Pub Date : 2024-11-25DOI: 10.1007/s10208-024-09674-7
Théophile Chaumont-Frelet, Martin Vohralík
We analyze constrained and unconstrained minimization problems on patches of tetrahedra sharing a common vertex with discontinuous piecewise polynomial data of degree p. We show that the discrete minimizers in the spaces of piecewise polynomials of degree p conforming in the (H^1), ({varvec{H}}(textbf{curl})), or ({varvec{H}}({text {div}})) spaces are as good as the minimizers in these entire (infinite-dimensional) Sobolev spaces, up to a constant that is independent of p. These results are useful in the analysis and design of finite element methods, namely for devising stable local commuting projectors and establishing local-best–global-best equivalences in a priori analysis and in the context of a posteriori error estimation. Unconstrained minimization in (H^1) and constrained minimization in ({varvec{H}}({text {div}})) have been previously treated in the literature. Along with improvement of the results in the (H^1) and ({varvec{H}}({text {div}})) cases, our key contribution is the treatment of the ({varvec{H}}(textbf{curl})) framework. This enables us to cover the whole de Rham diagram in three space dimensions in a single setting.
我们分析了共享一个共同顶点的四面体斑块上的有约束和无约束最小化问题，这些斑块具有度数为 p 的不连续片断多项式数据。我们证明了在符合 (H^1)、({varvec{H}}(textbf{curl}))或({varvec{H}}({text {div}}))空间的 p 度分片多项式空间中的离散最小化与这些整个（无限维）Sobolev 空间中的最小化一样好，直到一个与 p 无关的常数。这些结果在有限元方法的分析和设计中非常有用，即在先验分析和后验误差估计中设计稳定的局部换向投影器和建立局部最优-全局最优等价。以前的文献已经讨论过 (H^1) 中的无约束最小化和 ({varvec{H}}({text {div}})) 中的有约束最小化。在改进了（H^1）和（{varvec{H}}({text {div}})）情况下的结果的同时，我们的主要贡献在于对（{varvec{H}}(textbf{curl})）框架的处理。这使我们能够在一个单一的环境中涵盖三维空间中的整个德拉姆图。
{"title":"Constrained and Unconstrained Stable Discrete Minimizations for p-Robust Local Reconstructions in Vertex Patches in the de Rham Complex","authors":"Théophile Chaumont-Frelet, Martin Vohralík","doi":"10.1007/s10208-024-09674-7","DOIUrl":"https://doi.org/10.1007/s10208-024-09674-7","url":null,"abstract":"<p>We analyze constrained and unconstrained minimization problems on patches of tetrahedra sharing a common vertex with discontinuous piecewise polynomial data of degree <i>p</i>. We show that the discrete minimizers in the spaces of piecewise polynomials of degree <i>p</i> conforming in the <span>(H^1)</span>, <span>({varvec{H}}(textbf{curl}))</span>, or <span>({varvec{H}}({text {div}}))</span> spaces are as good as the minimizers in these entire (infinite-dimensional) Sobolev spaces, up to a constant that is independent of <i>p</i>. These results are useful in the analysis and design of finite element methods, namely for devising stable local commuting projectors and establishing local-best–global-best equivalences in a priori analysis and in the context of a posteriori error estimation. Unconstrained minimization in <span>(H^1)</span> and constrained minimization in <span>({varvec{H}}({text {div}}))</span> have been previously treated in the literature. Along with improvement of the results in the <span>(H^1)</span> and <span>({varvec{H}}({text {div}}))</span> cases, our key contribution is the treatment of the <span>({varvec{H}}(textbf{curl}))</span> framework. This enables us to cover the whole de Rham diagram in three space dimensions in a single setting.</p>","PeriodicalId":55151,"journal":{"name":"Foundations of Computational Mathematics","volume":"113 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142713198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-25DOI: 10.1007/s00021-024-00908-w
Ningning Li, Yongqian Zhang
We study an inverse problem of determining the shape of a bending wall with a given surface pressure distribution in the two-dimensional steady supersonic potential flow. The given pressure distribution on the wall surface is assumed to be a small perturbation of the pressure distribution corresponding to a bending convex wall and to have a bounded total variation. In this setting, we first give the background solution which only contains strong rarefaction waves generated by a bending convex wall. Then, we construct the approximate boundaries and corresponding approximate solutions of the inverse problem within a perturbation domain of this background solution. To achieve this, we employ a modified wave-front tracking algorithm. Finally, we show that the limit of approximate solutions provides a global entropy solution for the inverse problem, and the limit of approximate boundaries gives a boundary profile representing the shape of a bending wall that yields the given pressure distribution.
