than the buckling value, the rod describes a continuous set of quasi-static forms and its end traces a (smooth, convex and simple) closed curve, which would be a circle if the rod were rigid. The closed curve is analytically determined through the integration of the Euler's elastica, so that for sufficiently small loads the mechanical system behaves as an 'elastica compass'...
February 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Graeme W Milton, Ornella Mattei
Field patterns occur in space-time microstructures such that a disturbance propagating along a characteristic line does not evolve into a cascade of disturbances, but rather concentrates on a pattern of characteristic lines. This pattern is the field pattern. In one spatial direction plus time, the field patterns occur when the slope of the characteristics is, in a sense, commensurate with the space-time microstructure. Field patterns with different spatial shifts do not generally interact, but rather evolve as if they live in separate dimensions, as many dimensions as the number of field patterns...
February 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Sue Ion
The science and engineering of materials have always been fundamental to the success of nuclear power to date. They are also the key to the successful deployment and operation of a new generation of nuclear reactor systems and their associated fuel cycles. This article reflects on some of the historical issues, the challenges still prevalent today and the requirement for significant ongoing materials R&D and discusses the potential role of small modular reactors.
February 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
W-N Zou, Q-C He
Resorting to the superposition principle, the solution of Eshelby's problem of a spherical inclusion located eccentrically inside a finite spherical domain is obtained in two steps: (i) the solution to the problem of a spherical inclusion in an infinite space; (ii) the solution to the auxiliary problem of the corresponding finite spherical domain subjected to appropriate boundary conditions. Moreover, a set of functions called the sectional and harmonic deviators are proposed and developed to work out the auxiliary solution in a series form, including the displacement and Eshelby tensor fields...
February 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Wanqing Zhao, Thomas H Beach, Yacine Rezgui
Least angle regression, as a promising model selection method, differentiates itself from conventional stepwise and stagewise methods, in that it is neither too greedy nor too slow. It is closely related to L1 norm optimization, which has the advantage of low prediction variance through sacrificing part of model bias property in order to enhance model generalization capability. In this paper, we propose an efficient least angle regression algorithm for model selection for a large class of linear-in-the-parameters models with the purpose of accelerating the model selection process...
February 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Adam C DeVoria, Kamran Mohseni
This paper studies low-aspect-ratio ([Formula: see text]) rectangular wings at high incidence and in side-slip. The main objective is to incorporate the effects of high angle of attack and side-slip into a simplified vortex model for the forces and moments. Experiments are also performed and are used to validate assumptions made in the model. The model asymptotes to the potential flow result of classical aerodynamics for an infinite aspect ratio. The [Formula: see text] → 0 limit of a rectangular wing is considered with slender body theory, where the side-edge vortices merge into a vortex doublet...
February 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
J Collis, D L Brown, M E Hubbard, R D O'Dea
In this work, we consider the spatial homogenization of a coupled transport and fluid-structure interaction model, to the end of deriving a system of effective equations describing the flow, elastic deformation and transport in an active poroelastic medium. The 'active' nature of the material results from a morphoelastic response to a chemical stimulant, in which the growth time scale is strongly separated from other elastic time scales. The resulting effective model is broadly relevant to the study of biological tissue growth, geophysical flows (e...
February 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
P Perdikaris, M Raissi, A Damianou, N D Lawrence, G E Karniadakis
Multi-fidelity modelling enables accurate inference of quantities of interest by synergistically combining realizations of low-cost/low-fidelity models with a small set of high-fidelity observations. This is particularly effective when the low- and high-fidelity models exhibit strong correlations, and can lead to significant computational gains over approaches that solely rely on high-fidelity models. However, in many cases of practical interest, low-fidelity models can only be well correlated to their high-fidelity counterparts for a specific range of input parameters, and potentially return wrong trends and erroneous predictions if probed outside of their validity regime...
February 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Angela Madeo, Patrizio Neff, Elias C Aifantis, Gabriele Barbagallo, Marco Valerio d'Agostino
In this paper, the role of gradient micro-inertia terms [Formula: see text] and free micro-inertia terms [Formula: see text] is investigated to unveil their respective effects on the dynamic behaviour of band-gap metamaterials. We show that the term [Formula: see text] alone is only able to disclose relatively simplified dispersive behaviour. On the other hand, the term [Formula: see text] alone describes the full complex behaviour of band-gap metamaterials. A suitable mixing of the two micro-inertia terms allows us to describe a new feature of the relaxed-micromorphic model, i...
February 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Johannes Schönke, Eliot Fried
A linear stability analysis is performed for a pair of coaxial vertical chains made from permanently magnetized balls under the influence of gravity. While one chain rises from the ground, the other hangs from above, with the remaining ends separated by a gap of prescribed length. Various boundary conditions are considered, as are situations in which the magnetic dipole moments in the two chains are parallel or antiparallel. The case of a single chain attached to the ground is also discussed. The stability of the system is examined with respect to three quantities: the number of balls in each chain, the length of the gap between the chains, and a single dimensionless parameter which embodies the competition between magnetic and gravitational forces...
