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Proceedings. Mathematical, Physical, and Engineering Sciences

P Huthwaite
Diffraction tomography is a powerful algorithm for producing high-resolution quantitative reconstructions across a wide range of applications. A major drawback of the method is that it operates on the scattered field, which cannot generally be directly measured, but must instead be calculated by subtracting the incident field, i.e. the equivalent field with no scatterer present. Unfortunately, often the incident field is not measurable and hence must be estimated, causing errors. This paper highlights an important, but not widely recognized, result: for particular widely used formulations of the algorithm, the subtraction of the incident field is unnecessary, and the algorithm can actually be applied directly to measured signals...
November 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Hongbin Fang, Suyi Li, K W Wang
A generic degree-4 vertex (4-vertex) origami possesses one continuous degree-of-freedom for rigid folding, and this folding process can be stopped when two of its facets bind together. Such facet-binding will induce self-locking so that the overall structure stays at a pre-specified configuration without additional locking elements or actuators. Self-locking offers many promising properties, such as programmable deformation ranges and piecewise stiffness jumps, that could significantly advance many adaptive structural systems...
November 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Natércia D N Rodrigues, Michael Staniforth, Vasilios G Stavros
The relationship between exposure to ultraviolet (UV) radiation and skin cancer urges the need for extra photoprotection, which is presently provided by widespread commercially available sunscreen lotions. Apart from having a large absorption cross section in the UVA and UVB regions of the electromagnetic spectrum, the chemical absorbers in these photoprotective products should also be able to dissipate the excess energy in a safe way, i.e. without releasing photoproducts or inducing any further, harmful, photochemistry...
November 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Souhayl Sadik, Arash Yavari
In this paper, we are concerned with finding exact solutions for the stress fields of nonlinear solids with non-symmetric distributions of defects (or more generally finite eigenstrains) that are small perturbations of symmetric distributions of defects with known exact solutions. In the language of geometric mechanics, this corresponds to finding a deformation that is a result of a perturbation of the metric of the Riemannian material manifold. We present a general framework that can be used for a systematic analysis of this class of anelasticity problems...
November 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
J J Bissell
By substituting the Cattaneo-Christov heat-flow model for the more usual parabolic Fourier law, we consider the impact of hyperbolic heat-flow effects on thermal convection in the classic problem of a magnetized conducting fluid layer heated from below. For stationary convection, the system is equivalent to that studied by Chandrasekhar (Hydrodynamic and Hydromagnetic Stability, 1961), and with free boundary conditions we recover the classical critical Rayleigh number [Formula: see text] which exhibits inhibition of convection by the field according to [Formula: see text] as [Formula: see text], where Q is the Chandrasekhar number...
November 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
P Huthwaite
Producing accurate thickness maps of corrosion damage is of great importance for assessing life in the petrochemical industry. Guided wave tomography provides a solution for this, by sending guided waves through the region of interest, then using tomographic imaging techniques to reconstruct the thickness map, importantly eliminating the need to take measurements at all points across the surface. However, to achieve accurate maps, the imaging algorithm must account for the way in which the guided waves interact with corrosion defects, and the complex scattering which occurs...
November 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Andrew Pickering, Hai-Qiong Zhao, Zuo-Nong Zhu
In this paper, we propose a new semidiscrete Hirota equation which yields the Hirota equation in the continuum limit. We focus on the topic of how the discrete space step δ affects the simulation for the soliton solution to the Hirota equation. The Darboux transformation and explicit solution for the semidiscrete Hirota equation are constructed. We show that the continuum limit for the semidiscrete Hirota equation, including the Lax pair, the Darboux transformation and the explicit solution, yields the corresponding results for the Hirota equation as [Formula: see text]...
November 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Mikhail Erementchouk, Soumitra Roy Joy, Pinaki Mazumder
States of the electromagnetic field confined near a periodically corrugated surface of a perfect conductor, spoof surface plasmon polaritons (SSPP), are approached systematically based on the developed adaptation of the mode matching technique to the transfer matrix formalism. Within this approach, in the approximation of narrow grooves, systems with arbitrary transversal structure can be investigated straightforwardly, thus lifting the restrictions of the effective medium description and usual implementations of mode matching...
November 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Graeme W Milton
The theory of inhomogeneous analytic materials is developed. These are materials where the coefficients entering the equations involve analytic functions. Three types of analytic materials are identified. The first two types involve an integer p. If p takes its maximum value, then we have a complete analytic material. Otherwise, it is incomplete analytic material of rank p. For two-dimensional materials, further progress can be made in the identification of analytic materials by using the well-known fact that a 90(°) rotation applied to a divergence-free field in a simply connected domain yields a curl-free field, and this can then be expressed as the gradient of a potential...
November 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Shou-Fu Tian
In this paper, we implement the Fokas method to study initial-boundary value problems of the mixed coupled nonlinear Schrödinger equation formulated on the half-line with Lax pairs involving 3×3 matrices. The solution can be written in terms of the solution to a 3×3 Riemann-Hilbert problem. The relevant jump matrices are explicitly expressed in terms of the matrix-value spectral functions s(k) and S(k), which are determined by the initial values and boundary values at x=0, respectively. Some of these boundary values are unknown; however, using the fact that these specific functions satisfy a certain global relation, the unknown boundary values can be expressed in terms of the given initial and boundary data...
