Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences最新文献

{"title":"An Eulerian hyperbolic model for heat transfer derived via Hamilton’s principle: analytical and numerical study","authors":"Firas Dhaouadi, Sergey Gavrilyuk","doi":"10.1098/rspa.2023.0440","DOIUrl":"https://doi.org/10.1098/rspa.2023.0440","url":null,"abstract":"In this paper, we present a new model for heat transfer in compressible fluid flows. The model is derived from Hamilton’s principle of stationary action in Eulerian coordinates, in a setting where the entropy conservation is recovered as an Euler–Lagrange equation. A sufficient criterion for the hyperbolicity of the model is formulated. The governing equations are asymptotically consistent with the Euler equations for compressible heat conducting fluids, provided the addition of suitable relaxation terms. A study of the Rankine–Hugoniot conditions and Clausius–Duhem inequality is performed for a specific choice of the equation of state. In particular, this reveals that contact discontinuities cannot exist while expansion waves and compression fans are possible solutions to the governing equations. Evidence of these properties is provided on a set of numerical test cases.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"19 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multi-parametric optimization for controlling bifurcation structures","authors":"A. Mélot, E. Denimal, L. Renson","doi":"10.1098/rspa.2023.0505","DOIUrl":"https://doi.org/10.1098/rspa.2023.0505","url":null,"abstract":"Bifurcations organize the dynamics of many natural and engineered systems. They induce qualitative and quantitative changes to a system’s dynamics, which can have catastrophic consequences if ignored during design. In this paper, we propose a general computational method to control the local bifurcations of dynamical systems by optimizing design parameters. We define an objective functional that enforces the appearance of local bifurcation points at targeted locations or even encourages their disappearance. The methodology is an efficient alternative to bifurcation tracking techniques capable of handling many design parameters ( <jats:inline-formula> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mo>&gt;</mml:mo> </mml:mrow> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>2</mml:mn> </mml:msup> </mml:math> </jats:inline-formula> ). The method is demonstrated on a Duffing oscillator featuring a hardening cubic nonlinearity and an autonomous van der Pol-Duffing oscillator coupled to a nonlinear tuned vibration absorber. The finite-element model of a clamped-free Euler–Bernoulli beam, coupled with a reduced-order modelling technique, is also used to show the extension to the shape optimization of more complicated structures. Results demonstrate that several local bifurcations of various types can be handled simultaneously by the bifurcation control framework, with both parameter and state target values.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"47 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multi-fidelity reduced-order surrogate modelling","authors":"Paolo Conti, Mengwu Guo, Andrea Manzoni, Attilio Frangi, Steven L. Brunton, J. Nathan Kutz","doi":"10.1098/rspa.2023.0655","DOIUrl":"https://doi.org/10.1098/rspa.2023.0655","url":null,"abstract":"High-fidelity numerical simulations of partial differential equations (PDEs) given a restricted computational budget can significantly limit the number of parameter configurations considered and/or time window evaluated. Multi-fidelity surrogate modelling aims to leverage less accurate, lower-fidelity models that are computationally inexpensive in order to enhance predictive accuracy when high-fidelity data are scarce. However, low-fidelity models, while often displaying the qualitative solution behaviour, fail to accurately capture fine spatio-temporal and dynamic features of high-fidelity models. To address this shortcoming, we present a data-driven strategy that combines dimensionality reduction with multi-fidelity neural network surrogates. The key idea is to generate a spatial basis by applying proper orthogonal decomposition (POD) to high-fidelity solution snapshots, and approximate the dynamics of the reduced states—time-parameter-dependent expansion coefficients of the POD basis—using a multi-fidelity <jats:italic>long short-term memory</jats:italic> network. By mapping low-fidelity reduced states to their high-fidelity counterpart, the proposed reduced-order surrogate model enables the efficient recovery of full solution fields over time and parameter variations in a non-intrusive manner. The generality of this method is demonstrated by a collection of PDE problems where the low-fidelity model can be defined by coarser meshes and/or time stepping, as well as by misspecified physical features.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"264 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An equivariant Reeb–Beltrami correspondence and the Kepler–Euler flow","authors":"Josep Fontana-McNally, Eva Miranda, Daniel Peralta-Salas","doi":"10.1098/rspa.2023.0499","DOIUrl":"https://doi.org/10.1098/rspa.2023.0499","url":null,"abstract":"We prove that the correspondence between Reeb and Beltrami vector fields presented in Etnyre &amp; Ghrist (Etnyre, Ghrist 2000 <jats:italic>Nonlinearity</jats:italic> <jats:bold>13</jats:bold> , 441–458 ( <jats:ext-link xmlns:xlink=\"http://www.w3.org/1999/xlink\" ext-link-type=\"uri\" xlink:href=\"http://dx.doi.org/10.1088/0951-7715/13/2/306\">doi:10.1088/0951-7715/13/2/306</jats:ext-link> )) can be made equivariant whenever additional symmetries of the underlying geometric structures are considered. As a corollary of this correspondence, we show that energy levels above the maximum of the potential energy of mechanical Hamiltonian systems can be viewed as stationary