We consider Steklov eigenvalues of nearly hyperspherical domains in with . In previous work, treating such domains as perturbations of the ball, we proved that the Steklov eigenvalues are analytic functions of the domain perturbation parameter. Here, we compute the first-order term of the asymptotic expansion and show that the first-order perturbations are eigenvalues of a Hermitian matrix, whose entries can be written explicitly in terms of Pochhammer’s and Wigner -symbols. We analyse the asymptotic expansion and show the following isoperimetric results among domains with fixed volume: (i) for an infinite subset of Steklov eigenvalues, the ball is not optimal and (ii) for a different infinite subset of Steklov eigenvalues, the ball is a stationary point.
{"title":"Steklov eigenvalues of nearly hyperspherical domains","authors":"Chee Han Tan, Robert Viator","doi":"10.1098/rspa.2023.0734","DOIUrl":"https://doi.org/10.1098/rspa.2023.0734","url":null,"abstract":"<p>We consider Steklov eigenvalues of nearly hyperspherical domains in <span><math><msup><mrow><mi mathvariant=\"double-struck\">R</mi></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup></math></span><span></span> with <span><math><mi>d</mi><mo>≥</mo><mn>3</mn></math></span><span></span>. In previous work, treating such domains as perturbations of the ball, we proved that the Steklov eigenvalues are analytic functions of the domain perturbation parameter. Here, we compute the first-order term of the asymptotic expansion and show that the first-order perturbations are eigenvalues of a Hermitian matrix, whose entries can be written explicitly in terms of Pochhammer’s and Wigner <span><math><mn>3</mn><mi>j</mi></math></span><span></span>-symbols. We analyse the asymptotic expansion and show the following isoperimetric results among domains with fixed volume: (i) for an infinite subset of Steklov eigenvalues, the ball is not optimal and (ii) for a different infinite subset of Steklov eigenvalues, the ball is a stationary point.</p>","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"233 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140591715","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}
Yanxing Wang, Hui Wan, Cody Barka, Tie Wei, Fangjun Shu
A quasi-steady-state model for accurately predicting the detailed diffusion-dominated dissolution process of polydisperse spheroidal (prolate, oblate and spherical) particle systems was presented in Part I of this study. In the present paper, the dissolution characteristics of typical polydisperse spheroidal particle systems have been extensively investigated. The effects of the distributions of particle size and shape have been studied by examining the detailed dissolution processes, such as the size reduction rates of individual particles, the increase in bulk concentration and the dissolution time of the polydisperse systems. Some important factors controlling the dissolution process, including initial particle concentration, smallest and largest particle sizes, and the smallest and largest Taylor shape parameters, have been identified.
{"title":"Quasi-steady-state modelling and characterization of diffusion-controlled dissolution from polydisperse spheroidal particles, II: characterization","authors":"Yanxing Wang, Hui Wan, Cody Barka, Tie Wei, Fangjun Shu","doi":"10.1098/rspa.2023.0768","DOIUrl":"https://doi.org/10.1098/rspa.2023.0768","url":null,"abstract":"<p>A quasi-steady-state model for accurately predicting the detailed diffusion-dominated dissolution process of polydisperse spheroidal (prolate, oblate and spherical) particle systems was presented in Part I of this study. In the present paper, the dissolution characteristics of typical polydisperse spheroidal particle systems have been extensively investigated. The effects of the distributions of particle size and shape have been studied by examining the detailed dissolution processes, such as the size reduction rates of individual particles, the increase in bulk concentration and the dissolution time of the polydisperse systems. Some important factors controlling the dissolution process, including initial particle concentration, smallest and largest particle sizes, and the smallest and largest Taylor shape parameters, have been identified.</p>","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"46 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140314302","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}
Alexander P. Browning, Maria Taşcă, Carles Falcó, Ruth E. Baker
Effective application of mathematical models to interpret biological data and make accurate predictions often requires that model parameters are identifiable. Approaches to assess the so-called structural identifiability of models are well established for ordinary differential equation models, yet there are no commonly adopted approaches that can be applied to assess the structural identifiability of the partial differential equation (PDE) models that are requisite to capture spatial features inherent to many phenomena. The differential algebra approach to structural identifiability has recently been demonstrated to be applicable to several specific PDE models. In this brief article, we present general methodology for performing structural identifiability analysis on partially observed reaction–advection–diffusion PDE models that are linear in the unobserved quantities. We show that the differential algebra approach can always, in theory, be applied to such models. Moreover, despite the perceived complexity introduced by the addition of advection and diffusion terms, consideration of spatial analogues of non-spatial models cannot exacerbate structural identifiability. We conclude by discussing future possibilities and the computational cost of performing structural identifiability analysis on more general PDE models.
