Proceedings. Mathematical, physical, and engineering sciences最新文献

{"title":"Uncertainties in the 2004 Sumatra-Andaman source through nonlinear stochastic inversion of tsunami waves.","authors":"D Gopinathan,&nbsp;M Venugopal,&nbsp;D Roy,&nbsp;K Rajendran,&nbsp;S Guillas,&nbsp;F Dias","doi":"10.1098/rspa.2017.0353","DOIUrl":"https://doi.org/10.1098/rspa.2017.0353","url":null,"abstract":"<p><p>Numerical inversions for earthquake source parameters from tsunami wave data usually incorporate subjective elements to stabilize the search. In addition, noisy and possibly insufficient data result in instability and non-uniqueness in most deterministic inversions, which are barely acknowledged. Here, we employ the satellite altimetry data for the 2004 Sumatra-Andaman tsunami event to invert the source parameters. We also include kinematic parameters that improve the description of tsunami generation and propagation, especially near the source. Using a finite fault model that represents the extent of rupture and the geometry of the trench, we perform a new type of nonlinear joint inversion of the slips, rupture velocities and rise times with minimal <i>a priori</i> constraints. Despite persistently good waveform fits, large uncertainties in the joint parameter distribution constitute a remarkable feature of the inversion. These uncertainties suggest that objective inversion strategies should incorporate more sophisticated physical models of seabed deformation in order to significantly improve the performance of early warning systems.</p>","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20170353"},"PeriodicalIF":3.5,"publicationDate":"2017-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspa.2017.0353","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35478552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the topology of the Lorenz system.","authors":"Tali Pinsky","doi":"10.1098/rspa.2017.0374","DOIUrl":"https://doi.org/10.1098/rspa.2017.0374","url":null,"abstract":"<p><p>We present a new paradigm for three-dimensional chaos, and specifically for the Lorenz equations. The main difficulty in these equations and for a generic flow in dimension 3 is the existence of singularities. We show how to use knot theory as a way to remove the singularities. Specifically, we claim: (i) for certain parameters, the Lorenz system has an invariant one-dimensional curve, which is a trefoil knot. The knot is a union of invariant manifolds of the singular points. (ii) The flow is topologically equivalent to an Anosov flow on the complement of this curve, and moreover to a geodesic flow. (iii) When varying the parameters, the system exhibits topological phase transitions, i.e. for special parameter values, it will be topologically equivalent to an Anosov flow on a knot complement. Different knots appear for different parameter values and each knot controls the dynamics at nearby parameters.</p>","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20170374"},"PeriodicalIF":3.5,"publicationDate":"2017-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspa.2017.0374","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35478554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cautionary tales on air-quality improvement in Beijing.","authors":"Shuyi Zhang,&nbsp;Bin Guo,&nbsp;Anlan Dong,&nbsp;Jing He,&nbsp;Ziping Xu,&nbsp;Song Xi Chen","doi":"10.1098/rspa.2017.0457","DOIUrl":"https://doi.org/10.1098/rspa.2017.0457","url":null,"abstract":"<p><p>The official air-quality statistic reported that Beijing had a 9.9% decline in the annual concentration of PM_2.5 in 2016. While this statistic offered some relief for the inhabitants of the capital, we present several analyses based on Beijing's PM_2.5 data of the past 4 years at 36 monitoring sites along with meteorological data of the past 7 years. The analyses reveal the air pollution situation in 2016 was not as rosy as the 9.9% decline would convey, and improvement if any was rather uncertain. The paper also provides an assessment on the city's PM_2.5 situation in the past 4 years.</p>","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20170457"},"PeriodicalIF":3.5,"publicationDate":"2017-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspa.2017.0457","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35479000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Accuracy of the hypothetical sky-polarimetric Viking navigation versus sky conditions: revealing solar elevations and cloudinesses favourable for this navigation method.","authors":"Dénes Száz,&nbsp;Alexandra Farkas,&nbsp;András Barta,&nbsp;Balázs Kretzer,&nbsp;Miklós Blahó,&nbsp;Ádám Egri,&nbsp;Gyula Szabó,&nbsp;Gábor Horváth","doi":"10.1098/rspa.2017.0358","DOIUrl":"https://doi.org/10.1098/rspa.2017.0358","url":null,"abstract":"<p><p>According to Thorkild Ramskou's theory proposed in 1967, under overcast and foggy skies, Viking seafarers might have used skylight polarization analysed with special crystals called sunstones to determine the position of the invisible Sun. After finding the occluded Sun with sunstones, its elevation angle had to be measured and its shadow had to be projected onto the horizontal surface of a sun compass. According to Ramskou's theory, these sunstones might have been birefringent calcite or dichroic cordierite or tourmaline crystals working as polarizers. It has frequently been claimed that this method might have been suitable for navigation even in cloudy weather. This hypothesis has been accepted and frequently cited for decades without any experimental support. In this work, we determined the accuracy of this hypothetical sky-polarimetric Viking navigation for 1080 different sky situations characterized by solar elevation <i>θ</i> and cloudiness <i>ρ</i>, the sky polarization patterns of which were measured by full-sky imaging polarimetry. We used the earlier measured uncertainty functions of the navigation steps 1, 2 and 3 for calcite, cordierite and tourmaline sunstone crystals, respectively, and the newly measured uncertainty function of step 4 presented here. As a result, we