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Proceedings. Mathematical, Physical, and Engineering Sciences

Julia M Fischer, David Mahlberg, Tanglaw Roman, Axel Groß
The adsorption of water on bimetallic PtRu/Pt(111) surface alloys has been studied based on periodic density functional theory calculations including dispersion corrections. The Ru atoms of the PtRu surface alloy interact more strongly with water than Pt atoms, as far as both single water molecules and ice-like hexagonal structures are concerned. Within the surface alloy layer, the lateral ligand effect reducing the local reactivity of the surface atoms with increasing Ru content is more dominant than the opposing geometric effect due to the tensile strain...
October 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Michael B Muhlestein, Caleb F Sieck, Andrea Alù, Michael R Haberman
Materials that require coupling between the stress-strain and momentum-velocity constitutive relations were first proposed by Willis (Willis 1981 Wave Motion3, 1-11. (doi:10.1016/0165-2125(81)90008-1)) and are now known as elastic materials of the Willis type, or simply Willis materials. As coupling between these two constitutive equations is a generalization of standard elastodynamic theory, restrictions on the physically admissible material properties for Willis materials should be similarly generalized. This paper derives restrictions imposed on the material properties of Willis materials when they are assumed to be reciprocal, passive and causal...
October 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Brian Conrey, Jonathan P Keating
We establish a connection between the conjectural two-over-two ratios formula for the Riemann zeta-function and a conjecture concerning correlations of a certain arithmetic function. Specifically, we prove that the ratios conjecture and the arithmetic correlations conjecture imply the same result. This casts a new light on the underpinnings of the ratios conjecture, which previously had been motivated by analogy with formulae in random matrix theory and by a heuristic recipe.
October 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Hongwei Yang, Béatrice A Baudet, Ting Yao
The surface roughness of soil grains affects the mechanical behaviour of soils, but the characterization of real soil grain roughness is still limited in both quantity and quality. A new method is proposed, which applies the power spectral density (PSD), typically used in tribology, to optical interferometry measurements of soil grain surfaces. The method was adapted to characterize the roughness of soil grains separately from their shape, allowing the scale of the roughness to be determined in the form of a wavevector range...
October 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Yurong Lu, Ze Jing, Huadong Yong, Youhe Zhou
The flux avalanche in type-II superconducting thin film is numerically simulated in this paper. We mainly consider the effect of non-uniform critical current density on the thermomagnetic stability. The nonlinear electromagnetic constitutive relation of the superconductor is adopted. Then, Maxwell's equations and heat diffusion equation are numerically solved by the fast Fourier transform technique. We find that the non-uniform critical current density can remarkably affect the behaviour of the flux avalanche...
October 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Xiaodong Xia, Yang Wang, Zheng Zhong, George J Weng
Unlike mechanical creep with inelastic deformation, electric creep with domain evolution is a rarely studied subject. In this paper, we present a theory of electric creep and related electromechanical coupling for both non-poled and fully poled ferroelectric ceramics. We consider electric creep to be a time-dependent process, with an initial condition lying on the D (electric displacement) versus E (electric field) hysteresis loop. Both processes are shown to share the same Gibbs free energy and thermodynamic driving force, but relative to creep, the hysteresis loop is just a field-dependent process...
October 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Kevin S Galloway, Eric W Justh, P S Krishnaprasad
We investigate low-dimensional examples of cyclic pursuit in a collective, wherein each agent employs a constant bearing (CB) steering law relative to exactly one other agent. For the case of three agents in the plane, we characterize relative equilibria and pure shape equilibria of associated closed-loop dynamics. Re-scaling time yields a reduction of phase space to two dimensions and effective tools for stability analysis. Study of bifurcation of a family of collinear equilibria dependent on a single CB control parameter reveals the presence of a rich collection of trajectories that are periodic in shape and undergo precession in physical space...
October 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
T Gao, Z Wang, J-M Vanden-Broeck
Generalized solitary waves propagating at the surface of a fluid of finite depth are considered. The fluid is assumed to be inviscid and incompressible and the flow to be irrotational. Both the effects of gravity and surface tension are included. It is shown that in addition to the classical symmetric waves, there are new asymmetric solutions. These new branches of solutions bifurcate from the branches of symmetric waves. The detailed bifurcation diagrams as well as typical wave profiles are presented.
October 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Y Watanabe, D M Ingram
When a steep, breaking wave hits a vertical sea wall in shallow water, a flip-through event may occur, leading to the formation of an up-rushing planar jet. During such an event, a jet of water is ejected at a speed many times larger than the approaching wave's celerity. As the jet rises, the bounded fluid sheet ruptures to form vertical ligaments which subsequently break up to form droplets, creating a polydisperse spray. Experiments in the University of Hokkaido's 24 m flume measured the resulting droplet sizes using image analysis of high-speed video...
October 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
J A Reeger, B Fornberg, M L Watts
The numerical approximation of definite integrals, or quadrature, often involves the construction of an interpolant of the integrand and its subsequent integration. In the case of one dimension it is natural to rely on polynomial interpolants. However, their extension to two or more dimensions can be costly and unstable. An efficient method for computing surface integrals on the sphere is detailed in the literature (Reeger & Fornberg 2016 Stud. Appl. Math.137, 174-188. (doi:10.1111/sapm.12106)). The method uses local radial basis function interpolation to reduce computational complexity when generating quadrature weights for any given node set...