{"title":"Structural identifiability analysis of linear reaction–advection–diffusion processes in mathematical biology","authors":"Alexander P. Browning, Maria Taşcă, Carles Falcó, Ruth E. Baker","doi":"10.1098/rspa.2023.0911","DOIUrl":"https://doi.org/10.1098/rspa.2023.0911","url":null,"abstract":"<p>Effective application of mathematical models to interpret biological data and make accurate predictions often requires that model parameters are identifiable. Approaches to assess the so-called structural identifiability of models are well established for ordinary differential equation models, yet there are no commonly adopted approaches that can be applied to assess the structural identifiability of the partial differential equation (PDE) models that are requisite to capture spatial features inherent to many phenomena. The differential algebra approach to structural identifiability has recently been demonstrated to be applicable to several specific PDE models. In this brief article, we present general methodology for performing structural identifiability analysis on partially observed reaction–advection–diffusion PDE models that are linear in the unobserved quantities. We show that the differential algebra approach can always, in theory, be applied to such models. Moreover, despite the perceived complexity introduced by the addition of advection and diffusion terms, consideration of spatial analogues of non-spatial models cannot exacerbate structural identifiability. We conclude by discussing future possibilities and the computational cost of performing structural identifiability analysis on more general PDE models.</p>","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"20 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140314385","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}
In this study, a mathematical model based on graph theory is developed to analyse the deformed structures and mechanical properties of thermoplastic elastomers (TPEs) using ABA-type triblock copolymers. TPEs exhibit a network structure formed by bridge chains; deformation of this network structure causes stress. During the deformation of TPEs, domain breakage and coalescence occur, accompanied by topological changes in the chains, such as conformational transitions between the bridge and loop chains. By employing the mathematical concepts of harmonic realization of graphs in the physical space and the tension tensor to quantify the stress in the bridge-chain network structure, an effective method for analysing topologicalchanges in microstructures caused by elongation is proposed. As an application of this method, optimal geometric structures of block copolymers with desired functionalities can be determined.
本研究基于图论建立了一个数学模型,用于分析使用 ABA 型三嵌段共聚物的热塑性弹性体(TPE)的变形结构和机械性能。TPE 具有由桥链形成的网络结构,这种网络结构的变形会产生应力。在 TPE 的变形过程中,会发生畴断裂和凝聚,同时伴随着链的拓扑变化,如桥链和环链之间的构象转变。通过采用物理空间中图形的谐波实现和张力张量的数学概念来量化桥链网络结构中的应力,提出了一种分析拉伸引起的微结构拓扑变化的有效方法。应用这种方法,可以确定具有所需功能的嵌段共聚物的最佳几何结构。
{"title":"A mathematical model of thermoplastic elastomers for analysing the topology of microstructures and mechanical properties during elongation","authors":"Hiroki Kodama, Hiroshi Morita, Motoko Kotani","doi":"10.1098/rspa.2023.0389","DOIUrl":"https://doi.org/10.1098/rspa.2023.0389","url":null,"abstract":"<p>In this study, a mathematical model based on graph theory is developed to analyse the deformed structures and mechanical properties of thermoplastic elastomers (TPEs) using ABA-type triblock copolymers. TPEs exhibit a network structure formed by bridge chains; deformation of this network structure causes stress. During the deformation of TPEs, domain breakage and coalescence occur, accompanied by topological changes in the chains, such as conformational transitions between the bridge and loop chains. By employing the mathematical concepts of harmonic realization of graphs in the physical space and the tension tensor to quantify the stress in the bridge-chain network structure, an effective method for analysing topologicalchanges in microstructures caused by elongation is proposed. As an application of this method, optimal geometric structures of block copolymers with desired functionalities can be determined.</p>","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"39 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140314386","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}
The heat exchange between a rigid body and a fluid is usually modelled by the Robin boundary condition saying that the heat flux through the interface is proportional to the difference between their temperatures. Such interface law describes only the unilateral heat exchange. The goal of this paper is to compare the Robin boundary condition starting with the transmission condition (the temperature and the flux continuity) using rigorous mathematical analysis. Our main results are the following. We first show that a generalized version of the Robin boundary condition can be justified. Second, we prove that replacing the generalized by the standard Robin condition can be justified for high convection velocity if the conductivity of the surrounding liquid is much lower than that of the body. On the other hand, if the fluid conducts much better than the body, then the effective boundary condition is shown not to be the Robin one, but it involves second-order derivatives. We strongly believe that those findings bring new insights to the physics of the heat exchange processes and, thus, could prove useful in engineering practice.
