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Proceedings. Mathematical, Physical, and Engineering Sciences

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https://www.readbyqxmd.com/read/29290735/the-complex-and-quaternionic-quantum-bit-from-relativity-of-simultaneity-on-an-interferometer
#1
Andrew J P Garner, Markus P Müller, Oscar C O Dahlsten
The patterns of fringes produced by an interferometer have long been important testbeds for our best contemporary theories of physics. Historically, interference has been used to contrast quantum mechanics with classical physics, but recently experiments have been performed that test quantum theory against even more exotic alternatives. A physically motivated family of theories are those where the state space of a two-level system is given by a sphere of arbitrary dimension. This includes classical bits, and real, complex and quaternionic quantum theory...
December 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29290734/predicting-acoustic-relaxation-absorption-in-gas-mixtures-for-extraction-of-composition-relaxation-contributions
#2
Tingting Liu, Shu Wang, Ming Zhu
The existing molecular relaxation models based on both parallel relaxation theory and series relaxation theory cannot extract the contributions of gas compositions to acoustic relaxation absorption in mixtures. In this paper, we propose an analytical model to predict acoustic relaxation absorption and clarify composition relaxation contributions based on the rate-determining energy transfer processes in molecular relaxation in excitable gases. By combining parallel and series relaxation theory, the proposed model suggests that the vibration-translation process of the lowest vibrational mode in each composition provides the primary deexcitation path of the relaxation energy, and the rate-determining vibration-vibration processes between the lowest mode and others dominate the coupling energy transfer between different modes...
December 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29290733/sub-wavelength-focusing-of-acoustic-waves-in-bubbly-media
#3
Habib Ammari, Brian Fitzpatrick, David Gontier, Hyundae Lee, Hai Zhang
The purpose of this paper is to investigate acoustic wave scattering by a large number of bubbles in a liquid at frequencies near the Minnaert resonance frequency. This bubbly media has been exploited in practice to obtain super-focusing of acoustic waves. Using layer potential techniques, we derive the scattering function for a single spherical bubble excited by an incident wave in the low frequency regime. We then propose a point scatterer approximation for N bubbles, and describe several numerical simulations based on this approximation, that demonstrate the possibility of achieving super-focusing using bubbly media...
December 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29290732/on-modelling-the-interaction-between-two-rotating-bodies-with-statistically-distributed-features-an-application-to-dressing-of-grinding-wheels
#4
A Spampinato, D A Axinte
The mechanisms of interaction between bodies with statistically arranged features present characteristics common to different abrasive processes, such as dressing of abrasive tools. In contrast with the current empirical approach used to estimate the results of operations based on attritive interactions, the method we present in this paper allows us to predict the output forces and the topography of a simulated grinding wheel for a set of specific operational parameters (speed ratio and radial feed-rate), providing a thorough understanding of the complex mechanisms regulating these processes...
December 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29290731/buckling-of-a-stiff-thin-film-on-an-elastic-graded-compliant-substrate
#5
Zhou Chen, Weiqiu Chen, Jizhou Song
The buckling of a stiff film on a compliant substrate has attracted much attention due to its wide applications such as thin-film metrology, surface patterning and stretchable electronics. An analytical model is established for the buckling of a stiff thin film on a semi-infinite elastic graded compliant substrate subjected to in-plane compression. The critical compressive strain and buckling wavelength for the sinusoidal mode are obtained analytically for the case with the substrate modulus decaying exponentially...
December 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29225508/theory-of-energy-harvesting-from-heartbeat-including-the-effects-of-pleural-cavity-and-respiration
#6
Yangyang Zhang, Bingwei Lu, Chaofeng Lü, Xue Feng
Self-powered implantable devices with flexible energy harvesters are of significant interest due to their potential to solve the problem of limited battery life and surgical replacement. The flexible electronic devices made of piezoelectric materials have been employed to harvest energy from the motion of biological organs. Experimental measurements show that the output voltage of the device mounted on porcine left ventricle in chest closed environment decreases significantly compared to the case of chest open...
