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Proceedings. Mathematical, Physical, and Engineering Sciences

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https://www.readbyqxmd.com/read/28690419/correction-to-homogenized-boundary-conditions-and-resonance-effects-in-faraday-cages
#1
D P Hewett, I J Hewitt
[This corrects the article DOI: 10.1098/rspa.2016.0062.].
June 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/28690418/new-conformal-mapping-for-adaptive-resolving-of-the-complex-singularities-of-stokes-wave
#2
Pavel M Lushnikov, Sergey A Dyachenko, Denis A Silantyev
A new highly efficient method is developed for computation of travelling periodic waves (Stokes waves) on the free surface of deep water. A convergence of numerical approximation is determined by the complex singularities above the free surface for the analytical continuation of the travelling wave into the complex plane. An auxiliary conformal mapping is introduced which moves singularities away from the free surface thus dramatically speeding up numerical convergence by adapting the numerical grid for resolving singularities while being consistent with the fluid dynamics...
June 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/28690417/the-effect-of-coherent-stirring-on-the-advection-condensation-of-water-vapour
#3
Yue-Kin Tsang, Jacques Vanneste
Atmospheric water vapour is an essential ingredient of weather and climate. The key features of its distribution can be represented by kinematic models which treat it as a passive scalar advected by a prescribed flow and reacting through condensation. Condensation acts as a sink that maintains specific humidity below a prescribed, space-dependent saturation value. To investigate how the interplay between large-scale advection, small-scale turbulence and condensation controls moisture distribution, we develop simple kinematic models which combine a single circulating flow with a Brownian-motion representation of turbulence...
June 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/28690416/non-reciprocal-wave-propagation-in-modulated-elastic-metamaterials
#4
H Nassar, H Chen, A N Norris, M R Haberman, G L Huang
Time-reversal symmetry for elastic wave propagation breaks down in a resonant mass-in-mass lattice whose inner-stiffness is weakly modulated in space and in time in a wave-like fashion. Specifically, one-way wave transmission, conversion and amplification as well as unidirectional wave blocking are demonstrated analytically through an asymptotic analysis based on coupled mode theory and numerically thanks to a series of simulations in harmonic and transient regimes. High-amplitude modulations are then explored in the homogenization limit where a non-standard effective mass operator is recovered and shown to take negative values over unusually large frequency bands...
June 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/28690415/windowed-green-function-method-for-the-helmholtz-equation-in-the-presence-of-multiply-layered-media
#5
O P Bruno, C Pérez-Arancibia
This paper presents a new methodology for the solution of problems of two- and three-dimensional acoustic scattering (and, in particular, two-dimensional electromagnetic scattering) by obstacles and defects in the presence of an arbitrary number of penetrable layers. Relying on the use of certain slow-rise windowing functions, the proposed windowed Green function approach efficiently evaluates oscillatory integrals over unbounded domains, with high accuracy, without recourse to the highly expensive Sommerfeld integrals that have typically been used to account for the effect of underlying planar multilayer structures...
June 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/28690414/a-free-boundary-model-of-diffusive-valley-growth-theory-and-observation
#6
Robert Yi, Yossi Cohen, Hansjörg Seybold, Eric Stansifer, Robb McDonald, Mark Mineev-Weinstein, Daniel H Rothman
Valleys that form around a stream head often develop characteristic finger-like elevation contours. We study the processes involved in the formation of these valleys and introduce a theoretical model that indicates how shape may inform the underlying processes. We consider valley growth as the advance of a moving boundary travelling forward purely through linearly diffusive erosion, and we obtain a solution for the valley shape in three dimensions. Our solution compares well to the shape of slowly growing groundwater-fed valleys found in Bristol, Florida...
June 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/28690413/extensional-channel-flow-revisited-a-dynamical-systems-perspective
#7
Francisco Marques, Alvaro Meseguer, Fernando Mellibovsky, Patrick D Weidman
Extensional self-similar flows in a channel are explored numerically for arbitrary stretching-shrinking rates of the confining parallel walls. The present analysis embraces time integrations, and continuations of steady and periodic solutions unfolded in the parameter space. Previous studies focused on the analysis of branches of steady solutions for particular stretching-shrinking rates, although recent studies focused also on the dynamical aspects of the problems. We have adopted a dynamical systems perspective, analysing the instabilities and bifurcations the base state undergoes when increasing the Reynolds number...
