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Proceedings. Mathematical, Physical, and Engineering Sciences

Michael Lockwood
No abstract text is available yet for this article.
January 2019: Proceedings. Mathematical, Physical, and Engineering Sciences
Mrityunjay Kothari, Moon-Hyun Cha, Victor Lefevre, Kyung-Suk Kim
As a sequel of part I (Kothari et al. 2018 Proc. R. Soc. A 474 , 20180054), we present a general thermodynamic framework of flexoelectric constitutive laws for multi-layered graphene (MLG), and apply these laws to explain the role of crinkles in peculiar molecular adsorption characteristics of highly oriented pyrolytic graphite (HOPG) surfaces. The thermodynamically consistent constitutive laws lead to a non-local interaction model of polarization induced by electromechanical deformation with flexoelectricity-dielectricity coupling...
January 2019: Proceedings. Mathematical, Physical, and Engineering Sciences
A E Madison, P A Madison
A multiple-cell approach is discussed as a possible alternative to the higher dimensional crystallography of icosahedral quasicrystals. It is based on the Socolar-Steinhardt tiling combined with the quasi-unit cell model. Quasi-unit cells fill the space without gaps and overlappings similar to those in periodic crystals. Similarly, the atoms can occupy general and special positions. The alloy stoichiometry and the packing density can be calculated through the relative tile frequencies, which in turn are determined as the components of the Perron-Frobenius eigenvector of the corresponding substitution matrix...
January 2019: Proceedings. Mathematical, Physical, and Engineering Sciences
S L Chen
Hydraulic fracturing is the primary method of stimulation in unconventional reservoirs, playing a significant role in oil and gas production enhancement. A key issue for the analysis of hydraulic fracture initiation is to accurately determine the stress distributions in the vicinity of the borehole caused by the injection of pressurized fluids. This paper develops an exact, three-dimensional, poroelastic coupled analytical solution for such stress analysis of an arbitrarily inclined borehole subjected concurrently to a finite-length fluid discharge and in situ stresses, using Fourier expansion theorem and the Laplace-Fourier integral transform technique...
January 2019: Proceedings. Mathematical, Physical, and Engineering Sciences
Edmund Barter, Thilo Gross
In the twenty-first century, ongoing rapid urbanization highlights the need to gain deeper insights into the social structure of cities. While work on this challenge can profit from abundant data sources, the complexity of this data itself proves to be a challenge. In this paper, we use diffusion maps, a manifold learning method, to discover hidden manifolds in the UK 2011 census dataset. The census key statistics and quick statistics report 1450 different statistical features for each census output area. Here, we focus primarily on the city of Bristol and the surrounding countryside, comprising 3490 of these output areas...
January 2019: Proceedings. Mathematical, Physical, and Engineering Sciences
Samad Khabbazi Oskouei, Stefano Mancini, Mark M Wilde
In this paper, we prove a quantum union bound that is relevant when performing a sequence of binary-outcome quantum measurements on a quantum state. The quantum union bound proved here involves a tunable parameter that can be optimized, and this tunable parameter plays a similar role to a parameter involved in the Hayashi-Nagaoka inequality (Hayashi & Nagaoka 2003 IEEE Trans. Inf. Theory 49 , 1753-1768. (doi:10.1109/TIT.2003.813556)), used often in quantum information theory when analysing the error probability of a square-root measurement...
January 2019: Proceedings. Mathematical, Physical, and Engineering Sciences
Qiwei Zhan, Mingwei Zhuang, Yuan Fang, Jian-Guo Liu, Qing Huo Liu
A compact Green's function for general dispersive anisotropic poroelastic media in a full-frequency regime is presented for the first time. First, starting in a frequency domain, the anisotropic dispersion is exactly incorporated into the constitutive relationship, thus avoiding fractional derivatives in a time domain. Then, based on the Radon transform, the original three-dimensional differential equation is effectively reduced to a one-dimensional system in space. Furthermore, inspired by the strategy adopted in the characteristic analysis of hyperbolic equations, the eigenvector diagonalization method is applied to decouple the one-dimensional vector problem into several independent scalar equations...
