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Proceedings. Mathematical, Physical, and Engineering Sciences

Agnès Maurel, Jean-Jacques Marigo, Jean-François Mercier, Kim Pham
We present a model based on a two-scale asymptotic analysis for resonant arrays of the Helmholtz type, with resonators open at a single extremity (standard resonators) or open at both extremities (double-sided resonators). The effective behaviour of such arrays is that of a homogeneous anisotropic slab replacing the cavity region, associated with transmission, or jump, conditions for the acoustic pressure and for the normal velocity across the region of the necks. The coefficients entering in the effective wave equation are simply related to the fraction of air in the periodic cell of the array...
February 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Sung-Ik Sohn, Takashi Sakajo, Sun-Chul Kim
We study the stability of a barotropic vortex strip on a rotating sphere, as a simple model of jet streams. The flow is approximated by a piecewise-continuous vorticity distribution by zonal bands of uniform vorticity. The linear stability analysis shows that the vortex strip becomes stable as the strip widens or the rotation speed increases. When the vorticity constants in the upper and the lower regions of the vortex strip have the same positive value, the inner flow region of the vortex strip becomes the most unstable...
February 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Luca Placidi, Emilio Barchiesi
In this paper, we exploit some results in the theory of irreversible phenomena to address the study of quasi-static brittle fracture propagation in a two-dimensional isotropic continuum. The elastic strain energy density of the body has been assumed to be geometrically nonlinear and to depend on the strain gradient. Such generalized continua often arise in the description of microstructured media. These materials possess an intrinsic length scale, which determines the size of internal boundary layers. In particular, the non-locality conferred by this internal length scale avoids the concentration of deformations, which is usually observed when dealing with local models and which leads to mesh dependency...
February 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Lawrence C Paulson
Computational logic is the use of computers to establish facts in a logical formalism. Originating in nineteenth century attempts to understand the nature of mathematical reasoning, the subject now comprises a wide variety of formalisms, techniques and technologies. One strand of work follows the 'logic for computable functions (LCF) approach' pioneered by Robin Milner, where proofs can be constructed interactively or with the help of users' code (which does not compromise correctness). A refinement of LCF, called Isabelle, retains these advantages while providing flexibility in the choice of logical formalism and much stronger automation...
February 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Jinbing Chen, Dmitry E Pelinovsky
Rogue periodic waves stand for rogue waves on a periodic background. The nonlinear Schrödinger equation in the focusing case admits two families of periodic wave solutions expressed by the Jacobian elliptic functions dn and cn . Both periodic waves are modulationally unstable with respect to long-wave perturbations. Exact solutions for the rogue periodic waves are constructed by using the explicit expressions for the periodic eigenfunctions of the Zakharov-Shabat spectral problem and the Darboux transformations...
February 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
I A Kuznetsov, A V Kuznetsov
We develop a mathematical model that enables us to investigate possible mechanisms by which two primary markers of Alzheimer's disease (AD), extracellular amyloid plaques and intracellular tangles, may be related. Our model investigates the possibility that the decay of anterograde axonal transport of amyloid precursor protein (APP), caused by toxic tau aggregates, leads to decreased APP transport towards the synapse and APP accumulation in the soma. The developed model thus couples three processes: (i) slow axonal transport of tau, (ii) tau misfolding and agglomeration, which we simulated by using the Finke-Watzky model and (iii) fast axonal transport of APP...
February 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Priscila Leal da Silva, Igor Leite Freire, Júlio Cesar Santos Sampaio
We consider a family of homogeneous nonlinear dispersive equations with two arbitrary parameters. Conservation laws are established from the point symmetries and imply that the whole family admits square integrable solutions. Recursion operators are found for two members of the family investigated. For one of them, a Lax pair is also obtained, proving its complete integrability. From the Lax pair, we construct a Miura-type transformation relating the original equation to the Korteweg-de Vries (KdV) equation...
February 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Daniel Rayneau-Kirkhope, Chengzhao Zhang, Louis Theran, Marcelo A Dias
In recent years, many structural motifs have been designed with the aim of creating auxetic metamaterials. One area of particular interest in this subject is the creation of auxetic material properties through elastic instability. Such metamaterials switch from conventional behaviour to an auxetic response for loads greater than some threshold value. This paper develops a novel methodology in the analysis of auxetic metamaterials which exhibit elastic instability through analogy with rigid link lattice systems...
February 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Yong Sun, Jinpeng Ma, Jürgen Kurths, Meng Zhan
The classic equal-area criterion (EAC) is of key importance in power system analysis, and provides a powerful, pictorial and quantitative means of analysing transient stability (i.e. the system's ability to maintain stable operation when subjected to a large disturbance). Based on the traditional EAC, it is common sense in engineering that there is a critical cleaning time (CCT); namely, a power system is stable (unstable) if a fault is cleared before (after) this CCT. We regard this form of CCT as bipartite...
February 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
J T Lloyd
A computational method is presented for representing twins via two-dimensional dislocation statics in an isotropic elastic solid. The method is compared with analytical approximations of twin shape and is used to study how twins evolve within grains subjected to an arbitrary external shear stress. Twin transfer across grains is then studied using the same computational method. The dislocation-based model for twin growth gives the following dependencies: twin thickness increases linearly with grain size and external stress, and increases substantially as the grain is able to traverse multiple grain boundaries with low misorientation angles; the model also predicts that twin transfer becomes less prominent across grain boundaries with high misorientation angles...