{"title":"An Inverse Problem for Steady Supersonic Potential Flow Past a Bending Wall","authors":"Ningning Li, Yongqian Zhang","doi":"10.1007/s00021-024-00908-w","DOIUrl":"10.1007/s00021-024-00908-w","url":null,"abstract":"<div><p>We study an inverse problem of determining the shape of a bending wall with a given surface pressure distribution in the two-dimensional steady supersonic potential flow. The given pressure distribution on the wall surface is assumed to be a small perturbation of the pressure distribution corresponding to a bending convex wall and to have a bounded total variation. In this setting, we first give the background solution which only contains strong rarefaction waves generated by a bending convex wall. Then, we construct the approximate boundaries and corresponding approximate solutions of the inverse problem within a perturbation domain of this background solution. To achieve this, we employ a modified wave-front tracking algorithm. Finally, we show that the limit of approximate solutions provides a global entropy solution for the inverse problem, and the limit of approximate boundaries gives a boundary profile representing the shape of a bending wall that yields the given pressure distribution.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714135","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-24DOI: 10.1016/j.chaos.2024.115728
Ashish Shukla, Vijaya Kumar Dunna, Arijit Sen
This paper introduces a containment control law for a multi-agent system (MAS) of double integrator agents using only relative position information. Unlike existing methods, this approach eliminates the need for velocity or exact position measurements as feedback, reducing communication and sensor requirements. Using the non-smooth Lyapunov analysis, we prove the convergence of the proposed control law under any detailed-balanced network with any positive gains. Moreover, the controller inherently guarantees bounded control effort and finite-time or fixed-time convergence without needing any additional update law. Finally, the numerical simulations demonstrate the effectiveness of the proposed method.
{"title":"Velocity-free containment control with binary relative measurements only","authors":"Ashish Shukla, Vijaya Kumar Dunna, Arijit Sen","doi":"10.1016/j.chaos.2024.115728","DOIUrl":"10.1016/j.chaos.2024.115728","url":null,"abstract":"<div><div>This paper introduces a containment control law for a multi-agent system (MAS) of double integrator agents using only relative position information. Unlike existing methods, this approach eliminates the need for velocity or exact position measurements as feedback, reducing communication and sensor requirements. Using the non-smooth Lyapunov analysis, we prove the convergence of the proposed control law under any detailed-balanced network with any positive gains. Moreover, the controller inherently guarantees bounded control effort and finite-time or fixed-time convergence without needing any additional update law. Finally, the numerical simulations demonstrate the effectiveness of the proposed method.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"190 ","pages":"Article 115728"},"PeriodicalIF":5.3,"publicationDate":"2024-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142701959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-23DOI: 10.1007/s00205-024-02072-x
Ben Pineau, Mitchell A. Taylor
We present a novel method for establishing large data local well-posedness in low regularity Sobolev spaces for general quasilinear Schrödinger equations with non-degenerate and nontrapping metrics. Our result represents a definitive improvement over the landmark results of Kenig, Ponce, Rolvung and Vega (Kenig et al. in Adv Math 196:373–486, 2005; Carlos et al. in Adv Math 206:402–433, 2006; Carlos et al. in Invent Math 134:489–545, 1998; Carlos et al. in Invent Math 158:343–388, 2004), as it weakens the regularity and decay assumptions to the same scale of spaces considered by Marzuola, Metcalfe and Tataru in (Jeremy et al. in Arch Ration Mech Anal 242:1119-1175, 2021), but removes the uniform ellipticity assumption on the metric from their result. Our method has the additional benefit of being relatively simple but also very robust. In particular, it only relies on the use of pseudodifferential calculus for classical symbols.