fluid flows, though the metric is not prescribed. In particular, we showcase the emblematic example of the <jats:inline-formula> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>n</mml:mi> </mml:math> </jats:inline-formula> -body problem and focus on the Kepler problem. We explicitly construct a compatible Riemannian metric that makes the Kepler problem of celestial mechanics a stationary fluid flow (of Beltrami type) on a suitable manifold, the <jats:italic>Kepler–Euler flow</jats:italic> .","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"1 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Toward a further understanding of the loop formation and elimination in twisted filament: experiments and validation","authors":"Jiongjiong Hu, Jiahui Teng, Lei Liu, Dabiao Liu","doi":"10.1098/rspa.2023.0719","DOIUrl":"https://doi.org/10.1098/rspa.2023.0719","url":null,"abstract":"Motivated by observations of loop formation and elimination phenomena in elastic filaments subjected to torsion and axial end displacement, we develop a tension–torsion tester to study the slack–extension responses of filaments with varied initial twists. The experiments are conducted by initially twisting the filament by a specific degree and subsequently adjusting the axial end displacement. By continuously monitoring the correlation between torque and filament configuration, we can accurately determine the critical points associated with buckling, loop formation and loop elimination. The interconversion of link, twist and writhe is also tracked in the experiment. We establish a relation between torque and end displacement of filament that provides an insight into the conditions leading to instabilities. Three buckling criteria are also evaluated in the context of measurement data. Simulations on the slack and extension of the twisted filaments based on the Cosserat rod theory are performed, providing reliable predictions of the configuration evolution. Our results highlight the importance of twist and slack in torsional buckling processes, providing guidance for the control of systems with twisted slender structures.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"171 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Direct method to determine singular point of enveloped surface and its application to worm wheel tooth surface","authors":"Jian Cui, Yaping Zhao, Qingxiang Meng, Gongfa Li","doi":"10.1098/rspa.2023.0369","DOIUrl":"https://doi.org/10.1098/rspa.2023.0369","url":null,"abstract":"A novel methodology for determining the singular point of an enveloped surface is put forward. Unlike some existing methods, the presented method starts directly from the equation of the enveloped surface instead of that of the generating surface, and it is thus called a direct method. The calculation for the normal vector of the enveloped surface is well simplified with the help of the moving frame approach, which makes the presented method feasible. The singularity condition equation is extracted by using the theory of linear algebra. For singular points with different properties, proper solving techniques are established, including resultant elimination and simple elimination. Applying the developed method, the undercutting characteristics of the Archimedes worm wheel are investigated from the perspective of spatial meshing. The numerical results demonstrate that the worm wheel generally has one undercutting limit line, whose trend is along the tooth width of the wheel. Locating on one side of the tooth surface and near the tooth root is a dangerous part of the worm wheel undercutting. The proposed method is beneficial for the development of gear meshing science.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"227 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Experimental studies on snaking in 3D-printed cylindrical shells under axial compression using photogrammetry","authors":"V. Ravulapalli, G. Raju, V. Narayanamurthy","doi":"10.1098/rspa.2023.0631","DOIUrl":"https://doi.org/10.1098/rspa.2023.0631","url":null,"abstract":"The buckling instability of cylindrical shells under axial compression has been one of the most renowned problems in structural engineering for several decades. Many pioneering works in the twentieth century have provided insights into understanding the shells’ infamous imperfection sensitivity and led to reliability-based designs. However, a recent surge in numerical studies of the snaking phenomenon explores the development of a localized stable post-buckling mode in axially compressed cylindrical shells. Hitherto, none of the experimental studies report on the evolution of azimuthal snaking. In this work, experimental studies are carried out with the objective of revealing the snaking phenomenon. The axial compression experiments are performed on 3D-printed shells made of thermoplastic polyurethane (TPU). The work’s novelty lies in the usage of TPU shells for slowing down the propagation of circumferential dimples and making it feasible to capture them using photogrammetry. Despite the match between the experimental and numerical mode shapes, the experiments reveal multiple routes for the snaking sequence. Furthermore, mode transitions such as reduction in circumferential wave number and transformation of symmetric mode into an asymmetric one are observed. These experimental results provide insights into the localized phenomenon of snaking and validate numerical solutions.