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

The quantum theory of time: a calculus for q-numbers. 时间的量子理论:q数的微积分。

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2022-07-01 Epub Date: 2022-07-27 DOI: 10.1098/rspa.2021.0970

Samuel Kuypers

引用次数: 1

Deeply subwavelength giant monopole elastodynamic metacluster resonators. 深亚波长巨型单极弹性动力亚团谐振器。

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2022-07-01 Epub Date: 2022-07-06 DOI: 10.1098/rspa.2022.0026

Philip A Cotterill, David Nigro, William J Parnell

{"title":"Deeply subwavelength giant monopole elastodynamic metacluster resonators.","authors":"Philip A Cotterill, David Nigro, William J Parnell","doi":"10.1098/rspa.2022.0026","DOIUrl":"https://doi.org/10.1098/rspa.2022.0026","url":null,"abstract":"The giant monopole resonance is a well-known phenomenon, employed to tune the dynamic response of composite materials comprising voids in an elastic matrix which has a bulk modulus much greater than its shear modulus, e.g. elastomers. This low frequency resonance (e.g. <math><msub><mi>λ</mi> <mi>p</mi></msub> <mrow><mo>/</mo></mrow> <mi>a</mi> <mo>≈</mo> <mn>100</mn></math> for standard elastomers, where <math><msub><mi>λ</mi> <mi>p</mi></msub> </math> and <math><mi>a</mi></math> are the compressional wavelength and void radius, respectively) has motivated acoustic material design over many decades, exploiting the subwavelength regime. Despite this widespread use, the manner by which the resonance arising from voids in close proximity is affected by their interaction is not understood. Here, we illustrate that for planar elastodynamics (circular cylindrical voids), coupling due to near-field shear significantly modifies the monopole (compressional) resonant response. We show that by modifying the number and configuration of voids in a metacluster, the directionality, scattering amplitude and resonant frequency can be tailored and tuned. Perhaps most notably, metaclusters deliver a lower frequency resonance than a single void. For example, two touching voids deliver a reduction in resonant frequency of almost 16% compared with a single void of the same volume. Combined with other resonators, such metaclusters can be used as meta-atoms in the design of elastic materials with exotic dynamic material properties.","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20220026"},"PeriodicalIF":3.5,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9257599/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40488855","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}

引用次数: 3

Integrable nonlinear evolution equations in three spatial dimensions. 三维空间可积非线性演化方程。

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2022-07-01 Epub Date: 2022-07-27 DOI: 10.1098/rspa.2022.0074

A S Fokas

引用次数: 0

Submarine channels formation driven by turbidity currents interacting with an erodible bed. 由浊流与可蚀河床相互作用驱动的海底水道形成。

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2022-07-01 Epub Date: 2022-07-13 DOI: 10.1098/rspa.2022.0137

Rajesh K Mahato, Subhasish Dey, Sk Zeeshan Ali

{"title":"Submarine channels formation driven by turbidity currents interacting with an erodible bed.","authors":"Rajesh K Mahato, Subhasish Dey, Sk Zeeshan Ali","doi":"10.1098/rspa.2022.0137","DOIUrl":"https://doi.org/10.1098/rspa.2022.0137","url":null,"abstract":"In this article, we explore the submarine channel formation driven by the interaction of turbidity currents with an erodible bed. The theoretical analysis considers the three-dimensional continuity and momentum equations of the fluid phase, and the advection-diffusion and Exner equations of the solid phase. The governing equations are linearized by imposing periodic perturbations on the base flow. We study the response of both the base flow (profiles of velocity and suspended sediment concentration) and perturbations (growth rate and perturbation fields) to changes in key parameters related to the flow and sediment transport. The growth rate and the critical wavenumber are examined for a given quintet formed by the gravitational parameter, longitudinal bed slope, sediment concentration at the edge of the driving layer, Rouse number and erosion coefficient. The critical wavenumber reduces with an increase in gravitational parameter, longitudinal bed slope, sediment concentration at the edge of the driving layer and erosion coefficient, while it increases with the Rouse number. For the submarine channel formation, we identify the upper threshold values for the gravitational parameter, longitudinal bed slope, sediment concentration at the edge of the driving layer and erosion coefficient and the lower threshold value for the Rouse number.","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20220137"},"PeriodicalIF":3.5,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9277707/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40507296","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}

引用次数: 3

Evidence for active upper mantle flow in the Atlantic and Indo-Australian realms since the Upper Jurassic from hiatus maps and spreading rate changes. 上侏罗世以来大西洋和印度-澳大利亚板块上地幔流动活跃的证据——来自间断图和扩张速率变化。

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2022-06-29 Epub Date: 2022-06-15 DOI: 10.1098/rspa.2021.0764

Berta Vilacís, Jorge N Hayek, Ingo L Stotz, Hans-Peter Bunge, Anke M Friedrich, Sara Carena, Stuart Clark

