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Proceedings. Mathematical, Physical, and Engineering Sciences

Arash Yavari, Alain Goriely
The elastic Ericksen problem consists of finding deformations in isotropic hyperelastic solids that can be maintained for arbitrary strain-energy density functions. In the compressible case, Ericksen showed that only homogeneous deformations are possible. Here, we solve the anelastic version of the same problem, that is, we determine both the deformations and the eigenstrains such that a solution to the anelastic problem exists for arbitrary strain-energy density functions. Anelasticity is described by finite eigenstrains...
December 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Elias G Dimitrakopoulos, Edwin Dat Win Fung
This paper characterizes the stability of a rigid rocking block subjected to a family of multi-lobe pulse ground motions. It unveils a counter to intuition plurality of overturning (OT) modes despite the short duration and bounded energy of the examined ground motions. Accordingly, it describes with original closed-form expressions the critical conditions of all OT modes involving a finite number of impacts. It also proposes pertinent semi-analytical, exact analytical and approximate analytical solutions with respect to the determination of the (unknown) times of impact, as appropriate...
December 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
B Enders, P Thibault
Ptychography is now a well-established X-ray microscopy tool for synchrotron end-stations equipped with a scanning stage and a pixelated detector. Ptychographic phasing algorithms use information from coherent diffraction to deliver quantitative images of the specimen at a resolution higher than the scanning resolution. These algorithms have traditionally been implemented in software on a per-instrument basis in various degrees of user-friendliness and sophistication. Here, we present Ptypy, a ptychography software written with the intention to serve as a framework across the diverse sets of available instruments and usage cases...
December 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
V V Nishawala, M Ostoja-Starzewski, M J Leamy, E Porcu
This paper reports on a generalization of Lamb's problem to a linear elastic, infinite half-space with random fields (RFs) of mass density, subject to a normal line load. Both, uncorrelated and correlated (with fractal and Hurst characteristics) RFs without any weak noise restrictions, are proposed. Cellular automata (CA) is used to simulate the wave propagation. CA is a local computational method which, for rectangular discretization of spatial domain, is equivalent to applying the finite difference method to the governing equations of classical elasticity...
December 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
N J Goffin, R L Higginson, J R Tyrer
In laser cladding, the potential benefits of wire feeding are considerable. Typical problems with the use of powder, such as gas entrapment, sub-100% material density and low deposition rate are all avoided with the use of wire. However, the use of a powder-based source material is the industry standard, with wire-based deposition generally regarded as an academic curiosity. This is because, although wire-based methods have been shown to be capable of superior quality results, the wire-based process is more difficult to control...
December 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Radu Pantilie
Motivated by the quaternionic geometry corresponding to the homogeneous complex manifolds endowed with (holomorphically) embedded spheres, we introduce and initiate the study of the 'quaternionic-like manifolds'. These contain, as particular subclasses, the CR quaternionic and the ρ-quaternionic manifolds. Moreover, the notion of 'heaven space' finds its adequate level of generality in this setting: (essentially) any real analytic quaternionic-like manifold admits a (germ) unique heaven space, which is a ρ-quaternionic manifold...
December 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Filippos Vallianatos, Giorgos Papadakis, Georgios Michas
Despite the extreme complexity that characterizes the mechanism of the earthquake generation process, simple empirical scaling relations apply to the collective properties of earthquakes and faults in a variety of tectonic environments and scales. The physical characterization of those properties and the scaling relations that describe them attract a wide scientific interest and are incorporated in the probabilistic forecasting of seismicity in local, regional and planetary scales. Considerable progress has been made in the analysis of the statistical mechanics of earthquakes, which, based on the principle of entropy, can provide a physical rationale to the macroscopic properties frequently observed...
December 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Ellen G Zweibel, Masaaki Yamada
Magnetic reconnection is a topological rearrangement of magnetic field that occurs on time scales much faster than the global magnetic diffusion time. Since the field lines break on microscopic scales but energy is stored and the field is driven on macroscopic scales, reconnection is an inherently multi-scale process that often involves both magnetohydrodynamic (MHD) and kinetic phenomena. In this article, we begin with the MHD point of view and then describe the dynamics and energetics of reconnection using a two-fluid formulation...
December 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Daniel J Ratliff, Thomas J Bridges
Multiphase wavetrains are multiperiodic travelling waves with a set of distinct wavenumbers and distinct frequencies. In conservative systems, such families are associated with the conservation of wave action or other conservation law. At generic points (where the Jacobian of the wave action flux is non-degenerate), modulation of the wavetrain leads to the dispersionless multiphase conservation of wave action. The main result of this paper is that modulation of the multiphase wavetrain, when the Jacobian of the wave action flux vector is singular, morphs the vector-valued conservation law into the scalar Korteweg-de Vries (KdV) equation...
December 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
F R Stephenson, L V Morrison, C Y Hohenkerk
New compilations of records of ancient and medieval eclipses in the period 720 BC to AD 1600, and of lunar occultations of stars in AD 1600-2015, are analysed to investigate variations in the Earth's rate of rotation. It is found that the rate of rotation departs from uniformity, such that the change in the length of the mean solar day (lod) increases at an average rate of +1.8 ms per century. This is significantly less than the rate predicted on the basis of tidal friction, which is +2.3 ms per century...
December 2016: Proceedings. Mathematical, Physical, and Engineering Sciences
Hsiu-Yu Yu, David M Eckmann, Portonovo S Ayyaswamy, Ravi Radhakrishnan
The reactive flux formalism (Chandler 1978 J. Chem. Phys.68, 2959-2970. (doi:10.1063/1.436049)) and the subsequent development of methods such as transition path sampling have laid the foundation for explicitly quantifying the rate process in terms of microscopic simulations. However, explicit methods to account for how the hydrodynamic correlations impact the transient reaction rate are missing in the colloidal literature. We show that the composite generalized Langevin equation (Yu et al. 2015 Phys. Rev. E91, 052303...
December 2016: 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
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