我们提出了一种在低正则性 Sobolev 空间中为具有非退化和非捕获度量的一般准线性薛定谔方程建立大数据局部好求的新方法。我们的结果代表了对 Kenig、Ponce、Rolvung 和 Vega 的里程碑式结果的明确改进（Kenig 等人，发表于 Adv Math 196:373-486, 2005 年；Carlos 等人，发表于 Adv Math 206:402-433, 2006 年；Carlos 等人，发表于 Invent Math 134:489-545, 1998 年；Carlos 等人，发表于 Invent Math 158:402-433, 2006 年）。杰里米等人在 Arch Ration Mech Anal 242:1119-1175, 2021 中）所考虑的空间尺度相同，但从他们的结果中删除了对度量的均匀椭圆性假设。我们的方法还有一个好处，就是相对简单，而且非常稳健。特别是，它只依赖于经典符号的伪微分计算。
{"title":"Low Regularity Solutions for the General Quasilinear Ultrahyperbolic Schrödinger Equation","authors":"Ben Pineau, Mitchell A. Taylor","doi":"10.1007/s00205-024-02072-x","DOIUrl":"10.1007/s00205-024-02072-x","url":null,"abstract":"<div><p>We present a novel method for establishing large data local well-posedness in low regularity Sobolev spaces for general quasilinear Schrödinger equations with non-degenerate and nontrapping metrics. Our result represents a definitive improvement over the landmark results of Kenig, Ponce, Rolvung and Vega (Kenig et al. in Adv Math 196:373–486, 2005; Carlos et al. in Adv Math 206:402–433, 2006; Carlos et al. in Invent Math 134:489–545, 1998; Carlos et al. in Invent Math 158:343–388, 2004), as it weakens the regularity and decay assumptions to the same scale of spaces considered by Marzuola, Metcalfe and Tataru in (Jeremy et al. in Arch Ration Mech Anal 242:1119-1175, 2021), but removes the uniform ellipticity assumption on the metric from their result. Our method has the additional benefit of being relatively simple but also very robust. In particular, it only relies on the use of pseudodifferential calculus for classical symbols.\u0000</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"248 6","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142691872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-23DOI: 10.1007/s11538-024-01383-0
Kun Wei, Jiecong Wang
In ant foraging, the manner of group-mass recruitment demonstrates remarkable adaptability between tandem running and mass recruitment. In contrast to tandem running, where a leader recruits only one worker, the first phase of group-mass recruitment is characterized by strong invitations from leaders that result in a large group of recruits leaving the nest together in a rush, thereby accelerating the process of recruiting towards discovered resources. Furthermore, unlike sole mass recruitment, the influence of leaders during this first phase enhances the accuracy of information about food qualities and ensures a more rational allocation of recruits compared to simply following a dominant pheromone trail. In this study, we propose a model that integrates the Kelly criterion for the first phase of group-mass recruitment, followed by a post-Kelly strategy incorporating a delayed Pólya urn with two stages for the second phase of group-mass recruitment. The analytical process and simulation demonstrate that the Kelly criterion aims to maximize recruitment intensity during the initial foraging phase, employing crowd tactics to capture all available food sources and enhance competitiveness with other food-exploiting species. On the other hand, the post-Kelly strategy elucidates how the crowding negative feedback mitigates congestion resulting from overexploitation and improves overall efficiency in food exploitation.
