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Proceedings. Mathematical, Physical, and Engineering Sciences

Graham J Hutchings, C R Catlow, Nicholas Turner
[This retracts the article DOI: 10.1098/rspa.2018.0414.].
August 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
C Howcroft, R G Cook, S A Neild, M H Lowenberg, J E Cooper, E B Coetzee
This paper proposes a low-order geometrically exact flexible beam formulation based on the utilization of generic beam shape functions to approximate distributed kinematic properties of the deformed structure. The proposed nonlinear beam shapes approach is in contrast to the majority of geometrically nonlinear treatments in the literature in which element-based-and hence high-order-discretizations are adopted. The kinematic quantities approximated specifically pertain to shear and extensional gradients as well as local orientation parameters based on an arbitrary set of globally referenced attitude parameters...
August 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
L C Auton, C W MacMinn
The radially outward flow of fluid through a porous medium occurs in many practical problems, from transport across vascular walls to the pressurization of boreholes in the subsurface. When the driving pressure is non-negligible relative to the stiffness of the solid structure, the poromechanical coupling between the fluid and the solid can control both the steady state and the transient mechanics of the system. Very large pressures or very soft materials lead to large deformations of the solid skeleton, which introduce kinematic and constitutive nonlinearity that can have a non-trivial impact on these mechanics...
August 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
G Mauri, F Messi, M Anastasopoulos, T Arnold, A Glavic, C Höglund, T Ilves, I Lopez Higuera, P Pazmandi, D Raspino, L Robinson, S Schmidt, P Svensson, D Varga, R Hall-Wilton, F Piscitelli
The Multi-Blade is a boron-10-based gaseous detector developed for neutron reflectometry instruments at the European Spallation Source in Sweden. The main challenges for neutron reflectometry detectors are the instantaneous counting rate and spatial resolution. The Multi-Blade has been tested on the CRISP reflectometer at the ISIS Neutron and Muon Source in the UK. A campaign of scientific measurements has been performed to study the Multi-Blade response in real instrumental conditions. The results of these tests are discussed in this paper...
August 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Tiago Anselmo, Rhodri Nelson, Bruno Carneiro da Cunha, Darren G Crowdy
We present a novel method to solve the accessory parameter problem arising in constructing conformal maps from a canonical simply connected planar region to the interior of a circular arc quadrilateral. The Schwarz-Christoffel accessory parameter problem, relevant when all sides have zero curvature, is also captured within our approach. The method exploits the isomonodromic tau function associated with the Painlevé VI equation. Recently, these tau functions have been shown to be related to certain correlation functions in conformal field theory and asymptotic expansions have been given in terms of tuples of the Young diagrams...
August 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
I Giorgio, P Harrison, F dell'Isola, J Alsayednoor, E Turco
We consider two 'comprehensive' modelling approaches for engineering fabrics. We distinguish the two approaches using the terms 'semi-discrete' and 'continuum', reflecting their natures. We demonstrate a fitting procedure, used to identify the constitutive parameters of the continuum model from predictions of the semi-discrete model, the parameters of which are in turn fitted to experimental data. We, then, check the effectiveness of the continuum model by verifying the correspondence between semi-discrete and continuum model predictions using test cases not previously used in the identification process...
August 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
M Rambausek, M-A Keip
For a long time, the search for magneto-electric materials concentrated on multi-ferroics and hard-matter composites. By contrast, rather recently the exploitation of strain-mediated magneto-electric (ME) coupling in soft composites was proposed. The basic idea behind this approach is to combine the magneto- and electro-mechanical responses of composites consisting of a soft matrix carrying magnetic inclusions. Despite that such composites are straightforward to manufacture and have cheap constituents, they did not gain much attention up to now...
August 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Gideon Steinitz, Peter Kotlarsky, Oksana Piatibratova
An enhanced confined mode (ECM) radon simulation experiment, tested in the laboratory in Jerusalem, was relocated to a subsurface geophysical observatory located 400 km apart, at a depth of 150 m and with a stable temperature. Five gamma sensors are placed around the ECM canister and lead shielding minimizes the influence of natural local gamma radiation. Simultaneous measurement of the geological radon and from radon in the ECM system indicates that the temporal variation of gamma radiation from radon in the ECM system contains annual, multi-day and daily signals, that correspond to signals in the local geological radon...
August 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Soumendu Bagchi, Abhilash Harpale, Huck Beng Chew
Carbon nanotubes (CNTs) are highly promising for strength reinforcement in polymer nanocomposites, but conflicting interfacial properties have been reported by single nanotube pull-out experiments. Here, we report the interfacial load transfer mechanisms during pull-out of CNTs from PMMA matrices, using massively- parallel molecular dynamics simulations. We show that the pull-out forces associated with non-bonded interactions between CNT and PMMA are generally small, and are weakly-dependent on the embedment length of the nanotube...
August 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
N Brierley, C Bellon, B Lazaro Toralles
The inspection of complex-shaped components, such as those enabled by additive manufacturing, is a major challenge in industrial quality assurance. A frequently adopted approach to volumetric non-destructive evaluation is X-ray computed tomography, but this has major drawbacks. Two-dimensional radiography can overcome some of these problems, but does not generally provide an inspection that is as capable. Moreover, designing a detailed inspection for a complex-shaped component is a labour-intensive task, requiring significant expert input...