January 2019: Proceedings. Mathematical, Physical, and Engineering Sciences
V Yu Filimonov, K B Koshelev
In this paper, the theoretical analysis of the critical autoignition conditions for exothermically reacting systems at any value of the reaction order was conducted. The calculated and approximate analytical dependencies for the relationship between the parameters at the ignition limit were obtained. On the basis of the obtained diagrams of critical parameters, the conditions of thermal explosion (TE) degeneration for reactions of arbitrary order were determined. It was established that the existing theory of TE gives the correct estimates of ignition temperatures for a given condition of exothermic reaction realization (heat transfer coefficient, specific surface area, initial concentration)...
January 2019: Proceedings. Mathematical, Physical, and Engineering Sciences
Ji-Feng Yan, Gan-Yun Huang
A generalized double-Hertz (D-H) model has been proposed to consider the adhesive contact between an elastic cylinder and an elastic half space under inclined forces. The normal traction is exactly the same as that in the conventional D-H model. The shear traction of finite value is distributed into a slipping zone and a non-slipping zone. In the slipping zone, the shear traction is proportional to the compressive pressure. With the model, adhesive contact behaviour between cylinders has been numerically illustrated...
January 2019: Proceedings. Mathematical, Physical, and Engineering Sciences
Gordon Slade
The self-avoiding walk, and lattice spin systems such as the φ 4 model, are models of interest both in mathematics and in physics. Many of their important mathematical problems remain unsolved, particularly those involving critical exponents. We survey some of these problems, and report on recent advances in their mathematical understanding via a rigorous non-perturbative renormalization group method.
January 2019: Proceedings. Mathematical, Physical, and Engineering Sciences
Siddhartha Mukherjee, Jayabrata Dhar, Sunando DasGupta, Suman Chakraborty
Augmenting the dispersion of a solute species and fluidic mixing remains a challenging proposition in electrically actuated microfluidic devices, primarily due to an inherent plug-like nature of the velocity profile under uniform surface charge conditions. While a judicious patterning of surface charges may obviate some of the concerning challenges, the consequent improvement in solute dispersion may turn out to be marginal. Here, we show that by exploiting a unique coupling of patterned surface charges with intrinsically induced thermal gradients, it may be possible to realize giant augmentations in solute dispersion in electro-osmotic flows...
January 2019: Proceedings. Mathematical, Physical, and Engineering Sciences
B-Y Cao, M Di Domenico, B-D Nie, A Sellitto
A theoretical model to describe heat transport in functionally graded nanomaterials is developed in the framework of extended thermodynamics. The heat-transport equation used in our theoretical model is of the Maxwell-Cattaneo type. We study the propagation of acceleration waves in functionally graded materials (FGMs). In the special case of functionally graded Si1- c Ge c thin layers, we point out the influence of the composition gradient on the propagation of heat pulses. A possible use of heat pulses as exploring tool to infer the inner composition of FGMs is suggested...
January 2019: Proceedings. Mathematical, Physical, and Engineering Sciences
Christophe Audouze, Prasanth B Nair
We consider the problem of learning a multivariate function from a set of scattered observations using a sparse low-rank separated representation (SSR) model. The model structure considered here is promising for high-dimensional learning problems; however, existing training algorithms based on alternating least-squares (ALS) are known to have convergence difficulties, particularly when the rank of the model is greater than 1. In the present work, we supplement the model structure with sparsity constraints to ensure the well posedness of the approximation problem...
January 2019: Proceedings. Mathematical, Physical, and Engineering Sciences
P Rogolino, V A Cimmelli
We consider a system of balance laws arising in extended irreversible thermodynamics of rigid heat conductors, together with its differential conse- quences, namely the higher-order system obtained by taking into account the time and space derivatives of the original system. We point out some mathematical properties of the differential consequences, with particular attention to the problem of the propagation of thermal perturbations with finite speed. We prove that, under an opportune choice of the initial conditions, a solution of the Cauchy problem for the system of differential consequences is also a solution of the Cauchy problem for the original system...
