Proceedings. Mathematical, physical, and engineering sciences最新文献_第3页

The mathematical foundations of anelasticity: existence of smooth global intermediate configurations. 非弹性的数学基础:光滑全局中间构型的存在性。

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2021-01-01 Epub Date: 2021-01-06 DOI: 10.1098/rspa.2020.0462

Christian Goodbrake, Alain Goriely, Arash Yavari

{"title":"The mathematical foundations of anelasticity: existence of smooth global intermediate configurations.","authors":"Christian Goodbrake, Alain Goriely, Arash Yavari","doi":"10.1098/rspa.2020.0462","DOIUrl":"https://doi.org/10.1098/rspa.2020.0462","url":null,"abstract":"A central tool of nonlinear anelasticity is the multiplicative decomposition of the deformation tensor that assumes that the deformation gradient can be decomposed as a product of an elastic and an anelastic tensor. It is usually justified by the existence of an intermediate configuration. Yet, this configuration cannot exist in Euclidean space, in general, and the mathematical basis for this assumption is on unsatisfactory ground. Here, we derive a sufficient condition for the existence of global intermediate configurations, starting from a multiplicative decomposition of the deformation gradient. We show that these global configurations are unique up to isometry. We examine the result of isometrically embedding these configurations in higher-dimensional Euclidean space, and construct multiplicative decompositions of the deformation gradient reflecting these embeddings. As an example, for a family of radially symmetric deformations, we construct isometric embeddings of the resulting intermediate configurations, and compute the residual stress fields explicitly.","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20200462"},"PeriodicalIF":3.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7897629/pdf/rspa20200462.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"25414297","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: 14

High-resolution thickness maps of corrosion using SH1 guided wave tomography. 使用SH1导波层析成像的高分辨率腐蚀厚度图。

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2021-01-01 Epub Date: 2021-01-13 DOI: 10.1098/rspa.2020.0380

Andreas A E Zimmermann, Peter Huthwaite, Brian Pavlakovic

{"title":"High-resolution thickness maps of corrosion using SH1 guided wave tomography.","authors":"Andreas A E Zimmermann, Peter Huthwaite, Brian Pavlakovic","doi":"10.1098/rspa.2020.0380","DOIUrl":"https://doi.org/10.1098/rspa.2020.0380","url":null,"abstract":"Quantifying corrosion damage is vital for the petrochemical industry, and guided wave tomography can provide thickness maps of such regions by transmitting guided waves through these areas and capturing the scattering information using arrays. The dispersive nature of the guided waves enables a reconstruction of wave velocity to be converted into thickness. However, existing approaches have been shown to be limited in in-plane resolution, significantly short of that required to accurately image a defect target of three times the wall thickness (i.e. 3 T) in each in-plane direction. This is largely due to the long wavelengths of the fundamental modes commonly used, being around 4 T for both A0 and S0 at the typical operation points. In this work, the suitability of the first-order shear-horizontal guided wave mode, SH1, has been investigated to improve the resolution limit. The wavelength at the desired operating point is significantly shorter, enabling an improvement in resolution of around 2.4 times. This is first verified by realistic finite-element simulations and then validated by experimental results, confirming the improved resolution limit can now allow defects of maximum extent 3T-by-3T to be reliably detected and sized, i.e. a long-pursued goal of guided wave tomography has been achieved.","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20200380"},"PeriodicalIF":3.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7897635/pdf/rspa20200380.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"25414296","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: 10

On non-autonomous differential-difference AKP, BKP and CKP equations. 非自治微分-差分AKP、BKP和CKP方程。

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2021-01-01 Epub Date: 2021-01-20 DOI: 10.1098/rspa.2020.0717

Wei Fu, Frank W Nijhoff

引用次数: 5

M-theory, black holes and cosmology. m理论，黑洞和宇宙学。

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2021-01-01 Epub Date: 2021-01-06 DOI: 10.1098/rspa.2020.0786