revealed the meteorological conditions under which Vikings could have used this hypothetical navigation method. We determined the solar elevations at which the navigation uncertainties are minimal at summer solstice and spring equinox for all three sunstone types. On average, calcite sunstone ensures a more accurate sky-polarimetric navigation than tourmaline and cordierite. However, in some special cases (generally at 35° ≤ <i>θ</i> ≤ 40°, 1 okta ≤ <i>ρ</i> ≤ 6 oktas for summer solstice, and at 20° ≤ <i>θ</i> ≤ 25°, 0 okta ≤ <i>ρ</i> ≤ 4 oktas for spring equinox), the use of tourmaline and cordierite results in smaller navigation uncertainties than that of calcite. Generally, under clear or less cloudy skies, the sky-polarimetric navigation is more accurate, but at low solar elevations its accuracy remains relatively large even at high cloudiness. For a given <i>ρ</i>, the absolute value of averaged peak North uncertainties dramatically decreases with increasing <i>θ</i> until the sign (±) change of these uncertainties. For a given <i>θ</i>, this absolute value can either decrease or increase with increasing <i>ρ</i>. The most advantageous sky situations for this navigation method are at summer solstice when the solar elevation and cloudiness are 35° ≤ <i>θ</i> ≤ 40° and 2 oktas ≤ <i>ρ</i> ≤ 3 oktas.</p>","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20170358"},"PeriodicalIF":3.5,"publicationDate":"2017-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspa.2017.0358","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35478553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Elastodynamic image forces on screw dislocations in the presence of phase boundaries.","authors":"Beñat Gurrutxaga-Lerma","doi":"10.1098/rspa.2017.0484","DOIUrl":"https://doi.org/10.1098/rspa.2017.0484","url":null,"abstract":"<p><p>The elastodynamic image forces acting on straight screw dislocations in the presence of planar phase boundaries are derived. Two separate dislocations are studied: (i) the injected, non-moving screw dislocation and (ii) the injected (or pre-existing), generally non-uniformly moving screw dislocation. The image forces are derived for both the case of a rigid surface and of a planar interface between two homogeneous, isotropic phases. The case of a rigid interface is shown to be solvable employing Head's image dislocation construction. The case of the elastodynamic image force due to an interface is solved by deriving the reflected wave's contribution to the global solution across the interface. This entails obtaining the fundamental solution (Green's function) for a point unit force via Cagniard's method, and then applying the convolution theorem for a screw dislocation modelled as a force distribution. Complete, explicit formulae are provided when available. It is shown that the elastodynamic image forces are generally affected by retardation effects, and that those acting on the moving dislocations display a dynamic magnification that exceed the attraction (or repulsion) predicted in classical elastostatic calculations.</p>","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20170484"},"PeriodicalIF":3.5,"publicationDate":"2017-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspa.2017.0484","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35479001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Keller-Rubinow model for Liesegang ring formation.","authors":"J M Duley,&nbsp;A C Fowler,&nbsp;I R Moyles,&nbsp;S B G O'Brien","doi":"10.1098/rspa.2017.0128","DOIUrl":"https://doi.org/10.1098/rspa.2017.0128","url":null,"abstract":"<p><p>We study the model of Keller & Rubinow (Keller & Rubinow 1981 <i>J. Chem. Phys</i><b>74</b>, 5000-5007. (doi:10.1063/1.441752)) describing the formation of Liesegang rings due to Ostwald's supersaturation mechanism. Keller and Rubinow provided an approximate solution both for the growth and equilibration of the first band, and also for the formation of secondary bands, based on a presumed asymptotic limit. However, they did not provide a parametric basis for the assumptions in their solution, nor did they provide any numerical corroboration, particularly of the secondary band formation. Here, we provide a different asymptotic solution, based on a specific parametric limit, and we show that the growth and subsequent cessation of the first band can be explained. We also show that the model is unable to explain the formation of finite width secondary bands, and we confirm this result by numerical computation. We conclude that the model is not fully posed, lacking a transition variable which can describe the hysteretic switch across the nucleation threshold.</p>","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20170128"},"PeriodicalIF":3.5,"publicationDate":"2017-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspa.2017.0128","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35581888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Singular diffusionless limits of double-diffusive instabilities in magnetohydrodynamics.","authors":"Oleg N Kirillov","doi":"10.1098/rspa.2017.0344","DOIUrl":"https://doi.org/10.1098/rspa.2017.0344","url":null,"abstract":"<p><p>We study local instabilities of a differentially rotating viscous flow of electrically conducting incompressible fluid subject to an external azimuthal magnetic field. In the presence of the magnetic field, the hydrodynamically stable flow can demonstrate non-axisymmetric azimuthal magnetorotational instability (AMRI) both in the diffusionless case and in the double-diffusive case with viscous and ohmic dissipation. Performing stability analysis of amplitude transport equations of short-wavelength approximation, we find that the threshold of the diffusionless AMRI via the Hamilton-Hopf bifurcation is a singular limit of the thresholds of the viscous and resistive AMRI corresponding to the dissipative Hopf bifurcation and manifests itself as the Whitney umbrella singular point. A smooth transition between the two types of instabilities is possible only if the magnetic Prandtl number is equal to unity, <i>Pm</i>=1. At a fixed <i>Pm</i>≠1, the threshold of the double-diffusive AMRI is displaced by finite distance in the parameter space with respect to the diffusionless case even in the zero dissipation limit. The complete neutral stability surface contains three Whitney umbrella singular points and two mutually orthogonal intervals of self-intersection. At these singularities, the double-diffusive system reduces to a marginally stable system which is either Hamiltonian or parity-time-symmetric.