{"title":"The Robin boundary condition for modelling heat transfer","authors":"Eduard Marušić-Paloka, Igor Pažanin","doi":"10.1098/rspa.2023.0850","DOIUrl":"https://doi.org/10.1098/rspa.2023.0850","url":null,"abstract":"<p>The heat exchange between a rigid body and a fluid is usually modelled by the Robin boundary condition saying that the heat flux through the interface is proportional to the difference between their temperatures. Such interface law describes only the unilateral heat exchange. The goal of this paper is to compare the Robin boundary condition starting with the transmission condition (the temperature and the flux continuity) using rigorous mathematical analysis. Our main results are the following. We first show that a generalized version of the Robin boundary condition can be justified. Second, we prove that replacing the generalized by the standard Robin condition can be justified for high convection velocity if the conductivity of the surrounding liquid is much lower than that of the body. On the other hand, if the fluid conducts much better than the body, then the effective boundary condition is shown not to be the Robin one, but it involves second-order derivatives. We strongly believe that those findings bring new insights to the physics of the heat exchange processes and, thus, could prove useful in engineering practice.</p>","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"46 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140314739","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}
Dmitry Shepelsky, Iryna Karpenko, Stepan Bogdanov, Jaroslaw E. Prilepsky
We consider the Riemann–Hilbert (RH) approach to the construction of periodic finite-band solutions to the focusing nonlinear Schrödinger (NLS) equation. An RH problem for the solution of the finite-band problem has been recently derived via the Fokas method (Deconinck et al. 2021 Lett. Math. Phys.111, 1–18. (doi:10.1007/s11005-021-01356-7); Fokas & Lenells. 2021 Proc. R. Soc. A477, 20200605. (doi:10.1007/s11005-021-01356-7)) Building on this method, a finite-band solution to the NLS equation can be given in terms of the solution of an associated RH problem, the jump conditions for which are characterized by specifying the endpoints of the arcs defining the contour of the RH problem and the constants (so-called phases) involved in the jump matrices. In our work, we solve the problem of retrieving the phases given the solution of the NLS equation evaluated at a fixed time. Our findings are corroborated by numerical examples of phases computation, demonstrating the viability of the method proposed.
{"title":"Periodic finite-band solutions to the focusing nonlinear Schrödinger equation by the Fokas method: inverse and direct problems","authors":"Dmitry Shepelsky, Iryna Karpenko, Stepan Bogdanov, Jaroslaw E. Prilepsky","doi":"10.1098/rspa.2023.0828","DOIUrl":"https://doi.org/10.1098/rspa.2023.0828","url":null,"abstract":"<p>We consider the Riemann–Hilbert (RH) approach to the construction of periodic finite-band solutions to the focusing nonlinear Schrödinger (NLS) equation. An RH problem for the solution of the finite-band problem has been recently derived via the Fokas method (Deconinck <i>et al.</i> 2021 <i>Lett. Math. Phys.</i> <b>111</b>, 1–18. (doi:10.1007/s11005-021-01356-7); Fokas & Lenells. 2021 <i>Proc. R. Soc. A</i> <b>477</b>, 20200605. (doi:10.1007/s11005-021-01356-7)) Building on this method, a finite-band solution to the NLS equation can be given in terms of the solution of an associated RH problem, the jump conditions for which are characterized by specifying the endpoints of the arcs defining the contour of the RH problem and the constants (so-called phases) involved in the jump matrices. In our work, we solve the problem of retrieving the phases given the solution of the NLS equation evaluated at a fixed time. Our findings are corroborated by numerical examples of phases computation, demonstrating the viability of the method proposed.</p>","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"38 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140316847","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}
The variational implicit-solvent model (VISM) is an efficient approach to biomolecular interactions, where electrostatic interactions are crucial. The total VISM free energy of a dielectric boundary (i.e. solute–solvent interface) consists of the interfacial energy, solute–solvent interaction energy and dielectric electrostatic energy. The last part is the maximum value of the classical and concave Poisson–Boltzmann (PB) energy functional of electrostatic potentials, with the maximizer being the equilibrium electrostatic potential governed by the PB equation. For the consistency of energy minimization and computational stability, here we propose alternatively to minimize the convex Legendre-transformed Poisson–Boltzmann (LTPB) electrostatic energy functional of all dielectric displacements constrained by Gauss’ Law in the solute region. Both integrable and discrete solute charge densities are treated, and the duality of the LTPB and PB functionals is established. A penalty method is designed for the constrained minimization of the LTPB functional. In application to biomolecular interactions, we minimize the total VISM free energy iteratively, while in each step of such iteration, minimize the LTPB energy. Convergence of such a min–min algorithm is shown. Our numerical results on the solvation of a single ion indicate that the LTPB performs better than the PB formulation, providing possibilities for efficient biomolecular simulations.
