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Proceedings. Mathematical, Physical, and Engineering Sciences

S R Otto
At its core, like many other sports, golf is a game of integers. The minimization of the number of strokes played is generally what determines the winner, whether each of these are associated with the shortest of putts or the longest of drives. The outcomes of these shots are influenced by very slight changes, but hopefully in a deterministic sense. Understanding the mechanics of golf necessitates the development of models and this is coupled more often than not to the use of statistics. In essence, the individual aspects of the sport can be modelled adequately via fairly simplistic models, but the presence of a human at one end of the kinematic chain has a significant impact on the variability of the entire process...
August 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
W Hamouche, C Maurini, S Vidoli, A Vincenti
We have designed and tested experimentally a morphing structure consisting of a neutrally stable thin cylindrical shell driven by a multi-parameter piezoelectric actuation. The shell is obtained by plastically deforming an initially flat copper disc, so as to induce large isotropic and almost uniform inelastic curvatures. Following the plastic deformation, in a perfectly isotropic system, the shell is theoretically neutrally stable, having a continuous set of stable cylindrical shapes corresponding to the rotation of the axis of maximal curvature...
August 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Gustavo Gioia, Pinaki Chakraborty
We show that the classic laws of the mean-velocity profiles (MVPs) of wall-bounded turbulent flows-the 'law of the wall,' the 'defect law' and the 'log law'-can be predicated on a sufficient condition with no manifest ties to the MVPs, namely that viscosity and finite turbulent domains have a depressive effect on the spectrum of turbulent energy. We also show that this sufficient condition is consistent with empirical data on the spectrum and may be deemed a general property of the energetics of wall turbulence...
August 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Gaetano Arena, Rainer M J Groh, Alex Brinkmeyer, Raf Theunissen, Paul M Weaver, Alberto Pirrera
This paper introduces conceptual design principles for a novel class of adaptive structures that provide both flow regulation and control. While of general applicability, these design principles, which revolve around the idea of using the instabilities and elastically nonlinear behaviour of post-buckled panels, are exemplified through a case study: the design of a shape-adaptive air inlet. The inlet comprises a deformable post-buckled member that changes shape depending on the pressure field applied by the surrounding fluid, thereby regulating the inlet aperture...
August 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Steffen Pfeiffer, Martin Franz-Xaver Wagner
Many crystalline materials exhibit twinned microstructures, where well-defined orientation relationships define the special symmetry between different, elastically anisotropic twin variants. When such twins are subjected to external loading, additional internal stresses necessarily occur at the twin boundaries in order to maintain compatibility. These compatibility stresses are constant inside each variant in repeating stacks of twins and considerably affect the local stress state. In this paper, we use anisotropic linear elasticity to derive general analytical solutions for compatibility stresses in a stack of twin variants in arbitrary materials, for arbitrary variant volume fractions and twin types, subjected to arbitrary applied stresses...
August 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Xiaoshuai Ding, Jinde Cao, Xuan Zhao, Fuad E Alsaadi
This paper is concerned with the drive-response synchronization for a class of fractional-order bidirectional associative memory neural networks with time delays, as well as in the presence of discontinuous activation functions. The global existence of solution under the framework of Filippov for such networks is firstly obtained based on the fixed-point theorem for condensing map. Then the state feedback and impulsive controllers are, respectively, designed to ensure the Mittag-Leffler synchronization of these neural networks and two new synchronization criteria are obtained, which are expressed in terms of a fractional comparison principle and Razumikhin techniques...
August 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Luis Dorfmann, Ray W Ogden
In the last few years, it has been recognized that the large deformation capacity of elastomeric materials that are sensitive to electric fields can be harnessed for use in transducer devices such as actuators and sensors. This has led to the reassessment of the mathematical theory that is needed for the description of the electromechanical (in particular, electroelastic) interactions for purposes of material characterization and prediction. After a review of the key experiments concerned with determining the nature of the electromechanical interactions and a discussion of the range of applications to devices, we provide a short account of the history of developments in the nonlinear theory...
August 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
I A Milne, R N Sharma, R G J Flay
The structure of turbulence in a rapid tidal flow is characterized through new observations of fundamental statistical properties at a site in the UK which has a simple geometry and sedate surface wave action. The mean flow at the Sound of Islay exceeded 2.5 m s(-1) and the turbulent boundary layer occupied the majority of the water column, with an approximately logarithmic mean velocity profile identifiable close to the seabed. The anisotropic ratios, spectral scales and higher-order statistics of the turbulence generally agree well with values reported for two-dimensional open channels in the laboratory and other tidal channels, therefore providing further support for the application of universal models...
August 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Andrea Nobili, Enrico Radi, Luca Lanzoni
The problem of a rectilinear crack propagating at constant speed in an elastically supported thin plate and acted upon by an equally moving load is considered. The full-field solution is obtained and the spotlight is set on flexural edge wave generation. Below the critical speed for the appearance of travelling waves, a threshold speed is met which marks the transformation of decaying edge waves into edge waves propagating along the crack and dying away from it. Yet, besides these, and for any propagation speed, a pair of localized edge waves, which rapidly decay behind the crack tip, is also shown to exist...
August 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Henri Gouin, Pierre Seppecher
Thanks to an expansion with respect to densities of energy, mass and entropy, we discuss the concept of thermocapillary fluid for inhomogeneous fluids. The non-convex state law valid for homogeneous fluids is modified by adding terms taking account of the gradients of these densities. This seems more realistic than Cahn and Hilliard's model which uses a density expansion in mass-density gradient only. Indeed, through liquid-vapour interfaces, realistic potentials in molecular theories show that entropy density and temperature do not vary with the mass density as it would do in bulk phases...