January 2019: Proceedings. Mathematical, Physical, and Engineering Sciences
Rami Abi-Akl, Rohan Abeyaratne, Tal Cohen
Surface growth by association or dissociation of material on the boundary of a body is ubiquitous in both natural and engineering systems. It is the fundamental mechanism by which biological materials grow, starting from the level of a single cell, and is increasingly applied in engineering processes for fabrication and self-assembly. A significant challenge in modelling such processes arises due to the inherent coupled interaction between the growth kinetics, the local stresses and the diffusing constituents needed to sustain the growth...
January 2019: Proceedings. Mathematical, Physical, and Engineering Sciences
L A Fullard, E C P Breard, C E Davies, A J R Godfrey, M Fukuoka, A Wade, J Dufek, G Lube
The dynamics of granular flow in a rectangular silo with two symmetrically placed exit openings is investigated using particle image velocimetry (PIV), flow rate measurements and discrete element modelling (DEM). The flow of mustard seeds in a Perspex silo is recorded using a high-speed camera and the resulting image frames are analysed using PIV to obtain velocity, velocity divergence and shear rate plots. A change in flow structure is observed as the distance L between the two openings is varied. The mass flow rate is shown to be at a maximum at zero opening separation, decreasing as L is increased; it then reaches a minimum before rising to an equilibrium rate close to two times that of an isolated (non-interacting) opening...
January 2019: Proceedings. Mathematical, Physical, and Engineering Sciences
J Orszaghova, H Wolgamot, S Draper, R Eatock Taylor, P H Taylor, And A Rafiee
Wave energy converters and other offshore structures may exhibit instability, in which one mode of motion is excited parametrically by motion in another. Here, theoretical results for the transverse motion instability (large sway oscillations perpendicular to the incident wave direction) of a submerged wave energy converter buoy are compared to an extensive experimental dataset. The device is axi-symmetric (resembling a truncated vertical cylinder) and is taut-moored via a single tether. The system is approximately a damped elastic pendulum...
January 2019: Proceedings. Mathematical, Physical, and Engineering Sciences
V V Zalipaev, S Yu Kosulnikov
Guided localized electromagnetic waves propagating along one-dimensional (1D) arrays of thin metallic parallel wires, finite and infinite, are studied. The arrays are embedded into the upper dielectric half-space close to the interface separating it from the lower dielectric medium with different permittivity and the same permeability. Firstly, a dependence of resonance frequencies of excited wave modes for finite array with respect to the array height above the interface is studied. The array is excited by a normally incident plane wave...
January 2019: Proceedings. Mathematical, Physical, and Engineering Sciences
Sophie Ramananarivo, Thomas Mitchel, Leif Ristroph
Aeronautical studies have shown that subtle changes in aerofoil shape substantially alter aerodynamic forces during fixed-wing flight. The link between shape and performance for flapping locomotion involves distinct mechanisms associated with the complex flows and unsteady motions of an air- or hydro-foil. Here, we use an evolutionary scheme to modify the cross-sectional shape and iteratively improve the speed of three-dimensional printed heaving foils in forward flight. In this algorithmic-experimental method, 'genes' are mathematical parameters that define the shape, 'breeding' is the combination of genes from parent wings to form a daughter, and a wing's measured speed is its 'fitness' that dictates its likelihood of breeding...
January 2019: Proceedings. Mathematical, Physical, and Engineering Sciences
Yuri A Godin, Boris Vainberg
We consider transverse propagation of electromagnetic waves through a two-dimensional composite material containing a periodic rectangular array of circular cylinders. Propagation of waves is described by the Helmholtz equation with the continuity conditions for the tangential components of the electric and magnetic fields on the boundaries of the cylinders. We assume that the cell size is small compared with the wavelength, but large compared with the radius a of the inclusions. Explicit formulae are obtained for asymptotic expansion of the solution of the problem in terms of the dimensionless magnitude q of the wavevector and radius a ...
January 2019: Proceedings. Mathematical, Physical, and Engineering Sciences
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