June 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/28690412/analytical-solutions-for-two-dimensional-stokes-flow-singularities-in-a-no-slip-wedge-of-arbitrary-angle
#8
Darren G Crowdy, Samuel J Brzezicki
An analytical method to find the flow generated by the basic singularities of Stokes flow in a wedge of arbitrary angle is presented. Specifically, we solve a biharmonic equation for the stream function of the flow generated by a point stresslet singularity and satisfying no-slip boundary conditions on the two walls of the wedge. The method, which is readily adapted to any other singularity type, takes full account of any transcendental singularities arising at the corner of the wedge. The approach is also applicable to problems of plane strain/stress of an elastic solid where the biharmonic equation also governs the Airy stress function...
June 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/28690411/addressing-the-discrepancy-of-finding-the-equilibrium-melting-point-of-silicon-using-molecular-dynamics-simulations
#9
Saeed Zare Chavoshi, Shuozhi Xu, Saurav Goel
We performed molecular dynamics simulations to study the equilibrium melting point of silicon using (i) the solid-liquid coexistence method and (ii) the Gibbs free energy technique, and compared our novel results with the previously published results obtained from the Monte Carlo (MC) void-nucleated melting method based on the Tersoff-ARK interatomic potential (Agrawal et al. Phys. Rev. B72, 125206. (doi:10.1103/PhysRevB.72.125206)). Considerable discrepancy was observed (approx. 20%) between the former two methods and the MC void-nucleated melting result, leading us to question the applicability of the empirical MC void-nucleated melting method to study a wide range of atomic and molecular systems...
June 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/28690410/ultrasonic-defect-characterization-using-parametric-manifold-mapping
#10
A Velichko, L Bai, B W Drinkwater
The aim of ultrasonic non-destructive evaluation includes the detection and characterization of defects, and an understanding of the nature of defects is essential for the assessment of structural integrity in safety critical systems. In general, the defect characterization challenge involves an estimation of defect parameters from measured data. In this paper, we explore the extent to which defects can be characterized by their ultrasonic scattering behaviour. Given a number of ultrasonic measurements, we show that characterization information can be extracted by projecting the measurement onto a parametric manifold in principal component space...
June 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/28690409/turbulent-boundary-layer-under-the-control-of-different-schemes
#11
Z X Qiao, Y Zhou, Z Wu
This work explores experimentally the control of a turbulent boundary layer over a flat plate based on wall perturbation generated by piezo-ceramic actuators. Different schemes are investigated, including the feed-forward, the feedback, and the combined feed-forward and feedback strategies, with a view to suppressing the near-wall high-speed events and hence reducing skin friction drag. While the strategies may achieve a local maximum drag reduction slightly less than their counterpart of the open-loop control, the corresponding duty cycles are substantially reduced when compared with that of the open-loop control...
June 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/28690408/wave-reflection-and-transmission-in-multiply-stented-blood-vessels
#12
T K Papathanasiou, A B Movchan, D Bigoni
Closed circulatory systems display an exquisite balance between vascular elasticity and viscous fluid effects, to induce pulse-smoothing and avoid resonance during the cardiac cycle. Stents in the arterial tree alter this balance through stiffening and because a periodic structure is introduced, capable of interacting with the fluid in a complex way. While the former feature has been investigated, the latter received no attention so far. But periodic structures are the building blocks of metamaterials, known for their 'non-natural' behaviour...
June 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/28690407/regularly-configured-structures-with-polygonal-prisms-for-three-dimensional-auxetic-behaviour
#13
Junhyun Kim, Dongheok Shin, Do-Sik Yoo, Kyoungsik Kim
We report here structures, constructed with regular polygonal prisms, that exhibit negative Poisson's ratios. In particular, we show how we can construct such a structure with regular n-gonal prism-shaped unit cells that are again built with regular n-gonal component prisms. First, we show that the only three possible values for n are 3, 4 and 6 and then discuss how we construct the unit cell again with regular n-gonal component prisms. Then, we derive Poisson's ratio formula for each of the three structures and show, by analysis and numerical verification, that the structures possess negative Poisson's ratio under certain geometric conditions...