February 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
David Firstbrook, Kevin Worrall, Ryan Timoney, Francesc Suñol, Yang Gao, Patrick Harkness
This work investigates the potential use of direct ultrasonic vibration as an aid to penetration of granular material. Compared with non-ultrasonic penetration, required forces have been observed to reduce by an order of magnitude. Similarly, total consumed power can be reduced by up to 27%, depending on the substrate and ultrasonic amplitude used. Tests were also carried out in high-gravity conditions, displaying a trend that suggests these benefits could be leveraged in lower gravity regimes.
February 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Bair V Budaev, David B Bogy
We develop a theory of thermal transport in nanoscale-layered structures based on wave processes. The theory incorporates two fundamental principles, first, that the spectra of thermally excited waves are determined by the temperature differential and the heat flux, and second, that the wave fields in the heat exchanging domains are coupled. The developed method includes classical theories as special cases that are valid in larger scales, and it naturally explains such phenomena as interface thermal resistance (Kapitsa resistance) and thermal rectification (asymmetry of thermal transport)...
February 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
N Joshi, C J Lustri, S Luu
We consider the asymptotic behaviour of the second discrete Painlevé equation in the limit as the independent variable becomes large. Using asymptotic power series, we find solutions that are asymptotically pole-free within some region of the complex plane. These asymptotic solutions exhibit Stokes phenomena, which is typically invisible to classical power series methods. We subsequently apply exponential asymptotic techniques to investigate such phenomena, and obtain mathematical descriptions of the rapid switching behaviour associated with Stokes curves...
February 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Matteo Petrera, Yuri B Suris
We give a construction of completely integrable four-dimensional Hamiltonian systems with cubic Hamilton functions. Applying to the corresponding pairs of commuting quadratic Hamiltonian vector fields the so called Kahan-Hirota-Kimura discretization scheme, we arrive at pairs of birational four-dimensional maps. We show that these maps are symplectic with respect to a symplectic structure that is a perturbation of the standard symplectic structure on [Formula: see text], and possess two independent integrals of motion, which are perturbations of the original Hamilton functions and which are in involution with respect to the perturbed symplectic structure...
February 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Mark Welland
No abstract text is available yet for this article.
January 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Patrizio Neff, Angela Madeo, Gabriele Barbagallo, Marco Valerio d'Agostino, Rafael Abreu, Ionel-Dumitrel Ghiba
For the recently introduced isotropic-relaxed micromorphic generalized continuum model, we show that, under the assumption of positive-definite energy, planar harmonic waves have real velocity. We also obtain a necessary and sufficient condition for real wave velocity which is weaker than the positive definiteness of the energy. Connections to isotropic linear elasticity and micropolar elasticity are established. Notably, we show that strong ellipticity does not imply real wave velocity in micropolar elasticity, whereas it does in isotropic linear elasticity...
January 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
P Łydżba, J Jacak
In this paper, we recall the topological approach to quantum Hall effects. We note that, in the presence of a magnetic field, trajectories representing elements of the system's braid group are of cyclotron orbit type. In two-dimensional spaces, this leads to the restriction of the full braid group, π1(Ω)-loopless generators (exchanges of M(N) coordinates or classical particles) are unenforceable. As a result, the identification of a possible Hall-like state comes down to the identification of a possible subgroup of π1(Ω)...
January 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
A Van Pamel, G Sha, S I Rokhlin, M J S Lowe
The scattering treated here arises when elastic waves propagate within a heterogeneous medium defined by random spatial fluctuation of its elastic properties. Whereas classical analytical studies are based on lower-order scattering assumptions, numerical methods conversely present no such limitations by inherently incorporating multiple scattering. Until now, studies have typically been limited to two or one dimension, however, owing to computational constraints. This article seizes recent advances to realize a finite-element formulation that solves the three-dimensional elastodynamic scattering problem...
January 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Keith W Myerscough, Jason Frank, Benedict Leimkuhler
Models used in simulation may give accurate short-term trajectories but distort long-term (statistical) properties. In this work, we augment a given approximate model with a control law (a 'thermostat') that gently perturbs the dynamical system to target a thermodynamic state consistent with a set of prescribed (possibly evolving) observations. As proof of concept, we provide an example involving a point vortex fluid model on the sphere, for which we show convergence of equilibrium quantities (in the stationary case) and the ability of the thermostat to dynamically track a transient state...
January 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
John Meurig Thomas
Electron microscopy (EM) is arguably the single most powerful method of characterizing heterogeneous catalysts. Irrespective of whether they are bulk and multiphasic, or monophasic and monocrystalline, or nanocluster and even single-atom and on a support, their structures in atomic detail can be visualized in two or three dimensions, thanks to high-resolution instruments, with sub-Ångstrom spatial resolutions. Their topography, tomography, phase-purity, composition, as well as the bonding, and valence-states of their constituent atoms and ions and, in favourable circumstances, the short-range and long-range atomic order and dynamics of the catalytically active sites, can all be retrieved by the panoply of variants of modern EM...
January 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
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