{"title":"Evidence for active upper mantle flow in the Atlantic and Indo-Australian realms since the Upper Jurassic from hiatus maps and spreading rate changes.","authors":"Berta Vilacís, Jorge N Hayek, Ingo L Stotz, Hans-Peter Bunge, Anke M Friedrich, Sara Carena, Stuart Clark","doi":"10.1098/rspa.2021.0764","DOIUrl":"https://doi.org/10.1098/rspa.2021.0764","url":null,"abstract":"Histories of large-scale horizontal and vertical lithosphere motion hold important information on mantle convection. Here, we compare continent-scale hiatus maps as a proxy for mantle flow induced dynamic topography and plate motion variations in the Atlantic and Indo-Australian realms since the Upper Jurassic, finding they frequently correlate, except when plate boundary forces may play a significant role. This correlation agrees with descriptions of asthenosphere flow beneath tectonic plates in terms of Poiseuille/Couette flow, as it explicitly relates plate motion changes, induced by evolving basal shear forces, to non-isostatic vertical motion of the lithosphere. Our analysis reveals a timescale, on the order of a geological series, between the occurrence of continent-scale hiatus and plate motion changes. This is consistent with the presence of a weak upper mantle. It also shows a spatial scale for interregional hiatus, on the order of 2000-3000 km in diameter, which can be linked by fluid dynamic analysis to active upper mantle flow regions. Our results suggest future studies should pursue large-scale horizontal and vertical lithosphere motion in combination, to track the expressions of past mantle flow. Such studies would provide powerful constraints for adjoint-based geodynamic inverse models of past mantle convection.","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20210764"},"PeriodicalIF":3.5,"publicationDate":"2022-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9199074/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40401913","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}

引用次数: 3

Rheology of particulate suspensions with non-Newtonian fluids in capillaries. 非牛顿流体在毛细血管中的颗粒悬浮液流变学。

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2022-06-01 Epub Date: 2022-06-15 DOI: 10.1098/rspa.2021.0615

Bin Xia, Paul S Krueger

{"title":"Rheology of particulate suspensions with non-Newtonian fluids in capillaries.","authors":"Bin Xia, Paul S Krueger","doi":"10.1098/rspa.2021.0615","DOIUrl":"https://doi.org/10.1098/rspa.2021.0615","url":null,"abstract":"Particulate suspensions occur in situations from blood flow to slurries in drilling applications. Existing investigations of these suspensions generally concentrate on the impact of particle volume fraction for suspensions in Newtonian fluids under free-flow conditions. Recently, particulate-polymer composites have been used in additive manufacturing (AM). Here, the polymer becomes a shear-thinning non-Newtonian fluid during extrusion, creating a particulate suspension. Motivated by the challenges in AM of particulate composites, this study investigates the rheology of suspensions of micrometre-sized particles in shear-thinning silicone while extruded through AM-scaled nozzles (millimetre-scale diameters). The suspensions were observed to follow a power-law behaviour and their rheology was investigated through the measured flow consistency ( <math><mi>K</mi></math> ) and behaviour ( <math><mi>n</mi></math> ) indices. The impact of the particle volume fraction ( <math><mi>ϕ</mi></math> ) and the ratio ( <math><mi>ω</mi></math> ) of the capillary inside diameter to the particle diameter on both indices were measured. <math><mi>n</mi></math> was found to be only impacted by the suspension fluid type and <math><mi>ϕ</mi></math> . <math><mi>K</mi></math> was found to be constant at large <math><mi>ω</mi></math> , but decreased and then increased to infinity with <math><mi>ω</mi></math> decreasing. Based on its behaviour, <math><mi>K</mi></math> was categorized into two conditions and analysed separately with semi-empirical models. The impact of particle size distribution was also investigated.","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20210615"},"PeriodicalIF":3.5,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9199073/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40399704","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}

引用次数: 2

Advection-dominated transport past isolated disordered sinks: stepping beyond homogenization. 通过孤立无序汇的平流主导运输:超越均质化。

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2022-06-01 Epub Date: 2022-06-15 DOI: 10.1098/rspa.2022.0032

George F Price, Igor L Chernyavsky, Oliver E Jensen

{"title":"Advection-dominated transport past isolated disordered sinks: stepping beyond homogenization.","authors":"George F Price, Igor L Chernyavsky, Oliver E Jensen","doi":"10.1098/rspa.2022.0032","DOIUrl":"https://doi.org/10.1098/rspa.2022.0032","url":null,"abstract":"We investigate the transport of a solute past isolated sinks in a bounded domain when advection is dominant over diffusion, evaluating the effectiveness of homogenization approximations when sinks are distributed uniformly randomly in space. Corrections to such approximations can be non-local, non-smooth and non-Gaussian, depending on the physical parameters (a Péclet number Pe, assumed large, and a Damköhler number Da) and the compactness of the sinks. In one spatial dimension, solute distributions develop a staircase structure for large <math> <mrow><mrow><mi>Pe</mi></mrow> </mrow> </math> , with corrections being better described with credible intervals than with traditional moments. In two and three dimensions, solute distributions are near-singular at each sink (and regularized by sink size), but their moments can be smooth as a result of ensemble averaging over variable sink locations. We approximate corrections to a homogenization approximation using a moment-expansion method, replacing the Green's function by its free-space form, and test predictions against simulation. We show how, in two or three dimensions, the leading-order impact of disorder can be captured in a homogenization approximation for the ensemble mean concentration through a modification to <math> <mrow><mrow><mi>Da</mi></mrow> </mrow> </math> that grows with diminishing sink size.","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20220032"},"PeriodicalIF":3.5,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9199076/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40401916","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}

引用次数: 0

The wave function as a true ensemble. 波函数作为一个真正的集合。

IF 3

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2022-06-01 Epub Date: 2022-06-22 DOI: 10.1098/rspa.2021.0705

Jonte R Hance, Sabine Hossenfelder

引用次数: 0

Unbiased estimation of the Hessian for partially observed diffusions. 部分观测扩散的黑森量无偏估计。

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2022-06-01 Epub Date: 2022-06-22 DOI: 10.1098/rspa.2021.0710

Neil K Chada, Ajay Jasra, Fangyuan Yu

引用次数: 2

Reviewers in 2021. 2021年的审稿人。