November 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29225507/how-to-characterize-a-nonlinear-elastic-material-a-review-on-nonlinear-constitutive-parameters-in-isotropic-finite-elasticity
#7
REVIEW
L Angela Mihai, Alain Goriely
The mechanical response of a homogeneous isotropic linearly elastic material can be fully characterized by two physical constants, the Young's modulus and the Poisson's ratio, which can be derived by simple tensile experiments. Any other linear elastic parameter can be obtained from these two constants. By contrast, the physical responses of nonlinear elastic materials are generally described by parameters which are scalar functions of the deformation, and their particular choice is not always clear. Here, we review in a unified theoretical framework several nonlinear constitutive parameters, including the stretch modulus, the shear modulus and the Poisson function, that are defined for homogeneous isotropic hyperelastic materials and are measurable under axial or shear experimental tests...
November 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29225506/nonlinear-mode-interaction-in-equal-leg-angle-struts-susceptible-to-cellular-buckling
#8
L Bai, F Wang, M A Wadee, J Yang
A variational model that describes the interactive buckling of a thin-walled equal-leg angle strut under pure axial compression is presented. A formulation combining the Rayleigh-Ritz method and continuous displacement functions is used to derive a system of differential and integral equilibrium equations for the structural component. Solving the equations using numerical continuation reveals progressive cellular buckling (or snaking) arising from the nonlinear interaction between the weak-axis flexural buckling mode and the strong-axis flexural-torsional buckling mode for the first time-the resulting behaviour being highly unstable...
November 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29225505/lagrangian-averaging-with-geodesic-mean
#9
Marcel Oliver
This paper revisits the derivation of the Lagrangian averaged Euler (LAE), or Euler-α equations in the light of an intrinsic definition of the averaged flow map as the geodesic mean on the volume-preserving diffeomorphism group. Under the additional assumption that first-order fluctuations are statistically isotropic and transported by the mean flow as a vector field, averaging of the kinetic energy Lagrangian of an ideal fluid yields the LAE Lagrangian. The derivation presented here assumes a Euclidean spatial domain without boundaries...
November 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29225504/symmetric-rearrangement-of-groundwater-fed-streams
#10
Robert Yi, Yossi Cohen, Olivier Devauchelle, Goodwin Gibbins, Hansjörg Seybold, Daniel H Rothman
Streams shape landscapes through headward growth and lateral migration. When these streams are primarily fed by groundwater, recent work suggests that their tips advance to maximize the symmetry of the local Laplacian field associated with groundwater flow. We explore the extent to which such forcing is responsible for the lateral migration of streams by studying two features of groundwater-fed streams in Bristol, Florida: their confluence angle near junctions and their curvature. First, we find that, while streams asymptotically form a 72° angle near their tips, they simultaneously exhibit a wide 120° confluence angle within approximately 10 m of their junctions...
November 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29225503/advection-and-taylor-aris-dispersion-in-rivulet-flow
#11
F H H Al Mukahal, B R Duffy, S K Wilson
Motivated by the need for a better understanding of the transport of solutes in microfluidic flows with free surfaces, the advection and dispersion of a passive solute in steady unidirectional flow of a thin uniform rivulet on an inclined planar substrate driven by gravity and/or a uniform longitudinal surface shear stress are analysed. Firstly, we describe the short-time advection of both an initially semi-infinite and an initially finite slug of solute of uniform concentration. Secondly, we describe the long-time Taylor-Aris dispersion of an initially finite slug of solute...
November 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29225502/on-the-analysis-of-the-double-hopf-bifurcation-in-machining-processes-via-centre-manifold-reduction
#12
T G Molnar, Z Dombovari, T Insperger, G Stepan
The single-degree-of-freedom model of orthogonal cutting is investigated to study machine tool vibrations in the vicinity of a double Hopf bifurcation point. Centre manifold reduction and normal form calculations are performed to investigate the long-term dynamics of the cutting process. The normal form of the four-dimensional centre subsystem is derived analytically, and the possible topologies in the infinite-dimensional phase space of the system are revealed. It is shown that bistable parameter regions exist where unstable periodic and, in certain cases, unstable quasi-periodic motions coexist with the equilibrium...
November 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29225501/the-grasshopper-problem
#13
Olga Goulko, Adrian Kent
We introduce and physically motivate the following problem in geometric combinatorics, originally inspired by analysing Bell inequalities. A grasshopper lands at a random point on a planar lawn of area 1. It then jumps once, a fixed distance d, in a random direction. What shape should the lawn be to maximize the chance that the grasshopper remains on the lawn after jumping? We show that, perhaps surprisingly, a disc-shaped lawn is not optimal for any d>0. We investigate further by introducing a spin model whose ground state corresponds to the solution of a discrete version of the grasshopper problem...