February 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Adrien Semin, Kersten Schmidt
The direct numerical simulation of the acoustic wave propagation in multiperforated absorbers with hundreds or thousands of tiny openings would result in a huge number of basis functions to resolve the microstructure. One is, however, primarily interested in effective and so homogenized transmission and absorption properties and how they are influenced by microstructure and its endpoints. For this, we introduce the surface homogenization that asymptotically decomposes the solution in a macroscopic part, a boundary layer corrector close to the interface and a near-field part close to its ends...
February 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
G Röst, Z Vizi, I Z Kiss
We present the generalized mean-field and pairwise models for non-Markovian epidemics on networks with arbitrary recovery time distributions. First we consider a hyperbolic partial differential equation (PDE) system, where the population of infective nodes and links are structured by age since infection. We show that the PDE system can be reduced to a system of integro-differential equations, which is analysed analytically and numerically. We investigate the asymptotic behaviour of the generalized model and provide an implicit analytical expression involving the final epidemic size and pairwise reproduction number...
February 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Adrian C Murza, Antonio E Teruel, Arghir D Zarnescu
We consider the Beris-Edwards model describing nematic liquid crystal dynamics and restrict it to a shear flow and spatially homogeneous situation. We analyse the dynamics focusing on the effect of the flow. We show that in the co-rotational case one has gradient dynamics, up to a periodic eigenframe rotation, while in the non-co-rotational case we identify the short- and long-time regimes of the dynamics. We express these in terms of the physical variables and compare with the predictions of other models of liquid crystal dynamics...
February 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Xiao Zhang, Yan Chen
This paper deals with constructing mobile assemblies of Bennett linkages inspired by four-crease origami patterns. A transition technique has been proposed by taking the thick-panel form of an origami pattern as an intermediate bridge. A zero-thickness rigid origami pattern and its thick-panel form share the same sector angles and folding behaviours, while the thick-panel origami and the mobile assembly of linkages are kinematically equivalent with differences only in link profiles. Applying this transition technique to typical four-crease origami patterns, we have found that the Miura-ori and graded Miura-ori patterns lead to assemblies of Bennett linkages with identical link lengths...
February 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Duncan A Forbes, Nate Bastian, Mark Gieles, Robert A Crain, J M Diederik Kruijssen, Søren S Larsen, Sylvia Ploeckinger, Oscar Agertz, Michele Trenti, Annette M N Ferguson, Joel Pfeffer, Oleg Y Gnedin
We discuss some of the key open questions regarding the formation and evolution of globular clusters (GCs) during galaxy formation and assembly within a cosmological framework. The current state of the art for both observations and simulations is described, and we briefly mention directions for future research. The oldest GCs have ages greater than or equal to 12.5 Gyr and formed around the time of reionization. Resolved colour-magnitude diagrams of Milky Way GCs and direct imaging of lensed proto-GCs at z ∼6 with the James Webb Space Telescope (JWST) promise further insight...
February 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
L R Chen, X Z Xiao, L Yu, H J Chu, H L Duan
A physically based theoretical model is proposed to investigate the mechanical behaviour and crystallographic texture evolution of irradiated face-centred cubic metals. This model is capable of capturing the main features of irradiated polycrystalline materials including irradiation hardening, post-yield softening and plasticity localization. Numerical results show a good agreement with experimental data for both unirradiated and irradiated stress-strain relationships. The study of crystallographic texture reveals that the initial randomly distributed texture of unirradiated metals under tensile loading can evolve into a mixture of [111] and [100] textures...
February 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Mark Warner, Cyrus Mostajeran
We solve the forward and inverse problems associated with the transformation of flat sheets with circularly symmetric director fields to surfaces of revolution with non-trivial topography, including Gaussian curvature, without a stretch elastic cost. We deal with systems slender enough to have a small bend energy cost. Shape change is induced by light or heat causing contraction along a non-uniform director field in the plane of an initially flat nematic sheet. The forward problem is, given a director distribution, what shape is induced? Along the way, we determine the Gaussian curvature and the evolution with induced mechanical deformation of the director field and of material curves in the surface (proto-radii) that will become radii in the final surface...
February 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Yang Liu, Joseph Páez Chávez, Ekaterina Pavlovskaia, Marian Wiercigroch
This paper studies a position feedback control strategy for controlling a higher order drifting oscillator which could be used in modelling vibro-impact drilling. Special attention is given to two control issues, eliminating bistability and suppressing chaos, which may cause inefficient and unstable drilling. Numerical continuation methods implemented via the continuation platform COCO are adopted to investigate the dynamical response of the system. Our analyses show that the proposed controller is capable of eliminating coexisting attractors and mitigating chaotic behaviour of the system, providing that its feedback control gain is chosen properly...
February 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Zhongjie Huang, Leonidas Siozos-Rousoulis, Tim De Troyer, Ghader Ghorbaniasl
This paper presents a time-domain method for noise prediction of supersonic rotating sources in a moving medium. The proposed approach can be interpreted as an extensive time-domain solution for the convected permeable Ffowcs Williams and Hawkings equation, which is capable of avoiding the Doppler singularity. The solution requires special treatment for construction of the emission surface. The derived formula can explicitly and efficiently account for subsonic uniform constant flow effects on radiated noise...
February 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
Valentina Beatini, Gianni Royer-Carfagni, Alessandro Tasora
The observation of old construction works confirms that masonry domes can withstand tensile hoop stresses, at least up to a certain level. Here, such tensile resistance, rather than a priori assumed as a property of the bulk material, is attributed to the contact forces that are developed at the interfaces between interlocked blocks under normal pressure, specified by Coulomb's friction law. According to this rationale, the aspect ratio of the blocks, as well as the bond pattern, becomes of fundamental importance...
January 2018: Proceedings. Mathematical, Physical, and Engineering Sciences
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