Renata Kallosh

{"title":"M-theory, black holes and cosmology.","authors":"Renata Kallosh","doi":"10.1098/rspa.2020.0786","DOIUrl":"https://doi.org/10.1098/rspa.2020.0786","url":null,"abstract":"This paper is dedicated to Michael J. Duff on the occasion of his 70th birthday. I discuss some issues of M-theory/string theory/supergravity closely related to Mike's interests. I describe a relation between STU black hole entropy, the Cayley hyperdeterminant, the Bhargava cube and a three-qubit Alice-Bob-Charlie triality symmetry. I shortly describe my recent work with Gunaydin, Linde and Yamada on M-theory cosmology (Gunaydin et al. 2020 M-theory cosmology, octonions, error-correcting codes (http://arxiv.org/abs/2008.01494)), inspired by the work of Duff with Ferrara and Borsten, Levay, Marrani et al. Here, we have seven-qubits, a party including Alice, Bob, Charlie, Daisy, Emma, Fred and George. Octonions and Hamming error-correcting codes are at the base of these models. They lead to seven benchmark targets of future cosmic microwave background missions looking for primordial gravitational waves from inflation. I also show puzzling relations between the fermion mass eigenvalues in these cosmological models, the exceptional Jordan eigenvalue problem and black hole entropy. The symmetry of our cosmological models is illustrated by beautiful pictures of a Coxeter projection of the root system of E7.","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20200786"},"PeriodicalIF":3.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7897631/pdf/rspa20200786.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"25414764","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: 1

Analytical continuation of two-dimensional wave fields. 二维波场的解析延拓。

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2021-01-01 Epub Date: 2021-01-06 DOI: 10.1098/rspa.2020.0681

Raphaël C Assier, Andrey V Shanin

引用次数: 7

Simulation of pandemics in real cities: enhanced and accurate digital laboratories. 真实城市流行病的模拟:增强和精确的数字实验室。

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2021-01-01 Epub Date: 2021-01-27 DOI: 10.1098/rspa.2020.0653

A Alexiadis, A Albano, A Rahmat, M Yildiz, A Kefal, M Ozbulut, N Bakirci, D A Garzón-Alvarado, C A Duque-Daza, J H Eslava-Schmalbach

{"title":"Simulation of pandemics in real cities: enhanced and accurate digital laboratories.","authors":"A Alexiadis, A Albano, A Rahmat, M Yildiz, A Kefal, M Ozbulut, N Bakirci, D A Garzón-Alvarado, C A Duque-Daza, J H Eslava-Schmalbach","doi":"10.1098/rspa.2020.0653","DOIUrl":"https://doi.org/10.1098/rspa.2020.0653","url":null,"abstract":"This study develops a modelling framework for simulating the spread of infectious diseases within real cities. Digital copies of Birmingham (UK) and Bogotá (Colombia) are generated, reproducing their urban environment, infrastructure and population. The digital inhabitants have the same statistical features of the real population. Their motion is a combination of predictable trips (commute to work, school, etc.) and random walks (shopping, leisure, etc.). Millions of individuals, their encounters and the spread of the disease are simulated by means of high-performance computing and massively parallel algorithms for several months and a time resolution of 1 minute. Simulations accurately reproduce the COVID-19 data for Birmingham and Bogotá both before and during the lockdown. The model has only one adjustable parameter calculable in the early stages of the pandemic. Policymakers can use our digital cities as virtual laboratories for testing, predicting and comparing the effects of policies aimed at containing epidemics.","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20200653"},"PeriodicalIF":3.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7897638/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"25407095","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: 4

Bitwise efficiency in chaotic models. 混沌模型的位效率。

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2017-09-01 Epub Date: 2017-09-06 DOI: 10.1098/rspa.2017.0144

Stephen Jeffress, Peter Düben, Tim Palmer

{"title":"Bitwise efficiency in chaotic models.","authors":"Stephen Jeffress, Peter Düben, Tim Palmer","doi":"10.1098/rspa.2017.0144","DOIUrl":"https://doi.org/10.1098/rspa.2017.0144","url":null,"abstract":"Motivated by the increasing energy consumption of supercomputing for weather and climate simulations, we introduce a framework for investigating the bit-level information efficiency of chaotic models. In comparison with previous explorations of inexactness in climate modelling, the proposed and tested information metric has three specific advantages: (i) it requires only a single high-precision time series; (ii) information does not grow indefinitely for decreasing time step; and (iii) information is more sensitive to the dynamics and uncertainties of the model rather than to the implementation details. We demonstrate the notion of bit-level information efficiency in two of Edward Lorenz's prototypical chaotic models: Lorenz 1963 (L63) and Lorenz 1996 (L96). Although L63 is typically integrated in 64-bit 'double' floating point precision, we show that only 16 bits have significant information content, given an initial condition uncertainty of approximately 1% of the size of the attractor. This result is sensitive to the size of the uncertainty but not to the time step of the model. We then apply the metric to the L96 model and find that a 16-bit scaled integer model would suffice given the uncertainty of the unresolved sub-grid-scale dynamics. We then show that, by dedicating computational resources to spatial resolution rather than numeric precision in a field programmable gate array (FPGA), we see up to 28.6% improvement in forecast accuracy, an approximately fivefold reduction in the number of logical computing elements required and an approximately 10-fold reduction in energy consumed by the FPGA, for the L96 model.","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20170144"},"PeriodicalIF":3.5,"publicationDate":"2017-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspa.2017.0144","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35581889","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: 12