October 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
R M J Groh, P M Weaver
The safe design of primary load-bearing structures requires accurate prediction of stresses, especially in the vicinity of geometric discontinuities where deleterious three-dimensional stress fields can be induced. Even for thin-walled structures significant through-thickness stresses arise at edges and boundaries, and this is especially precarious for laminates of advanced fibre-reinforced composites because through-thickness stresses are the predominant drivers in delamination failure. Here, we use a higher-order equivalent single-layer model derived from the Hellinger-Reissner mixed variational principle to examine boundary layer effects in laminated plates comprising constant-stiffness and variable-stiffness laminae and deforming statically in cylindrical bending...
October 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Xiaowei Tian, Xiang Lai, Pingan Zhu, Liqiu Wang
Energy is conserved by the first law of thermodynamics; its quality degrades constantly due to entropy generation, by the second law of thermodynamics. It is thus important to examine the entropy generation regarding the way to reduce its magnitude and the limit of entropy generation as time tends to infinity regarding whether it is bounded or not. This work initiates such an analysis with one-dimensional heat conduction. The work not only offers some fundamental insights of universe and its future, but also builds up the relation between the second law of thermodynamics and mathematical inequalities via developing the latter of either new or classical nature...
October 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
T Economou, D B Stephenson, J C Rougier, R A Neal, K R Mylne
Warnings for natural hazards improve societal resilience and are a good example of decision-making under uncertainty. A warning system is only useful if well defined and thus understood by stakeholders. However, most operational warning systems are heuristic: not formally or transparently defined. Bayesian decision theory provides a framework for issuing warnings under uncertainty but has not been fully exploited. Here, a decision theoretic framework is proposed for hazard warnings. The framework allows any number of warning levels and future states of nature, and a mathematical model for constructing the necessary loss functions for both generic and specific end-users is described...
October 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Feng Xu, Oliver E Jensen
We examine theoretically the spreading of a viscous liquid drop over a thin film of uniform thickness, assuming the liquid's viscosity is regulated by the concentration of a solute that is carried passively by the spreading flow. The solute is assumed to be initially heterogeneous, having a spatial distribution with prescribed statistical features. To examine how this variability influences the drop's motion, we investigate spreading in a planar geometry using lubrication theory, combining numerical simulations with asymptotic analysis...
October 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Junhua Zhao, Sudong Ben, Peishi Yu
The vibration of tightly helical nanosprings affected by van der Waals (vdW) interactions is investigated based on continuum modelling. Explicit solutions are derived to clarify the influence of initial pitch, stiffness and the number of nanosprings on the period, frequency and amplitude of the vibration. Unlike classic linear/nonlinear springs, the waveform of the vibration is always asymmetric for tightly helical nanosprings due to the asymmetry of vdW attraction and repulsion. The at most three equilibrium positions for the nanosprings strongly depend on the deformation due to competition between the vdW interactions and the elastic energy of the nanosprings...
October 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
P A Whigham, G Dick, M Parry
Network rewiring as a method for producing a range of structures was first introduced in 1998 by Watts & Strogatz (Nature393, 440-442. (doi:10.1038/30918)). This approach allowed a transition from regular through small-world to a random network. The subsequent interest in scale-free networks motivated a number of methods for developing rewiring approaches that converged to scale-free networks. This paper presents a rewiring algorithm (RtoS) for undirected, non-degenerate, fixed size networks that transitions from regular, through small-world and scale-free to star-like networks...
October 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Jianghong Yuan, Canan Dagdeviren, Yan Shi, Yinji Ma, Xue Feng, John A Rogers, Yonggang Huang
Conformal modulus sensors (CMS) incorporate PZT nanoribbons as mechanical actuators and sensors to achieve reversible conformal contact with the human skin for non-invasive, in vivo measurements of skin modulus. An analytic model presented in this paper yields expressions that connect the sensor output voltage to the Young moduli of the epidermis and dermis, the thickness of the epidermis, as well as the material and geometrical parameters of the CMS device itself and its encapsulation layer. Results from the model agree well with in vitro experiments on bilayer structures of poly(dimethylsiloxane)...
October 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Ivan Argatov, Gennady Mishuris
The pipette aspiration testing technique is considered, and the elastic half-space model, which was originally introduced in the isotropic incompressible case, is revisited and generalized for the case of transverse isotropy. Asymptotic solutions are obtained in the two limiting cases of a wide and a narrow pipette.
September 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Y P Liu, C G Wang, H F Tan, M K Wadee
A model is proposed based on a Fourier series method to analyse the interactive bending wrinkling behaviour of inflated beams. The whole wrinkling evolution is tracked and divided into three stages by identifying the bifurcations of the equilibrium path. The critical wrinkling and failure moments of the inflated beam can then be predicted. The global-local interactive buckling pattern is elucidated by the proposed theoretical model and also verified by non-contact experimental tests. The effects of geometric parameters, internal pressure and boundary conditions on the buckling of inflated beams are investigated finally...
September 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Habib Ammari, Matias Ruiz, Wei Wu, Sanghyeon Yu, Hai Zhang
In this paper, we derive an impedance boundary condition to approximate the optical scattering effect of an array of plasmonic nanoparticles mounted on a perfectly conducting plate. We show that at some resonant frequencies the impedance blows up, allowing for a significant reduction of the scattering from the plate. Using the spectral properties of a Neumann-Poincaré type operator, we investigate the dependency of the impedance with respect to changes in the nanoparticle geometry and configuration.
September 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
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