November 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29225500/multi-scale-mechanics-of-granular-solids-from-grain-resolved-x-ray-measurements
#14
R C Hurley, S A Hall, J P Wright
This work discusses an experimental technique for studying the mechanics of three-dimensional (3D) granular solids. The approach combines 3D X-ray diffraction and X-ray computed tomography to measure grain-resolved strains, kinematics and contact fabric in the bulk of a granular solid, from which continuum strains, grain stresses, interparticle forces and coarse-grained elasto-plastic moduli can be determined. We demonstrate the experimental approach and analysis of selected results on a sample of 1099 stiff, frictional grains undergoing multiple uniaxial compression cycles...
November 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29225499/analysing-causal-structures-with-entropy
#15
REVIEW
Mirjam Weilenmann, Roger Colbeck
A central question for causal inference is to decide whether a set of correlations fits a given causal structure. In general, this decision problem is computationally infeasible and hence several approaches have emerged that look for certificates of compatibility. Here, we review several such approaches based on entropy. We bring together the key aspects of these entropic techniques with unified terminology, filling several gaps and establishing new connections, all illustrated with examples. We consider cases where unobserved causes are classical, quantum and post-quantum, and discuss what entropic analyses tell us about the difference...
November 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29225498/on-the-buckling-of-an-elastic-holey-column
#16
C G Johnson, U Jain, A L Hazel, D Pihler-Puzović, T Mullin
We report the results of a numerical and theoretical study of buckling in elastic columns containing a line of holes. Buckling is a common failure mode of elastic columns under compression, found over scales ranging from metres in buildings and aircraft to tens of nanometers in DNA. This failure usually occurs through lateral buckling, described for slender columns by Euler's theory. When the column is perforated with a regular line of holes, a new buckling mode arises, in which adjacent holes collapse in orthogonal directions...
November 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29225497/swelling-induced-wrinkling-in-layered-gel-beams
#17
P Nardinocchi, E Puntel
Gels are widely employed in smart mechanical devices and biomedical applications. Swelling-induced bending actuation can be obtained by means of a simple bilayer gel beam. We show that this system can also exhibit wrinkling patterns of potential interest for structural morphing and sensing. We study swelling-induced wrinkling at the extrados of a bilayer gel beam with the softer layer on top. The bent configuration at finite strain is recovered first and, starting from it, a linear perturbation analysis is performed...
November 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29225496/age-distribution-dynamics-with-stochastic-jumps-in-mortality
#18
Salvatore Calabrese, Amilcare Porporato, Francesco Laio, Paolo D'Odorico, Luca Ridolfi
While deterministic age distribution models have been extensively studied and applied in various disciplines, little work has been devoted to understanding the role of stochasticity in birth and mortality terms. In this paper, we analyse a stochastic M'Kendrick-von Foerster equation in which jumps in mortality represent intense losses of population due to external events. We present explicit solutions for the probability density functions of the age distribution and the total population and for the temporal dynamics of their moments...
November 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29225495/force-direction-patterns-promote-whole-body-stability-even-in-hip-flexed-walking-but-not-upper-body-stability-in-human-upright-walking
#19
Roy Müller, Christian Rode, Soran Aminiaghdam, Johanna Vielemeyer, Reinhard Blickhan
Directing the ground reaction forces to a focal point above the centre of mass of the whole body promotes whole body stability in human and animal gaits similar to a physical pendulum. Here we show that this is the case in human hip-flexed walking as well. For all upper body orientations (upright, 25°, 50°, maximum), the focal point was well above the centre of mass of the whole body, suggesting its general relevance for walking. Deviations of the forces' lines of action from the focal point increased with upper body inclination from 25 to 43 mm root mean square deviation (RMSD)...
November 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
https://www.readbyqxmd.com/read/29225494/rolling-resistance-of-shallow-granular-deformation
#20
Keaton J Burns, Neil J Balmforth, Ian J Hewitt
Experiments are conducted to measure the resistance experienced by light cylinders rolling over flat beds of granular media. Sand and glass spheres are used for the beds. The trajectories of the rolling cylinders are determined through optical tracking, and velocity and acceleration data are inferred through fits to these trajectories. The rolling resistance is dominated by a velocity-independent component, but a velocity-dependent drag exceeding the expected strength of air drag is also observed. The results are compared to a theoretical model based on a cohesionless Mohr-Coulomb rheology for a granular medium in the presence of gravity...
November 2017: Proceedings. Mathematical, Physical, and Engineering Sciences
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