{"title":"Variational implicit solvation with Legendre-transformed Poisson–Boltzmann electrostatics","authors":"Zunding Huang, Bo Li","doi":"10.1098/rspa.2023.0731","DOIUrl":"https://doi.org/10.1098/rspa.2023.0731","url":null,"abstract":"<p>The variational implicit-solvent model (VISM) is an efficient approach to biomolecular interactions, where electrostatic interactions are crucial. The total VISM free energy of a dielectric boundary (i.e. solute–solvent interface) consists of the interfacial energy, solute–solvent interaction energy and dielectric electrostatic energy. The last part is the maximum value of the classical and concave Poisson–Boltzmann (PB) energy functional of electrostatic potentials, with the maximizer being the equilibrium electrostatic potential governed by the PB equation. For the consistency of energy minimization and computational stability, here we propose alternatively to minimize the convex Legendre-transformed Poisson–Boltzmann (LTPB) electrostatic energy functional of all dielectric displacements constrained by Gauss’ Law in the solute region. Both integrable and discrete solute charge densities are treated, and the duality of the LTPB and PB functionals is established. A penalty method is designed for the constrained minimization of the LTPB functional. In application to biomolecular interactions, we minimize the total VISM free energy iteratively, while in each step of such iteration, minimize the LTPB energy. Convergence of such a min–min algorithm is shown. Our numerical results on the solvation of a single ion indicate that the LTPB performs better than the PB formulation, providing possibilities for efficient biomolecular simulations.</p>","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"3 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140314388","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}
Invariant measures encode the long-time behaviour of a dynamical system. In this work, we propose an optimization-based method to discover invariant measures directly from data gathered from a system. Our method does not require an explicit model for the dynamics and allows one to target specific invariant measures, such as physical and ergodic measures. Moreover, it applies to both deterministic and stochastic dynamics in either continuous or discrete time. We provide convergence results and illustrate the performance of our method on data from the logistic map and a stochastic double-well system, for which invariant measures can be found by other means. We then use our method to approximate the physical measure of the chaotic attractor of the Rössler system, and we extract unstable periodic orbits embedded in this attractor by identifying discrete-time periodic points of a suitably defined Poincaré map. This final example is truly data-driven and shows that our method can significantly outperform previous approaches based on model identification.
{"title":"Data-driven discovery of invariant measures","authors":"Jason J. Bramburger, Giovanni Fantuzzi","doi":"10.1098/rspa.2023.0627","DOIUrl":"https://doi.org/10.1098/rspa.2023.0627","url":null,"abstract":"<p>Invariant measures encode the long-time behaviour of a dynamical system. In this work, we propose an optimization-based method to discover invariant measures directly from data gathered from a system. Our method does not require an explicit model for the dynamics and allows one to target specific invariant measures, such as physical and ergodic measures. Moreover, it applies to both deterministic and stochastic dynamics in either continuous or discrete time. We provide convergence results and illustrate the performance of our method on data from the logistic map and a stochastic double-well system, for which invariant measures can be found by other means. We then use our method to approximate the physical measure of the chaotic attractor of the Rössler system, and we extract unstable periodic orbits embedded in this attractor by identifying discrete-time periodic points of a suitably defined Poincaré map. This final example is truly data-driven and shows that our method can significantly outperform previous approaches based on model identification.</p>","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"13 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140314702","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}
In current scientific and technological scenarios, studies of transmittance of surface waves across structured interfaces have gained some wind amidst applications to metasurfaces, electronic edge-waves, crystal grain boundaries, etc. The results presented in the present article shed a light on the influence of material inhomogeneities on propagation of surface waves. Within the framework of classical mechanics, an analogue of the Gurtin–Murdoch model is employed where elastic properties on surface are assumed to be distinct from bulk. Restricting to scalar waves on prototype square lattice half-plane, particles on considered structured surface have piecewise-constant mass and surface force-constants across an interfacial point. Particles in bulk lattice interact with nearest neighbours in a way that involves unequal force-constants parallel to surface versus normal to it. A surface wave band exists for such lattice structure wherein the waveform decays exponentially inside the half-plane. A formula for surface wave transmittance is given based on an exact solution on half-plane, and, thus, previous work (Sharma & Eremeyev 2019 Int. J. Eng. Sci.143, 33–38 (doi:10.1016/j.ijengsci.2019.06.007)) is extended. An explicit expression for fraction of energy influx leaked via bulk waves is a highlight. Included are graphical results for several illustrative values of surface structure parameters.