{"title":"The Post-Kelly Strategy: A Negative Feedback Model of Reallocating Ant Foragers.","authors":"Kun Wei, Jiecong Wang","doi":"10.1007/s11538-024-01383-0","DOIUrl":"https://doi.org/10.1007/s11538-024-01383-0","url":null,"abstract":"<p><p>In ant foraging, the manner of group-mass recruitment demonstrates remarkable adaptability between tandem running and mass recruitment. In contrast to tandem running, where a leader recruits only one worker, the first phase of group-mass recruitment is characterized by strong invitations from leaders that result in a large group of recruits leaving the nest together in a rush, thereby accelerating the process of recruiting towards discovered resources. Furthermore, unlike sole mass recruitment, the influence of leaders during this first phase enhances the accuracy of information about food qualities and ensures a more rational allocation of recruits compared to simply following a dominant pheromone trail. In this study, we propose a model that integrates the Kelly criterion for the first phase of group-mass recruitment, followed by a post-Kelly strategy incorporating a delayed Pólya urn with two stages for the second phase of group-mass recruitment. The analytical process and simulation demonstrate that the Kelly criterion aims to maximize recruitment intensity during the initial foraging phase, employing crowd tactics to capture all available food sources and enhance competitiveness with other food-exploiting species. On the other hand, the post-Kelly strategy elucidates how the crowding negative feedback mitigates congestion resulting from overexploitation and improves overall efficiency in food exploitation.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 1","pages":"3"},"PeriodicalIF":2.0,"publicationDate":"2024-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142695233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-23DOI: 10.1016/j.dam.2024.11.008
Ervin Győri , Binlong Li , Nika Salia , Casey Tompkins
Chung and Graham considered the problem of minimizing the number of edges in an -vertex graph containing all -vertex trees as a subgraph. They showed that such a graph has at least edges. In this note, we improve this lower estimate to .
Chung 和 Graham 考虑了在包含所有 n 个顶点的树作为子图的 n 个顶点图中尽量减少边数的问题。他们的研究表明，这样的图至少有 12nlogn 条边。在本说明中，我们将这一较低估计值改进为 nlogn-O(n)。
{"title":"A note on universal graphs for spanning trees","authors":"Ervin Győri , Binlong Li , Nika Salia , Casey Tompkins","doi":"10.1016/j.dam.2024.11.008","DOIUrl":"10.1016/j.dam.2024.11.008","url":null,"abstract":"<div><div>Chung and Graham considered the problem of minimizing the number of edges in an <span><math><mi>n</mi></math></span>-vertex graph containing all <span><math><mi>n</mi></math></span>-vertex trees as a subgraph. They showed that such a graph has at least <span><math><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mi>n</mi><mo>log</mo><mi>n</mi></mrow></math></span> edges. In this note, we improve this lower estimate to <span><math><mrow><mi>n</mi><mo>log</mo><mi>n</mi><mo>−</mo><mi>O</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></math></span>.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"362 ","pages":"Pages 146-147"},"PeriodicalIF":1.0,"publicationDate":"2024-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142706125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-23DOI: 10.1016/j.camwa.2024.11.020
Wensi Wang , Hailing Xuan , Xiaoliang Cheng , Kewei Liang
We present a mathematical model describing the equilibrium of a viscoelastic body with long-term memory in frictional contact with a sliding foundation. The process is quasistatic, and material damage resulting from excessive stress or strain is captured by a damage function. We assume the material is inhomogeneous, leading to multiple contact boundary conditions. The contact interface is partitioned into two segments: One part takes into account the wear of the contact surface, utilizing Archard's law. Here, contact is modeled with a normal compliance condition with unilateral constraints, coupled with a sliding version of Coulomb's law of dry friction. In the other part, contact is modeled with a nonmonotone condition involving normal compliance and a subdifferential frictional boundary condition. Variational formulation of the model is governed by a coupled system consisting of a variational–hemivariational inequality for the displacement field, a parabolic variational inequality for the damage field and an integral equation for the wear function. We study a fully discrete scheme for numerical approximation with an error estimation of the solution to this problem. Optimal error estimates for the linear finite element method are derived, followed by numerical simulations illustrating the behavior of the model.