June 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/28690406/the-cutting-of-metals-via-plastic-buckling
#14
Anirudh Udupa, Koushik Viswanathan, Yeung Ho, Srinivasan Chandrasekar
The cutting of metals has long been described as occurring by laminar plastic flow. Here we show that for metals with large strain-hardening capacity, laminar flow mode is unstable and cutting instead occurs by plastic buckling of a thin surface layer. High speed in situ imaging confirms that the buckling results in a small bump on the surface which then evolves into a fold of large amplitude by rotation and stretching. The repeated occurrence of buckling and folding manifests itself at the mesoscopic scale as a new flow mode with significant vortex-like components-sinuous flow...
June 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/28690405/knotted-fields-and-explicit-fibrations-for-lemniscate-knots
#15
B Bode, M R Dennis, D Foster, R P King
We give an explicit construction of complex maps whose nodal lines have the form of lemniscate knots. We review the properties of lemniscate knots, defined as closures of braids where all strands follow the same transverse (1, ℓ) Lissajous figure, and are therefore a subfamily of spiral knots generalizing the torus knots. We then prove that such maps exist and are in fact fibrations with appropriate choices of parameters. We describe how this may be useful in physics for creating knotted fields, in quantum mechanics, optics and generalizing to rational maps with application to the Skyrme-Faddeev model...
June 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/28690404/energy-based-analysis-of-biomolecular-pathways
#16
Peter J Gawthrop, Edmund J Crampin
Decomposition of biomolecular reaction networks into pathways is a powerful approach to the analysis of metabolic and signalling networks. Current approaches based on analysis of the stoichiometric matrix reveal information about steady-state mass flows (reaction rates) through the network. In this work, we show how pathway analysis of biomolecular networks can be extended using an energy-based approach to provide information about energy flows through the network. This energy-based approach is developed using the engineering-inspired bond graph methodology to represent biomolecular reaction networks...
June 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/28690403/on-the-regularization-of-impact-without-collision-the-painlev%C3%A3-paradox-and-compliance
#17
S J Hogan, K Uldall Kristiansen
We consider the problem of a rigid body, subject to a unilateral constraint, in the presence of Coulomb friction. We regularize the problem by assuming compliance (with both stiffness and damping) at the point of contact, for a general class of normal reaction forces. Using a rigorous mathematical approach, we recover impact without collision (IWC) in both the inconsistent and the indeterminate Painlevé paradoxes, in the latter case giving an exact formula for conditions that separate IWC and lift-off. We solve the problem for arbitrary values of the compliance damping and give explicit asymptotic expressions in the limiting cases of small and large damping, all for a large class of rigid bodies...
June 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/28690402/nonlinear-model-identification-and-spectral-submanifolds-for-multi-degree-of-freedom-mechanical-vibrations
#18
Robert Szalai, David Ehrhardt, George Haller
In a nonlinear oscillatory system, spectral submanifolds (SSMs) are the smoothest invariant manifolds tangent to linear modal subspaces of an equilibrium. Amplitude-frequency plots of the dynamics on SSMs provide the classic backbone curves sought in experimental nonlinear model identification. We develop here, a methodology to compute analytically both the shape of SSMs and their corresponding backbone curves from a data-assimilating model fitted to experimental vibration signals. This model identification utilizes Taken's delay-embedding theorem, as well as a least square fit to the Taylor expansion of the sampling map associated with that embedding...
June 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/28690401/is-a-time-symmetric-interpretation-of-quantum-theory-possible-without-retrocausality
#19
Matthew S Leifer, Matthew F Pusey
Huw Price has proposed an argument that suggests a time symmetric ontology for quantum theory must necessarily be retrocausal, i.e. it must involve influences that travel backwards in time. One of Price's assumptions is that the quantum state is a state of reality. However, one of the reasons for exploring retrocausality is that it offers the potential for evading the consequences of no-go theorems, including recent proofs of the reality of the quantum state. Here, we show that this assumption can be replaced by a different assumption, called λ-mediation, that plausibly holds independently of the status of the quantum state...
June 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/28588420/correction-to-microprocessors-the-engines-of-the-digital-age
#20
Steve Furber
[This corrects the article DOI: 10.1098/rspa.2016.0893.].
May 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
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