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Proceedings. Mathematical, Physical, and Engineering Sciences

Steve Furber
[This corrects the article DOI: 10.1098/rspa.2016.0893.].
May 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Mark Welland
No abstract text is available yet for this article.
May 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Fan Wu, Inmaculada Campos, De-Wen Zhang, Steffi Krause
Light-addressable potentiometric sensors (LAPS) and scanning photo-induced impedance microscopy (SPIM) use photocurrent measurements at electrolyte-insulator-semiconductor substrates for spatio-temporal imaging of electrical potentials and impedance. The techniques have been used for the interrogation of sensor arrays and the imaging of biological systems. Sensor applications range from the detection of different types of ions and the label-free detection of charged molecules such as DNA and proteins to enzyme-based biosensors...
May 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Lewis A Baker, Scott Habershon
Photosynthetic pigment-protein complexes (PPCs) are a vital component of the light-harvesting machinery of all plants and photosynthesizing bacteria, enabling efficient transport of the energy of absorbed light towards the reaction centre, where chemical energy storage is initiated. PPCs comprise a set of chromophore molecules, typically bacteriochlorophyll species, held in a well-defined arrangement by a protein scaffold; this relatively rigid distribution leads to a viewpoint in which the chromophore subsystem is treated as a network, where chromophores represent vertices and inter-chromophore electronic couplings represent edges...
May 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Vicki Saward
Much has been written about the benefits that mathematics can bring to the UK economy and the manufacturing sector in particular, but less on the value of mathematicians and a mathematical training. This article, written from an industry perspective, considers the value of mathematicians to the UK's industrial base and the importance to the UK economy of encouraging young people in the UK to choose to study mathematics at school as a gateway to a wide range of careers. The points are illustrated using examples from the author's 20 years' experience in the security and intelligence and manufacturing sectors...
May 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Matteo Pezzulla, Norbert Stoop, Xin Jiang, D P Holmes
We investigate how thin structures change their shape in response to non-mechanical stimuli that can be interpreted as variations in the structure's natural curvature. Starting from the theory of non-Euclidean plates and shells, we derive an effective model that reduces a three-dimensional stimulus to the natural fundamental forms of the mid-surface of the structure, incorporating expansion, or growth, in the thickness. Then, we apply the model to a variety of thin bodies, from flat plates to spherical shells, obtaining excellent agreement between theory and numerics...
May 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Poul G Hjorth
This paper presents a brief review of how industrial mathematics, inspired by the Oxford Study Group activity, organized itself in Europe, gave rise to the European Consortium for Mathematics in Industry, the series of European Study Groups with Industry, and to new modes of productive contacts between industry and applied mathematicians in academia.
May 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Michael Ruzhansky, Durvudkhan Suragan
We give relations between main operators of quantum mechanics on one of most general classes of nilpotent Lie groups. Namely, we show relations between momentum and position operators as well as Euler and Coulomb potential operators on homogeneous groups. Homogeneous group analogues of some well-known inequalities such as Hardy's inequality, Heisenberg-Kennard type and Heisenberg-Pauli-Weyl type uncertainty inequalities, as well as Caffarelli-Kohn-Nirenberg inequality are derived, with best constants. The obtained relations yield new results already in the setting of both isotropic and anisotropic [Formula: see text], and of the Heisenberg group...
May 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Duncan Joyce, William J Parnell, Raphaël C Assier, I David Abrahams
In Parnell & Abrahams (2008 Proc. R. Soc. A464, 1461-1482. (doi:10.1098/rspa.2007.0254)), a homogenization scheme was developed that gave rise to explicit forms for the effective antiplane shear moduli of a periodic unidirectional fibre-reinforced medium where fibres have non-circular cross section. The explicit expressions are rational functions in the volume fraction. In that scheme, a (non-dilute) approximation was invoked to determine leading-order expressions. Agreement with existing methods was shown to be good except at very high volume fractions...
May 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Zhen Chen, Jinjie Zhu, Xianbin Liu
We consider the noise-induced escapes in an excitable system possessing a quasi-threshold manifold, along which there exists a certain point of minimal quasi-potential. In the weak noise limit, the optimal escaping path turns out to approach this particular point asymptotically, making it analogous to an ordinary saddle. Numerical simulations are performed and an elaboration on the effect of small but finite noise is given, which shows that the ridges where the prehistory probability distribution peaks are located mainly within the region where the quasi-potential increases gently...
May 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Christopher C Green, Christopher J Lustri, Scott W McCue
New numerical solutions to the so-called selection problem for one and two steadily translating bubbles in an unbounded Hele-Shaw cell are presented. Our approach relies on conformal mapping which, for the two-bubble problem, involves the Schottky-Klein prime function associated with an annulus. We show that a countably infinite number of solutions exist for each fixed value of dimensionless surface tension, with the bubble shapes becoming more exotic as the solution branch number increases. Our numerical results suggest that a single solution is selected in the limit that surface tension vanishes, with the scaling between the bubble velocity and surface tension being different to the well-studied problems for a bubble or a finger propagating in a channel geometry...