{"title":"Numerical analysis and simulation of a quasistatic frictional bilateral contact problem with damage, long-term memory and wear","authors":"Wensi Wang , Hailing Xuan , Xiaoliang Cheng , Kewei Liang","doi":"10.1016/j.camwa.2024.11.020","DOIUrl":"10.1016/j.camwa.2024.11.020","url":null,"abstract":"<div><div>We present a mathematical model describing the equilibrium of a viscoelastic body with long-term memory in frictional contact with a sliding foundation. The process is quasistatic, and material damage resulting from excessive stress or strain is captured by a damage function. We assume the material is inhomogeneous, leading to multiple contact boundary conditions. The contact interface is partitioned into two segments: One part takes into account the wear of the contact surface, utilizing Archard's law. Here, contact is modeled with a normal compliance condition with unilateral constraints, coupled with a sliding version of Coulomb's law of dry friction. In the other part, contact is modeled with a nonmonotone condition involving normal compliance and a subdifferential frictional boundary condition. Variational formulation of the model is governed by a coupled system consisting of a variational–hemivariational inequality for the displacement field, a parabolic variational inequality for the damage field and an integral equation for the wear function. We study a fully discrete scheme for numerical approximation with an error estimation of the solution to this problem. Optimal error estimates for the linear finite element method are derived, followed by numerical simulations illustrating the behavior of the model.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"177 ","pages":"Pages 130-146"},"PeriodicalIF":2.9,"publicationDate":"2024-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-23DOI: 10.1016/j.chaos.2024.115786
Nasser A. Saeed , Y.Y. Ellabban , Lei Hou , G.M. Moatimid , Shun Zhong , Faisal Z. Duraihem
It is well-established that shaped bio-inspired structures function effectively as low-frequency vibration isolators when excitation frequencies remain below the structure's natural frequency. However, when subjected to high-frequency excitations, the nonlinear behavior of these structures dominates, leading to the emergence of multistable solutions and strong vibrations, even with small base excitation amplitudes. The primary objective of this work is to mitigate strong vibrations and eliminate solution bifurcations in such isolators under high-frequency excitations while maintaining their high-performance low-frequency isolation capabilities. For the first time, an layer shaped vibration absorber has been integrated into an layer bio-inspired shaped low-frequency vibration isolator system to enhance the overall vibration isolation performance. The mathematical model governing the oscillatory behavior of the combined isolator-absorber system was derived as a two-degree-of-freedom nonlinear dynamical system using the principles of Lagrangian mechanics. By applying the harmonic balance method, an accurate analytical solution for the isolator-absorber system was obtained. The evolution of steady-state oscillation amplitudes for both the isolator and absorber was then explored as a function of both the base excitation frequencies and the excitation force amplitude. The effects of various shaped absorber parameters, such as rod length, number of layers, stiffness coefficient, mass, and inclination angle, on the isolator's oscillatory behavior were thoroughly investigated. The key findings confirm that a multilayer, high-stiffness shaped absorber system can effectively eliminate multistable solutions and mitigate resonant vibrations of the isolator system under high-frequency excitations, without compromising the system's low-frequency vibration isolation performance. However, a poor design of the shaped absorber parameters may destabilize the motion of the shaped isolator system, leading to the emergence of a quasi-periodic or chaotic response rather than enhancing its vibration isolation performance.