August 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
K R Daly, S D Keyes, T Roose
We show how a combination of X-ray computed tomography (X-CT) and image-based modelling can be used to calculate the effect of moisture content and compaction on the macroscopic structural properties of soil. Our method is based on the equations derived in Daly & Roose (2018 Proc. R. Soc. A 474 , 20170141. (doi:10.1098/rspa.2017.0141)), which we have extended so they can be directly applied to the segmented images obtained from X-CT. We assume that the soils are composed of air-filled pore space, solid mineral grains and a mixed phase composed of both clay particles and water...
July 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
H S Battey, D R Cox
Recently, Cox and Battey (2017 Proc. Natl Acad. Sci. USA 114 , 8592-8595 (doi:10.1073/pnas.1703764114)) outlined a procedure for regression analysis when there are a small number of study individuals and a large number of potential explanatory variables, but relatively few of the latter have a real effect. The present paper reports more formal statistical properties. The results are intended primarily to guide the choice of key tuning parameters.
July 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Graham J Hutchings, C R Catlow, Nicholas Turner
No abstract text is available yet for this article.
July 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
M Garau, G Carta, M J Nieves, I S Jones, N V Movchan, A B Movchan
We demonstrate a new method of achieving topologically protected states in an elastic hexagonal system of trusses by attaching gyroscopic spinners, which bring chirality to the system. Dispersive features of this medium are investigated in detail, and it is shown that one can manipulate the locations of stop-bands and Dirac points by tuning the parameters of the spinners. We show that, in the proximity of such points, uni-directional interfacial waveforms can be created in an inhomogeneous lattice and the direction of such waveforms can be controlled...
July 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Ritabrata Dutta, Antonietta Mira, Jukka-Pekka Onnela
Infectious diseases are studied to understand their spreading mechanisms, to evaluate control strategies and to predict the risk and course of future outbreaks. Because people only interact with few other individuals, and the structure of these interactions influence spreading processes, the pairwise relationships between individuals can be usefully represented by a network. Although the underlying transmission processes are different, the network approach can be used to study the spread of pathogens in a contact network or the spread of rumours in a social network...
July 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Michael Pan, Peter J Gawthrop, Kenneth Tran, Joseph Cursons, Edmund J Crampin
Mathematical models of cardiac action potentials have become increasingly important in the study of heart disease and pharmacology, but concerns linger over their robustness during long periods of simulation, in particular due to issues such as model drift and non-unique steady states. Previous studies have linked these to violation of conservation laws, but only explored those issues with respect to charge conservation in specific models. Here, we propose a general and systematic method of identifying conservation laws hidden in models of cardiac electrophysiology by using bond graphs, and develop a bond graph model of the cardiac action potential to study long-term behaviour...
June 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Mrityunjay Kothari, Moon-Hyun Cha, Kyung-Suk Kim
Here, we report the discovery of a new, curvature-localizing, subcritical buckling mode that produces shallow-kink corrugation in multi-layer graphene. Our density functional theory (DFT) analysis reveals the mode configuration-an approximately 2 nm wide boundary layer of highly localized curvature that connects two regions of uniformly but oppositely sheared stacks of flat atomic sheets. The kink angle between the two regions is limited to a few degrees, ensuring elastic deformation. By contrast, a purely mechanical model of sandwich structures shows progressive supercritical curvature localization spread over a 50-100 nm wide boundary layer...
June 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
R Reuvers
A quantum state's entanglement across a bipartite cut can be quantified with entanglement entropy or, more generally, Schmidt norms. Using only Schmidt decompositions, we present a simple iterative algorithm to maximize Schmidt norms. Depending on the choice of norm, the optimizing states maximize or minimize entanglement, possibly across several bipartite cuts at the same time and possibly only among states in a specified subspace. Recognizing that convergence but not success is certain, we use the algorithm to explore topics ranging from fermionic reduced density matrices and varieties of pure quantum states to absolutely maximally entangled states and minimal output entropy of channels...
June 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
E Nolde, A V Pichugin, J Kaplunov
A direct asymptotic integration of the full three-dimensional problem of elasticity is employed to derive a consistent governing equation for a beam with the rectangular cross section. The governing equation is consistent in the sense that it has the same long-wave low-frequency behaviour as the exact solution of the original three-dimensional problem. Performance of the new beam equation is illustrated by comparing its predictions against the results of direct finite-element computations. Limiting behaviours for beams with large (and small) aspect ratios, which can be established using classical plate theories, are recovered from the new governing equation to illustrate its consistency and also to illustrate the importance of using plate theories with the correctly refined boundary conditions...
June 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
L Renson, T L Hill, D A Ehrhardt, D A W Barton, S A Neild
Nonlinear normal modes (NNMs) are widely used as a tool for developing mathematical models of nonlinear structures and understanding their dynamics. NNMs can be identified experimentally through a phase quadrature condition between the system response and the applied excitation. This paper demonstrates that this commonly used quadrature condition can give results that are significantly different from the true NNM, in particular, when the excitation applied to the system is limited to one input force, as is frequently used in practice...
June 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
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