November 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
G O Antoine, E de Langre, S Michelin
Vortex-induced vibrations (VIV) of flexible cables are an example of flow-induced vibrations that can act as energy harvesting systems by converting energy associated with the spontaneous cable motion into electricity. This work investigates the optimal positioning of the harvesting devices along the cable, using numerical simulations with a wake oscillator model to describe the unsteady flow forcing. Using classical gradient-based optimization, the optimal harvesting strategy is determined for the generic configuration of a flexible cable fixed at both ends, including the effect of flow forces and gravity on the cable's geometry...
November 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Feodor M Borodich, Boris A Galanov
Contact probing is the preferable method for studying mechanical properties of thin two-dimensional (2D) materials. These studies are based on analysis of experimental force-displacement curves obtained by loading of a stretched membrane by a probe of an atomic force microscope or a nanoindenter. Both non-adhesive and adhesive contact interactions between such a probe and a 2D membrane are studied. As an example of the 2D materials, we consider a graphene crystal monolayer whose discrete structure is modelled as a 2D isotropic elastic membrane...
November 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
S Yakubovich, P Drygas, V Mityushev
Closed-form formulae for the conditionally convergent two-dimensional (2D) static lattice sums S2 (for conductivity) and T2 (for elasticity) are deduced in terms of the complete elliptic integrals of the first and second kind. The obtained formulae yield asymptotic analytical formulae for the effective tensors of 2D composites with circular inclusions up to the third order in concentration. Exact relations between S2 and T2 for different lattices are established. In particular, the value S2=π for the square and hexagonal arrays is discussed and T2=π/2 for the hexagonal is deduced...
November 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
E K Lenzi, H V Ribeiro, A A Tateishi, R S Zola, L R Evangelista
Diffusion of particles in a heterogeneous system separated by a semipermeable membrane is investigated. The particle dynamics is governed by fractional diffusion equations in the bulk and by kinetic equations on the membrane, which characterizes an interface between two different media. The kinetic equations are solved by incorporating memory effects to account for anomalous diffusion and, consequently, non-Debye relaxations. A rich variety of behaviours for the particle distribution at the interface and in the bulk may be found, depending on the choice of characteristic times in the boundary conditions and on the fractional index of the modelling equations...
November 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
D A Zanin, L G De Pietro, Q Peter, A Kostanyan, H Cabrera, A Vindigni, Th Bähler, D Pescia, U Ramsperger
We perform scanning tunnelling microscopy (STM) in a regime where primary electrons are field-emitted from the tip and excite secondary electrons out of the target-the scanning field-emission microscopy regime (SFM). In the SFM mode, a secondary-electron contrast as high as 30% is observed when imaging a monoatomic step between a clean W(110)- and an Fe-covered W(110)-terrace. This is a figure of contrast comparable to STM. The apparent width of the monoatomic step attains the 1 nm mark, i.e. it is only marginally worse than the corresponding width observed in STM...
November 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Laura M Barge, Silvana S S Cardoso, Julyan H E Cartwright, Ivria J Doloboff, Erika Flores, Elena Macías-Sánchez, C Ignacio Sainz-Díaz, Pablo Sobrón
Rio Tinto in southern Spain has become of increasing astrobiological significance, in particular for its similarity to environments on early Mars. We present evidence of tubular structures from sampled terraces in the stream bed at the source of the river, as well as ancient, now dry, terraces. This is the first reported finding of tubular structures in this particular environment. We propose that some of these structures could be formed through self-assembly via an abiotic mechanism involving templated precipitation around a fluid jet, a similar mechanism to that commonly found in so-called chemical gardens...
November 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Jing Meng, Junfeng Liu, Yuan Xu, Dabo Guan, Zhu Liu, Ye Huang, Shu Tao
Globalization pushes production and consumption to geographically diverse locations and generates a variety of sizeable opportunities and challenges. The distribution and associated effects of short-lived primary fine particulate matter (PM2.5), a representative of local pollution, are significantly affected by the consumption through global supply chain. Tele-connection is used here to represent the link between production and consumption activity at large distances. In this study, we develop a global consumption-based primary PM2...
November 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Hung-Chu Hsu, Marc Francius, Pablo Montalvo, Christian Kharif
This paper considers two-dimensional periodic gravity-capillary waves propagating steadily in finite depth on a linear shear current (constant vorticity). A perturbation series solution for steady periodic waves, accurate up to the third order, is derived using a classical Stokes expansion procedure, which allows us to include surface tension effects in the analysis of wave-current interactions in the presence of constant vorticity. The analytical results are then compared with numerical computations with the full equations...
November 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Lin Chen, Dragomir Ž Ðoković
We investigate the separable states ρ of an arbitrary multi-partite quantum system with Hilbert space [Formula: see text] of dimension d. The length L(ρ) of ρ is defined as the smallest number of pure product states having ρ as their mixture. The length filtration of the set of separable states, [Formula: see text], is the increasing chain [Formula: see text], where [Formula: see text]. We define the maximum length, [Formula: see text], critical length, Lcrit, and yet another special length, Lc, which was defined by a simple formula in one of our previous papers...
November 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Piergiulio Tempesta
We shall prove that the celebrated Rényi entropy is the first example of a new family of infinitely many multi-parametric entropies. We shall call them the Z-entropies. Each of them, under suitable hypotheses, generalizes the celebrated entropies of Boltzmann and Rényi. A crucial aspect is that every Z-entropy is composable (Tempesta 2016 Ann. Phys.365, 180-197. (doi:10.1016/j.aop.2015.08.013)). This property means that the entropy of a system which is composed of two or more independent systems depends, in all the associated probability space, on the choice of the two systems only...
November 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
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