众所周知，当激振频率低于结构的固有频率时，X 型生物启发结构可有效发挥低频隔振功能。然而，当受到高频激励时，这些结构的非线性行为会占主导地位，导致出现多稳态解和强烈振动，即使基础激励振幅很小。这项工作的主要目标是在保持高性能低频隔离能力的同时，减轻此类隔离器在高频激励下的强烈振动并消除解分叉。我们首次将 m 层 X 型吸振器集成到 n 层生物启发 X 型低频隔振器系统中，以提高整体隔振性能。利用拉格朗日力学原理，将控制组合隔振器-吸收器系统振荡行为的数学模型推导为两自由度非线性动力系统。通过应用谐波平衡法，得到了隔振器-减震器系统的精确解析解。然后，探讨了隔振器和吸收器的稳态振幅随基本激振频率和激振力振幅的变化情况。深入研究了各种 X 形吸收器参数（如杆长、层数、刚度系数、质量和倾角）对隔振器振荡行为的影响。主要研究结果证实，多层、高刚度 X 型吸收器系统可以有效消除多稳态解决方案，减轻隔振器系统在高频激励下的共振振动，同时不影响系统的低频隔振性能。然而，如果 X 型吸收器参数设计不当，可能会破坏 X 型隔振系统的运动稳定性，导致出现准周期或混乱响应，而不是提高其隔振性能。
{"title":"Nonlinear dynamics of a bio-inspired 2-DOF low-frequency X-shaped vibration isolator with m-to-n layers driven harmonically under simultaneous primary and 1:1 internal resonances","authors":"Nasser A. Saeed , Y.Y. Ellabban , Lei Hou , G.M. Moatimid , Shun Zhong , Faisal Z. Duraihem","doi":"10.1016/j.chaos.2024.115786","DOIUrl":"10.1016/j.chaos.2024.115786","url":null,"abstract":"<div><div>It is well-established that <span><math><mi>X</mi><mo>−</mo></math></span>shaped bio-inspired structures function effectively as low-frequency vibration isolators when excitation frequencies remain below the structure's natural frequency. However, when subjected to high-frequency excitations, the nonlinear behavior of these structures dominates, leading to the emergence of multistable solutions and strong vibrations, even with small base excitation amplitudes. The primary objective of this work is to mitigate strong vibrations and eliminate solution bifurcations in such isolators under high-frequency excitations while maintaining their high-performance low-frequency isolation capabilities. For the first time, an <span><math><mi>m</mi><mo>−</mo></math></span>layer <span><math><mi>X</mi><mo>−</mo></math></span>shaped vibration absorber has been integrated into an <span><math><mi>n</mi><mo>−</mo></math></span>layer bio-inspired <span><math><mi>X</mi><mo>−</mo></math></span>shaped low-frequency vibration isolator system to enhance the overall vibration isolation performance. The mathematical model governing the oscillatory behavior of the combined isolator-absorber system was derived as a two-degree-of-freedom nonlinear dynamical system using the principles of Lagrangian mechanics. By applying the harmonic balance method, an accurate analytical solution for the isolator-absorber system was obtained. The evolution of steady-state oscillation amplitudes for both the isolator and absorber was then explored as a function of both the base excitation frequencies and the excitation force amplitude. The effects of various <span><math><mi>X</mi><mo>−</mo></math></span>shaped absorber parameters, such as rod length, number of layers, stiffness coefficient, mass, and inclination angle, on the isolator's oscillatory behavior were thoroughly investigated. The key findings confirm that a multilayer, high-stiffness <span><math><mi>X</mi><mo>−</mo></math></span>shaped absorber system can effectively eliminate multistable solutions and mitigate resonant vibrations of the isolator system under high-frequency excitations, without compromising the system's low-frequency vibration isolation performance. However, a poor design of the <span><math><mi>X</mi><mo>−</mo></math></span>shaped absorber parameters may destabilize the motion of the <span><math><mi>X</mi><mo>−</mo></math></span>shaped isolator system, leading to the emergence of a quasi-periodic or chaotic response rather than enhancing its vibration isolation performance.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"190 ","pages":"Article 115786"},"PeriodicalIF":5.3,"publicationDate":"2024-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142701866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-23DOI: 10.1016/j.chaos.2024.115748
Saad Ihsan Butt, Dawood Khan
The goal of this study is to introduce a new class of superquadraticity, which is known as superquadratic interval valued function (superquadratic I-V-F) and establish its properties via order relations of intervals. By utilizing the definitions and properties of superquadratic I-V-F, we come up with new integral inequalities such that Jensen’s, converse Jensen’s, Mercer Jensen’s and Hermite–Hadamard types. In addition to this, we provide a fractional version of Hermite–Hadamard’s type inequalities for superquadratic I-V-Fs. The findings are validated by specific numerical computations and graphical illustrations that include a certain number of relevant examples. We also offer the applications of the established results in information theory such that we determine the novel estimates for Shannon’s and relative entropies.