May 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
I A Kuznetsov, A V Kuznetsov
In this paper, we first develop a model of axonal transport of tubulin-associated unit (tau) protein. We determine the minimum number of parameters necessary to reproduce published experimental results, reducing the number of parameters from 18 in the full model to eight in the simplified model. We then address the following questions: Is it possible to estimate parameter values for this model using the very limited amount of published experimental data? Furthermore, is it possible to estimate confidence intervals for the determined parameters? The idea that is explored in this paper is based on using bootstrapping...
May 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
H Berjamin, N Favrie, B Lombard, G Chiavassa
In heterogeneous solids such as rocks and concrete, the speed of sound diminishes with the strain amplitude of a dynamic loading (softening). This decrease, known as 'slow dynamics', occurs at time scales larger than the period of the forcing. Also, hysteresis is observed in the steady-state response. The phenomenological model by Vakhnenko et al. (2004 Phys. Rev. E 70, 015602. (doi:10.1103/PhysRevE.70.015602)) is based on a variable that describes the softening of the material. However, this model is one dimensional and it is not thermodynamically admissible...
May 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Sara Ying Zhang, Jason Zheng Jiang, Simon A Neild
Linear passive vibration absorbers, such as tuned mass dampers, often contain springs, dampers and masses, although recently there has been a growing trend to employ or supplement the mass elements with inerters. When considering possible configurations with these elements broadly, two approaches are normally used: one structure-based and one immittance-based. Both approaches have their advantages and disadvantages. In this paper, a new approach is proposed: the structure-immittance approach. Using this approach, a full set of possible series-parallel networks with predetermined numbers of each element type can be represented by structural immittances, obtained via a proposed general formulation process...
May 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Allan P Fordy, Pavlos Xenitidis
We recently introduced a class of [Formula: see text] graded discrete Lax pairs and studied the associated discrete integrable systems (lattice equations). In this paper, we introduce the corresponding Yang-Baxter maps. Many well-known examples belong to this scheme for N=2, so, for N≥3, our systems may be regarded as generalizations of these. In particular, for each N we introduce a class of multi-component Yang-Baxter maps, which include H(B)III (of Papageorgiou et al. 2010 SIGMA 6, 003 (9 p). (doi:10.3842/SIGMA...
May 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
J T Stone, R H Self, C J Howls
The downstream propagation of high-frequency acoustic waves from a point source in a subsonic jet obeying Lilley's equation is well known to be organized around the so-called 'cone of silence', a fold catastrophe across which the amplitude may be modelled uniformly using Airy functions. Here we show that acoustic waves not only unexpectedly propagate upstream, but also are organized at constant distance from the point source around a cusp catastrophe with amplitude modelled locally by the Pearcey function. Furthermore, the cone of silence is revealed to be a cross-section of a swallowtail catastrophe...
May 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Claudio Carmeli, Teiko Heinosaari, Jussi Schultz, Alessandro Toigo
Determining the state of a quantum system is a consuming procedure. For this reason, whenever one is interested only in some particular property of a state, it would be desirable to design a measurement set-up that reveals this property with as little effort as possible. Here, we investigate whether, in order to successfully complete a given task of this kind, one needs an informationally complete measurement, or if something less demanding would suffice. The first alternative means that in order to complete the task, one needs a measurement which fully determines the state...
May 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
Maciej Błaszak, Artur Sergyeyev
In this paper, we introduce a multi-dimensional version of the R-matrix approach to the construction of integrable hierarchies. Applying this method to the case of the Lie algebra of functions with respect to the contact bracket, we construct integrable hierarchies of (3+1)-dimensional dispersionless systems of the type recently introduced in Sergyeyev (2014 (
May 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
T Barker, D G Schaeffer, M Shearer, J M N T Gray
Continuum modelling of granular flow has been plagued with the issue of ill-posed dynamic equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb friction law are ill-posed regardless of the deformation, whereas the rate-dependent μ(I)-rheology is ill-posed when the non-dimensional inertial number I is too high or too low. Here, incorporating ideas from critical-state soil mechanics, we derive conditions for well-posedness of partial differential equations that combine compressibility with I-dependent rheology...
May 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
R G Halburd
Second-order discrete equations are studied over the field of rational functions [Formula: see text], where z is a variable not appearing in the equation. The exact degree of each iterate as a function of z can be calculated easily using the standard calculations that arise in singularity confinement analysis, even when the singularities are not confined. This produces elementary yet rigorous entropy calculations.
May 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
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