{"title":"Scattering of surface waves by inhomogeneities in crystalline structures","authors":"Basant Lal Sharma","doi":"10.1098/rspa.2023.0683","DOIUrl":"https://doi.org/10.1098/rspa.2023.0683","url":null,"abstract":"<p>In current scientific and technological scenarios, studies of transmittance of surface waves across structured interfaces have gained some wind amidst applications to metasurfaces, electronic edge-waves, crystal grain boundaries, etc. The results presented in the present article shed a light on the influence of material inhomogeneities on propagation of surface waves. Within the framework of classical mechanics, an analogue of the Gurtin–Murdoch model is employed where elastic properties on surface are assumed to be distinct from bulk. Restricting to scalar waves on prototype square lattice half-plane, particles on considered structured surface have piecewise-constant mass and surface force-constants across an interfacial point. Particles in bulk lattice interact with nearest neighbours in a way that involves unequal force-constants parallel to surface versus normal to it. A surface wave band exists for such lattice structure wherein the waveform decays exponentially inside the half-plane. A formula for surface wave transmittance is given based on an exact solution on half-plane, and, thus, previous work (Sharma & Eremeyev 2019 <i>Int. J. Eng. Sci.</i> <b>143</b>, 33–38 (doi:10.1016/j.ijengsci.2019.06.007)) is extended. An explicit expression for fraction of energy influx leaked via bulk waves is a highlight. Included are graphical results for several illustrative values of surface structure parameters.</p>","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"70 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140168351","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}
Farzaneh Goli, Yongquan Zhang, Mo Qu, Yue Zang, Mozafar Saadat, Duc Truong Pham, Yongjing Wang
Disassembly is a crucial step in remanufacturing and is currently mainly performed by humans. Automating disassembly can reduce labour costs and make remanufacturing more economically attractive. This paper focuses on identifying and characterizing a common disassembly task, dual peg-hole disassembly, with the aim of building a robotic disassembly system for this task. We enumerate the possible contact states and their geometric conditions during the extraction of two studs in a dual peg-hole. This paper focuses on jamming in the extraction and conducts geometrical and quasi-static analyses to determine the boundary conditions of jamming. Based on the analyses, this paper also investigates the role of active compliance as a solution to avoid jamming. We also simulate critical variables and examine key parameters such as the degree of compliance, the location of the compliance centre and initial position errors. Finally, we conduct experimental studies on dual peg-hole extraction with different compliance centres obtained using active compliance.
{"title":"Jamming problems and the effects of compliance in dual peg-hole disassembly","authors":"Farzaneh Goli, Yongquan Zhang, Mo Qu, Yue Zang, Mozafar Saadat, Duc Truong Pham, Yongjing Wang","doi":"10.1098/rspa.2023.0364","DOIUrl":"https://doi.org/10.1098/rspa.2023.0364","url":null,"abstract":"<p>Disassembly is a crucial step in remanufacturing and is currently mainly performed by humans. Automating disassembly can reduce labour costs and make remanufacturing more economically attractive. This paper focuses on identifying and characterizing a common disassembly task, dual peg-hole disassembly, with the aim of building a robotic disassembly system for this task. We enumerate the possible contact states and their geometric conditions during the extraction of two studs in a dual peg-hole. This paper focuses on jamming in the extraction and conducts geometrical and quasi-static analyses to determine the boundary conditions of jamming. Based on the analyses, this paper also investigates the role of active compliance as a solution to avoid jamming. We also simulate critical variables and examine key parameters such as the degree of compliance, the location of the compliance centre and initial position errors. Finally, we conduct experimental studies on dual peg-hole extraction with different compliance centres obtained using active compliance.</p>","PeriodicalId":20716,"journal":{"name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"20 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140168252","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}