{"title":"Superquadratic function and its applications in information theory via interval calculus","authors":"Saad Ihsan Butt, Dawood Khan","doi":"10.1016/j.chaos.2024.115748","DOIUrl":"10.1016/j.chaos.2024.115748","url":null,"abstract":"<div><div>The goal of this study is to introduce a new class of superquadraticity, which is known as superquadratic interval valued function (superquadratic I-V-F) and establish its properties via order relations of intervals. By utilizing the definitions and properties of superquadratic I-V-F, we come up with new integral inequalities such that Jensen’s, converse Jensen’s, Mercer Jensen’s and Hermite–Hadamard types. In addition to this, we provide a fractional version of Hermite–Hadamard’s type inequalities for superquadratic I-V-Fs. The findings are validated by specific numerical computations and graphical illustrations that include a certain number of relevant examples. We also offer the applications of the established results in information theory such that we determine the novel estimates for Shannon’s and relative entropies.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"190 ","pages":"Article 115748"},"PeriodicalIF":5.3,"publicationDate":"2024-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142701867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-22DOI: 10.1016/j.csda.2024.108097
Hyungjin Kim , Chuljin Park , Heeyoung Kim
We propose a novel framework for efficient parameter estimation in simulation models, formulated as an optimization problem that minimizes the discrepancy between physical system observations and simulation model outputs. Our framework, called multi-task optimization with Bayesian neural network surrogates (MOBS), is designed for scenarios that require the simultaneous estimation of multiple sets of parameters, each set corresponding to a distinct set of observations, while also enabling fast parameter estimation essential for real-time process monitoring and control. MOBS integrates a heuristic search algorithm, utilizing a single-layer Bayesian neural network surrogate model trained on an initial simulation dataset. This surrogate model is shared across multiple tasks to select and evaluate candidate parameter values, facilitating efficient multi-task optimization. We provide a closed-form parameter screening rule and demonstrate that the expected number of simulation runs converges to a user-specified threshold. Our framework was applied to a numerical example and a semiconductor manufacturing case study, significantly reducing computational costs while achieving accurate parameter estimation.
{"title":"Multi-task optimization with Bayesian neural network surrogates for parameter estimation of a simulation model","authors":"Hyungjin Kim , Chuljin Park , Heeyoung Kim","doi":"10.1016/j.csda.2024.108097","DOIUrl":"10.1016/j.csda.2024.108097","url":null,"abstract":"<div><div>We propose a novel framework for efficient parameter estimation in simulation models, formulated as an optimization problem that minimizes the discrepancy between physical system observations and simulation model outputs. Our framework, called multi-task optimization with Bayesian neural network surrogates (MOBS), is designed for scenarios that require the simultaneous estimation of multiple sets of parameters, each set corresponding to a distinct set of observations, while also enabling fast parameter estimation essential for real-time process monitoring and control. MOBS integrates a heuristic search algorithm, utilizing a single-layer Bayesian neural network surrogate model trained on an initial simulation dataset. This surrogate model is shared across multiple tasks to select and evaluate candidate parameter values, facilitating efficient multi-task optimization. We provide a closed-form parameter screening rule and demonstrate that the expected number of simulation runs converges to a user-specified threshold. Our framework was applied to a numerical example and a semiconductor manufacturing case study, significantly reducing computational costs while achieving accurate parameter estimation.</div></div>","PeriodicalId":55225,"journal":{"name":"Computational Statistics & Data Analysis","volume":"204 ","pages":"Article 108097"},"PeriodicalIF":1.5,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142701344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号