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"84 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Estimation of auto-covariance of log hydraulic conductivity from Generalized Sub-Gaussian porosity and particle size random fields","authors":"M. Harrison, M. Riva, M. Mousavi Nezhad, A. Guadagnini","doi":"10.1098/rspa.2023.0476","DOIUrl":"https://doi.org/10.1098/rspa.2023.0476","url":null,"abstract":"We derive analytical formulations relating the spatial covariance ( <jats:inline-formula> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>Y</mml:mi> </mml:msub> </mml:math> </jats:inline-formula> ) of (log-transformed) hydraulic conductivities to auto- and cross-covariances of porosity ( <jats:inline-formula> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>ϕ</mml:mi> </mml:math> </jats:inline-formula> ) and representative soil particle sizes within the framework of the classical Terzaghi model. The latter provides an empirical relationship which is widely used to obtain conductivity estimates. We frame the study within recent stochastic approaches and conceptualize appropriate transformations of <jats:inline-formula> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>ϕ</mml:mi> </mml:math> </jats:inline-formula> and representative soil particle size as Generalized Sub-Gaussian (GSG) spatially cross-correlated random processes. Consistency of the theoretical framework against sample distributions of <jats:inline-formula> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>ϕ</mml:mi> </mml:math> </jats:inline-formula> and particle size is assessed through the analysis of field data. A perturbation-based approach yields workable expressions of <jats:inline-formula> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>Y</mml:mi> </mml:msub> </mml:math> </jats:inline-formula> upon truncating the otherwise exact analytical solution at given orders of approximations. Our analytical (truncated) log-conductivity covariance is in agreement with its Monte Carlo-based counterpart. A Global Sensitivity Analysis relying on classical Sobol indices quantifies the relative importance of all parameters embedded in the formulation of <jats:inline-formula> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>Y</mml:mi> </mml:msub> </mml:math> </jats:inline-formula> . We show that parameters driving the GSG nature of the distribution of (transformed) porosity are key to the main features of <jats:inline-formula> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>Y</mml:mi> </mml:msub> </mml:math> </jats:inline-formula> . We also document the relevance of properly capturing emergences of possible cross-correlations between <jats:inline-formula> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>ϕ</mml:mi> </mml:math> </jats:inline-formula> and representative particle size to reconstruct conductivity fields.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"5 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025114","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Thermal convection with a Cattaneo heat flux model","authors":"M. Gentile, B. Straughan","doi":"10.1098/rspa.2023.0771","DOIUrl":"https://doi.org/10.1098/rspa.2023.0771","url":null,"abstract":"The problem of thermal convection in a layer of viscous incompressible fluid is analysed. The heat flux law is taken to be one of Cattaneo type. The time derivative of the heat flux is allowed to be a material derivative, or a general objective derivative. It is shown that only one objective derivative leads to results consistent with what one expects in real life. This objective derivative leads to a Cattaneo–Christov theory, and the results for linear instability theory are in agreement with those for a material derivative. It is further shown that none of the theories allow a standard nonlinear, energy stability analysis. A further heat flux due to P.M. Mariano is added and then an analysis is performed for stationary convection, oscillatory convection, and fully nonlinear theory. For the material derivative case, the analysis proceeds and global nonlinear stability is achieved. For Cattaneo–Christov theory, it appears necessary to add a regularization term in the equation for the heat flux, and even then the analysis only works in two space dimensions, and is conditional upon the size of the initial data. For the three-dimensional situation, it is shown how a nonlinear stability analysis may be achieved with a Navier–Stokes–Voigt fluid rather than a Navier–Stokes one.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"1 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical direct scattering transform for breathers","authors":"I. I. Mullyadzhanov, A. S. Gudko, R. I. Mullyadzhanov, A. A. Gelash","doi":"10.1098/rspa.2023.0529","DOIUrl":"https://doi.org/10.1098/rspa.2023.0529","url":null,"abstract":"We consider the model of the focusing one-dimensional nonlinear Schrödinger equation (fNLSE) in the presence of an unstable constant background, which exhibits coherent solitary wave structures—breathers. Within the inverse scattering transform (IST) method, we study the problem of the scattering data numerical computation for a broad class of breathers localized in space. Such a direct scattering transform (DST) procedure requires a numerical solution of the auxiliary Zakharov–Shabat system with boundary conditions corresponding to the background. To find the solution, we compute the transfer matrix using the second-order Boffetta–Osborne approach and recently developed high-order numerical schemes based on the Magnus expansion. To recover the scattering data of breathers, we derive analytical relations between the scattering coefficients and the transfer matrix elements. Then we construct localized single- and multi-breather solutions and verify the developed numerical approach by recovering the complete set of scattering data with the built-in accuracy providing the information about the amplitude, velocity, phase and position of each breather. To combine the conventional IST approach with the efficient dressing method for multi-breather solutions, we derive the exact relation between the parameters of breathers in these two frameworks.","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"47 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}