Irreversible particle motion in surfactant-laden interfaces due to pressure-dependent surface viscosity. 由于压力依赖的表面粘度，表面活性剂负载界面中不可逆的颗粒运动。

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2017-09-01 Epub Date: 2017-09-20 DOI: 10.1098/rspa.2017.0346

Harishankar Manikantan, Todd M Squires

引用次数: 4

Can a quantum state over time resemble a quantum state at a single time? 随着时间的推移，量子态能像单一时间的量子态吗?

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2017-09-01 Epub Date: 2017-09-20 DOI: 10.1098/rspa.2017.0395

Dominic Horsman, Chris Heunen, Matthew F Pusey, Jonathan Barrett, Robert W Spekkens

{"title":"Can a quantum state over time resemble a quantum state at a single time?","authors":"Dominic Horsman, Chris Heunen, Matthew F Pusey, Jonathan Barrett, Robert W Spekkens","doi":"10.1098/rspa.2017.0395","DOIUrl":"https://doi.org/10.1098/rspa.2017.0395","url":null,"abstract":"The standard formalism of quantum theory treats space and time in fundamentally different ways. In particular, a composite system at a given time is represented by a joint state, but the formalism does not prescribe a joint state for a composite of systems at different times. If there were a way of defining such a joint state, this would potentially permit a more even-handed treatment of space and time, and would strengthen the existing analogy between quantum states and classical probability distributions. Under the assumption that the joint state over time is an operator on the tensor product of single-time Hilbert spaces, we analyse various proposals for such a joint state, including one due to Leifer and Spekkens, one due to Fitzsimons, Jones and Vedral, and another based on discrete Wigner functions. Finding various problems with each, we identify five criteria for a quantum joint state over time to satisfy if it is to play a role similar to the standard joint state for a composite system: that it is a Hermitian operator on the tensor product of the single-time Hilbert spaces; that it represents probabilistic mixing appropriately; that it has the appropriate classical limit; that it has the appropriate single-time marginals; that composing over multiple time steps is associative. We show that no construction satisfies all these requirements. If Hermiticity is dropped, then there is an essentially unique construction that satisfies the remaining four criteria.","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20170395"},"PeriodicalIF":3.5,"publicationDate":"2017-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspa.2017.0395","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35478999","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: 60

On the differing growth mechanisms of black-smoker and Lost City-type hydrothermal vents. 黑烟型和失落之城型热液喷口生长机制的差异研究。

IF 3.5

Proceedings. Mathematical, physical, and engineering sciences Pub Date : 2017-09-01 Epub Date: 2017-09-13 DOI: 10.1098/rspa.2017.0387

Silvana S S Cardoso, Julyan H E Cartwright

{"title":"On the differing growth mechanisms of black-smoker and Lost City-type hydrothermal vents.","authors":"Silvana S S Cardoso, Julyan H E Cartwright","doi":"10.1098/rspa.2017.0387","DOIUrl":"https://doi.org/10.1098/rspa.2017.0387","url":null,"abstract":"Black smokers and Lost City-type springs are varieties of hydrothermal vents on the ocean floors that emit hot, acidic water and cool, alkaline water, respectively. While both produce precipitation structures as the issuing fluid encounters oceanic water, Lost City-type hydrothermal vents in particular have been implicated in the origin of life on the Earth. We present a parallel-velocity flow model for the radius and flow rate of a cylindrical jet of fluid that forms the template for the growth of a tube precipitated about itself and we compare the solution with previous laboratory experimental results from growth of silicate chemical gardens. We show that when the growth of the solid structure is determined by thermal diffusion, fluid flow is slow at the solid-liquid contact. However, in the case of chemical diffusive transport, the fluid jet effectively drags the liquid in the pores of the solid precipitate. These findings suggest a continuum in the diffusive growth rate of hydrothermal vent structures, where Lost City-type hydrothermal vents favour contact between the vent fluid and the external seawater. We explore the implications for the road to life.","PeriodicalId":520758,"journal":{"name":"Proceedings. Mathematical, physical, and engineering sciences","volume":" ","pages":"20170387"},"PeriodicalIF":3.5,"publicationDate":"2017-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspa.2017.0387","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35478556","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: 16