</p>","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20170344"},"PeriodicalIF":3.5,"publicationDate":"2017-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspa.2017.0344","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35478550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Meso-scale defect evaluation of selective laser melting using spatially resolved acoustic spectroscopy.","authors":"M Hirsch,&nbsp;S Catchpole-Smith,&nbsp;R Patel,&nbsp;P Marrow,&nbsp;Wenqi Li,&nbsp;C Tuck,&nbsp;S D Sharples,&nbsp;A T Clare","doi":"10.1098/rspa.2017.0194","DOIUrl":"https://doi.org/10.1098/rspa.2017.0194","url":null,"abstract":"<p><p>Developments in additive manufacturing technology are serving to expand the potential applications. Critical developments are required in the supporting areas of measurement and in process inspection to achieve this. CM247LC is a nickel superalloy that is of interest for use in aerospace and civil power plants. However, it is difficult to process via selective laser melting (SLM) as it suffers from cracking during rapid cooling and solidification. This limits the viability of CM247LC parts created using SLM. To quantify part integrity, spatially resolved acoustic spectroscopy (SRAS) has been identified as a viable non-destructive evaluation technique. In this study, a combination of optical microscopy and SRAS was used to identify and classify the surface defects present in SLM-produced parts. By analysing the datasets and scan trajectories, it is possible to correlate morphological information with process parameters. Image processing was used to quantify porosity and cracking for bulk density measurement. Analysis of surface acoustic wave data showed that an error in manufacture in the form of an overscan occurred. Comparing areas affected by overscan with a bulk material, a change in defect density from 1.17% in the bulk material to 5.32% in the overscan regions was observed, highlighting the need to reduce overscan areas in manufacture.</p>","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20170194"},"PeriodicalIF":3.5,"publicationDate":"2017-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspa.2017.0194","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35581892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Rate-based structural health monitoring using permanently installed sensors.","authors":"Joseph Corcoran","doi":"10.1098/rspa.2017.0270","DOIUrl":"https://doi.org/10.1098/rspa.2017.0270","url":null,"abstract":"<p><p>Permanently installed sensors are becoming increasingly ubiquitous, facilitating very frequent <i>in situ</i> measurements and consequently improved monitoring of 'trends' in the observed system behaviour. It is proposed that this newly available data may be used to provide prior warning and forecasting of critical events, particularly system failure. Numerous damage mechanisms are examples of positive feedback; they are 'self-accelerating' with an increasing rate of damage towards failure. The positive feedback leads to a common time-response behaviour which may be described by an empirical relation allowing prediction of the time to criticality. This study focuses on Structural Health Monitoring of engineering components; failure times are projected well in advance of failure for fatigue, creep crack growth and volumetric creep damage experiments. The proposed methodology provides a widely applicable framework for using newly available near-continuous data from permanently installed sensors to predict time until failure in a range of application areas including engineering, geophysics and medicine.</p>","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20170270"},"PeriodicalIF":3.5,"publicationDate":"2017-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspa.2017.0270","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35478549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The steady aerodynamics of aerofoils with porosity gradients.","authors":"Rozhin Hajian,&nbsp;Justin W Jaworski","doi":"10.1098/rspa.2017.0266","DOIUrl":"https://doi.org/10.1098/rspa.2017.0266","url":null,"abstract":"<p><p>This theoretical study determines the aerodynamic loads on an aerofoil with a prescribed porosity distribution in a steady incompressible flow. A Darcy porosity condition on the aerofoil surface furnishes a Fredholm integral equation for the pressure distribution, which is solved exactly and generally as a Riemann-Hilbert problem provided that the porosity distribution is Hölder-continuous. The Hölder condition includes as a subset any continuously differentiable porosity distributions that may be of practical interest. This formal restriction on the analysis is examined by a class of differentiable porosity distributions that approach a piecewise, discontinuous function in a certain parametric limit. The Hölder-continuous solution is verified in this limit against analytical results for partially porous aerofoils in the literature. Finally, a comparison made between the new theoretical predictions and experimental measurements of SD7003 aerofoils presented in the literature. Results from this analysis may be integrated into a theoretical framework to optimize turbulence noise suppression with minimal impact to aerodynamic performance.</p>","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20170266"},"PeriodicalIF":3.5,"publicationDate":"2017-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspa.2017.0266","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35581893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}