August 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
J S Fannon, A C Fowler, I R Moyles
We summarize the present form of the instability theory for drumlin formation, which describes the coupled subglacial flow of ice, water and sediment. This model has evolved over the last 20 years, and is now at the point where it can predict instabilities corresponding to ribbed moraine, drumlins and mega-scale glacial lineations, but efforts to provide numerical solutions of the model have been limited. The present summary adds some slight nuances to previously published versions of the theory, notably concerning the constitutive description of the subglacial water film and its flow...
August 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Jean-Claude Michel, Pierre Suquet
This study presents a family of estimates for effective potentials in nonlinear polycrystals. Noting that these potentials are given as averages, several quadrature formulae are investigated to express these integrals of nonlinear functions of local fields in terms of the moments of these fields. Two of these quadrature formulae reduce to known schemes, including a recent proposition (Ponte Castañeda 2015 Proc. R. Soc. A471, 20150665 (doi:10.1098/rspa.2015.0665)) obtained by completely different means. Other formulae are also reviewed that make use of statistical information on the fields beyond their first and second moments...
August 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Stefano Maffei, Andrew Jackson, Philip W Livermore
We consider fluid-filled spheres and spheroidal containers of eccentricity ϵ in rapid rotation, as a proxy for the interior dynamics of stars and planets. The fluid motion is assumed to be quasi-geostrophic (QG): horizontal motions are invariant parallel to the rotation axis z, a characteristic which is handled by use of a stream function formulation which additionally enforces mass conservation and non-penetration at the boundary. By linearizing about a quiescent background state, we investigate a variety of methods to study the QG inviscid inertial wave modes which are compared with fully three-dimensional (3D) calculations...
August 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Abhishek Deshpande, Manoj Gopalkrishnan, Thomas E Ouldridge, Nick S Jones
We consider the challenge of operating a reliable bit that can be rapidly erased. We find that both erasing and reliability times are non-monotonic in the underlying friction, leading to a trade-off between erasing speed and bit reliability. Fast erasure is possible at the expense of low reliability at moderate friction, and high reliability comes at the expense of slow erasure in the underdamped and overdamped limits. Within a given class of bit parameters and control strategies, we define 'optimal' designs of bits that meet the desired reliability and erasing time requirements with the lowest operational work cost...
August 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Irene Brito, Filipe C Mena
We prove that, for a given spherically symmetric fluid distribution with tangential pressure on an initial space-like hypersurface with a time-like boundary, there exists a unique, local in time solution to the Einstein equations in a neighbourhood of the boundary. As an application, we consider a particular elastic fluid interior matched to a vacuum exterior.
August 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Cormac Browne, Tristan Farrow, Oscar C O Dahlsten, Robert A Taylor, Vedral Vlatko
We demonstrate with an experiment how molecules are a natural test bed for probing fundamental quantum thermodynamics. Single-molecule spectroscopy has undergone transformative change in the past decade with the advent of techniques permitting individual molecules to be distinguished and probed. We demonstrate that the quantum Jarzynski equality for heat is satisfied in this set-up by considering the time-resolved emission spectrum of organic molecules as arising from quantum jumps between states. This relates the heat dissipated into the environment to the free energy difference between the initial and final state...
August 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
N M Mangan, J N Kutz, S L Brunton, J L Proctor
We develop an algorithm for model selection which allows for the consideration of a combinatorially large number of candidate models governing a dynamical system. The innovation circumvents a disadvantage of standard model selection which typically limits the number of candidate models considered due to the intractability of computing information criteria. Using a recently developed sparse identification of nonlinear dynamics algorithm, the sub-selection of candidate models near the Pareto frontier allows feasible computation of Akaike information criteria (AIC) or Bayes information criteria scores for the remaining candidate models...
August 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Baran Yildirim, Hankang Yang, Andrew Gouldstone, Sinan Müftü
The impact mechanics of micrometre-scale metal particles with flat metal surfaces is investigated for high-velocity impacts ranging from 50 m s(-1) to more than 1 km s(-1), where impact causes predominantly plastic deformation. A material model that includes high strain rate and temperature effects on the yield stress, heat generation due to plasticity, material damage due to excessive plastic strain and heat transfer is used in the numerical analysis. The coefficient of restitution e is predicted by the classical work using elastic-plastic deformation analysis with quasi-static impact mechanics to be proportional to [Formula: see text] and [Formula: see text] for the low and moderate impact velocities that span the ranges of 0-10 and 10-100 m s(-1), respectively...
August 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Renato Maia Matarazzo Orsino
This paper proposes a novel approach to the modelling of lumped-parameter dynamic systems, based on representing them by hierarchies of mathematical models of increasing complexity instead of a single (complex) model. Exploring the multilevel modularity that these systems typically exhibit, a general recursive modelling methodology is proposed, in order to conciliate the use of the already existing modelling techniques. The general algorithm is based on a fundamental theorem that states the conditions for computing projection operators recursively...
August 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Jianfeng Lu, Stefan Steinerberger
The purpose of this short paper is to give a variation on the classical Donsker-Varadhan inequality, which bounds the first eigenvalue of a second-order elliptic operator on a bounded domain Ω by the largest mean first exit time of the associated drift-diffusion process via [Formula: see text]Instead of looking at the mean of the first exit time, we study quantiles: let [Formula: see text] be the smallest time t such that the likelihood of exiting within that time is p, then [Formula: see text]Moreover, as [Formula: see text], this lower bound converges to λ1...
August 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
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